1982-09 Spring 1982

SOUTHERN METHODIST UNP Oil Refinery Project - Linear

Programming

Stanley D. Strifler

SENIOR DESIGN

OREM 4390

STANLEY D. STRIFLER

OIL REFINERY P1JECI' - LINEZR PRN1ING

DEPARTMENT OF OPERATIONS RESEARCH AND ENGINEERING MANAGEMENT

SCHOOL OF ENGINEERING AND APPLIED SCIENCE

DALLAS, TEXAS 727

SENIOR DESIGN

OREM 4390

STANLEY D. STRIFLER

OIL REFINERY PIOJECT - LINEAR PROGRAMING

I. Background and Overview

An oil refinery located in northeast Texas purchases crude fran two

different sources. One of these sources being in Okiahana and the

other in West Texas. The oil refinery has a contract with each of

these suppliers to buy a minim= of 5,000 bbls of oil per day (ie...

the oil refinery is cxitinitted to purchasing a total of 10,000 bbls/day).

The oil refinery has a maxinun capacity of 20,000 bbls/day and

obviously desires to maximize their profits. This maximization of

profit is the purpose of the following linear program (12) model. The

main decision at hand is how much nore crude, if any, should the oil

refinery purchase from one or both sources in order to realize a

maximization of profit. All data provided including prices, product

demands, refinery unit yields, etc... are included in this presentation.

II. Model Descriptions

Care was taken to establish an area for all possible future constraints

to fit neatly into the model and consideration was also given to any

possible changes to the model that might take place. As seen on the

Row and Colurn specifications for the LP model, areas have been

established to accarodate any changes in product quality specifications

and product minimum and maximum demands. I tried to establish a "base

case" with mid-range variable values as opposed to pushing extremes

in order that a more realistic picture of the profit equation might

be seen. I chose to create minimum demands for the products in the model

because several of the refinery's products ware not being produced and

I made the assumption that the refinery would not have been built to

produce some product if at some point it did not have an established

demand. Pricing of the raw materials and final products was very

conservative due to the current soft market for the refinery's products.

The model consisted of 66 decision variables and 82 active constraints

at this tine. Of the 82 constraints, 69 are less than (flow streams -

for the most part), 1 is an equality (the operating costs), and

12 are greater than constraints (made up mostly of minimum product

demands).

III. Solution Phase

Actually getting to the point of solving the LP model proved to

be a tedious part of the project. Collecting data concerning product

demands, refinery unit output yields, and product vapor, density,

sulfur and octane specifications proved to be time consuming and

without the help of Dr. Julius Aronofsky and his book MANAGERIAL

PLANNING WITH LINEAR PROGRAMMING: In Process Industry Operations

may have been a severe setback. Hover, after establishing the basic

assumptions noted in section II the solution phase of the project

proceeded at a good pace. I have included a copy of the Southern

Methodist University BLP output of the optimal solution with this

report.

Our objective function included the cost of the four raw materials

used (Oklahoma set crude, West Texas crude, isobutane, and feed

stock) and the revenues of the seven products produced (#6 flux,

#6 fuel oil, fuel gas, LPG, regular gasoline, #2 fuel, and jet fuel)

as well as a $500/bbl charge for any barrel of product produced that

did not meet the vapor, density, sulfur, or octane specifications.

We took into consideration the physical and management implications

of the manner in which equations were written for yields, splits at

junction points, material balances, and quality specifications. For

example, while yields (outputs) could never be greater than the quantity

of material fed in (inputs), it might be feasible for input to be

greater than output, thus, any constraint row that represented a yield,

or a split at a junction point, or volurretric blending was written as

a less than or equal to constraint with a nonnegative right hand

side, such as

-inputs + outputs .^- 0

A look at the table of row designations shows that a large majority

of constraints (69 of 82) re written in this form. Since such

constraints did not reauire the use () artificial vectors, fewer

• calculations were used, and thus shorter caputer processing time

was needekas well.

IV. Analysis

As mentioned earlier, this 12 model was approached from a profit

maximization standpoint as opposed to a cost minimization standpoint.

This approach treated crude input supplies and product output demands

as values for the model to determine rather than as given. This approach

was considered realistic for a small refinery, such as the one we

chose to use, whose size of operation, requirements of raw materials

and barrels of production output do not affet4 supply and demand for

materials and products, and whose operations are unrestricted by any

parent organizations needs. The maximum profit in the optimal solution

turned out to be $61,452. 30/day on the use of the maximum allowed

20,000 bbls/day or $3. 073/bbl/day. The model used the minimum

requirement of 5,000 bbls/day of Oklahoma sweet crude and 15,000 bbls/day

of West Texas crude. The products were optimally produced in the

following manner:

#6 Flux 1,500 bbls/day (minimum demand)

#6 Fuel Oil 500 bbls/day (minimum demand)

Fuel Gas 1,000 bbls/day (minimum demand)

LPG 500 bbls/day (minimum demand)

Peg Gasoline 11,095 bbls/day

#2 Fuel 4,125 bbls/day

Jet Fuel 2,915 bbls/day

Total operating costs cane to a total of $107,094/day and no penalties

for quality constraint specifications were imposed.

Some interesting notes provided by a study of the marginal values

of the model constraints shows that for each barrel of total production

capacity we could add and additional $5.183 of profit could be attained

which is more than the $3. O73/bbl/day of profit now being attained.

Also, for each additional barrel of isobutane and feed stock

available to the model $30.738 and $9.15 of additional profit,

respectively, could be added. Each additional barrel of Oklahoma sweet

crude required reduces profit by $. 123/day, while each additional

barrel of #6 Flux, #6 Fuel Oil, Fuel Gas, and LPG reduces profit

by $23.85, $18.15, $1.65, and $27.60 respectively.

Other interesting notes were provided by parametric analysis done on

Oklahoma Sweet and West Texas crude as well as on isobutane and

feed stock. According to the analysis on the two crudes, should the

price of Oklahoma Sweet crude drop by $. 13/bbl or the price of West

Texas crude rise by $. 13/bbl then the desired amounts of the respective

crudes would completely reverse. The model would require the minimum

purchase of 5,000 bbls/day of West Texas crude and 15,000 bbls/day of

Oklahoma Sweet crude. The analysis of isobutane and feed stock showed that

should prices rise to $39.45 and $47.30 respectively then their use

would be cut to 0 bbls/day.

V. conclusions

I feel the nodel will be very useful to the people involved at the

refinery, especially when the proper flow and quality specifications

are obtained. My recrrrendations in this sorrewhat artificial case

would be to not renew contracts which require the production of

#6 flux, #6 fuel oil, fuel gas, and 12G. Also to analyse the possibility

and costs of increasing refinery capacities and to try to acquire

more isobutane and feed stock.

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CRUDE UNIT OUTPUTS

PRODUCT DESTINATIONS

VACUUM SECTION

'ICCUNIT

GASOLINE TREATER

DISTILLATE BLENDING .

BENDER TREATER

NEROX TREATER

#6 FLUX #6 FUEL OIL FUEL GAS LPG PEG GAS #2 FUEL JET

• X

• . . X. . X X X X

• . . • . • • X

• • • • • . • • •

• • • • . . • •

• . • • • • . . . • • X

PROCESS DESTINATIONS (Unit Numbers)

VACUUM SECTION

'ICC UNIT

GASOLINE TREATER

DISTILLATE BLENDING

BENDER TREATER

NEROX TREPJaER

1 2 3 4 5 6 7 8 9 10 11 12

X x X X x X X X

X x x X X

X X• X

X X

X X X

X X

CAPACITIES OF REFINERY PIJCESS UNITS

(bbl/day)

CRUDE UNIT (1)

VACUUM SECTICN UNIT (2)

TOC UNIT (3)

GASOLINE TREATER UNIT (4)

BENDER TREATER UNIT (5)

MEPDX TREATER UNIT (6)

ASPHALT OXIDIZER UNIT (7)

AU(Y FEED TREATER UNIT (8)

DISTILLATE BLENDING UNIT (9)

ASPHALT BLENDING UNIT (10)

ALKYLATIJ UNIT (11)

GASOLINE BLENDING UNIT (12)

20,000

LSJAII1I

"Jo dyl-ly0i

REFINERY COSTS, PRODUCT SALE PRICES

RAW MATERIAL COSTS ($/bbi)

OKLAHOMA SWEET CRUDE (Ti)

44.00

WEST TEXAS CRUDE (T2)

44.00

ISOBtJTANE (X7)

8.71

FEED STOCK (X8)

38.15

OPERATING COSTS ($/bbl processed)

THE OIL REFINERY HAS DECIDED TO ASSIGN A PER BARREL PRUCESSED COST OF $4.95 RATHER THAN ASSIGN AN OPERATING COST ¶10 EACH PROCESSING UNIT IN THE REFINERY.

PRODUCT PRICES ($4b1)

#6 FLUX (Y7) 31.90

#6 FUEL OIL (Y8) 34.10

FUEL GAS (Y9) 50.60

LPG (Y0) 24.65

REGULAR GASOLINE (Zi) 52.25

#2 FUEL (Z2) 51.35

JET FUEL (Z3) 53.45

AVAILABILITY OF RAW MATERIALS

(bbl/day)

OKLAfla4A SWEET CRUDE (Ti) UNLIMITED

WEST TEXAS CRUDE (T2) UNLIMITED

ISOBUT1NE (X7) 430

FEED S'IOCK (X8) 600

PRODUCT DEMANDS

(1±1/day)

#6 FLUX (Y7) 1500

#6 FUEL OIL (Y8) 500

FUEL GAS (Y9) 1000

LPG (Y0) 500

REGULAR GASOLINE (zi) 2500

#2 FUEL (Z2) 500

JET FUEL (Z3) 1000

PRODUCT QUALITY SPECIFICATIONS

CLEAR RESEARCH VAPOR DENSITY OCTPNE # PRESSURE (lb/bbl)

#6 FLUX (Y7) 200-400

#6 FUEL OIL (YB) . 300

FUEL GAS (Y9)

LPG (Y0) 14.1

REGULAR GASOLINE (Zi) 91.5 11.5

#2 FUEL (Z2)

JET FUEL (Z3) 94.5 12.0

SULFUR (lb/bbl)

1.0 c

'OLUMIT DESIGNATIONS FOR LI? M)DEL

ODLtN NUMBERS QjvvT5 ON FUNCTION SERVED

1-2 INPUT FLCS OF OKEJAHCt'4A SWEET AND WEST TEXAS CRUDES

3-14 OUTPUT FLOW STREAMS FROM CRUDE UNIT (1)

15-20 OUTPUT FLOW STREAMS FROM VAJUM SECTION UNIT (2)

21-32 OUTPUT FLOW STREAMS FROM TCC UNIT (3)

33-34 OUTPUT FLCW STREAMS FROM GASOLINE TREATER UNIT (4)

35-36 OUTPUT FlOW STREAMS FROM BENDER TREATER UNIT (5)

37-38 OUTPUT FILW STREAMS FROM NEROX TREATER UNIT (6)

39-40 OUTPUT FILW STREAMS FROM ASPHALT OXIDIZER UNIT (7)

41-46 OUTPUT FLCIIJ STREAMS FROM ALKY FEED TREATER UNIT (8)

47 INPUT FLOW OF ISOBUTANE

48 INPUT FLL'7 OF FEED STOCK

49-50 OUTPUT FLCX'.7 STREAMS FROM DISTILLATE BLENDING UNIT (9)

51-52 OUTPUT FLOW STREAMS FROM ALK LATIa1 UNIT (11)

53-54 OUTPUT FILE STREAMS FROM ASPHALT BLENDING UNIT (10)

55-56 OUTPUT FlOW STREAMS FROM GASOLINE BLENDING UNIT (12)

57 OUTPUT FLOWOF #6 FLUX PRODUCT (1) 0

58 OUTPUT FLCX'J OF #6 FUEL OIL PRODUCT (2)

59 OUTPUT FILE OF FUEL GAS PRODUCT (3)

60 OUTPUT FLOW OF LPG PRODUCT (4)

61 OUTPUT FLOW OF REGULAR GASOLINE PRODUCT (5)

62 OUTPUT FLCW OF #2 FUEL PRODUCT (6)

63 OUTPUT FLCW OF JET FUEL PRODUCT (7)

0r13It.N DESITIIS FOR LP MODEL (CONTINUED)

COLUMN NUMBER aZ?4MENTS ON FUNCTION SERVED

64 DUNWV2RIABIE USED '10 REElECT COSTS OF VIOLATING VAPOR, DENSITY, OR SULFUR SPECIFICATIONS

65 SUM OF OPERATING COSTS OF MAJOR REFINERY UNITS

66 DLR4vlY V?JREA3LE USED '10 REFLECT COSTS OF VIOLATING OCTANE SPECIFICATIONS

ROW DESIGNATIONS FOR LP MODEL

ROW NUMBERS CCENTS ON FLJNCrION SERVED

1-2 AVAILABILITY OF OKLAHOMA SWEET AND WEST TEXAS CRUDES

3-14 CAPACITIES OF EACH INDIVIDUAL REFINERY UNIT

15-21 VAPOR PRESSURE SPECIFICATIONS

22-28 DENSITY SPECIFICATIONS

29-35 SULFUR SPECIFICATIONS

36-47 YIELDS FOR OUTPUT STREAMS OF CRUDE UNIT (1)

48-49 YIELDS FOR CXYL?UT STREAMS OF VACUUM SECTION UNIT (2)

50-51 SPLITTING PRODUCT FROM VACUUM SECTION UNIT (2)

52-53 YIELDS FOR CXJTPtJT STREAMS OF ¶LC UNIT (3)

54-55 SPLITTING PRODUCT FROM TCX UNIT (3)

56-57 YIELDS FOR OUTPUT STREAMS OF GASOLINE TREATER UNIT (4)

58-59 YIElDS FOR OUTPUT STREAMS OF BENDER TREATER UNIT (5)

60-61 YIELDS FOR OUTPUT STREAMS OF MEROX TREATER UNIT (6)

62-63 YIELDS FOR OUTPUT STREAMS OF ASPHALT OXIDIZER UNIT (7)

64-65 YIELDS FOR OUTPUT STREAMS OF ALKY FEED TREATER UNIT (8)

66-67 YIELDS FOR OUTPUT STREAMS OF DISTILLATE BLENDING UNIT (9)

68-69 YIELDS FOR OUTPUT STREAMS OF ASPHALT BLENDING UNIT (10)

70-71 SPLITTING PRODUCT FROM ALKY FEED TREATER UNIT (8)

72 AVAILABILITY OF ISOBt.YTANE (X7)

73-74 YIELDS FOR OUTPUT STREAMS OF ALKYLATECI UNIT (11)

75 AVAILABILITY OF FEED S'IOCK (X8)

ROW DESIGNATIONS FOR LP MODEL

(CaTINUED)

(X4MDJTS ON FUNCTION SERVED

YIELDS FOR OUTPUT STREAM OF GASOLINE BLENDING UNIT (12)

VOLUMETRIC BLENDING FOR PRODUCTS

SUM OF OPERATING COSTS

SUM OF PRODUCTS

OCTANE SPECIFICATIONS

DENSITY SPECIFICATION

MINIMUM PURCHASES OF OI<I2H SWEET AND WEST TEXAS CRUDE

MINIMUM DEMANDS FOR PRODUCTS

76-77

78-84

85

86-92

93-99

100

101-102

103-109

PARAMETRIC ANALYSIS OF OKUua1A SWEET CRUDE (Ti)

400

345.226

300

200

100

62.452

0

-93.547

-100

43.88

cXJST ($/bbl))

I I I I

PROFIT $1000/day)

I I I I I I I I I I I I I

PARAMETRIC ANALYSIS OF WEST TEXAS CRUDE (T2)

400

346.452

300

200

100

62.452

-94.774

-10025 35 45 55 65 75

44.12

COST ($/bbl)

39.45

COST ($/bbl)

11

PARAMETRIC ANALYSIS OF ISOBIJTANE (X7)

80

PIFIT 60 ($1000/day) 55.962

48.234

1 40

20

El

.tu 00 47.30

COST ($/bbl)

84.342

75

55.962

50

25

El

P1RM1ETBIC ANALYSIS OF FEED STOCK (X8)

pPROFIT

($1000/day)

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IUl U2 U3 U4 U5 U6 U7 U8 U9 UO

1 11 12 13 14 15 16 17 18 19 20

I Vi V2 V3 V4 VS V6 V7 V8 V9 Va

1 21 22 23 24 25 26 27 28 29 30

Wl W2 W3 W4 W5 W6 W7 W8 W9 WO

31 32 33 34 35 36 37 38 39 40

Xl X2 X3 X4 X5 X6 X7 X8 X9 XO

41 42 43 44 45 46 47 48 49 50

1 Yl Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 . YO

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Zl Z2 Z3 Z4 Z5 Z6

61 62 63 64 65 66

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