Prem B. SemwalIndian Institute of Petroleum

Dehradun, India

Ram G. VarshneyDBS Postgraduate College

Dehradun, India

Refiners use pour point blending correlations to determine the optimum blend compositions of finished fuel and lubricating oils. These optimum compositions thus ensure that desired product specifications are met.

In a typical case study of a diesel oil blend, the application of one of the new pour point correlations saved a calculated 23% of high-value product, thus increasing profits more than 5%.

### BACKGROUND

The consumption of diesel fuel is increasing faster than that of gasoline, particularly in developing countries. To meet the high demand, some refiners are considering all possible methods of increasing diesel yields.

For example, the diesel fuel produced at Indian refineries is blended from as many as 14 refinery streams which differ significantly in key properties. The amount of thermal and catalytically cracked components in Indian diesel fuels varies from 10 to 25%.

Because of the variations in the streams used to produce diesel, existing correlations need to be updated or new ones developed."

The pour point of a liquid is the temperature below which it ceases to flow. Knowledge of this property therefore is important, particularly in cold climates, where pour point is often a prime factor for blend formulations of fuel oil.

Refiners frequently use pour point blending correlations in linear and nonlinear programming models to meet required cold-flow property limits for finished fuel oils, including diesel, fuel, and lubricating oils.

### EXISTING CORRELATIONS

In 1970, Hu and Bum proposed a one-parameter (x) pour point equation. The equation is shown as Equation 1 (Equations, Nomenclature).l

In 1951, Reid and Allen used pour point blending indexes to predict blend pour point linearly.' A polynomial equation was then developed to predict accurate pour point indexes using pour point (Equation 2).

### NEW CORRELATIONS

More recently, the authors attempted several new correlations using 64 fuel oil blends, the pour points of which were determined experimentally using the ASTM D-87 method (Equations 3-5).3 Of these correlations, Equation 3 is used for the pour point range of 9 to 51 C. (Gr-1), Equation 4 is used for the range of - 12 to 21 C., and Equation 5 is used for the range of - 21 to -6 C.

These new two-parameter pour point correlations (using power terms of Vi and Ti) were found to be 5-30% more accurate than the updated Hu-Burn equation (Equation 1) for different pour point ranges.

The values of x in the existing Hu equation were updated in Reference 3, and were found to be, for Equations 3, 4, and 5, respectively, 0.073, 0.079, and 0.186.

### CASE STUDY

To determine the effects on optimal blend formulation of different correlations, Canadian refinery streams of light cycle oil (LCO), light gas oil (LGO), and kerosine were used to produce a furnace fuel oil (FFO) blend that is equivalent to diesel fuel in composition and properties.

The properties of the blend streams to be used in the new correlations are presented in Table 1.

### MODEL FORMULATION

The formulations of the objective function (Z) and the material and pour point property constraints were developed using data from Table 1. For example, to calculate minimum production cost, the objective function is defined by Equation 6.

The higher cost of kerosine (designated C3) Will minimize use of the key product in the model. Further, based on the availability of blend streams (Wi), material constraints are imposed, as shown in Equations 7-10.

The ambient temperature in some areas of Canada is less than O F. Therefore, to obtain a pour point of 460 R. (Ti) for furnace fuel oil from the streams given in Table 1, the property constraints for different pour point methods were determined using four different correlations:

- equation 11 uses the new correlation (Equation 5). (For Equation 11, A = 1.105 and B = 10.8697.)
- Equation 12 uses the updated Hu-Burn method.3
- Equation 13 uses the Reid-Allen index method.2
- Equation 14 uses the existing Hu-Burn method.1

The values of Ci, Ti, Vi, Di, and PPIi are given in Table 1

### OPTIMIZATION

To solve the optimization problems of Equations 6-11 using nonlinear pour point property constraints with a linear volume term (Equations 12-14), the authors used the Simplex technique. 5

The modified nonlinear optimization method, based on the Fiacco-Micormic algorithm, was used to solve Equations 6-11 for a nonlinear pour point property constraint with a nonlinear volume term (Equation 11).5 This method determines the minimum of the multivariate linear/nonlinear functions, subject to linear/nonlinear inequalities and equality constraints.

### OPTIMAL BLENDS

The different optimal solutions obtained using each pour point correlation are presented in Table 2.

Comparative savings of high-value kerosine using the new correlation and the index method were, respectively, 23.3% and 8%. Profits increased 5.4% and 1.0%, respectively, using the new correlation and the index method, compared to the Hu-Bum correlation (Fig. 1).

### ACKNOWLEDGMENT

The authors wish to thank Dr. T.S.R. Prasada Rao, director of the Indian Institute of Petroleum, for his interest in this study and permission to publish this article.

### REFERENCES

- Hu, J., and Bums, A.M., "New Method Predicts Cloud, Pour, Flash Points of Distillate Blends," Hydrocarbon Processing, 1970, 49 (11), pp. 213-16.
- Reid, E.B., and Allen, H.L., "Estimating Pour Points of Petroleum Dist.Blends," Petroleum Refiner, 1951, 30 (5), pp. 93-95,
- Semwal, Prem B., and Varshney, R.G., "Predicting Pour Points of Present Fuel oil Blends - Application to Optimization Model, unpublished.
- Knepper J.I., and Hulton, R.P., "Blends for Lower Pour Points," Hydrocarbon Processing, 1975, 54 (9), pp. 129 36.
- Kuester, J.L., and Mize, J.H., Optimization Techniques with Fortran, McGraw-Hill Book Co., New York, 1973, pp. 9-26, 412-63.

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