Operational Optimization of Crude Oil Distillation Systems ...
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Operational Optimization of Crude Oil Distillation Systems with Limited Information A thesis submitted to The University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2019 Xiao Yang Department of Chemical Engineering and Analytical Science
Transcript of Operational Optimization of Crude Oil Distillation Systems ...
Operational Optimization of
Crude Oil Distillation Systems with
Limited Information
A thesis submitted to The University of Manchester
for the degree of Doctor of Philosophy
in the Faculty of Science and Engineering
2019
Xiao Yang
Department of Chemical Engineering and Analytical Science
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List of Contents
Contents
Operational Optimization of Crude Oil Distillation Systems with Limited
Information ................................................................................................................... 1
List of Contents ............................................................................................................ 3
List of Figures .............................................................................................................. 7
Abbreviations ............................................................................................................... 8
Abstract ........................................................................................................................ 9
Declaration ................................................................................................................. 11
Copyright Statement .................................................................................................. 13
Acknowledgement...................................................................................................... 15
Dedication .................................................................................................................. 17
1. Introduction ........................................................................................................ 19
1.1. Challenges for operational optimization of crude oil distillation systems .. 20
1.2. Objectives of this work ................................................................................ 21
1.3. Overview of this work ................................................................................. 21
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2. Literature Review ............................................................................................... 25
2.1. Features of crude oil distillation systems .................................................... 25
2.2. Crude oil distillation models for optimization ............................................. 28
2.2.1. Rigorous models ................................................................................... 28
2.2.2. Shortcut models .................................................................................... 30
2.2.3. Data-driven models .............................................................................. 31
2.3. Real-time optimization and related techniques ........................................... 34
2.3.1. Role of real-time optimization in refinery decision hierarchy ............. 34
2.3.2. Components of real-time optimization systems ................................... 36
2.3.3. Applications of real-time optimization ................................................ 38
2.3.4. Emerging and related techniques ......................................................... 38
2.4. Practical barriers and research gaps ............................................................. 41
2.4.1. Limited information of crude feed compositions ................................. 41
2.4.2. Balance of accuracy, complexity and robustness of models ................ 42
3. Real-time Optimization of Crude Oil Distillation Systems via Adaptive Linear
Models ........................................................................................................................ 43
4. Data-driven Real-time Optimization of Crude Oil Distillation Systems ........... 45
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5. Robust Operational Optimization of Crude Oil Distillation Systems ................ 47
6. Investigating Uncertainty Sets and Reducing Optimization Loss for Robust
Operational Optimization ........................................................................................... 49
7. Conclusions and Future Work ............................................................................ 51
7.1. Conclusions ................................................................................................. 51
7.1.1. Philosophy of using limited information in operational optimization . 51
7.1.2. Mechanisms for reacting to crude feed changes .................................. 53
7.1.3. Strength and weakness of simplified linear models and robust linear
models 55
7.2. Future work ................................................................................................. 56
References .................................................................................................................. 59
Appendix A. Description and Screenshots of Rigorous Simulation in Aspen HYSYS
.................................................................................................................................... 67
Appendix B. Python Scripts ....................................................................................... 71
B.1. Link Python to Aspen HYSYS ....................................................................... 71
B.2. Get current operating conditions in simulation .............................................. 73
B.3. Get values of objective function in simulation ............................................... 73
B.4. Get duties of pump-arounds ........................................................................... 74
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B.5. Converge column and HEN pump-around duties ........................................... 75
B.6. Generate random samples ............................................................................... 76
Total word count: 34381
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List of Figures
Figure 1.1. Methods to handle information in operational optimization……………..22
Figure 2.1. A typical crude oil distillation system……………………………………26
Figure 2.2. Refinery decision hierarchy………………………………………..……35
Figure 7.1. Comparison of different philosophies of using limited information in
operational optimization……………………………………………………….…….51
Figure 7.2. Risk grading of operational optimization potentials with limited
information……………………………………………………….….………………52
Figure A.1. A screenshot of the whole Aspen HYSYS environment…………………67
Figure A.2. A screenshot of column connections tab………………………………...68
Figure A.3. A screenshot of column monitor tab……………………………………..68
Figure A.4. A screenshot of the HEN arrangement…………………………………..69
Figure A.5. A screenshot of heat exchanger Parameters tab………………………….69
Figure A.6. A screenshot of heat exchanger Specs tab……………………………….70
Figure A.7. A screenshot of the economic spreadsheet………………………………70
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Abbreviations
AGO Atmospheric Gas Oil
ANN Artificial Neural Network
ASTM American Society for Testing and Materials
DCS Distributed Control Systems
EMPC Economic Model Predictive Control
FCCU Fluid Catalytic Cracking Unit
FUG Fenske-Underwood-Gilliland shortcut method
HEN Heat Exchanger Network
MPC Model Predictive Control
NLP Nonlinear Programming
PA Pump-around
PID Proportional–Integral–Derivative controller
RTO Real-time Optimization
SQP Sequential Quadratic Programming
TBP True Boiling Point
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Abstract
Crude oil distillation is the locomotive of refining and petrochemical industries. Due
to massive throughput and energy demand of industrial crude oil distillation systems,
even a minor improvement in their operations can bring significant economic and
social benefits. However, there are two major practical challenges for operational
optimization of crude oil distillation systems. One is that limited information of crude
feed compositions is known for optimization. The other one is that it’s difficult to
balance accuracy, complexity and robustness of optimization models.
In this work, two types of methods are proposed with different philosophies of utilizing
limited information during the procedure of operational optimization. The first type of
method, real-time optimization, tries to use more amount of information during
optimization by parameter estimation. The second type of method, robust operational
optimization, tries to use less amount of information during optimization and treats
limited information as uncertainty.
For real-time optimization methods, a framework to simplify rigorous models with
crude feed estimation is proposed. The simplified linear models are shown to have the
advantage of small size and convexity with accepted accuracy loss compared to
rigorous models. Second, a model correction mechanism is proposed to further
improve model accuracy and reduce mismatches between models and the process.
Third, a framework to mine historical data for building data-driven models based on
crude feed estimation is proposed.
For robust operational optimization, a method to describe the crude feed uncertainty
based on simplified linear models is proposed. Second, a framework to update both
certain and uncertain parameters from schedule of crude oil operations and real-time
plant measurements for online use is proposed. Third, a method to determine the best
shape and size of the uncertainty set and reduce loss of optimization potential is
proposed.
Case studies show that both real-time optimization and robust operational optimization
can help to make operational optimization decisions with limited information. Real-
time optimization can be expected to obtain more optimization potentials but also takes
risks of worse operating conditions or infeasible operations caused by bad parameter
estimation. Robust operational optimization makes conservative optimization
decisions but can provide safeguard against the assumption of perfect parameter
estimation implied by real-time optimization.
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Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning.
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Copyright Statement
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thesis) owns certain copyright or related rights in it (the “Copyright”) and
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Acknowledgement
A lot of things happened during the four years after I moved to UK. If I look back in
the last minute of my life, I will probably consider the four years as one of the most
important periods in my life. During this period, I found a way to live with a complex
medical condition, became self-aware and started to see both the inner and outer
worlds in a peaceful and objective attitude.
Regarding the PhD research, I would like to thank Mr Shibo Wang and Process
Integration Limited for their financial support. Moreover, Mr Shibo Wang also helped
me to form a top-down thinking strategy, which fundamentally improved my problem-
solving skills.
I would like to express my great gratitude to my supervisor Dr Nan Zhang. His
experience and wisdom in the refining industry gave me tremendous help on every
piece of my research work. Nan also helped me to build the ability of grabbing key
factors from noisy and limited information. Without his strong support and patience
during a period when I came across serious problems with my research, finishing the
thesis is impossible.
I would also like to thank Prof Megan Jobson and Prof Robin Smith. Megan’s detailed
comments on my reports and Robin’s feedback and advice on my presentations helped
me a lot to improve my academic communication skills. I would also like to appreciate
valuable discussions with my colleagues from Process Integration Limited, Yongwen,
Lu and Xueqin. They all helped me a lot to understand crude oil distillation systems
and optimization.
Finally, I would like to thank several friends, Honglei, Nan Yu, Luyi, Fei, Chengjun,
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Yunrui, Kexin, for their supports of my life. To Honglei and Nan Yu, thanks for helping
me to go through every difficult part of my life. I hope your (future) kids can grow up
healthy and happily.
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Dedication
To my parents
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1. Introduction
Crude oil distillation is the locomotive of refining and petrochemical industries. It
connects crude oil with almost every corner of the modern daily life from
transportation fuels to numerous materials and chemicals. As the first step in refineries,
crude oil distillation systems process nearly all oil consumed by the world (about 82
million barrels per day in 2017 [1]). Moreover, crude oil distillation systems are energy
intensive, accounting for about 35-45% of overall energy use in refineries [2]. Due to
the massive throughput and energy demand, even a minor improvement can bring
significant economic and social benefits.
Industrial crude oil distillation is a complex heat-integrated separation system. The
complexity arises from three aspects, i.e., complex feed composition, complex column
configurations and complex heat recovery systems. As a result, operations of crude oil
distillation systems have many degrees of freedom to adjust and multiple possible
bottlenecks to concern. Therefore, making decisions of the best operating conditions
for crude oil distillation systems is not an obvious task.
Operational optimization can help existing crude oil distillation systems to improve
performance at zero cost in a competitive global market. Operating variables, such as
throughput, product flowrates, furnace outlet temperature, stripping steam flowrates
and pump-around flowrates, can be adjusted to obtain more valuable products with
less utility use. At the same time, process constraints including operating bounds,
product specifications and equipment capacities need to be satisfied during the
optimization.
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1.1. Challenges for operational optimization of crude oil
distillation systems
Apart from the intrinsic complexity, there are two major practical barriers for
operational optimization of crude oil distillation systems (see more details in Chapter
2):
(1) Limited information of crude feed compositions
Crude feed compositions are the major factor affecting decisions of the optimal
operating conditions. However, perfect knowledge of crude feed compositions is not
available in many refineries. This is caused by several practical situations: (a) Crude
feed compositions may change frequently as a result of scheduling of crude oil
operations; (b) Conventional analysis methods for crude feed compositions are time-
consuming; (c) Online crude oil composition analyzers are expensive and not
commonly used in refineries. Therefore, decisions of operational optimization of crude
oil distillation systems are made with limited information.
(2) Balance of accuracy, complexity and robustness of models
Rigorous models and advanced data-driven models such as artificial neural networks
(ANNs) have the advantage of high accuracy. However, there is a hidden assumption
that true model parameters are known. This is not the real situation when limited
information is available. Models without robustness to inaccurate parameter
estimation may yield infeasible solutions. Moreover, rigorous models and advanced
data-driven models have a high degree of complexity. The complexity makes them
difficult to understand and causes high cost of maintenance. Therefore, the balance of
accuracy, complexity and robustness of models needs to be considered for operational
optimization in the situation of limited information.
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1.2. Objectives of this work
To overcome the above-mentioned challenges, this work aims at developing
operational optimization frameworks for crude oil distillation systems with little
capital investment in expensive online crude oil composition analyzers. To achieve this
goal, several problems need to be addressed:
(1) How to utilize limited information of crude feed compositions to make
decisions in the procedure of operational optimization.
(2) What is the mechanism to update optimization models from limited
information?
(3) How to obtain simple models with acceptable accuracy and robustness to
inaccurate parameter estimation.
1.3. Overview of this work
Limited information of crude feed compositions is the primary barrier for operational
optimization of crude oil distillation systems. It is obvious that better decisions can be
made when more information of good quality in hand. However, information is not
free. Therefore, there is a trade-off between how much one pays for improving quality
of information and how much one can obtain from it. In general, there are three ways
to handle information in operational optimization, see Figure 1.1.
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Limited
Information
Quality of
Information
Information used
Investment
EstimationUncertainty
Robust Operational
Optimization
Real-time
Optimization
Figure 1.1. Methods to handle information in operational optimization.
The first way is to invest in online analyzers to improve quality of information. This
is a common method for real-time optimization implementations when budgets are
generous and there are reliable online analysis techniques available in the market. This
method is beyond the scope of this work.
The second way is to estimate missing information and use the estimated information
for operational optimization. This is also a common method for real-time optimization
when budgets are limited. This method has the advantage of utilizing as much
information as possible to make the most out of what is available currently. However,
decision makers also have to take the risk of wrong information caused by inaccurate
parameter estimation.
The first half of this work (Chapter 3 and 4) focuses on developing methods to estimate
unknown crude feed TBP curves and construct simplified optimization models based
on the estimation. Based on information sources for model construction, the first half
of the work is further divided into two pieces. The first one (Chapter 3) uses a
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calibrated rigorous model, and the second one (Chapter 4) uses real-time plant
measurements.
The third way is to treat missing information as uncertainty. Based on this philosophy,
a new operational optimization framework, the so-called robust operational
optimization is proposed. In contrast to real-time optimization, robust operational
optimization does not incorporate more information into the procedure of operational
optimization by investment or estimation, but treats missing information as uncertainty
when making decisions. Since less information is used in the decision-making
procedure, robust operational optimization can lose a certain amount of optimization
potentials compared to real-time optimization with perfect information. However, it is
robust to inaccurate parameter estimation in nature.
The second half of this work (Chapter 5 and 6) focuses on developing robust
operational optimization frameworks. The first piece of work in the second half
(Chapter 5) develops the framework of robust operational optimization and methods
to construct robust optimization models. The second piece of work in the second half
(Chapter 6) tries to find methods to reduce loss of optimization potentials compared to
real-time optimization with perfect information.
The overall structure of the whole thesis is as follows:
Chapter 1 introduces background of this work and presents significance, objectives
and overview of this work.
Chapter 2 reviews related literature and identifies practical barriers and research gaps.
Chapter 3 is the first piece of work related to real-time optimization with simplified
models. This chapter proposes a method to construct simplified models from a
calibrated rigorous model.
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Chapter 4 is the second piece of work related to real-time optimization with simplified
models. This chapter proposes a method to construct simplified models from real-time
plant measurements.
Chapter 5 is the first piece of work related to robust operational optimization. This
chapter develops a systematic framework for robust operational optimization and a
method to build robust optimization models.
Chapter 6 is the second piece of work related to robust operational optimization. This
chapter investigates different mathematical representations of uncertainty to reduce
loss of optimization potentials compared to real-time optimization with perfect
information.
Chapter 7 compares strength and drawbacks of different methods proposed in this
work and draws conclusions. Future work is also suggested to further overcome
drawbacks of the proposed methods and answer some open questions.
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2. Literature Review
Industrial crude oil distillation is performed in a strongly interacted complex
distillation and heat recovery system. The crude oil distillation system has some
special features which are very different from simple distillation devices and are
crucial to its operation, modelling and optimization. These features are discussed in
the first part of this chapter.
In the area of optimization of crude oil distillation systems, main advancements focus
on development of crude oil distillation models. The second part of the chapter reviews
previous works on different types of crude oil distillation models. The third part of this
chapter discusses frameworks for implementing operational optimization, including
real-time optimization and related techniques. Finally, key research gaps for
operational optimization of crude oil distillation systems are concluded.
2.1. Features of crude oil distillation systems
The main purpose of crude oil distillation is to fractionate crude oil into several
intermediate products based on their boiling ranges for secondary processing units,
such as fluid catalytic cracking, hydrocracking and delayed coking. Figure 2.1
illustrates a typical crude oil distillation system. Unlike standard binary distillation
towers, crude oil distillation systems have several features which are vital to their
design and operation due to the nature of crude oil separation tasks.
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Furnace
Residue
Off-gas
Naphtha
Diesel
AGO
HEN1
Crude
Kerosene
HEN2
Desalter
Steam
Steam
Steam
Pump-around
Pump-around
Pump-around
Figure 2.1. A typical crude oil distillation system.
(1) Complex feed composition
Crude oil is a complex mixture of hydrocarbons. To describe properties of such a
complex mixture, crude oil is characterized by ASTM (American Society for Testing
Materials) test methods conducted in laboratories. The ASTM methods represent crude
oil or its products using distillation curves of boiling temperatures with respect to
fraction of the original sample vaporized (e.g., 5%, 10%, …, 95%) [3].
There are several types of ASTM test methods performed in different distillation
devices [3]. Two types of ASTM test methods are commonly used in refineries. One is
the so-called true boiling point (TBP) distillation (ASTM D2892). It is carried out in
distillation devices with multiple theoretical stages. The TBP curves are usually used
to characterize crude oil. Another popular type of ASTM method is performed in
single-stage distillation devices. It can be done at either atmospheric (ASTM D86) or
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vacuum (ASTM D1160) conditions. These methods are usually used to characterize
products such as naphtha, diesel and gas oil. ASTM D86 tests are usually used for light
products. For heavy products, ASTM D1160 tests are usually used to avoid thermal
cracking. Different distillation curves can be converted into one another by established
methods [4].
(2) Complex column configurations
Crude oil distillation systems have multiple products with light to heavy boiling ranges
such as naphtha, kerosene, diesel, atmospheric gas oil (AGO) and residue. Current
industrial practices favor complex column configurations with pump-arounds and
side-strippers [5] over a sequence of simple towers. Liebmann et al. [6] proved that
complex column configurations of crude oil distillation systems can be decomposed
into an equivalent sequence of simple columns.
Pump-arounds are heat removal equipment apart from top condensers. The primary
reason for introducing pump-arounds is to reduce flow variations along the column
occurring when heat is only removed from the top condenser [7]. Another benefit is
that pump-arounds offer hot streams at relatively high temperature and therefore help
to recover more energy through heat exchanger networks (HENs) [5]. Side strippers
are used to enhance sharpness of separation by carrying light components up. Steam
injection and reboiling are two main approaches for stripping [6].
(3) Complex heat recovery systems
HENs play an vital role in improving energy efficiency of crude oil distillation systems,
especially after the pinch design method was developed by Linnhoff and coworkers
[8]. HENs boost energy efficiency by preheating crude oil using column products and
pump-around draws. The whole heat recovery system is usually divided into two
sections by a desalter. Crude oil is first heated to about 130 °C, which is suitable for
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operation of the desalter. After water and dissolved salts are removed, crude oil is
further heated in the second section before entering furnaces.
The complex distillation column has strong interaction with its associated HEN [9].
Changes in flowrates of pump-arounds affect not only heat removed by each pump-
around, but also crude oil temperature entering the furnace after being preheated by
the HEN. Without simultaneous consideration of HEN, operating conditions may not
be feasible. Therefore, operational optimization of crude oil distillation systems is not
a simple task.
2.2. Crude oil distillation models for optimization
There are three types of optimization problems for crude oil distillation systems,
namely, design optimization, operational optimization and retrofit optimization. The
three types of problems share similar challenges for modeling complex crude oil
distillation columns. They are also very different in nature. For example, discrete
variables such as feed locations are considered in design optimization problems. By
contrast, only continuous operating conditions are optimized in operational
optimization problems. This part reviews previous modeling techniques for crude oil
distillation, with a special focus on operational optimization. In general, crude oil
distillation models fall into three categories, rigorous models, shortcut models and
data-driven models.
2.2.1. Rigorous models
Rigorous models are formulated from fundamental theories including mass balance
(M), heat balance (H), phase equilibrium (E) and molar fraction summation (S) on
each tray [10]. The four blocks together form the well-known MESH models for
general distillation. For crude oil distillation, MESH equations are constructed based
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on pseudo-components generated from crude oil TBP curves [10]. Commercial
simulators like Aspen Plus, Aspen HYSYS and SimSci PRO/II provide user-friendly
graphical user interface for implementation of rigorous models.
Rigorous models have been applied to design optimization problems by both step-by-
step modification methods [11] and mathematical programming methods [12], [13].
For operational optimization problems, Kumar et al. [14] developed an iteration
algorithm to solve MESH equations for online application. A special choice of iteration
variables, i.e., molar fractions of pseudo-components, temperature, total liquid and
total vapor flowrates on each stage, is claimed to make MESH models numerically
stable and robust. In addition, an improved numbering scheme of equilibrium stages
is proposed to reduce computation time.
Basak et al. [15] proposed a systematic framework to estimate unknown parameters
for rigorous models, including stage efficiencies and crude feed TBP curves. Stage
efficiencies are tuned online by minimizing deviations between plant data and the
rigorous model. Crude feed TBP curves are estimated by real-time plant measurements,
which will be discussed in detail later.
Inamdar et al. [16] considered operational optimization of crude oil distillation
columns with multiple objectives. A specialized genetic algorithm is developed to
solve rigorous column models with two conflicting objectives, such as profit and
property deviation. The multi-objective method can help achieve higher profit by
acceptable compromise on product properties. Similarly, Al-Mayyahi et al. [17]
proposed an multi-objective optimization method to balance CO2 emissions and
economic objectives.
The strength of rigorous models is high accuracy and wide industrial applications.
However, rigorous models also have higher risk of failure to converge [18], especially
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when plant measurements are not reliable and good initial values are not available.
Another weakness of rigorous models is high computational complexity due to large
model size. The MESH models consist of (2𝐶 + 3) ∗ 𝑆 equations for a distillation
column with 𝑆 stages and 𝐶 components [19]. Most of the equations are nonlinear,
rendering optimization models to be nonlinear and possibly trapped in sub-optimal
solutions [20].
2.2.2. Shortcut models
Shortcut models reduce tray-by-tray MESH models to simpler forms under certain
assumptions. A well-known approach is Fenske [21]-Underwood [22]-Gilliland [23]
(FUG) models under the assumption of constant relative volatility for simple towers.
The FUG method consists of three components:
(1) Fenske [21] calculates minimum number of stages to achieve a specified
separation based on relative volatilities of key components.
(2) Underwood [22] estimates minimum reflux ratio.
(3) Gilliland [23] correlates actual reflux ratios and total numbers of theoretical
stages based on results of Fenske [21] and Underwood [22].
The FUG method was originally proposed for binary distillation columns with near-
ideal multicomponent mixtures. The FUG method cannot be directly applied to crude
oil distillation columns because they are complex columns with multiple products. To
overcome this barrier, Suphanit [24] first decomposed complex crude oil distillation
columns into a sequence of simple towers based on Liebmann’s method [6] and then
applied the FUG method to each of the simple tower.
Gadalla [25] extended the FUG method to retrofit problems. Chen [26] further
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enhanced the approach by systematically selecting key components and their
recoveries based on cut point specifications of refining products.
The major advantage of the FUG models is to make it easier to optimize crude oil
distillation columns and heat exchanger networks simultaneously. This is because it
has much fewer nonlinear equations than rigorous models. However, model accuracy
is also compromised.
Another type of simplified models is based on Geddes’ fractionation index model [27].
Geddes’ method extends the Fenske equation [21] from minimum number of stages
and total reflux conditions to real stage conditions by replacing the number of stages
in the original equation by a regressed parameter called fractionation index. It can be
used to predict distribution of components in top and bottom products of a column.
Gilbert et al. [28] extends the use of fractionation index models to crude oil distillation
units by proposing a correlation between fractionation index and product TBPs.
incorporated the model to refinery planning optimization problems.
Alattas et al. [18] claims the fractionation index method is a better way than the FUG
method for shortcut calculation of crude oil distillation units for refinery planning
optimization. However, for operational optimization, the fractionation index method
cannot consider how operating conditions such as pump-around duties and flowrates
of stripping steam affect the separation.
2.2.3. Data-driven models
Unlike rigorous and shortcut models, data-driven models do not rely on knowledge
from unit operation theories. Data-driven models correlate relations between output
variables (or response variables) and input variables (explanatory variables) of crude
oil distillation systems from data samples using statistical methods.
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The simplest form of data-driven models can be considered as linear models widely
used in refinery production planning optimization. Fixed-yield and swing-cut models
are the standard linear techniques in commercial applications [18]. Fixed-yield models
simply specify yield values for all products of a specific kind of crude oil for a crude
oil distillation system. For different kinds of crude oil, different sets of product yield
values can be specified.
Product cut points cannot be optimized by fixed-yield models. To make optimization
of product cut points possible, swing-cut models introduce virtual product cuts, i.e.,
the so-called swing cuts, between two adjacent products [29]. During optimization,
swing cuts can be flexibly mixed into their two adjacent products so that product cut
points can be finely tuned.
Due to simplicity of modeling and established algorithms of linear programming, such
linear models are well-accepted in commercial refinery planning optimization
platforms such as Aspen PIMS and Honeywell RPMS. However, refinery planning
models emphasizes on optimization at the enterprise level. Therefore, operating
conditions are ignored by existing linear models.
More sophisticated nonlinear data-driven models have also been developed. Liau et al.
[30] first established an artificial neural network (ANN) model for operational
optimization of crude oil distillation columns. The ANN input variables are crude oil
properties and operating variables such as energy supply inputs, reflux ratio and
product flow ratios. The ANN output variables are product qualities. The ANN model
is trained by plant experimental data. The trained ANN model is then integrated into a
nonlinear optimization model and solved in MATLAB. Motlaghi et al. [31] builds a
similar ANN model for crude oil distillation columns and solves the operational
optimization problem using genetic algorithm.
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Mahalec and Sanchez [32] proposed a hybrid model for operational optimization of
crude oil distillation columns. One part of hybrid model is rigorous mass and heat
balance. The other part of the hybrid model is data-driven correlations between column
operating conditions (pump-around duties, feed properties, stripping steam and
product flows) and product properties. They reported the hybrid model can predict
product TBP curves with 1-2% errors compared to the rigorous model.
Yao and Chu [33] constructed a support vector regression model for crude oil
distillation columns. They compared support vector regression models with ANN
models. The results from the case study showed support vector regression models had
better fitting performance than ANN models.
Lopez et al. [34] proposed to use second-order polynomial function with binary
interaction to relate column input and output variables. They built an optimization
model on top of the quadratic crude oil distillation model for simultaneous
optimization of crude oil blending and column operating conditions for multiple crude
oil distillation columns.
Ochoa-Estopier et al. [35] extended the ANN modeling method to optimization of both
crude oil distillation columns and their associated heat exchanger networks. A two-
stage procedure was proposed to achieve this goal. In the first stage, operating
conditions of the crude oil distillation column is optimized. In the second stage, heat
exchanger networks are designed based on optimal results of the first stage. More
recently, Ochoa-Estopier et al. [36] and Ibrahim et al. [37] further extended the use of
ANN models for design and retrofit of heat-integrated crude oil distillation systems.
The strength of nonlinear data-driven models is that they can reduce computational
complexity of rigorous models with little compromise of accuracy when the models
are well trained using validated datasets. The Universal Approximation Theorem [38]
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states that a neural network with only one hidden layer can approximate any
continuous function for inputs within a specific range under mild assumptions on
activation functions. However, good nonlinear data-driven models such as ANN
usually require a large number of data samples of good quality. To obtain such a
datasets, long time of plant or simulation experiments are needed. In addition, solution
of nonlinear optimization models may be trapped at local optimums due to
nonconvexity.
2.3. Real-time optimization and related techniques
2.3.1. Role of real-time optimization in refinery decision hierarchy
Operational optimization is vital to the success of modern refineries in a highly
competitive global market. For a process with little change, infrequent offline
operational optimization is enough. However, for a process with frequent change in
feedstock as well as prices of feedstock and products, an optimization framework
which can respond to the changes in time is needed to capture all optimization
opportunities. Real-time optimization (RTO) is currently the most widely used
technique for this purpose.
Decision-making in refineries is structured in a hierarchical way (see Figure 2.2) due
to high complexity of refinery operations [39]. RTO sits in the middle between
enterprise-wide decision levels (planning and scheduling) and plant-wide execution
levels (model predictive control and distributed control systems).
35
Planning
Scheduling
RTO
Model Predictive Control
Distributed Control System
Figure 2.2. Refinery decision hierarchy.
On the top level, planning is responsible for what feedstocks to buy, what products to
produce as well as throughputs and operating modes of each plant. The planning layer
is highly connected to the markets of feedstocks and products and requires forecast of
their prices. Planning decisions are usually made on a monthly basis. On the next layer,
scheduling is concerned with how to realize a selected plan. The scheduling layer
needs to answer time-related questions, such as when to change throughputs or switch
operating modes for the next week or a few days.
At the bottom level, distributed control systems (DCS) regulate processes at desired
(not necessarily optimal) operating conditions, typically by PID controllers. On top of
DCS, the model predictive control (MPC) layer groups multiple manipulated and
controlled variables by optimizing a linear dynamic model for better control
performance. MPC enables the process to have limited closed-loop optimization
functions in relatively small envelopes when active constraints can be determined in
prior and do not change [39].
Real-time optimization (RTO) can help to make better decisions for complex
optimization problems in the whole plant level. Based on an optimization model,
optimal operating conditions are obtained when feedstocks or other external conditions
36
are detected to have changed and then passed to MPCs. MPCs help to find the best
trajectory to realize these setpoints.
2.3.2. Components of real-time optimization systems
A standard RTO system consists of four functional components, i.e., steady-state
detection, data reconciliation, model updating as well as optimization models and
solution [40].
(1) Steady-state detection
Standard RTO systems typically rely on steady-state models for optimization [39].
Therefore, it is necessary to detect whether the process has reached a steady state
before updating models and triggering optimization. Steady-state detection is not an
easy task because plant measurements are usually noisy and even corrupted [40].
Various methods have been developed for steady-state detection [41], [42], [43]. Most
of these methods use appropriate statistical tests to compare averages, variances or
slopes of selected plant measurements on sliding windows [44]. Subsets of available
plant measurements are carefully selected for steady-state tests, normally including
temperatures and compositions [39].
(2) Data reconciliation
Raw process data directly collected from sensors usually do not obey physical laws
like mass and heat balance due to noises and errors of measurements. There are two
types of measurement errors, i.e., random errors and gross errors [45]. The random
errors are usually assumed to be normally distributed with zero means [40], while gross
errors are usually assumed to be a constant deviation from real values caused by sensor
malfunctions or process leaks [40].
37
Both random errors and gross errors are needed to be removed to reveal the true states
of the process. In the absence of gross errors, random errors are typically removed by
solving a constrained weighted least-squares optimization problem minimizing total
deviations between measured and estimated values [46]. However, the presence of
gross errors can distort the results of the least-squares procedure [44]. Therefore, gross
errors are usually detected and eliminated prior to the removal of random errors by
statistical hypothesis testing approaches [47].
(3) Model updating
The key to the success of RTO is an up-to-date model which can accurately represent
the current state of the process. Mismatches between the model and the real plant can
lead to worse operating conditions or violation of process constraints [48]. In the model
updating step, unknown changing parameters such as feed composition, distillation
stage efficiencies and heat transfer coefficients are estimated by minimizing
mismatches between the model and the real plant.
The standard method for parameter estimation is also solving a constrained weighted
least-squares optimization problem [39], which is very similar with data reconciliation.
Therefore, the two problems can be solved simultaneously using an integrated model
[39]. However, the maximum number of parameters which can be estimated reliably
is determined by unknown parameters and sensor availability [49]. Otherwise, the
results from parameter estimation cannot be trusted. Some heuristic optimization
algorithms like particle swarm optimization can help to construct confidence regions
of estimated parameters [50].
(4) Optimization models and solution
Due to nonlinear nature of mass and heat transfer, operational optimization is typically
formulated as constrained nonlinear programming problems (NLP). Solution
38
algorithms for NLP can be divided into two categories, deterministic algorithms such
as sequential quadratic programming (SQP) and stochastic algorithms such as genetic
algorithm. Deterministic algorithms, especially SQP, are widely used for real-time
optimization [48]. However, SQP tends to get trapped at local minimum [51]. The
fundamental reason for this is that global optimum cannot be guaranteed due to
nonconvexity of the NLPs for operational optimization [20].
2.3.3. Applications of real-time optimization
As of year 2011, it is estimated by Darby et al. [39] that there were 250-300 sets of
industrial implementations of RTO systems, not including in-house implementations.
In the authors’ opinion, applications of RTO in ethylene plants enjoy the most success.
Among refining processes, crude oil distillation units and fluid catalytic cracking units
(FCCU) have seen the most applications.
In academic literature, olefin plants [52] and FCCUs [53], [54], [55], [56] are also the
most active areas for industrial applications of RTO. RTO applications for other
refining processes like hydrocrackers [57], steam reforming hydrogen plants [58] and
gasoline blending [59] have also been studied. However, although good operations of
crude oil distillation systems are vital to refineries, there are only several publications
[15], [60] focusing on RTO of crude oil distillation units, which will be discussed in
detail later in Section 2.4.
2.3.4. Emerging and related techniques
In recent years, alternative RTO methods and several related techniques have emerged
to overcome drawbacks of standard RTO frameworks.
(1) Nonlinear dynamic models and one-layer architecture
39
One drawback of the traditional RTO is steady-state wait time caused by the two-layer
architecture consisting of an upper RTO layer and a lower MPC layer [39], [61]. The
execution of model adaptation and optimization needs to wait until the process reaches
a new steady state, and therefore potential opportunities during the transition are lost.
This motivates attempts to merge RTO and MPC into one layer, which directly leads
to the development of dynamic RTO [62], [63] and economic MPC (EMPC) [64]. Both
dynamic RTO and EMPC use dynamic nonlinear models. Their main differences are
that dynamic RTO tends to run less frequently and EMPC is more feedback control
oriented [64]. However, the use of dynamic nonlinear models results in a high
computational cost and the improvement against static optimization may not be
significant for processes which are mostly run in steady state.
(2) Self-optimizing control
Apart from dynamic RTO and EMPC, an alternative way to unify process optimization
and process control into the same layer is to carefully select controlled variables which
can maintain the process at near-optimal operating conditions when controlled at
certain constant setpoints. This is the idea of the so-called self-optimizing control [65],
[66]. The required controlled variables are usually not a single process variables, but
can be a function, such as linear combinations of available plant measurements [67],
[68]. Self-optimizing control is a model-free method when executing online. However,
the required controlled variables are not straightforward and are difficult to understand
in an intuitive way.
(3) Modifier adaptation
Another drawback of the traditional RTO is that the parameter estimation procedure
for model adaptation does not necessarily yield models matching plant data closely.
Instead of updating model parameters, modifier adaptation techniques [69], [70]
40
propose to update correction terms for the objective function and constraints. Modifier
adaptation has the advantage to handle the mismatch between the model and plant data.
However, to calculate the correction terms, values of the objective function and
constraints need to be directly measured, which may not be available in real-world
applications [61].
(4) Robust optimization
Parameter estimation is crucial to the success of real-time optimization because it
provides missing information of current states of the process. However, estimated
parameters can be far away from true values [48]. Operational optimization based on
biased information from inaccurate parameter estimation can result in worse operating
parameters or even infeasible operations. Therefore, operational optimization should
be robust to a certain degree of errors in missing information.
Robust optimization [71] is a systematic method to handle uncertainty in model
parameters. Conventional optimization considers models parameters as exact
information. On the contrary, robust optimization treats model parameters as uncertain
information lying in a predefined uncertainty set [72]. When making decisions, robust
optimization tries to find a conservative optimal solution which is feasible for any
possible parameter values in the predefined uncertainty set [72].
Robust optimization has been actively studied for planning and scheduling of refining
and chemical processes [73], [74]. However, it has not been applied to operational
optimization yet. The main barrier for application of robust optimization in operational
optimization is that it requires special forms of mathematical formulation, like linear
programs and conic programs, for computational tractability [71].
41
2.4. Practical barriers and research gaps
2.4.1. Limited information of crude feed compositions
The major practical barrier for operational optimization of crude oil distillation
systems is limited information of crude feed compositions. Composition of crude oil
is usually characterized by the so-call true boiling point (TBP) distillation curves [4],
which are corresponding temperatures for different distilled percentages of a crude oil
sample. TBP curves are usually obtained from distillation devices in laboratories. The
analysis is expensive and time-consuming (up to three days [75]).
On the other hand, composition of crude oil can change frequently due to scheduling
of crude oil operations. Different types of crudes are unloaded, stored and blended in
multiple tanks before entering crude oil distillation systems [76]. The complex
procedure of crude oil operations makes it difficult to track composition of currently
processed crude feed. Considering long lag time caused by the conventional TBP
analysis procedure, operational optimization faces the problem of limited information
of real-time crude oil compositions.
However, most of the publications mentioned in Section 2.2 assume that TBP curves
are known information for optimization. Dave et al. [60] considered the problem and
proposed an online crude TBP estimation method from measured column operating
parameters, including temperatures of feed and product drawing trays, flowrates of the
feed, products, reflux and injections steam, as well as pump-around duties. The
strength of Dave’s method is that crude TBP curves can be estimated in real time.
However, some parameters in the model are crude specific and it is difficult to regress
their values without prior knowledge of crude TBP.
42
2.4.2. Balance of accuracy, complexity and robustness of models
Another problem for operational optimization is the balance among accuracy,
complexity and robustness of optimization models. Conventional real-time
optimization implementations usually employ rigorous models [39]. As discussed in
Section 2.2, rigorous models are accurate. However, the accuracy is at a cost of
complexity. Refineries face tighter budgets and staffing reduction in a more
competitive global market, making it a practical challenge to maintain complex models
[39].
From a mathematical viewpoint, rigorous models, shortcut models and complex data-
driven models are all nonconvex in nature. Nonconvexity means global optimum
cannot be guaranteed and the solution is likely to be trapped at a local optimum [20].
Moreover, widely used numerical method for nonlinear programming like SQP may
fail to converge in certain situations [48].
Another drawback of nonlinear models is that it’s difficult to incorporate robust
optimization to make the solution robust to inaccurate parameter estimation. The use
of nonlinear models for operational optimization implies the assumption of accurate
parameter estimation, which cannot be practically guaranteed. Considering possible
large deviation of estimated parameters, the advantage of accuracy of nonlinear models
may be compromised.
43
3. Real-time Optimization of Crude Oil
Distillation Systems via Adaptive Linear
Models
This chapter is the first piece of work for real-time optimization methods with
simplified linear models. In this work, missing information of crude oil compositions
is estimated by mass balance of crude oil distillation columns. With the estimation, a
simplified linear model is generated from a calibrated rigorous model.
Please note that this chapter is prepared in a journal paper format and is attached with
its own page numbering system.
44
Blank page
* Corresponding author. Email: [email protected]
Real-time Optimization of Crude Oil
Distillation Systems via Adaptive
Linear Models
Xiao Yang, Nan Zhang*, Robin Smith
Centre for Process Integration, School of Chemical Engineering and Analytical
Science, The University of Manchester, Manchester M13 9PL, UK
Highlights
• A real-time optimization framework for crude oil distillation systems is
proposed.
• Unknown crude feed composition can be approximated by product back-
blending.
• Small-size linear optimization models can be generated from rigorous
simulations.
• Adaptive linear models can improve solution performance with small accuracy
loss.
• A proposed indicator can help monitor crude changes and trigger new
2
optimization.
3
Abstract
Real-time optimization (RTO) of crude oil distillation systems can bring significant
economic and environmental benefits considering their massive throughput and
extensive energy use. Challenges for RTO of crude oil distillation systems include lack
of knowledge of crude feed composition, detection of crude changes as well as solution
problems caused by nonlinearity and nonconvexity of optimization models. This paper
presents a systematic RTO framework for heat-integrated crude oil distillation systems.
The RTO framework consists of an offline preparation phase, a monitoring phase and
an optimization phase. In the offline preparation phase, a rigorous simulation model is
built and slowly changing equipment parameters are estimated. In the monitoring
phase, crude feed is approximated by product back-blending using plant data. In
addition, a proposed indicator is used to monitor how much crude feed has changed
and trigger new optimization accordingly. In the optimization phase, linear models are
adapted when crude changes are detected using data sets generated from rigorous
simulation. The effectiveness of the RTO framework is demonstrated by case studies
in Aspen HYSYS.
Keywords: crude oil distillation system, real-time optimization, adaptive linear models
4
Blank page
5
1. Introduction
Operational optimization of crude oil distillation systems has the potential to deliver
significant economic and environmental benefits considering their massive throughput
and energy demand. In 2017, more than 80 million barrels of crude oil were processed
by crude oil distillation systems per day worldwide [1]. Besides, crude oil distillation
is an energy-intensive process, accounting for 35-45% of total energy consumption in
refineries [2]. Therefore, even a minor operational improvement can help refineries
achieve a nontrivial increase in profit.
Frequent changes in the feed of crude oil distillation systems in many refineries make
regular operational optimization vital to seize all potential profit-increasing
opportunities. The changes in crude feed mainly stem from scheduling of crude oil
operations [3]. Compositions of the feed for crude oil distillation systems are a result
of decisions made in the scheduling process for storage, movement and mixing of
crudes of different grades. Hence, feed compositions change over time according to
crude oil operations. Moreover, changes in feed compositions have major impacts on
operations of crude oil distillation systems [4]. Therefore, operational optimization is
needed to run regularly to maintain feasibility and optimality of operations.
Compared with occasional operational optimization, regular operational optimization
requires not only an optimization model, but also additional functions to monitor
process status, identify changes, update models and trigger new optimization. These
roles are usually played by real-time optimization (RTO) systems [5], [6]. As suggested
by the name, RTO can be viewed as sophisticated operational optimization techniques
responding to changes (e.g., feed composition, product and feedstock prices) in real
time. The term ‘real-time’ often refers to time intervals of hours to days [5], [6],
according to the frequency of changes.
6
RTO generally utilizes steady-state rigorous models to calculate optimal operating
conditions [6]. The optimal operating conditions are then passed to the control layer
as its setpoints. In the control layer, model predictive control (MPC) mainly uses
dynamic linear models to steer the process to the RTO generated setpoints [7]. In
addition to the two-layer RTO and MPC architecture, RTO typically incorporates a
model adaptation procedure to keep models consistent with plant data by updating
model parameters [8], [9]. More recently, a new model updating scheme, modifier
adaptation, has been proposed to update model correction terms instead of model
parameters [10].
To date, RTO has found many applications in the industry. The most successful
applications include ethylene plants and fluid catalytic cracking units [6]. In recent
years, RTO systems have also been developed for parallel compressor networks [11],
gold cyanidation leaching processes [12], cogeneration plants [13], and ethylbenzene
dehydrogenation processes [14], to name a few. However, few studies have focused on
crude oil distillation systems.
One challenge for RTO of crude oil distillation systems is lack of knowledge in feed
compositions. Since crude oil is a mixture of very complex components, its
composition is usually characterized by the so-called true boiling point (TBP)
distillation curves [15]. A TBP curve is temperatures versus distilled percentages of a
crude oil sample analyzed by a distillation device in a laboratory. Unfortunately, TBP
analysis is expensive and time-consuming [15]. The TBP analysis procedure can take
up to three days [16], which makes it unrealistic for RTO implementation. Dave et al.
[4] developed an online crude TBP estimation method from measured column
operating parameters, including temperatures of feed and product drawing trays,
flowrates of the feed, products, reflux and injections steam, as well as pump-around
duties. Basak et al. [17] proposed an RTO system for crude oil distillation systems
based on the estimation method. Dave’s method has the advantage of fast estimation
7
because only measurement data are used. Nevertheless, some coefficients in their
estimation model are needed to be regressed and these coefficients are crude specific.
The crude-specific coefficients are difficult to obtain without prior knowledge of crude
TBP, which results in a causality dilemma.
The second challenge for RTO of crude oil distillation systems is complexity and scope
of optimization models. A crude oil distillation system is usually a complex heat-
integrated system consisting of distillation columns and heat exchanger networks
(HENs). Rigorous optimization models for the distillation column were proposed by
Basak et al. [17] and Inamdar et al. [18] and solved by deterministic approaches like
sequential quadratic programming [17] or stochastic approaches like genetic
algorithms [18]. Despite rigorous models are accurate, they are prone to convergence
failures [19], which may be especially frustrating for RTO because manual remedies
should be avoided.
To simplify rigorous models, various approaches have been developed. Mahalec and
Sanchez [20] simplified rigorous models using a hybrid method combining mass and
heat balance with correlation models for product quality prediction. Lopez et al. [21]
developed a quadratic empirical model to optimize column operating conditions as
well as crude blending for multiple crude oil distillation units. More advanced
empirical modeling techniques have also been introduced, including artificial neural
networks (ANN) [22], [23], [24], [25] and support vector regression (SVR) [26]. These
methods can effectively simplify rigorous models. However, these methods assume
crude TBP curves are known and the resulting models are still nonlinear. The
nonlinearity makes the optimization problem nonconvex and therefore the solution is
likely to be trapped at a local optimum. Another drawback for ANN and SVR
approaches is that many data sets (e.g., 800 data sets in [24]) generated from rigorous
simulations are required to train the models. The time-consuming model generation
procedure may not be suitable for real-time applications.
8
Regarding the optimization scope, most of the previous work only considered
distillation columns. However, operational feasibility cannot be guaranteed without
considering the interaction between distillation columns and HENs. Lopez et al. [21]
included models of HENs based on rigorous heat balance and heat transfer rate
calculation. The resulting HEN model is nonlinear and has the same disadvantages as
distillation column models due to nonlinearity and nonconvexity.
The third challenge for RTO of crude oil distillation systems is how to determine when
new optimization should be run. Since static models are used in RTO, whether a new
optimization is needed should be evaluated every time the plant reaches a new steady
state. Although general steady-state detection methods [27] are available, they are not
tailored to the crude changing problem faced by crude oil distillation systems.
The objective of this work is to construct a new RTO framework for crude oil
distillation systems to overcome the challenges. Three key improvements are: (1) real-
time crude feed TBP reconstruction by product back-blending; (2) an optimization
trigger based on a proposed crude change detection method; (3) (convex) small-size
adaptive linear models considering the interaction between distillation columns and
HENs generated from rigorous simulations.
2. Problem statement
2.1. Scope of optimization
Modern crude oil distillation systems are heat-integrated systems consisting of
complex columns and HENs. A typical crude oil distillation system is depicted in
Figure 1. In this work, both the distillation column and HEN are considered in the
scope of optimization.
9
Several products with different boiling ranges are drawn from the main column. Heat
removal is carried out not only in the top condenser, but also by the so-called pump-
arounds. Pump-arounds draw liquids from intermediate positions of the main column
and sent the cooled liquids back to trays above [28]. Another feature of the complex
column is the use of side-strippers to enhance separation by stripping down-flowing
liquid of light components.
HENs boost energy efficiency by preheating crude oil using column products and
pump-around draws. The heat recovery system is usually divided into two sections by
the desalter. Crude oil feed is first heated to about 130 °C, which is suitable for
operation of the desalter. After water and dissolved salts are removed, the crude is
further heated in the second section before entering the furnace. Changes in either the
main column or HEN affect the operation of each other. Due to the strong interaction
between the two, the optimal operating conditions may not be feasible if only
distillation columns are considered in optimization.
10
Furnace
Residue
Off-gas
Naphtha
Diesel
AGO
HEN1
Crude
Steam
Kerosene
HEN2
Desalter
Figure 1. A typical crude oil distillation system.
2.2. The operational optimization problem
Operational optimization aims at improving performance (e.g., profit) of crude oil
distillation systems indicated by an objective function via adjustment of design
variables, i.e., operating parameters in the plant. At the same time, process constraints
including operating bounds, product qualities and equipment capacities should be
maintained. The optimization problem can be stated in the following general form:
max 𝑦 (1)
Subject to:
x𝑘L ≤ 𝑥𝑘 ≤ x𝑘
U 𝑘 = 1,2, … ,K
p𝑚L ≤ 𝑝𝑚 ≤ p𝑚
U 𝑚 = 1,2, … ,M (2)
11
e𝑛L ≤ 𝑒𝑛 ≤ e𝑛
U 𝑛 = 1,2, … ,N
where 𝑥 , 𝑦 , 𝑝 and 𝑒 denote the design variables, objective function, physical
properties and equipment capacities, respectively. The superscripts L and U refer to
lower and upper bounds.
Increasing profit is the most common demand of refineries. Therefore, profit of crude
oil distillation systems is considered as the objective function in this work. It is
obtained by gains in product values minus operating costs.
𝑦 = Values of products − Value of crude oil − Operating cost (3)
Operating costs mainly come from fuel burned in the furnace, stripping steam and
cooling water. The value of crude oil feed changes according to scheduling of crude
oil operations and is difficult to be calculated precisely. Fortunately, when operational
optimization is considered each time, crude oil is already fed into crude oil distillation
systems and therefore its value cannot be changed by operational optimization. As a
result, the value of crude oil can be omitted in the optimization problem without
affecting its optimal solution.
Design variables, including throughput, product cut points (or overflash flowrate for
the heaviest side draw), furnace outlet temperature, stripping steam flowrates (or
reboiler duty if reboilers are used for stripping) and pump-around flowrates are
optimized. For the main column, the duty and flowrate of each pump-around are two
independent specifications. But when the HEN is considered together, duties and
flowrates become dependent on each other. Since pump-around flowrates can be
directly adjusted in the plant, they are considered as design variables instead of pump-
around duties in this work. There are two reasons to choose product cut points instead
of their flowrates. First, product cut points are usually configured as controlled
variables of plant MPCs and their optimal values from RTO can be directly passed
12
down. Second, the proposed framework requires runs of rigorous simulation to
generate simplified models. Product cut points as column specifications may cause
less convergence issues because there is less risk of violating mass balance than
specifying product flowrates.
Apart from bounds of design variables, two types of process constraints are considered
in the optimization problem, product qualities and equipment capacities. Product
qualities include boiling ranges and other physical properties such as density and flash
point. Common equipment limits include column hydraulic performance, heat transfer
capacities of the furnace and heat exchangers, and pump capacities for pump-arounds.
2.3. The RTO problems
In addition to the operational optimization problem, the proposed RTO framework in
this work aims to find methods for:
(1) how to estimate crude feed TBP curves in real time;
(2) how to detect crude feed changes and trigger new optimization.
3. The RTO framework
The proposed RTO framework for crude oil distillation systems consists of three parts
(see Figure 2):
• Offline preparation
• Monitoring phase
• Optimization phase
13
In offline preparation, a rigorous simulation model is created and calibrated. Slowly
changing parameters, including distillation column stage efficiencies and heat transfer
coefficients, are estimated in the stage. These model parameters need to be reviewed
when significant change of equipment performance occurs.
In the monitoring phase, crude feed TBP curves are reconstructed from product back-
blending using plant data. Moreover, real-time crude feed TBP curves are continuously
estimated each time new product plant data are available. An indicator measuring how
much crude feed has changed is proposed to help detect crude feed changes and trigger
new optimization accordingly.
In the optimization phase, a linear model is adapted and solved when crude feed
changes are detected. The linear models are generated from datasets obtained from
rigorous simulation.
Optimization Phase
Monitoring Phase
Reconstruct crude TBP
Real-time
product plant data
Compare real-time TBP to
TBP at last optimization
Indicator > threshold?
Maintain current operation
No
Generate
linear models
Yes
Generate data sets from
rigorous simulation
Yes
Real-time
TBP
Rigorous simulation
for real-time TBP
Update rigorous simulation Solve linear models
No
Significant constraint
violation?
Validate optimal results in
rigorous simulation
Adapt linear
models
Calculate
correction terms
Rigorous
simulation model
Real-time
TBP
Offline Preparation
Create and calibrate
rigorous simulation model
Rigorous
simulation model
Pass optimal operating
parameters to control system
Figure 2. RTO framework.
14
3.1. Offline preparation
A rigorous simulation model is created and calibrated offline for generating linear
models for optimization. The rigorous model can be created in any simulation package,
such as Aspen Plus, Aspen HYSYS and SimSci Pro/II. Aspen HYSYS (version 8.8) is
used in this work.
The rigorous simulation model is created and calibrated offline. Parameters including
distillation stage efficiencies and heat transfer coefficients (or fouling factors if heat
exchangers are modeled in a more detailed manner) can be calibrated to match plant
data and simulation results closely. The parameter estimation can be done either
according to experience or by an optimization procedure proposed by Dave et al. [4].
When used online for data set generation, these parameters are assumed to be constants
and only crude feed TBP and operating conditions are updated online.
3.2. Monitoring phase
3.2.1. Reconstruct crude TBP
Crude feed TBP curves are reconstructed by product back-blending in this work. The
idea is based on the mass balance of crude oil distillation systems. Products of crude
oil distillation systems are usually routinely sampled and analyzed in refinery
laboratories for quality control. According to the mass balance, unknown crude feed
can be approximated by the mixture of crude oil distillation products, see Figure 3.
Crude feed TBP curves can be estimated in real time based on real-time product
flowrates and the latest product analysis.
15
Plant crude oil distillation systems
Unknown
crude feed
Product 1
Product 2
Product N
Product 3
Back-
blend
by
simulation
Reconstructed
crude feed
Product flowrates
and distillation curves
Figure 3. Crude TBP reconstruction by product back-blending.
Product flowrates and composition are required to back-blend products into crude feed.
The flowrates of each product can usually be read from flow meters. Like crude oil,
compositions of crude oil distillation products are also represented by distillation
curves. Since TBP analysis is expensive and time-consuming, two different distillation
curves are commonly used to characterize products in refineries, namely ASTM D86
and ASTM D1160. Both ASTM D86 and D1160 analysis are faster than TBP analysis
because their test methods are very simple and convenient [15]. Compared with the
long analysis procedure of TBP curves (up to three days [16]), runtime for ASTM D86
is only about 30 minutes [29]. ASTM D86 curves are mostly used for light products
like naphtha, kerosene and diesel. For heavy products like atmospheric gas oil (AGO)
and residue, ASTM D1160 curves obtained from distillation at reduced pressures
(usually 10 mmHg) are used due to cracking of hydrocarbons at high temperatures
[15].
In this work, ASTM D86 curves for light products and ASTM D1160 curves for heavy
products are assumed to be available in refineries. If other types of distillation curves
are used by refineries, like simulated distillation by gas chromatography [15], [16],
they can also be applied directly in the proposed framework because different types of
distillation curves can be converted into one another using established methods [15].
16
Back-blending of products into crude feed can be calculated by simulation packages.
This work uses Aspen HYSYS to back-blend crude oil distillation products into
reconstructed crude feed. At least five points on distillation curves for each product are
required by Aspen HYSYS as input data. After providing product flowrates and
distillation curves, Aspen HYSYS can blend them together and generate detailed TBP
data of the mixture.
3.2.2. Detect crude change
Another function of the monitoring phase is to track how much crude feed has changed
and determine whether to start new optimization. Changes in product prices can also
affect optimal operating conditions but as update of prices is straightforward, crude
feed changes are focused in this work. Each time new product flowrates or distillation
curves are available, real-time crude TBP curves can be reconstructed. Then, real-time
TBP curves need to be compared with TBP data at last optimization. If there is large
deviation between the two TBP curves, the RTO system needs to enter the optimization
phase to evaluate optimal operating conditions.
A crude similarity indicator is proposed in this work to compare two TBP curves. The
indicator measures the deviation of two sets of TBP data by their Euclidean distance:
Indicator = √∑ (TBP𝑗1-TBP𝑗
0)2𝐽
𝑗=1 (4)
where TBP𝑗 is the TBP data point for a specific percentage of liquid volume distilled.
TBP points at 5%, 10%, 20%, 30%, 40% 50%, 60%, 70%, 80%, 90% and 95% on
distillation curves are used to calculate the indicator value.
Small values of the indicator mean the two TBP curves are relatively similar to each
17
other. If the value of the indicator is less than a predefined threshold, it can be
considered the crude oil doesn’t have significant change, so there is no need to readjust
the design variables. If the value of the indicator is greater than the predefined
threshold, a new run of optimization is triggered.
The next question is how to choose the value for the threshold. Since crude feed TBP
curves are reconstructed from product plant data, changes in product flowrates and
distillation curves affect results of reconstructed TBP curves. Besides, product
flowrates and distillation curves are not only determined by crude feed, but also
operating conditions. Therefore, even with the same crude feed, reconstructed TBP
curves can be slightly different under different operating conditions. The threshold
value needs to accommodate variations of reconstructed TBP curves caused by
different operating conditions so that unnecessary optimization runs can be avoided.
This work uses randomly generated simulation cases under different operating
conditions for the same crude feed to find such a threshold value, which will be
demonstrated in Section 4.3.
3.3. Optimization phase
In the optimization phase, a linear model is adapted and solved when crude changes
are detected in the monitoring phase. In this section, the proposed linear model is first
presented. Then, how to generate the linear model from rigorous simulations and how
to solve it are described.
3.3.1. Proposed linear models
A process model is required to reflect how the objective function and constraints
respond to changes in design variables in the operational optimization model. The idea
behind the proposed linear model is to skip rigorous column and HEN models and
18
build direct correlations between the objective function, constraints and design
variables instead. The correlations are in linear forms to keep the model simple and
convex:
𝑦 = y0 + ∑ c𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
(5)
𝑝𝑚 = p𝑚,0 + ∑ a𝑚,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
𝑚 = 1,2, … ,M (6)
𝑒𝑛 = e𝑛,0 + ∑ b𝑛,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
𝑛 = 1,2, … ,N (7)
where a, b, c, x0, y0, p0 and e0 are model parameters. The parameters a, b and
c are slopes of the linear relations, while x0, y0, p0 and e0 are the values of the
design variables, objective function, physical properties and equipment capacities
under current operating conditions. These model parameters are associated with a
specific crude feed and need to be adapted when crude changes are detected.
Process models and the real process can hardly match perfectly. First, the mathematical
form of models, no matter rigorous or linear, has limitation for full description of the
complex reality. Second, accurate model parameter estimation cannot be guaranteed
regardless of complexity of models. Third, linear models lose extra accuracy compared
to rigorous models. Since allowed ranges of operating variables are usually narrow,
accuracy loss by linearity is relatively small for operational optimization problems.
3.3.2. Generate linear models using rigorous simulation data sets
To generate the linear models, parameters a , b , c , x0 , y0 , p0 and e0 need to be
calculated. First, the rigorous simulation model is updated with real-time crude feed
19
TBP and current operating conditions. The parameters for current operating conditions
x0, y0, p0 and e0 can then be calculated from the simulation results.
In the next step, the slopes a, b and c are calculated using data sets generated from
rigorous simulations. To calculate a slope, two points are required. In this work, two
simulation cases are generated for each design variable at its lower and upper bounds
while keeping values of other design variables flat. Data sets of the objective function
and constraints are then collected from the two simulation cases. The slopes are
computed by the following equations:
a𝑚,𝑘 =𝑝𝑚(x𝑘
U) − 𝑝𝑚(x𝑘L )
x𝑘U − x𝑘
L 𝑘 = 1,2, … ,K 𝑚 = 1,2, … ,M (8)
b𝑛,𝑘 =𝑒𝑛(x𝑘
U) − 𝑒𝑛(x𝑘L)
x𝑘U − x𝑘
L 𝑘 = 1,2, … ,K 𝑛 = 1,2, … ,N (9)
c𝑘 =𝑦(x𝑘
U)−𝑦(x𝑘L )
x𝑘U−x𝑘
L 𝑘 = 1,2, … ,K (10)
3.3.3. Solve linear models
The generated linear models can be easily solved by available software packages,
including professional modeling software such as MATLAB and GAMS, and
spreadsheet-based Microsoft Excel. The Solver add-in as part of Microsoft Excel
implements the simplex algorithm for linear programming. In this work, the generated
linear models are constructed in Microsoft Excel and are solved using the built-in
Solver add-in.
Linear models have the advantages of robustness and high efficiency during the
solution phase. However, the accuracy may not be as good as rigorous models. To
20
avoid large violation of the constraints, the optimal solution of the linear model is sent
back to the rigorous simulation. If the optimal solution causes significant violation of
the constraints, the linear model is adapted by constraint correction terms, which is a
variation of the modifier adaptation method [30]. A correction term, which is the
difference between constraint values of rigorous simulation and linear models, is added
to the original linear model:
𝑝𝑚𝑡+1 = p𝑚,0 + ∑ a𝑚,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
+ ∑(𝑝𝑚𝑡,𝑟𝑖𝑔
− 𝑝𝑚𝑡 )
𝑡
𝑡=0
𝑚 = 1,2, … ,M (11)
𝑒𝑛𝑡+1 = e𝑛,0 + ∑ b𝑛,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
+ ∑(𝑒𝑛𝑡,𝑟𝑖𝑔
− 𝑒𝑛𝑡 )
𝑡
𝑡=0
𝑛 = 1,2, … ,N (12)
where 𝑝𝑚𝑡 and 𝑝𝑚
𝑡,𝑟𝑖𝑔 are constraint values calculated by rigorous simulation and
linear models in 𝑡 iteration, respectively.
Intuitively, the method is to tighten the corresponding bounds in the linear optimization
model which are significantly violated in rigorous simulation. For example, suppose
an upper bound of condenser duty at Qmax is imposed and the rigorous simulation
finds its value is Qmax+∆Q for the optimal solution. If ∆Q is not significant, the
slight violation can usually be accommodated by the flexibility of the process.
However, if ∆Q is large, the upper bound of condenser duty should be tightened to
Qmax-∆Q , and the optimization model should be solved again. The solution and
validation procedure may need to be repeated for several times until no significant
violation incurs.
21
4. Case studies
4.1. Description of crude oil distillation system
The crude oil distillation system shown in Figure 1 is studied in this work. The crude
oil is separated into five products, i.e., naphtha, kerosene, diesel, AGO and residue.
There are 34 stages in the main column. The column has three pump-arounds and three
side-strippers attached. The kerosene stripper is driven by a reboiler, and the strippers
for diesel and AGO use steam injection. The structural configuration of the main
column is summarized in Table 1.
Table 1. Column configuration (numbered top-down)
Number of trays in the main column 34
Condenser 0
Pump-around 1 return 1
Pump-around 1 draw 3
Kerosene stripper return 8
Kerosene stripper draw 9
Pump-around 2 return 11
Pump-around 2 draw 13
Diesel stripper return 17
Diesel stripper draw 18
Pump-around 3 return 20
Pump-around 3 draw 22
AGO stripper return 26
AGO stripper draw 27
CDU feed 31
Main steam injection 34
Number of trays in the kerosene stripper 3
Number of trays in the diesel stripper 4
Number of trays in the AGO stripper 4
The HEN in the system is shown in Figure 4. The HEN consists of ten process stream
heat exchangers, four before the desalter and six after. The crude oil is mixed with
22
fresh water before entering the desalter. The mixing process brings down the
temperature of the crude oil. It is assumed that 4°C is dropped during the desalting
process.
E-101 DesalterE-102 E-103 E-104
Crude
Furnace
Kerosene PA1 Residue
E-105 E-106 E-107 E-108 E-109 E-110
PA2
Diesel
AGO PA3
HEN1 HEN2
Figure 4. HEN structure.
To test the effectiveness of the RTO framework, seven crude scenarios are used. The
crude feed is assumed to be a mixture of three different crudes shown in Table 2 (see
Table S1 in the supplementary material for detailed bulk properties and TBP data). The
recipe of the three crudes is changing over time from scenario 1 to 7 according to
scheduling of crude oil operations. It is assumed that current crude feed is scenario 4.
Table 2. Crude feed test scenarios
Crude 1 Crude 2 Crude 3
API 33.2 29.7 25.6
Sulfur (wt%) 0.37 2.85 0.41
Acidity (mgKOH/g) 0.12 0.11 1.3
Crude scenarios (wt%)
1 0.6 0.4 0
2 0.5 0.4 0.1
3 0.4 0.4 0.2
4 (Current) 0.3 0.4 0.3
5 0.2 0.4 0.4
6 0.1 0.4 0.5
7 0 0.4 0.6
23
4.2. Rigorous simulation models
The rigorous simulation model is built in Aspen HYSYS for linear model generation
in later steps. The assumption of equipment parameters such as distillation stage
efficiencies and overall heat transfer coefficients are summarized in Table 3 and 4.
Table 3. Column stage efficiencies
Stages Efficiency Notes
1 - 3 0.6 Pump-around 1
4 - 9 0.8 Naphtha to kerosene section
10 0.8 Kerosene to diesel section
11 - 13 0.4 Pump-around 2
14 - 18 0.8 Kerosene to diesel section
19 0.7 Diesel to AGO section
20 - 22 0.4 Pump-around 3
23 - 27 0.7 Diesel to AGO section
28 - 30 0.7 AGO to flash zone section
31 - 34 0.4 Steam stripping section
Kerosene stripper 0.7
Diesel stripper 0.4
AGO stripper 0.4
24
Table 4. UA† of heat exchangers
Heat exchanger UA, kJ/(°C•h)
E-101 2.5 × 105
E-102 1.0 × 106
E-103 5.0 × 105
E-104 1.1 × 106
E-105 1.1 × 106
E-106 7.0 × 105
E-107 8.0 × 105
E-108 2.0 × 105
E-109 8.0 × 105
E-110 2.5 × 106
† U and A denote overall heat transfer coefficients and areas of heat exchangers,
respectively.
4.3. Test for crude TBP reconstruction
To test whether crude TBP curves can be reconstructed by product back-blending,
reconstructed TBP curve is compared to the real TBP curve for the current crude
scenario (scenario 4). Product flowrates and distillation curves (see Table S2) are first
calculated using rigorous simulation. Then, these data are used by the back-blending
procedure to compute the reconstructed TBP curve.
Figure 5 compares the real TBP curve and the reconstruction result. The two curves
have good agreement. The deviation of the two curves is larger for the first several
points, because light ends are not included in the TBP reconstruction procedure. This
is due to practical consideration that light ends are usually not routinely analyzed in
some refineries to the knowledge of the authors. However, it is not a big issue because
light ends have little impact on the operating parameters.
25
Figure 5. Real versus reconstructed TBP curves.
4.4. Test for crude change detection
Whether crude feed has changed is detected by comparing the value of the proposed
indicator with a predefined threshold. As discussed in Section 3.1.2, the threshold
needs to accommodate TBP variations caused by different operating conditions with
the same crude feed. One hundred random cases under different operating conditions
for the current crude scenario (scenario 4) are generated and reconstructed TBP curves
for these cases are calculated. Then, indicators for the reconstructed TBP curves are
computed. The values of the indicators are shown in Figure 6 as blue circles. Although
the real crude feed is the same for all the cases, there are slight variations among
reconstructed TBP curves. A threshold value of 8.0 is selected to accommodate the
variations.
Next, whether the threshold value can help to detect different crude scenarios is tested.
One hundred random cases under different operating conditions for the other six crude
scenarios are further generated and indicators for reconstructed TBP curves of these
cases and crude scenario 4 are computed. The results are shown in Figure 6 (Plots for
scenario 1, 2 and 3 are hided because they are overlapped with scenario 5, 6 and 7). It
can be seen all indicator values for other crude scenarios are greater than the threshold
-100
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50 60 70 80 90 100
Te
mpera
ture
, °C
Liquid volume percent
Real
Reconstructed
26
value. Therefore, changes in crude feed scenarios can be effectively detected.
Figure 6. Crude change detection.
4.5. Linear model generation
In this part, the linear model generation procedure is implemented for the current crude
scenario (scenario 4). The generated linear model is compared with the rigorous model
in terms of accuracy through randomly generated cases.
4.5.1. Prices and constraints
The goal of RTO is to increase profit of the system. Prices for calculating profit using
Equation (3) are shown in Table 5.
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70 80 90 100
Indic
ato
r
Random cases
Crude scenario 4 Crude scenario 5
Crude scenario 6 Crude scenario 7
Threshold = 8
27
Table 5. Prices
Item Prices
Crude 1 280 USD/t
Crude 2 265 USD/t
Crude 3 250 USD/t
Naphtha 480 USD/t
Kerosene 520 USD/t
Diesel 420 USD/t
AGO 240 USD/t
Residue 180 USD/t
Furnace duty 9 USD/GJ
Reboiler duty 14 USD/GJ
Steam 27 USD/t
Cooling water 1 USD/GJ
Thirteen design variables, including throughput, product cut points, overflash flowrate,
furnace outlet temperature, stripping steam flowrates and pump-around flowrates, are
considered in the optimization problem. Table 6 lists their current values, lower and
upper bounds.
28
Table 6. Design variables and process constraints
Variables Current
value Lower bound Upper bound
𝑥1: Throughput 600.0 t/h 540.0 t/h 660.0 t/h
𝑥2: Naphtha D86 FBP 170.0 °C 165.0 °C 175.0 °C
𝑥3: Kerosene D86 FBP 240.0 °C 235.0 °C 245.0 °C
𝑥4: Diesel D86 95% 360.0 °C 355.0 °C 365.0 °C
𝑥5: Overflash flowrate 15.0 t/h 12.0 t/h 20.0 t/h
𝑥6: Furnace outlet temperature 360.0 °C 355.0 °C 365.0 °C
𝑥7 : Main stripping steam
flowrate 6.0 t/h 3.0 t/h 9.0 t/h
𝑥8 : AGO stripping steam
flowrate 1.0 t/h 0.5 t/h 1.5 t/h
𝑥9 : Diesel stripping steam
flowrate 3.5 t/h 1.0 t/h 6.0 t/h
𝑥10: Kerosene reboiler duty 0.5 GJ/h 0.2 GJ/h 0.8 GJ/h
𝑥11: Pump-around 1 flowrate 400.0 m3/h 320.0 m3/h 480.0 m3/h
𝑥12: Pump-around 2 flowrate 300.0 m3/h 240.0 m3/h 360.0 m3/h
𝑥13: Pump-around 3 flowrate 250.0 m3/h 200.0 m3/h 300.0 m3/h
𝑝1: Kerosene flash point 52.5 °C 38.0 °C -
𝑒1: Furnace duty 199.5 GJ/h - 210.0 GJ/h
𝑒2: Condenser duty 123.0 GJ/h - 124.0 GJ/h
𝑒3: Desalter inlet temperature 132.1 °C 125.0 °C 140.0 °C
Table 6 also shows the four process constraints considered in the optimization problem,
including one product property constraint and three equipment capacity constraints.
The flash point of kerosene should be greater than 38.0 °C to ensure safety for storage.
The furnace and column top condenser have maximum capacities of 210.0 GJ/h and
124.0 GJ/h, respectively. At current operating condition, condenser duty (123.0 GJ/h)
is close to the capacity limit. In addition, the temperature of crude oil entering the
desalter needs to be within a predefined range to maintain efficiency of the desalter.
4.5.2. Model generation results
As described in Section 3.2.3, for each design variable, two cases are generated in
29
Aspen HYSYS at its lower and upper bounds with all other design variables flat. The
two data sets are taken from the simulation results to calculate the slopes for the design
variable. Table 7 lists the slope parameters in the generated linear model.
Table 7. Linear model generation results
Variables
Kerosene
flash point
a1
Furnace
duty
b1
Condenser
duty
b2
Desalter inlet
temperature
b𝟑
Profit
c
𝑥1 0.00 0.45 0.24 -0.05 40.79
𝑥2 0.48 -0.04 0.08 0.17 -68.22
𝑥3 0.21 -0.20 -0.27 0.10 104.34
𝑥4 0.00 -0.16 -0.06 0.12 166.38
𝑥5 0.00 -0.12 0.00 0.11 -55.05
𝑥6 0.03 1.36 1.00 -0.02 150.46
𝑥7 0.12 1.03 4.19 -0.32 338.44
𝑥8 0.11 0.61 3.86 -0.03 250.35
𝑥9 0.21 0.57 4.43 -0.41 49.72
𝑥10 0.05 0.01 -0.55 0.16 -17.70
𝑥11 0.00 -0.01 -0.03 0.02 0.17
𝑥12 0.00 -0.02 -0.04 0.01 0.14
𝑥13 0.00 -0.06 -0.06 0.00 0.46
The model generation procedure requires 2K rigorous simulations. The number of
design variables K is 13 in the case study, so 26 rigorous simulations were run to
generate the linear model. It is reported that in the work of [24], 800 rigorous
simulation data sets were generated to train the ANN model. Compared with advanced
modeling techniques, the linear method needs much less effort in the model generation
procedure.
30
4.5.3. Model size
The generated model has a small size. It has 13 design variables and 5 linear equations
in total. The number of equations in the optimization model equals the number of
concerned process constraints (possible bottlenecks) plus one objective function. For
a distillation column comprising S stages with C components, the equilibrium stage
based rigorous model consists of (2C+3)×S equations [31], including C mass
balance equations for each component on each stage, C equilibrium equations for each
component on each stage, two summation equations for vapor and liquid phases on
each stage and one heat balance equation on each stage. The rigorous model of the
case study in Aspen HYSYS has 50 components. The main column has 34 stages. This
results in 3502 equations for the column model. Most of these equations are nonlinear,
and it does not count many other equations such as enthalpy calculation, K-value
calculation, and the HEN model. Therefore, the linear method significantly simplifies
the rigorous model.
4.5.4. Model accuracy
Although linear models have the advantage of robustness and high efficiency for the
solution procedure, they may not be as accurate as rigorous models. The accuracy of
the linear model is tested by comparison with the rigorous model for randomly
generated cases. One hundred cases are generated with all operating parameters
randomly distributed within their bounds. The prediction of the objective function and
constraints are then compared to rigorous simulation results in Aspen HYSYS. Figure
7 shows the results from the linear and rigorous models for the one hundred random
cases. It can be seen that the linear model has good accuracy.
31
Figure 7. Linear versus rigorous model in Aspen HYSYS.
In addition, furnace duty and desalter inlet temperature are determined by both the
main column and HEN. This is because with pump-around flowrates varying, heat
22
24
26
28
30
32
22 24 26 28 30 32
Lin
ear
model
Rigorous model
Profit, kUSD/h
R2 = 0.994
49
51
53
55
57
49 51 53 55 57
Lin
ear
model
Rigorous model
Kerosene flash point, °C
R2 = 0.969
160
180
200
220
240
160 180 200 220 240
Lin
ear
model
Rigorous model
Furnace duty, GJ/h
R2 = 0.999
90
110
130
150
170
90 110 130 150 170
Lin
ear
model
Rigorous model
Condenser duty, GJ/h
R2 = 0.991
125
130
135
140
125 130 135 140
Lin
ear
model
Rigorous model
Desalter inlet temperature, °C
R2 = 0.992
32
recovered by the HEN and furnace inlet temperature change accordingly. The close
results between linear and rigorous models for furnace duty and desalter inlet
temperature reflect that the linear model can describe the interaction between the
column and HEN.
4.6. Linear model solution
The linear optimization model is solved by the simplex LP solver of Microsoft Excel
Solver add-in. The optimal solution is summarized in Table 8. The profit increases by
16.0% from 26,662 USD/h to 30,926 USD/h. The improvement is attributed to
increase in throughput and more profitable products. It is achieved by the adjustment
of cut points of products, as well as higher furnace outlet temperature and more steam
injection to drive more distillates out of the residue.
The optimal solution shows that furnace and condenser capacities are bottlenecks of
the system. Note under the current operating condition, condenser duty is close to its
capacity limit. The increase in pump-around flowrates helps relieve burden of the top
condenser so that more throughput and higher furnace inlet temperature are possible.
Besides, although detailed hydraulic performance is not modeled explicitly, it is
roughly constrained by condenser’s capacity limit. If necessary, correlations for
hydraulic constraints can be added to the linear model.
33
Table 8. Optimal solution
Variables Current Optimal
(Linear)
Optimal (Aspen
HYSYS)
Profit 26,662 USD/h 30,926 USD/h 30,916 USD/h
Throughput 600.0 t/h 618.0 t/h 618.0 t/h
Naphtha D86 FBP 170.0 °C 165.0 °C 165.0 °C
Kerosene D86 FBP 240.0 °C 245.0 °C 245.0 °C
Diesel D86 95% 360.0 °C 365.0 °C 365.0 °C
Overflash flowrate 15.0 t/h 12.0 t/h 12.0 t/h
Furnace outlet temperature 360.0 °C 365.0 °C 365.0 °C
Main stripping steam flowrate 6.0 t/h 9.0 t/h 9.0 t/h
AGO stripping steam flowrate 1.0 t/h 1.0 t/h 1.0 t/h
Diesel stripping steam
flowrate 3.5 t/h
1.0 t/h 1.0 t/h
Kerosene reboiler duty 0.5 GJ/h 0.8 t/h 0.8 t/h
Pump-around 1 flowrate 400.0 m3/h 480.0 m3/h 480.0 m3/h
Pump-around 2 flowrate 300.0 m3/h 360.0 m3/h 360.0 m3/h
Pump-around 3 flowrate 250.0 m3/h 300.0 m3/h 300.0 m3/h
Kerosene flash point 52.6 °C 51.0 °C 51.3 °C
Furnace duty 199.5 GJ/h 210.0 GJ/h 209.7 GJ/h
Condenser duty 123.0 GJ/h 124.0 GJ/h 128.3 GJ/h
Desalter inlet temperature 132.1 °C 133.4 °C 133.4 °C
The optimal solution from the linear optimization model is validated by the rigorous
model to check whether significant violation of constraints occurs. The results of the
rigorous simulation are also listed in Table 8. At the optimal point, the results from the
linear model are very close to the rigorous simulation results.
4.7. Inaccurate models and model correction over time
Apart from model inaccuracy risks caused by linearity, other factors may also
contribute to mismatches between models and the process, such as poor parameter
estimation. The model correction mechanism proposed in Section 3.3.3 can help to
correct linear models from interactions with rigorous models or the process. A case
34
study is carried out to test the behavior of the optimization framework when models
are inaccurate.
Assume that the real crude oil is crude scenario 5 in Table 2. However, the estimated
crude oil is crude scenario 4 and the linear model is built based on crude scenario 4.
Because the model is not accurate, after the execution of the optimal solution, there
will be differences between model predictions and the process. Rigorous simulation
under crude scenario 5 is used to represent the real process. The inaccurate linear
model is adapted by adding correction terms repeatedly.
Figure 8 and Table 9 show the steady states over time during the model correction
procedure. Note that time for reaching these steady states are not considered due to the
limitation of steady-state models. After four steady states the adapted linear models
and the process converge. With the correction mechanism, model inaccuracy can be
gradually reduced.
35
Figure 8. Model correction from interactions with the process.
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
199
201
203
205
207
209
211
0 1 2 3 4
Fu
rnace d
uty
, G
J/h
Iteration (Steady State)
Error
Furnace duty (LP)
Furnace duty (Process)
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
120
121
122
123
124
125
126
0 1 2 3 4
Condenser
duty
, G
J/h
Iteration (Steady State)
Error
Condenser duty (LP)
Condenser duty (Process)
36
Table 9. Steady states over time during model correction
Variables Current Steady
State 1
Steady
State 2
Steady
State 3
Steady
State 4
Profit, USD/h 26,812 31,120 31,487 31,363 31,432
Throughput, t/h 600.0 618.0 626.8 627.9 627.0
Naphtha D86 FBP, °C 170.0 165.0 165.0 165.0 165.0
Kerosene D86 FBP, °C 240.0 245.0 245.0 245.0 245.0
Diesel D86 95%, °C 360.0 365.0 365.0 365.0 365.0
Overflash flowrate, t/h 15.0 12.0 12.0 12.0 12.0
Furnace outlet temperature, °C 360.0 365.0 365.0 365.0 365.0
Main stripping steam flowrate,
t/h 6.0 9.0 9.0 8.8 9.0
AGO stripping steam flowrate,
t/h 1.0 0.95 0.82 0.50 0.64
Diesel stripping steam flowrate,
t/h 3.5 1.0 1.0 1.0 1.0
Kerosene reboiler duty, GJ/h 0.5 0.8 0.8 0.8 0.8
Pump-around 1 flowrate, m3/h 400.0 480.0 480.0 480.0 480.0
Pump-around 2 flowrate, m3/h 300.0 360.0 360.0 360.0 360.0
Pump-around 3 flowrate, m3/h 250.0 300.0 300.0 300.0 300.0
Kerosene flash point, °C 52.7 51.4 51.5 51.4 51.4
Furnace duty, GJ/h 187.9 206.1 209.9 210.1 210.0
Condenser duty, GJ/h 121.1 122.4 125.9 122.8 123.9
Desalter inlet temperature, °C 133.7 134.8 134.5 134.4 134.4
5. Conclusions
In this work, a new framework for RTO of crude oil distillation systems is proposed.
In the monitoring phase of RTO, it is shown that crude feed TBP can be effectively
reconstructed in real time through product back-blending. Due to relatively short
runtime of ASTM D86 and D1160 tests for products compared to TBP analysis for
crude oil, optimization can be triggered in time. In addition, the proposed indicator for
comparing two TBP curves can help detect crude changes with a carefully chosen
threshold.
37
In the optimization phase, the optimization model can be significantly simplified by
reducing the rigorous model to linear forms. The model generation procedure is faster
than advanced empirical modeling techniques like ANN because much less data sets
from rigorous simulation are required. The linearity and small size of the generated
linear models make it robust and efficient to solve without much loss of accuracy
compared to rigorous models. Besides, close prediction results of linear and rigorous
models for variables like furnace duty and desalter inlet temperature reflect that the
linear model can describe interactions between the column and HEN. Moreover, the
proposed correction mechanism can further improve model accuracy based on
interactions with rigorous simulation or the real process.
A weakness of the proposed RTO framework is that although runtime of ASTM D86
and D1160 tests are relatively short, there is still wait time for obtaining new test data.
Future work will consider methods to reduce the wait time to make RTO respond to
changes more quickly. Another improvement can be made to consider the use of plant
data for training models so that online runs of rigorous simulations can be avoided.
38
Acknowledgements
The first author would like to acknowledge the financial support for the research
program from Mr Shibo Wang and Process Integration Limited. The valuable
discussions about crude oil distillation simulations and operations with Dr Lu Chen
and Ms Xueqin Gan from Process Integration Limited are also much appreciated.
39
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43
Supplementary material
Table S1 summarizes crude bulk properties and TBP data.
Table S1. Crude bulk properties and TBP data
Crude 1 Crude 2 Crude 3
Bulk properties
API 33.2 29.7 25.6
Viscosity 1 T, °C 20.0 20.0 20.0
Viscosity 1, cSt 13.9 20.9 54.5
Viscosity 2 T, °C 50.0 50.0 50.0
Viscosity 2, cSt 6.1 8.0 15.1
TBP curve vol% T, °C vol% T, °C vol% T, °C 4.4 50.0 4.6 50.0 2.0 50.0 10.8 100.0 11.5 100.0 5.2 100.0 18.5 150.0 18.7 150.0 10.0 150.0 26.7 200.0 27.8 200.0 15.4 200.0 35.5 250.0 35.9 250.0 23.8 250.0 44.4 300.0 44.0 300.0 33.8 300.0 53.7 350.0 52.1 350.0 44.7 350.0 61.8 400.0 59.9 400.0 54.5 400.0 69.8 450.0 67.3 450.0 64.5 450.0 77.0 500.0 74.0 500.0 72.8 500.0 82.9 550.0 80.3 550.0 79.8 550.0 87.6 600.0 85.7 600.0 85.6 600.0 91.2 650.0 90.0 650.0 90.4 650.0 93.9 700.0 93.5 700.0 94.3 700.0
44
Table S2 summarizes product D86 or D1160 for crude TBP reconstruction test.
Table S2. Product D86 and D1160
vol% Naphtha
D86
Kerosene
D86
Diesel
D86
AGO
D1160
Residue
D1160
5 52.4 170.1 247.0 197.6 225.7
10 69.4 177.4 255.2 214.9 252.0
30 95.0 187.3 273.7 239.2 311.9
50 111.8 195.1 293.1 251.9 364.7
70 128.4 203.9 315.2 267.4 434.4
90 147.6 218.9 346.7 296.3 568.1
95 157.2 225.4 360.0 309.2 649.5
45
4. Data-driven Real-time Optimization of Crude
Oil Distillation Systems
This chapter is the second piece of work for real-time optimization methods with
simplified linear models. This work uses a different method to generate simplified
linear models compared with Chapter 3. In this work, simplified linear models are
generated by linear regression of filtered historical data.
Please note that this chapter is prepared in a journal paper format and is attached with
its own page numbering system.
46
Blank page
* Corresponding author. Email: [email protected]
Data-driven Real-time Optimization
of Crude Oil Distillation Systems
Xiao Yang, Nan Zhang*, Robin Smith
Centre for Process Integration, School of Chemical Engineering and Analytical
Science, The University of Manchester, Manchester M13 9PL, UK
Highlights
• A fully data-driven real-time optimization framework is proposed.
• Historical scenario identification and online model training modules are added.
• Data-driven models relieve solution difficulties with good fit to historical data.
2
Blank page
3
Abstract
Effective utilization of data assets is key to success of the process industry in an era of
big data. Real-time optimization (RTO) is an important part of a smart factory. This
paper presents a fully data-driven RTO framework and applies it to crude oil
distillation systems. The proposed RTO framework adds historical scenario
identification and online model training modules to standard RTO schemes. Historical
scenario identification helps to filter training datasets for the current scenario from all
historical operating data. A case study of crude oil distillation systems show that data-
driven models can help to reduce model complexities and computational efforts for
optimization with good fit to historical operating data.
Keywords: Crude oil distillation systems, Real-time optimization, Data-driven
4
Blank page
5
1. Introduction
The success of data science and technology in the internet industry has inspired a trend
of digital transformation in the manufacturing sector. Strategic plans towards smart
manufacturing [1] have been proposed around the world, such as Industry 4.0 and
Made-in-China 2025 [2]. As a major manufacturing industry, the process industry can
also gain significant potential benefits from effective utilization of data.
The process industry is rich in data. Distributed control systems (DCS), manufacturing
execution systems (MES), laboratory information management systems (LIMS) and
enterprise resource planning (ERP) systems are commonly implement in the process
industry like refineries [3]. As an asset, these data not only help to record and manage
daily operations, but also can provide deep insights into process monitoring, control
and optimization [4].
Operational optimization, including real-time optimization (RTO) [5], plays an
essential role in smart manufacturing by enabling plants to improve their operations
when there is a change in feedstock or other conditions. A standard RTO system
consists of four modules, i.e., steady-state detection [6], data reconciliation [7],
parameter estimation and optimization. Real-time plant data are collected and
processed in the first three steps. In the optimization step, rigorous first-principle
models are commonly used [8]. The strength of rigorous models is high accuracy.
However, they are also difficult to solve and prone to failure of convergence [9].
Crude oil distillation systems are one of the most important processes in the process
industry. Operational optimization of crude oil distillation systems can deliver both
economic and environmental benefits due to their tremendous throughput and huge
energy consumption [10]. Early works on operational optimization of crude oil
distillation systems employ rigorous models [11], [12]. Data-driven models have also
6
gained attention to simplify rigorous models. Neural network distillation models were
built in expert systems for operational optimization by Liau et al. [13] and Motlaghi et
al. [14]. The method was further extended by Ochoa-Estopier et al. [15] to include
consideration of heat exchanger networks (HENs). Apart from neural networks, Yao
and Chu [16] proposed another data-driven modeling method based on support vector
regression. These works show that data-driven models have competitive accuracy.
However, most of these works (except [11]) assume crude feed composition, usually
characterized by true boiling point (TBP) distillation curves [17], is known for model
construction.
Real-time crude feed TBP data are not available in many plants due to the fact that
crude feed frequently changes in many refineries and TBP tests take long time, e.g.,
up to three days [18]. In the work of [11], a crude feed TBP estimation procedure
proposed by Dave et al. [19] is integrated. The method uses real-time plant
measurements, including temperatures of feed and product drawing trays, flowrates of
feed, reflux, products and stripping steam, and pump-around duties, to estimation
crude feed TBP curves. Equilibrium flash vaporization (EFV) temperatures are first
computed by energy balance and then converted into TBP temperatures through
correlation. However, the correlation parameters are crude specific and are difficult to
generate with limited information of crude feed.
This work aims to establish a full data-driven RTO framework and apply it to crude
oil distillation systems. Data-driven models are trained online using historical
operating data and employed in the optimization step to relieve computational
difficulties of commonly used rigorous models. To prepare datasets for training the
model from historical operating data, several additional modules are added to standard
RTO schemes.
The rest of the paper is structured as follows. Section 2 describes the proposed data-
7
driven RTO framework. In Section 3, the proposed method is applied to a typical crude
oil distillation system to test its effectiveness. Section 4 draws main findings.
2. Data-driven RTO framework
The proposed data-driven RTO framework consists of seven modules, see Figure 1.
The main difference with standard rigorous model based RTO systems is that it learns
from historical operating data to construct models for optimization. To train models
representing the current operating scenario, similar operating scenarios in history need
to be identified so that corresponding operating data can be extracted. In the case of
crude oil distillation systems, operating data for scenarios processing similar crude
feed with the current feedstock need to be filtered out of all historical data. In addition,
several data-preprocessing procedures are used to improve data quality.
8
Data pre-processing
Steady-state detection
Data reconciliation
Parameter estimation /
Soft sensers
Historical
scenario identification
Model training
Optimization and
implementation
Time alignment Missing data handling
Outlier detection Gross error removal
Data sources
MES LIMS ERP
Real-time data Historical data
DCS
Figure 1. Data-driven RTO framework.
2.1. Data pre-processing
After being retrieved from DCS, MES, LIMS and ERP, relevant raw data need to go
through a series of data pre-processing procedures to improve data quality. These steps
are vital to obtain meaningful data-driven models. For example, if outliers enter the
model training procedure, they may significantly weaken accuracy of the model.
Typically, the following four steps are required:
• Time alignment: Data records with the same timestamp does not necessarily
9
mean they represent variables of a process at the same time. For example,
system clocks may not be consistent across different databases. Another issue
is caused by holdups. A change in feedstock or operating conditions takes some
time to be reflected by changes in products especially when there are large
holdups in the process. A simple method is to estimate the time delay from
operating experience and shift the time axis accordingly.
• Missing data handling: There may be some missing values due to temporary
instrument or system faults. Missing data can either be discarded or be
estimated. An overview of missing data handling techniques can be found in
Imtiaz and Shah [20].
• Outlier detection: Outliers need to be detected and removed to avoid
misleading the model training procedure. Various outlier detection method
have been proposed and a comparative study is carried out by Domingues et al.
[21].
• Gross error removal: Gross errors can also significantly reduce accuracy and
reliability of data-driven models. They can be removed according to operating
experience or by comparison with a calibrated rigorous simulation.
Mathematical methods are also available in Narasimhan and Jordache [7].
2.2. Steady-state detection
The proposed RTO framework assumes that operational optimization is performed
when the process is in steady state. Moreover, historical steady states also need to be
10
detected to prepare training datasets. Therefore, a steady-state detection procedure is
employed. Various established methods [6], [22] can be used for the procedure.
2.3. Data reconciliation
Plant measurements usually violate first-principle rules such as mass and heat balance.
In this paper, data reconciliation techniques are used to map plant measurements to
reconciled data following mass balance for crude feed TBP reconstruction. The
reconciled data are calculated by an optimization procedure to minimize the deviation
between measured and reconciled data subject to mass balance of distillation columns:
minw0(𝑓𝑖𝑛 − 𝑓��𝑛)2+ ∑w𝑗(𝑓𝑜𝑢𝑡
𝑗− 𝑓��𝑢𝑡
𝑗)2
𝑗
(1)
Subject to:
𝑓𝑖𝑛 = ∑𝑓𝑜𝑢𝑡𝑗
𝑗
(2)
where 𝑓𝑖𝑛 and 𝑓𝑜𝑢𝑡𝑗
are reconciled flowrates for column feed and the 𝑗th product. 𝑓
is the corresponding measured flowrates, which is the average measured data in a time
window to remove high-frequency noise. The parameter w denotes how accurate an
measurement is. A measurement with a larger value of w is more reliable than a
measurement with a smaller value of w. If such information is not available, all values
of w can be set to 1.
11
2.4. Parameter estimation – crude feed TBP
reconstruction
Unknown parameters need to be estimated online if they change frequently, such as
feed composition. Parameter estimation can be realized in either an explicit or an
implicit way. Explicit methods, i.e., soft sensors, computes unknown parameters by an
explicit model based on plant measurements. Implicit methods use optimization
models to estimate unknown parameters.
The real-time reconciled flowrates, together with the latest product analysis from
LIMS, are used to reconstruct crude feed TBP curves using the method proposed in
Chapter 3. The method is based on mass balance of the distillation column. If products
are blended together, crude feed TBP curves can be computed from mass balance.
Product analysis, usually ASTM D86 for light products and ASTM D1160 for heavy
products, is regularly carried out in plants. These tests are not done in real time, but
product distillation curves usually have little change due to product quality control.
Therefore, the latest product analysis can be used to calculate crude feed TBP curves.
The product back-blending procedure is mass balance based on distillation curves,
including underlying conversion among TBP, ASTM D86 and ASTM D1160
distillation curves. It can be computed by either established methods [17] or simulation
packages. This work uses Aspen HYSYS to perform calculation of product back-
blending.
2.5. Historical scenario identification
Once crude feed TBP curves are reconstructed from real-time plant measurements and
the latest product analysis, historical operating data with the same crude feed scenario
need to be extracted from database for model construction. The idea is to compare
12
crude feed TBP curves to find similar historical operating scenarios. First, data
reconciliation and crude feed TBP reconstruction are performed for historical
operating data. It yields an augmented historical operating database indexed by
reconstructed crude feed TBP curves. Then, similarity between real-time TBP curves
and each historical scenario are measured by the proposed indicator:
Indicator = √∑(TBP𝑗crude2-TBP𝑗
crude1)2
𝑗
(3)
where TBP𝑗 represents the 𝑗th temperature point on the TBP distillation curves.
The indictor is the Euclidean distance of two TBP curves from a mathematical point
of view. The larger the indicator is, the more the two crude feed scenarios differ from
each other. If the value of the indictor is smaller than a predefined threshold, the two
crude feed scenarios can be considered similar to each other. Therefore, historical
operating data in similar crude feed scenarios can be filtered by the following condition:
Indicator ≤ Threshold (4)
The threshold value can be tuned by users. Small threshold values are strict and may
result in insufficient coverage of operating data for model construction. Large
threshold values can allow more historical operating data to feed into model generation
but may result in less accuracy for the current crude feed scenario.
2.6. Model training
Historical scenario identification prepares datasets for training data-driven models.
Various types of data-driven models can be employed, such as neural networks and
support vector regression. A linear model for crude oil distillation systems is proposed
in Chapter 3 and found to have small accuracy loss to rigorous models. This work
13
trains the linear model from historical data:
max𝑦 = y0 + ∑ c𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
(5)
Subject to:
𝑝𝑚 = p𝑚,0 + ∑ a𝑚,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
𝑘 = 1,2, … ,M (6)
𝑒𝑛 = e𝑛,0 + ∑ b𝑛,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=1
𝑛 = 1,2, … ,N (7)
x𝑘L ≤ 𝑥𝑘 ≤ x𝑘
U 𝑘 = 1,2, … ,K
p𝑚L ≤ 𝑝𝑚 ≤ p𝑚
U 𝑚 = 1,2, … ,M (8)
e𝑛L ≤ 𝑒𝑛 ≤ e𝑛
U 𝑛 = 1,2, … ,N
where 𝑥 , 𝑦 , 𝑝 and 𝑒 denote operating parameters, objective function, physical
properties and equipment capacities, respectively. The superscripts (∙)L and (∙)U
refer to lower and upper bounds. The subscript (∙)0 refers to profit and constraint
values under current operating conditions, which can be read or calculated from plant
data. Constants a, b, and c need to be computed from filtered historical data.
These constants are generated using linear regression of the filtered historical data.
The linear regression procedure is identical for objective function and each process
constraint, so only the procedure for objective function is illustrated for brevity.
Suppose there are I datasets identified by scenario identification. For each dataset,
the linear model has a prediction error:
14
y(𝑖) = y0 + ∑ c𝑘(x𝑘(𝑖) − x𝑘,0)
K
𝑘=1
+ 𝜖(𝑖) (9)
where 𝜖 is prediction errors. The superscript 𝑖 represents the 𝑖th data entry.
Equation (9) can be rearranged into equation (10):
∆y(𝑖) = ∑ c𝑘∆x𝑘(𝑖)
K
𝑘=1
+ 𝜖(𝑖) (10)
∆y(𝑖) = y(𝑖) − y0 (11)
∆x𝑘(𝑖) = x𝑘
(𝑖) − x𝑘,0 (12)
By denoting the datasets in matrix forms, equation (10) can be rewritten as follows:
∆Y=∆XC+E (13)
∆Y = [∆y(1) ∆y(2) ⋯ ∆y(I)]𝑇 (14)
∆X =
[ ∆x1
(1)∆x2
(1)⋯ ∆xK
(1)
∆x1(2)
∆x2(2)
⋯ ∆xK(2)
⋮ ⋮ ⋮ ⋮
∆x1(I) ∆x2
(I) ⋯ ∆xK(I)
]
(15)
C = [c1 c2 ⋯ cK]𝑇 (16)
E = [𝜖(1) 𝜖(2) ⋯ 𝜖(I)]𝑇 (17)
Then the slope vector C can be computed by the following equation:
C=(∆𝑋𝑇∆𝑋)−1∆𝑋𝑇∆Y (18)
15
In the same way, the model parameters for each process constraint can be calculated
from identified historical data.
2.7. Optimization and implementation
The proposed model can be solved in any software package supporting linear
programming. In this work, Microsoft Excel Solver add-in is used. The built-in solver
add-in uses the simplex algorithm to solve linear optimization problems, which is a
standard solution method for linear programming [23]. The optimal solution can be
sent back to rigorous simulation for validation. If there is large deviation, the optimal
solution can be adjusted using the method proposed in Chapter 3.
3. Case study
3.1. Problem description
A typical crude oil distillation system shown in Figure 2 is studied to investigate
effectiveness of the proposed method. The associated HEN is depicted in Figure 3. The
crude feed first goes through a preheat train for heat recovery. It is further heated by a
furnace before entering the main column. The column splits the crude feed into five
products from light to heavy, including naphtha, kerosene, diesel, AGO and residue.
The main column has 34 stages and three pump-arounds as well as three side strippers
attached. The kerosene stripper uses a reboiler and the other two utilize steam injection.
16
Furnace
Residue
Off-gas
Naphtha
Diesel
AGO
HEN1
Crude
Steam
Kerosene
HEN2Desalter
Figure 2. A typical crude oil distillation system.
E-101 DesalterE-102 E-103 E-104
Crude
Furnace
Kerosene Pump-around 1 Residue
E-105 E-106 E-107 E-108 E-109 E-110
Pump-around 2
Diesel
AGO Pump-around 3
HEN1 HEN2
Figure 3. The HEN flowsheet.
It is assumed that the crude oil distillation system processes seven crude feed scenarios
blended from three types of crude oil in history, see Table 1.
17
Table 1. Crude feed scenarios
Crude 1 Crude 2 Crude 3
API 33.2 29.7 25.6
Sulfur (wt%) 0.37 2.85 0.41
Acidity (mgKOH/g) 0.12 0.11 1.3
Crude scenarios (wt%)
1 0.6 0.4 0
2 0.5 0.4 0.1
3 0.4 0.4 0.2
4 0.3 0.4 0.3
5 0.2 0.4 0.4
6 0.1 0.4 0.5
7 0 0.4 0.6
The profit of the crude oil distillation system is maximized for the optimization
problem. Table 2 shows prices for computing profit.
Table 2. Prices
Item Price
Crude 1 280 USD/t
Crude 2 265 USD/t
Crude 3 250 USD/t
Naphtha 480 USD/t
Kerosene 520 USD/t
Diesel 420 USD/t
AGO 240 USD/t
Residue 180 USD/t
Furnace duty 9 USD/GJ
Reboiler duty 14 USD/GJ
Steam 27 USD/t
Cooling water 1 USD/GJ
Suppose the CDU is currently operated under crude feed scenario 4. The throughput,
product cut points, overflash flowrate, steam injection and pump-around flowrates are
considered as design variables in the optimization problem. Table 3 shows their current
18
operating values and operating bounds. Under the current operating condition, the
profit of the system is 26662.5 USD/h. Four process constraints need to be satisfied
during the optimization, including product property constraint and three equipment
capacity constraints. The flash point of kerosene is required to be greater than 38.0 °C
for safe storage. The furnace and condenser duty are constrained by corresponding
equipment capacity. An inlet temperature range is imposed for the requirement of the
desalter. Their bounds are summarized in Table 3. Note for the real plant the values of
profit and process constraints can be easily computed from plant data. For example,
the condenser duty can be calculated by the flowrate of cooling water and its inlet and
outlet temperatures. In the case study, these values come from the rigorous simulation
results in Aspen HYSYS.
19
Table 3. Design variables and process constraints
Variables Current
value Lower bound Upper bound
𝑥1: Throughput 600.0 t/h 540.0 t/h 660.0 t/h
𝑥2: Naphtha D86 FBP 170.0 °C 165.0 °C 175.0 °C
𝑥3: Kerosene D86 FBP 240.0 °C 235.0 °C 245.0 °C
𝑥4: Diesel D86 95% 360.0 °C 355.0 °C 365.0 °C
𝑥5: Overflash flowrate 15.0 t/h 12.0 t/h 20.0 t/h
𝑥6: Furnace outlet temperature 360.0 °C 355.0 °C 365.0 °C
𝑥7 : Main stripping steam
flowrate 6.0 t/h 3.0 t/h 9.0 t/h
𝑥8 : AGO stripping steam
flowrate 1.0 t/h 0.5 t/h 1.5 t/h
𝑥9 : Diesel stripping steam
flowrate 3.5 t/h 1.0 t/h 6.0 t/h
𝑥10: Kerosene reboiler duty 0.5 GJ/h 0.2 GJ/h 0.8 GJ/h
𝑥11: Pump-around 1 flowrate 400.0 m3/h 320.0 m3/h 480.0 m3/h
𝑥12: Pump-around 2 flowrate 300.0 m3/h 240.0 m3/h 360.0 m3/h
𝑥13: Pump-around 3 flowrate 250.0 m3/h 200.0 m3/h 300.0 m3/h
𝑝1: Kerosene flash point 52.6 °C 38.0 °C -
𝑒1: Furnace duty 199.5 GJ/h - 210.0 GJ/h
𝑒2: Condenser duty 123.0 GJ/h - 124.0 GJ/h
𝑒3: Desalter inlet temperature 132.1 °C 125.0 °C 140.0 °C
Historical operating data for the seven crude feed scenarios are generated from
rigorous simulation. For each crude feed scenario, 100 random operating conditions
within their bounds are sent into rigorous simulation in Aspen HYSYS. The simulation
results are assumed to be historical plant data.
3.2. Data reconciliation and crude feed TBP
reconstruction
Data reconciliation is carried out for the base case (crude feed scenario 4 under the
current operating conditions). The real values of flowrates are retrieved from rigorous
20
simulation. Random noise uniformly distributed in [−1,1] is added to each
measurement. In many refineries, the measurement of off-gas is either inaccurate or
not available. Therefore, the data reconciliation procedure forces mass balance
between crude feed and products except off-gas. The results for data reconciliation are
summarized in Table 4.
Table 4. Reconciled flowrates
Flowrates Real, t/h Measurements, t/h Reconciled, t/h
Crude feed 600.0 599.7 598.8
Off-gas 6.5 - 0.0
Naphtha 80.8 80.2 81.1
Kerosene 54.8 55.6 56.6
Diesel 149.9 150.1 151.0
AGO 36.8 37.5 38.4
Residue 271.2 270.7 271.7
The reconciled flowrates are used to back-blend crude feed and estimate its TBP curves.
Figure 4 compares the real TBP curve calculated by mixing ratios of the three crudes
and the reconstructed TBP curve. Figure 4 shows the two curves have a good
agreement.
Figure 4. Real versus reconstructed crude feed TBP curves.
-100
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50 60 70 80 90 100
Te
mpera
ture
, °C
Liquid volume percent
Real
Reconstructed
21
3.3. Historical scenario identification
After the crude feed TBP curve is reconstructed, historical operating data in similar
crude feed scenarios need to be filtered from the database for optimization model
training. This work assumes that similar crude feed scenario can be found in history.
First, historical crude feed TBP curves are reconstrued using back-blending for each
randomly generated historical data entry.
The reconstructed TBP data for the current operating condition in the previous step is
compared with each historical data entry by the proposed similarity indicator. TBP
temperatures at 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95% of
distilled volume are used for computing the indicator. The histogram of indicator
values for all crude feed scenarios are plotted in Figure 5. The figure shows that
different crude feed scenarios are grouped into different clusters and a threshold value
10 can successfully filter operating data for crude feed scenario 4 out of whole
historical data.
Figure 5. Compare TBP curves for different scenarios.
0 5 10 15 20 25 30 35 40 45 50
Similarity indicator
Scenario 1 Scenario 2 Scenario 3 Scenario 4
Scenario 5 Scenario 6 Scenario 7
22
3.4. Model accuracy
The identified historical operating data are then used to generate the optimization
model by linear regression. Table 5 summarized the regressed slope values of the linear
model for crude feed scenario 4.
Table 5. Generated linear model parameters
Variables
Kerosene
flash point
a1
Furnace
duty
b1
Condenser
duty
b2
Desalter inlet
temperature
b𝟑
Objective
c
𝑥1 0.00 0.45 0.24 -0.05 41.94
𝑥2 0.56 -0.04 -0.08 0.21 -67.66
𝑥3 0.24 -0.21 -0.24 0.11 111.79
𝑥4 0.01 -0.13 0.13 0.13 163.49
𝑥5 0.03 -0.14 0.27 0.14 -48.29
𝑥6 0.03 1.34 1.02 -0.03 155.50
𝑥7 0.12 0.96 4.18 -0.32 323.38
𝑥8 0.39 0.42 4.02 0.08 267.85
𝑥9 0.17 0.54 4.45 -0.40 35.12
𝑥10 0.13 -0.26 0.76 0.26 -92.98
𝑥11 0.00 -0.01 -0.04 0.02 -0.37
𝑥12 0.00 -0.03 -0.03 0.01 0.02
𝑥13 -0.01 -0.05 -0.05 0.00 0.59
The predicted values of the profit and process constraints from the generated linear
model are compared with the historical data, see Figure 6. The plots and R-squared
values for the linear regression indicate that the generated linear model is accurate so
that they should not cause large violation of process constraints at the optimal solution.
23
Figure 6. Comparason between linear models and historical data.
Another benefit of the proposed linear model is that it has a small size. For the case
study, the generated linear model only contains 5 linear equations and 13 design
22000
24000
26000
28000
30000
32000
220002400026000280003000032000
Lin
ear
model
Historical data
Profit, USD/h
R2 = 0.996
48
50
52
54
56
58
48 50 52 54 56 58
Lin
ear
model
Historical data
Kerosene flash point, °C
R2 = 0.984
160
180
200
220
240
160 180 200 220 240
Lin
ear
model
Historical data
Furnace duty, GJ/h
R2 = 0.999
90
110
130
150
170
90 110 130 150 170
Lin
ear
model
Historical data
Condenser duty, GJ/h
R2 = 0.972
125
130
135
140
125 130 135 140
Lin
ear
model
Historical data
Desalter inlet temperature, °C
R2 = 0.989
24
variables. The linearity and small size of the proposed optimization model can reduce
the difficulties of the solution. In addition, the linearity also makes the model convex,
which means the global optimal solution can be guaranteed [23].
3.5. Optimization results
The generated optimization model is then solved by the built-in simplex solver in
Microsoft Excel. Table 6 shows the optimal solution. The profit has increased by
15.8%. The improvement of profit is mainly due to increased throughput and adjusted
cut points of the products. More valuable products are obtained. The optimal solution
also favors steam injection from lower section of the column. The reason for this is
that steam injected at lower section also takes effect when it goes up but not vice versa.
The flowrates of pump-arounds are increased to recover more energy so that operating
cost is saved. The optimal solution is validated in Aspen HYSYS. The results show
that the linear model does not cause significant deviations from rigorous simulation.
25
Table 6. Optimal solution
Variables Current Optimal
(Linear)
Optimal (Aspen
HYSYS)
Profit 26662.5
USD/h
30871.2
USD/h 30914.1 USD/h
Throughput 600.0 t/h 618.4 t/h 618.4 t/h
Naphtha D86 FBP 170.0 °C 165.0 °C 165.0 °C
Kerosene D86 FBP 240.0 °C 245.0 °C 245.0 °C
Diesel D86 95% 360.0 °C 365.0 °C 365.0 °C
Overflash flowrate 15.0 t/h 12.0 12.0
Furnace outlet temperature 360.0 °C 365.0 °C 365.0 °C
Main stripping steam flowrate 6.0 t/h 9.0 t/h 9.0 t/h
AGO stripping steam flowrate 1.0 t/h 0.6 t/h 0.6 t/h
Diesel stripping steam
flowrate 3.5 t/h 1.0 t/h 1.0 t/h
Kerosene reboiler duty 0.5 GJ/h 0.2 t/h 0.2 t/h
Pump-around 1 flowrate 400.0 m3/h 480.0 m3/h 480.0 m3/h
Pump-around 2 flowrate 300.0 m3/h 360.0 m3/h 360.0 m3/h
Pump-around 3 flowrate 250.0 m3/h 300.0 m3/h 300.0 m3/h
Kerosene flash point 52.6 °C 50.3 °C 51.2 °C
Furnace duty 199.5 GJ/h 210.0 GJ/h 209.6 GJ/h
Condenser duty 123.0 GJ/h 124.0 GJ/h 126.2 GJ/h
Desalter inlet temperature 132.1 °C 132.9 °C 133.3 °C
4. Conclusions
This work presents a data-driven RTO framework and applies it to crude oil distillation
systems. Compared with standard RTO systems based on rigorous models, data-driven
models generated from historical operating data are used. To facilitate the model
training procedure, additional modules including historical scenario identification and
model training are added to standard RTO systems.
Through the case study of a typical crude oil distillation system, it is validated that
crude feed TBP curves can be accurately estimated from reconciled plant
measurements and product analysis data. The case study also shows that historical
26
operating data for the current crude feed scenario can be efficiently extracted by
computing the similarity indicator. In addition, the linear model generated from
historical operating data is tested to have small loss of accuracy and can effectively
find improved operating conditions.
The main limitation of the work is that it assumes identified historical operating data
have a good coverage of various operating conditions. However, it may not be true in
real plants. Therefore, a systematic method to measure the quality of coverage will be
considered in future. In addition, if the coverage is poor, methods for data
augmentation from rigorous simulation are needed.
27
Acknowledgements
The first author would like to acknowledge the financial support for the research
program from Mr Shibo Wang and Process Integration Limited.
28
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29
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5. Robust Operational Optimization of Crude
Oil Distillation Systems
This chapter is the first piece of work for robust operational optimization methods.
Compared to real-time optimization methods studied in Chapter 3 and 4, robust
operational optimization treats limited information of crude feed compositions as
uncertainty and tries to make conservative optimization for a range of possible crude
feed scenarios. This chapter develops a systematic framework for robust operational
optimization and a method to build robust optimization models.
Please note that this chapter is prepared in a journal paper format and is attached with
its own page numbering system.
48
Blank page
* Corresponding author. Email: [email protected]
Robust Operational Optimization of
Crude Oil Distillation Systems
Xiao Yang, Nan Zhang*, Robin Smith
Centre for Process Integration, School of Chemical Engineering and Analytical
Science, The University of Manchester, Manchester M13 9PL, UK
Highlights
• Robust operational optimization does not rely on accurate crude feed TBP data.
• Simplified linear models make solution computationally tractable.
• Robust operational optimization can effectively maintain feasibility.
• Robust operational optimization loses 2.0% of optimization potentials.
2
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3
Abstract
Operational optimization of crude oil distillation systems can bring significant
economic and environmental benefits considering their massive throughput and
extensive energy use. However, crude feed compositions, characterized by true boiling
point (TBP) curves, are usually not available due to complex crude oil movement and
mixing operations. Instead of employing expensive online crude composition
analyzers, this work develops a low-cost method without exact feed TBP data based
on the so-called robust optimization technique.
The method can return the optimal operating conditions satisfying process constraints
for a range of predefined crude scenarios. Certain parameters in the optimization
model are updated from real-time plant measurements. Uncertain parameters are
analyzed and updated less frequently based on schedule of crude oil operations. With
the help of simplified linear models, the robust optimization problem can be
reformulated into linear programming problems for box uncertainty sets. A case study
shows robust operational optimization can effectively maintain feasibility against
uncertainty and about 2.0% of optimization potentials are lost, making it a good
alternative option for refineries favoring low-cost solution.
Keywords: operational optimization, robust optimization, crude oil distillation system
4
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5
1. Introduction
Operational optimization is crucial to the success of a refinery in a highly competitive
global market. Among all units in refineries, crude oil distillation systems are of major
importance because they are the first step of a refinery and have the largest throughput
and energy consumption. It is estimated that energy consumed by crude oil distillation
systems globally is roughly equivalent to total energy use of the United Kingdom [1].
Operational optimization can help refineries increase profit and reduce energy use with
little capital investment.
The main challenge for operational optimization of crude oil distillation systems is that
crude feed composition is usually unknown and changing over time. Crude feed can
change frequently because refineries often mix crudes of different grades into the feed
of crude oil distillation systems in a complex scheduling procedure of crude oil
operations [2]. Moreover, analysis of crude oil composition is time-consuming. Crude
oil composition is commonly characterized by true boiling point (TBP) distillation
curves [3]. The test procedure to obtain TBP curves can take up to three days [4]. The
significant wait time for TBP analysis makes it difficult to know crude feed
composition when operational optimization is needed.
Most of previous works on operational optimization of crude oil distillation systems
focus on advancement of process models. Inamdar et al. [5] developed an algorithm to
solve multi-objective optimization problems handling two conflicting objectives like
maximizing profit and minimizing energy cost based on a rigorous model. Mahalec
and Sanchez [6] constructed a hybrid model joining mass and heat balances and
empirical models for product property prediction to simplify rigorous models. Lopez
et al. [7] simultaneously optimized crude oil blending and operation of crude oil
distillation systems using a second-order polynomial distillation model. More
6
advanced modeling approaches like artificial neural networks [8], [9] and support
vector regression [10] have also gained interest for simplifying rigorous models.
However, crude feed TBP curves are assumed to be known in these works, so they
cannot be applied directly when such information is not available.
One way to overcome the challenge is to estimate and update crude feed TBP curves.
Dave et al. [11] established an online estimation method calculated from plant
measurements. The method first uses heat balance to compute equilibrium flash
vaporization (EFV) temperatures. Then these EFV points are converted into
corresponding TBP temperatures by correlations. The crude feed TBP estimation
method in [11] is later integrated into a real-time optimization (RTO) system by Basak
et al. [12]. However, the correlation parameters for converting EFV points to TBP
points are crude specific, which are difficult to obtain before crude TBP data are known.
Another possible way to overcome the challenge is to optimize operating parameters
considering a range of possible crude feed scenarios. Although exact crude feed TBP
data are difficult to know without performing a TBP analysis, the range of possible
crude feed scenarios can be predefined following the schedule of crude oil operations.
Therefore, if the optimization procedure can produce improved feasible operating
conditions for all possible crude feed scenarios, crude feed TBP estimation is not
necessary.
Robust optimization [13], [14] is an optimization technique for making optimal
decisions which are robust against uncertainty in model parameters. Conventional
optimization assumes model parameters are exact values. By contrast, robust
optimization assumes uncertain model parameters lie in a predefined set and attempts
to find the best solution which is feasible for any possible value of uncertain
parameters in the uncertainty set. Compared to stochastic programming, robust
7
optimization does not require a priori knowledge of probability distribution of
uncertain parameters [13]. Robust optimization has received much attention from
researchers in many fields. In refining and chemical processes, it has been actively
studied for planning and scheduling [15], [16].
The major limitation of robust optimization is that the solution procedure is not
computationally tractable for general nonlinear problems [13]. The solution is
computationally tractable for special types of optimization, like linear programs and
conic programs [13]. However, crude oil distillation systems are a complex heat-
integrated mass and heat transfer process, involving complex distillation columns and
heat exchanger networks (HENs). The models for crude oil distillation systems are
usually nonconvex nonlinear models which cannot be converted to a computationally
tractable robust optimization problem directly. Chapter 3 proposed a model
simplification method to establish a linear model for crude oil distillation systems from
datasets generated from rigorous simulations. Chapter 3 showed that the resulting
linear model does not lose significant accuracy compared to rigorous models in Aspen
HYSYS. The simplification method makes it possible to implement robust
optimization for crude oil distillation systems.
The objective of the work is to establish a low-cost operational optimization
framework for crude oil distillation systems without additional online analyzers or
estimators for crude feed TBP curves. The primary contribution of the work is to
establish a novel operational optimization framework utilizing combined information
from both scheduling of crude oil operations and plant measurements, thereby
avoiding investment in expensive online analyzers. The second contribution of the
work is to introduce simplified linear models so that it is computationally tractable to
apply the robust optimization paradigm.
8
The remainder of the paper is organized as follows. Section 2 gives a brief introduction
to the basic idea of robust optimization and the method for solution for readers not
familiar with it. Section 3 introduces the robust operational optimization model for
crude oil distillation systems. In Section 4, the framework to update information from
scheduling of crude oil operations and plant measurements and implement the
operational optimization online is described. Section 5 uses a case study to test the
proposed method. Finally, main conclusions are drawn in Section 6.
2. Preliminary: Introduction to robust
optimization
2.1. Philosophy behind robust optimization
The fundamental distinction between conventional optimization and robust
optimization is they view model parameters differently. Take the following linear
programming problem for example:
min𝑥
{𝜔𝑇𝑥: Α𝑥 ≤ 𝛽} (1)
where 𝑥 ∈ ℛ𝑘 is the vector of design variables. The 𝑞 × 𝑘 matrix Α, vectors 𝛽 ∈
ℛ𝑞 and 𝜔 ∈ ℛ𝑘 are model parameters.
Conventional optimization assumes these model parameters are perfectly known.
Therefore, these parameters are treated as constants. However, for real-word problems,
the model parameters can hardly be known perfectly. There is usually a certain degree
of uncertainty for these parameters. Moreover, Ben-Tal et al. [13] showed that even
slight perturbations of the parameters are likely to cause severe violation of the
constraints. To overcome the problem, model parameters are considered uncertain and
9
assumed to lie in a predefined set in robust optimization (see Figure 1). The uncertainty
set can be of different shapes such as boxes and balls [13]. Box uncertainty sets are
selected in this work due to their simplicity and will be further discussed.
Figure 1. Illustration of different views of model parameters by conventional and
robust optimization (Two model parameters).
Take the following constraint for example:
∑𝛼𝑘𝑥𝑘
𝑘
≤ 𝛽𝑝 (2)
As described previously, conventional optimization views 𝛼 and 𝛽 as exact
numbers. By contrast, robust optimization considers these parameters to be uncertain.
It can be proved that uncertain parameters in the objective function and right-hand
sides of constraints can be moved to the left-hand sides of constraints by reformulation
[17]. Hence, it is assumed that only the left-hand side parameters 𝛼 are uncertain and
the assumption does not result in loss of generality. To distinguish uncertain parameters
from exact numbers, symbols with the tilde (∙) denote uncertain parameters
throughout the paper:
∑��𝑘𝑥𝑘
𝑘
≤ 𝛽𝑝 (3)
��
��
𝛼
𝛼
𝛼
𝛼
��
��
𝛼
𝛼
𝛼
𝛼
ConventionalRobust (Box)
Robust (Ball)
10
Box uncertainty sets consider each uncertain parameter to lie in a predefined interval:
��𝑘 = 𝛼𝑘 + 𝜂𝛼 𝑘 (4)
where 𝛼 𝑘 is the radius of the interval for ��𝑘 and 𝜂 ∈ [−1,1] is a random number.
The parameters 𝛼𝑘 used in conventional optimization can be viewed as nominal
values (the best estimation) of the uncertain parameters. Box uncertainty sets extend
their possible values to the interval [𝛼𝑘 − 𝛼 𝑘, 𝛼𝑘 + 𝛼 𝑘].
In addition to the introduction of uncertain parameters, another basic idea of robust
optimization is to find the optimal decision satisfying the worst cases of all constraints.
It means that the solution to a robust optimization problem must make every constraint
feasible for any possible parameter value in the predefined uncertainty set. Based on
this idea, the constraint (3) can be converted to:
max𝜂
∑��𝑘(𝜂)𝑥𝑘
𝑘
≤ 𝛽𝑝 (5)
Note on one hand, the idea makes the solution robust against uncertainty in model
parameters. On the other hand, the robustness is at the cost of conservativeness. The
larger space the uncertainty set covers, the more conservative the solution is.
2.2. Reformulation and solution
Optimization problems with constraint (5) cannot be solved directly due to the
presence of the max (∙) function. To solve the problem, the left-hand side of
constraint (5) needs to be simplified. Substitute equation (4) into (5):
max𝜂
(∑𝛼𝑘𝑥𝑘
𝑘
+ ∑𝜂𝛼 𝑘𝑥𝑘
𝑘
) ≤ 𝛽𝑝 (6)
11
Since ∑ 𝛼𝑘𝑥𝑘𝑘 does not change with the random parameter 𝜂 , equation (6) is
equivalent to:
∑𝛼𝑘𝑥𝑘
𝑘
+ max𝜂
∑𝜂𝛼 𝑘𝑥𝑘
𝑘
≤ 𝛽𝑝 (7)
Noting 𝜂 ∈ [−1,1] and the radius 𝛼 𝑘 is greater than zero, we then have:
max𝜂
∑𝜂𝛼 𝑘𝑥𝑘
𝑘
= ∑|𝛼 𝑘𝑥𝑘|
𝑘
= ∑𝛼 𝑘|𝑥𝑘|
𝑘
(8)
Combining equation (7) with (8):
∑𝛼𝑘𝑥𝑘
𝑘
+ ∑𝛼 𝑘|𝑥𝑘|
𝑘
≤ 𝛽𝑝 (9)
Note in equation (9), the random parameter 𝜂 has been eliminated. However, the
presence of absolute values in the formulation renders the problem non-smooth. Li et
al. [18] showed constraint (9) can be reformulated into the following equivalent form
to cancel absolute values by introducing an auxiliary variable 𝑢𝑘 and an additional
constraint |𝑥𝑘| ≤ 𝑢𝑘:
∑𝛼𝑘𝑥𝑘
𝑘
+ ∑𝛼 𝑘𝑢𝑘
𝑘
≤ 𝛽 (10)
−𝑢𝑘 ≤ 𝑥𝑘 ≤ 𝑢𝑘
With the introduction of the auxiliary variable, the original worst-case constraint (5) is
reformulated into a linear form. Therefore, the robust optimization problem with box
uncertainty sets can then be solved by linear programming techniques.
12
2.3. Uncertain parameters in the objective function
The previous section describes how to handle uncertain constraints. If there are
uncertain parameters in the objective function, they can be moved to the left-hand side
of a constraint. Consider the objective function in model (1) with uncertain parameters
��:
min𝑥
��𝑇𝑥 (11)
By introducing an auxiliary variable 𝑡, it is equivalent to:
min𝑥,𝑡
𝑡 (12)
Subject to:
��𝑇𝑥 − 𝑡 ≤ 0 (13)
Note by the reformulation technique, there is no uncertain parameter in the new
objective function (12), and the uncertain parameters �� in the original objective
function have been moved to the left-hand side of an additional constraint (13). Then,
the constraint (13) can be handled in the same way described in Section 2.2.
3. Robust operational optimization models for
crude oil distillation systems
In Chapter 3, a simplified linear model is proposed for operational optimization of
crude oil distillation systems:
13
max𝑦 = y0 + ∑c𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=
(14)
𝑝𝑚 = p𝑚,0 + ∑a𝑚,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=
𝑚 = 1,2, … ,M (15)
𝑒𝑛 = e𝑛,0 + ∑b𝑛,𝑘(𝑥𝑘 − x𝑘,0)
K
𝑘=
𝑛 = 1,2, … ,N (16)
x𝑘L ≤ 𝑥𝑘 ≤ x𝑘
U 𝑘 = 1,2, … ,K
p𝑚L ≤ 𝑝𝑚 ≤ p𝑚
U 𝑚 = 1,2, … ,M (17)
e𝑛L ≤ 𝑒𝑛 ≤ e𝑛
U 𝑛 = 1,2, … ,N
where 𝑥 and 𝑦 are the design variables and objective function, respectively. Process
constraints are grouped into two categories, product properties 𝑝 and equipment
capacities 𝑒. Model parameters a, b and c are constants calculated from datasets
generated from rigorous simulations. The subscript (∙)0 refers to the current states of
the design variables, objective function and process constraints. The superscripts (∙)L
and (∙)U refer to lower and upper bounds.
Profit is considered as the objective function in this work. It equals the difference of
crude oil and product values minus operating costs. The operating cost includes the
cost of fuel burned in the furnace, stripping steam and cooling
water.
𝑦 = Values of products − Value of crude oil − Operating cost (18)
The throughput, product cut points (or overflash flowrate for the heaviest side draw),
14
furnace outlet temperature, stripping steam flowrates (or reboiler duty if reboilers are
used for stripping) and pump-around flowrates are considered as design variables.
Possible process constraints can be identified according to experience of operations,
such as flash point for some products and the capacity of the furnace.
The model parameters a , b and c are associated with a specific crude feed TBP
curve. Therefore, the values of these parameters vary for different crude feed TBP
curves. If exact TBP information is not available but a set of possible crude feed
scenarios are known, these model parameters can be considered to lie in predefined
intervals. Then, the operational optimization problem (14) – (17) can be converted into
the following robust optimization problem:
min−∑ ��𝑘∆𝑥𝑘
K
𝑘=
(19)
p𝑚,0 + ∑��𝑚,𝑘∆𝑥𝑘
K
𝑘=
≤ p𝑚U 𝑚 = 1,2, … ,M (20)
p𝑚,0 + ∑��𝑚,𝑘∆𝑥𝑘
K
𝑘=
≥ p𝑚L 𝑚 = 1,2, … ,M (21)
e𝑛,0 + ∑��𝑛,𝑘∆𝑥𝑘
K
𝑘=
≤ e𝑛U 𝑛 = 1,2, … ,N (22)
e𝑛,0 + ∑��𝑛,𝑘∆𝑥𝑘
K
𝑘=
≥ e𝑛L 𝑛 = 1,2, … ,N (23)
x𝑘L ≤ 𝑥𝑘 ≤ x𝑘
U 𝑘 = 1,2, … ,K (24)
15
where ∆𝑥𝑘 = 𝑥𝑘 − x𝑘,0 is how much the design variables move from the current
states. The parameters ��, �� and �� are uncertain due to lack of exact information of
crude feed TBP curves. By rearrangement, the robust constraints (20) – (23) can be
transformed to the standard form as Equation (3). The objective function (19) can be
reformulated using the technique described in Section 2.3.
4. Online implementation framework
For online implementation of the robust operational optimization, model parameters
in (19) – (24) need to be estimated and updated. There are two types of model
parameters in the robust optimization model, certain parameters and uncertain
parameters. The current states of the process constraints are certain parameters, which
can be directly read or calculated from real-time plant data. The slopes ��, �� and ��
are uncertain parameters due to lack of exact crude feed TBP data. Therefore, the two
types of model parameters are treated in different ways. Certain parameters are adapted
in real time when new plant data are available. For uncertain parameters, their intervals
are analyzed based on predefined crude feed scenarios from the schedule of crude oil
operations, usually on a weekly basis.
Figure 2 illustrates the online implementation framework of robust operational
optimization. The framework can be divided into three steps, update of uncertainty
sets, update of current states and solution. In the step of update of uncertainty sets,
uncertain parameters are adapted based on latest schedule of crude oil operations. In
the step of update of current states, certain parameters are calculated from real-time
plant data. In the solution step, updated certain and uncertain parameters are combined
into the robust operational optimization model and then the model is solved.
16
Solution
Update of current statesUpdate of uncertainty sets
Linear model generation
for each
crude feed scenario
Schedule of
crude oil operations
Crude feed scenarios
Analysis of
uncertainty sets
Solution of the robust
optimization model
Uncertain parameters
Real-time
plant data
Online adaptation of
current states
Certain parameters
Robust optimal
operating conditions
Update of the robust
optimization model
Figure 2. Online implementation framework of robust operational optimization.
4.1. Update of uncertainty sets
In this step, the uncertainty set of the slopes are analyzed and updated based the latest
schedule of crude oil operations, usually on a weekly basis according to how often the
refinery updates the schedule. First, possible crude feed scenarios are identified. Types
of crudes processed next week and rough mixing ratios for several different crude feed
scenarios can usually be known in advance from weekly schedule of crude oil
operations. In case crude feed scenarios are not determined in the scheduling phase,
evenly distributed crude feed scenarios can be generated based on the types of crudes
planned to be processed next week.
For each predefined crude feed scenario, datasets are generated from rigorous
simulation and are then used to construct the linear model using the method in Chapter
3. Different values of the slopes 𝑎, 𝑏 and 𝑐 are computed for different crude feed
17
scenarios. The box uncertainty set is used in this work due to its simplicity. As
discussed in Section 2.1, each uncertain parameter is considered to lie in an interval
for box uncertainty sets. The minimum and maximum values among the slopes for
different crude feed scenarios are used to determine the uncertain interval for each
slope parameter:
��𝑚,𝑘L = min(a𝑚,𝑘
( ) , a𝑚,𝑘( ) , … , a𝑚,𝑘
(S) ) 𝑚 = 1,2, … ,M 𝑘 = 1,2, … , K (25)
��𝑚,𝑘U = max(a𝑚,𝑘
( ) , a𝑚,𝑘( ) , … , a𝑚,𝑘
(S) ) 𝑚 = 1,2, … ,M 𝑘 = 1,2, … , K (26)
��𝑚,𝑘 = [��𝑚,𝑘L , ��𝑚,𝑘
U ] 𝑚 = 1,2, … ,M 𝑘 = 1,2, … , K (27)
where a𝑚,𝑘(s)
denotes the slope value for the 𝑠th crude feed scenario. The uncertain
intervals for slopes 𝑏 and 𝑐 are identified in the same way.
The nominal (central) value and radius of the interval can then be computed by:
𝑎𝑚,𝑘 =��𝑚,𝑘
L + ��𝑚,𝑘U
2 𝑚 = 1,2, … ,M 𝑘 = 1,2, … , K (28)
𝑎 𝑚,𝑘 = ��𝑚,𝑘U − 𝑎𝑚,𝑘 𝑚 = 1,2, … ,M 𝑘 = 1,2, … , K (29)
For uncertain parameters 𝑏 and 𝑐, the nominal value and radius of the interval can
be calculated in the same way.
4.2. Update of current states
In this step, the current states of the process constraints need to be adapted based on
real-time plant data. Properties like flash point and density can be directly updated
18
from latest online or laboratory analysis. Equipment capacities like furnace duty and
condenser duty can also be calculated by real-time plant data:
Furnace duty = 𝑓fuel ∗ LHV ∗ 𝜂 (30)
Condenser duty = 𝑓cw ∗ cp ∗ Δ𝑇 (31)
where 𝑓fuel, LHV and 𝜂 are the flowrate of fuel used by the furnace, lower heating
value of the fuel and efficiency of the furnace, respectively; 𝑓cw, cp and Δ𝑇 denote
the flowrate cooling water used by the condenser, heat capacity of cooling water and
temperature increase of cooling water, respectively.
4.3. Solution
Combining the low-frequency updated uncertainty set and the high-frequency updated
current states, the robust operational optimization model is generated. By using the
reformulation technique described in Section 2, uncertain model parameters can be
canceled, and the model is converted into an equivalent linear programming (LP)
problem. The resulted LP is ready to be solved by established algorithms, like the
simplex method, which is implemented in many modeling systems, like MATLAB and
Microsoft Excel.
5. Case study
5.1. Problem description
Operational optimization of a typical crude oil distillation system depicted in Figure 3
is studied to test the proposed optimization framework. The crude oil distillation
19
process is a heat-integrated process consisting of a complex column and a heat
exchanger network (HEN). Five products are drawn from the column, i.e., naphtha,
kerosene, diesel, atmospheric gas oil (AGO) and residue. Three pump-arounds and
three side strippers are attached to the main column. Structural details of the complex
column are listed in Table S1.
Furnace
Residue
Off-gas
Naphtha
Diesel
AGO
HEN1
Crude
Steam
Kerosene
HEN2
Desalter
PA1
PA2
PA3
Figure 3. A typical crude oil distillation system. PA: Pump-around.
The structure of the associated HEN is shown in Figure 4. The HEN is broken down
into two sections by the desalter. In the first section, the crude feed is heated to about
130°C for removing water and soluble salts. It is assumed that there is a 4°C
temperature drop when the crude feed passes through the desalter. In the second section,
the crude feed is further heated before entering the furnace.
20
E-101 DesalterE-102 E-103 E-104
Crude
Furnace
Kerosene PA1 Residue
E-105 E-106 E-107 E-108 E-109 E-110
PA2
Diesel
AGO PA3
HEN1 HEN2
Figure 4. Structure of the HEN.
To generate linear models for each crude feed scenario using the method proposed in
Chapter 3, rigorous simulation of the process is required. In this work, the rigorous
simulations to produce datasets for linear model generation are carried out in Aspen
HYSYS (version 8.8). Model parameters used in rigorous simulation including stage
efficiencies of the column and rating parameters of the heat exchangers are listed in
Table S2 and S3.
In the case study, it is assumed that three crudes are processed following the schedule
of crude oil operations next week. Bulk properties and TBP data of the three crudes
are assumed to be available (see Table S4). It is also assumed that seven crude feed
scenarios listed in Table 1 are scheduled for operations of the next week. However,
real-time crude feed TBP information is not available. There are several practical
factors making it difficult to accurately track crude feed TBP curves without an online
analyzer. One reason is that there are usually several layers of tanks from storage of
crudes to charging tanks and compositions of the remainder of every tank are not
known. Another reason is that crude oil operations may not follow the schedule exactly.
However, these crude feed scenarios can provide a good estimation for the operating
range of crude feed properties.
21
Table 1. Predefined crude feed scenarios
Crude 1 Crude 2 Crude 3
API 33.2 29.7 25.6
Sulfur (wt%) 0.37 2.85 0.41
Acidity (mgKOH/g) 0.12 0.11 1.30
Crude feed scenarios (wt%)
1 0.6 0.4 0
2 0.5 0.4 0.1
3 0.4 0.4 0.2
4 0.3 0.4 0.3
5 0.2 0.4 0.4
6 0.1 0.4 0.5
7 0 0.4 0.6
Profit is the objective of the operational optimization in the case study. The prices for
computing the profit is summarized in Table 2. It is assumed that four possible process
constraints are identified for the optimization based on previous experience of
operations, including lower limit of kerosene flash point, furnace and condenser
capacities, and operating range of the desalter inlet temperature. The bounds for the
process constraints are listed in Table 3.
22
Table 2. Prices
Item Prices
Crude 1 280 USD/t
Crude 2 265 USD/t
Crude 3 250 USD/t
Naphtha 480 USD/t
Kerosene 520 USD/t
Diesel 420 USD/t
AGO 240 USD/t
Residue 180 USD/t
Furnace duty 9 USD/GJ
Reboiler duty 14 USD/GJ
Steam 27 USD/t
Cooling water 1 USD/GJ
Table 3. Concerned process constraints
Variables Lower bound Upper bound
Kerosene flash point 38.0 °C -
Furnace duty - 210.0 GJ/h
Condenser duty - 124.0 GJ/h
Desalter inlet temperature 125.0 °C 140.0 °C
The starting operating conditions for the seven predefined crude feed scenarios are
assumed as in Table 4.
23
Table 4. Starting operating conditions
Variables Current value
Throughput 600.0 t/h
Naphtha D86 FBP 170.0 °C
Kerosene D86 FBP 240.0 °C
Diesel D86 95% 360.0 °C
Overflash flowrate 15.0 t/h
Furnace outlet temperature 360.0 °C
Main stripping steam flowrate 6.0 t/h
AGO stripping steam flowrate 1.0 t/h
Diesel stripping steam flowrate 3.5 t/h
Kerosene reboiler duty 0.5 GJ/h
Pump-around 1 flowrate 400.0 m3/h
Pump-around 2 flowrate 300.0 m3/h
Pump-around 3 flowrate 250.0 m3/h
5.2. Model generation of robust operational optimization
Linear models are generated for the seven predefined crude feed scenarios from
datasets obtained in rigorous simulations using the method in Chapter 3. Different
slope values for the seven predefined crude feed scenarios are analyzed to determine
the box uncertainty set. The identified uncertainty intervals are listed in Table 5.
Current states of process constraints for the seven predefined crude feed scenarios are
computed by rigorous simulations and listed in Table 6. Note that in real-world cases
the current states can be collected or computed based on real-time plant data.
24
Table 5. Uncertain intervals for the slope parameters
Variables Profit
Kerosene flash
point Furnace duty Condenser duty
Desalter inlet
temperature
Center Radius Center Radius Center Radius Center Radius Center Radius
Throughput 40.592 0.283 0.000 0.000 0.452 0.022 0.240 0.034 -0.055 0.001
Naphtha D86 FBP -67.187 6.173 0.479 0.012 -0.047 0.010 -0.028 0.110 0.172 0.012
Kerosene D86 FBP 104.074 2.772 0.208 0.016 -0.197 0.002 -0.197 0.093 0.097 0.013
Diesel D86 95% 165.417 1.275 0.001 0.003 -0.161 0.030 0.012 0.088 0.120 0.009
Overflash flowrate -55.186 1.422 0.000 0.001 -0.119 0.033 0.005 0.016 0.106 0.003
Furnace outlet
temperature 152.167 21.961 0.033 0.005 1.354 0.054 1.111 0.133 -0.020 0.017
Main stripping steam
flowrate 343.920 63.915 0.122 0.005 1.025 0.038 4.192 0.117 -0.320 0.020
AGO stripping steam
flowrate 250.178 6.408 0.120 0.009 0.592 0.037 4.097 0.237 -0.014 0.019
Diesel stripping steam
flowrate 48.486 1.662 0.201 0.009 0.588 0.015 4.333 0.098 -0.423 0.017
Kerosene reboiler duty -15.996 11.381 0.072 0.027 -0.022 0.036 -0.075 0.473 0.192 0.030
Pump-around 1 flowrate 0.142 0.037 0.000 0.000 -0.006 0.001 -0.019 0.008 0.018 0.001
Pump-around 2 flowrate 0.142 0.044 -0.001 0.001 -0.025 0.003 -0.029 0.014 0.013 0.001
Pump-around 3 flowrate 0.456 0.056 -0.002 0.000 -0.057 0.005 -0.059 0.007 0.003 0.000
25
Table 6. Current states of process constraints
Crude feed
scenarios
Kerosene
flash point Furnace duty
Condenser
duty
Desalter inlet
temperature
1 52.4 209.7 139.5 128.2
2 52.5 206.2 135.0 129.6
3 52.5 202.7 130.1 130.9
4 52.5 199.5 123.0 132.1
5 52.7 195.6 121.1 133.7
6 52.8 192.1 116.0 135.1
7 52.8 188.6 111.2 136.5
5.3. Results of robust operational optimization
The robust optimization models for the seven crude feed scenarios are built with the
parameters listed in Table 5 and 6. As mentioned in Section 4.3, the robust operational
optimization problem is reformulated into a LP. The LP is solved by the Simplex LP
solver in the built-in Solver add-in of Microsoft Excel.
The profit gained by robust operational optimization for the seven crude feed scenarios
is listed in Table 7. Scenario 1 has the smallest profit increase (8.1%), while Scenario
7 has the largest (18.7%). From Scenario 1 to 7, more profit increase is achieved by
robust operational optimization. The reason is that the crude feed becomes heavier
from Scenario 1 to 7. The lighter the crude feed is, the easier it is to reach full capacities
of the furnace and condenser. In fact, it can be seen from Table 6 that the condenser
duties under the starting operating conditions in Scenario 1, 2 and 3 are beyond the
upper limit (124.0 GJ/h).
26
Table 7. Profit increase
Crude feed
scenarios Starting, USD/h Robust optimal, USD/h Profit increase
1 26,077 28,200 8.1%
2 26,297 28,839 9.7%
3 26,498 29,503 11.3%
4 26,663 30,273 13.5%
5 26,813 30,744 14.7%
6 26,943 31,438 16.7%
7 27,055 32,116 18.7%
The robust optimal operating conditions for the seven crude feed scenarios are shown
in Figure 5. In all the seven crude feed scenarios, the products are all recut to produce
more valuable products (kerosene > naphtha > diesel > AGO > residue in the case
study). The furnace inlet temperature stays the same as the starting condition. The
throughput increases steadily from Scenario 1 to 7. Increase in throughput is attributed
to raising pump-around flowrates to full capacities because it can help to reduce the
burden of the top condenser. The flowrates of main steam injection also have an
increasing trend from Scenario 1 to 7. By contrast, flowrates of stripping stream (or
reboiler duty) at upper positions (AGO, diesel and kerosene) either decrease or do not
change. This is because light components (which affects properties like flash point) in
kerosene, diesel and AGO do not lead to active concerned constraints in this case.
27
520
540
560
580
600
620
640
660
680
1 2 3 4 5 6 7
Th
roughput,
t/h
Scenario
Current
Optimal
160
165
170
175
180
1 2 3 4 5 6 7
Naphth
a F
BP
, °C
Scenario
Current
Optimal
230
235
240
245
250
1 2 3 4 5 6 7
Kero
sene F
BP
, °C
Scenario
Current
Optimal
350
355
360
365
370
1 2 3 4 5 6 7
Die
se
l 9
5%
, °C
Scenario
Current
Optimal
28
10
12
14
16
18
20
22
1 2 3 4 5 6 7
Overf
lash, t/
h
Scenario
Current
Optimal
350
355
360
365
370
1 2 3 4 5 6 7
Fu
rnace o
utle
t te
mpera
ture
, °C
Scenario
Current
Optimal
2
4
6
8
10
1 2 3 4 5 6 7
Main
ste
am
, t/
h
Scenario
Optimal
Current
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1 2 3 4 5 6 7
AG
O s
tea
m, t/
h
Scenario
Optimal
Current
29
0.5
1.5
2.5
3.5
4.5
5.5
6.5
1 2 3 4 5 6 7
Die
sel ste
am
, t/
h
Scenario
Optimal
Current
0.1
0.3
0.5
0.7
0.9
1 2 3 4 5 6 7
Kero
sene r
eboile
r duty
, G
J/h
Scenario
Optimal
Current
300
350
400
450
500
1 2 3 4 5 6 7
PA
1 flo
wra
te, m
3/h
Scenario
Optimal
Current
200
240
280
320
360
400
1 2 3 4 5 6 7
PA
2 flo
wra
te, m
3/h
Scenario
Optimal
Current
30
Figure 5. Robust optimal operating conditions.
180
200
220
240
260
280
300
320
1 2 3 4 5 6 7
PA
3 flo
wra
te, m
3/h
Scenario
Optimal
Current
31
The values for the concerned process constraints are illustrated in Figure 6. The blue
lines show the values of the process constraints under the starting operating conditions.
There is a downward trend in furnace and condenser duty and an upward trend in
desalter inlet temperature from Scenario 1 to 7 due to increase in density of crude feed.
As mentioned earlier, condenser duties for scenario 1 (139.5 GJ/h), 2 (135.0 GJ/h) and
3 (130.1 GJ/h) are beyond its upper limit (124.0 GJ/h) under the starting operating
conditions. Furnace duty of Scenario 1 (209.7 GJ/h) is also close to its full capacity
(210.0 GJ/h). The operations are more constrained with light crude feed scenarios.
The orange lines show the worst-case values of the process constraints, which means
the worst possible values for any possible type of crude feed among the predefined
crude feed scenarios. Furnace and condenser duties are at their upper bounds (210.0
GJ/h for furnace duty and 124.0 GJ/h for condenser duty) for all crude feed scenarios.
In contrast, worst-case values for kerosene flash point and desalter inlet temperature
are still within their bounds. The results confirm that furnace and condenser duties are
the real bottlenecks for operations with the predefined crude feed scenarios.
The green dashed lines show the real values of process constraints when processing
the corresponding crude feed scenario at its robust optimal operating conditions. It can
be observed that there are margins between the real values and worst-case values. The
margins are derived from the philosophy of robust optimization to ensure feasibility
against uncertainty. Note that the optimal operating conditions in all crude feed
scenarios are within their bounds. Infeasible starting operating conditions for
condenser duties in Scenario 1, 2 and 3 are pulled back to the feasible region by robust
optimization. These results show that robust operational optimization can effectively
maintain feasibility when uncertainty cannot be eliminated.
32
185
190
195
200
205
210
215
1 2 3 4 5 6 7
Fu
rnace d
uty
, G
J/h
Scenario
Current
Worst
Real
110
115
120
125
130
135
140
1 2 3 4 5 6 7
Condenser
duty
, G
J/h
Scenario
Current
Worst
Real
45
46
47
48
49
50
51
52
53
54
55
1 2 3 4 5 6 7
Kero
sene fla
sh p
oin
t, °
C
Scenario
Current
Worst
Real
33
Figure 6. Process constraints.
5.4. Robust operational optimization versus conventional
RTO
Previous discussion shows that robust operational optimization has the strength to
safeguard feasibility against uncertainty. However, the protection of feasibility does
not come for free. Some of the optimization potential is lost to cope with uncertainty.
Robust optimal solutions are natural to underperform optimal solutions with perfect
knowledge of the reality. There is a trade-off between investment in analyzers and lose
of optimization potential. In this section, robust operational optimization is compared
with conventional RTO which assumes exact crude feed information is available.
For each crude feed scenario, results of conventional RTO are obtained from
operational optimization assuming that crude feed TBP can be accurately evaluated by
an online analyzer. The results of robust operational optimization and conventional
RTO are compared in Figure 7. As expected, conventional RTO achieves greater profit
increase compared to robust operational optimization in all crude feed scenarios. On
average, 2.0 % of optimization potential is lost by robust operational optimization
compared to robust RTO. The comparison further validates that robust operational
128
130
132
134
136
138
1 2 3 4 5 6 7
Desalter
inle
t te
mpera
ture
, °C
Scenario
Current
Worst Lower
Worst Upper
Real
34
optimization provides safeguard against uncertainty at the cost of losing optimization
potentials. However, most of optimization potentials can still be achieved by robust
operational optimization. Therefore, robust operational optimization can be an
alternative option for plants favoring low-cost optimization solutions.
Figure 7. Robust operational optimization versus conventional RTO.
6. Conclusions
In this work, a novel robust operational optimization framework for crude oil
distillation systems is proposed. Compared to conventional RTO methods, accurate
crude feed TBP data are not required for optimization. Instead of relying on expensive
online analyzers, the proposed method combines information from schedule of crude
oil operations and plant measurements to make optimization decisions. On the
optimization method, the work introduces a simplified linear model to make the
solution computationally tractable. After reformulation, the robust operational
optimization problem is converted into an LP with box uncertainty sets, which can be
efficiently solved by established algorithms.
The case study shows the robust operational optimization method can effectively
maintain operational feasibility against uncertainty derived from limited knowledge in
0%
5%
10%
15%
20%
25%
1 2 3 4 5 6 7
Pro
fit in
cre
ase
Scenario
Robust
Conventional RTO
35
crude feed TBP information. Margins between real and worst-case process constraints
help to ensure operational feasibility. Violations of feasibility at starting operating
conditions can also be pulled back to feasible regions.
In terms of optimality, robust operational optimization is naturally more conservative
than conventional RTO because less accurate information is required and used. The
case study shows that robust optimal solutions lose 2.0 % of optimization potentials
compared with the situation that perfect crude feed TBP data is available. In spite of
this, robust operational optimization can still achieve most of the optimization
potentials. Therefore, it’s an alternative option when low-cost solutions are preferred.
Future work will consider methods like adaptive robust optimization to reduce the
margins between the real and worst-case values to release more optimization potential.
36
Acknowledgements
The first author would like to acknowledge the financial support for the research
program from Mr Shibo Wang and Process Integration Limited.
37
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39
Supplementary material
Table S1 lists structural details of the complex column.
Table S1. Structural details of the complex column (numbered top-down)
Number of trays in the main column 34
Condenser 0
Pump-around 1 return 1
Pump-around 1 draw 3
Kerosene stripper return 8
Kerosene stripper draw 9
Pump-around 2 return 11
Pump-around 2 draw 13
Diesel stripper return 17
Diesel stripper draw 18
Pump-around 3 return 20
Pump-around 3 draw 22
AGO stripper return 26
AGO stripper draw 27
CDU feed 31
Main steam injection 34
Number of trays in the kerosene stripper 3
Number of trays in the diesel stripper 4
Number of trays in the AGO stripper 4
Table S2 and S3 list model parameters used in rigorous simulations for linear model
generation.
40
Table S2. Column stage efficiencies
Stages Efficiency Notes
1 - 3 0.6 Pump-around 1
4 - 9 0.8 Naphtha to kerosene section
10 0.8 Kerosene to diesel section
11 - 13 0.4 Pump-around 2
14 - 18 0.8 Kerosene to diesel section
19 0.7 Diesel to AGO section
20 - 22 0.4 Pump-around 3
23 - 27 0.7 Diesel to AGO section
28 - 30 0.7 AGO to flash zone section
31 - 34 0.4 Steam stripping section
Kerosene stripper 0.7
Diesel stripper 0.4
AGO stripper 0.4
Table S3. UA† of heat exchangers
Heat exchanger UA, kJ/(°C•h)
E-101 2.5 × 105
E-102 1.0 × 106
E-103 5.0 × 105
E-104 1.1 × 106
E-105 1.1 × 106
E-106 7.0 × 105
E-107 8.0 × 105
E-108 2.0 × 105
E-109 8.0 × 105
E-110 2.5 × 106
† U and A denote overall heat transfer coefficients and areas of heat exchangers,
respectively.
Table S4 summarizes crude bulk properties and TBP data.
41
Table S4. Crude bulk properties and TBP data
Crude 1 Crude 2 Crude 3
Bulk properties
API 33.2 29.7 25.6
Viscosity 1 T, °C 20.0 20.0 20.0
Viscosity 1, cSt 13.9 20.9 54.5
Viscosity 2 T, °C 50.0 50.0 50.0
Viscosity 2, cSt 6.1 8.0 15.1
TBP curve vol% T, °C vol% T, °C vol% T, °C 4.4 50.0 4.6 50.0 2.0 50.0 10.8 100.0 11.5 100.0 5.2 100.0 18.5 150.0 18.7 150.0 10.0 150.0 26.7 200.0 27.8 200.0 15.4 200.0 35.5 250.0 35.9 250.0 23.8 250.0 44.4 300.0 44.0 300.0 33.8 300.0 53.7 350.0 52.1 350.0 44.7 350.0 61.8 400.0 59.9 400.0 54.5 400.0 69.8 450.0 67.3 450.0 64.5 450.0 77.0 500.0 74.0 500.0 72.8 500.0 82.9 550.0 80.3 550.0 79.8 550.0 87.6 600.0 85.7 600.0 85.6 600.0 91.2 650.0 90.0 650.0 90.4 650.0 93.9 700.0 93.5 700.0 94.3 700.0
42
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49
6. Investigating Uncertainty Sets and
Reducing Optimization Loss for Robust
Operational Optimization
This chapter is the second piece of work for robust operational optimization methods.
Based on the method proposed in Chapter 5, this chapter further investigates the effects
of the size and shape of uncertainty sets to reduce loss of optimization potentials.
Please note that this chapter is prepared in a journal paper format and is attached with
its own page numbering system.
50
Blank page
* Corresponding author. Email: [email protected]
Investigating Uncertainty Sets and
Reducing Optimization Loss for
Robust Operational Optimization
Xiao Yang, Nan Zhang*, Robin Smith
Centre for Process Integration, School of Chemical Engineering and Analytical
Science, The University of Manchester, Manchester M13 9PL, UK
Highlights
• Box uncertainty sets give smaller optimization loss than ball and polyhedral.
• Searching for appropriate 𝜌 values can help balance optimality and
robustness.
• The universal 𝜌 method cuts optimization loss by 66% for box uncertainty
sets.
• Finely tuning individual 𝜌 values can further cut optimization loss.
2
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3
Abstract
Operational optimization plays an important role in stepping into Industry 4.0 and
smart manufacturing for crude oil distillation systems, the first and most important
step in refineries. The main challenge for operational optimization of crude oil
distillation systems is absence of real-time crude feed compositions characterized by
true boiling point (TBP) distillation curves. Robust operational optimization is a
technique to make optimization decisions with limited information of crude feed TBP
data. However, there is usually an optimization loss compared to conventional real-
time optimization (RTO) methods assuming reliable crude feed TBP data can be
obtained. To reduce the optimization loss, this paper investigates different types of
uncertainty sets and proposes two methods to determine the size of uncertainty sets. A
case study shows that box uncertainty sets can achieve small optimization losses
compared to ball and polyhedral uncertainty sets. In addition, by searching for
appropriate sizes of uncertainty sets, optimization losses can be effectively reduced.
Keywords: Crude oil distillation system, Robust operational optimization, Uncertainty
sets
4
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5
1. Introduction
During the past few years, both industry and academia have seen a trend of embracing
Industry 4.0 and smart manufacturing [1], [2]. Operational optimization plays an
important role in smart manufacturing by giving plants the ability to ‘think’ and make
decisions of the optimal operations. Refining is one of the most energy-consuming
sectors of industry due to extensive use of high energy-demanding distillation
processes [3]. Within refineries, crude oil distillation systems are the most important
step and their optimization is key to success of a smart refinery.
True boiling point (TBP) distillation curves [4] are the most widely-used method to
characterize crude feed composition. Crude feed TBP data is vital to operational
optimization of crude oil distillation systems. However, real-time TBP data are not
available in many refineries due to changing crude feed caused by schedule of crude
oil operations [5] and long run time for TBP tests [6]. Therefore, the absence of real-
time crude feed TBP data is the main challenge for operational optimization of crude
oil distillation systems.
Conventional real-time operational optimization (RTO) techniques [7] integrates an
parameter estimation module to handle unknown data. For crude oil distillation
systems, Dave et al. [8] proposed an online crude feed TBP estimation method based
on available plant measurements, including temperatures of feed and product drawing
trays, flowrates of feed, reflux, products and stripping steam, and pump-around duties.
First, equilibrium flash vaporization (EFV) curves are computed according to heat
balance. Then, EFV temperatures are transformed into TBP temperatures through
correlation. Dave’s method is embedded into an RTO system proposed by Basak et al.
[9]. However, the correlation between EFV and TBP temperatures are not easily
established because the correlation parameters are crude-sensitive. Lee et al. [10]
6
proposed an inferential model for estimation of crude feed TBP curves from column
operating conditions. In Lee’s method, TBP curves are assumed to follow a probability
distribution characterized by two parameters. To calculate the two distribution
parameters, two TBP points are needed to be known. The two TBP points are
calculated from a linear correlation with operating parameters. However, the
correlation may change for different crude oil feedstocks. Crude feed TBP curves can
also be estimated by online analyzers, such as near infrared spectroscopy [11].
However, it requires capital investment and its performance is not very reliable to the
knowledge of the authors.
A new paradigm to cope with limited crude feed information, i.e., robust operational
optimization, is recently proposed in Chapter 5. Unlike conventional RTO techniques,
this method employs robust optimization techniques [12] and does not rely on exact
crude feed TBP data. A range of possible crude feed scenarios derived from schedule
of crude oil operations are considered in the method instead of an exact crude feed.
The range of crude feed scenarios cause some of model parameters to be uncertain.
These uncertain parameters are handled by robust optimization. The main limitation
of the method is that there can be a large optimization loss compared to conventional
RTO assuming perfect crude feed TBP data are available.
The objective of the work is to reduce optimization loss of robust operational
optimization by investigating different types of uncertainty sets and searching for the
best sizes of uncertainty sets. The remainder of the paper is structured as follows.
Section 2 summarizes mathematical formulations and robust counterparts for box, ball
and polyhedral uncertainty sets. Section 3 presents two methods for determining
appropriate sizes of uncertainty sets to balance optimality and robustness. Section 4
investigates performance of the three types of uncertainty sets for a typical crude oil
distillation system. Key conclusions are drawn in Section 5.
7
2. Shapes of uncertainty sets and robust
counterparts
This section introduces three popular types of uncertainty sets and their robust
counterparts. A preliminary introduction to robust optimization, including the concepts
of uncertainty sets and robust counterparts, is not fully contained in this paper and is
referred to Chapter 5 or [13], [12]. In conventional optimization methods, a general
linear constraint can be stated as follows:
∑𝛼𝑘𝑥𝑘
K
𝑘=1
≤ 𝛽 (1)
where 𝑥 ∈ ℛ𝑘 is the vector of design variables. Constants 𝛼 ∈ ℛ𝑘 and 𝛽 are
model parameters.
By contrast, model parameters are considered as random vectors lying in predefined
uncertainty sets by robust optimization. Without loss of generality, only the left-hand
side parameters are considered uncertain because right-hand side parameters can be
rearranged and moved to the left-hand side [13]. To denote the distinction between
constant and uncertain parameters, 𝛼 is replaced by ��:
∑��𝑘𝑥𝑘
K
𝑘=1
≤ 𝛽, ∀�� ∈ 𝑈 (2)
where 𝑈 is a predefined uncertainty set.
The uncertainty set is defined based on random intervals for each uncertain parameter:
��𝑘 = 𝛼𝑘 + 𝜂��𝑘, 𝑘 = 1,2, … ,K (3)
8
where 𝛼𝑘 and ��𝑘 are the center and radius of the interval for ��𝑘, respectively, and
𝜂 ∈ [−1,1] is a random number.
Based on uncertain intervals of each parameter, different types of uncertainty sets can
be defined. They have different shapes in the space of uncertain parameters. In this
work, three mostly used types of uncertainty sets are investigated, i.e., box, ball and
polyhedral. Figure 1 illustrates the three types of uncertainty sets for two uncertain
parameters.
Figure 1. Illustration of box, ball and polyhedral uncertainty sets (Two uncertain
parameters).
Note the uncertain constraint (2) must be feasible for any possible value of �� in the
uncertainty set 𝑈. Therefore, it is equivalent to infinite number of constraints. As a
result, robust optimization cannot be directly solved by existing algorithms. Robust
constraints need to be reformulated into equivalent conventional constraints, i.e., the
so-called robust counterparts. Mathematical formulations of the three types of
uncertainty sets and their robust counterparts are introduced below.
2.1. Box uncertainty sets
Box uncertainty sets are the most straightforward type. Mathematically, they are
��1
��
𝛼1
𝛼
��
��1
��1
��
𝛼1
𝛼
��
��1
Conventional Robust (Box) Robust (Ball)
��1
��
𝛼1
𝛼
��
��1
Robust (Polyhedral)
9
described by ∞-norm of the uncertain parameter vector:
𝑈box = {𝜂|‖𝜂‖∞ ≤ 𝜌} = {𝜂||𝜂𝑘| ≤ 𝜌, 𝑘 = 1,2, … ,K} (4)
where 𝜌 is a parameter to adjust the size of uncertainty sets. When 𝜌 = 1 , each
parameter is bounded in the interval [𝛼𝑘 − ��𝑘, 𝛼𝑘 + ��𝑘] . When 𝜌 > 1 , the box
uncertainty set is enlarged. When 𝜌 < 1, it is shrunk.
The robust counterpart for box uncertainty sets is proved to be as follows [14]:
∑𝑎𝑘𝑥𝑘 + 𝜌∑ ��𝑘|𝑥𝑘|
K
𝑘=1
K
𝑘=1
≤ 𝛽 (5)
Since the absolute value operator makes the optimization problem discontinuous and
may undermine performance of solvers, a reformulation technique is used to eliminate
the absolute value operator by introducing an auxiliary variable 𝑢 [14]:
∑𝑎𝑘𝑥𝑘 + 𝜌∑ ��𝑘𝑢𝑘
K
𝑘=1
K
𝑘=1
≤ 𝛽 (6)
−𝑢𝑘 ≤ 𝑥𝑘 ≤ 𝑢𝑘 , 𝑘 = 1,2, … ,K (7)
Note the above continuous reformulation of the robust counterpart for box uncertainty
sets is still linear (and convex). Therefore, the global optimum can be reached by
existing solvers [15].
2.2. Ball uncertainty sets
Ball uncertainty sets are described by 2-norm of the uncertain parameter vector:
10
𝑈ball = {𝜂|‖𝜂‖ ≤ 𝜌} = {𝜂|√∑𝜂𝑘
K
𝑘=1
≤ 𝜌} (8)
The adjusting parameter 𝜌 plays the same role as for box uncertainty sets.
The robust counterpart for ball uncertainty sets is proved to be as follows [14]:
∑𝑎𝑘𝑥𝑘
K
𝑘=1
+ 𝜌√∑ ��𝑘 𝑥𝑘
K
𝑘=1
≤ 𝛽 (9)
Note the robust counterpart is not linear anymore. However, it is proved to be still
convex [16]. Therefore, the global optimum can be guaranteed by existing solvers.
2.3. Polyhedral uncertainty sets
Polyhedral uncertainty sets are described by 1-norm of the uncertain parameter vector:
𝑈polyhedral = {𝜂|‖𝜂‖1 ≤ 𝜌} = {𝜂|∑|𝜂𝑘|
K
𝑘=1
≤ 𝜌} (10)
The adjusting parameter 𝜌 plays the same role as for box uncertainty sets.
The robust counterpart for polyhedral uncertainty sets is proved to be as follows [14]:
∑𝑎𝑘𝑥𝑘
K
𝑘=1
+ 𝜌𝑣 ≤ 𝛽 (11)
𝑣 ≥ ��𝑘|𝑥𝑘|, 𝑘 = 1,2, … ,K (12)
11
where 𝑣 is an auxiliary variable.
To eliminate the absolute value operator and make the optimization problem
continuous, the constraint (12) can be reformulated into an equivalent continuous form
[14]:
𝑣 ≥ ��𝑘𝑢𝑘, 𝑘 = 1,2, … ,K (13)
−𝑢𝑘 ≤ 𝑥𝑘 ≤ 𝑢𝑘 , 𝑘 = 1,2, … ,K (14)
where 𝑢 is an auxiliary variable.
The above continuous reformulation of the robust counterpart for polyhedral
uncertainty sets is still linear (and convex). Therefore, the global optimum can be
found by existing solvers.
3. Balance optimality and robustness by
searching 𝝆 values
3.1. Robust operational optimization for crude oil
distillation systems
To perform operational optimization when exact crude feed TBP data is not known,
Chapter 5 proposed a robust optimization model for crude oil distillation systems:
min−𝑦 = −𝑦0 −∑ ��𝑘∆𝑥𝑘
K
𝑘=1
(15)
12
p𝑚,0 +∑��𝑚,𝑘∆𝑥𝑘
K
𝑘=1
≤ p𝑚U 𝑚 = 1,2, … ,M (16)
p𝑚,0 +∑��𝑚,𝑘∆𝑥𝑘
K
𝑘=1
≥ p𝑚L 𝑚 = 1,2, … ,M (17)
e𝑛,0 +∑��𝑛,𝑘∆𝑥𝑘
K
𝑘=1
≤ e𝑛U 𝑛 = 1,2, … ,N (18)
e𝑛,0 +∑��𝑛,𝑘∆𝑥𝑘
K
𝑘=1
≥ e𝑛L 𝑛 = 1,2, … ,N (19)
x𝑘L ≤ 𝑥𝑘 ≤ x𝑘
U 𝑘 = 1,2, … ,K (20)
where ∆𝑥𝑘 is design variables representing how much operating variables should
move from the current operating condition. The optimization objective is to
maximizing profit 𝑦 (minimizing −𝑦) computed by product values minus crude feed
values and operating costs.
𝑝 and 𝑒 represents values for two types of constraints, properties of products and
equipment capacities, respectively. Uncertain parameters ��, �� and �� are regressed
coefficients correlating profit and constraint values with design variables. For crude
feed with known TBP data, these parameters are constants calculated from datasets
generated from rigorous simulation. Since a range of predefined crude feed scenarios
are known instead of exact crude feed TBP data, these parameters vary and are treated
as uncertain parameters by robust optimization. The subscript (∙)0 refers to profit and
constraint values under current operating conditions. They are constant values which
can be updated from real-time plant data. The superscripts (∙)L and (∙)U refer to
lower and upper bounds.
13
For robust optimization, when intervals for each uncertain parameter is predefined,
shapes of uncertainty sets and the parameter 𝜌 to adjust coverage can still be tuned.
When 𝜌 is increased, the uncertainty set is enlarged. As a result, the optimal solution
is more robust against uncertainty caused by changing crude feed. On the other hand,
the optimal solution is also more conservative, meaning more optimization potential
is lost. Therefore, a systematic method to find appropriate 𝜌 values is needed to help
balance optimality and robustness.
In this work, two strategies for searching the best values for 𝜌 are proposed. In the
first strategy, a universal 𝜌 value is associated with all robust constraints. In the
second strategy, each robust constraint is associated with an individual 𝜌 value.
3.2. The universal 𝜌 method
Robust optimization guarantee feasibility for worst cases in the predefined uncertainty
set. Therefore, when a robust constraint is active, it is the constraint value for the worst
case that hits the bound, not the constraint value for the current scenario. There is
usually a margin between the constraint value for the current scenario and the bound,
unless the current scenario happens to be the worst case for the constraint. If there are
margins for all predefined crude feed scenarios for an active robust constraint, the
uncertainty set is over-sized and 𝜌 values can be reduced. With the uncertainty set
shrinking, margins between constraint values for the current crude feed scenario and
the bounds also reduce. When 𝜌 decreases to a specific value, there is zero margin
for some crude feed scenario. In this case, 𝜌 cannot decrease anymore because further
reduction results in infeasibility in that scenario. The universal 𝜌 method tries to find
such 𝜌 values.
Figure 2 shows the flowchart to find the best universal 𝜌 value. An initial value 𝜌 =
14
1 is used to solve robust models for each crude feed scenario. Then, constraint values
under the robust optimal conditions are calculated for each scenario. The status of
constraints should fall into three categories. The first situation is that all constraints
still have margins to their bounds for all crude feed scenarios. The uncertainty set can
be safely reduced to allow more optimization potential. Therefore, the 𝜌 value should
decrease. The second possible result is that there is one or more constraints violated
for any crude feed scenario. It means coverage of uncertainty sets is not enough to
ensure feasibility, so the 𝜌 value should increase. For the above two situations, the 𝜌
value is updated accordingly, and the search process is repeated. The last possible
situation is that there is zero margin for a constraint in some crude feed scenario. In
this case, the 𝜌 value gives the most optimization potential while keeping all
constraints within their bounds for all crude feed scenarios. Therefore, the search
process stops.
ρ = ρ + 0.01
Any constraint
violated
constraint status
ρ = 1.00
ρ = ρ - 0.01
All constraints
have margins
in all scenarios
Solve robust models for
each crude feed scenario
Calculate constraint values
under optimal conditions
for each scenario
Zero margin for any constraint
Optimal ρ
Figure 2. Search universal 𝜌 values.
15
3.3. The individual 𝜌 method
The universal 𝜌 method stops searching when one constraint is found having no
margin for at least one crude feed scenario. However, other active robust constraints
may still have margins for all crude feed scenarios and their conservativeness can be
further reduced. The individual 𝜌 method tries to finely tune individual 𝜌 values for
each active robust constraint.
The individual 𝜌 method starts with the best 𝜌 value found by the universal 𝜌
method. First, active robust constraints are identified from the universal 𝜌 search.
Then, these constraints are checked whether still having margins for all crude feed
scenarios. For each active robust constraint having margins for all scenarios, the
corresponding 𝜌 value is reduced until the constraint has zero margin for at least one
scenario. The procedure is looped over all active robust constraints having margins for
all crude feed scenarios until no such constraint can be found.
16
Zero margin
for all active
constraints?
Optimal
universal ρ
No
Identify
active robust constraints
in universal ρ solutions
Calculate margins
for each active constraint
Yes
Optimal individual
ρ values
For each constraint j having margins
ρj = ρj - 0.01
Solve robust models for
each crude feed scenario
Constraint j
zero margin
No
Calculate
constraint margins
ρj
Yes
Figure 3. Search individual 𝜌 values.
3.4. Optimization loss compared to conventional RTO
Robust operational optimization can only achieve less profit increase compared to
conventional RTO. This is because robust operational optimization is more constrained
due to inherent robustness to uncertainty. It is fair because robust operational
optimization uses less information of crude feed TBP data than conventional RTO.
However, profit increase by conventional RTO can be used as a benchmark to compare
different settings for robust operational optimization. In this work, optimization losses
of robust operational optimization are used to compare different types of uncertainty
sets and 𝜌 values:
Optimization loss = ProfitRTO − ProfitRobust (21)
where ProfitRTO is the optimal profit obtained by conventional RTO assuming crude
17
feed TBP data are known. ProfitRobust is the optimal profit obtained by robust
operational optimization. The loss is always positive. The smaller optimization loss is,
the better robust operational optimization performs.
4. Case study
4.1. Case description
The crude oil distillation system studied in Chapter 5 is used to compare different
settings of robust operational optimization. Figure 4 and 5 illustrate the flowsheet of
the crude oil distillation system and its associated heat exchanger network (HEN),
respectively. The crude feed is cut into naphtha, kerosene, diesel, atmospheric gas oil
(AGO) and residue.
Furnace
Residue
Off-gas
Naphtha
Diesel
AGO
HEN1
Crude
Steam
Kerosene
HEN2
Desalter
PA1
PA2
PA3
Figure 4. A typical crude oil distillation system. PA: Pump-around.
18
E-101 DesalterE-102 E-103 E-104
Crude
Furnace
Kerosene PA1 Residue
E-105 E-106 E-107 E-108 E-109 E-110
PA2
Diesel
AGO PA3
HEN1 HEN2
Figure 5. Structure of the HEN.
The crude oil distillation system is assumed to process mixture of three different types
of crude oil. It is also assumed that the recipe of the mixture is changing over time and
real-time analysis of TBP curves is not available. Seven crude feed scenarios are
identified from schedule of crude oil operations, listed in Table 1.
Table 1. Predefined crude feed scenarios
Crude 1 Crude 2 Crude 3
API 33.2 29.7 25.6
Sulfur (wt%) 0.37 2.85 0.41
Acidity (mgKOH/g) 0.12 0.11 1.30
Crude feed scenarios (wt%)
1 0.6 0.4 0
2 0.5 0.4 0.1
3 0.4 0.4 0.2
4 0.3 0.4 0.3
5 0.2 0.4 0.4
6 0.1 0.4 0.5
7 0 0.4 0.6
The objective of operational optimization of the system is to increase profit by
manipulating operating variables including throughput, product cut points, furnace
outlet temperature, flowrates of stripping steam and pump-arounds. Four concerned
constraints, including kerosene flash point, furnace duty, condenser duty and desalter
19
inlet temperature, are identified by operating experience and considered in the
optimization. Robust operational optimization models are constructed from data sets
generated from rigorous simulation of the process. Detailed parameters for rigorous
simulation and model generation, including equipment parameters, crude oil TBP data
and prices for computing profit, can be found in Chapter 5.
Uncertain parameters in the robust optimization model are analyzed and their uncertain
intervals are extracted in Chapter 5. Their center and radius values are summarized in
Table 2. Constant parameters in the robust optimization model, i.e., constraint values
of starting operating conditions, are list in Table 3. Bounds for the concerned process
constraints are summarized in Table 4.
20
Table 2. Uncertain parameters
Variables Profit
Kerosene flash
point Furnace duty Condenser duty
Desalter inlet
temperature
Center Radius Center Radius Center Radius Center Radius Center Radius
Throughput 40.592 0.283 0.000 0.000 0.452 0.022 0.240 0.034 -0.055 0.001
Naphtha D86 FBP -67.187 6.173 0.479 0.012 -0.047 0.010 -0.028 0.110 0.172 0.012
Kerosene D86 FBP 104.074 2.772 0.208 0.016 -0.197 0.002 -0.197 0.093 0.097 0.013
Diesel D86 95% 165.417 1.275 0.001 0.003 -0.161 0.030 0.012 0.088 0.120 0.009
Overflash flowrate -55.186 1.422 0.000 0.001 -0.119 0.033 0.005 0.016 0.106 0.003
Furnace outlet
temperature 152.167 21.961 0.033 0.005 1.354 0.054 1.111 0.133 -0.020 0.017
Main stripping steam
flowrate 343.920 63.915 0.122 0.005 1.025 0.038 4.192 0.117 -0.320 0.020
AGO stripping steam
flowrate 250.178 6.408 0.120 0.009 0.592 0.037 4.097 0.237 -0.014 0.019
Diesel stripping steam
flowrate 48.486 1.662 0.201 0.009 0.588 0.015 4.333 0.098 -0.423 0.017
Kerosene reboiler duty -15.996 11.381 0.072 0.027 -0.022 0.036 -0.075 0.473 0.192 0.030
Pump-around 1 flowrate 0.142 0.037 0.000 0.000 -0.006 0.001 -0.019 0.008 0.018 0.001
Pump-around 2 flowrate 0.142 0.044 -0.001 0.001 -0.025 0.003 -0.029 0.014 0.013 0.001
Pump-around 3 flowrate 0.456 0.056 -0.002 0.000 -0.057 0.005 -0.059 0.007 0.003 0.000
21
Table 3. Constraint values under starting operating conditions
Crude feed
scenarios
Kerosene
flash point Furnace duty
Condenser
duty
Desalter inlet
temperature
1 52.4 209.7 139.5 128.2
2 52.5 206.2 135.0 129.6
3 52.5 202.7 130.1 130.9
4 52.5 199.5 123.0 132.1
5 52.7 195.6 121.1 133.7
6 52.8 192.1 116.0 135.1
7 52.8 188.6 111.2 136.5
Table 4. Concerned process constraints
Variables Lower bound Upper bound
Kerosene flash point 38.0 °C -
Furnace duty - 210.0 GJ/h
Condenser duty - 124.0 GJ/h
Desalter inlet temperature 125.0 °C 140.0 °C
4.2. Results for the universal 𝜌 method
The robust counterparts of the robust operational optimization models are coded in
General Algebraic Modeling System (GAMS) environment [17] and solved by the
CONOPT solver. The universal 𝜌 method is first applied to the case study. The best
universal 𝜌 values found for box, ball and polyhedral uncertainty sets are 0.26, 1.03
and 2.36, respectively. Figure 6 illustrates average optimization losses of the seven
crude feed scenarios for the three types of uncertainty sets. For the box uncertainty set,
the starting value 𝜌 = 1 gives a very conservative result with average optimization
loss 532 USD/h. The universal 𝜌 method cuts the optimization loss by 66% to 180
USD/h. While for ball and polyhedral uncertainty sets, the starting value 𝜌 = 1
cannot guarantee feasibility for all crude feed scenarios. Hence, the universal 𝜌
method increases their 𝜌 values. Comparing the three uncertainty sets, the box
uncertainty set has the smallest optimization loss, followed by the ball uncertainty set.
22
The polyhedral uncertainty set gives the largest optimization loss, 77% more loss than
the box uncertainty set.
Figure 6. Average optimization losses for the universal 𝜌 method.
The reason for their different performance is revealed by analysis of active robust
constraints. The three uncertainty sets all identify condenser and furnace capacities as
active robust constraints. However, they have different margin profiles for each crude
feed scenario. Figure 7 shows condenser and furnace duties under robust optimal
operations.
For condenser duties, scenario 5 has zero margin for all three types of uncertainty sets.
For other crude feed scenarios, there are still margins between constraint values and
the bound. Among the three types of uncertainty sets, the box uncertainty set presents
less margins than the other two. By contrast, the polyhedral uncertainty set has the
largest margins. The phenomena are also observed for furnace duty. Therefore, the box
uncertainty set can give more profit increase compared to the other two thanks to its
tight margin profiles.
532
180219 224
165
319
ρ = 1.00 ρ = 0.26 ρ = 1.00 ρ = 1.03 ρ = 1.00 ρ = 2.36
Box Ball Polyhedral
Avera
ge lo
ss, $/h
23
Figure 7. Active robust constraints for the universal 𝜌 method.
4.3. Results for the individual 𝜌 method
In Figure 7, furnace duties have margins in all crude feed scenarios. It indicates the 𝜌
values over-protect feasibility against uncertainty for furnace duty. However, they
cannot be further reduced by the universal 𝜌 method due to condenser duties having
zero margin. This shows the potential for the individual 𝜌 method to give further
improvement.
The individual 𝜌 method is applied to finely tune 𝜌 values. Table 5 shows finely
tuned individual 𝜌 values. The 𝜌 values for furnace duty can be significantly
reduced for all three uncertainty sets. Another interesting result is that 𝜌 values for
116
117
118
119
120
121
122
123
124
1 2 3 4 5 6 7
Condenser
duty
, G
J/h
Scenario
Worst
Box (ρ = 0.26)
Ball (ρ = 1.03)
Polyhedral (ρ = 2.36)
207.0
207.5
208.0
208.5
209.0
209.5
210.0
1 2 3 4 5 6 7
Fu
rnace d
uty
, G
J/h
Scenario
Worst
Box (ρ = 0.26)
Ball (ρ = 1.03)
Polyhedral (ρ = 2.36)
24
condenser duty can also be further reduced by the individual 𝜌 method. This indicates
tuning 𝜌 values for one constraint may also affect other constraints.
Table 5. Individual 𝜌 values
Constraints Box Ball Polyhedral
Kerosene flash point 0.26 1.03 2.36
Furnace duty 0.05 0.13 0.15
Condenser duty 0.25 0.95 1.58
Desalter inlet temperature 0.26 1.03 2.36
Figure 8 shows average optimization losses for the individual 𝜌 method.
Optimization losses of the three types of uncertainty sets can all be cut by finely tuning
individual 𝜌 values. The box uncertainty set releases 13% more optimization
potential. The ball and polyhedral uncertainty sets cut 19% and 30% of optimization
losses, respectively.
Figure 8. Average optimization losses for the individual 𝜌 method.
Most of the optimization loss cut comes from tightening furnace duty margins. Figure
9 shows that after finely tuning individual 𝜌 values, all three uncertainty sets have
smaller margins compared with the tightest margin profile (box) in the universal 𝜌
value group. While for condenser duty, margins for the box uncertainty set are slightly
180 224 319157 180 222
13%
19%
30%
0%
5%
10%
15%
20%
25%
30%
35%
0
50
100
150
200
250
300
350
Box Ball Polyhdral
Universal Individual Improvement
25
reduced. Condenser duty margins for the ball and polyhedral uncertainty sets are also
tightened. However, they still have wider margins than the box uncertainty set in the
universal 𝜌 value group.
Figure 9. Active robust constraints for the individual 𝜌 method.
5. Conclusions
This paper investigates performance of robust operational optimization for different
types of uncertainty sets and presents two methods to help balance optimality and
robustness by searching for appropriate 𝜌 values. The case study for a typical crude
oil distillation system shows that box, ball and polyhedral uncertainty sets have
different performance. Among the three, the box uncertainty set achieves the smallest
117
118
119
120
121
122
123
124
1 2 3 4 5 6 7
Condenser
duty
, G
J/h
Scenario
WorstBox IndividualBall IndividualPolyhedral IndividualBox Universal
208.9
209.1
209.3
209.5
209.7
209.9
1 2 3 4 5 6 7
Fu
rnace d
uty
, G
J/h
Scenario
WorstBox IndividualBall IndividualPolyhedral IndividualBox Universal
26
optimization loss by both the universal and individual 𝜌 methods. The polyhedral
uncertainty set has the largest optimization loss. The box uncertainty set has 44% and
29% less optimization loss compared to the polyhedral uncertainty set by the universal
and induvial 𝜌 methods, respectively. The reason for different behaviors of the three
is that the box uncertainty set has tighter margin profiles than the other two for active
robust constraints.
The case study also shows that both the universal and individual 𝜌 methods can
effectively help reduce optimization loss for robust operational optimization. In the
case study, the universal 𝜌 method cuts optimization loss by 66% for the box
uncertainty set. Finely tuning individual 𝜌 values can give further improvements. The
individual 𝜌 method reduces optimization loss by 13%, 19% and 30% for the box,
ball and polyhedral uncertainty sets, respectively.
27
Acknowledgements
The first author would like to acknowledge the financial support for the research
program from Mr Shibo Wang and Process Integration Limited.
28
Blank page
29
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51
7. Conclusions and Future Work
7.1. Conclusions
7.1.1. Philosophy of using limited information in operational
optimization
In this work, two types of methods are proposed for operational optimization of crude
oil distillation systems with limited information of crude feed TBP curves. The two
types of methods have different philosophies of utilizing information in the procedure
of operational optimization. Figure 7.1 compares the two types of methods.
Limited
Information
Quality of
Information
Information used
Investment
EstimationUncertainty
Robust Operational
Optimization
Real-time
Optimization
Conservative
Robust
No potential loss
Risk of bad
estimation
Accurate
Expensive
Figure 7.1. Comparison of different philosophies of using limited information in
operational optimization.
The first type of method, real-time optimization, tries to use more amount of
information during operational optimization by parameter estimation. Since more
52
information is used, better decision-making results can be theoretically expected.
However, since the quality of information is not fundamentally improved by
investment in hardware, there are risks of worse operating conditions or infeasible
operations caused by bad parameter estimation.
The second type of method, robust operational optimization, tries to use less amount
of information during operational optimization and treat limited information as
uncertainty. Since less information is used, loss of optimization potentials is
theoretically expected compared to real-time optimization with perfect knowledge of
crude feed TBP information. However, conservative decision-making results provide
safeguard against the assumption of perfect parameter estimation implied by real-time
optimization.
Robust Operational
Optimization
Real-time
Optimization
Low-risk
Optimization
Potentials
High-
risk
Figure 7.2. Risk grading of operational optimization potentials with limited
information.
In summary, when there is no budget for investment in improving quality of
information, there is a trade-off between loss of optimization potentials and risks of
optimization. Two levels of operational optimization potentials can be graded based
on their risk exposure to inaccurate parameter estimation, see Figure 7.2. Robust
operational optimization aims at low-risk optimization potentials. Real-time
optimization aims at both low-risk and high-risk optimization potentials.
53
The high-risk optimization potentials are dropped by robust operational optimization
at a cost of protection for inaccurate parameter estimation. From the case study in
Chapter 5, about two percent of total optimization potentials can be graded as high-
risk potentials and are lost by robust operational optimization. Based on the case study
in Chapter 6, more than half of the two percent loss can be further saved by careful
design of the size and the shape of uncertainty sets. In addition, the amount of
uncertainty considered in robust operational optimization is determined by how much
information can be obtained from scheduling of crude oil operations. Improvement of
scheduling of crude oil operations can help to reduce the amount of uncertainty and
loss of optimization potentials.
Robust operational optimization and real-time optimization are not competing
methods. In fact, robust operational optimization can be considered as a method to
freely choose the sweet spot between optimization potentials and risks based on risk
appetite of decision makers in different refineries.
7.1.2. Mechanisms for reacting to crude feed changes
Limited information of crude feed TBP curves is a result of unavailability of fast and
reliable crude oil analysis tools and frequent changes of crude feedstocks in many
refineries. A direct consequence of such a situation is that decision-making of
operational optimization has long lag time and cannot keep pace with changes of crude
feedstocks. Both real-time optimization and robust operational optimization proposed
in this work can overcome the long lag time, but in different ways.
Real-time optimization reduces the long lag time by real-time estimation. The
estimation is based on the assumption of mass balance of crude oil distillation columns.
Two pieces of information are used during the estimation, product flowrate
measurements and product laboratory analysis. Product flowrate measurements are
54
usually available in real time, while product laboratory analysis is usually carried out
every few hours in refineries. Therefore, the reconstructed crude TBP curves are not
strictly up to date. However, product specifications do not change frequently unless
operating modes shift. Hence, real-time estimation from mass balance is reliable in
most situations.
Model updates of real-time optimization are triggered after crude feed changes are
detected. The first method to update models requires dozens of runs of rigorous models
to calculate slopes, which does not take long time. The second method to update
models requires to search similar crude feedstocks in historical database and regress
linear models, which also does not take long time. Therefore, the whole estimation and
model updates procedure can reduce long lag time caused by conventional TBP
analysis procedure.
Robust operational optimization reduces the long lag time by reducing the amount of
real-time information required by operational optimization. Only the current states of
constraints are required in real time by robust operational optimization, which can be
easily read or calculated from plant measurements. Real-time crude feed TBP curves
are not required. Instead, only a range of possible crude feed scenarios are required,
which can be obtained from schedule of crude oil operations.
The two pieces of information in robust optimization models are updated in different
frequencies. Certain parameters, which are the current states of constraints, are updated
in real time from plant measurements. Uncertain parameters, which represents the
range of possible crude feed scenarios, are updated when new schedule of crude oil
operations is made, usually on a weekly basis. Therefore, updates of robust
optimization models can also reduce long lag time caused by conventional TBP
analysis procedure.
55
7.1.3. Strength and weakness of simplified linear models and
robust linear models
In this work, simplified linear models and robust linear models are used for operational
optimization. They have several advantages compared to rigorous models and other
nonlinear models:
(1) Simplicity and easy maintenance: Linear models are obviously simpler and
easier to understand than nonlinear models. Due to its simplicity, its
maintenance reduces burdens of technicians to understand a lot of algorithmic
and statistical background required by rigorous and advanced data-driven
models, which is a practical advantage for low-budget refineries.
(2) Convexity: Convexity of optimization models can guarantee global optimums.
Simplified linear models and robust counterparts of robust linear models, have
the advantage of convexity. On the contrary, nonlinear process models cause
the overall optimization models to be nonconvex, and therefore are likely to be
trapped at local optimums and lose optimization potentials.
(3) Robustness: Linear models also have computational tractability when extended
to robust linear models. For nonlinear models, it is difficult to apply the idea
of robust optimization because of the limitation of robust optimization
techniques.
The major weakness of linear models is their accuracy. Chapter 3 shows that linear
models do not lose much accuracy compared with rigorous models. This is possibly
due to the nature of operational optimization. Although first principles indicate that the
process has nonlinear behaviors, they can still be well approximated by linear models
because operating variables can only change in relatively small intervals in practical.
Moreover, in the situation of limited information, reliable parameter estimation can
56
not be taken for granted. Considering inaccurate parameter estimation, comparison of
accuracies of linear and more complex nonlinear models is still an open question.
7.2. Future work
Some open questions and weaknesses of this work can be further investigated in future
work:
(1) Real-time estimation of crude feed TBP curves is based on mass balance of
crude oil distillation columns in this work. The information of crude feed TBP
curves may also be implied by plant measurements of column temperatures,
pressures and flowrates. If plant measurements can provide sufficient
information, soft sensors of crude feed TBP curves can be constructed by data-
driven methods like ANNs.
(2) Regarding the work of Chapter 3, model updates from rigorous models require
online runs of rigorous simulations, which is not always reliable. Methods to
move online runs of rigorous simulations to offline preparation of a rigorous
simulation database can be studied to reduce risks of online convergence
failures and time of model updates.
(3) Regarding the work of Chapter 4, it assumes identified historical operating data
have a good coverage of various operating conditions. However, it may not be
true in real plants. Therefore, a systematic method to measure the quality of
coverage should be considered. Moreover, if the coverage is poor, methods for
data augmentation from rigorous simulation are needed.
(4) Robust operational optimization in this work only uses information from
schedule of crude oil operations. However, new information of crude feed TBP
57
curves is revealed by real-time plant measurements. How to use information
from plant measurements to further reduce uncertainty in crude feed TBP
curves can be studied.
(5) Comparison of accuracies of linear and more complex nonlinear models
considering the effects of limited information and inaccurate parameter
estimation can be studied.
58
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59
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Appendix A. Description and Screenshots of
Rigorous Simulation in Aspen HYSYS
The atmospheric tower and its associated HEN are simulated in Aspen HYSYS v8.8.
Figure A.1 shows a screenshot of the whole Aspen HYSYS simulation environment.
Figure A.1. A screenshot of the whole Aspen HYSYS environment.
Figure A.2 and A.3 show screenshots of Connections and Monitor tabs for the
atmospheric tower, respectively.
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Figure A.2. A screenshot of column connections tab.
Figure A.3. A screenshot of column monitor tab.
Figure A.4 shows a screenshot of the HEN arrangement.
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Figure A.4. A screenshot of the HEN arrangement.
Each heat exchanger is simulated in rating mode with UA specified. Figure A.5 and
A.6 show screenshots of Parameters and Specs tabs of E-101, respectively.
Figure A.5. A screenshot of heat exchanger Parameters tab.
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Figure A.6. A screenshot of heat exchanger Specs tab.
The economic performance of the crude oil distillation system is calculated in a
HYSYS spreadsheet, shown in Figure A.7.
Figure A.7. A screenshot of the economic spreadsheet.
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Appendix B. Python Scripts
B.1. Link Python to Aspen HYSYS
def get_design_vars(hysys_case):
"""
Define design variables, their units and bounds, and then get
connection to them in the Hysys simulation.
"""
cdu_cfs = hysys_case.Flowsheet.Operations.Item('T-100').ColumnFlowsheet
raw_crude_str = hysys_case.Flowsheet.MaterialStreams.Item('Raw Crude')
cdu_feed_str = hysys_case.Flowsheet.MaterialStreams.Item('CDU Feed')
diesel_steam_str = hysys_case.Flowsheet.MaterialStreams.Item('Diesel
Steam')
ago_steam_str = hysys_case.Flowsheet.MaterialStreams.Item('AGO Steam')
main_steam_str = hysys_case.Flowsheet.MaterialStreams.Item('Main
Steam')
# Throughput
throughput = {'name': 'Throughput',
'link': raw_crude_str.MassFlow,
'unit': 'tonne/h',
'lb': 540,
'ub': 660}
# Mass balance: cutting points
naphtha_fbp = {'name': 'Naphtha FBP',
'link': cdu_cfs.Specifications.Item('Naphtha FBP').Goal,
'unit': 'C',
'lb': 165,
'ub': 175}
kerosene_fbp = {'name': 'Kerosene FBP',
'link': cdu_cfs.Specifications.Item('Kero FBP').Goal,
'unit': 'C',
'lb': 235,
'ub': 245}
diesel_95 = {'name': 'Diesel 95%',
'link': cdu_cfs.Specifications.Item('Diesel 95%').Goal,
'unit': 'C',
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'lb': 355,
'ub': 365}
overflash = {'name': 'Overflash flow',
'link': cdu_cfs.Specifications.Item('Overflash Flow').Goal,
'unit': 'tonne/h',
'lb': 12,
'ub': 20}
# Heat inputs and steam injections: bottom-up
furnace_t = {'name': 'Furnace outlet T',
'link': cdu_feed_str.Temperature,
'unit': 'C',
'lb': 355,
'ub': 365}
main_steam = {'name': 'Main steam',
'link': main_steam_str.MassFlow,
'unit': 'tonne/h',
'lb': 3,
'ub': 9}
ago_steam = {'name': 'AGO steam',
'link': ago_steam_str.MassFlow,
'unit': 'tonne/h',
'lb': 0.5,
'ub': 1.5}
diesel_steam = {'name': 'Diesel steam',
'link': diesel_steam_str.MassFlow,
'unit': 'tonne/h',
'lb': 1,
'ub': 6}
kerosene_duty = {'name': 'Kerosene reboiler duty',
'link': cdu_cfs.Specifications.Item('Kero Reb
Duty').Goal,
'unit': 'GJ/h',
'lb': 0.2,
'ub': 0.8}
pa1_rate = {'name': 'PA1 rate',
'link': cdu_cfs.Specifications.Item('PA_1_Rate(Pa)').Goal,
'unit': 'm3/h',
'lb': 320,
'ub': 480}
pa2_rate = {'name': 'PA2 rate',
'link': cdu_cfs.Specifications.Item('PA_2_Rate(Pa)').Goal,
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'unit': 'm3/h',
'lb': 240,
'ub': 360}
pa3_rate = {'name': 'PA3 rate',
'link': cdu_cfs.Specifications.Item('PA_3_Rate(Pa)').Goal,
'unit': 'm3/h',
'lb': 200,
'ub': 300}
design_vars = [throughput, naphtha_fbp, kerosene_fbp, diesel_95,
overflash, furnace_t, main_steam, ago_steam, diesel_steam, kerosene_duty,
pa1_rate, pa2_rate, pa3_rate]
return design_vars
B.2. Get current operating conditions in simulation
def get_current_values(design_vars):
"""
This function returns the current operating values as a list.
"""
current_values =
[design_vars[k]['link'].GetValue(design_vars[k]['unit'])
for k in range(len(design_vars))]
return current_values
B.3. Get values of objective function in simulation
def get_obj_cons(hysys_case, hen=0):
"""
Get the values of the objective function and constraints as a list.
If 'hen' is 0, only information of the column is retrieved. And if
'hen' is 1, information of the HEN is also returned.
The function returns a list as follows:
[objective, constraint 1, constraint 2, ..., constraint n]
[profit, furnace duty, condenser duty, kerosene flash point, [desalter
74
T]]
If the column is not converged, all values are set to -999.
"""
cdu_cfs = hysys_case.Flowsheet.Operations.Item('T-100').ColumnFlowsheet
spreadsheet_ss = hysys_case.Flowsheet.Operations.Item('ColEco')
crude_duty_str = hysys_case.Flowsheet.EnergyStreams.Item('Crude Duty')
atmos_cond_str = hysys_case.Flowsheet.EnergyStreams.Item('Atmos Cond')
if cdu_cfs.CfsConverged:
profit = spreadsheet_ss.Cell(7, 10).CellValue
crude_duty = crude_duty_str.HeatFlow.GetValue('GJ/h')
cond_duty = atmos_cond_str.HeatFlow.GetValue('GJ/h')
kero_flash_point = spreadsheet_ss.Cell(1, 13).CellValue
obj_cons = [profit, crude_duty, cond_duty, kero_flash_point]
if hen == 1:
q_trim = hysys_case.Flowsheet.EnergyStreams.Item('Q-Trim')
t_desalter =
hysys_case.Flowsheet.MaterialStreams.Item('4').Temperature
obj_cons[1] += q_trim.HeatFlow.GetValue('GJ/h')
obj_cons.append(t_desalter.GetValue('C'))
else:
if hen == 1:
obj_cons = [-999] * 5
else:
obj_cons = [-999] * 4
return obj_cons
B.4. Get duties of pump-arounds
def get_pa_duties(hysys_case):
"""
This function returns pump-around duties calculated from HEN as a list:
[PA1 duty, PA2 duty, PA3 duty]
"""
hx_pa1 = hysys_case.Flowsheet.Operations.Item('E-102')
hx_pa2 = hysys_case.Flowsheet.Operations.Item('E-105')
hx_pa3 = hysys_case.Flowsheet.Operations.Item('E-109')
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pa_duties = []
pa_duties.append(hx_pa1.Duty.GetValue('GJ/h'))
pa_duties.append(hx_pa2.Duty.GetValue('GJ/h'))
pa_duties.append(hx_pa3.Duty.GetValue('GJ/h'))
return pa_duties
B.5. Converge column and HEN pump-around duties
def converge_cdu_hen(hysys_case):
"""
This function converges the simulation of the CDU and HEN. Pump-around
duties are sent back to the column until convergence.
"""
cdu_cfs = hysys_case.Flowsheet.Operations.Item('T-100').ColumnFlowsheet
pa1_duty = cdu_cfs.Specifications.Item('PA_1_Duty(Pa)').Goal
pa2_duty = cdu_cfs.Specifications.Item('PA_2_Duty(Pa)').Goal
pa3_duty = cdu_cfs.Specifications.Item('PA_3_Duty(Pa)').Goal
duty_error = 1
while duty_error > 0.05:
duty_hen_0 = get_pa_duties(hysys_case)
hysys_case.Solver.CanSolve = False
pa1_duty.SetValue(- duty_hen_0[0], 'GJ/h')
pa2_duty.SetValue(- duty_hen_0[1], 'GJ/h')
pa3_duty.SetValue(- duty_hen_0[2], 'GJ/h')
hysys_case.Solver.CanSolve = True
if not cdu_cfs.CfsConverged:
cdu_cfs.Reset()
cdu_cfs.Run()
if cdu_cfs.CfsConverged:
duty_hen_1 = get_pa_duties(hysys_case)
duty_error = abs(duty_hen_1[0] - duty_hen_0[0]) + \
abs(duty_hen_1[1] - duty_hen_0[1]) + \
abs(duty_hen_1[2] - duty_hen_0[2])
else:
print('Convergence of Col&Hen failed: ' + hysys_case.FullName)
break
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return None
B.6. Generate random samples
def generate_samples(hysys_file, hen=0, number_of_samples=100):
"""
Generate random samples within operating bounds.
If 'hen' is 0, only information of the column is retrieved. And if
'hen' is 1, information of the HEN is also recorded.
The coordinate profiles are kept in the following csv file.
random_samples.csv
format:
values of design variables, values of objective function and
constraints
"""
try:
os.remove('random_samples.csv')
except FileNotFoundError:
pass
hysys_app = win32com.client.Dispatch('Hysys.Application')
hysys_case = hysys_app.SimulationCases.Open(hysys_file)
hysys_case.Visible = True
design_vars = get_design_vars(hysys_case)
initial_values = get_current_values(design_vars)
cdu_cfs = hysys_case.Flowsheet.Operations.Item('T-100').ColumnFlowsheet
if hen == 1:
pa1_duty = cdu_cfs.Specifications.Item('PA_1_Duty(Pa)').Goal
pa2_duty = cdu_cfs.Specifications.Item('PA_2_Duty(Pa)').Goal
pa3_duty = cdu_cfs.Specifications.Item('PA_3_Duty(Pa)').Goal
pa1_base = pa1_duty.GetValue('GJ/h')
pa2_base = pa2_duty.GetValue('GJ/h')
pa3_base = pa3_duty.GetValue('GJ/h')
for k in range(number_of_samples):
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cdu_cfs.Reset()
random_values = []
for i in range(len(design_vars)):
coordinate = design_vars[i]
c_link = coordinate['link']
c_unit = coordinate['unit']
c_lb = coordinate['lb']
c_ub = coordinate['ub']
c_random = random.uniform(c_lb, c_ub)
random_values.append(c_random)
c_link.SetValue(c_random, c_unit)
cdu_cfs.Run()
if cdu_cfs.CfsConverged and hen == 1:
converge_cdu_hen(hysys_case)
with open('random_samples.csv', 'a', newline='') as csv_file:
if cdu_cfs.CfsConverged:
csv_row = random_values + get_obj_cons(hysys_case, hen=hen)
+ get_product_rates(hysys_case) + get_bpdata(hysys_case)
else:
if hen == 1:
csv_row = random_values + [-999] * 5
else:
csv_row = random_values + [-999] * 4
csv_writer = csv.writer(csv_file, delimiter=',')
csv_writer.writerow(csv_row)
cdu_cfs.Reset()
for i in range(len(design_vars)):
coordinate = design_vars[i]
c_link = coordinate['link']
c_unit = coordinate['unit']
c_link.SetValue(initial_values[i], c_unit)
if hen == 1:
pa1_duty.SetValue(pa1_base, 'GJ/h')
pa2_duty.SetValue(pa2_base, 'GJ/h')
pa3_duty.SetValue(pa3_base, 'GJ/h')
cdu_cfs.Run()
hysys_case.Save()
hysys_case.Close()
hysys_app.Quit()
return None
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