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Keywords: approximation
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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203972-MS
... to resolve 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...
Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203998-MS
... applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields...
Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203903-MS
... on a fully 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...
Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203957-MS
...Abstract 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...
Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203961-MS
...Abstract Abstract Combining the Perpendicular Bisector (PEBI) grids with the Two Point Flux Approximation (TPFA) scheme demonstrates a potential to accurately model on unstructured grids, conforming to the geological and engineering features of real grids. However, with the increased complexity...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193817-MS
... , y ) = 1 | E | ∬ E q w ( S w ) d x     d y , where ν l is the outward unit normal to the l -th facet of the boundary of E . We approximate each boundary integral using a 2-point Gauss quadrature rule with points ( x l,k , y l,k ) and weights...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193875-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193874-MS
..., at each front edge a tangent plane defined by averaging the normals to the front edge vertices is approximated, and a new point in a direction normal to the front edge is created, so as to form a quality simplex in the tangent plane. In order to ensure that the mesh follows the actual surface...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193919-MS
... of freedom in 2D, that include the standard cell-centred pressure in the approximation together with edge values, which increases to a factor of four in 3D (on structured grids). The mixed hybrid finite-element method (MHFEM) ( Brezzi and Fortin, 1991 ; Abushaikha et al., 2017 ) and mimetic methods...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193831-MS
... of an existing ‘dynamic’ approach which requires multiple surrogate evaluations to model the solutions at different time instances, the other is a ‘steady-state’ approach that evaluates all time instances simultaneously, reducing the local approximation error. The ability of these approaches to estimate...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193904-MS
... the extended Dynamic Mode Decomposition (EDMD) as a suitable data-driven framework for learning the reservoir dynamics entailed by flow/fracture interactions in unconventional shales. The proposed EDMD approach builds on the approximation of infinite dimensional linear operators combined with the power of deep...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193925-MS
... for computing the derivatives needed in the basic optimization algorithm employed. Here, we present a methodology for the solution of an optimization problem with nonlinear and linear constraints where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193927-MS
... grid quality and method stability with respect to flux approximation in the presence of strongly anisotropic full-tensor permeability fields.K-orthogonal grid generation is only possible for low anisotropy ratios. Quasi K-orthogonal grid generation involves satisfying the K-orthogonal condition...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193918-MS
... Artificial Intelligence approximation machine learning Upstream Oil & Gas minimization problem history matching proposal distribution reservoir simulation gmm approximation covariance matrix reservoir simulator prediction reservoir simulation run Reynolds posterior PDF...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193886-MS
... Abstract A novel discrete fracture model (DFM) approximation is presented and coupled with the control-volume distributed multi-point flux approximation (CVD-MPFA) formulation. The reduced-dimensional discrete discontinuous pressure model for intersecting fractures is extended to two-phase flow...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193912-MS
... deep learning algorithms to train the elements of the reduced model discrete system. In this case, deep learning architectures will be employed to approximate the elements of the discrete system and reduced-order model basis functions. The numerical results will use deep learning architectures...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193887-MS
... approximation geomechanics system-amg approach solver Modeling & Simulation Fluid Dynamics subsystem Applicability application multigrid matrix operator Artificial Intelligence Upstream Oil & Gas approximation uzawa scheme iteration fracture In fully coupled reservoir...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182716-MS
... The approximation to the flux as solely a τ gradient is the primary approximation that we make when transforming from the 3-D to the 1-D diffusivity equation. In specific applications, the validity of this approximation should be tested. Fig. 2 shows the impact of heterogeneity and boundary...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182677-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182690-MS
... Abstract Reservoir geology has traditionally been described using corner-point grids. For such grid and general polyhedral grids, two-point flux-approximation (TPFA) schemes, or modifications thereof, are simple and robust methods which, despite grid-orientation errors and a general lack...

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