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Keywords: dimension
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Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212196-MS
... dimension convx1 architecture procedure reconstruction implementation petroleum science Introduction Ensemble data assimilation methods are becoming industry standards in history-matching applications because their stability, fast convergence, and scalability for large-scale problems. Among...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203934-MS
... dimensions. If the results in one dimension establish a new state of the art, improvements are expected for the two dimensional cases. We believe that they are related to the same issues encountered in one dimension and are related to the existence of sharp discontinuities inherent to this class...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203994-MS
... index and can be calculated as: WI = 2 πα k h ln ( r o r w ) + S K I N , where α is a unit conversion factor, h is the height of the reservoir gridblock, r o is the grid block dimension equivalent radius, r w is the wellbore radius SKIN...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193816-MS
... dimension) and by avoiding tables extrapolations. In this paper we discuss the new workflow and the new dynamic generalized VLP table construction in details. well performance Upstream Oil & Gas Modeling & Simulation inflow performance process simulation new framework decoupled approach...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193817-MS
... for the saturation equation of two-phase flow in porous media in two space dimensions. The keys to high order accuracy are to use WENO reconstruction in space (which handles shocks and steep fronts) combined with a two-stage Radau-IIA Runge-Kutta time integrator. The saturation is approximated by its averages over...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193878-MS
... it in a compositional simulator to replace the traditional flash calculation module, speeding the simulation by 30%. deep learning Phase Behavior machine learning PVT measurement proxy neural network dimension flash calculation phase classification step preconditioner input parameter calculation module...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173319-MS
... intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173320-MS
...-dimensional problem is convergent in that, (0.10) ‖ u ( x ) − I h ∞ U h ‖ = O ( h p ) , where p ≥ 1. Assuming Fréchet differentiability, Newton's method is well-defined in infinite dimensions, and it can be applied directly in order to solve Equation 0.8...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173291-MS
.... [ 20 ] used dimensional adaptivity of the sparse grid for multi-crieria decision making of CO 2 storage management from which the authors showed that this method can be employed efficiently. In this work, we implement the dimension-wise technique based on the Smolyak sparse grid representation...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, January 31–February 2, 2005
Paper Number: SPE-93115-MS
... the same kinetics of matrix-fracture transfer as the reference one, whatever the number of flow dimensions. Fig. 6 presents the produced oil versus time in three cases involving one-, two- or three-dimensional transfers. The mobility ratio was modified by changing the oil viscosity μ o . The two...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, January 31–February 2, 2005
Paper Number: SPE-93691-MS
... in Two Dimensions The higher dimensional extension of the above scheme is based on a generalization of the one dimensional discrete flux. The flow equations Eq. 1 are integrated in space and time over a discrete control-volume Ω CV with surface δΩ CV by direct use of the Gauss divergence...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, January 31–February 2, 2005
Paper Number: SPE-93430-MS
... of the finite volume method in three dimensions follows much the same lines as described above for two dimensions. The interpolation to grid nodes naturally uses a three dimensional linear function, with four undetermined coefficients instead of three. This requires at least four neighbouring cell centre values...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 3–5, 2003
Paper Number: SPE-79708-MS
... dfn model permeability hydraulic fracturing small-scale fracture interference test formulation reservoir simulation fracture network dimension analytical solution matrix block drillstem testing drillstem/well testing equation of state spe 79708 dual-porosity model fracture...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 3–5, 2003
Paper Number: SPE-79665-MS
... with displacement s = l . The generalization of equation (B.7) to two and three dimensions is straight forward. We only give the equation for three dimensions, since this equation may easily be reduced to two dimensions. For a three-dimensional grid the determining equations are (B.8) ∑ i = 0...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 3–5, 2003
Paper Number: SPE-79682-MS
... permeability equation well model implementation dimension multiblock grid grid formulation fluid dynamics reservoir simulation procedure upstream oil & gas scaling method spe 79682 plane enhanced recovery flow in porous media boundary drillstem/well testing reservoir characterization...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 11–14, 2001
Paper Number: SPE-66357-MS
...-point schemes (e.g., a nine-point stencil in two dimensions and a 27-point stencil in three dimensions). Flux-continuous methods, designed to handle full tensor permeabilities and/or non-orthogonal grids, have been presented previously for two dimensional 9 – 11 and three dimensional 12 , 13...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 11–14, 2001
Paper Number: SPE-66358-MS
...) error in velocity field. The focus of this paper is on the development of finite volume schemes that maintain consistent full tensor flux approximations while retaining standard diagonal tensor Jacobian matrix inversion in three dimensions on structured and unstructured grids. Three dimensional...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 11–14, 2001
Paper Number: SPE-66379-MS
... size underscoring the need for judicious upscaling. Of greater importance is to demonstrate, for the chosen grid dimensions, that the upscaled representation is both reasonable and optimal in the sense that a significantly better template would be difficult to obtain. We consider two non-uniformly...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 11–14, 2001
Paper Number: SPE-66395-MS
... and intensity to stochastically generate a static model of the fractured reservoir. The dynamic behavior of the fractured system was reproduced by a finite element flow model able to simulate transient flow through three-dimensional rock masses with discrete fracture networks. Consistency was required between...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 14–17, 1999
Paper Number: SPE-51918-MS
...One-Dimensional Interpolation Consider a one-dimensional grid with nodes selected such that for i = 1 to n-1, x i = x i-1 + Δx. The boundary nodes are x 0 and x n . It can be assumed that function values or function derivatives are given at the boundary nodes independently of the remaining...

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