A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

Ankur Taneja, Jonathan Higdon

Research output: Research - peer-reviewArticle

Abstract

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

LanguageEnglish (US)
Pages341-372
Number of pages32
JournalJournal of Computational Physics
Volume352
DOIs
StatePublished - Jan 1 2018

Fingerprint

Petroleum reservoirs
Polynomials
two phase flow
crude oil
permeability
Multiphase flow
Geology
Tensors
Flow of fluids
Crude oil
Engineers
Fluids
Industry
Uncertainty
mesh
polynomials
multiphase flow
Galerkin method
geology
partial differential equations

Keywords

  • Discontinuous Galerkin method
  • Reservoir simulation
  • Spectral element method

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs. / Taneja, Ankur; Higdon, Jonathan.

In: Journal of Computational Physics, Vol. 352, 01.01.2018, p. 341-372.

Research output: Research - peer-reviewArticle

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