...-logs. We employ a local Gauss-Newton (GN) optimizer that requires about half the number of simulations compared to equivalent gradient-based or serial optimizers. We approximate the sensitivity matrix by interpolating the resulting predictions with Duchon splines, i.e., radial basis functions, opposite...

... and face f . To get a cell-centered scheme, we introduce a similar approximation inside cell j , assume continuity of fluxes, v i,f = − vj, f . We can then eliminate the unique pressure p f at the continuity point to obtain an expression for the flux through face f (3) ( ∇ p...

... stress finite volume approximation available in the open-source library PorePy. We investigate the capability of the reduced model to accurately reproduce new scenarios by comparing the outcome with a standard numerical solution. We can observe how the DL-ROM can be used in place of full-physics...

... Let the constants c = { c 1 , c 2 , c 3 } denote the mesh CFL numbers for a target time increment over which approximate solutions are to be obtained. The system of residual equations for the new state, U , given the old solution state, U old , takes the form, R 1 ( U...

... neural network machine learning upstream oil & gas artificial intelligence deep learning reservoir characterization journal united states government reservoir geomechanics differential equation accuracy porous media approximation physics-informed neural network application simulation...

... of the objective function may be too expensive to compute for realistic applications in the absence of the implementation of the adjoint method. In this paper, we develop a quasi-Newton method based on the stochastic simplex approximate gradient (StoSAG), which requires only objective-function values. We have...

... Abstract In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE), within the Operator-Based Linearization (OBL) simulation framework, and discover the physical space for a physics-based proxy model with reduced degrees...

... 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...

... of the stress tensor in mixed finite element methods was also developed in Arnold et al. (2007) and then used in combination with multi-point stress approximation in Ambartsumyan et al. (2020) . Introducing Discontinuity (18) K i n = λ i n + γ i...

... and accurate approximation of the continuous mathematical equations describing the fluid flow in porous media. High quality grids with special qualities allow simple (and computationally cheap) numerical methods to provide accurate approximations. On the other hand, sophisticated (and possibly computationally...

... 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 with a chemical solver connected to geochemical databases. The numerical...

... to physical data, or portions of the physical boundary, are often met in real 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...

.... An adaptive implicit flux is employed at the matrix fracture interface. For the fractures, a reduced-dimensional discrete-fracture model (DFM) Ahmed et al. (2015 , 2017 ) is used and extended to an implicit two-phase flow approximation. The reduced-dimensional DFM model has a significant effect...

... to reflect the requirements of the Uzawa scheme to be applicable. We demonstrate the performance for widely used test cases as well as for real-world problems of practical interest. flow in porous media linear system algebraic multigrid system-amg approach reservoir simulation schur approximation...

... Abstract Quasi K-orthogonal grid generation is presented, to improve 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...

... of an optimization problem with nonlinear and linear constraints where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic gradients based on an improved stochastic simplex approximate gradient (StoSAG). For the most part, our discussion is focused on the application...

... 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...

... Many approaches have been proposed to increase the order of approximation. These include the mixed finite element methods (e.g., Durlovsky & Chien 1993; Hoteit & Firoozabadi 2008 ; Zidane & Firoozabadi 2018 ), mimetic methods (e.g., Alpak 2007 ; Guevara-Jordan & Jhonnanthan...

... where f is an unknown function representing the governing equations. In order to approximate it, one notes that N t samples of it are given, namely (4) α 1 = f ( α 0 ) ,   α 2 = f ( α 1 ) ,   ⋯ ,   α N t = f ( α N t − 1...

... below. Local sub-interface pressures 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...