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Modeling of multicomponent diffusions and natural convection in unfractured and fractured media by discontinuous Galerkin and mixed methods
Author(s) -
Hoteit Hussein,
Firoozabadi Abbas
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5753
Subject(s) - finite element method , discontinuous galerkin method , initialization , computation , convection , natural convection , mechanics , numerical diffusion , finite difference , mathematics , computer science , mathematical analysis , physics , thermodynamics , algorithm , programming language
Summary 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.