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Keywords: approximation
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Proceedings Papers
Implementing a Duchon Spline Based on Gauss-Newton Distributed Optimizer for Coupled Flow and Geomechanics
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, March 25–27, 2025
Paper Number: SPE-223866-MS
...-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...
Proceedings Papers
Grid-Orientation Effects in the 11th SPE Comparative Solution Project Using Unstructured Grids and Consistent Discretizations
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, March 25–27, 2025
Paper Number: SPE-223885-MS
... 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...
Proceedings Papers
Enhancing Computational Efficiency of Numerical Simulation for Subsurface Fluid-Induced Deformation Using Deep Learning Reduced Order Models
Available to PurchaseE. Ballini, A. Cominelli, L. Dovera, A. Forello, L. Formaggia, A. Fumagalli, S. Nardean, A. Scotti, P. Zunino
Publisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, March 25–27, 2025
Paper Number: SPE-223897-MS
... 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...
Proceedings Papers
Learning to Solve Parameterized Single-Cell Problems Offline to Expedite Reservoir Simulation
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212175-MS
... 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...
Proceedings Papers
A Physics-Informed Neural Network for Temporospatial Prediction of Hydraulic-Geomechanical Processes
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212202-MS
... 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...
Proceedings Papers
A Quasi-Newton Method for Well Location Optimization Under Uncertainty
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
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
Application of Deep Neural Networks to the Operator Space of Nonlinear PDE for Physics-Based Proxy Modelling
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
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
Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203957-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
A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203903-MS
... 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...
Proceedings Papers
Grid Quality Measures for PEBI Grids
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203961-MS
... 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...
Proceedings Papers
High-Order Adaptive Scheme for Reactive Transport in Heterogeneous Porous Media
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203972-MS
... 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...
Proceedings Papers
The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203998-MS
... 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...
Proceedings Papers
Unstructured CVD-MPFA Reduced-Dimensional DFM Models for Two-Phase Flow, Coupled with Higher Resolution Hybrid Upwind Methods
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193886-MS
.... 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...
Proceedings Papers
System-AMG for Fully Coupled Reservoir Simulation with Geomechanics
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193887-MS
... 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...
Proceedings Papers
Quasi-K-Orthogonal Grid Generation
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
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
An SQP-Filter Algorithm with an Improved Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear Constraints
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
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
Higher Resolution Unstructured Spectral Finite-Volume Method for Flow in Porous Media
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
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
Von Neumann Stable, Implicit, High Order, Finite Volume WENO Schemes
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193817-MS
... 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...
Proceedings Papers
Non-Intrusive Reduced Order Modelling for Reconstruction of Saturation Distributions
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193831-MS
... 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...
Proceedings Papers
A Three-Dimensional Symmetric Positive Definite Control-Volume Distributed Multi-Point Flux Approximation for Flow Computation on Tetrahedral Grids
Available to PurchasePublisher: Society of Petroleum Engineers (SPE)
Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193919-MS
... 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...
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