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Keywords: approximation
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Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212202-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212212-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212217-MS
... 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...
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-203961-MS
... 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, 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
... approximation (TPFA) is written as: (14) ( λ t T ) i + 1 / 2 ( p i − p i + 1 ) − ( λ t T ) i − 1 / 2 ( p i − 1 − p i ) = − q t , i , Before introducing the adaptive transport scheme for the reactive...
Proceedings Papers

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

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193817-MS
... Abstract Simulation of flow and transport in petroleum reservoirs involves solving coupled systems of advection diffusion-reaction equations with nonlinear flux functions, diffusion coefficients, and reactions/wells. It is important to develop numerical schemes that can approximate all three...
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
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193831-MS
... 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...
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 Introduction In fully coupled...
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
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193927-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193918-MS
... and reservoir simulation predictions as well as the assumption that the reservoir parameters follows a Gaussian distribution, and these assumptions do not hold for most practical applications. When these assumptions do not hold, ensemble methods only provide a rough approximation of the posterior probability...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193886-MS
... & Root (1963) ; Kazemi et al. (1976) , and discrete fracture model (DFM) Kim & Deo (2000) ; Karimi-Fard & Firoozabadi (2003) ; Karimi-Fard (2004) ; Hoteit & Firoozabadi, 2008 (B); Sandve et al. (2012) ; Ahmed et al. (2015) have been proposed to approximate and characterize...

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