# Estimation Of Coefficient Of Isothermal Oil Compressibility For Undersaturated Reservoir By Cubic Equation Of State

## Abstract

Evaluation of reservoir performance for petroleum reservoirs require accurate knowledge of the volumetric behavior of hydrocarbon mixtures, both liquid and gaseous. Prior to the evaluation of reservoir performance, coefficient of Isothermal oil compressibility is required in transient fluid flow problems, extension of fluid properties from values at the bubble point pressure to lower pressures of interest and in material balance calculations.

The coefficient of isothermal oil compressibility is a measure of the fractional change in volume as pressure is changed at constant temperature. It is usually obtained from reservoir fluid analysis. Reservoir fluid sampling and analysis is often expensive and time consuming operation that cannot be carried out whenever the volumetric properties of reservoir fluids are needed. Hence, engineers resort to correlations developed for estimating fluid properties including the coefficient of isothermal oil compressibility.

In this project, a new mathematical model for estimating the coefficient of isothermal oil compressibility based on Soave Redlich Kwong equation of state (EOS) was developed and an Excel based program. Data from four fields were used as case study and the results obtained showed that the new coefficient of isothermal oil compressibility matches closely with the experimentally values. Also, the new correlation was validated with other models and gave the least average absolute relative error range of 2.45 – 5.19 while that of Soave Redlich Kwong EOS is between 21.2 – 27. 7 and Peng Robinson EOS is between 11.8 – 16.5.

## Chapter Five

### Conclusions and Recommendations

#### 5.1 Conclusions

The following conclusions can be drawn from this project:

- A mathematical model based on Peng-Robinson equation of state for calculating the coefficient of isothermal oil compressibility was developed.
- The mathematical model was extended to pressures below the bubble point, using the two phase flash calculations.
- A mathematical model based on Peng-Robinson equation of state was also developed to predict the coefficient of isothermal gas compressibility at pressures below the bubble point.
- A mathematically consistent additive technique was developed to add the resultant coefficient of isothermal oil compressibility and the coefficient of isothermal gas compressibility at pressures below the bubble point.
- A good degree of accuracy was obtained between the predicted coefficient of isothermal oil compressibility from the developed EOS based mathematical model and the experimentally derived coefficient of isothermal compressibility.
- The predicted molar volume from the two phase calculation was reported and compared with the experimental measured molar volume from Pressure-Volume relations; a good degree of accuracy was achieved.
- A computer algorithm (using FORTRAN) was developed to compute the coefficient of isothermal oil compressibility using the developed mathematical model.

#### 5.2 Recommendations

- Research is very active in the area of two phase calculation to determine the equilibrium quantity and composition of liquid and vapor in the two phase region. A more robust two phase flash algorithm is recommended to increase the accuracy of the predicted coefficient of isothermal oil compressibility at pressures below the bubble point pressure.
- A further work is recommended in tuning the developed mathematical model, using the constant parameters of the Peng-Robinson EOS (i.e. “a” and “b”) and the binary interaction parameter in order to achieve a higher level of accuracy.
- In order to predict the isothermal compressibility of gas condensate reservoirs, it is recommended that the developed mathematical model be coupled with the simulation of constant volume depletion experiment.
- Observations bothering on the analysis of the differential vaporization experiment suggested that the accuracy of equation 3.45 be validated. The reason for this validation is the slope change observed in the graph of the formation volume factor and the pressure, at pressures above and below the bubble point pressure.
- The developed model can also be extended to gas fields to predict the coefficient of isothermal gas compressibility.

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