Process Design for Environment: A Multi-objective Framework under Uncertainty

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Process Design for Environment A
Multi-objective Framework under Uncertainty
Yan Fu and Urmila M. Diwekar Carnegie Mellon
University Pittsburgh, PA 15213 Tel
412-268-3003, email urmila_at_cmu.edu Douglas Young
and Heriberto Cabezas National Risk Management
Research Laboratory U.S. Environmental Protection
Agency Cincinnati, OH 45268
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Integrated Approach to Pollution Prevention
Operability Controllability
Environmental Impacts
Environmental Economic Objectives
LCA Considerations
Environmental Control Strategies
Profitability
Process Simulation
Products
Raw Materials
Process Integration Options
Process Synthesis
Chemical Synthesis
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Operations Research
Environmental
Efficient Algorithms Uncertainty
Analysis Optimization Under Uncertainty Fractal
Dimension Approach Multi-objective
Optimization AI Optimization
NOx Reduction Renewable Energy Nuclear Waste
Management Solvent Selection Recycling
Process Design Batch Distillation Design,
Optimization, Optimal Control Synthesis
Feasibility Efficiency. Molecular Design Under
Uncertainty
Multi-criteria Decision Analysis Value of Research

Chemical
Policy
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Environmentally Benign Chemical Processes Design
A Multi-objective Optimization Framework under
Uncertainty

• Modeling ASPEN simulator
• Defining Objectives Potential Environmental
  Impacts (WAR) and Economics
• Theory of Optimization (Algorithm) a New and
  Efficient Multi-objective Optimization Algorithm
  Stochastic Optimization

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Benchmark Example

• The hydrodelkylation of toluene to form benzene
  (HDA) process

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Modeling the HDA Process
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Defining Objectives Potential Environmental
Impacts and Economics of Chemical Process

• Min. potential environmental impacts the
  generalized Waste Reduction (WAR) algorithm

• Max. the annualized profit

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Comparison Single and Multi-objective
Optimization Problem
Single Objective - e.g. Min Cost Min/Max Z Z
f(x) Subject to h(x) 0 g(x) lt 0 x -
Decision variables
Multi-Objective -e.g. Min Cost, Max Safety, Min
emissions,Max Flexibility Min/Max Z(Z1,Z2,..,Zp)
Zi fi(x) Subject to h(x) 0 g(x) lt 0 x
- Decision variables
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A Simple Multi-objective Linear Example
Max Z1 6x1 x2 Z2 - x1
3x2 subject to 3x1 2x2 ? 12
3x1 6x2 ? 24 x1 ? 3
x1, x2 ? 0
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Decision Space
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Objective Space
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Weighting Method Max.Y?1Z1?2Z2
?2 ? ?
?1 ? ?
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Constraint Method Max. Z1 s.t. Z2? ?1


Pareto set
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A New and Efficient Multi-objective Optimization
Algorithm

• Solution of multiple optimization problems
• Results in a Pareto Set
• Algorithm Max. Z1

New Efficient ? Min. No. of
optimization problems to be solved ?
Constraints are chosen by HSS technique
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An Efficient Multi-objective Optimization
Framework
Pareto Set/ Optimal Designs
Input
Formulate NLP problems Choose objective Choose ?i
by HSS, i 2,,p
Optimal Design
Decision Variables
Obj.Funs. Cons.
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A Schematic Diagram of the Multi-objective
Optimization Framework for the HDA Process Using
the Public Version of ASPEN Simulator
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Objectives of the Ten Different Designs for the
HDA Process with Diphenyl as a Pollutant
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Objectives of the Ten Different Designs for the
HDA Process with Diphenyl as a Byproduct
1 dominate 8
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Comparison Same Designs in Two Case Studies
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Brief Summary for Determinate Case Studies

• Design for environment is a multi-objective
  optimization problem
• An optimization framework has been presented that
  allows for the efficient determination the
  approximation of the Pareto set of a
  multi-objective problem
• A methodology to augment traditional chemical
  process simulator, like ASPEN, with the capacity
  to design for environmentally friendly and cost
  effective processes and products
• Comparison of two cases aim to emphasize the
  sustainable development spirit

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Environmental Impact Indexes for Different
Components in the HDA Process under Uncertainty
a
b
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Stochastic Modeling

• Quantifying the uncertainties in key input
  parameters in terms of probability distributions.
• Sampling the distributions of these key
  parameters in an iterative fashion.
  
• Propagating the effects of uncertainties through
  the flowsheet.
• Applying statistical techniques to analyze the
  results.

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Stochastic Modeling
CDF
Profit
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Important Properties of Sampling Techniques

• Independence / Randomness
• Uniformity
• In most applications, the actual relationship
  between successive points in a sample has no
  physical significance, hence, randomness of the
  sample for approximating a uniform distribution
  is not critical (Knuth, 1973).
• Once it is apparent that the uniformity
  properties are critical to the design of sampling
  techniques, constrained or stratified sampling
  becomes appealing (Morgan and Henrion, 1990).

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New Sampling Technique

• HSS shows better uniformity than LHS or MCS.
• HSS sampling is at least 3 to 100 times faster
  than LHS or MCS.
• HSS is preferred sampling for stochastic modeling
  and/or stochastic optimization, and
  multi-objective optimization.

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Framework for Stochastic Optimization
Optimal Design

• An efficient sampling methodology
• An efficient interaction between the optimizer
  and the sampling loop

Input
OPTIMIZER
Decision Variables
Prob. Obj. Func. Cons.
Optimizer
SAMPLING BLOCK
Uncertain Parameters
Sampling Loop for N Samples
Sampling Loop
MODEL
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An Efficient Multi-objective Optimization
Framework under Uncertainty
Uncertain Parameters
Sampling Loop
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CDF of Each Objective for Max.Profit
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41
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40.5
41
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Mean of Objectives of the Ten Different Designs
for the HDA Process with Diphenyl as a Byproduct
under Uncertainty
4 dominate 9
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Objectives of the Ten Different Designs for the
HDA Process with Diphenyl as a Byproduct without
Uncertainty
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Decision Space Changing under Uncertainty
Totally Different Designs !!!
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Conclusions

• Design for environmental is a multi-objective
  optimization problem
• Provides trade-offs among objectives
• Provides designs which are environmentally
  friendly and economical efficient
• Uncertainties change the design significantly

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Acknowledgement
Funding

• EPA multi-objective optimization algorithm
  development case study
• NSF algorithm theory
• UEF conference