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Advances in Optimization and its Applications in Process Industries. Lorenz T Biegler Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213 July , 2012 . http://capd.cheme.cmu.edu. Chemical Engineering Department. Pittsburgh, PA. Carnegie Mellon Campus.

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slide1

Advances in Optimization and its Applications in Process Industries

Lorenz T Biegler

Department of Chemical Engineering

Carnegie Mellon University

Pittsburgh, PA 15213

July , 2012 

http://capd.cheme.cmu.edu

slide3

Center for Advanced Process Decision-making

(CAPD) Faculty and Researchers

Jeff Siirola

Erik Ydstie

Ignacio Grossmann

Nick Sahinidis

Larry Biegler

PhD Students: 28 MS Students: 11

Post Docs: 7 Visitors: 10

slide4

Long term goal: from molecular to enterprise level

CAPD Goals

  • Provide intellectual leadership on complex modeling, design and operational problems faced by process industries
  • Promote and Enhance PSE Science Base: optimization, control, computer science, systems engineering, business

Basic methodologies

Process modeling

Mathematical programming

Systems Engineering

Process control

Advanced computing

Areas of application

Process and product synthesis

Energy Systems

Supply chain optimization

Molecular Design

Systems Biology

capd principal investigators
L. T. Biegler

Nonlinear Programming and Parameter Estimation

Optimization of Differential Algebraic Systems

Nonlinear Optimization-based Control

I. E. Grossmann

Mixed Integer Nonlinear Programming for Process Synthesis

Planning and Scheduling of Batch and Continuous Processes

Design under Uncertainty

N. Sahinidis

Global Optimization Algorithms, and Software

Modeling of metabolic and signaling pathways

Design of environmentally benign chemicals

J. J. Siirola

Process Synthesis of Advanced Energy Systems

Synthesis of Nonideal Separation Systems

Product and Process Design

B. E. Ydstie

Adaptive and Robust Control Strategies

Thermodynamic Approaches to Process Control

Discrete Events and Scheduling

 Solar Cell Modeling

CAPD Principal Investigators
optimal design of responsive process supply chains
Optimal Design of Responsive Process Supply Chains

Ignacio Grossmann

Max: Net present value

Max: Responsiveness

(Expected Lead Time)

Supply chain: an integrated network of business units for the supply, production, distribution and consumption of the products.

supply chain case study
Supply Chain Case Study
  • Problem Size MINLP:
    • # of Discrete Variables: 215
    • # of Continuous Variables: 8126
    • # of Constraints: 14617
  • Solution Time:
    • Solver: GAMS/BARON
    • Direct Solution: > 2 weeks
    • Proposed Algorithm: ~ 4 hours
slide8
Decisions:

Number and capacity of TLP/FPSO facilities

Installation schedule for facilities

Number of sub-sea/TLP wells to drill

Oil production profile over time

Optimal Development Planning under Uncertainty

  • Offshore oilfield having several reservoirs under uncertainty
  • Maximize the expected net present value (ENPV) of the project

Tarhan, Grossmann (2009)

facilities

TLP

FPSO

Reservoirs

wells

Uncertainty:

  • Initial productivity per well
  • Size of reservoirs
  • Water breakthrough time for reservoirs
distribution of net present value oilfield planning
Distribution of Net Present Value Oilfield Planning

Deterministic Mean Value = $4.38 x 109

Multistage Stoch Progr = $4.92 x 109

=> 12% higher, more robust

Computation: Algorithm 1: 120 hrs; Algorithm 2: 5.2 hrs

Nonconvex MINLP: 1400 discrete vars, 970 cont vars, 8090 Constraints

simulation based optimization
Simulation-based Optimization

Nick Sahinidis

  • Goals:
    • Efficient optimization of complex chemical processes
    • Accurate solutions using function evaluations from high fidelity simulators
  • Challenges and solutions:
    • Lack of an algebraic model → Build surrogate models
    • Computationally costly simulations → Selectively choose a minimal data set
    • Often noisy function evaluations → Use regression surrogate models
    • Scarcity of fully robust simulations → Disaggregate the process

Process simulation

Optimization model

Function evaluation

automated learning of algebraic models for optimization
Automated Learning of Algebraic Models for Optimization

Process Simulation

Disaggregation and modeling

Optimization

Block 1

Model 1

Block 2

Model 2

Surrogate model generation using ALAMO

Algebraic optimization

Block 3

Model 3

True vs. Empirical

Error

Ideal Model

New

Model

Build simple and accurate models with a functional form tailored for an optimization framework

Locate

model

error

Data points

Complexity

New point

Error maximization

Rebuild model

Combine surrogate models along with design specs, heat/mass balances, logical constraints, etc. to formulate an algebraic optimization model

Iterative design of experiments

Model functional form

co 2 capture case study
CO2 Capture Case Study

Outlet gas

Solid feed

Minimize the increased cost of electricity

Maximize %CO2 removal ( )

Cooling

water

CO2 rich gas

CO2 rich solid outlet

Surrogate model

Simulation

Tradeoff:

Cost

vs. Environmental impact

Generate a low-complexity surrogate model of %CO2 removal as a function of reactor bed depth and cooling water flow from Aspen Custom Model runs

2. Surrogate model generation

3. Results: Pareto Analysis

1. Optimize a CO2 fluidized bed reactor

process control research at cmu erik ydstie
Process Control Research at CMUErik Ydstie

Research topics:

Solar Energy (Production processes and DSSC)

Dynamic modeling and Control of Supply Chains

Modeling and Control of Particulate Systems

Adaptive Control and Adaptive Optimization

Plant wide Simulation and Control

Process Automation and Safety

Fundamental Control Theory

slide14

Feed Forward Adaptive Control

Applied to Propane Cracker - DOW Chemicals

  • Control Objectives:
  • Stabilize pressure (CV) in response to frequent disturbances
  • Optimally choose cheapest fuel

CV: Pressure

MV: Low-pressure Flow

DV1: Off-gas

DV2: Residue

DV3: Fuel flow to Propane cracker

  • PI Control (green)
  • PI with adaptive optimization (blue)

B Erik Ydstie, CMU

slide15

Plantwide Control Systems? From Sand to Windshields(with Dr Yu Jiao PPG Inc, Glass Technology Research Center)

Silicate Sand

Soda-ash

Iron Oxide

++

8 flat glass plants

10 windshield lines

Accuracy of shape, color, distortion (optical properties) depend on mix, melting conditions in furnace and operation of the tin bath.

slide16

Results from Trial at Wichita Falls TX

Conditioner temperature (KPI)

  • Yield improved by 3-5%
  • Excellent operator acceptance
  • Maintainable and expandable
  • Implemented on all PPG plants
  • $30-40M per year saving

Defects Measured

process optimization l t biegler
Large Scale Nonlinear Programming Algorithms: process optimization for design, control and operations

Evolution of NLP Solvers:

Process OptimizationL. T. Biegler

SQP

rSQP

IPOPT

rSQP++

IPOPT 3.x

’80s: Flowsheet optimization

over 100 variables and constraints

’90s: Static Real-time optimization (RTO)

over 100 000 variables and constraints

’00s: Simultaneous dynamic optimization

over 1 000 000 variables and constraints

Object Oriented Codes to tailor structure, architecture to problems

large scale optimization l t biegler

Grade Transitions - Polymer Processes

Large-Scale Optimization (L. T. Biegler)
  • Periodic Adsorption Process Optimization

Simulated Moving Bed - Optimal Operation

CPU Time for optimization: 9.03 min

34098 variables, 34013 equations

Real-time Dynamic Optimization

slide19

Dynamic Optimization Problem

s.t.

t, time

z, differential variables

y, algebraic variables

tf, final time

u, control variables

p, time independent parameters

slide20

Collocation on

finite Elements

Nonlinear Programming

Problem (NLP)

Discretized variables

NonlinearProgrammingFormulation

Nonlinear Dynamic

Optimization Problem

(Piecewise)

Continuous profiles

slide21

Nonlinear Programming Problem

s.t.

Finite elements, hi, can also be variable to determine break points for u(t).

Add hu ≥hi≥ 0, S hi=tf

Can add constraints g(h, z, u) ≤ e for approximation error

process optimization with dynamic reactor models
Process Optimization with Dynamic Reactor Models
  • Optimal Catalyst Distribution in Graded Fixed Bed Reactors (Y. Nie, Dr. Paul Witt, Dr. AnshulAgarwal)
  • Dynamic Modeling and Recipe Optimization of Polyether Polyol Processes (Y. Nie, Dr. Carlos Villa)
  • Combined Recipe Optimization and Product Scheduling (YisuNie, Dr. John Wassick)
  • Characteristics:
  • Large-scale, nonlinear, (often) exothermic reactive systems
  • Modeled with simultaneous collocation methods
  • Need to capture nonlinear, (often) unstable modes and runaways, enable highly efficient and safe operation
  • Fast solution of optimization problems
slide29

Recipe Optimization

Semi-Batch Polyether Polyol Process (Yisu Nie)

slide34

Special industrial interest group:

Enterprise-wide Optimization for Process Industries

Multidisciplinary team:

Chemical engineers, Operations Research, Industrial Engineering

Researchers:

Carnegie Mellon: Ignacio Grossmann (ChE)

Larry Biegler (ChE)

John Hooker (OR)

Nicola Secomandi (OR)

Lehigh University: Katya Scheinberg (Ind. Eng)

Univ. Pittsburgh: Andrew Schaeffer (Ind. Eng.)

Overall Goal:

  • Novel planning and scheduling models, including consideration of uncertainty
  • Effective integration of Production Planning, Scheduling and Real–time Optimization
  • Optimization of Entire Supply Chains
slide35

Hierarchy of Enterprise Wide Optimization

  • Supply Chain, Planning and Scheduling
    • Large LP and MILP models
    • Many Discrete Decisions
    • Few Nonlinearities
    • Essential link needed to process models
    • Decisions need to be feasible at lower levels
slide36

Process Operations Applications

  • Real-time Optimization and Control
    • Large, Complex Process Models
    • Few Discrete Decisions
    • Nonlinearities and Dynamics
    • Essential to Link with Logistics and Planning
    • “Time-limited” on-line optimization
    • Optimal performance needs to be passed to higher levels
slide37

Multiscale temporal and

spatial integration

Multi-site Production Planning

Polymer plants (25 grades)

Objective: Production Planning and Distribution

Model for Batch Polymerization Reactors

production planning and scheduling
Production Site:

Raw material availability and Raw material costs

Storage tanks with associated capacity

Transportation costs to each customer

Reactors:

Materials it can produce

batch sizes (lbs) for each material it can produce

operating costs ($/hr) for each material

Sequence dependent clean out times (hrs per transition for each material pair)

Time the reactor is available during a given month (hrs)

STORAGE

Reaction 1

A

F1

INTERMEDIATE

STORAGE

F2

STORAGE

Reaction 2

B

F3

STORAGE

Reaction 3

C

F4

Production Planning and Scheduling
  • Customers:
  • Monthly forecasted demands for desired products
  • Price paid for each product
  • Materials:
  • Raw materials, Intermediates, Finished products
  • Unit ratios (lbs of needed material per lb of material produced)
real time optimization for asus
Real-time Optimization for ASUs
  • Air Separation Unit, key unit in IGCC-based Power Plants
  • Need for high purity O2
  • Respond quickly to changes in process demand
  • Large, highly nonlinear dynamic separation (MESH) models
  • Related work:
  • Methanol distillation (Diehl, Bock et al., 2005)
      • 40 trays, 210 DAEs, 19746 discretized equations
  • Argon Recovery Column
      • 50 trays, 260 DAEs, 21306 discretized equations
  • Double Column ASU Case Study
      • 80 trays, 1520 DAEs, 116,900 discretized equations
real time optimization components

w

Real-time Optimization: Components

Plant

APC

y

u

RTO

c(x, u, p) = 0

DR-PE

c(x, u, p) = 0

p

  • Data reconciliation – identify gross errors and inconsistency in data
  • Periodic update of process model identification
  • Usually requires APC loops (MPC, DMC, etc.)
  • RTO/APC interactions: Assume decomposition of time scales
    • APC to handle disturbances and fast dynamics
    • RTO to handle static operations
  • Typical cycle: 1-2 hours, closed loop
  • What if steady state and dynamic models are inconsistent?
dynamic real time optimization rto

d

Plant

Dynamic Real-time Optimization (RTO)

m

PC

u

y

Real-time Optimization

Dynamic Models

State Estimation

Model Updates

p

  • Goal: Integrate On-line Optimization with Advanced Process Control
  • Requires time-critical calculations
  • Current optimization makes this available in practice
  • Links to Decision-making at other scales/levels
  • Several applications in Chemical Industry
  • Essential for:
    • Inherently Dynamic Energy Systems
    • Handling Uncertainties in prices, supplies and demands
    • Optimal disturbance rejection
on line optimization nonlinear model predictive control nmpc

NMPC Estimation and Control

On-line Optimization: Nonlinear Model Predictive Control (NMPC)
  • Why NMPC?
  • Track a profile – evolve from linear dynamic models (MPC)
  • Severe nonlinear dynamics (e.g, sign changes in gains)
  • Operate process over wide range (e.g., startup and shutdown)

z : differential states

y : algebraic states

Process

d : disturbances

u : manipulated

variables

NMPC Controller

ysp : set points

Model Updater

NMPC Subproblem

what about fast nmpc
What about Fast NMPC?
  • Fast NMPC is not just NMPC with a fast solver (Engell, 2007)
  • Computational delay – between receipt of process measurement and injection of control, determined by cost of dynamic optimization
  • Leads to loss of performance and stability(see Findeisen and Allgöwer, 2004; Santos et al., 2001)

As larger NLPs are considered for NMPC, can computational delay be overcome?

can we avoid on line optimization
Can we avoid on-line optimization?
  • Divide Dynamic Optimization Problem:
    • preparation, feedback response and transition stages
    • solve complete NLP in background (‘between’ sampling times)

as part of preparation and transition stages

    • solve perturbed problem on-line based on NLP sensitivity
    • > two orders of magnitude reduction in on-line computation
  • Based on NLP sensitivity of z0 for dynamic systems
    • Extended to Collocation approach – Zavala et al. (2008, 2009)
    • Similar approach for Moving Horizon Estimation – Zavala et al. (2008)
  • Stability Properties (Zavala et al., 2009)
    • Nominal stability – no disturbances nor model mismatch
      • Lyapunov-based analysis for NMPC
    • Robust stability – some degree of mismatch
      • Input to State Stability (ISS) from Magni et al. (2005)
    • Extension to economic objective functions
slide50

Advanced Step Nonlinear MPC (Zavala, B., 2008)

Solve NLP in background (between steps, not on-line)

Update using sensitivity on-line

x(k)

xk+1|k

u(k)

tk tk+1 tk+2

tk+N

Solve NLP(k) in background (between tk and tk+1)

slide51

Advanced Step Nonlinear MPC (Zavala, B., 2008)

Solve NLP in background (between steps, not on-line)

Update using sensitivity on-line

xk+1|k

x(k)

x(k+1)

u(k+1)

u(k)

tk tk+1 tk+2

tk+N

Solve NLP(k) in background (between tk and tk+1)

Sensitivity to update problem on-line to get (u(k+1))

slide52

Advanced Step Nonlinear MPC (Zavala, B., 2008)

Solve NLP in background (between steps, not on-line)

Update using sensitivity on-line

xk+2|k+1

x(k)

x(k+1)

u(k+1)

u(k)

tk tk+1 tk+2

tk+N

Solve NLP(k) in background (between tk and tk+1)

Sensitivity to update problem on-line to get (u(k+1))

Solve NLP(k+1) in background (between tk+1 and tk+2)

slide53

Nonlinear Model Predictive Control

Air Separation Unit (Huang, B., 2011)

Objective: minimize operating cost subject to demand specifications

4manipulated variables.

4 output variables.

Horizon: 100minutes in 20

finite elements.

Sampling time: 5 minutes.

First Principle Index 1 Model:

1520 DAEs

OCFE Discretization:

Variables: 117,140

Constraints: 116,900

slide54

NMPC Ramping for Air Separation Unit

(Huang, Zavala, B., 2009)

At t = 30-60 min, product rates are ramped down by 40%.

At t =1000-1030 min, they are ramped back. 5% disturbance is added to Mi.

N = 20, K = 3

320 ODEs, 1200 AEs.

Variables: 117,140

Constraints: 116,900

400 NLPs solved

Background: 200 CPUs, 6 iters.

Online: 1 CPUs

Computational Feedback Delay Reduced from 200 1 CPUs

Blue dashed lines are ideal NMPC profile

Red lines are AS-NMPC profile.

In contrast, linearized controller is unstable

slide56

D-RTO to Minimize Electricity Cost

Min SiPriceix (MA+EA)i + Regi

S.t. ASU model

time horizon 2hrs

sampling time 6 min

D-RTO with day ahead costs

slide57

Dynamic Optimization for Day Ahead Strategy

Air Separation Unit

ASU Compressor feeds follow trend of electricity price. Output profiles satisfied for demand specifications.

Optimal D-RTO: $12,511

Optimal set-point tracking: $13,042

4.25% ($100k/yr) decrease over

Optimal setpoint tracking.

slide59

Online ARIMA model for Price Estimation

Energy Price

Update ARIMA price model with moving horizon estimation.

Predicted price for a 24 hour period

slide60

Dynamic Real-time Optimization for Real Time Pricing

Same formulation as in day ahead strategy but using predicted price.

Cost of the proposed method: $5,939

Cost of set-point tracking: $6,307

6.19% ($135k/yr) savings over optimal setpoint tracking

slide61

Projects with EWO partners

ABB: Optimal Design of Supply Chain for Electric Motors

Contact: Iiro Harjunkoski Ignacio Grossmann, Analia Rodriguez

Air Liquide: Optimal Coordination of Production and Distribution of Industrial Gases

Contact: Jean Andre, Jeffrey Arbogast Ignacio Grossmann, Vijay Gupta, Pablo Marchetti

Air Products: Design of Resilient Supply Chain Networks for Chemicals and Gases

Contact: James Hutton Larry Snyder, Katya Scheinberg

Braskem: Optimal production and scheduling of polymer production

Contact: Rita Majewski, Wiley Bucey Ignacio Grossmann, Pablo Marchetti

Cognizant: Optimization of gas pipelines

Contact: Phani Sistu Larry Biegler, Ajit Gopalakrishnan

Dow: Multisite Planning and Scheduling Multiproduct Batch Processes

Contact: John Wassick Ignacio Grossmann, Bruno Calfa

Dow: Batch Scheduling and Dynamic Optimization

Contact: John Wassick Larry Biegler, Yisu Nie

Ecopetrol: Nonlinear programming for refinery optimization

Contact: Sandra Milena Montagut Larry Biegler, Yi-dong Lang

ExxonMobil: Global optimization of multiperiod blending networks

Contact: Shiva Kameswaran, Kevin Furman Ignacio Grossmann, Scott Kolodziej

ExxonMobil: Design and planning of oil and gasfields with fiscal constraints

Contact: Bora Tarhan Ignacio Grossmann, Vijay Gupta

Praxair:Capacity Planning ofPower Intensive Networks with Changing Electricity Prices

Contact: Jose Pinto Ignacio Grossmann, Sumit Mitra

UNILEVER: Scheduling of ice cream production

Contact: Peter Bongers Ignacio Grossmann, Martijn van Elzakker

BP*:Refinery Planning with Process Models

Contact: Ignasi Palou-Rivera Ignacio Grossmann, Abdul Alattas

PPG*: Planning and Scheduling for Glass Production

Contact: Jiao Yu Ignacio Grossmann, Ricardo Lima

TOTAL*:Scheduling of crude oil operations

Contact: Pierre Pestiaux Ignacio Grossmann, Sylvain Mouret

Projects and Seminars: http://egon.cheme.cmu.edu/ewocp

slide62

Collaborative Cyberinfrastructure for (MINLP) minlp.org

CMU:Ignacio Grossmann, PietroBelotti, Lorenz Biegler, Pedro Castro, Francois Margot,

Juan Ruiz, NikolaosSahinidis

  • Objectives http://www.minlp.org:
  • Create a library of optimization problems that can be
  • generally formulated as MINLP models.
  • Provide high level descriptions of the problems with one or several model
  • formulations with corresponding input files for one or several instances.
slide63

http://www.minlp.org

  • MILP, NLP and MINLP models in diverse areas: engineering, physics, biology, finance

- Formulation of models is emphasized

which allows comparison and

evaluation of numerical performance

of different codes

- Supports discussion through forum

  • Future:
  • Guidelines for modeling
  • Contribute open problems
slide64

ABB

Air Liquide

Air Products

Braskem

Cognizant

Dow Chemical

Eastman Chemical

Ecopetrol

ExxonMobil

FICO

GS Eng. & Constr.

GAMS

CAPD Industrial Members

Mitsubishi Electric Res. Lab.

NETL

Neste Engineering Oy

Paragon Decision

Petrobras

Pfizer

Procter & Gamble

Praxair

Rockwell Automation

Sasol

Total

Unilever

slide65

Industrial Impact of CAPD

  • Large number of graduates in petroleum, chemical, consulting companies
  • Refinery and batch scheduling –ABB
  • NLP optimization of gas separation plants -Air Products
  • Flowsheet optimization with SQP- Air Products, Aspen Technology
  • LSSQP, SPLIT - Aspen Technology
  • Combustion Verification – Alcoa
  • Optimal synthesis of separation of olefins -BP
  • Optimal synthesis of crystallization process –BP
  • Energy optimization in corn-based ethanol plants - Cargill
  • Optimal planning polymer plants –Dow
  • Large-scale supply chain optimization under uncertainty - Dow
  • Gasfield development model under uncertainty – ExxonMobil
  • Control and optimization of polymerization reactors - ExxonMobil
  • DICOPT, LOGMIP - GAMS
  • IPOPT Large-scale NLP software -IBM
  • Glass Furnace Control – PPG
  • Solar Grade Silicon – REC Silicon
  • Power plant control systems – Emerson Process Management
slide66

CAPD Academic Impact

    • Largest PSE group in US
    • Graduates in academia
    • Achenie (VPI), Bañares (Oxford), Bullard (UNC), Floudas (Princeton), Govind (Cincinnati), Halemane (Karnataka), Hrymak (Western Ontario), Laird (Texas A&M), Lee (CCNY), Kawajiri (GaTech), Maravelias (Wisconsin), Oliveira (Coimbra), Pekny (Purdue), Pinto (Polytechnic), Pistikopoulos (Imperial), Rico (Celaya), Sahinidis (CMU), Swaney (Wisconsin), Turkay (Koc), Zamora (UAM), You (Northwestern)
    • 3. Textbook: Systematic methods of chemical process design
    • Biegler, Grossmann, Westerberg (Prentice-Hall)
    • 4. Adoption of CMU-research and software
    • MINLP, SQP, collocation, passivity theory, fault trees,ASCEND, BARON, SQP, IPOPT, DICOPT, LOGMIP
  • 5. Assoc. Editors Journals: AIChE J. (Grossmann), I&EC Res. (Biegler),
  • Optimization Methods and Software, Adaptive Control and Signal
  • Processing (Ydstie)
slide67

PSE Research@CAPD

  • Strong Scientific Research Base
  • Numerical analysis  Simulation
  • Math. Programming  Process Optimization
  • Systems/Control Theory  Process Control
  • Computer Science  Software/Advanced Computing
  • Operations Research  Business/Operations
  • Strong Industrial Interactions
  • Enterprise Wide Optimization
  • Energy Systems
  • Process and Product Design and Development
  • Control, Dynamics and Real-time Optimization
  • Synergy of Modern Optimization Algorithms and Optimization Models
  • Design and Operation under Uncertainty
  • Planning, Scheduling and Operations
  • Optimization in Real-time
  • For more information: http//:capd.cheme.cmu.edu
  • http//:numero.cheme.cmu.edu
slide68

Research Collaborations

Across Carnegie Mellon

  • Tepper School of Business
  • Institute for Complex Engineered Systems (ICES)
  • Mechanical Engineering
  • Electrical and Computer Engineering
  • Biomedical Engineering
  • Software Engineering Institute
  • Computer Science
  • Mathematical Sciences
  • Material Science and Engineering
slide69

Research Collaborations

Around the World

  • Imperial College (UK)
  • ETH (Zürich)
  • RWTH-Aachen + IWR-Heidelberg + TUBerlin + MPI Magdeburg (Germany)
  • Abo Akademi + Jyvaskyla (Finland)
  • NTNU (Trondheim)
  • UPC + Alicante + Cantabria (Spain)
  • Coimbra + Porto (Portugal)
  • Maribor (Slovenia)
  • INTEC+INGAR+PLAPIQUI (Argentina)
  • Antofagasta + PUC + USACH (Chile)
  • UIA+Tec Celaya (Mexico)
  • Kyoto (Japan)
  • KAIST (Korea)
  • Tsinghua + Zhejiang+ECUST (China)
  • IIT Bombay (India)
slide70

Process Systems Engineering Research

Process Systems Engineering is concerned with the systematic analysis and optimization of decision making processes for the discovery, design, manufacture and distribution of chemical products.