William E. MorrisConsultant

Wilmington, Del.

William E. SmithConsultant

Newark, Del.

Ronald D. SneeJoiner Associates

Madison, Wis.

The interaction approach to gasoline blending gives refiners an accurate, simple means of reevaluating blending equations and increasing profitability.

With reformulated gasoline specifications drawing near, a detailed description of this approach, in the context of reformulated gasoline, is in order.

Simple mathematics compute blending values from interaction equations and interaction coefficients between mixtures. A timely example of such interactions is: Blending a mixture of catalytically cracked gasoline plus light straight run (LSR) from one tank with alkylate plus reformate from another.

### BLENDING EQUATIONS

Without accurate blending equations, any attempt to optimize the compositions of different gasoline grades can be expected to achieve nonoptimum results. The hidden costs of using the results of such a study can be quite large.

It is widely believed that most refineries use inaccurate blending equations most of the time. In these cases, obtaining accurate blending equations for octane, ASTM distillation, and Rvp can be quite profitable.

Blending relationships between gasoline components are nonlinear, and blending values vary with the composition of the blend. For these reasons, the quality of the gasoline pool is affected by the apportionment of components between the gasoline grades.

With a nonoptimum blending scheme, the pool Rvp can be 0.1 psi greater than the optimum level. Similarly, the pool octane can be 0.1 octane number (ON), or more, less than that of the optimum blending scheme. Use of such a blending scheme can incur a cost of $1 million/year or more for a large refinery (assuming $0.3/octane bbl).

Accurate blending relationships are necessary to determine optimum gasoline compositions. The interaction approach is widely used to provide accurate blending relationships.

This approach works well with octane, Rvp, and ASTM distillation blending.1 The key element in interaction equations is the interaction coefficient, bi,j, where i and j denote different components (see Nomenclature).

Equation 1 describes octane numbers of blends of two components (Equations). The interaction coefficient can be developed by testing each component and the 50/50 blend of the two components. An example of an interaction blending curve is shown in Fig. 1.

The 50/50 blend of light gasoline from the fluid catalytic cracking unit (called "light FCC") and alkylate is 0.6 MON less than the average (represented by the dotted fine in Fig. 1). Equation 2 is the equation of the curve plotted in Fig. 1.

The measured octane values at 20, 40, 60, and 80% alkylate are within experimental error of the octane values predicted by Equation 2.

With systems of three components, three interaction coefficients are required (Equation 3). With n components, n(n 1)/2 interaction coefficients are required.

Equations with two way interaction coefficients, as described here, have been found to fit the data quite closely for blends of three or more components.1 It should be noted that, for some mixtures, an accurate description of mixture behavior can require additional terms.2 But fortunately, those additional terms are not required for gasoline blending.

Octane blending equations for gasoline containing lead or manganese antiknock additives require terms describing the antiknock effect on interaction.1

### USING INTERACTION

Interaction equations provide accurate information on the blending behavior of gasoline components. Accurate blending information is necessary to determine the optimum compositions of the different gasoline grades.

The connection between interactions and optimum compositions is illustrated by Fig. 2. Some pairs of components have positive interactions (represented by a filled circle) and some have negative interactions (represented by an open circle).

Pairs with positive interaction should be put together in the same gasoline grade, and those with negative interactions should be separated in different grades. This is accomplished, to the extent allowed by various constraints, by the use of programs that optimize compositions.

Interaction equations can be used with nonlinear programming, or with linear programming (LP). With LP, linear blending values are required. Blending values for a pair of components are obtained by drawing a tangent to the blending curve, as illustrated in Fig. 3.

The blending value of Component 1 can be calculated from Equation 4. At 100% of Component 1, the value of (1 X1) becomes 0, and the blending value is equal to the octane number. At 0% of Component 1, the incremental blending value is equal to the interaction coefficient, as illustrated by Equation 5.

Blending value minus octane number is also called deltaBV, incremental blending value, or blending bonus. From a practical standpoint, deltaBV at 0% does not apply when the component is present. But experience shows that the use of blending values based on 10% for components present at less than 10% is helpful in linear programming.

It is therefore reasonable to calculate deltaBV at 10% concentration for components that are not in the blend. At 10%, deltaBV is defined as shown in Equation 6.

When more than two components are present, deltaBV is complicated by the dilution effects of components. For example, if Component 1 has no interaction, while Components 2 and 3 have a positive interaction, the presence of Component 1 in a blend Limits the positive octane effect of having Components 2 and 3 together.

Because Component 1 "dilutes" this positive effect, its blending value is less than its octane, even though it has no interaction with either of the other components.

The deltaBV of Component 1 is affected not only by its own interaction coefficient, but also by the interaction coefficients between pairs of other components. The general relationship for q components is Equation 7.

As an example, assume that a blend of four components has the interaction coefficients shown in Table 1. For Component 1, BV1 is calculated using Equation 8. Example calculations are shown in Table 2.

### MIXTURE INTERACTIONS

When interaction coefficients between individual components are known, interactions between mixtures can be calculated. A specific application of interest is the case of component splitting.

For example, if FCC gasoline is split, producing 30% light FCC and 70% heavy FCC, the interaction coefficient for alkylate and full-boiling FCC (bfb,alk) can be calculated using Equation 9. Thus, if interaction coefficients are obtained for light and heavy fractions of a component, it is not necessary to measure interaction coefficients for the full boiling component.

This example for split components is a specific case of the general relationship for interaction coefficients between mixtures. Assume that two tanks, S and T, contain q components. Individual components may be present in both tanks; volume fractions can range from 0 to 1.

Composition in Tank S is S1, S2 ... Sq and composition in Tank T is T1, T2 ... Tq. The interaction coefficient between tanks, B1,2, is given by Equation 10.

Applying Equation 10 to the FCC splitting example, with "It" being Component 1, "hy" Component 2, and "alk" Component 3, compositions are:

- For Tank S (full boiling FCC) S = (0.3, 0.7, 0)
- For Tank T (alkylate) T = (0, 0, 1).

Thus the interaction coefficient between tanks is defined by Equation 11.

Details regarding interaction blending relationships between gasoline component mixtures are explained in the box on the previous two pages of this article.

The general relationship in Equation 10 applies to tanks with ans, number of components. With appropriate information, this equation can be used to estimate the interaction between two gasolines.

As a practical matter, interaction coefficients for pairs of gasolines can be expected to be quite small.

### OTHER BLENDING PROBLEMS

The interaction approach is favored by statisticians and is ideal for evaluating gasoline octane, Rvp, and ASTM distillation. In the case of ASTM distillation, equations are more accurate in terms of % evaporated at specified temperatures, rather than in terms of temperature at which 10%, for example, is evaporated.3

The interaction approach works well with fuel oil distillation blending.4 Other products and parameters may be amenable to the interaction approach.

It may be necessary to transform the data mathematically so that blending is approximately linear, then develop interaction coefficients to cover deviations of blends from linearity on the transformed basis.

### OBTAINING EQUATIONS

Interaction equations can be developed by carrying out interaction blending studies. To obtain good results, considerable technical supervision is required. Accurate test data are needed; just "fitting the tests in" may not be sufficient.

The blending task is not trivial; blend compositions must be accurate. The real cost of a blending study can be expected to be $10,000-$100,000. Experience shows that results of blending studies become outdated an must be repeated periodically. Another way to obtain interaction equations is by using generalized relationships that predict interaction coefficients for pairs of gasoline components. The bases of the generalized relationships are:

- Octane - General relationships of interaction coefficients with component types and octane levels; based on detailed blending studies, including studies for many refineries.
- ASTM distillation - Correlations based on distillation curve parameters, with special treatment for narrow boiling components and oxygenates.
- Rvp - Relationships based on a chemical engineering model of the Rvp test, taking into account deviations from ideal vapor pressure behavior.

Accurate interaction blending equations obtained either from generalized relationships or from a thorough blending study are helpful when evaluating the ability to meet new gasoline specifications. Accurate interaction blending equations can be the basis for changing from nonoptimum to optimum blending schemes. The result is increased profits without capital investment.

### REFERENCES

- Morris, William E., "The Interaction Approach to Gasoline Blending," NPRA Paper AM-7530, National Petroleum Refiners Association annual meeting, March 1975.
- Cornell, J.A., Experiments with Mixtures, John Wiley & Sons, New York, 1981.
- Morris, William E., "Prediction of mogas blend distillations can be improved," OGJ, Apr. 25, 1983, p. 71.
- Morris, William E., "Interaction blending approach works for diesel, fuel oil" OGJ, Sept. 23, 1985, P. 119.

*Copyright 1994 Oil & Gas Journal. All Rights Reserved.*