Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media

Cusini, Matteo; Fryer, Barnaby; Kruijsdijk, C.P.J.W. van; Hajibeygi, Hadi

doi:10.1016/j.jcp.2017.10.052

Cited by 29 publications

(14 citation statements)

References 40 publications

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“…which is a finite-volume restriction operator to assure mass conservation, i.e., 21Note that different interpolators are used for each variable (Cusini et al, 2018a;HosseiniMehr et al, 2018). The pressure prolongation operator uses fully-coupled multilevel multiscale basis functions, whereas the prolongation operator of fluid temperature uses constant interpolators, i.e.,…”

Section: Fg-adm Operatorsmentioning

confidence: 99%

Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation

HosseiniMehr

Arbarim

Cusini

et al. 2019

Day 1 Wed, April 10, 2019

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A dynamic multilevel method for fully-coupled simulation of flow and heat transfer in heterogeneous and fractured geothermal reservoirs is presented (FG-ADM). The FG-ADM develops an advanced simulation method which maintains its efficiency when scaled up to field-scale applications, at the same time, it remains accurate in presence of complex fluid physics and heterogeneous rock properties. The embedded discrete fracture model is employed to accurately represent fractures without the necessity of unstructured complex grids. On the fine-scale system, FG-ADM introduces a multi-resolution nested dynamic grid, based on the dynamic time-dependent solution of the heat and mass transport equations. The fully-coupled implicit simulation strategy, in addition to the multilevel multiscale framework, makes FG-ADM to be stable and efficient in presence of strong flow-heat coupling terms. 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 of the simulation, and are reused during the entire dynamic timedependent simulation. For several heterogeneous test cases with complex fracture networks we show that, by employing only a fraction of the fine-scale grid cells, FG-ADM can accurately represent the complex flow-heat solutions in the fractured subsurface formations.

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Section: Fg-adm Operatorsmentioning

confidence: 99%

Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation

HosseiniMehr

Arbarim

Cusini

et al. 2019

Day 1 Wed, April 10, 2019

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“…The characteristics of this region are defined based on the Rankine-Hugoniot condition, see equ. (12). Finally, the region 3 refers to a fan characteristic (rarefaction), where the saturation changes are more continuous.…”

Section: Multiscale Reconstruction In Physicsmentioning

confidence: 99%

“…But most of the multi-scale methods are limited to the elliptic solution (global pressure or conductive temperature), without improving the hyperbolic part (saturation or composition). The only exception is the work by - [11] -where they used different operators for saturation reconstruction in the heuristic-driven front tracking and, [12] -where they used an adaptive mesh refinement based on an algebraic multi-scale.…”

Section: Introductionmentioning

confidence: 99%

Multiscale reconstruction in physics for compositional simulation

Ganapathy

Voskov

2018

Journal of Computational Physics

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A compositional formulation is a reliable option for understanding the complex subsurface processes and the associated physical changes. However, this type of model has great computational cost, since the number of equations that needs to be solved in each grid block increases proportionally with the number of components employed. To address this issue, we herewith propose a multiscale reconstruction strategy in physics for compositional simulation. The ideology consists of two stages, wherein two different sets of restriction and prolongation operators are defined based on the dynamics of compositional transport. In the first stage, an operator restricting the arbitrary number of components to only two equations for flow and transport is implemented with the objective of accurately reconstructing the multiphase boundaries in space. The prediction of multiphase front propagation is the most critical aspect of the approach, as they involve a lot of uncertainties. Once the position of two-phase boundaries is identified, the full conservative solution in the single-phase region can be accurately reconstructed based on the prolongation interpolation operator. Subsequently, in the second stage, the solution for the multicomponent problem (full system) in the two-phase region is reconstructed by solving just two transport equations with the aid of restriction operator defined based on an invariant thermodynamic path. The proposed reconstruction strategy results in coarsening of the compositional problem in terms of the physical representation (number of equations), thereby appreciably reducing the simulation time by several folds without significant loss in the accuracy. We demonstrate the applicability of the proposed multiscale strategy for several challenging gas injection problems.

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“…The main two unknowns are pressure and saturation of the flooding phase. Once the fine-scale discretized system is obtained using pEDFM, it is mapped to a dynamic multilevel grid (i.e., ADM grid) which is constructed based on hierarchically nested and multilevel coarse grids [10], [11], [12]. The mapping process is done fully algebraically where sequences of restriction (R) and prolongation (P) operators are used to map across multiple coarsening levels.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Multilevel Multiscale Simulation of Naturally Fractured Reservoirs with Generic Fracture-Matrix Conductivity Contrasts

HosseiniMehr

Kobaisi

Vuik

et al. 2019

Day 2 Wed, September 18, 2019

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An algebraic dynamic multilevel (ADM) method for multiphase flow in heterogeneous fractured porous media using the projection-based embedded discrete fracture model (pEDFM) is presented. The fine-scale discrete system is obtained independently for matrix and each lower-dimensional fracture. On the finescale high resolution computational grids, an independent dynamic multilevel gird (i.e., ADM grid) is imposed. The fully implicit discrete system is mapped completely algebraically to this ADM grid resolution using sequences of restriction and prolongation operators. Multilevel multiscale basis functions are locally computed and employed to honor the heterogeneity contrasts of the fractured domain by interpolating the solution accurately. These basis functions are computed only at the beginning of the simulation to increase the computational efficiency. Once the ADM system is solved for all unknowns (i.e., pressure and saturation), the solution at ADM resolution is prolonged back to fine-scale resolution in order to obtain an approximated fine-scale solution. This dynamic multilevel system employs the fine-scale grid cells only at the sharp gradient of the solution (e.g., at the moving front). With two fractured test-cases (homogeneous and heterogeneous), the performance of ADM is assessed by comparing it to fine-scale results as reference solution. It will be shown that ADM is able to reduce the computational costs and provide efficiency while maintaining the desired accuracy.

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Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media

Cited by 29 publications

References 40 publications

Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation

Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation

Multiscale reconstruction in physics for compositional simulation

Dynamic Multilevel Multiscale Simulation of Naturally Fractured Reservoirs with Generic Fracture-Matrix Conductivity Contrasts

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