Numerical simulation of a nonlinear diffusion type equation in a two phase media with linear porosity and permeability model

Authors

  • I. D. Dorothy
    Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Benue-Nigeria
  • I. M. Echi
    Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Benue-Nigeria
  • A. N. Amah
    Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Benue-Nigeria

Keywords:

Permeability, Porosity, Nonlinear pressure diffusion equation, Numerical simulation

Abstract

Predicting and understanding the behavior of pressure is important in reservoir maintenance and evaluation. This work studies the behavior of fluid pressure in a reservoir by numerical simulation of the pressure diffusion type equation in a two phase media with a linear porosity and permeability model. Because the porosity and permeability are pressure dependent, the resulting diffusion type equation is nonlinear and is solved using a backward-forward finite difference method. The simulation code was ran using a constant porosity and permeability model and a linear porosity and permeability model. The results from the linear porosity and permeability model was compared to that of the constant porosity and permeability model. In both cases the pressure gradient was greatest at the wellbore and decreases as the radial distances away from the wellbore increases. The pressure in both cases also decreased with time. However, at each location and time the pressure drop was lower in the linear porosity and permeability model than with the constant porosity and permeability. The backward-forward finite difference method proved to be useful in solving numerically the nonlinear diffusion type equation. This work can be applied in the oil and gas industry to predict pressure behavior in reservoirs and make investment decisions, production and maintenance decision.

Dimensions

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Values for Rock and Fluid Properties.

Published

2024-02-01

How to Cite

Numerical simulation of a nonlinear diffusion type equation in a two phase media with linear porosity and permeability model. (2024). African Scientific Reports, 3(1), 119. https://doi.org/10.46481/asr.2024.3.1.119

Issue

Volume 3, Issue 1, April 2024

Section

PHYSICS SECTION
Copyright & Licensing

Copyright (c) 2024 I. D. Dorothy, I. M. Echi, A. N. Amah

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Numerical simulation of a nonlinear diffusion type equation in a two phase media with linear porosity and permeability model. (2024). African Scientific Reports, 3(1), 119. https://doi.org/10.46481/asr.2024.3.1.119

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