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Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203903-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203957-MS
...Spectral volume discretisation method 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203972-MS
... demonstrate the sequential solution procedure considering the uniform one-dimensional discretization of the domain shown in Figure 1 ; extension to two- and three-dimensional domains in cartesian grids is straightforward. The finite-volume representation of Eq. (13) based on the two-point flux...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203993-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193886-MS
... (2017), Schmid et al. (2013) and Matthäi et al. Matthäi et al. (2007 , 2010 ). The control-volume distributed multi-point flux approximation (CVD-MPFA) method Friis et al. (2008) is flux continuous, locally conservative, allows the use of unstructured grids to represent complex geometries, and has...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182666-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182701-MS
... reservoir pressures at time t + Δ t are known, total volumetric fluxes can be computed and the transport of fluid species over the time step can be computed by solving Eq. 1 . This usually involves a fractional formulation, in which each phase flux is expressed as a fraction of the total volumetric flux...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182695-MS
... ) ,  otherwise    α = w , o It has been shown that nonlinear properties of the numerical flux have large impact on the convergence behavior of the Newton-based iterative process ( Wang and Tchelepi 2013 ). In this section we review some existing numerical flux schemes, including the recently...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182677-MS
..., the modeling of deviated wells and complex depositional environments, suggests the use of unstructured polygonal (in 2-D) or polyhedral meshes (in 3-D). In general, Two-Point Flux Approximation (TPFA) and First Order Upwind Scheme (FOUS) are used to approximate, respectively, the diffusive and advective fluxes...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182689-MS
... each fine cell of a coarse cell pair with a specified total flow between them, computed 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173312-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173306-MS
... optimization problem Reservoir Management Multiscale Method solver fine grid flow diagnostic basis function ensemble grid krogstad flux partition equation heterogeneity møyner Lorenz coefficient realization møyner Introduction Computational tools for reservoir modeling play a critical...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173293-MS
... cell face coarse cell effective permeability diffusive time simulator flux scaling method steady state boundary condition diffusivity equation fine cell transmissibility equation permeability coarse cell face society of petroleum engineers Introduction The detailed requirements...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173267-MS
... where R is the residual and u T is constant. The first term on the right-hand side is the accumulation term, and the second term is the flux term. Because the accumulation term is linear, the nonlinearity of Eq. (13) lies solely in the flux function f w . Here, we analyze the flux...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 18–20, 2013
Paper Number: SPE-163612-MS
... (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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 18–20, 2013
Paper Number: SPE-163626-MS
... consider the elliptic (pressure) equation 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 18–20, 2013
Paper Number: SPE-163593-MS
... reservoir simulation vertex MPFA method flux Denote equation concentration pressure equation Introduction Multiphase flow in porous media can be described by a set of conservation equations ( Aziz and Settari 1979 ; Chen et al. 2006 ; Peaceman 1977 ). Numerical methods for solving...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 18–20, 2013
Paper Number: SPE-163658-MS
... 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...

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