optimal design of reliable integrated chemical production site
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Optimal Design of Reliable Integrated Chemical Production Site
Sebastian Terrazas-MorenoIgnacio E. Grossmann
John M. Wassick
EWO Meeting Carnegie Mellon University
September 2009
In collaboration with The Dow Chemical Company
111
Large scale chemical companies operate integrated chemical complexes for the manufacture of many products
Contents of this slide based on: Wassick , J. M. Computers & Chemical Engineering , 2009
Dow’s Texas Operations (huge chemical complex) manufactures 21% of Dow products sold globally
Motivation
222
Motivation
Population >12,000
~3 miles
Plant B
333Contents of this slide based on: Wassick , J. M. Computers & Chemical Engineering , 2009
These type of sites should deliver their target production capacity in spite of uncertain events (plant outages)
There is a need to develop systematic design methods to optimize the reliability and flexibility of integrated sites
Motivation
444
Goal
Provide a computational tool that:
Optimizes the use of available capital for the design of an Integrated Site
With the objective of:
Maximizing the probability of meeting operational targets consistently
55
An integrated site (IS) is a large network of processes
66
Design challenge: Different uncertainties affect an IS
Uncertain demand
Uncertain Supply
Continuous uncertainties
Plant 1
Plant 2 Plant 4 Plant 5
Plant 3
Intermediate A
Intermediate B
Product C
Intermediate D
IntermediateE
Product F
Plant 1
Plant 2 Plant 4 Plant 5
Plant 3
Intermediate A
Intermediate
B
Product C
Intermediate D
Intermediate
E
Product F
Discrete uncertain events
Plant failure
77
E(SF) useful metric. Interpret as Service Level
Expected stochastic flexibility E(SF)
Probabilistic measure of a system’s ability to tolerate discrete and continuous uncertainties
(1)
(1) Straub D. A., I. E. Grossmann. Computers & Chemical Engineering , 1990
Service level SL
Probability of meeting entire demand (while subject to discrete and continuous uncertainties).
(2)
(2) Gupta A., C. D. Maranas. Computers & Chemical Engineering , 2003
In this problem
E(SF) ≈ Service Level (SL)
88
Parallel production units, intermediate storage and spare production capacity increase service levels
Unit 1I
I2
I3
A C
I1
B
Unit 1II
Unit 2
Unit 3
Plant 1
Plant 2
Plant 3
Unit 1I
I2
I3
A C
I1
B
Unit 1II
Unit 2
Unit 3
Plant 1
Plant 2
Plant 3
Parallel production units
Intermediate Storage
Intermediate Storage Intermediate
Storage
But require extra capital investment
99
Problem statement
Given Determine
Objectives
•The superstructure of an integrated site
•Materials consumed and produced.
•Unit ratios (yield coefficients)
•Supply and demand probability distributions
•Reliability data
•A cost function
• The selection of production units
• Total production capacity of each unit
• Size of intermediate storage
• Average inventory (set point)
Maximize Service Level
Minimize capital investment
Bi-criterion optimization model
101010
Our modeling approach uses a state space representation
P1 P2
A C
B
P3
P1 P2
A C
B
P3
State 2
State 1
P1 P2
A C
B
P3
P1
A C
B
P3
State 4
State 3
P2
The system continuously transitions among states
111111
The following parameters are given for each state
• probs probability associated with each state How likely it is to find a combination of active and failed plants
• tcs cycle time Time interval between successive visits to a state
• frs frequency for visiting each state How often the system enters into a state (visits / unit time)
• mrts mean residence time Average time spent in each state
• vrts variance of residence time Dispersion for time spent in each state in different visits
12
Stochastic flexibility: Ability to operate under cont. uncertainties
P1 P2
A C
B
P3
Uncertain demand of CSupply of A
Stochastic Flexibility (SF) represents area of feasible operation under probability distribution
e.g. SF = 0.67
Demand of C
P
F
13
Expected Stochastic Flexibility E(SF) ≈ Service Level
P1 P2
A C
B
P3
P1 P2
A C
B
P3
State 1
State 2
Define:
prob1: probability of finding system in State 1
SF1 : Stochastic Flexibility in State 1
prob2: probability of finding system in State 2
SF2 : Stochastic Flexibility in State 2
Service Level ≈ E(SF) = prob1SF1 + prob2SF2
Demand of C
F
Demand of C
F
14
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
-10 ton/ hr
1414
Intermediate storage is affected by the sequence and duration of discrete states
The exact inventory levels depend on the sequence of system states
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
2 ton/ hr
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
-10 ton/ hr
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
-10 ton/ hr
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
0 ton/ hr
P1 P2
Capacity 12 ton/ hr
Capacity 10 ton/ hr
0 ton/ hr
15
Each sequence of events results in a trajectory for inventory levels
I(t)In
In
In
In
Probability Distribution of In(Mean & Variance)
VTank Capacity
E[In]0
PDF Decision Variable
Time (t)
1616
Proposed approach: Describe inventory levels as a random variable
I(t)
t 1 2 3 nn - 1
In
X0
0
X1 X3 Xn-1
1
00
n
iin XII
X2
1717
Calculations of inventory set point and required tank size
sSs
ssn mrtfrtIIE
0][
sSs
ssn vrtfrtIVar
2][
S set of discrete states
inventory rate
rt residence time
fr frequency for visiting each state
mrt mean residence time
vrt variance of residence time 0][
][
Sssssn
Sssssn
tfrvrtIE
VtfrvrtIE
1818
A case study adapted from Straub & Grossmann (1990)
Unit 1I
I2
I3
A C
I1
B
Unit 1II
Unit 2
Unit 3
Plant 1
Plant 2
Plant 3
Unit 1I
I2
I3
A C
I1
B
Unit 1II
Unit 2
Unit 3
Plant 1
Plant 2
Plant 3
1919
Problem parameters
Supply of A [103 ton / day] Mean = 12
Stand. Dev = 1
Demand of C [103 ton / day] Mean = 7
Stand. Dev = 1
Probability of operation
Unit 1I 0.95
Unit 1II 0.95
Unit 2 0.92
Unit 3 0.87
Mass balance coefficient 1I=0.92 1II=0.92 2=0.85 3=0.75 Base capacity [103 ton / day] 5 5 7 9 Mean time to repair [day] 0.25 0.25 0.25 0.25 Mean time to failure [day] 4.75 4.75 2.88 1.67
Input (given) data
2020
Results: set of Pareto-optimal solutions
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0 10 20 30 40 50 60Capital Investment [MM USD]
E(SF) SLFix cost of installing a plant 10 MM USDVariable cost for extra plant capacity 1 MM USDVariable cost for storage capacity 1 MM USD
tsLevelService
. max
raintsodel const rest of m
InvestmentCapital
212121
Results: Details of some of the designs in the Pareto-optimal set
I1II1231v2v3v 1inv2inv3inv
Capital Investment =25 MM USDSL = 0.87
P3
I3
A C
B
I1
P1I
P1II
P2
I2
Maximum capacityexpansion
Large storagetank
222222
Results: Details of some of the designs in the Pareto-optimal set
I1II1231v2v3v 1inv2inv3inv
Capital Investment =35 MM USDSL = 0.96
P3
I3
A C
B
I1
P1I
P1II
P2
I2
Small capacityexpansion
Small storagetank
Large capacityexpansion
Large storagetank
232323
Results: Details of some of the designs in the Pareto-optimal set
I1II1231v2v3v 1inv2inv3inv
Capital Investment =45 MM USDSL = 0.98
P3
I3
A C
B
I1
P1I
P1II
P2
I2
Small capacityexpansion
Small storagetank
Small capacityexpansion
Large storagetank
Small capacityexpansion
2424
Summarizing: current capabilities and limitation of the proposed approach
•Mathematical formulation captures the main trade-off between performance (service level) and capital investment.
•The effect of intermediate storage on service level is included.
•A superstructure approach is used for integrated site design
•Algorithmic techniques are required to solve large-scale problems
•Extend model to include schedule maintenance
252525
Acknowledgements
John Wassick, Naoko Akiya, Ramkumar Karuppiah, Scott Bury, and Jee Park from The Dow Chemical Company.
The Dow Chemical Company for providing financial support.
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