Numerical schemes for anomalous diffusion of single-phase fluids in porous media

Abeeb A. Awotunde, Ryad Ghanam, Suliman S. Al-Homidan, Nasser eddine Tatar

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system.In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

Original languageEnglish
Pages (from-to)381-395
Number of pages15
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume39
DOIs
Publication statusPublished - 1 Oct 2016

Fingerprint

Anomalous Diffusion
Numerical Scheme
Porous Media
Porous materials
Fluid
Fluids
Flow of fluids
Flow in Porous Media
Anomalous
Fluid Flow
Reservoir management
Numerical Solution
Petroleum reservoirs
Reservoir Simulation
Small Deviations
Profitability
Fractals
Diffusion Process
Experimental Study
Fractal

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Numerical schemes for anomalous diffusion of single-phase fluids in porous media. / Awotunde, Abeeb A.; Ghanam, Ryad; Al-Homidan, Suliman S.; Tatar, Nasser eddine.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 39, 01.10.2016, p. 381-395.

Research output: Contribution to journalArticle

Awotunde, Abeeb A. ; Ghanam, Ryad ; Al-Homidan, Suliman S. ; Tatar, Nasser eddine. / Numerical schemes for anomalous diffusion of single-phase fluids in porous media. In: Communications in Nonlinear Science and Numerical Simulation. 2016 ; Vol. 39. pp. 381-395.
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