1

Pyosyn – flexible platform for conceptual designIgnacio Grossmann, Qi Chen

IDAES Stakeholder Meeting, May 16, 2019

Why Conceptual Design?

▪ Determine optimal process configuration

• Given inputs and desired outputs

▪ Answer strategic process investment questions:

• What process flowsheet should we select for the new new facility or plant?

• Is this new process technology worth our investment?

• How can we overcome process bottlenecks?

2

Motivations for Conceptual Design

Process Intensification

▪ Intensification is “any

chemical engineering

development that leads to a

substantially smaller,

cleaner, and more energy-

efficient technology” [1]

▪ Prominent examples:

• Reactive distillation

• Dividing wall columns

• Rotating packed bed

• Microreactors

Traditional

▪ Competitive advantage

through cost-effective design

▪ Increased production rate

▪ Guide research and

development towards

maximum impact directions

Modular Manufacturing

▪ Modular design involves

partition of the system into

multiple easily

interconnected, self-

contained units (skids)

• “Numbering up” instead of

scaling up

▪ Main benefits:

• Reduced investment risk

• Improved time to market

• Increased flexibility

• Improved safety

• Reduced on-site construction

[1] Stankiewicz & Moulijn, 2000

Process Design Studies – Status Quo

3

• Extensive search space ✓

• Realize synergies between processes ✓

• Simple input/output models

• Performance prediction maybe erroneous

• No commercial tool; mostly academic

Techno-economic Studies

• Detailed steady-state models ✓

• Reasonable cost estimates ✓

• Not extensive, case by case analysis

• Difficult to realize synergistic advantages

• More a sensitivity study

Validate design

Update model

Conceptual Design Studies

I

II

I

II

III

IV

I

II

III

4

Need for Automated Computational Tools

Evaluating process alternatives

State of the art

▪ Trial and error in commercial simulators

▪ Heuristic rules of thumb (e.g. PROSYN) [1]

Industry

Conceptual Design

[1] Schembecker et al., 1994

𝟐𝟒 = 𝟏𝟔 flowsheets

Can optimize Superstructure to avoid enumeration

Commercial process simulators

5

Superstructure-based Conceptual Design

3. Solve synthesis problem

▪ Solve mathematical program

to obtain optimal flowsheet

configuration and operating

conditions

• Equipment selection and

interconnection

• Flows, temperatures,

pressures

▪ Various commercial and

academic solver codes

available

1. Define process alternatives

▪ Postulate a superstructure

which represents all

practical alternatives

• Existing, proposed,

and/or hypothetical

process technologies

2. Symbolic-algebraic representation

▪ Formulate an mathematical

model that captures the

design problem logic

▪ Normally a mixed-integer

nonlinear programming

(MINLP) or generalized

disjunctive programming

(GDP) problem

min 𝑍 = 𝑓 𝑥, 𝑦

s.t. ℎ 𝑥, 𝑦 = 0

𝑔 𝑥, 𝑦 ≤ 0

𝑥 ∈ 𝑋, 𝑦 ∈ 0,1 𝑚

( )

Ω

,0)(

0)(

)(min

1

falsetrue,Y

Rc,Rx

trueY

K k

γc

xg

Y

Jj

xs.t. r

xfc Z

jk

k

n

jkk

jk

jk

k

kk

=

=

+=

6

Challenges/barriers

There is no commercial software for synthesis

Only academic codes, some prototypes PROSYN [1], ICAS [2], MIPSYN [3]

Lack of robustness of nonlinear optimization (NLP, MINLP)

Difficulties with convergence:

Good initialization required; zero flows cause singularities; nonconvexities

give rise to local optima

However significant progress has been made

Synthesis tools require expert users

How to postulate superstructure? How to develop best computational strategy?

Unclear how to address Process Intensification, Modular Design

Increased demand for synthesis of new flowsheets

Shale gas revolution => many new plants in US

325 projects announced since 2010 $194 billion (American Chemistry Council)

New driving force

7

Pyosyn – Conceptual Design in IDAES

IDAES Framework

Pyosyn

process synthesis

ALAMO (data →thermodynamics)

RIPE (data → kinetics)

IDAES Model Library (standard unit models)

Detailed simulation

Visualization

Dynamic optimization

8

Pyosyn central principles

▪ Intuitive modeling contexts

– Generalized Disjunctive Programming (GDP)

• Prototype logical expression system

• Implication, Equivalence

– Pyomo.Network

▪ Flexible solution approaches

– MINLP reformulation

– Logic-based decomposition algorithms

– Logic-based relaxation tightening (basic steps)

Ports figure adapted from Menezes et al., 2015

9

Example: Kaibel column conceptual design

▪ Intensified distillation column

– One column shell, 4 product separations

– Variant of the dividing wall column

▪ Objectives:

– Attain product quality specifications

– Minimize capital and operating costs

• Total annualized cost

▪ Major design decisions:

– Number of trays in each section

– Feed tray selection

– Product (R1, R2) tray selection

– Reboiler and condenser duties

– Liquid/vapor distributor ratios (fixed)

▪ Steady state tray-by-tray MESH model

– Mass balance, equilibrium, summation

(conservation), enthalpy (H) balances

Figure from Rawlings et al., 2019

For up to 58 trays

42 million combinations

of feed and products tray location

10

Superstructure column distillation model

Condenser Tray

(permanent)

Rectification Trays

(conditional)

Feed Tray

(permanent)

Stripping Trays

(conditional)

Reboiler Tray

(permanent)Heavy Product

Feed

Light

Product

}

-OR-

-OR-

-OR-

-OR-

}Vapor Flow

Liquid Flow

Equilibrium Stage

Non-equilibrium Stage

•Permanent and conditional trays:

MESH equations for condenser,

reboiler and feed trays

Mass & energy balances for

rectification and stripping trays.

•Conditional trays only:

Use disjunctions as modeling tool

If Yn=True apply VLE constraints

OR Yn=False NO VLE

Disjunctions for existence/absence of conditional trays

11

Kaibel column conceptual design

▪ Components: Methanol, ethanol, n-propanol,

n-butanol

– 99% purity for each component

▪ GDP model written using Pyomo.GDP

– 5715 constraints

• 2124 nonlinear

– 100 disjunctions

• 3599 variables

– 178 binary

– 3421 continuous

▪ Solved in 639 sec using GDPopt-LOA solver

– Logic-based outer approximation algorithm

– 4 iterations

▪ Resulting design:

– 46 trays (21% reduction vs. base case)

– Dividing wall between 12th and 26th tray

– Feed at 18th tray

– Side outlets at 13th and 22nd trays

ABCD

A

B

C

D

Optimal Design Kaibel Column reduces energy consumption in the reboiler

and condenser by more than 40 % compared to conventional columns

12

Effective Generalized Disjunctive Programming

models for Modular Plant Design

• Maximize Net Present Value (NPV) profit

– Sales revenue

– Raw material costs

– Production costs

– Investment costs (related to facility size)

– Transportation costs (raw materials, products, and modules)

• Discrete decisions

– Selection of sites

– Selection of modules

– Selection of transportation links

• Continuous decisions

– Production levels at each site

– Shipment quantities along each link

GDP -> MINLP (big-M or hull reformulation)

13

Modular standardization

continuous decisions ⟶ discrete decisions

NLP ⟶ MILP

Special structure: rewrite nonlinear relations as mixed-

integer linear

Example: batch processing*

𝐶𝑜𝑠𝑡 =

𝑖

𝛼𝑖𝑆𝑖0.6

If each reactor available in discrete sizes 𝑠1, 𝑠2, 𝑠3,

then we can write

𝐶𝑜𝑠𝑡 =

𝑖,𝑗

𝑘𝑖𝑗𝑦𝑖𝑗

𝑘𝑖𝑗 = 𝛼𝑖𝑠𝑖0.6 constant

𝑦𝑖𝑗 ∈ 0, 1

for all reactors 𝑖 and size options j ∈ {1, 2, 3}Equivalent to basic step with hull reformulation on

disjunction between sizes [3]

*Grossmann et. al., 1992; Voudouris & Grossmann, 1991

Induced linearity reformulation

14

Case study: multiple market capacity expansion

• Given:

– 5 distributed customer markets

– time-varying demand (10 year horizon)

• Optimize:

– Facility locations, size, product shipment quantities/routes

– Minimize system cost to satisfy demand

• Allow relocation of modules between sites

Nonlinear GDP:

2224 variables (718 integer), 1387 constraints, 13 disjunctions

Used big-M reformulation.

MINLP solved in 7s DICOPT solver

via Pyomo-GAMS solver interface and GAMS version 25.1.3.

Demands

Location Markets

15

Case study: multiple market capacity expansion

Results

16

Concluding Remarks

Conceptual design allows the systematic examination of many design alternatives

Superstructure-Modeling-Solution paradigm is the basis of modern conceptual design tools

Progress in representations and discrete/continuous models and algorithms major driver for new tools

Scope can be expanded to process intensification and modular designs

Pyosyn: new unique state-of-the-art IDAES tool can accomplish four points listed above

See poster: Advanced Tools for Conceptual Design (Qi Chen/Michael Bynum)

Disclaimer This presentation was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

idaes.org

We graciously acknowledge funding from the U.S. Department of Energy, Office of Fossil Energy,

through the Crosscutting Research Program and the Advanced Combustion Systems Program.

The IDAES Technical Team: • National Energy Technology Laboratory: David Miller, Tony Burgard, John Eslick, Andrew Lee, Miguel Zamarripa,

Jinliang Ma, Dale Keairns, Jaffer Ghouse, Emmanuel Ogbe, Gary Kocis, Ben Omell, Chinedu Okoli, Richard Newby,

Grigorios Panagakos, Maojian Wang

• Sandia National Laboratories: John Siirola, Bethany Nicholson, Carl Laird, Katherine Klise, Dena Vigil, Michael

Bynum, Ben Knueven

• Lawrence Berkeley National Laboratory: Deb Agarwal, Dan Gunter, Keith Beattie, John Shinn, Hamdy Elgammal,

Joshua Boverhof, Karen Whitenack

• Carnegie Mellon University: Larry Biegler, Nick Sahinidis, Chrysanthos Gounaris, Ignacio Grossmann, Owais Sarwar,

Natalie Isenberg, Chris Hanselman, Marissa Engle, Qi Chen, Cristiana Lara, Robert Parker, Ben Sauk, Vibhav

Dabadghao, Can Li, David Molina Thierry

• West Virginia University: Debangsu Bhattacharyya, Paul Akula, Anca Ostace, Quang-Minh Le

• University of Notre Dame: Alexander Dowling, Xian Gao

17

For more information visit us at: https://idaes.org/

David C. Miller, Ph.D.

Technical Director

David.Miller@NETL.DOE.GOV

19

Pyosyn flexible solution strategies

▪ Vision: write model once, try several solution strategies

GDP model

𝑔1 𝑥 ≤ 0∨

𝑔2 𝑥 ≤ 0

Big-M

HR

Cutting planes

MINLP model𝑔 𝑥, 𝑦 ≤ 0

Basic Step

GDP solvers

MINLP solvers

Model Solution

Model Reformulation Solver

GDP to MINLP reformulations

▪ Standard reformulations to MINLP▪ Big-M Reformulation (BM)

▪ Hull Reformulation (HR)

▪ Advanced reformulations to MINLP▪ Cutting-plane based hybrid BM/HR

reformulation

▪ Single-line automatic model reformulation

20

Pyosyn flexible solution strategies

▪ Vision: write model once, try many solution strategies

GDP model

𝑔1 𝑥 ≤ 0∨

𝑔2 𝑥 ≤ 0

Big-M

HR

Cutting planes

MINLP model𝑔 𝑥, 𝑦 ≤ 0

Basic Step

GDP solvers

MINLP solvers

Model Solution

Model Reformulation Solver

GDP to MINLP reformulations

▪ MindtPy decomposition-based MINLP solver▪ Open source python implementation

▪ Traditional outer approximation

▪ Feasibility Pump

▪ Level-based outer approximation

▪ Interface to commercial solvers▪ Via GAMS

▪ Via AMPL

NEW

NEW

21

Pyosyn flexible solution strategies

▪ Vision: write model once, try many solution strategies

GDP model

𝑔1 𝑥 ≤ 0∨

𝑔2 𝑥 ≤ 0

Big-M

HR

Cutting planes

MINLP model𝑔 𝑥, 𝑦 ≤ 0

Basic Step

GDP solvers

MINLP solvers

Model Solution

Model Reformulation Solver

GDP to MINLP reformulations

▪ GDPopt solver

▪ Logic-based outer approximation

▪ Global logic-based outer approximation

▪ MC++ interface – McCormick envelope computation

▪ Disjunctive range reduction using feasibility-based bounds tightening or optimality-based bounds tightening

▪ GDPbb solver

▪ Nonlinear disjunctive branch and bound

▪ Z3 satisfiability solver interface –infeasible node screening

NEW

NEW

NEW

NEW

NEW

22

Pyosyn flexible solution strategies

▪ Vision: write model once, try many solution strategies

GDP model

𝑔1 𝑥 ≤ 0∨

𝑔2 𝑥 ≤ 0

Big-M

HR

Cutting planes

MINLP model𝑔 𝑥, 𝑦 ≤ 0

Basic Step

GDP solvers

MINLP solvers

Model Solution

Model Reformulation Solver

GDP to MINLP reformulations

▪ Basic step operation▪ Improves linear approximation of GDP

model at expense of model size