Computational methods for multiphase flows in porous media

By Beatrice Riviere. Mathematics of Computation, 2007

935 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8cc9499b7447cb18b2b781431531c3de26a3224c

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Citations in the corpus

ON ITERATIVE IMPES FORMULATION FOR TWO-PHASE FLOW WITH CAPILLARITY IN HETEROGENEOUS POROUS MEDIA (2010, background): “There are numerous improved versions of IMPES for two-phase flow, for example, [16,52,68,70].”
Numerical modeling of formation damage by two-phase particulate transport processes during CO2 injection in deep heterogeneous porous media (2011, methodology): “The total fluid flow velocity dependence on the global pressure is given as follows (for more details see [23]):”
Efficient and Accurate Quantification of Uncertainty for Multiphase Flow With the Probabilistic Collocation Method (2009, background): “On the other hand, some other stochastic approaches have been developed in the context of subsurface hydrology in the last two decades (Dagan 1989; Gelhar 1993; Cushman 1997; Neuman 1997; Zhang 2002; Rubin 2003) that could be applied to the petroleum industry. Zhang and Tchelepi (1999) and Zhang et ”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, methodology): “flow problems when applied to the global flow (or pressure) equation in fractional flow formulations (Chavent et al., 1984; Gerritsen and Durlofsky, 2005; Hoteit and Firoozabadi, 2005; Chen et al., 2006).”
Critical review of the impact of tortuosity on diffusion (2007, background): “Conservation of mass of the species in the fluid phase is given by Bear (1972) and Chen et al. (2006) ( c ) t = −∇ · (c u − D∇c) + q, (2.1) where is the porosity of the porous medium (the fraction of a representative elementary volume available for the fluid), is the density of the fluid per unit…”
A Stochastic Simplex Approximate Gradient (StoSAG) for optimization under uncertainty (2017, background): “Reservoir simulation is a branch of fluid mechanics concerned with the numerical simulation of multiphase flow through heterogeneous porous media in the form of subsurface hydrocarbon (oil and gas) reservoirs; for example, [1] or [2].”
Evaluation of Gaussian approximations for data assimilation in reservoir models (2012, unknown): “From standard arguments, it can be shown that (s, p) is the solution to the following system [8]:”
A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocityand continuous capillary pressure (2013, unknown): “For completeness, we present the IMPES equations below.”
Cell‐centered finite volume discretizations for deformable porous media (2014, methodology): “[4] or [5]), and is implemented as such in the industry standard simulation software Eclipse by Schlumberger and Stars by CMG.”
Fully mass-conservative IMPES schemes for incompressible two-phase flow in porous media (2019, methodology): “The IMplicit Pressure Explicit Saturation (IMPES) scheme [11, 12, 14, 15, 16, 23, 45, 46, 52] has been widely used to solve the coupled nonlinear system for the two-phase flow in porous media.”
The effect of microporosity on transport properties in porous media (2014, background): “Darcy’s equation can be obtained and is commonly used in larger scale reservoirs [17].”