PROCESS OPTIMIZATIONINDUSTRIAL APPLICATIONS

ZULFAN ADI PUTRA, PDENG

OFFICE: 04-03-31TELP: 05 368 7562

EMAIL: Zulfan.adiputra@utp.edu.my

PROCESS OPTIMIZATIONINDUSTRIAL APPLICATIONS

ZULFAN ADI PUTRA, PDENG

OFFICE: 04-03-31TELP: 05 368 7562

EMAIL: Zulfan.adiputra@utp.edu.my

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What to optimize?Other resources:- Fuel (e.g. for energy)- Water (e.g. for wash)- Solvents

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Raw materials

By productsWasteWastewater

Product

Investment(Capital Expenditure or CAPEX)

COURSE OVERVIEW

1. Objectiveand Constraints

formulation

Multi variable

One variable

Unconstrainedoptimization

Methods:• Function value,

• Bracketing,• Newton,• Secant

Methods:• Simplex,• Newton,• Steepest

descent1. Objective

and Constraintsformulation

ConstrainedOptimization

Methods:• Simplex,• Newton,• Steepest

descentLagrange multiplier

and Karush KuhnTucker algorithm

Linear programmingvia Simplex method

Non Linearprogramming

Methods:• SQP,• GRG,

• PenaltyInteger programmingvia Branch and Bound

OBJECTIVE FUNCTION AND PROBLEM FORMULATION

You are process engineers. New comers!Your boss has to optimize the profit for the day.Your task is to advise him on what to do.Good luck!!!

CatalyticReforming

Hydrotreating

Hydrocracking

Heavy naphtha(A)

Gasoil(B)

Residue(C)

Gasoline high octane(E)

Treated Gasoil(F)

Gasoline(G)

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CatalyticReforming

Hydrotreating

Hydrocracking

Heavy naphtha(A)

Gasoil(B)

Residue(C)

Gasoline high octane(E)

Treated Gasoil(F)

Gasoline(G)

Raw materials Availability, max(kg/day) Cost ($/kg)

A 40000 1.5B 30000 2C 25000 2.5

Products Reactantrequirement

Processingcost ($/kg)

Selling price($/kg)

E 2/3A + 1/3B 1.5 4F 2/3A + 1/3B 0.5 3.3G 1/2A + 1/6B + 1/3C 1 3.8

On your working table, there is a note:Develop the mathematical optimization model!

Your boss is not so happy with the current gas supply flowrate. Since you’re anewbie, he thinks that it will be a good starting point for you to learn. He asksyou to formulate to him how to maximize the his profit! He gives you a blurred compressor curve and tells that the dP of the gasshould be at least 8000 (unit is not relevant in this case). The only relevant cost is the compressor power cost (C2), while the gas priceis C1 (volumetric based).

MAXIMUM COMPRESSOR FLOW

GasV(Nm3/hr)

Surge flow to avoid (Vsurge)

Your boss is not so happy with the current gas supply flowrate. Since you’re anewbie, he thinks that it will be a good starting point for you to learn. He asksyou to formulate to him how to maximize the his profit! He gives you a blurred compressor curve and tells that the dP of the gasshould be at least 8000 (unit is not relevant in this case). The only relevant cost is the compressor power cost (C2), while the gas priceis C1 (volumetric based).

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GasV(Nm3/hr)

Customer

Your new office has no insulation. Winter is coming and it can be -20oC. Even though there is a hot water heater, but it can only beopened until 3 m/s, due to the size of the pipe. Hence, it may not beenough to keep the office warm. The central heating unit also askyou to pay 1 RM for every kW of heating. Your non-engineering colleagues ask you buy an insulation materialfor the office. The price depends on the R-value (R = 1/UA) of thematerial, which is about 100 RM for every R-value. Your highly demanding non-engineering colleagues request you tohave the room temperature to be in between 20 and 25 oC forcomfort. Your finance manager asks you to formulate the problem!

WHAT INSULATION MATERIAL TO BUY? Your new office has no insulation. Winter is coming and it can be -20oC. Even though there is a hot water heater, but it can only beopened until 3 m/s, due to the size of the pipe. Hence, it may not beenough to keep the office warm. The central heating unit also askyou to pay 1 RM for every kW of heating. Your non-engineering colleagues ask you buy an insulation materialfor the office. The price depends on the R-value (R = 1/UA) of thematerial, which is about 100 RM for every R-value. Your highly demanding non-engineering colleagues request you tohave the room temperature to be in between 20 and 25 oC forcomfort. Your finance manager asks you to formulate the problem!

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Hot water

You are a process engineer, working in a very simple plant, with minimalinstrumentation system. Your boss gives you an assignment to design two dischargepumps from a distillation column, each to storage tanks. He has sketched for youbelow diagram this morning. Please tell your boss the capacity of those two pumps. By the way, he likes doing things in Matrix!

LET’S USE MATRIX IN REAL LIFE

Distillate (D)Purity B = 99%

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Reactor Distillationcolumn

A100 mol/hr

Bottom (B)Purity A = 99%

A 2BConversion A = 80%

Your new asssignment is to check a revamped compressor train. The process engineerwho designed the train has left the company and the client complains that the supply gasdoes not achieve the new flowrate. The compressor train consists of two compressors inseries, which compresses the gas with ΔP of 20 bar and 25 bar, sequentially.Feed gas contains component A (80%wt), B (15%wt), and C (5%wt), according to theirrelative volatilities. In the 1st separator, lab people confirm that the condensed liquidcontains 5 %wt of A and 60%wt of B. In 2nd separator, the liquid does not containanymore C. It does have 5%wt of A. The pressurized gas contains 95wt% of A, asdesigned.Compressor vendor informs that both compressor motors have 70% efficiency. Gasdensities can be assumed constant at 10 kg/m3 and 15 kg/m3 for the 1st and the 2ndcompressor, respectively.According to the operators, the compressor motors should be OK. Both motors are of600 kW each. But your boss thinks otherwise. What do you think? Your boss still likes itif you show him matrix calculations.

IS THE COMPRESSOR MOTOR OK?Your new asssignment is to check a revamped compressor train. The process engineerwho designed the train has left the company and the client complains that the supply gasdoes not achieve the new flowrate. The compressor train consists of two compressors inseries, which compresses the gas with ΔP of 20 bar and 25 bar, sequentially.Feed gas contains component A (80%wt), B (15%wt), and C (5%wt), according to theirrelative volatilities. In the 1st separator, lab people confirm that the condensed liquidcontains 5 %wt of A and 60%wt of B. In 2nd separator, the liquid does not containanymore C. It does have 5%wt of A. The pressurized gas contains 95wt% of A, asdesigned.Compressor vendor informs that both compressor motors have 70% efficiency. Gasdensities can be assumed constant at 10 kg/m3 and 15 kg/m3 for the 1st and the 2ndcompressor, respectively.According to the operators, the compressor motors should be OK. Both motors are of600 kW each. But your boss thinks otherwise. What do you think? Your boss still likes itif you show him matrix calculations.

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Gas low pressure10000 kg/hr

Condensed liquid Condensed liquid

Pressurized gas

You are a process engineer, working in a simple section of a bigger plant. Your bosshas been around the plant for quite some time and so confused. Especially with thecost functions that the finance manager gives him below.• Steam cost (RM) = 1 + 0.003*S + 2.10-6*S2• Additive cost (RM) = 2 + 10*Xa + 20*Xa2

He asks himself if there exist(s) operating condition(s) that he can manipulate tomaximize his plant profit. He knows that he can manipulate the yield with the belowempirical equation:• Yield P (mole P) = 0.1 + 0.3*Xa + 0.001*S + 0.0001*Xa*S

One day, he comes to your office and sketches the below figure. Then, he asks, “Couldyou please tell me if we can find an optimum condition to get the maximum profit?”

CASE STUDY

You are a process engineer, working in a simple section of a bigger plant. Your bosshas been around the plant for quite some time and so confused. Especially with thecost functions that the finance manager gives him below.• Steam cost (RM) = 1 + 0.003*S + 2.10-6*S2• Additive cost (RM) = 2 + 10*Xa + 20*Xa2

He asks himself if there exist(s) operating condition(s) that he can manipulate tomaximize his plant profit. He knows that he can manipulate the yield with the belowempirical equation:• Yield P (mole P) = 0.1 + 0.3*Xa + 0.001*S + 0.0001*Xa*S

One day, he comes to your office and sketches the below figure. Then, he asks, “Couldyou please tell me if we can find an optimum condition to get the maximum profit?”

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ReactorFeed (F) Product (P)Price = 50 RM/mol P

Additive(Xa, mol A/mol F)

Steam(S = mole Steam / mole F)

UNCONSTRAINED ONE VARIABLE (DEMISTER)Your boss is very unhappy today. One of your colleagues changed a demisterin a KO drum, upstream of a gas supply compressor few days ago. When thecompressor was started up this morning, your boss heard some cavitation-like sound when the gas flow is at normal condition of 8 m/s. He suspectedthe cause to be the new demister, but he is not sure yet. Because of thismess, he asks you to fix this.

You contacted the demister vendor and they give you only the followingefficiency function of the demister; efficiency = -v2+20v , where v is the gassuperficial velocity. What are you going to say to your boss?

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Your boss is very unhappy today. One of your colleagues changed a demisterin a KO drum, upstream of a gas supply compressor few days ago. When thecompressor was started up this morning, your boss heard some cavitation-like sound when the gas flow is at normal condition of 8 m/s. He suspectedthe cause to be the new demister, but he is not sure yet. Because of thismess, he asks you to fix this.

You contacted the demister vendor and they give you only the followingefficiency function of the demister; efficiency = -v2+20v , where v is the gassuperficial velocity. What are you going to say to your boss?

Gas inwith droplets

Supply gas

Liquid,intermittent blowdown

The new demister

CASE STUDY

For your good work in Demister case, your boss was about to be happy when anotherproblem came in. There is a small column, whose reflux does not work anymore.Hence, the only reflux is the feed to the column. The feed is 5 ton/hr. One of theoperators accidentally broke the thermocouple that measures the reboilertemperature. The reboiler is heated by a hot oil, which luckily has a flowmeter andtemperature measurements.

Liquidfeed

Offspec To maintain a good product specification, theoperator says that we have to control the boil-uprate, according to:efficiency = – x4 + 8x3 -24x2 + 32x + 84x is the boil-up rate (the amount of liquid feed tobe boiled in the reboiler) in kg/hr. Heat ofevaporation of the product is 2000 kJ/kg.

The operator also says that the oil has a heatcapacity of 3 kJ/kg.K and it is allowed to gives offheat for 50oC of temperature reduction.

The question is, “What are you going to tell toyour boss?”

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ProductOil In, 150oC

Oil out

T

To maintain a good product specification, theoperator says that we have to control the boil-uprate, according to:efficiency = – x4 + 8x3 -24x2 + 32x + 84x is the boil-up rate (the amount of liquid feed tobe boiled in the reboiler) in kg/hr. Heat ofevaporation of the product is 2000 kJ/kg.

The operator also says that the oil has a heatcapacity of 3 kJ/kg.K and it is allowed to gives offheat for 50oC of temperature reduction.

The question is, “What are you going to tell toyour boss?”

Because you have completed the previous assignments in an excellent way,you’re now promoted as a senior process engineer. As a senior, your newassignment is to reduce the byproduct of a batch reactor. In the reactorlogbook, you find a record on an empirical byproduct yield as follows:38500005 – 20000*mixer (rpm) +4*mixer2 (rpm) +4*Jacket_temp3 (oC) The operators tell you that the mixer can only operate until 5000 rpm. Andthey never operate it below 1000 rpm because the mixing won’t be goodenough. They also inform you that the heating oil in the jacket is controlledby an electrical heater that can only heat the oil until 200 oC. Your previouscolleague informs that at least you have to run the heating oil at 150oC.Otherwise, your main reaction will not proceed. With the above information, the operators are now waiting for yourinstructions. What are you going to say?

CONSTRAINED MULTI VARIABLE CASE STUDY

Because you have completed the previous assignments in an excellent way,you’re now promoted as a senior process engineer. As a senior, your newassignment is to reduce the byproduct of a batch reactor. In the reactorlogbook, you find a record on an empirical byproduct yield as follows:38500005 – 20000*mixer (rpm) +4*mixer2 (rpm) +4*Jacket_temp3 (oC) The operators tell you that the mixer can only operate until 5000 rpm. Andthey never operate it below 1000 rpm because the mixing won’t be goodenough. They also inform you that the heating oil in the jacket is controlledby an electrical heater that can only heat the oil until 200 oC. Your previouscolleague informs that at least you have to run the heating oil at 150oC.Otherwise, your main reaction will not proceed. With the above information, the operators are now waiting for yourinstructions. What are you going to say?

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Hot oil outHot oil inT = …?

Mixerrpm = …?

Your company just bought two lubricant factories as subsidiary companies.Until now, they are only selling the lubricants via historical partnershipwith their customers. Apparently, they have two same customers. This situation does not make the new supply chain manager happy. So, hecalls you as the recommended senior process engineer within the company. He tells you that the 1st factory has 400 tons of lubricants in their storage,while the other has 300 tons. The 1st customer needs 200 tons oflubricants, while the other requires 300 tons. The supply chain managershows you the cost of shipments ($/ton) as shown below.

Then, he asks for your advice on how much lubricant from each factoryshould be sent to each customer. What are you going to say?

LINEAR PROGRAMMING CASE STUDY

Your company just bought two lubricant factories as subsidiary companies.Until now, they are only selling the lubricants via historical partnershipwith their customers. Apparently, they have two same customers. This situation does not make the new supply chain manager happy. So, hecalls you as the recommended senior process engineer within the company. He tells you that the 1st factory has 400 tons of lubricants in their storage,while the other has 300 tons. The 1st customer needs 200 tons oflubricants, while the other requires 300 tons. The supply chain managershows you the cost of shipments ($/ton) as shown below.

Then, he asks for your advice on how much lubricant from each factoryshould be sent to each customer. What are you going to say?13

INTEGER PROGRAMMING CASE STUDY

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