..., the adjoint method facilitates efficient determination of sensitivities to all parameters in a single backward calculation. However, its implementation requires knowledge of the partial differential equations used to develop the forward model, which is not available for commercial simulators. This study...

... Abstract Physics-Informed Neural Networks (PINNs) gains attentions as a promising approach for applying deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, due to the challenging regions within the solutions of ‘stiff’ PDEs, e.g., shock...

... At a given pressure, Equations (1) to (5) allow determination of the moles of CO 2 in grid blocks, the molar fluid enthalpy, the liquid and vapor phase mole fraction and the temperature. All the above equations are solved simultaneously for independent variables such as pressure, temperature, moles...

... intelligence modeling & simulation geological subdiscipline aqueous phase geochemical solver interaction reservoir simulation rock type geochemistry geochemical characterization equilibrium fraction matrix conservation equation simulator figure figure show nacl coupling climate change...

...-driven Interwell Simulator (INSIM), which is referred to as INSIM-BHP, we addressed the issue of pressure accuracy during waterflooding. In this study, we improve the INSIM formulation by incorporating the saturation information into the pressure equation and prove that the INSIM-based approach’s...

... hydrate inhibition wax inhibition flow assurance spe comparative solution project injection fraction equation local grid refinement Introduction With the growing concern about climate change, Geological Carbon Storage (GCS) is considered one of the most promising approaches to reduce CO2...

... a close to even distribution of implicit equations among domains. Performance timings for the main linear solver kernels on multicore hardware reveal an improved distribution of computations among threads, resulting in significant enhancements in linear solver performance. geologist algorithm...

... Following the Buckley-Leverett (1942) solution, and implementing Equations 4 and 5 : Abstract This work quantifies the applicability of an analytical hydrogen pressure buildup equation for real geological conditions. Analytical results are compared against multiple simulation models...

... Newton's method by orders of magnitude. We further validate the proposed scheme by simulating water-flooding problems on a highly heterogeneous reservoir with speed-ups ranging from a factor of 2 to 5, depending on the extent of gravitational influence. Introduction equation flow in porous media...

...: in Section 2 and Section 3 we introduce the reduced order model based on neural networks utilized in this work. In Section 4 we show the governing equations for the coupled fluid-solid problem. Two synthetic case studies are then presented in Section 5 to prove the accuracy and efficiency of our DL-ROM...

... and longer migration periods. The preconditioner leverages the Proper Orthogonal Decomposition (POD) method to construct a ROM approximation of the linearized pressure equation. Key ingredients of the new adaptation are on-the-fly training and inference during a single simulation without requiring any prior...

... ( W T − 1 + K T − 1 + b T − 1 ) ∘ … ∘ σ 1 ( W 0 + K 0 + b 0 ) ∘ Abstract Current reservoir simulators solve Advection-Diffusion-Reaction equations on unstructured grids to a high degree of accuracy but are computationally expensive...

..., we established the pressure equation based on the material balance principle. After upstream and downstream nodes are decided according to the well nodes' pressure solutions, we solve a 2 by 2 system of saturation equations based on the front tracking method. Specifically, for the sub-Riemann problem...

... geologist asset and portfolio management equation application reservoir simulation enhanced recovery iterative solver network model waterflooding modeling & simulation algorithm jacobian matrix history matching solver matrix solution method simulation mesh sparsity pattern vertex cell...

... of multiphase models, with high mobility ratios and large upscaling ratios, upscaling of only single-phase parameters is insufficient. Established methods, therefore, use transport coefficients and/or dynamic pseudo-functions in the coarse-scale conservation equation to capture the dynamic behavior of the fine...

... : ρ α , i j = 1 2 ( ρ α , i + ρ α , j ) Integrating equation (5) in time using a first-order method yields the fully-discrete residual form (9) R α , i = M α , i n + 1 − M α , i n + Δ t ∑ j ∈ ℒ ( i ) T...

... matching process, where physical parameters need to be adjusted to match production data. Through this process, partial differential equations (PDEs) are solved in complex grids using numerical reservoir simulators, where the resulting model has high accuracy, however with a challenging computational...

... presents one instance of input and output data. The data in blue is the one set of input of ANN and the number in red is the output of ANN. Abstract There are several methods for solving fluid flow equations in porous media using numerical techniques such as finite-element, finite-difference...

.... equation flow in porous media rehbinder united states government reservoir characterization fluid dynamics reservoir simulation wheeler upstream oil & gas reservoir geomechanics conservation enriched galerkin coefficient comput method appl mech eng thermoporoelasticity problem simulating...

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