optimal design of reliable integrated chemical production site

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




P3

I3

A C

B

I1

P1I

P1II

P2

I2

Small capacityexpansion

Small storagetank

Large capacityexpansion

Large storagetank

232323




P3

I3

A C

B

I1

P1I

P1II

P2

I2


Small storagetank


Large storagetank


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.

optimal design of reliable integrated chemical production site

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