Alwin MullerConsultant Worth, Germany

The solution of a linear equation system gives individualized octane deviations from the ideal blend values.

The method needs little data, produces simpler correlations, and is more accurate than others because it is highly adaptable.

The deviations calculated by this method are characteristic of each gasoline component and grade. The values are derived directly from original refinery data and therefore reflect refinery-specific situations.

By using these values in an LP-optimized blending model, it is possible to allocate the available components into the different gasoline grades while maximizing the output of premium gasoline.

A computer-based octane improvement system is especially beneficial to refiners who have already squeezed the relevant process units to their limits to improve octane quality.

### INITIAL SITUATION

Hydrocarbon mixtures show, despite their low or nonexistent polarity, a certain deviation from ideal blending behavior. Therefore, the final properties of gasoline blends cannot be predicted accurately from volumetric compositions and properties of pure, simple components.

Hydrocarbon blends obey Raoult's Law closely enough to predict vapor pressure, but not closely enough to predict or simulate distillation. Deviations from linearity, for both density and octane number, occur during daily blending operations.

Refiners without in-line blending facilities to provide continuous quality control are especially concerned with unexpected blending behavior. Reblending of product disturbs normal refinery operation and wastes octane potential.

Attention should be focused on the nonlinearity of the blended octane number because this is the most important property in all grades of gasolines. In general it is not necessary to distinguish between research and motor octane number (RON and MON) when methods for handling real octane blending behavior are described.

Known methods, such as Interaction and the Ethyl method, as well as the new alternative method described in the following text, are valid for both MON and RON.

Refineries that must use a high volume of fluid catalytic cracked (FCC) gasoline in the total gasoline pool are more limited by the specified MON than by the RON, and thus might be obliged to give away RON potential. Those that have a more balanced component pool will pay closer attention to both RON and MON optimization.

In the following, it is simply "octane number" that is under discussion.

### EXCESS OCTANE NUMBER

Deviations from the ideal property of a solution are called excess properties according to physical chemistry terminology. The term "excess" must be understood in a mathematical sense. These excess values may be negative or positive. Many investigations have been performed using binary liquid solutions because the values are measurable and the deviations can be illustrated graphically. This is not the case for systems of three or more components.

The most well-known binary systems show negative deviations from the linearity representing specific volumes or thermodynamic properties.

The difference between the blended octane number (ON) and the octane number for an ideal blend (ONid) may analogously be called excess values (Equation 1). The ON of a real blend can be expressed as shown in Equation 2.

The blend octane value of the pure Component "i" is the sum of its octane number and an excess value (Equation 3). The combination of Equations 1, 2, and 3 gives the deviation of a real blend from an ideal blend (Equation 4).

Because the excess octane number (EON) of each component is a function of its volumetric fraction and because each gasoline grade normally has its own typical composition, it is necessary to mark the value with an additional index "j" representing the different gasoline grades. This extends Equation 4, as shown in Equation 5.

The target will now be to evaluate the ONEij's for each component in each gasoline grade with its characteristic composition.

Having available the EONS, the measured octane numbers of the pure components in the LP-optimized refinery blending model can be extended by these terms (as in Equation 3). This gives the LP-algorithm an incentive to assign the available components produced in a planning cycle to the different grades in such a way that an optimum is obtained,

That means the highest possible or allowed premium-to-regular ratio is calculated, driven by the higher price of the premium grades as compared to regular. The formulas are universal and are applicable in a lead-free as well as a leaded environment. The blending system is of no importance.

### DATA COLLECTION

The new procedure estimates octane blending behavior directly from the blending data. A complete gasoline blending study must be carried out, beginning with data collection and ending with evaluation of the collected data. The most time-consuming and costly part of the work will be the data collection.

Because the gasoline components are somewhat characteristic of individual refineries as well as their operations and crude slates, the results of a gasoline study cannot be simply transfered and used in general. Therefore, a series of laboratory tests on all the components used for gasoline blending at a specific refinery should be performed for the study.

Only those components used for blending the gasoline grades will give reliable EONS. These EONs can be recombined with the pure octane numbers (Equation 3) to form the individual blending values that are finally implemented in the LP-model.

The components should be sampled, obtaining sufficient volumes for the various lab tests because resampling is not possible. The first step is the determination of the pure octane number for each component. For butenes, bibliographical data are just as good.

Next, the blend octane value for each grade blended from those components, in the prevailing composition, should be determined. These mixtures, which contain all the components, represent the base fuels.

To evaluate the influence of each component in a fuel blend, the samples being tested are blended, omitting subsequently and alternately one component after another. In this way on ' e obtains a series of "rest-blends," each missing one component as compared to the base fuel.

The absolute volumes of each component (Vij) used in the test blend remains constant. Of course, the total volume of the test blend varies as individual components are withdrawn, thus changing the volumetric ratios of the components.

A sampling schedule for a given grade of gasoline is shown in Table 1. The diagonal of the rows of different volume mixtures is zero, reflecting the missing component throughout the series of rest-blends.

The number of rest-blends is, following this procedure, equal to the number of components (n) used in the total fuel blend. The number of components used for each rest-blend is n 1.

The right-hand column in Table 1 represents the octane numbers for these rest-blends, determined by the ASTM knock engine test.

It can be seen that the sampling schedule can be easily transformed into a system of simultaneous linear equations, where the volumes and octane numbers are the coefficients, and the octane blend values are the unknowns. The task is to determine their values.

### EVALUATION

A very rough method of determining blend values of components (which imply their EONS) is direct calculation from the base fuel and the respective rest-blend missing the component in question (Equation 6).

It may be useful to explain why this method does not deliver results with enough accuracy. Two main reasons can be given:

- Measurement inaccuracies will falsify the result, especially for those components of small volumes in the gasoline grade (e.g., butenes).
- Leaving high-volume components out of the blend changes the composition of the rest-blend severely and, consequently, the blend values of the remaining components.

The direct evaluation of an individual octane blend value assumes constant values of the components in the rest-blend, which is incorrect. Because Equation 6 uses this incorrect assumption, the resultant blend value is also incorrect.

A correct estimation of blend values must take into account their variable character. A correlation with n variables can be solved if n different equations are available. This is why the testing procedure should be carried out as described.

To transfer the test results into a linear equation system, some modifications and completions must be done, proceeding from the sampling schedule.

First, it is useful to transfer the absolute volumes of the sampling schedule into volume fractions. Using absolute volumes eases the laboratory work, but is unsuitable for the evaluation in Equation 7.

These volume fractions represent the coefficients on the left side of the equation system, whereas the measured octane numbers are the coefficients on the right side (Equation 8). The goal is to compute the values of the variables that simultaneously satisfy the equations.

The solution of a linear equation system suggests the application of the Gaussian elimination method. This can be easily transferred to a computer program with sufficient numeric stability.

The algorithm consists of two main steps. First, the values of the coefficients below the diagonal of the matrix are transfered to zero by forward elimination. Second, the variables are determined beginning with the last row of the equation system by backward substitution.

The data for this case were evaluated with a Pascal program containing the Gaussian algorithm. The number of necessary computer runs equals the number of gasoline grades, j. The excess values are finally calculated from the pure octane values and the blend values (Equation 3).

Table 2 presents the results for the excess values of four gasoline grades currently on the market in Germany. In this example the evaluation method was directed at MON because the pool contains a high amount of cracked gasolines with a wide spread of MON vs. RON. This usually limits the specified MON.

The composition of the gasoline pool is characteristic of a refinery with the complexity of topping, reforming, cracking, and isomerization. The FCC gasoline is split into light and heavy fractions to provide greater blending flexibility.

The isomerate is the product of a C5/C6 isomerization unit with hexane recycling, and contains the isopentane reformed from the n-pentane. The separated isopentane stream flows from a deisopentanizer preceeding the isomerization unit.

The use of imported toluene is low and is primarily for raising some product densities.

Most of the resultant EON values were negative, indicating that the linearly calculated pool MON must be higher than the average MON of the finished products.

From experience, real MON blends show mostly negative deviations from linearity, whereas RON blends often remain above the ideal curve. A founded interpretation for this apparition is not known.

Not surprisingly, the second column of Table 2 shows the highest values for paraffins, isomerate, and isopentane because the values include the lead response at 0.15 g/l. Pb.

It is remarkable, however, that the excess values are negative for two components despite the lead. That means the blend values are even less than the values of the pure components.

The obtained values are not identical to those of the pure components but very close to them (Fig. 1). For example, the number for the isomerate implies a lead response of 6.9 ON, compared to an increment of 7.4 measured for the pure component.

These approximate agreements are an indicator of the reliability of the calculated numbers in Table 2, assuming no additional interaction occurs when the antiknock additive is added.

It is not possible, upon first seeing this table, to recognize how the LP-optimized blends will be composed. This becomes easier if the EONs have extreme values, as is the case in the second column of Table 2.

An LP-optimized gasoline blending program will maximize the content of isomerate in the leaded premium to benefit from this grade's high EON. The content of such a high octane, but light component, will then be limited mostly by the specified volatility.

It is proved again that the paraffins deliver cheap octane potential, as long as one leaded grade is left in the product pattern.

Computer runs using these numbers showed, furthermore, that it is not best to blend the most expensive component into the most expensive product, in contrast to common opinion. For example, the MTBE can even be used for regular blends if this frees a component that is more appropriate for another gasoline grade.

### NUMBER OF DATA SETS

To increase the accuracy of the method, the EON data set should be changed if the gasoline compositions are changed because of seasonal specification requirements, or if the crude type is changed.

It has been proven in practice that it is sufficient to separate crudes into two categories: paraffinics and aromatics. The estimation of data sets for each individual crude cannot be justified even though crudes are singly processed in the subsequent conversion and reforming units.

Fig. 2 is a schematic showing the number of EON data sets that should be made available.

Proceeding from the crude category, sets of EON values should be created according to the number of different local volatility and Rvp specifications. It will then be easy to implement the data tables in advance into the LP-computer programs and activate the data set momentarily when needed, by means of a macroroutine or a defined hot key.

### BLENDING AND PLANNING

Before using new blend values in a field test, their reliability should be verified through laboratory tests. The subsequent field test will represent normal operation because all conditions and parameters reflect normal operation. The test serves primarily to acquaint the user with the new procedure.

Refineries equipped with on-line gasoline blending systems must implement the EON values in their proper LP-optimizer blending model. The model ensures the most economic usage of the given components within the given constraints: for example, equipment, component availability, market demand, and final product qualities. The calculated results are then directly downloaded to a ratio controller.

Refineries without on-line blending facilities are obliged to determine a fixed blend ratio before the blend starts. There is no opportunity to correct the component ratio because the quality is not continuously analyzed during the blend batch runs.

It is obvious that those refineries need especially reliable blend data to meet the required quality on the first blend within a small tolerance (usually -- 0.2 ON). If a blend fails, time-consuming and operation-disturbing reblends will be necessary.

To manage this situation LP-optimized spreadsheets with the implemented blending values proved to be an attractive, timesaving, tool for people responsible for product blending.

After a satisfactory field test, the EONs are finally implemented into the remaining production-planning tools. Such tools include the refinery simulation program and LP programs for long-range production and project planning, as well as impact studies on expected future specifications.

### ECONOMIC SUMMARY

An improved blending operation is apparently confirmed through reduced consumption of high-octane components such as reformate and MTBE.

After a successful field test, the shipment of premium-grade gasoline will be increased to the debit of regular, or the operational severity of the reformer must be adjusted to balance the component tankage. To quantify the improvement, a calculated comparison between the situations before and after implementation of the revised blending procedure must be carried out.

The evaluation of the economics is given in Table 3, comparing the octane pool for the two periods at a European refinery. The reduction in variance after implementation indicates a lower octane dissipation than previously.

The octane dissipation is defined as the difference between the linearly calculated component pool (using pure octane values) and the average octane potential of the finished gasoline products. The net octane gain of 0.31 MON represents the actual improvement of a refinery with a crude capacity of 100,000 b/sd.

Because the specified MON spread between regular and premium is only 2.5 numbers, an increase of 12.4 vol % premium gasoline on the total pool could be obtained, to the debit of regular, at otherwise constant conditions.

This benefit results from the pool quantity and the price difference between the two gasoline grades.

For example, a refinery having enough demand for premium and a monthly gasoline production of 900,000 bbl can make full use of the benefits:

900,000 bbl x 0.124 X $2/bbl = $223,200

(Assuming $2/bbl price difference between Premium and regular).

In comparison, for refineries having enough spare octane potential, the net uplift will come from the saved additional processing costs and higher yields, or, in short, from a lower-severity operation.

Complete realization of the possible benefits will require sufficient intermediate storage capacity for gasoline components and adequate blending facilities.

This is true because the optimized blending recipes for the different grades are normally different from the average pool composition.

Adaptable timing for blending operations becomes more important in avoiding a surplus or deficit of a given component.

### SIMILAR METHODS

Known literature on the subject names two similar procedures to cope with real gasoline blending behavior: the Interaction method and the Ethyl method.

The Interaction method is not truly comparable because the ONs of blended gasoline can be determined, but not the individual blending values.

The Ethyl method delivers blending values but has the disadvantage of being hardly adaptable by the user if no satisfactory agreement with the measurements can be obtained.

Deviations of 1 ON, or even more, from the actual blend result cannot be tolerated and imply that the blending values are inaccurate. Such inaccuracies provided the motive for developing the preceeding method.

The Ethyl method takes into account the changing blend values that result from changing composition, but the formulas cannot be implemented directly into LP programs without breaking the linearity restriction of the LP algorithm.

Fine tuning then becomes an iterative process for both the Ethyl method and the new method.

Because the first iteration step has the biggest impact and the convergence cannot be guaranteed for further iterations, it is often preferable to remain with the first estimation.

### BIBLIOGRAPHY

Alberty, Robert A., Physical Chemistry, John Wiley & Sons, 1987.

Morris, William E., "Optimum blending gives best pool octane," OGJ, Jan. 20, 1986, p. 63.

Klamann, D., and Fischer, N., "Einfluss von Kraftstoff-Komponenten. Chemie-Ing.Technki, 1966, Heft 9.

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