Modeling of multicomponent diffusions and natural convection in unfractured and fractured media by discontinuous Galerkin and mixed methods

Hussein Hoteit*, Abbas Firoozabadi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Computation of the distribution of species in hydrocarbon reservoirs from diffusions (thermal, molecular, and pressure) and natural convection is an important step in reservoir initialization. Current methods, which are mainly based on the conventional finite-difference approach, may not be numerically efficient in fractured and other media with complex heterogeneities. In this work, the discontinuous Galerkin (DG) method combined with the mixed finite element (MFE) method is used for the calculation of compositional variation in fractured hydrocarbon reservoirs. The use of unstructured gridding allows efficient computations for fractured media when the cross flow equilibrium concept is invoked. The DG method has less numerical dispersion than the upwind finite-difference methods. The MFE method ensures continuity of fluxes at the interface of the grid elements. We also use the local DG (LDG) method instead of the MFE to calculate the diffusion fluxes. Results from several numerical examples are presented to demonstrate the efficiency, robustness, and accuracy of the model. Various features of convection and diffusion in homogeneous, layered, and fractured media are also discussed.

Original languageEnglish (US)
Pages (from-to)535-556
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Volume114
Issue number5
DOIs
StatePublished - May 4 2018

Bibliographical note

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.

Keywords

  • compositional modeling
  • convection-diffusion flow equations
  • discontinuous Galerkin method
  • discrete fracture model
  • fractured porous media
  • mixed finite element method

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics
  • Numerical Analysis

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