Optimization a mathematical model (Excel Solver) with professional report.

· Outline

· Company Background 3

· Literature Review 4

· Situation Information 5

· Model Formulation 7

· Objective

· Decision Variables

· Objective Function

· Input Data

· Constrains

· Results And Finding 9

· Sensitivity Analysis 11

· Solver Table Analysis 12

· Conclusion And Recommendation 13

· References 16

· Company Background

SATORP is a world class refinery that has been established as a joint venture between Aramco & Total to build a mixed of refined and chemical products. SATORP was officially born in June 2008 and started the operation six years later in June 2014 by producing a high proportion of white products from heavy crude oil. This giant refinery is one of the most advanced refineries in the world. SATORP has a very clear vision to become a leading in Asia and the middle east to perform refining and petrochemical products to the customers. SATORP processing almost 400,000 barrels per day of Arabian heavy crude oil and produce the following 9 main products:

·

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· LPG

· GASOLINE

· DIESEL

· JET

· COKE

· SULFUR

· PARAXYLENE

· BENZEN

· PROPYLENE

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There is a lot of variety to use the above products in almost all sectors, LPG is mainly used to generate heat and fuel, Benzene on the other hand is mainly used to process a heavy new chemical product, Paraxylene is used to produce fibers, films and polyethylene. Gasoline, however, is heavily used as fuel in light vehicles, while JET is mainly used as air-plane fuel and it can be used as heating oil. Diesel is mainly used in heavy vehicle fuel and Propylene is mainly used to produce polypropylene in petrochemicals, Coke which is the least desired product is mainly used as fuel in very few counties such as China, and finally, Sulfur is mainly used as component to produce Sulfuric acid. With all these variety, SATORP is committing to achieve best in class products mix with the best quality that can be made, and that can’t be achieved without respecting and following the 4 core values of SATORP, People, Professionalism, and Pride & Partnership.

· Literature Review

Oil and gas along with the petrochemical businesses will continue to be a very competitive market. It is always important to find and produce the right amount of all finished products and by-products to ensure the best formula to maximize the profit or reduce the cost. Temperature plays a very important role to specify which product is going to be generated from the refining process. More specifically, the optimization of Gasoline refinery in specific, will for sure lead to a high positive impact in terms of profit generation or cost reduction, by knowing what is the best mixture of products to be refined in order to meet all specs and generate the highest value. Linear programing is a tool to find the most optimal answer based on the agreed objective and under some constrains. The report will study and use Linear programming in order to find the least possible cost to refine gasoline in order to have at most 6 components under a certain constraint. We choose the Linear programming method because of the following criadera:

· LP is widely used in all refinery optimization problems.

· Gasoline refinery problems has no constraints in terms of integer and binary numbers

· Linear Programming will give the ability to find a unique/ multiple solution under a very specified constraint

· In all gasoline refinery problems, complexity occur due to the operations complications and needs, LP will grasp and use the objective and all constraints to give the optimal possible solution

· Situation Information

SATORP planning and scheduling department want to determine how to produce gasoline product (G92 gasoline) by blending available input streams so that the specification is met and achieving the lowest cost. In addition to that, they need to evaluating new opportunity of integration with neighboring company SADARA. The new opportunity offers exchanges of two different steams between the tow companies. Therefore, SATORP need to know the cost of the current blend and whether the new stream will increase or decrease the cost of blend. In this report, CASE 1 represent SATORP’s current blend recipe and cost before new exchanges with SADARA and CASE 2 represent SATORP’s new blend recipe and cost after the new exchange with SADARA. In both cases, both internal and external constraint are considering as well as the final product production capacity and specification.

· Internal constraints

· Each component has an availability that SATORP can’t exceed

· G92 Gasoline should be less than or equal 9.5 RVP

· G92 Gasoline should be greater than or equal 92 RON

· G92 Gasoline production capacity should be greater than or equal 276000 tons per month

· Specification and cost of blending components as illustrated on below table:

· External Agreement

· SATORP is obligated to pump 13 KT of light cracked Naphtha to SADARA per month

· SATORP pump 38,000 ton per month of Heavy Aromatics to SADARA in return SADARA will pump C8+ to SATORP blending pool with the below specification and cost:

· Model Formulation

· Objective

To develop LP model of the company blending pool in order to determine the optimal blend cost using the available components capacity and analyze the impact on blending cost after modifying the blend recipe and introducing new components to the blend pool .

· Decision Variables

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X1=Heavy Aromatic

X2 =Medium Cracked Naphtha

X3=Light Cracked Naphtha

X4=Raffinate

X5=Alkylation

X6 =Normal Butane

X7=SADARA C8+ ( Only Used in Case 2)

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· Objective Function

The objective function to obtain the optimal blend cost of G 92 Gasoline product by satisfying all internal and external constraints and applying the following objective function:

Minimize Blend Cost = 601 X1+ 669 X2 + 629 X3 + 581 X4 + 707 X5 + 456 X6 + 600 X7

· Input Data

· Constraints

· Availability (ton per month)

· RVP limitation

G92 Gasoline RVP ≤ 9.5 (X1 + X2 + X3 + X4 + X5 + X6 + X7)

· RON Limitation

G92 Gasoline RON ≥ 92 (X1 + X2 + X3 + X4 + X5 + X6 + X7)

· Production capacity ( ton per month)

G92 Gasoline production > 276,000

· SATORP-SADARA partnership (ton per month)

X3 Balance (Availability – Production) = 13,000

· Non-negativity

X1, X2 , X3 , X4 , X5 , X6 ,X7 > 0

· Results and Finding

· Sensitivity Analysis

· CASE 1

CASE 1 represent the current blending recipe before any modification and utilizing the available blending components. The optimal blending recipe will take the following components:

· X1 = 108 KT, X2 = 24.4 KT, X3 = 50.3 KT, X4 = 56.6 KT, X5 = 16.6 KT and X6 = 19.8 KT

· The reduce cost for X1 and X2 implies that the cost per unit would have to decrease by at least $ 165 & $ 39 respectively before it would be optimal to produce any unit of them

· G92 gasoline production capacity allowable increase is 4874 tons and allowable decrease is 8188 and the company can gain $ 204 per ton of production increased

· Allowable increase of X3 component to SADARA is 40 KT and can gain $ 30 per ton pumped

· RVP and RON has strict specification, but if relaxed it has allowable increase and allowable decrease and it have significate impact on the blending cost as well.

· CASE 2

CASE 2 represent the changes on the blending recipe after reducing X1 component available capacity and introducing new component capacity to the blending pool. To maintain the same blending cost as case 1 the new blend recipe will take the flowing components

· X1 = 70 KT, X2 = 24.4 KT, X3 = 50.3 KT, X4 = 61.4 KT, X5 = 20.9 KT, X6 = 18.7 KT and X 7 = 30 KT

· The reduce cost for X1, X2 and X3 implies that the cost per unit would have to decrease by at least $ 165 , $ 39 and $ 216 respectively before it would be optimal to produce any unit of them

· G92 gasoline production capacity allowable increase is 6121 tons and allowable decrease is 6941 and the company can gain $ 204 per ton of production increased

· Allowable increase of X3 component to SADARA is 34 KT and can gain $ 30 per ton pumped

· RVP and RON has strict specification, but if relaxed it has allowable increase and allowable decrease and it have significate impact on the blending cost as well

· Solver Tables Analysis

Solvertables analysis helps to evaluate the new SADARA’s stream C8+ and its impacts on SATORP blend cost . Two factors were considered in this analysis , quantity and RON . The results shown in the below tables :

· Profit impact by C8+ quantity supply

· Profit impact by C8+ RON

· Conclusion and Recommendation

The current blend recipe cost SATORP $ 168,496,915 per month to produce 276 KT of G92 gasoline utilizing the refinery available streams. However, this analysis has shown that there is an opportunity to integrate with SADARA to achieve the following objectives:

1) Maintain or minimize the blend cost

2) Increase the profit by selling more of X3 component

3) Increase the gasoline production capacity

It is very important to know that the specification of new stream (RON and RVP) has very strong impact on the blending cost, it might lower the cost or increase it and its correlated to the exchange quantities as it was illustrated in solver tables analysis .

The below table shows the blending components yield for both cases:

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