LP MODELING PIECES TOGETHER REFORMULATION PUZZLE

John H. Jenkins
Pace Consultants Inc.
Houston

Pace Consultants Inc. has been working for well over a year to improve its linear programming (LP) modeling capability for both reformulated and California Air Resources Board (CARB)-type specifications. Pace has completed numerous assignments modeling single refineries and world refining areas.

A history of the modifications made to Pace's model and a procedure for analyzing a refinery's operations and options will provide refiners with an indispensable tool in meeting future gasoline specifications.

BACKGROUND

There is no way a refiner can properly analyze options to produce reformulated or CARB gasoline without the use of some type of linear model. There are simply too many variables, too many specifications, and too many options to examine without a sophisticated solution or optimization tool. Further, the best solutions frequently are not obvious. "Rules of thumb" regarding new unit economics, octane costs, or constraints do not work.

UPGRADING THE MODEL

Pace's comprehensive Linear Programming Model uses the Pace Refinery Data Base and Generalized Refining Transportation Marketing Planning System (Grtmps), which is licensed from Haverly Systems.

The model is used on personal computers.

ADDING PROPERTIES

Prior to 1990, very few linear programs carried the data base necessary to analyze reformulated or CARB gasoline production. Data for benzene, sulfur, T90, olefins, and total aromatics must be added to existing gasoline blendstock properties.

It is important to add properties for all possible blending components, whether internally produced or purchased as an outside blendstock. In some early work, for example, Pace was amazed to find the model purchasing toluene until it determined that it had not provided data on aromatics content for purchased toluene.

Seeing a high-octane, non-aromatic blendstock with no benzene or olefins, the model would "pay" almost any price.

FLEXIBILITY

In addition to adding gasoline properties, it will be necessary to increase the flexibility of the model to put materials into pools that are not traditional. For example, it may be effective to reroute heavier naphtha from the reformer feed into kerosine, light heating oil, or road diesel.

If such flexibility is added, it is obviously necessary to provide a full set of distillate properties for these cuts.

In addition to the fairly obvious "reroutings" such as heavy naphtha to distillate, flexibility changes should include some decidedly nontraditional and un obvious possibilities. For example, in refineries that sell naphtha, Pace has sometimes found it more effective to process lighter cuts and sell heavier naphtha.

The feasibility of marketing such a naphtha depends on buyer requirements, but in some cases the possibility has considerable merit. New "open specification" pools such as a highly aromatic blendstock or benzene concentrate should also be considered in refineries where petrochemical sale or sale offshore can reasonably be considered.

Flexibility should also be included in feedstock purchasing. Obviously MTBE, ethanol, and any other available outside oxygenates should be provided as possible purchases. This is true even in refineries that are capable of producing sufficient oxygenates internally. In some situations, the make/buy economics may be surprising.

Crude selection should also be considered a variable. Because different crude oils have different benzene precursors, fluid catalytic cracking unit (FCCU) gasoline sulfur, and light naphtha properties, traditional pricing relationships will change in the reformulated/CARB world. These relationships will become much more refinery specific.

Although it is generally not reasonable for a refiner to assume that he can produce new grades of gasoline based solely on crude selection, Pace has found that eliminating or adding crude oils to the slate can affect the solution and should be considered.

Another facet of flexibility that should be included is a significant increase in the number of gasoline fractions. In a traditional refinery, it was entirely reasonable to specify all FCCU gasoline, from C5 to 430 F., as one pool.

Now, the radical differences between aromatics, olefins, and sulfur in the light portion of FCCU naphtha vs. the heavy cut make it important to segregate cuts. Pace usually models FCCU naphtha as two or three cuts with different properties.

The addition of cuts also implies different pool possibilities. For example, Pace usually opens its medium and heaviest-cut naphtha to kerosine and diesel pools. Again, more properties must be added to accommodate new blending possibilities.

In some cases such flexibility implies fractionation capability that does not currently exist. For these reasons, Pace models gasoline separation systems as separate units with their own utility and capital costs. Pace believes the reformulated/CARB refinery will include far more product separation than the traditional refinery.

Table 1 is a simplified representation of possible outlets for various virgin and processed streams. In a large aggregate model, the number of pools can become quite large because of the number of gasoline and distillate grades required.

NEW STRUCTURE

In addition to structure added to accommodate new blending possibilities and properties, it is necessary to add considerable new structure around conversion units. For Pace, this area was by far the most technically challenging, both from a linear modeling standpoint and in terms of yield representation.

THE REFORMER

Consider, for example, the modeling of the catalytic reformer. In an unreformulated world, it was reasonable to represent a reformer as a unit that could bring in feed of a given fractionation range and paraffin/olefin/naphthene/armoatic content (PONA), and produce a defined yield as a function of octane.

In the reformulated world, it also becomes necessary to predict benzene and aromatics as a function of octane and feed properties. Further, the model must be able to recognize differences between moderately heavy feed reformate (to 350 F.) and heavy feed reformate (to 400 F.).

Finally, operations must be congruous and reasonable. One cannot, for example, have the light portion of feed at one severity, the middle portion going to distillate, and the heavy naphtha operating at some other severity.

Fig. 1 shows a simplified schematic of the reformer structure.

Products can be blended either to a single reformate or to gasoline pools separately.

THE FCCU

The FCCU also presented a considerable challenge. It is relatively easy to add structure to predict sulfur distribution in FCCU products as a function of feed sulfur, However, distribution is different if the FCCU feed has been hydrotreated than it is with virgin low-sulfur feeds. This difference makes it necessary to create a different structure.

Although Pace's model is capable of varying conversion in the FCCU, Pace has not yet been successful at inputting structure to change properties as a function of conversion. Because early tests of this approach led to convergence problems, Pace normally uses its FCCU simulation model to improve the property estimates after an LP solution is obtained.

Pace also had to modify the structure to allow global specifications. This is necessary to guarantee that anti dumping provisions are met, and that all of the blend optimization is recognized when producing several grades of gasoline.

Certainly, Pace's need to have a generalized linear model that can be used for any refinery makes the technical problems of modeling more difficult than that of a company modeling a single refinery. For example, Pace's model includes three gasoline reformers of different pressure levels, and a benzene/toluene/xylenes (BTX) reformer. A new structure was required for each.

However, a model that does not properly recognize the possible flexibility of existing units or the flexibility that could be easily added will not find the best answers to the reformulation puzzle.

NEW UNITS

Adding new units to linear models for the analysis of reformulated/CARB gasoline is the first activity that many companies undertake. It is also the easiest and, in some cases, the least critical.

Data on yields, costs, and properties are generally available from licensors and usually can be added fairly easily. For study purposes, Pace recommends the following addition to normal linear model data bases for reformulation:

Alkylation. Includes C3, C5, and additions to C4 capability.
MTBE/TAME from FCCU streams. Here, the user should be certain to include any necessary front-end fractionation to the cost and utility balances because some licensors do not include this.
Benzene saturation. A unit to saturate benzene in light reformate and isomerize light paraffins is frequently required for benzene specifications.
Heavy naphtha destruction. In some situations a unit designed to produce a naphthenic middle-range gasoline from heavy naphtha may be considered. UOP's Informing is such a process.
Hydrogen production/management. If reformer throughput/severity decreases in a hydrogen-tight facility, it may be necessary to consider a new source, either by production or improved hydrogen recovery.

In a CARB environment, other units that should be added to the data base include:

FCCU gasoline hydrotreating. Be certain to recognize the impact of olefin saturation on octane.
FCCU feed hydrotreating. Again, sulfur distribution is influenced by hydrotreating.
Additional FCCU gasoline fractionation.

The influence of capital additions on the objective function should be part of the model formulation. At Pace, capital addition has always been an important part of single client assignments; as a result, capital tables are included in the model.

For some models, however, adding such structure is difficult. Some of Pace's clients have resorted to "faking" capital costs by increasing fuel usage in an effort to better recognize the influence on profitability.

MAKING RUNS

After completing the considerable effort of modifying the model, the problem of making reformulated/CARB gasoline can be analyzed. First, recognize that the examination of refinery options will take more than a few runs.

Producing the new gasolines, especially CARB, is, in Pace's experience, the most complex, constrained linear programming work ever undertaken. There are far more variables, possibilities, constraints, and options than in typical project analysis.

Do not expect an answer in a few days. After all, the decisions you make are probably the most important of the 1990s. Although there is no "cook book" for making runs, the following procedures and tips have proven helpful to our linear modeling experts:

Start by fixing major products and varying crude oils. Pace consultants typically begin by fixing gasoline and transportation fuels and allowing fuel oils and feedstocks to float.
Find the noncapital possibilities first. For reformulation, most refineries can produce at least a portion of their gasoline pool as reformulated with minimal or no capital. This may involve some deleterious trade off-increased sale of lower-value naphtha, for example-but the exercise is helpful in establishing constraints. Produce as high a percentage of reformulated as possible before the model goes infeasible. CARB LP runs typically become constricted much earlier than reformulated runs.
Be very careful in analyzing runs, especially early in the project. Every property of every component in every pool should be checked. Watch for "gotcha's" left over from nonreformulated days. For example, Pace's original data base included a nonzero "placeholder" for sulfur in reformate that was put in years ago. On inspection, this placeholder was found to be 10 ppm-certainly too high for reformate and high enough to influence CARB results.
Draw a simple flow sheet showing connectivity and unit operations. Check each unit's weight balance, yield pattern, and operating mode. Check the overall weight balance and the utility requirements. If your model does not show weight balances, it should be added. Again, this may seem unduly tedious, but the model has just undergone major surgery. Finding errors early will save immeasurable pain later.
Find the constraints. When runs begin to become infeasible or require unusual configurations to converge, it is important to define binding constraints. In this way, a solution, whether capital or operational, can address the specific problem.
Vary the fixed parameters. Once a constraint is found, try changing the fixed product constraints. Will more gasoline production help or hinder? How about less premium? More middle distillate?
Examine the shadow prices. Because the new gasolines, especially CARB, are binding on almost every specification, there are plenty of "shadow" prices on feeds and in the blend pools. (A shadow price is the price a model will pay for the next increment of supply.) These are probably the best indications of constraints.
Once constraints are found, look at both capital and noncapital approaches. If aromatics are a constraint, for example, consider selling blendstock offshore as well as adding a saturation unit. Never make more than one move at a time. It is important to construct a cause and effect history.
Watch the influence of pricing. In order to run any linear model, it is necessary to input prices for all feeds and products. If the analyst is not careful, the "best" answer will be a result of the prices. Pace does not use the objective function as an indication of the "goodness" of the run, but rather constructs a complete charge and yields, with pricing for each case in a spreadsheet format. In this way, the "cost" of producing new gasoline can be computed on a consistent basis. Assumptions regarding margins, purchase prices, and capital costs can quickly be varied to determine whether a "good" solution is actually highly premise dependent.
Look at any reasonable operating variable or product mix. Pace increasingly finds that some of the best solutions may imply significant changes in marketing or feedstock acquisition. In this sense, the project should include input and iteration not only with refining and modeling personnel, but also with marketing and the strategic planning group as well.

In short, the analysis of options is the building of a matrix of solutions in which many parameters have been varied. To evaluate a strategy, consider not only numeric indicators such as cost and profitability, but also more global properties such as flexibility, consistency with probable complex model rules, and compliance with corporate goals.

FUTURE

Pace is not yet through with its linear program work. It is now looking at linearizing segments of the simple model to more accurately deal with the benzene/aromatic trade off, and also dealing with recurrent problems on regression/conversion.

As the complex model becomes more defined, Pace will doubtlessly be including structure to internally compute these parameters. Its linear program and data base likely will be in an evolutionary mode for at least another year.

No model can "give" an answer; the best solution will come from the creativity, capability, and expertise of the project team.

Pace's advice to those working on reformulated/CARB problems: let your mind roam. You are preparing to battle a very difficult problem. Enter the fight with the sharpest possible sword. Do not dismiss any solution as being too far outside normal operations until you have truly analyzed the possibility.