Industrial plant optimization in reduced dimensional spaces
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Industrial Plant Optimization in Reduced Dimensional Spaces
Fields Optimization LectureToronto, ON
Giles LaurierJune 4, 2013
Capstone Technology
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Agenda
Review of optimization in oil refining Real Time Optimization Reduced Space Optimization
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Petroleum refining
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Flowsheet
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Refining optimization history
Head office Refining early adopters
(Exxon 1950’s) Crude selection, operating
modes 1961 early SLP paper
(Shell oil) LP not just a fast solution
technique Tools to interpret the solution
and run what-if’s.
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Basic Process Control
Valve
Flow input Controll
er
Output
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Refining optimization history
Refineries Improving process control
Cold
Hot
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Advanced Control
1980’s insight that complicated process control problems could be formulated and solved by LP and QP
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Refining Optimization Hierarchy
Short Term Plan
Advanced Control
Regulatory Control
Operating Objectives, Component Prices, Constraints
Operating Targets
Controller Setpoints
Valve Positions
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Why Optimize in Real Time? Short term planning model based on
“sustainable” average operation But things change.....
Crude oil may be different Processes may be cleaner/more fouled May be hotter/colder
Real process is nonlinear Real time optimization intended to
capture these opportunities
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RTO Approach
Model plant with engineering equations Heat + mass + hydraulic + equilibrium
relationships Run simulation in parallel to the plant
and calibrate to the plant measurements
Optimize the model
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Steady state operation
0)( xf x
Flow, temperatures, pressures, size f(x)
Nonlinear algebraic equations Conservation mass, energy, chemical equilibrium
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Building the simulated plant
)( inii
outi xFx
Block 2
inix out
ixBlock
1
Blocks are solved in the order of material flow
Sequential modular
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Sequential modular
Recycles become awkward and need iterationBlock1 Block2
Block3
Block4 Block5
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Open Equations
Complete plant model expressed in one large set of (sparse) equations
Run it through a nonlinear root solver Encouraged by success in solving non
linear constraints
0)( xf
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Simple still
F zi
V yi
L xi
( 1)0
1 ( 1)
i i
ii
Z KV KF
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Inputs
Need to fix certain variables to reach solution
Plant instruments have error
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Reconciliation
2: ( 100)Min A
2 2 2 2 2A: W ( 100) W ( 50) W (C 28) W (D 35) W ( 43)
subject to :0
0, , , , 0
B C D EMin A B E
A B C DD EA B C D E
A: 100
B: 50C: 28D: 35
E: 43
0)( xf
Find the smallest set of adjustments to the plant measurements that satisfy the equations
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Initial Basis
Offline design software used to fit base case
Results used to provide initial basis for open equations
Thereafter, converged online solutions used as starting basis for next online run
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Optimization engine
Minos Projected augmented Lagrangian
Analytic derivatives Convergence not guaranteed!
Good starting values Sensible bounds Tuning parameters
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Gross error detection
Least squares based reconciliation works well when the measurement s are considered to be normally distributed around their true values with approximately known error
Large errors (eg. instrument failures) violate these assumptions and bias reconciliation
RTO systems include pre-screening to eliminate values obviously in error (Wi=0)
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Optimization
Fix instrument adjustments and other reconciled performance values
Change objective function Maximize Profit: Products - Feed – Utilities New setpoints = Old setpoints ± rate limits
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RTO Sequence
Check recent history to confirm that plant is steady
Eliminate bad measurements Fit model to plant data Calculate new setpoints to
increase profit Check process steady,
controls available
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Technical challenges Solving 20+K non linear equations is
not fool proof 95% convergence failures occurred
during reconciliation phase Could have put more time trying to
make constraints more linear2 21 2
04.814 4.8141 2
... TK K P P
d d
4.8141/i ix dEg: transformations
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Catalytic cracker Ultramar QC ~ 27,500 equations ~ 29,500 variables ~ 111,000 derivatives Reconciliation – 500+ measurements Optimization 60 setpoints Execution – 25-40 minutes/cycle
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Case study – 40KBPD crude unit
Stream Before (KBPD)
After (KBPD)
Change (KBPD)
LSR 2.47 2.51 0.041 Naphtha 5.15 4.91 -.246 Distillate 4.66 5.03 0.368 VLGO 1.1 1.1 0 LVGO 1.33 1.22 -.103 HVGO 7.68 7.6 -.075 Asphalt 13 13.02 0.018 NET PROFIT
$2220/Day
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RTO Benefits
Unit BenefitCrude units $.01- $.05/BBLHydrocracker $.07-$0.3/BBLFCCU 2% unit profitEntire refinery $0.50/BBL (Solomon)
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Doubts and uneaseWas the optimization solution correct?
Stream Before (KBPD)
After (KBPD)
Change (KBPD)
LSR 2.47 2.51 0.041 Naphtha 5.15 4.91 -.246 Distillate 4.66 5.03 0.368 VLGO 1.1 1.1 0 LVGO 1.33 1.22 -.103 HVGO 7.68 7.6 -.075 Asphalt 13 13.02 0.018 NET PROFIT
$2220/Day
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Profit = Product – Energy - PayrollIntuitive answer:
Profit will improve by:
1. Reduce the terms with negative signs
2. Increase the terms with positive
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Online performance
-12-10-8-6-4-20246
20-May 22-May 24-May 26-May 28-May 30-May
Gas Yield
Profit
Yiel
d (%
) & P
rofit
(%)
Liquid Yield
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Optimization geometry
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Constraints
On paper constraints are just a line In real life – people spend their time
avoiding trouble Constraints can be benign or
emotionally charged In RTO, the operators experienced
first hand the simplex method
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PROFIT PATH ANALYSIS
71007200730074007500760077007800790080008100
510 515 520 525 530RISER TEMPERATURE
CH
AR
GE
Tower Flood
Profit = $272k/d
$270k/d
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A drop in the bucket
Oct 28 Feb 05 May 15 Aug 23 Dec 01 Mar 11 1015202530
Crude Oil Price $/BBL
1996
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Behavioural Economics
How emotions and perceptions affect economic decisions
People math ≠ Algebraic math Risk, reward, gains, losses, time are
perceived differently
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Prospect theory - gains and losses
Objective gains
Objective losses
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RTO Path
Feed Max Path
Subjective profit
Objective profit
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Familiarity
Pattern recognition 10,000 hour rule (Gladwell)
Practice makes perfect Value proposition of advanced
control is to imitate the best operator Value proposition of RTO is to seek
out incremental, non-intuitive benefits
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Technology for people
Interactive Familiarity
Cruise control Smart phones
Hidden Out of sight ....
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RTO Approach Rethought
Familiar How best to model a plant?
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Modeling the plant
Fundamental design models? Design:
What are the best arrangements and sizes of equipment to maximize ROI
Operating plant Equipment and capability is fixed Processes must be operated around 70%
of design to break even RTO benefits consistently estimated to
be around 3-5%
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Can we model a plant just from its historical operating data?
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Projection methods (PCA/PLS) Technique to find patterns in sets of
data Linear algebra (singular value
decomposition)T TX UWV TP
1 0
0 n
w
w
VTU=X
m×n
m×n
n×nn×n
VTV = I
UTU = I
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Two dimensional example
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-3
-2
-1
0
1
2
3
1st Principal compo-nentdirection of maxi-mum variation (92%)
2nd Principal componentperpendicular to 1st (8%)
t1
t2
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Projection Methods
PCA Find an optimal (least squares)
approximation to a matrix X using T1..Tk
k<<n PLS
Find a projection that approximates X well, and correlates with Y
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Partial least squares (PLS) Approximate X and Y
T
T
X TP
Y TC
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Happenstance plant data
Number of measurements >> rank (true dimensionality)
Every engineering relationship removes 1 degree of freedom
However operator rules of thumb also remove degrees of freedom
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Projection Model
Models the correlation between variables caused by: Fundamental engineering relationships Operator preferences
This is not the full space It is a subspace within which the
operator is familiar
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Flow example revisited
A
B
C
D E
1 1 1 1 1
2 2 2 2 2
m m m m m
A B C D EA B C D E
A B C D E
Although we have 5 columns, the rank of the matrix =3A = B + C + DD = E
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Latent space optimization
subject to
Xl Y u
T
( , ) c xT tmaximize F x y d y
2
i
i Ti
T Bs
Boundaries of sphere
PCA model (linear)
TX TPTY TC PLS model
(linear)
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Key ideas
First principal models need to be calibrated against the plant Model the plant data directly
Operators don’t like surprises Model the operator
Does it work? Is this optimal?
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Case Study
Chemical company If we expand our feed system, what is
the capacity of the downstream units?
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Flowsheet
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Dimensions and data
70 operator setpoints and valve positions
22 lab analyses 1 year of operating data (hourly
averages)
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PCA analysis results
1 2 3 4 5 6 7 8 9 10111213141516171819202122230
0.10.20.30.40.50.60.70.80.9
1X Variance Explained
Component
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Conclusions
Although there were 70 setpoints… The underlying dimensionality of this
data was much lower With a purely linear model
13 components could explain 90% of the variation
23 components could explain > 97% of the variation Nonlinearity is not significant over the
operating range studied
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Results
Latent space optimization Plant capable of 10% rate increase while
keeping product qualities within specification
Identified bottlenecks (valves wide open) Optimum plausible and familiar
Restricted to “typical” plant envelope Actual
Post audit test run New production record: within 0.2% of
prediction
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Globally optimal?
Probably not Better and feasible
Certainly
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Final thoughts
Optimization math ≠ human math Our ability to make sense of high
dimensional and complicated situations is limitedPolitics is the art of the possible Bismarck