Analysis of pressure variation of fluid in bounded circular reservoirs under the “No Flow” outer boundary condition

Abstract

Predicting the pressure at the wellbore in bounded circular reservoir has been the hub in the study of Reservoir Engineering. Predicting the pressures outside the reservoir was not an easy task. The Ei function method has been the only method for determining the pressure outside the wellbore of a bounded circular reservoir. The disadvantage of the Ei function method is that it involves rigorous iterations. This study sorts to use another approach to determine the pressure within and outside the wellbore at a glance. The finite element method was used in this study. The reservoir domain was divided into smaller subdomains and analysed. The results from these subdomains were assembled to represent pressure in the entire reservoir. The results obtained where shown tabular form (dimensionless pressure and dimensionless time) for dimensionless radii of 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 9, and 10. It was shown that the relationship between dimensionless pressure and dimensionless time was linear. The result obtained at the wellbore was compared with the results obtained by Van Everdigen and Hurst. It was shown that there was a  strong positive correlation between the results.

Keywords: Bounded circular reservoir, constant terminal rate, dimensionless variables, diffusivity equation, and Crank-Nicholson scheme. Nomenclature