New equations help rapidly determine alkylate octane numbers

Lyle F. Albright, Roger E. Eckert
Purdue University
West Lafayette, Ind.

Both research and motor octane numbers of all isoparaffins in alkylates produced in refineries can be predicted, some for the first time, using mathematical models developed in the present investigation.

Employing a gas chromatographic unit for analysis, the octane numbers of the alkylates can now be predicted with improved accuracy in about 30-40 min.

Rapid determination of the RON and the MON of alkylates (C₅-C₁₆ isoparaffins) is useful in optimizing the operation of refinery alkylation units. Typically, alkylates have 94-97 RON values and slightly lower MON values.

Based on results in this study, heavy isoparaffins are not preferred products in alkylate, but some heavy isoparaffins are better than others. Knowledge of how heavy isoparaffins and olefin feeds affect alkylate quality and yield allows the refiner to make educated process decisions. Those refineries that separate some heavy end isoparaffins from alkylates may decide to vary the separation procedure when different olefins are used.

The mathematical models developed in this study can be modified so that both nuclear-magnetic resonance (NMR) and near infrared (IR) results can be employed to more rapidly predict octane numbers-perhaps within several seconds to 2 min.

Alkylate makeup

Alkylates account for about 11-13% of the total U.S. gasoline pool when isobutane is alkylated in refineries with C ₃-C ₅ olefins. ¹ Although most of the alkylate mixtures consist of C ₅-C ₈ isoparaffins, C ₉+ isoparaffins often account for 10-20 wt % of the mixture. Most refineries do not fractionate the heavier isoparaffins from the alkylate before blending it into the gasoline pool.

Octane numbers have been measured for all C₅-C₈ isoparaffins found in alkylates.^{2 3} Octane numbers are also known for at least two C₉ isoparaffins, but none are known for C₁₀ and heavier isoparaffins. The octane number of alkylate mixtures can be approximated as the weighted average of the octane numbers of pure hydrocarbons in the mixture.

For the C₅-C₉ isoparaffins produced during alkylation, there are 12 structural (or constitutional) isomeric families. Each family contains one, two, or three methyl side groups. The RON values of different members of a structural family generally agree within ±5 units of the numerical average of the family.

Isomeric families with different number of methyl side groups (for example, two as compared to three methyl side groups) often have octane numbers that differ by 35-40 units. For example, the average RON values of three isomeric families of C₈ isoparaffins have the following relationship:

RON of trimethylpentanes RON of dimethylhexanes RON of monomethylheptanes.

In addition, RON values are significantly higher for isoparaffins that have shorter chain lengths, but have the same number of methyl side groups.

RON of dimethylbutanes RON of dimethylpentanes RON of dimethylhexanes.

The relative order of MON values for different structural families is identical to that of the RON values. Octane numbers of C₁₀-C₁₆ isoparaffins likely follow the same general rules as C₅-C₉ isoparaffins. Since heavy isoparaffins are often significant fractions of alkylates, they obviously affect alkylate quality.

For C₁₀-C₁₂ isoparaffins, Albright and Wood⁴ recently identified nine structural isomeric families. The most important families are trimethylheptanes, tetramethylheptanes, trimethyloctanes, pentamethylheptanes, and tetramethyloctanes; four to ten isomers were found in each family.

The amounts of C₁₃-C₁₆ in alkylates tend to be relatively small, but five isomeric families were detected for these isoparaffins. Their identities are unknown, but they can be predicted based on the generally accepted chemistry for producing C₁₀-C₁₆ isoparaffins by alkylation.

Models for octane numbers

The authors developed the following two mathematical models using previously gathered ^{2 3} experimental RON and MON values of 24 C ₄-C ₉ n-paraffins and isoparaffins:

RON = 116.7 - 2.16X₁ - 5.01X₃ + 22.46 (X₄ - X₂) + 6.47X₅ (1)

MON = 112.8 - 2.01X₁ - 8.29X₃ + 9.94 (X₄ - X₂) + 3.56X₅ - 5.86X₆ - 1.81X₇² + 5.54X₈ (2)

The values of X₁ through X₈ in the above equations were determined by counting the number of each of the eight types of carbon atoms or groups of atoms in a given isoparaffin or n-paraffin molecule. The same atomic arrangements, such as certain methylene groups, can count in more than a single type. The eight group types are defined in Table 1 [76,970 bytes].

Equations 1 and 2 are at least semitheoretical since several features of the chemical structures were considered in developing the models.

Types 3 and 4 significantly affected the octane value. Type 3 is the sum of the number of the two types of tertiary carbon atoms. Tertiary carbon atoms connected to quaternary carbon atoms do not, however, make a significant contribution to octane value.

Six methylene groups bonded in different ways were significant in developing the models. They are included in Types 5 and 6 (each the sum of different methods of bonding). Some methylene groups in series are also counted in Type 7. A methylene group located between quaternary and tertiary carbon atoms does not, however, contribute significantly to the octane value. Of course, each methylene still counts as part of Type 2.

Table 1 [56,946 bytes] indicates values of X₁ through X₈ for several isoparaffins and n-paraffins in alkylates. These compounds contain examples of all eight groups.

Based on experimental data

The results of API Research Project2 No. 45 are generally thought to provide the most reliable octane numbers although they are not considered highly accurate. First, duplicate runs were generally not made. Second, portions of the data were collected over a period of about 18 years in two different test engines. The engines and the personnel making the tests probably changed with time.

Several repeat runs with a given hydrocarbon at different times indicated that the experimental values sometimes differed by ±2 octane numbers.² It was reported that the standard deviation for tests at the same time was about ±1.0 octane number.

The octane numbers of 2-methylpentane and of 2,5-dimethylhexane, as predicted here, did not agree well with experimental values. In addition, experimental numbers of these two isoparaffins did not interpolate well with experimental numbers of other 2-methyl isoparaffins and other 2,5-dimethyl isoparaffins, respectively. The experimental results of these two isoparaffins are considered highly questionable and hence were not used in developing Equations 1 and 2.

A stepwise regression procedure was used to develop Equations 1 and 2. Since there were no duplicate data to use, the residual means square was employed as an estimate of error in judging the significance of the terms.

The 24 hydrocarbons employed in developing the model had experimental octane numbers varying from 0 for n-heptane to 109.6 RON (99.9 MON) for 2,2,3-trimethylpentanes. Also, 2,2,4-trimethylpentanes were used with defined values of 100 for both RON and MON.

The two most important terms affecting the octane number were the number of quaternary carbon atoms (defined as X₄) and the total number methylene groups (X₂), respectively. Quaternary carbon atoms promote high octane numbers, whereas methylene groups diminish the numbers.

The normal boiling point of the hydrocarbon was not found to be significant for modeling. Equations 1 and 2 predict the experimental data of the 24 isoparaffins and n-paraffins within standard deviations of 1.8 for RON and 2.3 for MON. These two equations are thought to be approximately as accurate as the experimental data.

Octane numbers of C₄-C₁₆ isoparaffins

Tables 3 and 4 report predicted and experimental RON and MON values, respectively, of the most important structural isomeric families of C4-C16 isoparaffins that are present in commercial alkylates. These tables include the weighted average of the experimental values for families of C ₄-C ₈ isoparaffins. For the C ₉-C ₁₆ isoparaffins, the RON and MON values were calculated using Equations 1 and 2, respectively.

Tables 3 and 4 indicate the range of RON and MON values, respectively, for each isomeric family. In addition, the average RON and MON values for each family were calculated for the alkylate produced at 10° C. using a C3-C4 mixture of olefins with sulfuric acid (H₂SO₄) as the catalyst.⁴

Average values were calculated as weighted average octane numbers of the groups. The average RON and MON values of each isomeric family of the other six alkylates reported by Albright and Wood generally differed only slightly from the values reported in Tables 3 and 4. These other alkylates were produced with other olefins and/or with hydrofluoric acid (HF) as the catalyst.

Albright and Wood⁴ were unable to identify a number of C₁₀-C₁₂ peaks obtained by gas chromatographic analyses. Such unidentified peaks were generally relatively small and also had relatively long elution times, which suggests isoparaffins with higher boiling points. Less branched (and hence lower octane number) isoparaffins generally have higher boiling points.

These unknown peaks probably consisted of two or more isoparaffins from different isomeric families. They were assumed to have octane numbers equal to the average values of the isomeric family with intermediate levels of branching (i.e., intermediate number of methyl side branches).

Octane numbers were also calculated for C₁₃-C₁₆ isoparaffins. These calculated values should be considered as only first approximations for several reasons. First, Equations 1 and 2 have to be extrapolated to a considerable extent; second, there is no known information on the identity of specific isoparaffins present in the five isomeric families in the C₁₃-C₁₆ range.⁴

These five families are predicted based on the probable chemical steps of production to be pentamethyloctanes, tetramethylnonanes, pentamethylnonanes, hexamethylnonanes, and heptamethylnonanes. RON and MON values were calculated for several members of the above families. Even less information is available for the rather numerous unidentified C₁₃-C₁6 isoparaffins. They are assumed to be isoparaffins with one less methyl side branch. Since the concentrations of the unidentified hydrocarbons are small, these hydrocarbons have only a small effect on the octane number of the alkylate.

Analyses of heavy ends in alkylates were reported by Albright and Wood4 for seven alkylates produced using different olefins and either H₂SO₄ or HF.

As shown in Table 3 and Table 4 [96,568 bytes], octane numbers were calculated for the five isomer families, discussed earlier, plus three other probable families.

In addition, average RON values were calculated for the entire mixtures of C₉-C₁₆ isoparaffins for the seven alkylates. These latter average values, as shown in Table 5 [102,758 bytes], vary from 73.4 to 83.0. The higher values were for the alkylates produced from mixed C₄ olefins and n-C₄ olefins.

Use of isobutylene and especially propylene as the olefin feed result in lower RON values for the heavy-end fraction. The results for propylene can be explained since propylene would result in fewer methyl branches. In addition, when HF is employed, 1-butene probably isomerizes to a lesser extent to form 2-butenes, hence fewer methyl branching would be expected.

Discussion of results

The models developed here are thought to be based on at least semimechanistic considerations. In the internal combustion engine, the hydrocarbons must first evaporate and mix with the air and then they presumably fragment to at least some extent during compression and heating prior to actual combustion. The type and ease of fragmentation depends on the structure, including branching of the isoparaffin molecules.

Tertiary and especially quaternary carbon atoms are sites at which C-C bonds easily fragment. Isoparaffins containing 2,2-dimethyl; 3,3-dimethyl; 4,4-dimethyl, etc. groups easily fragment. 2,2,4-; 2,2,3-; and 2,3,3-trimethylpentanes are also examples of such isoparaffins; they also have high octane numbers.

Fragmentation also occurs readily between adjacent tertiary carbon atoms, of which 2,3,4-trimethylpentane is an example; it also has high octane numbers. Groups of adjacent methylene (-CH2-) groups, however, do not easily fragment; normal paraffins containing only adjacent methylene groups have low octane numbers.

The RON values for C₉-C₁₆ isoparaffins, as predicted using this model, seem in all cases to be reasonable values based on the following criteria:

1. The qualitative rules presented for C₄-C₉ isoparaffins at the beginning of this article, and
2. Graphical extrapolation of RON or MON values.

For example, graphs were prepared of both RON and MON values of trimethylbutane, trimethylpentanes, and trimethylhexanes. RON and MON values based on extrapolation of these graphs to trimethylheptanes agreed with values predicted by the model.

Unfortunately, there is no known experimental information to test the predicted results for C₁₀ and heavier isoparaffins, but hopefully such tests can be made in the near future. When such experimental data are obtained, the model may need to be modified. For example, the model may need to account for ethyl or isopropyl side groups that may occur in some heavier isoparaffins.

Table 5 indicates that heavy-end isoparaffins often have RON values in the 73.4-83.0 range. This is consistent with the "thinking" in some refineries. Refiners may vary the separation and production procedure based on the olefin used to optimize alkylate quality and yield.

Rapid prediction of octane numbers

Analyzing alkylates using gas chromatography can indicate the composition of commercial alkylates in about 30-40 min. This information, used in combination with information reported in this study, particularly in Table 2 [56,946 bytes] and Table 3 [113,435 bytes], can be used to predict the octane numbers of alkylates.

The findings that octane numbers can be predicted using the mathematical models in Equations 1 and 2 strongly suggest that NMR and near-IR results can be used to predict octane numbers. Both analytical procedures can identify and determine the concentrations of various types of carbon atoms in the alkylate; for example, quartenary and tertiary carbon atoms and methylene groups. These two analytical procedures can probably be used to determine some if not all X₁ through X₈ values for the alkylate. With such information, equations similar to Equations 1 and 2 can be developed to predict octane numbers using NMR or near-IR results.

To support this postulate, Process NMR Associates Inc., working in cooperation with Foxboro Co., is currently developing NMR procedures to be used in refineries to predict octane numbers.5 In addition, a major oil company is reportedly using near-IR results to calculate octane numbers. NMR or near-IR results may eventually be used to predict alkylate octane numbers in 1-2 min, or even seconds. Such a quick turnaround on alkylate quality will be important for improved alkylation unit operations.

References

1. Scheckler, J.C., and Schmidt, R.J., "Motor Fuel Alkylation Advances Beyond Liquid Acid Catalysis," AM 97-47 presented at NPRA annual meeting, San Antonio, Mar. 16-18, 1997.

2. American Society for Testing Materials, "Knocking Characteristic of Pure Hydrocarbons," American Petroleum Institute Research Project No. 45, 1958.

3. Hutson, T., and Logan, R.S., "Estimate Alky Yield and Quality," Hydrocarbon Processing, September 1975, pp. 107-8.

4. Albright, L.F., and Wood, K.V., "Alkylation of Isobutane with C₃-C₄ Olefins: Identification and Chemistry of Heavy-End Production," Ind. Eng. Chem. Research, Vol. 36, No. 2110, 1997.

5. Edwards, J.C., NMR Associates, Danbury, Conn., personal communications, 1998.

The Authors