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Here, we present some Reduced Basis (RB) methods for fluid infiltration problems through certain porous media modeled as dual-continuum with localized uncertainties. We apply dimension reduction techniques to construct a reduced order model. In the RB methods, to perform the offline–online computation decomposition, the model inputs need to be affinely dependent on the uncertainties. We develop a Proper Orthogonal Decomposition and Greedy (POD-Greedy) RB method for stochastic dual-continuum models. In the POD-Greedy RB framework, for heterogeneous porous media, we need to solve the stochastic dual-continuum models many times using very fine grid to construct a set of snapshots for building optimal reduced basis. This offline computation may be very expensive. To improve the offline computational efficiency, we further develop a local–global RB method, which integrates the coupled multiscale and multicontinuum approach using Generalized Multiscale Finite Element Method (GMsFEM) to the POD-Greedy RB method. To illustrate the efficiency of the proposed methods, we present two numerical examples for stochastic dual-continuum models. Our numerical results show that both the POD-Greedy RB method and the local–global RB method greatly improve the computation efficiency with high approximation accuracy. [ABSTRACT FROM AUTHOR]

A Multiscale Locally Conservative Galerkin (MsLCG) method is proposed to accurately simulate multiphase flow in heterogeneous and fractured porous media. MsLCG employs a coarse partition of the fine grids and multiscale basis function for mapping the fine-scale information to the coarse-scale unknowns. Different from standard Multiscale Finite Element Method (MsFEM), the main improvement of our MsLCG is to use the property of local conservation at steady state conditions to define a numerical flux at element boundaries. MsLCG provides a way to extend standard MsFEM to handle challenging multiphase flow problems in heterogeneous and fractured porous media. MsLCG preserves all the advantages of the standard MsFEM while it provides explicitly conservative fluxes through each element. We present a number of representative numerical examples to demonstrate that our method is efficient and accurate for simulating multiphase flow through heterogeneous and fractured porous media. [ABSTRACT FROM AUTHOR]

Simulation of mass transfer in shale porous media continues to challenge the hydrocarbon recovery industry due the involved complex porous media transport mechanisms and complicated porous structures. In this paper, we present a new multiscale approach to improve the simulation of gas flow in shale porous media based on a coupled triple-continuum and discrete fracture model. Gas transport in shale formations entails porous media flow through matrix (which contains organic and inorganic matters) and fractures. The fractures consist of small-scale natural fractures and large-scale artificial fractures from hydraulic fracturing. In the triple-continuum model, kerogen matrix, inorganic matrix and natural fractures are modeled as three superimposed continua. The hydraulic fractures are handled by discrete fracture model. Using a framework via the multiscale mixed finite element method, our methodology couples the triple-continuum model and discrete fracture model in a rigorous and systematic approach. The method can capture the small-scale features of gas flow through multiscale basis functions calculated based on the triple-continuum background. We go beyond multiple-continuum modeling by enabling explicit discrete fracture representation in our multiscale framework. As a result, our approach could avoid some oversimplified assumptions made in conventional triple-continuum models and enjoy explicit fracture treatment with high computational efficiency. Numerical aspects of the new approach are detailed with examples demonstrating its efficiency and accuracy for simulating gas flow in shale porous media with multiscale porous features. [ABSTRACT FROM AUTHOR]

Inherently coupled flow and geomechanics processes in fractured shale media have implications for shale gas production. The system involves highly complex geo-textures comprised of a heterogeneous anisotropic fracture network spatially embedded in an ultra-tight matrix. In addition, nonlinearities due to viscous flow, diffusion, and desorption in the matrix and high velocity gas flow in the fractures complicates the transport. In this paper, we develop a multiscale model reduction approach to couple gas flow and geomechanics in fractured shale media. A Discrete Fracture Model (DFM) is used to treat the complex network of fractures on a fine grid. The coupled flow and geomechanics equations are solved using a fixed stress-splitting scheme by solving the pressure equation using a continuous Galerkin method and the displacement equation using an interior penalty discontinuous Galerkin method. We develop a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM constructs the multiscale basis functions in a systematic way to capture the fracture networks and their interactions with the shale matrix. Numerical results and an error analysis is provided showing that the proposed approach accurately captures the coupled process using a few multiscale basis functions, i.e. a small fraction of the degrees of freedom of the fine-scale problem. [ABSTRACT FROM AUTHOR]

Fractured vuggy porous media continue to challenge the flow simulation research involving mass and/or heat transfer processes. Here, we report a coupled multiscale and multi-continuum approach developed to improve the modeling of multiphase flow through fractured vuggy porous media involving multi-continuum mass transfers. Multiple levels of fractures can be not only modeled as different superimposed continua but also embodied as discrete fracture networks based on their geometrical characteristics. Different configurations of vuggy existence can also be handled by a continuum and/or their discrete representations. We develop a systematic coupling using Multiscale Finite Element Method (MsFEM) as a framework for coarsening and refinement. MsFEM is used to capture subgrid scale heterogeneities and interactions through multiscale basis functions calculated based on the multi-continuum background. Unstructured mesh is applied to model discrete fractures in arbitrary directions and discrete vugs with complex geometries. This paper presents a significant advancement in terms of elevating the limitations of the multi-continuum models in handling complex fracture and/or vug geometry and extending the model reduction capability of MsFEM. Several numerical examples are carried out to demonstrate the capability of the proposed coupling method. [ABSTRACT FROM AUTHOR]

We present an adaptive Multiscale Mixed Finite Element Method (MsMFEM) for modeling multiphase flow in highly heterogeneous reservoir. In this framework, fractional flow model is used to approximate pressure and velocity solution on coarse scale, while resolution in fine scale is honored by the basis functions, which are calculated by local problems on fine scale. The adaptive computation in the flow problem is permitted by two different basis functions. In the numerical examples, our adaptive MsMFEM is applied to solve two dimensional and three dimensional reservoir simulation problems with highly heterogeneous porosity and permeability fields. The preliminary numerical simulation results presented show a significant speedup in comparison with the reference numerical method, which encourage and is beneficial for further investigation of the proposed method for reservoir numerical simulation. [ABSTRACT FROM AUTHOR]

Simulating flow in a highly heterogeneous reservoir with multiscale characteristics is computationally demanding. To tackle this problem, we propose a numerical scheme based on the Generalized Multiscale Finite Element Method (GMsFEM) and a triple-continuum model. The aim is to obtain a more efficient numerical approach that can explicitly represent the interactions among different continua. To enhance the applicability of our proposed model, we combine the Discrete Fracture Model (DFM) to model the local effects of discrete fractures. In the proposed model, the GMsFEM, as an advanced model reduction technique, enables capturing the multiscale flow dynamics. This is accomplished by systematically generating an approximation space through solving a series of local snapshot and spectral problems. The resulting eigenfunctions can pass the local features to the global level when acting as basis functions in the global coarse problems. Our goal in this paper is to further improve the accuracy of flow simulation in complicated reservoirs especially for the case when multiple discrete fractures located in single coarse neighborhood. Several numerical experiments are conducted to confirm the success of our proposed method, and a rigorous convergence proof is also given. [ABSTRACT FROM AUTHOR]