Volume 7, Issue 6, December 2018, Page: 242-259
Development of Finite Difference Explicit and Implicit Numerical Reservoir Simulator for Modelling Single Phase Flow in Porous Media
Aphu Elvis Selase, College of Public Administration, Huazhong University of Science and Technology, Wuhan, China
Brantson Eric Thompson, School of Energy Resources, China University of Geosciences (Beijing), Beijing, China
Addo Bright Junior, Department of Economics and Geography & Resource Development, University of Ghana, Legon, Ghana
Akunda Doreen, College of Public Administration, Huazhong University of Science and Technology, Wuhan, China
Received: Jun. 26, 2018;       Accepted: Oct. 4, 2018;       Published: Oct. 29, 2018
DOI: 10.11648/j.earth.20180706.11      View  176      Downloads  15
Abstract
Every petroleum reservoir requires some means of predicting future performances as well as optimizing recovery of hydrocarbons under various operating conditions. Moreover, there is a need to simulate fluid flow in porous media due to the uncertainty and heterogeneity that is associated with petroleum reservoirs. Therefore, this study developed 1D finite difference explicit and implicit numerical reservoir simulator for modeling single phase flow in porous media. The explicit and implicit simulator developments consist of physical modeling, mathematical modeling, discretization of the models with finite difference scheme and transformation of the models into computer algorithms. Matlab codes were written to describe the fluid flow process to obtain the reservoir pressure distributions for each grid block at each timestep calculation. The explicit formulation linear equation was solved by the direct method while the implicit method was solved by the Jacobi iterative method. The numerical examples graphical plots generated from the simulator illustrate the average reservoir pressure depletion for the finite difference grid blocks. The plots for both the explicit and implicit method indicate decline in average reservoir pressure with time. The explicit and implicit simulators show that the implicit formulation is unconditionally stable than the explicit formulation. This is because the explicit method under certain conditions generates errors in the numerical solutions which tend to go zero during subsequent timestep calculations. Additionally, the porosity sensitivity analyses performed show that the average reservoir pressure decline as the porosity decreases from 30% to 10%. Material balance method was used to determine the average reservoir pressure decline for a one-year production period. The estimated recovery factor at the bubble point pressure is 0.68% of the original oil in place. This low recovery factor is a characteristic of an expansion-drive reservoir which has the least efficient recovery mechanism. Finally, the 1D explicit and implicit finite difference numerical simulators for predicting single phase flow reservoir pressure distributions during production periods are stepping stone towards implementing multiphase fluid flow formulations.
Keywords
Explicit and Implicit Simulators, Material Balance Method, Jacobi Iterative Method, Explicit and Implicit Formulation, Numerical Simulator
To cite this article
Aphu Elvis Selase, Brantson Eric Thompson, Addo Bright Junior, Akunda Doreen, Development of Finite Difference Explicit and Implicit Numerical Reservoir Simulator for Modelling Single Phase Flow in Porous Media, Earth Sciences. Vol. 7, No. 6, 2018, pp. 242-259. doi: 10.11648/j.earth.20180706.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Aziz, K. and Settari, A., Petroleum Reservoir Simulation, Applied Science Publishers, 1979.
[2]
Zhangxin Chen, Mathematical Techniques in Oil Recovery, SIAM, 2007.
[3]
T. Ahmed (2006), Reservoir Engineering Handbook, Society of Petroleum Engineers, Richardson, TX.
[4]
Z. Chen, J. Adams, D. Carruthers, H. Chen, I. Gates, G. Huan, S. Larter, W. Li, and G. Zhou (2007b), Coupled reservoir simulation and basin models: Reservoir charging and fluid mixing, to appear.
[5]
I. Gates (2007), Basic Reservoir Engineering, in progress.
[6]
The MathWorks, Inc., MATLAB: The Language of Technical Computing, Getting Started with MATLAB Version 6, c cc COPYRIGHT 1984 – 2001.
[7]
Ertekin, T., Abou-Kassem, J. H., and King, G. R., Basic Applied Reservoir Simulation, SPE Textbook Volume 10, 2007.
[8]
Abbas, F., Thermodynamics of Hydrocarbon Reservoirs, McGraw-Hill, 2006.
[9]
Abou-Kassem, J. H., Farouq Ali, S. M., and Islam, M. R., Petroleum Reservoir Simulation: A Basic Approach, Gulf Publishing Company, Houston, TX, USA, 2006.
[10]
Jaan Kiusalaas, Numerical methods in engineering with Matlab®. The Pennsylvania State University, Cambridge University press, New York, 2006.
[11]
Ferreira, A. J. M. (2009). MATLAB Codes for Finite Element Analysis. Springer. ISBN 978-1-4020-9199-5.
[12]
Brian R. Hunt, Ronald L. Lipsman and Jonathan M. Rosenberg, A Guide to MATLAB®: for Beginners and Experienced Users: Third Edition, 2014.
[13]
Dake, L. P., Fundamentals of Reservoir Engineering, Elsevier, Amsterdam, Netherlands, 2010.
[14]
Fanchi, J. R., Principles of Applied Reservoir Simulation, Houston, Tex, Gulf Pub, 2008.
[15]
Tarek., Reservoir Engineering Handbook, Third Edition, Gulf Professional Publishing, 2006.
Browse journals by subject