Analysis of pressure variation of fluid in bounded circular reservoirs under the constant pressure outer boundary condition

Abstract

In this work, we have investigated the well pressure distribution in a bounded circular reservoir under the condition of constant pressure outer boundaries. The diffusivity equation was used in the analysis. The finite element technique, using Lagrange quadratic shape elements was employed to carry out the analysis over the cross-section of the reservoir which involves discretizing the domain into finite element, analysing these finite element, assembling the results from the analysis of the analysed finite element, imposing the boundary conditions and finally, getting the results that represent the entire domain. The results obtained where shown in a log log plot (dimensionless pressure against dimensionless time) for dimensionless radii of 1 to 1,000,000 in log cycles. It was shown that the relationship between dimensionless pressure and dimensionless time was linear whose slope was zero. 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. The result obtained from the analysis also shows the pressure variation outside wellbore of the same reservoir. It is important to note that solutions from existing literature only state the pressure at the wellbore at a particular time but this work predicts the pressure variation in the entire reservoir from the wellbore to the external boundary at the same time.

Keywords: Reservoir, Constant Terminal Rate, Dimensionless Variables, Diffusivity Equation, Wellbore And Weak Formulation.