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Keywords: basis function
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Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203939-MS
... and Hou 2003 ; Jenny et al. 2003 ; Aarnes 2004 ; Aarnes et al. 2005 ; Efendiev and Hou 2009 ; Manea et al. 2016 ). A common approach in various multiscale developments is to use solutions (called basis functions) to locally constructed versions of the problem to construct a coarser version...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193870-MS
.... This method does not require any coarse partitioning and, hence, can be applied to general unstructured topology of the fine scale. Inspired by smoothing aggregation algebraic multigrid solver, the algebraic smoothing aggregation preconditioner constructs basis functions which allow mapping of some high...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193809-MS
... dynamics robust fuzzy timestep selector fuzzy timestep selector society of petroleum engineers timestep selector basis function linear iteration Timestep Introduction Fully implicit reservoir simulation ( Dogru 2009 ; Cheshire, 1980 ) is the established technology for robust and efficient...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193880-MS
... AMS parallel implementation shows good scalability for the solution stage, its setup stage is less efficient compared to the CPU, mainly due to the dependence on a QR-based basis functions solver. scaling method solution phase Implementation reservoir simulation Hajibeygi algorithm...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193912-MS
... for each layer. Novel proper orthogonal basis functions will be constructed such that the degrees of freedom have physical meanings (e.g., represent the solution values at selected locations) and basis functions have limited support, which will allow localizing the forward dynamics. This will allow writing...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193894-MS
.... Furthermore, its finite-volume formulation preserves local conservation for both mass and heat fluxes. Multi-level local basis functions for pressure and temperature are introduced, in order to accurately represent the heterogeneous fractured rocks. These basis functions are constructed at the beginning...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193889-MS
... | i = 1 , ⋯ , N } , K i is the i -th coarse element, N is the number of coarse elements in T H and H > 0 is the coarse mesh size. Our NLMC upscaled system is based on this coarse mesh, choice of continua and basis functions. For every coarse element K i , we...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, April 10–11, 2019
Paper Number: SPE-193934-MS
... engineers time step møyner partition grid møyner discretization refinement fine grid solver equation flow in porous media reordering transport equation basis function compositional simulation cubature rule Introduction Simulation of multiphase flow in porous media is a truly...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182707-MS
... parameter reservoir model basis function ensemble parameter estimation reservoir simulation background tensor decomposition algorithm decomposition realization permeability field Introduction It is important to understand that the elements of S , i.e. s i 1 i 2 ··· i N...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182620-MS
... with the flexibility of the StoSAG technique (several different parameters/responses can be easily considered) allows for a flexible and efficient optimization strategy suitable for large-scale problems. Artificial Intelligence optimization problem optimal control strategy optimization basis function...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182686-MS
... Hou [ 11 ] presented a MsMFE method, which treat both the pressure and velocity as unknowns instead of only pressure in MsFV and express them in terms of two different sets of a basis function. In this paper, a new dual grid method is presented in 3D with complex geological structures...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182682-MS
... by updating the POD subspace and the DEIM approximation of the nonlinear functions. These global online basis function updates improve the accuracy of snapshot approximation. Since the adaption is performed infrequently, the new methodology does not add a significant computational overhead due...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182694-MS
... an efficient parallel implementation procedure as to how to enrich a given multiscale formulation with additional local basis functions. These additional basis functions, constructed in parallel computational platform, aim to resolve large error components for a generic fine-scale system with no right-hand...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182652-MS
... Chebyshev polynomial Polynomial Approximation reservoir simulation parameterization iteration optimization problem approximation snapshot matrix Upstream Oil & Gas control trajectory equation algorithm matrix decision variable fine scale optimal control basis function reduction...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182701-MS
.... The key idea of these methods is to define a coarse partition of the simulation grid, and compute a set of locally defined basis functions that map between degrees of freedom associated with the fine and coarse grid. Using these basis functions, one can derive reduced flow problems on the coarse grid...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182679-MS
...Introduction Modeling & Simulation composition basis function reservoir simulation simulator Multiscale Solver scaling method Upstream Oil & Gas Comput finite-volume method Tchelepi equation fraction formulation permeability solver grid møyner Artificial Intelligence...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, February 20–22, 2017
Paper Number: SPE-182654-MS
... first divide the global domain into overlapping local problems, over which local basis functions (interpolators) are solved. A coarse system is then constructed in which the coarse cell transmissibility values are obtained using these basis functions. Once the coarse-scale system is solved, its solution...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173200-MS
... is presented for fractured porous media, which enables the treatment of fractures with multiple length scales and wide ranges of conductivity contrasts. To this end, fully integrated local basis functions for both matrix and fractures are constructed. These basis functions are employed to construct...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173259-MS
...-level algorithm that employs domain decomposition with a localization assumption. In AMS, basis functions, which are local (subdomain) solutions computed during the setup phase, are used to construct the coarse-scale system and grid transfer operators between the fine and coarse levels. The solution...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 23–25, 2015
Paper Number: SPE-173226-MS
... for the pressure solution. The multiscale method has proved to be accurate and reliable for large real-data models. The new solver is capable of solving very large models an order-of-magnitude faster than the current commercial version of the solver. scaling method reservoir simulator basis function...

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