M. Al-Blehed, M. H. Sayyouh, S. M. DesoukyKing Saud University

Riyadh, Saudi Arabia

A new correlation estimates the viscosity of Saudi crude oils in the undersaturated oil regions as a function of pressure, temperature, and API-gravity.

Field data of 182 crude oil samples obtained from the major producing areas of Saudi reservoirs were statistically treated and used to derive the viscosity correlation.

The accuracy of the developed correlation was determined using statistical error analysis. Statistical error analysis techniques were employed to check the validity of the developed correlation as compared to other published crude oil viscosity correlations using the field data of Saudi reservoirs.

The results show that the developed correlation provides a more accurate estimation of crude oil viscosity with an average relative error of -13.58%.

The development of viscosity correlations has received considerable attention in petroleum research. Of particular interest, it is required in the calculations of simulation studies of two and multi-phase flow in vertical and horizontal pipes, well testing, and design of production equipment.

In view of the different correlations proposed for estimating the viscosity of crude oils above the bubble point, there are two main distinct approaches: compositional dependence and compositional independence.

Lohrenz, et al.,1 Lowal,2 Saeedi and Rowe,3 and Little and Kennedy,4 conducted the investigation of the first approach. Their developed correlations were based on the compositions of the studied crude oils at desired pressure and temperature.

The compositional independence correlations were expressed as functions of pressure, temperature, and bubble point pressure and viscosity.

Beal,5 Vazquez,6 and Khan, et al.,7 developed different empirical correlations for predicting crude oil viscosity above bubble point. The advantages and defects of each approach are outlined in Table 1.

This table clearly indicates that, although the compositional dependence approach is more accurate than compositional independence, it makes viscosity prediction more complex and less useful for practical purposes. Therefore, the collected field data of Saudi crude oils were used to develop the new empirical correlation for viscosity as a function of pressure, temperature, and API gravity.

The developed correlation should be applied to crude oils that exist above the bubble point pressure. The parameters used in the correlation were statistically treated to determine the confidence levels at which the evidence of the developed correlation should be judged.

The accuracy of the developed correlation was determined using statistical error analysis.8 This involved the calculation of the Durbin-Watson statistic, correlation coefficient, average relative error, and graphical representation of the errors (crossplot).

### CORRELATION DEVELOPMENT

The present study starts with the investigation of the reservoir parameters that affect the estimation of oil viscosity above the bubble point. Preference was given to those parameters which could be easily and commonly measured in the field or in the laboratory.

It was found that, above the bubble point, the only reservoir parameters that can affect oil viscosity are pressure, temperature, and API gravity. Neither solution gas-to-oil ratio (GOR) nor oil composition improved the accuracy of the correlation to any significant extent.

This is due to the fact that both solution GOR and oil composition are almost constant above the bubble point. Therefore, the field data of viscosity, pressure, temperature, and API gravity on a total of 182 crude oil samples obtained from the major producing areas of the Saudi reservoirs, were used to derive the desired correlation.

Before proceeding to discuss the technique used to derive the viscosity correlation, it might be advisable to check first the normality of the distribution of the reservoir parameters. This is the basis for statistical judgments.

In terms of a standard normal variate, the probability of a normally distributed variable is expressed by the following probability density equation.8

[SEE FORMULA (1)]

Equation 1 was used to check the normality of the reservoir parameters distribution. The results are given in Table 2.

This table shows that the estimated variabilities and confidence levels for normally distributed parameters are ranged from 0.898 to 0.998, and from 0.796 to 0.996, respectively. Applying the multiple linear regression technique to the data of the Saudi reservoirs, the following correlation for crude oil viscosity above bubble point was derived:

[SEE FORMULA (2)]

### CORRELATION ACCURACY

In order to determine the accuracy of the developed correlation, statistical error analyses have been carried out. This involved the calculations of the Durbin-Watson statistic (DWS), correlation coefficient, average relative error, and graphical representation of errors (crossplot).

The results show that the values of DWS, correlation coefficient, and the average deviation between the field data and those estimated from Equation 2 were 1.66, 0.926, and -13-58%, respectively.

The values of these statistical measures emphasize the evidence of the accuracy of the developed viscosity correlation relative to the field data at the tested confidence level.

In addition, the field data are plotted against the estimated ones, and a 45-straight line is drawn on the same plot as shown in Fig. 1. This figure reveals the closeness of the plotted data points to the 450 straight line. This ensures a good fit of the data to the curve.

### COMPARISONS

Equation 2 and Beal and Vazquez correlations were used to estimate the viscosity of Saudi crude oils above the bubble point.

Following this, a comparison was made between the measured viscosity of Saudi crude oils and the calculated ones.

The results are given in Table 3, from which it can be observed that the developed correlation reveals the least average absolute relative error.

Hence, the developed correlation should be valid for either Saudi crude oils or other crude oils falling within the range of data used in the study.

### ACKNOWLEDGMENT

This study was supported by the Research Center of the College of Engineering, King Saud University, under project No. 6/409.

### REFERENCES

- Lohrenz, J., Bray., B.G., and Clark, C.R., "Calculating Viscosity of Reservoir Fluid From Their Compositions," Journal of Petroleum Technology, October 1964, pp. 1171-1176.
- Lowal, A.S.L., "Improved Fluid Prop" Prediction for Reservoir Compositional Simulation," PhD Thesis, University of Texas, 1985.
- Saeedi, J., and Rowe, A.M., "Viscosity Correlations for Compositional Reservoir Simulators," SPE 9642, Middle East Oil Tech. Conf., Bahrain, 1981.
- Little, J.E., Kennedy, M.H., and Eakin, B.E., "The Viscosity of Methane-ndecane Mixtures," J. Chem. Eng. Data, Vol. 11, 1966, p. 281.
- Beal, C., "The Viscosity of Air, Water, Natural Gas, Crude Oil, and its Associated Gases at Oil-Field Temperatures and Pressures," AIME, Vol. 165,1946, pp. 94-115.
- Vazquez, M.E., "Correlations for Fluid Physical Property Prediction," MS thesis, University of Tulsa, 1976.
- Khan, S.A., Al-Marhoun, M.A., Daffua, S., and Abu-Khamsin, S.R., "Viscosity Correlations for Saudi Arabian Crude Oils," SPE 15720, Middle East Tech. Conf., Bahrain, 1987.
- Volk, W., Applied Statistics for Engineers, McGraw-Hill Book Co., New York, 1969.

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