miguel j. bagajewicz

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Miguel J. Bagajewicz

August, 2019

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We review the past first

• Because some people in industry still use tools form the past.

• Because some professors still teach it!!!

Morale: The old has not died yet and the new is

not fully accepted either.

Process Systems Engineering in

Academia and Industry

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An area of chemical engineering that is

concerned with:

• Synthesize and design more efficient and sustainable processes.

• Develop and improve procedures for stable, sustainable and cost

efficient operations procedure (Monitoring, control, scheduling,

planning, etc.)

Focus: Process Systems Engineering in

Chemical Engineering

Process engineering of the seventies

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- Trial and verify calculations

Heat Exchanger Design

Old Fashion design (Kern)

1) Decide on the type of exchanger.2) Select a trial value for U.3) Calculate the mean temperature difference, DTm, Calculate FT4) Calculate area required.5) Decide on the exchanger layout.6) Calculate individual heat transfer coefficients. Calculate U. If significant difference from assumed in step (2), substitute in (2) and repeat.7) Calculate the pressure drop. If it is not satisfactory back to 5)

Process engineering of the seventies

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- Simple models:

* McCabe Thiele (2 components).

* Fenske-Underwood-Gilliland

(many comp., constant volatility)

* First computer algorithms (Thiele Geddes) for distillation (Fortran)

* Still CSTR- PFR (mostly isothermal)

Industry in the 70’s

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- Pressure for profits gave rise to

* HTRI (Heat transfer Research Institute)

* Complex modeling started (Crude Columns, FCC)

* First simulators (Flowtran, Chess) (limited capacity)

The engineering of the 80’s

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- Conceptual Engineering is proposed:

Pinch design method .

• Process Engineering

* Still mostly equipment design- Trial and verify

* Flowsheeting emerges

- Process Synthesis

- Process Simulation


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- Industry

* Simulators are used in Mainframe. No Graphical User interface

* Conceptual engineering is widespread known not widespread used.

* Process Operations Optimization Starts: Real time optimization

(Romeo, etc).

* Simulation goes commercial Aspentech and Simsci are formed

The engineering of the 90’s

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- Desktop Computers * Simulation becomes pervasive

* Mathematical Programming Emerges

Heat exchanger network (Magnets, Synheat)

Complex Distillation (Petlyuk and other), Distillation networks, etc..

* Pinch technology shows some limitations but stays popular.

* Design for Flexibility and under uncertainty emerges (in Academia).

* The paradigm of simple models/decomposition reaches its limit.

* Supply Chain studies and planning models start


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- Industry

* Simulators in PC are popular.

* Conceptual engineering is widespread known to exist but still not

widespread used.

* Process Operations Optimization becomes popular: Real time

optimization (Romeo, etc.) Data Reconciliation. Supply Chain

scheduling

The engineering of the 2000’s,2010’s

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- Optimization Vs. Algorithms/Conceptual Eng.

* Algorithmic design, heuristics, and conceptual engineering cannot deal

with large and complex systems.

* Product Design emerges and Optimal Equipment Design is established.

* Optimization matures, but is not robust.

* Frustrates Academia. Global Optimization shows as the only route

* Industry cannot embrace optimization efficiently.

- Modeling Scope and Complexity

* Simple models can be misleading.

* From plants to Supply Chains

* Retrofit

- Modeling under Uncertainty* Emerging methods (Two Stage Stochastic Programming)

* Financial Risk is considered

- Integration with business. * Business investment planning models merge with process models


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- Industry

* Scheduling of batch plants using Optimization methods makes its

debut.

* Long term Planning starts to be applied to real life problems

* Conceptual engineering continues to be widespread known to exist

and not widespread used.

* Process Operations Optimization becomes popular: Real time

optimization (Romeo, etc.) Data Reconciliation. Supply Chain

scheduling.

Product engineering (briefly)

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Product Design

- Systematic Methods became popular in Academia only

recently

- Prevailing procedure both in industry and academia is

the STAGE GATE procedure.

- At stage One, many times new products are conceived

using the concept of “best product”, or what is

perceived as most needed..

Product engineering (briefly)

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Product Design

- Alternative paradigms (Bagajewicz) propose to solve

stage one with more information about other stages

- Build preference functions based on product attributes

- For skin lotion: Smoothness, effectiveness, thickness, color…

- Connect product attributes to properties

- For skin lotion: viscosity, density, surface tension, etc.

- Connect properties to design

- For skin lotion: Composition, size, etc.

- Use pricing demand models

- Maximize NPV and simultaneously determine

- the product characteristics

- the portion of market demand to cover

- The selling price

Process engineering

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Relationship of Academia with Industry

(Not all the time)

Process engineering

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It happens in real life !!!!

Letter to a VP:

We have so many irons in the fire at this point that we don’t have the capacity to review this opportunity. Thanks for thinking of us and giving us the opportunity to look at it, but we will have to pass at this time.

The University of Oklahoma has developed a new technology for xxxxxx . Basically, our technology reduces the cost by around 60%. Please let me know if you want to hear some more about it.

Answer

Process engineering

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However:

- Big companies keep looking for new technologies.

- But not in the traditional process engineering (with some notable exceptions such as catalysis)

- Effort is in nanotechnology, biomedicine, etc.

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Teaching of Process Engineering

Engineering projects in capstone classes

Before the eighties

“Design a plant to produce chemical X, with capacity Y”

In the eighties

“Design a flexible plant to produce chemical X, with capacity Y,

capable of working in the given ranges of raw materials availability

and quality and product specifications”

In the nineties:

“Design a plant to produce chemical X, taking into account uncertain raw

materials and product prices, process parameters, raw material availability

and product demand, given the forecasts and determine when the plant

should be built as well as what expansions are needed”

Substitute “plant” by “network of processes” or by “product” and you have supply

chain problems or product engineering.

Process engineering

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What is in the future?

The engineering of the XXI century

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- Optimization more pervasive in Industry

What needs to happen?

* Graphic User Interface need to supplant programming language.

* Optimization needs to be robust and relatively fast

The only hope is global optimization.

* Computer clusters/ Supercomputers will be used in Industry

- Modeling under UncertaintyDeterministic Design using mean values abandoned. Academia will

lag behind again (books are outdated)

- Operations will automate (Smart Plants)Massive data handling. Strategic, tactical and real time decision

making intertwined.

The engineering of the XXI century

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- Equipment Design

What needs to happen?

* Departure from Heuristics and migration to optimization models.

* Optimization –models need to be distributed.

- Methodology* Enumeration and Set trimming methods are alternatives

- Merging with Business and Finance Models* Especially in Scheduling & Operations/Investment Planning

models

* Several models addressing Uncertainty, Financial Risk, Contracts,

option contracts, etc. are already being generated and used

Parallel Processing-w/o Broadcasting

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( )

. .

( , ) 0

0,1

i i

i

k s

i

Min c q f x

s t

q x k I

q i

+

1 2 3

11 12 13 21 22 23

0 1 2

Master Worker

3 Level 1

Processor Space Tree Space

Parallel Processing -Broadcasting

23

( )

. .

( , ) 0

0,1

i i

i

k s

i

Min c q f x

s t

q x k I

q i

+

Processor

0

Processor

1

Processor

2

Processor

(n-1)

Master Worker

Update of better cost

Broadcast Current Best Cost

Leader

………..

Financial Tools

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Planning and scheduling as well as Design/Synthesis

under Uncertainty already exists.cing)

Add Financial Risk:

(Example is for Refinery Panning with Pricing)

GRM (Million US$)

-15 -10 -5 0 5 10 15 20 25 30 35 40

Ris

k

0.0

0.2

0.4

0.6

0.8

1.0

Deterministic

EGRM = 6.942 US$M

Stochastic

EGRM = 8.360 US$M

Deterministic (1 scenario)

GRM = 7.376 US$M

Financial Tools

- Value at Risk (VaR) &

Opportunity Value (OV)

- Downside Risk

- Standard Deviation (Less

and less used)

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Future of Process & Product Design

Customer

-Needs

-Potential

Reactions

etc.

Chemical Supply Chain

-Modeled from the molecule to the

multi-company enterprise

- Using process Engineering Tools

- Integrating Business tools

Customer

-Demands

-Satisfaction

-Feedback

etc.

Management and Finances

-Working Capital Models

-Risk Analysis

-Budgeting Models

- etc.

Advertising

Human

Relations

(Labor)

Sociology

Psychology

Public Policy

Advertising

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THE NEW EMERGING TREND OF INTEGRATION OF FINANCIAL

AND ENGINEERING TOOLS NEEDS TO BE REINFORCED WITH

NEW MODELS AND PROCEDURES.

MAXIMIZATION OF SHAREHOLDER VALUE IS THE ULTIMATE

OBJECTIVE.

TWO-STAGE STOCHASTIC PROGRAMMING IS ADVOCATED TO

BE THE INTEGRATING TOOL.

RISK IN DESIGN AND DECISION MAKING (SCHEDULING,

PLANNING, ETC.) SHOULD BE MANAGED USING A

MULTIOBJETIVE FRAMEWORK.

CONTRACTS, OPTIONS, PRICING, ETC. CAN BE EASILY ADDED.


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OPTIMIZATION WILL BECOME PERVASIVE.

OUR DESIRE TO BE AS ACCURATE AS POSSIBLE IN OBTAINING

THE BEST RESULT WILL TILT THE TOOL TOWARDS

MATHEMATICAL PROGRAMMING

RIGOROUS GLOBAL OPTIMIZATION WILL BECOME THE TOOL

OF CHOICE

SUPERCOMPUTERS OR COMPUTING IN THE CLOUD MIMICKING

PARALLEL COMPUTATION WILL BE USED

CONCEPTUAL ENGINEERING WILL FADE AS A TOOL FOR

DESIGN AND WILL REMAIN AS A TOOL FOR QUALITATIVE

UNDERSTANDING (As McCabe Thiele is today for distillation).


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Current “Hot” Issues

• Mathematical Optimization vs. Conceptual Engineering

• Individual Equipment & Plants

• Supply Chains

• Deterministic Design vs. Design under Uncertainty

• Relationship with Industry

• Level of Detail in models

• Parallel Processing

• New Solution Procedures: Enumeration & Set Trimming

Message

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- Do not simplify models. Actually, do the opposite

- Decompose only if needed (Descartes advice)

- Use robust global optimization when possible

- Incorporate Uncertainty

- Consider retrofit models

- Continue to pursue integration with business tools

- Integrate product, process and business.

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André L. H. Costaa,*, Miguel J. Bagajewiczb

aRio de Janeiro State University (UERJ)bSchool of Chemical, Biological and Materials Engineering, University of Oklahoma

OUTLINE

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• HEURISTICS-BASED EQUIPMENT DESIGN IS

SUBOPTIMAL AT BEST

• PROPERLY REFORMULATED MINLP IS NEEDED

• GLOBAL OPTIMALITY MAKES A DIFFERENCE

• ALTERNATIVES TO MINLP: ENUMERATION AND SET

TRIMMING

• DISTRIBUTED (MORE COMPLEX) MODELS ARE THE

BEST ANSWER. THEY MODIFY THE SYSTEM

• PARALELL COMPUTING IS IN OUR FUTURE

IECR 100 Anniversary article (under revision)

INTRODUCTION

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Significant advances were made by the PSE

community in the use of optimization models

and solution algorithms.

However, basic equipment design procedures

still are heuristics-based.

INTRODUCTION

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Indeed, basic equipment design heuristics

procedures use Trial and verification

• Propose the value of some parameters or

geometrical variable.

• Calculate the rest of the variables using heuristics

• If the solution is viable stop. Otherwise correct.

It is still the recommended method in

most texts

INTRODUCTION

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QUESTIONS:

• What are the reasons that restrain the

utilization of mathematical programming

for the solution of equipment design

problems?

• How can these obstacles be removed?

HEURISTICS-BASED PROCEDURES

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Shell-and-Tube Heat Exchanger Design

1) Propose a heat exchanger type

2) Propose a value of U and obtain Area

3) Propose Shell & tubes D, Length, baffles, # passes

4) Check if the design is acceptable (Ucalc>Uassumed)

5) If the solution is OK, stop

6) Otherwise, propose modifications (step 3 or step 2)

We call this “Trial and Verification”


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Trial and Verification is:

• Strongly based on human intervention

• Experienced designers are needed

• Not even locally optimal.


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Similar design approaches:

- Vertical and horizontal flash-units;

- Distillation column tray design.

- etc.

OPTIMIZATION MODELS

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In the last 10-15 years, a limited number

of papers address the use of

mathematical programming for the design

of heat exchangers.

OPTIMIZATION MODELS

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EVOLUTION

Earlier approaches: NLP

Last 10 years: Non-Convex MINLP

OPTIMIZATION MODELS

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Limitations:

➔ Lack of robustness of NLP and MINLP models:

- Convergence problems

- Multiple local optima

OPTIMIZATION MODELS

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Observation :

➔ Models are based on analytical solutions

- LMTD method with correction factors

➔ Not looking at distributed states along the

exchanger

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These challenges in heat exchanger design have

been and are addressed in our international

research group as follows:

OPTIMIZATION MODELS

▪ Problem reformulation

▪ Alternative procedures to Mathematical Programming

▪ Distributed Models

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Several design variables are only available

in discrete values:

- Commercial alternatives, e.g.:

Tube diameter: ¾ in, 1 in, 1 ¼ in, etc.

- Physical nature, e.g.:

Number of baffles: 1, 2, 3, etc.

REFORMULATION

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Typical tube-side heat transfer coefficient

x

σ𝑠𝑑𝑚𝑖𝑛𝑠𝑑𝑚𝑎𝑥 𝑦𝑑𝑠𝑑 = 1

Nt𝑡 = σ𝑠𝑑=1𝑠𝑑𝑚𝑎𝑥 𝑝𝑁𝑡𝑡𝑠𝑁𝑡𝑡 y𝑁𝑡𝑡𝑠𝑁𝑡𝑡

σ𝑠𝑁𝑡𝑡𝑚𝑖𝑛𝑠𝑁𝑡𝑡𝑚𝑎𝑥 𝑦𝑁𝑡𝑡𝑠𝑁𝑡𝑡 = 1

REFORMULATION

ℎ𝑡 =0.023 𝑅𝑒𝑡0.8 𝑃𝑟𝑡𝑛 𝑘𝑡

𝑑𝑡𝑖

𝑑𝑡𝑖 = σ𝑠𝑑=1𝑠𝑑𝑚𝑎𝑥𝑝𝑑𝑡𝑖𝑠𝑑 𝑦𝑑𝑠𝑑

(

2

)

𝑅𝑒𝑡 =𝑑𝑡𝑖 𝑣 ෞ𝜌𝑡

ෝ𝜇𝑡=

4 ෞ𝑚𝑡

𝑁𝑡𝑡 𝜋 ෝ𝜇𝑡 𝑑𝑡𝑖

Heat transfer coefficient

Reynolds number

Diameter in terms of discrete options

Number of tubes is discrete

THE OVERALL MODEL IS A NONCONVEX MINLP

We write

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Tube-side heat transfer coefficient

Step 1: Reformulation of summation terms

REFORMULATION

ℎ𝑡 =0.023 𝑅𝑒𝑡0.8 𝑃𝑟𝑡𝑛 𝑘𝑡

𝑑𝑡𝑖

ℎ𝑡 =0.023𝑃𝑟𝑡𝑛𝑘𝑡

(σ𝑠𝑑𝑚𝑖𝑛𝑠𝑑𝑚𝑎𝑥 𝑝𝑑𝑡𝑖𝑠𝑑 𝑦𝑑𝑠𝑑)

1.8

4ෞ𝑚𝑡

𝜋 ෝ𝜇𝑡 σ𝑠𝑑=1𝑠𝑑𝑚𝑎𝑥 𝑝𝑁𝑡𝑡𝑠𝑁𝑡𝑡 y𝑁𝑡𝑡𝑠𝑁𝑡𝑡

0.8

ℎ𝑡 = 0.023 𝑃𝑟𝑡𝑛 𝑘𝑡4 ෞ𝑚𝑡

𝜋 ෝ𝜇𝑡

0.8

𝑠𝑑=1

𝑠𝑑𝑚𝑎𝑥

𝑠𝑁𝑡𝑡=1

𝑠𝑁𝑡𝑡𝑚𝑎𝑥𝑦𝑁𝑡𝑡𝑠𝑁𝑡𝑡𝑦𝑑𝑠𝑑

𝑝𝑑𝑡𝑖𝑠𝑑1.8𝑝𝑁𝑡𝑡𝑠𝑁𝑡𝑡

0.8

This is the key step

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Step 1: Reformulation of summation terms

REFORMULATION


𝜋 Ƹ𝜇

0.8

𝑠𝑑=1


𝑠𝑁𝑡𝑡=1



0.8

RESULTING MODEL IS NON-LINEAR BUT BINARY

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Step 2: Conversion to a linear model

REFORMULATION


𝜋 Ƹ𝜇

0.8

𝑠𝑑=1


𝑠𝑁𝑡𝑡=1



0.8


𝜋 Ƹ𝜇

0.8

𝑠𝑑=1


𝑠𝑁𝑡𝑡=1

𝑠𝑁𝑡𝑡𝑚𝑎𝑥𝑤𝑦𝑁𝑡𝑡𝑑𝑠𝑁𝑡𝑡,𝑠𝑑


0.8

𝑤𝑦𝑁𝑡𝑡𝑑𝑠𝑁𝑡𝑡,𝑠𝑑 ≤ 𝑦𝑁𝑡𝑡𝑠𝑁𝑡𝑡𝑤𝑦𝑁𝑡𝑡𝑑𝑠𝑁𝑡𝑡,𝑠𝑑 ≤ 𝑦𝑑𝑡𝑠𝑑𝑤𝑦𝑁𝑡𝑡𝑑𝑠𝑁𝑡𝑡,𝑠𝑑 ≥ 𝑦𝑑𝑡𝑠𝑑 + 𝑦𝑁𝑡𝑡𝑠𝑁𝑡𝑡-1

RESULTING MODEL IS MIL OR MILDLY MINL

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Our experience using this approach:

- Shell-and tube heat exchanger (Kern)Gonçalves et al. (2017)

REFORMULATION

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Our experience using this approach:

- Shell-and tube heat exchanger (Kern) (AICHE J.)

- Shell-and tube heat exchanger (Bell-Delaware) (AICHE J.)

- Shell-and tube heat exchanger / Fouling Modeling (AICHE J.)

- Air coolers with fixed air flow rate. (AICHE J.)

- Air coolers paired with fans. (Advanced Thermal Engineering).

- Plate heat exchangers (ESCAPE)

- Double pipe heat exchangers (ESCAPE)

- Flash vessels’ tray design (To be submitted)

- Separation Colum Tray Design (In Preparation)

REFORMULATION

IMPORTANCE

– CONVERSION OF HIGHLY NON-LINEAR

MODELS TO LINEAR OR MILDLY LINEAR

MODELS RENDERS

❑ Global solutions

❑ Robustness (Solution is always obtained)

❑ Easy insertion in other models (i.e. Heat exchanger

Network Synthesis with simultaneous HEX design51

DEPARTURE FROM MINLP

– Nomenclature issue

o Mixed integer nonlinear models

(MINLM) are the minimization problem

o MINLP is one procedure to solve a

MINLM (P stands for “programming”)

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– OTHER PROCEDURES TO SOLVE A MINLM

o Smart Enumeration

o Set Trimming

o Combination of both and eventually

followed by a MINLP

53

Heat Exchanger Design (TAC optimization)

• Consider discrete geometric parameters

- Shell and Tube diameters (Do and do)

- Length (L)

- Number of passes (Np)

- Number of tubes per pass (Ntp)

- Number of baffles (Nb)

- Each combination (Do , do, L , Np, Ntp , Nb) Area (A)

SMART ENUMERATION

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SMART ENUMERATION

List all (M) exchangers in increasing order by AREA

- (Do,i , do,j, Lk, Np, Ntp , Nb) A1

- (Do,i , do,j, Lk, Np, Ntp , Nb) A2

- ....

- (Do,i , do,j, Lk, Np, Ntp , Nb) AM

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SMART ENUMERATION

Find first feasible Exchanger

- A1 infeasible

- A2 infeasible

- ....

- As feasible

- Calculate COST (For minimum area problem, this is the optimum)

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SMART ENUMERATION

Inspect using Updating & Stopping criteria

First feasible exchanger is the Incumbent Exchanger.

Updating

If COST(An)< COST of Incumbent An is now

the new Incumbent.

Stopping

If COST(An)< Incumbent Area Cost Stop

(A lower cost will never be found)

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Heat Exchanger Design with fouling modeling

SET TRIMMING

Geometrically

unfeasible

Exchangers

Geometrically

Feasible

ExchangersAll Exchangers (S)

Geometrically

unfeasible

Not

Viable

clean

Viable clean

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SET TRIMMING

Geometrically

unfeasible

Not

Viable

clean

Viable cleanViable

dirty

Area >

A of Best

Clean

Area <

Area of

Best

Clean

Not

Viable

clean

Viable

clean


Geometrically

unfeasible

Not

viable

clean Viable clean

Geometrically

unfeasible

Best clean

59

SET TRIMMING

Area < Area of Best

Clean + Viable for

Rf=Rfmax

Geometrically

unfeasible

Viable dirty,

but not viable

for Rf=Rfmax

Area >

A of Best

Clean

Geometrically

unfeasible

Area < Area of Best

Clean + Viable for

Rf=Rfmax

Area >

A of Best

Clean

Area >

“cross”

Area <

“cross”


Area >

A of Best

Clean

Area <

Area of

Best

Clean

Not

Viable

clean

Viable

clean

60

Not

Viable

clean

Not

Viable

clean

Viable

clean

Viable

clean

Geometrically

unfeasible

Best

OPT


Enumeration and/or Set Trimming:

• Render GLOBALLY OPTIMAL SOLUTIONS

• Are not prohibitive computationally

Example: Air cooler design

61

Globally Optimal Design of Air Coolers Considering Fan Performance. de Carvalho et al. (Submitted)

Number of geometry options = 3,333,960.

Set trimming : 3,540 seconds

Smart Enumeration: 1,609 Using Matlab

MINLP Local and Global

Solvers fail to solve!!!

DISTRIBUTED MODELS

– Moving away from simplified models based

on analytical solutions (e.g. LMTD method)

– Use of conservation equations and state

evaluation locally

62

DISTRIBUTED MODELS

Design of double pipe heat exchangers

63

DISTRIBUTED MODELS

Design of double pipe heat exchangers

Rigorous

Average

Conservative

64

Larger!!!

Too large!!!

DISTRIBUTED MODELS

We are now investigating local models applied to

the design of air coolers

𝑈𝜋𝐷𝑡𝑒 𝑁𝑡𝑟 𝑇ℎ − 𝑇𝑐 =ෝ𝑚ℎ

𝑁𝑟𝐶𝑝ℎ

𝑑𝑇ℎ

𝑑𝑦

𝑈𝑟,𝑠,𝑗𝜋𝐷𝑡𝑒 𝑇ℎ𝑟,𝑠,𝑗 −𝑇𝑐𝑟,𝑠,𝑗 + 𝑇𝑐𝑟+1,𝑠,𝑗

2=ෝ𝑚ℎ

𝑁𝑟𝐶𝑝ℎ𝑟,𝑠,𝑗

𝑇ℎ𝑟,𝑠,𝑗+1 − 𝑇ℎ𝑗−1

𝛿𝑟,𝑠,𝑗

W

FOLGA

FOLGA

H

x

z

AR FRIO

AR QUENTE

De

Df

X

z

x

65

DISTRIBUTED MODELSParaphrasing Decartes:

“Simplify and Decompose every engineering problem in as many

parts as needed to solve it”

- Before we had computers we did this. It was right!!!

- When we got computers we still insisted with “simple” and

“Conceptual”. It is not working.

- Mathematical Modeling is prevailing. More complex modeling gives

different answers.

66

IT IS TIME WE MOVE IN THE OTHER DIRECTION

OF MORE COMPLEX MODELS

Parallel Processing-w/o Broadcasting

67

( )

. .

( , ) 0

0,1

i i

i

k s

i

Min c q f x

s t

q x k I

q i

+

1 2 3

11 12 13 21 22 23

0 1 2

Master Worker

3 Level 1

Processor Space Tree Space

Air cooler design: 24 seconds using 25processors

Parallel Processing -Broadcasting

68

( )

. .

( , ) 0

0,1

i i

i

k s

i

Min c q f x

s t

q x k I

q i

+

Processor

0

Processor

1

Processor

2

Processor

(n-1)

Master Worker

Update of better cost

Broadcast Current Best Cost

Leader

………..

Parallel Processing

69

It ameliorates and improves upon two current

problems

▪ Computational time

▪ Problem Size (One can partition the Feasible

region)

FUTURE WORK

70

• Medium term objectives:

– Put together units of similar kind:

HEN

– Put together models of units of different kinds:

+ Distillation Column

+ Condenser

+ Reboiler

In preparation using Enumeration and MIL models

OUR NIRVANA (and yours)

71

THINK OF

SIMPLIFY AND DECOMPOSE AS NEEDED

(Decartes & Art Westerberg dixit)

A WHOLE FLOWSHEET-Distributed equipment models

- Globally optimal- Under Uncertainty

- Multipurpose and Multiperiod- Financial Risk Managed

- etc.

CONCLUSIONS

72

• Equipment design problems:

Traditional trial-and-verification approach

• Limitations of current PSE tools:

- Lack of robustness & Oversimplified models

• Proposed:

- Reformulation simplifies models

- Use Smart Enumeration & Set Trimming + MINLP

- Distributed Models (Do not simplify. Go complex)

- Parallel Computing is the answer to memory & time

OPTIMIZE FIRST!! (Larry Biegler dixit)

miguel j. bagajewicz

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