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

... 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 implemented the BFGS quasi-Newton updating algorithm together with line-search and trust-region optimization strategies. We...

... 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...

... 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 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...

... 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...

... 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...

... ) , where q ( S w ) = q w ( S w ) + q n ( S w ) is the total well source term and λ( S w )ρ( S w ) = λ w ( S w )ρ w + λ n ( S w )ρ n . Many approaches have been proposed to increase the order of approximation. These include the mixed finite element methods (e.g...

... 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...

... distributed multi-point flux approximation (CVD-MPFA) schemes are compared and contrasted together with the methods. Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. The geological features are classified into two groups; 1) involving layers...

... 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 the water saturation distributions expected during a gas flood through a 2D, dipping reservoir...

... 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...

... 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 Introduction In fully coupled...

... 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...

... 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...

... 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 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...

... distribution were not highly successful. More recently, Li and Reynolds (2017 ) used a Gaussian mixture model (GMM) approximation of the target pdf as a proposal distribution in a Metropolis-Hastings MCMC framework in order to accelerate convergence. (9) ∇ m O ( m ) = C M − 1...

... 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...