... unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations, as the unknowns share the same discrete locations on the mesh. Additionally, a multi-point flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy...

... Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection...

... these scales properly. To address these challenges, we extend the adaptive transport scheme for the simulation of reactive transport in heterogeneous porous media developed previously ( Deucher and Tchelepi, 2021 ) to account for (a) higher-order approximation of the convective fluxes and (b) coupling...

... during streamline tracing. In this work, we present a robust streamline tracing algorithm for DPDK models and apply the new algorithm to rate allocation optimization in a waterflood reservoir. In the proposed method, streamlines are traced in both fracture and matrix domains. The inter-fluxes between...

... Abstract A three-dimensional symmetric positive definite (SPD) cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) is presented for porous media flow simulation on tetrahedral grids. The scheme depends on a single degree of freedom per control-volume and is derived...

... reservoir simulation approximation saturation equation flux approximation Artificial Intelligence Fluid Dynamics edwards flux formulation capillary pressure Upstream Oil & Gas two-phase flow gravity matrix flow in porous media equation pressure model resolution Firoozabadi...

... discretization method for multiphase flow in reservoir simulation is the two-point flux-approximation (TPFA) method. This finite-volume method is mass conservative, but only conditionally consistent and hence susceptible to grid-orientation effects. In the second part of the paper, we review a series...

... efficiently compute approximate pressures to within a prescribed accuracy and still provide mass-conservative fluxes. We present an adaptive and flexible framework for combining multiple sets of such multiscale approximations. Each multiscale approximation can target a certain scale; geological features like...

... Abstract In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead...

... equation is discretized by a non-orthodox linear Multi-Point Flux Approximation (MPFA-HD) method capable to handle heterogeneous and highly anisotropic media. Following the MPFA-D (MPFA-Diamond) scheme and some existent non-linear cell centered strategies, the key point in the construction of our scheme...

... at a characteristic time for pressure transients across the cells. The ratio of volume averaged flux and pressure gradient is used to obtain the effective transmissibility between the cell pair. The application of pressure transient concepts has allowed us to develop completely local upscaling and downscaling...

... the discretized (numerical) flux function for the interface between two cells. The numerical flux is expressed in terms of the saturations of the two cells. Discontinuities in the first derivative of the flux function (referred to as kinks) and inflection lines are identified as the cause of convergence...

... provide a numerical scheme based on multipoint stencil more physical than two point flux approximation methods. This paper presents the implementation of VAG and MPFA schemes inside a next generation reservoir simulator starting from a source code calculating multi-point flux non neighbor connections...

... Abstract A novel cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-matrix simulations in three-dimensions. The grid is aligned with the fractures and barriers which are then modelled as lower...

... diagnostic basis function ensemble grid krogstad flux partition equation heterogeneity møyner Lorenz coefficient realization møyner Introduction Computational tools for reservoir modeling play a critical role in the development of long-term strategies for optimal recovery of hydrocarbon...

... of accuracy in performance prediction. reservoir simulation Upstream Oil & Gas Modeling & Simulation calculation diffuse source algorithm cell face coarse cell effective permeability diffusive time simulator flux scaling method steady state boundary condition diffusivity equation...

... (6) Ƒ = Ƒ a + Ƒ v = ( ρ c K ( ∇ p ) μ ) i + 1 / 2 + ( ρ D ∇ c ) i + 1 / 2 The key difference between the MLS and the TPFA finite-volume methods is the manner in which the flux across an interface is evaluated. Shown...

... Abstract This paper focuses on methods for fine scale modelling and presents development of multiscale methods with particular emphasis on the numerical flux approximation. Families of Darcy-flux approximations have been developed for consistent approximation of the general tensor pressure...

... Abstract The multipoint-flux approximation (MPFA) methods have been popular for reservoir simulation, since they handle permeability anisotropy and heterogeneity on irregular grids, they are locally mass conservative and have an explicit expression for the flux. However, they are in general...

... in porous media Simulation co 2 lattice Boltzmann equation concentration field Schmidt number collision operator distribution function equation relaxation time density-driven convection reservoir simulation reservoir characterization Fluid Dynamics Rayleigh number flux horizontal wall...