MTBE Chemical Production Optimization

Megan Bryant

Department of Mathematical SciencesClemson University

Clemson, South Carolina 29634

mrlebla@g.clemson.edu

December 9th, 2013

The Client

The Saudi European Petrochemical Company (Ibn Zahr) is aprivate company in the oil and gas industry.

Ibn Zahr operates out of Jubail Industrial City, Saudi Arabia.

They produce over 4.7 million tons of petrochemicals a year.

MTBE is one of these petrochemicals.

Megan Bryant (Clemson) MTBE December 9th, 2013 2 / 1

The Client

The Saudi European Petrochemical Company (Ibn Zahr) is aprivate company in the oil and gas industry.

Ibn Zahr operates out of Jubail Industrial City, Saudi Arabia.

They produce over 4.7 million tons of petrochemicals a year.

MTBE is one of these petrochemicals.

Megan Bryant (Clemson) MTBE December 9th, 2013 2 / 1

The Client

The Saudi European Petrochemical Company (Ibn Zahr) is aprivate company in the oil and gas industry.

Ibn Zahr operates out of Jubail Industrial City, Saudi Arabia.

They produce over 4.7 million tons of petrochemicals a year.

MTBE is one of these petrochemicals.

Megan Bryant (Clemson) MTBE December 9th, 2013 2 / 1

The Client

The Saudi European Petrochemical Company (Ibn Zahr) is aprivate company in the oil and gas industry.

Ibn Zahr operates out of Jubail Industrial City, Saudi Arabia.

They produce over 4.7 million tons of petrochemicals a year.

MTBE is one of these petrochemicals.

Megan Bryant (Clemson) MTBE December 9th, 2013 2 / 1

MTBE

Methyl tert-butyl ether (MTBE) is an organic compound.

Figure: C5H120

MTBE additives act to raise the octane raise the octanenumber of fuel.Ibn Zahr currently produces 500,000 tons of MTBE per year.

Megan Bryant (Clemson) MTBE December 9th, 2013 3 / 1

MTBE

Methyl tert-butyl ether (MTBE) is an organic compound.

Figure: C5H120

MTBE additives act to raise the octane raise the octanenumber of fuel.

Ibn Zahr currently produces 500,000 tons of MTBE per year.

Megan Bryant (Clemson) MTBE December 9th, 2013 3 / 1

MTBE

Methyl tert-butyl ether (MTBE) is an organic compound.

Figure: C5H120

MTBE additives act to raise the octane raise the octanenumber of fuel.Ibn Zahr currently produces 500,000 tons of MTBE per year.

Megan Bryant (Clemson) MTBE December 9th, 2013 3 / 1

Production Process

Figure: MTBE Production Process

Megan Bryant (Clemson) MTBE December 9th, 2013 4 / 1

Objective

Ibn Zahr wishes to optimize MTBE production at their facility.

The facility has 3 reactors & each reactor has 6 possiblesetups.

It was our job to select the optimal setup for each reactor.

Megan Bryant (Clemson) MTBE December 9th, 2013 5 / 1

Objective

Ibn Zahr wishes to optimize MTBE production at their facility.

The facility has 3 reactors & each reactor has 6 possiblesetups.

It was our job to select the optimal setup for each reactor.

Megan Bryant (Clemson) MTBE December 9th, 2013 5 / 1

Objective

Ibn Zahr wishes to optimize MTBE production at their facility.

The facility has 3 reactors & each reactor has 6 possiblesetups.

It was our job to select the optimal setup for each reactor.

Megan Bryant (Clemson) MTBE December 9th, 2013 5 / 1

Model Formulation

Let:R The set of reactorsS The set of setups for each reactorOij Output of reactor i at setting j, for i ∈ R, j ∈ SIij Required materials input for reactor i at setting j, for i ∈ R, j ∈ SGij Gas by-product released from reactor i at setting j, for i ∈ R, j ∈ SE Limit of gas byproduct released as pollution, per reactorCij Cost of setting reactor i at setting j, for i ∈ R, j ∈ SP Selling price of MTBE per ton

xij

(

1, if reactor i operated at setting j

0, otherwise, for i ∈ R, j ∈ S

Megan Bryant (Clemson) MTBE December 9th, 2013 6 / 1

Model Formulation

The objective of the model is to maximize profit:

Maximize P∗∑

j∈SO|R|,jx|R|,j −∑

i∈R

∑

j∈SCijxij

A single setup must be selected for each reactor:∑

j∈Sxij = 1, for i ∈ R

The output of reactor i must match the input of reactor i+ 1:∑

j∈SOi−1,jxi−1,j −∑

j∈SIi,jxi,j ≥ 0, for i ∈ R

The selected set-up for each reactor must satisfy the requiredpollution limit:

∑

j∈SGijxij ≤ E, for i ∈ R

Megan Bryant (Clemson) MTBE December 9th, 2013 7 / 1

Model Formulation

The objective of the model is to maximize profit:

Maximize P∗∑

j∈SO|R|,jx|R|,j −∑

i∈R

∑

j∈SCijxij

A single setup must be selected for each reactor:∑

j∈Sxij = 1, for i ∈ R

The output of reactor i must match the input of reactor i+ 1:∑

j∈SOi−1,jxi−1,j −∑

j∈SIi,jxi,j ≥ 0, for i ∈ R

The selected set-up for each reactor must satisfy the requiredpollution limit:

∑

j∈SGijxij ≤ E, for i ∈ R

Megan Bryant (Clemson) MTBE December 9th, 2013 7 / 1

Model Formulation

The objective of the model is to maximize profit:

Maximize P∗∑

j∈SO|R|,jx|R|,j −∑

i∈R

∑

j∈SCijxij

A single setup must be selected for each reactor:∑

j∈Sxij = 1, for i ∈ R

The output of reactor i must match the input of reactor i+ 1:∑

j∈SOi−1,jxi−1,j −∑

j∈SIi,jxi,j ≥ 0, for i ∈ R

The selected set-up for each reactor must satisfy the requiredpollution limit:

∑

j∈SGijxij ≤ E, for i ∈ R

Megan Bryant (Clemson) MTBE December 9th, 2013 7 / 1

Model Formulation

The objective of the model is to maximize profit:

Maximize P∗∑

j∈SO|R|,jx|R|,j −∑

i∈R

∑

j∈SCijxij

A single setup must be selected for each reactor:∑

j∈Sxij = 1, for i ∈ R

The output of reactor i must match the input of reactor i+ 1:∑

j∈SOi−1,jxi−1,j −∑

j∈SIi,jxi,j ≥ 0, for i ∈ R

The selected set-up for each reactor must satisfy the requiredpollution limit:

∑

j∈SGijxij ≤ E, for i ∈ R

Megan Bryant (Clemson) MTBE December 9th, 2013 7 / 1

Complete Model Statement

The complete statement of the model is given as follows:

Maximize P∗∑

j∈SO|R|,jx|R|,j −∑

i∈R

∑

j∈SCijxij

subject to∑

j∈Sxij = 1, for i ∈ R

∑

j∈SOi−1,jxi−1,j −∑

j∈SIi,jxi,j ≥ 0, for i ∈ R

∑

j∈SGijxij ≤ E, for i ∈ R

xij ∈ {0,1},∀i ∈ R, j ∈ S

Megan Bryant (Clemson) MTBE December 9th, 2013 8 / 1

Results and Analysis

The solved model provides the following optimal solution:

Reactor 1 employs setup 1

Reactor 2 employs setup 1

Reactor 3 employs setup 6

Under this operational policy, Ibn Zahr will produce MTBE at arate of 62 tons per hour.

This rate will result in 1,488 tons of MTBE daily.

Gross profits are estimated to be $1,982,016.

Megan Bryant (Clemson) MTBE December 9th, 2013 9 / 1

Results and Analysis

The solved model provides the following optimal solution:

Reactor 1 employs setup 1

Reactor 2 employs setup 1

Reactor 3 employs setup 6

Under this operational policy, Ibn Zahr will produce MTBE at arate of 62 tons per hour.

This rate will result in 1,488 tons of MTBE daily.

Gross profits are estimated to be $1,982,016.

Megan Bryant (Clemson) MTBE December 9th, 2013 9 / 1

Results and Analysis

The solved model provides the following optimal solution:

Reactor 1 employs setup 1

Reactor 2 employs setup 1

Reactor 3 employs setup 6

Under this operational policy, Ibn Zahr will produce MTBE at arate of 62 tons per hour.

This rate will result in 1,488 tons of MTBE daily.

Gross profits are estimated to be $1,982,016.

Megan Bryant (Clemson) MTBE December 9th, 2013 9 / 1

Results and Analysis

The solved model provides the following optimal solution:

Reactor 1 employs setup 1

Reactor 2 employs setup 1

Reactor 3 employs setup 6

Under this operational policy, Ibn Zahr will produce MTBE at arate of 62 tons per hour.

This rate will result in 1,488 tons of MTBE daily.

Gross profits are estimated to be $1,982,016.

Megan Bryant (Clemson) MTBE December 9th, 2013 9 / 1

Results and Analysis

The solved model provides the following optimal solution:

Reactor 1 employs setup 1

Reactor 2 employs setup 1

Reactor 3 employs setup 6

Under this operational policy, Ibn Zahr will produce MTBE at arate of 62 tons per hour.

This rate will result in 1,488 tons of MTBE daily.

Gross profits are estimated to be $1,982,016.

Megan Bryant (Clemson) MTBE December 9th, 2013 9 / 1

Results and Anaylsis

Even at the optimum production the daily net profit will benegative.

It is estimated that Ibn Zahr run a daily deficit of $1,932.

Ibn Zahr should seek to lower operating costs or expand theMTBE market.

Megan Bryant (Clemson) MTBE December 9th, 2013 10 / 1

Results and Anaylsis

Even at the optimum production the daily net profit will benegative.

It is estimated that Ibn Zahr run a daily deficit of $1,932.

Ibn Zahr should seek to lower operating costs or expand theMTBE market.

Megan Bryant (Clemson) MTBE December 9th, 2013 10 / 1

Results and Anaylsis

Even at the optimum production the daily net profit will benegative.

It is estimated that Ibn Zahr run a daily deficit of $1,932.

Ibn Zahr should seek to lower operating costs or expand theMTBE market.

Megan Bryant (Clemson) MTBE December 9th, 2013 10 / 1

Sensitivity Analysis

A full sensitivity analysis was performed and the model wasfound to be stable.

The constraint relating to the number of setups per reactor istight.

The optimum setup will not be affected by allowing easysetup changes.

Once the reactors are in the optimum setups, changing thesetup will not be beneficial.

Megan Bryant (Clemson) MTBE December 9th, 2013 11 / 1

Sensitivity Analysis

A full sensitivity analysis was performed and the model wasfound to be stable.

The constraint relating to the number of setups per reactor istight.

The optimum setup will not be affected by allowing easysetup changes.

Once the reactors are in the optimum setups, changing thesetup will not be beneficial.

Megan Bryant (Clemson) MTBE December 9th, 2013 11 / 1

Sensitivity Analysis

A full sensitivity analysis was performed and the model wasfound to be stable.

The constraint relating to the number of setups per reactor istight.

The optimum setup will not be affected by allowing easysetup changes.

Once the reactors are in the optimum setups, changing thesetup will not be beneficial.

Megan Bryant (Clemson) MTBE December 9th, 2013 11 / 1

Sensitivity Analysis

A full sensitivity analysis was performed and the model wasfound to be stable.

The constraint relating to the number of setups per reactor istight.

The optimum setup will not be affected by allowing easysetup changes.

Once the reactors are in the optimum setups, changing thesetup will not be beneficial.

Megan Bryant (Clemson) MTBE December 9th, 2013 11 / 1