Jones D.S.J., Pujado P.R. Handbook of Petroleum Processing

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A DICTIONARY OF TERMS AND EXPRESSIONS 1337

Table E.1. An extract from a typical base data ﬁle. TABLE TEF—H2 TREAT OF

CRACKED GAS OILS.

KGO VBO CYO

COKER VIS BR CAT CY

GAS GAS OIL LE OIL

OIL

REFORMER H2 FOEB 0.0244 0.0209 0.0096 XX+H2F

GAS, FOEB – – – XX+GS1

PROPANE – – – XX+C3S

ISOBUTANE – – – XX+IC4

N-BUTANE – – – XX+NC4

C5-380 HYDRO GASL −0.0916 −0.0550 −0.0527 XX+TNP

LOSS OR GAIN −0.0169 −0.0109 −0.0034 XX+LOS

DESULF COKER GAS O −0.9159 – – XX+SKO

LT COKER GAS OIL 1.0000 – – XX+KGO

LT VIS BR GAS OIL – 1.0000 – XX+VBO

H2 TREAT LT VIS GO – −0.9550 – XX+SVO

H2 TRTED CYCLE OI – – −0.9603 XX+SCY

CYCLE OIL – – 1.0000 XX+CYO

FUEL MMBTU/UNIT 0.1113 0.1113 0.1113 XX+FUL

ELEC KWH/UNIT 3.0764 3.0764 3.0764 XX+KWH

STEAM MLB/UNIT 0.0029 0.0029 0.0029 XX+STM

CHEM ROYALTY CATAL 0.0023 0.0023 0.0023 XX+CRC

REPT FEED COLLECTO 1.0000 1.0000 1.0000 XX+FOR

****** – – – STOPIT

REPORT WRITER AID 1.0000 1.0000 1.0000 UNPACK

SULFUR TO RECOVER −8.8500 −5.1400 −5.9800 XX+SUA

H2 TRT LT GO CAP 1.0000 1.0000 1.0000 HTXCPE

GAS PLANT MAX CAP – – – GPXCAP

is shown in Table E.1. From this tabulation, a matrix generator, called GAMMA

1,2

was used to assemble the many submodels into a complete LP matrix. The matrix

was solvable by a linear programming system called OMEGA

. These tabular input

arrays were also used by the solution report writers as we shall see later.

This complete mathematical model of the reﬁnery was displayed by an equation listing

of the entire contents of the data. The equations showed the inter-relationships of the

many variables, including the reﬁnery streams, the blending constraints, the unit to

investment ties, etc. These were also in a form which was ecognizable to the engineers

working on the project.

Having now assembled all the data in a manner usable for linear programming, it was

necessary to check it for errors. Various computer techniques had been developed for

1338 A DICTIONARY OF TERMS AND EXPRESSIONS

this purpose, and these, together with a secondary check by the process engineers,

substantially eliminated the possibilities of obvious error and invalid data.

However, as an added safeguard, a ﬁnal checkout was carried out by actually solving

a test case. These results were scrutinized to ensure that the output gave a realistic

reﬁnery conﬁguration and that all was in balance.

Optimizing and other techniques

A major value of linear programming is that once environment is reﬂected within

a LP framework, this environment can be optimized. In this study, optimization

could be accomplished either by maximizing proﬁt or minimizing expense, and in

this speciﬁc case, the former was selected. It should be emphasized that optimiza-

tion can only be achieved for the environment reﬂected in the model. Great care

was taken therefore to reﬂect all the meaningful, worthwhile options known to be

available.

There are many reﬁnery variables that are of a non-linear nature. Among these

non-linearities are the effects of blending on motor gasoline, the capital expendi-

tures in relation to size of the units, and many severity effects within the various

processes. When these effects could be described on a cost basis by a CONVEX

curve, they were generally included in the model as linear segments of a curve (see

Fig. E.1).

If the severity to value of product relationship was a concave curve, only one variable

could be used to reﬂect changing severity. This by nature has to be an estimate with

a review of the estimate upon solution.

The blend to octane relationship is highly non-linear and a new approach was used

to reﬂect this in the model. This approach had considerable advantage over the older

techniques in that it was relatively easy to understand and use.

It was capable of reﬂecting the value of octane susceptibility to the individual com-

ponents available for the blends. It also had the capability to represent accurately

more than one type of octane (i.e., research, motor, road, etc.) with these effects also

reﬂected back to the various components.

This technique required the aid of a recursive routine to update various model coef-

ﬁcients that reﬂected the actual susceptibilities at the solution point. The model then

re-optimized with the recalculated octane for various blendstocks and again they were

checked. This was repeated until no further change was required.

A DICTIONARY OF TERMS AND EXPRESSIONS 1339

Figure E.1. LP representation of the convex and concave.

The non-linearities of the capital expenditures are concave in nature. Thus, the initial

investment cost estimate was updated by means of a recursive routine which calculated

the investment cost per unit of activity at the solution level. This recursive routine

is described in detail next. Among the various factors that could be considered in

investment costs are total investment cost to size relationships, offsites, insurances,

taxes (both income and property), overhead, maintenance, labor, royalties, escalation,

plant or service factors, depreciation, and the expected economic life of the various

facilities.

Solution approach

In a study of capital expenditure (commonly called facilities planning) such as this,

there are many possible mathematical techniques which can be used to obtain a

solution. Experience has shown, however, that linear programming on a computer is

by far the most economic approach to solving this type of problem. By this method,

most of the many possible solutions can be examined quickly and effectively. Before

discussing the solution approach used in this study, let us quickly review the invest-

ment environment for any typical reﬁnery unit. This is illustrated in a simpliﬁed form

in Fig. E.2.

1340 A DICTIONARY OF TERMS AND EXPRESSIONS

Figure E.2. Cost parameters for any typical reﬁnery unit.

The total cost curve, on linear graph paper, shows that as a volume throughput is

increased, the total cost of a unit will increased, However, the plot of unit volume cost

($/bpcd) against throughput shows the reverse; that is, the cost per unit of throughput

will decrease as the volume of throughput increases. It is this type of cost that is

reﬂected in an LP model.

Figure E.2 also shows a plot of the average cost slope and the incremental cost slope at

a given throughput level. This average cost slope includes all the costs associated with

a particular unit. The slope is linear and must pass through the origin. The incremental

cost slope reﬂects the change in cost per unit throughput over a short range. This slope

is always tangential to the total cost curve at any throughput under consideration.

It can be seen that the average cost gives the model ‘greater than to be expected’

incentive for changing the size of the unit, while the incremental cost curve on the

other hand gives the expected incentive. The incremental cost ignores all ﬁxed costs

at the solution level, and consists mainly of the expected return on investment.

The technique used in this study was to begin the solution by establishing a very

nominal cost on all units. This allowed any unit to be chosen in the solution. Once the

LP had selected an optimal unit conﬁguration with those nominal costs, a recursive

program for investment cost estimating was used to determine average cost of the

units at the solution throughputs. These average costs were based on a minimum

A DICTIONARY OF TERMS AND EXPRESSIONS 1341

return of investment, and an expected economic life calculated on a discounted cash

ﬂow basis.

These new calculated costs were then substituted for the original arbitrary cost in

the model. This average costing tended to delete the very unrealistically small units

that may have been chosen in the unrestricted conﬁguration. Again, the model was

optimized with these new costs.

The recursions and solutions were repeated until no further cost, conﬁguration or size

changes were required. All the items described above were carried out in a single

computer run, and this solution was saved on tape and reported. Close scrutiny of

the results then followed to make sure that they were reasonable and that there was

no automatically restricted unit that might have been selected had a different solution

path been used.

A second step was then commenced which restored the solution of the ﬁrst step based

on the average cost to the computer. The investment costs for the conﬁguration were

then recalculated using the incremental cost concept. This incremental cost required

no return on investment and an inﬁnite economic life was assumed for the units. The

only costs that were recognized in this step were the incremental maintenance for

each unit. Therefore, the building costs did not economically suppress the size of

units or the total investment. The unit sizes and total investment were optimized on

the premised product slate and available raw materials. A similar recursive step was

again used, but this time it included only the incremental maintenance cost.

The model contains a variable that carries the sum total of the investment. This

variable is updated at the same time as the unit costs are updated by the recursive

operations described. Using this total investment variable it was possible to step down

(paramatrize) on the total investment, until a feasible solution was no longer possible.

An infeasible solution in this context is that in which the cash ﬂow for the conﬁguration

becomes less than zero.

As the total investment are reduced, the unit sizes, the product slates and raw ma-

terials are changed within the framework of the overall premises. Therefore, by this

parametric sweep, the reﬁnery conﬁgurations (both in size and form) could now be

found which would satisfy the following requirements:

Maximum investment

Maximum return on investment

Maximum expected cash ﬂow

Minimum investment

The results of each parametric step were reported and documented.

1342 A DICTIONARY OF TERMS AND EXPRESSIONS

Table E.2. An extract of a typical BI/DJ output

Status Label Cost BI/DJ Status Label Cost BI/DJ

BI FU+VIS .000 12.9443 BI FU/VBR .000 .0000

BI FU/CYO .000 1.4567 GO−DIN .000 .0574

BI FU/HBA .000 .0000 BI GO−SPG .000 .0029

FU/HBB .000 .0591 GO−XXX −10.000 14.1623

BI FU/HBE .000 .0000 BI GO−446 .000 8.7949

FU/HBF .000 .0000 BI GO−675 .000 12.5429

FU/HBG .000 .1084 BI GO+POR .000 1.9087

FU/HBH .000 1.3164 BI GO+SPG .000 .0097

FU/HBM .000 .6095 GO+SUL .000 .0754

Solution analysis

Besides the specially designed report writing technique already discussed, the LP also

has a standard number of solution reports and these are generally of a more technical

nature. Although of great value, they do not readily lend themselve to immediate and

apparent interpretation. It is imperative, however, that some members of a team using

an LP can read and interpret these outputs, particularly as one major use of these

reports is to highlight any obvious errors that may have been overlooked. Some of

these reports used in this study were called the BI/DJ and Range output. They warrant

a brief explanation.

The BI/DJ output (see Table E.2) gives the solution level activities (BI) for all the

variables that were selected in the optimum solution. For those variables that were not

selected, the cost or decrease in proﬁt that would occur were they forcibly included

in the conﬁguration (or basis) is given by the DJ value.

The Range information is a complementary report to the BI/DJ. The ranges give the

incremental volume associated with the DJ’s and the cost ranges associated with the

basis variables. The valuable use of the BI/DJ and the range ﬁles can best be expressed

by an example, using the extracts shown in Tables E.2, E.3, and E.4.

Consider the component CYO that has been selected in the conﬁguration. (The code

FU/CYO in this case indicates that the reﬁnery stream CYO is routed to fuel.) The

quantity of the stream CYO that enters the fuel blend is 1,457 bpcd. Now consider

the component ‘HBM’. This has not been selected in the basis, and this stream has

a DJ value (i.e., no preﬁx). To route the ‘HBM’stream to fuel forcibly would cost

$0.6095/bbl. This information is interesting, but has no real value unless the ranges

for their streams are known.

A DICTIONARY OF TERMS AND EXPRESSIONS 1343

Table E.3. An extract of the corresponding primal range output

Limits of range

Negative Positive

Variable Cost Variable Cost

LP label LP cost affected increment affected increment

MD/KER .000000 MD/HDF −.005291 MD+SUL .131973

FU/CYO .000000 HF/CYO −.000000 XX+VBR .028074

FU/HBA .000000 HF/HBA −.000000 GO/HDA 1.293871

FU/HBE .000000 HF/HBE −.000000 H3FHCE 1.085441

FU/HRB .000000 HF+POR −.000000 HF+VIS .000000

FU/HRE .000000 HF/HRE −.000000 HVFHBE .164348

FU/HRG .000000 HF/HRG −.000000 GO/HDG 1.243582

FU/HSB .000000 HF/HSB −.000003 GO/HDB 1.510931

FU/KEX .000000 XX+KEX −2.541661 SLYKER 19.910502

Because the FU/CYO item is selected in the basis, the range data for this is found in

the primal range output (Table E.4). Interpreting the statement for this stream in this

output means that optimum volume levels of the solution would not have changed

even if the variable had a very small negative incentive (less than $0.000001). Further,

the situation would not have changed even if this variable had a positive cost incentive

of up to $0.02807/bbl.

Let us now look at the ‘HBM’variable. this was not chosen in the basis and it appears

in the dual range output (Table E.5). Interpreting the data for this item shows that to

route ‘HBM’to fuel would cost 60 cents/bbl for the ﬁrst 549 bpcd. All that is known

thereafter is that the cost per barrel over 549 bpcd would increase.

Table E.4. An extract of the corresponding dual range

output

Limits of range

Original Variable Positive volume

LP label activity affected increment

FU/HBB .000000 FU/HRB .000000

FU/HBF .000000 HF/HBF .000000

FU/HBG .000000 CCFHSG .000000

FU/HBH .000000 TEFCYO .109287

FU/HBM .000000 FU/CYO .549070

FU/HRA .000000 FU/VBR .000000

FU/HRF .000000 FU/VBR .000000

FU/HRH .000000 FU/VBR .000000

FU/HSA .000000 CCFHSA .000000

1344 A DICTIONARY OF TERMS AND EXPRESSIONS

Table E.5. Material and economic balance

Product or feed price M B/CD M $/CD MM $/YR

Premium gasoline – – – –

Inter. gasoline – – – –

Regular gasoline – – – –

Hi. vis. hvy fuel – – – –

Kerosene, regular – – – –

Propane LPG – – – –

Marine diesel – – – –

Sulfur MM LBS (Actual data has been deleted )

Shortage and fuel – – – –

Total production – – – –

Crude – – – –

Total feedstocks – – – –

Tel. in liters – – – –

Production margin – – – –

Expenses

Utilities chem. and royalties – – −6.064 –

Operating labor, super, and lab. – – −2.930 –

Maint., ins., tax, and overhead – – −3.061 –

Capital recovery – – −12.817 4.678

Total expenses – – −24.872 –

Earnings (loss) – – −4.202 −1.534

Cash ﬂow, earning plus capital recovery – – – 3.144

Investment MM $

Plant 27.929

Offsite –

Catalyst and royalties –

Added offsites, wharfs, etc. –

Total 27.929

Year to payout, inv./cash ﬂow* 8.882

ROI 7 years, percent 3.0

ROI 10 years, percent 10.5

ROI 16 years, percent 15.1

∗

Figures reported before income tax withdrawn.

The example chosen here describes the economic analysis of two optional streams

which can be logically routed ao a fuel blend. It is emphasized that the BI/DJ and

range outputs, however, contain similar information for all variables whether process

units, reﬁnery streams, product speciﬁcations, etc. contained in the model.

Computer report writer

The data generated by the computer contains all facts relevant to the solution. However,

to all but a few highly trained people the data in this form would be meaningless and

of no practical use. The LP system used in this study contained a specially designed

A DICTIONARY OF TERMS AND EXPRESSIONS 1345

report writer, coded in a language called DART

4,5

. This converted and assembled the

computer LP output into management orientated reports that could easily be read and

understood without sacriﬁcing the relevant technical content.

In this particular case, too, much of data, as produced by the report writing sequence,

was in such a form as to be reproducible and able to be included in the ﬁnal documen-

tation. Table E.5 shows an example of such a report. (Note: the actual calculated data

in this example has been deleted).

For the parametric series discussed above, a special report writing technique was

developed which allowed each succeeding parametric step to be repeated in a case

stacking fashion. This type of report was considerably condensed from the reports

described earlier.

Final documentation

When the solutions to the four premises of the problem had been determined, using

the techniques described, they existed, hidden among the mass of tabulated data that

formed the computer output. It remained now to extract the pertinent section of the

output and to present it so that the objective of the study, which was to provide

management with information to make a good decision, could be achieved. The most

common means of doing this—and the one chosen on this occasion—is by a written

report in which the data is summarized, discussed and the conclusion stated.

Although it is not proposed to discuss the general techniques of technical report

writing here, some fundamental requirements of a complex presentation such as this

are worth highlighting. This report had to satisfy two principal functions. The ﬁrst,

to present as succinctly as possible the conclusions, and the interpretation of those

conclusions, for the convenience of the client’s management. Secondly, it had to

present all the back-up data in as short a form as possible that would be necessary to

enable the client’s own staff to check and conﬁrm the conclusions reached.

This second function was satisﬁed in this report in the form of an appendix. This

included copies of the actual pertinent computer printouts complete with tabular

listing of the submodels, economic balances, etc. These data were further augmented

by the summary of the economic and yield output for the respective parametric runs.

The main body of the report consisted of a short description of the study, together

with discussion of the result. The results were however succinctly described by two

illustrations for each of the four cases of the problem. The ﬁrst illustration showed

the ultimate reﬁnery complex which satisﬁed the premise of the case studied, and a

typical example is shown in Fig. E.3. The second illustration, typiﬁed by Fig. E.4,

1346 A DICTIONARY OF TERMS AND EXPRESSIONS

Figure E.3. Typical ﬁnal optimum conﬁguration.

Figure E.4. Bar chart summarising economic studies for conﬁguration in Fig E.3.