An Introduction to the Numerics of Flow in Porous Media using Matlab

Aarnes, Jørg E.; Gimse, Tore; Lie, Knut–Andreas

doi:10.1007/978-3-540-68783-2_9

Cited by 117 publications

(99 citation statements)

References 22 publications

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“…We used an approach known as the implicit pressure explicit saturation (IMPES) model [52] to simulate the transport of the invading water phase in our device. The model relies on an implicit formulation of conservation of mass and momentum to reduce the computational cost of the simulation [53].…”

Section: Theory and Simulationmentioning

confidence: 99%

“…Substituting Equation (2) into Equation (1) and applying the assumption that porosity does not change with time yields [52] …”

Section: Theory and Simulationmentioning

confidence: 99%

“…The solution to these systems of equations is based on the approach of Aarnes et al [52] and was coded in MATLAB. The simulation approach is summarized here.…”

Section: Theory and Simulationmentioning

confidence: 99%

“…We attribute these differences to the fact that our IMPES simulation models do not count interfacial tension and porous structure effects. To mimic the structure of the randomly packed spheres, we modeled the permeability using values drawn from a log-normal distribution [52], although the procedure was designed to model porous rock rather than a packed bed of spheres. although 2D optical video microscopy measurements of 3D fluid flow phenomena have been in good agreement with theoretical predictions based on mass conservation [68].…”

Section: Impesmentioning

confidence: 99%

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Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Yeh

Juárez

2018

Colloids and Interfaces

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Abstract:In this study, we examine microscale waterflooding in a randomly close-packed porous medium. Three different porosities were prepared in a microfluidic platform and saturated with silicone oil. Optical video fluorescence microscopy was used to track the water front as it flowed through the porous packed bed. The degree of water saturation was compared to water containing two different types of chemical modifiers, sodium dodecyl sulfate (SDS) and polyvinylpyrrolidone (PVP), with water in the absence of a surfactant used as a control. Image analysis of our video data yielded saturation curves and calculated fractal dimension, which we used to identify how morphology changed the way in which an invading water phase moved through the porous media. An inverse analysis based on the implicit pressure explicit saturation (IMPES) simulation technique used mobility ratio as an adjustable parameter to fit our experimental saturation curves. The results from our inverse analysis combined with our image analysis show that this platform can be used to evaluate the effectiveness of surfactants or polymers as additives for enhancing the transport of water through an oil-saturated porous medium.

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Section: Theory and Simulationmentioning

confidence: 99%

“…Substituting Equation (2) into Equation (1) and applying the assumption that porosity does not change with time yields [52] …”

Section: Theory and Simulationmentioning

confidence: 99%

“…The solution to these systems of equations is based on the approach of Aarnes et al [52] and was coded in MATLAB. The simulation approach is summarized here.…”

Section: Theory and Simulationmentioning

confidence: 99%

Section: Impesmentioning

confidence: 99%

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Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Yeh

Juárez

2018

Colloids and Interfaces

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“…The implementation of the mixed MsFEM is based on the code of Aarnes. For further details we refer to [5,18].…”

Section: Acknowledgmentmentioning

confidence: 99%

Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations

2013

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In this paper, we propose multilevel Monte Carlo (MLMC) methods that use ensemble level mixed multiscale methods in the simulations of multiphase flow and transport. The contribution of this paper is twofold: (1) a design of ensemble level mixed multiscale finite element methods and (2) a novel use of mixed multiscale finite element methods within multilevel Monte Carlo techniques to speed up the computations. The main idea of ensemble level multiscale methods is to construct local multiscale basis functions that can be used for any member of the ensemble. In this paper, we consider two ensemble level mixed multiscale finite element methods: (1) the no-local-solve-online ensemble level method (NLSO); and (2) the local-solve-online ensemble level method (LSO). The first approach was proposed in Aarnes and Efendiev (SIAM J. Sci. Comput. 30(5):2319-2339, 2008) while the second approach is new. Both mixed multiscale methods use a number of snapshots of the permeability media in generating multiscale basis functions. As a result, in the off-line stage, we construct multiple basis functions for each coarse region where basis functions correspond to different realizations. In the no-local-solve-online ensemble level method, one uses the whole set of precomputed basis functions to approximate the solution for an arbitrary realization. In the local-solve-online ensemble level method, one uses the precomputed functions to construct a multiscale basis for a particular realization. With this basis, the solution corresponding to this particular realization is approximated in LSO mixed multiscale finite element method (MsFEM). In both approaches, the accuracy of the method is related to the number of snapshots computed based on different realizations that one uses to precompute a multiscale basis. In this paper, ensemble level multiscale methods are used in multilevel Monte Carlo methods (Giles 2008a, Oper.Res. 56(3):607-617, b). In multilevel Monte Carlo methods, more accurate (and expensive) forward simulations are run with fewer samples, while less accurate (and inexpensive) forward simulations are run with a larger number of samples. Selecting the number of expensive and inexpensive simulations based on the number of coarse degrees of freedom, one can show that MLMC methods can provide better accuracy at the same cost as Monte Carlo (MC) methods. The main objective of the paper is twofold. First, we would like to compare NLSO and LSO mixed MsFEMs. Further, we use both approaches in the context of MLMC to speedup MC calculations

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Adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media

Moortgat

2017

Water Resources Research

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This work presents adaptive implicit first‐order and second‐order discontinuous Galerkin (DG) methods for the transport of multicomponent compressible fluids in heterogeneous and fractured porous media, discretized by triangular, quadrilateral, and hexahedral grids. The adaptive implicit method (AIM) combines the advantages of purely explicit or implicit methods (in time). In grid cells with high fluxes or low pore volumes, the transport update is done implicitly to alleviate the Courant‐Friedrichs‐Lewy (CFL) time step constraints of the conditionally stable explicit approach. Grid cells with a large CFL condition are updated explicitly. Combined, this allows higher efficiency than explicit methods, but it reduces the “penalty” of implicit methods, which exhibit high numerical dispersion and are more computationally and storage expensive per time step. The advantages of AIM are modest for uniform grids and rock properties. However, in heterogeneous or fractured reservoirs explicit methods may become impractical, while a fully implicit approach introduces unnecessary numerical dispersion and is overkill for low‐permeability layers and matrix blocks. In such applications, AIM is shown to be significantly more efficient and accurate. The division between explicit and implicit grid cells is made adaptively in space and time. This allows for a high level of explicitness and can also adapt to high fluxes caused by, e.g., viscous and gravitational flow instabilities. Numerical examples demonstrate the powerful features of AIM to model, e.g., solute transport, carbon sequestration in saline aquifers, and miscible gas injection in fractured oil and gas reservoirs.

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An Introduction to the Numerics of Flow in Porous Media using Matlab

Cited by 117 publications

References 22 publications

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Waterflooding of Surfactant and Polymer Solutions in a Porous Media Micromodel

Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations

Adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media

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