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Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulations provide time-lapse dynamics of the coupled poromechanical processes within the reservoir and its over-, under-, and side-burden environments. For more reliable operations, it is crucial to connect these reservoir simulation results with the seismic surveys (i.e., observation data). However, despite being crucial, such integration is challenging due to the fact that the reservoir dynamics alters the seismic parameters. In this work, a coupled reservoir simulation and time-lapse seismic methodology is developed for multiphase flow operations in subsurface reservoirs. To this end, a poromechanical simulator is designed for multiphase flow and connected to a forward seismic modeller. This simulator is then used to assess a novel methodology of seismic monitoring by isolating the reservoir signal from the entire reflection response. This methodology is shown to be able to track the development of the fluid front over time, even in the presence of a highly reflective overburden with strong time-lapse variations. These results suggest that the proposed methodology can contribute to a better understanding of fluid flow in the subsurface. Ultimately, this will lead to improved monitoring of reservoirs for underground energy storage or production. [ABSTRACT FROM AUTHOR]

Geological porous reservoirs provide the volume capacity needed for large scale underground hydrogen storage (UHS). To effectively exploit these reservoirs for UHS, it is crucial to characterize the hydrogen transport properties inside porous rocks. In this work, for the first time in the community, we have performed H 2 /water multiphase flow experiments at core scale under medical X-ray CT scanner. This has allowed us to directly image the complex transport properties of H 2 when it is injected or retracted from the porous rock. The important effective functions of capillary pressure and relative permeability are also measured, for both drainage and imbibition. The capillary pressure measurements are combined with MICP data to derive a receding contact angle for the H 2 /water/sandstone rock system. The rock core sample is a heterogeneous Berea sandstone (17 cm long and 3.8 cm diameter). Our investigation reveals the interplay between gravitational, capillary, and viscous forces. More specifically, it illustrates complex displacement patterns in the rock, including gravity segregation, enhancement of spreading of H 2 due to capillary barriers, and the formation of fingers/channel during imbibition which lead to significant trapping of hydrogen. These findings shed new light on our fundamental understanding of the transport characteristics of H 2 /water relevant for UHS. [ABSTRACT FROM AUTHOR]

Underground hydrogen storage (UHS) in initially brine-saturated deep porous rocks is a promising large-scale energy storage technology, due to hydrogen's high specific energy capacity and the high volumetric capacity of aquifers. Appropriate selection of a feasible and safe storage site vitally depends on understanding hydrogen transport characteristics in the subsurface. Unfortunately there exist no robust experimental analyses in the literature to properly characterise this complex process. As such, in this work, we present a systematic pore-scale modelling study to quantify the crucial reservoir-scale functions of relative permeability and capillary pressure and their dependencies on fluid and reservoir rock conditions. To conduct a conclusive study, in the absence of sufficient experimental data, a rigorous sensitivity analysis has been performed to quantify the impacts of uncertain fluid and rock properties on these upscaled functions. The parameters are varied around a base-case, which is obtained through matching to the existing experimental study. Moreover, cyclic hysteretic multiphase flow is also studied, which is a relevant aspect for cyclic hydrogen-brine energy storage projects. The present study applies pore-scale analysis to predict the flow of hydrogen in storage formations, and to quantify the sensitivity to the micro-scale characteristics of contact angle (i.e., wettability) and porous rock structure. [ABSTRACT FROM AUTHOR]

• pEDFM is incorporated into a compositional model tailored to CO 2 storage. • Hydrodynamic trapping mechanisms are described in a unified framework. • The upward flow of brine via conductive fractures may enhance residual trapping. • Barriers can assist dissolution trapping by creating complex flow configurations. • Findings from single fracture geometry are observed in complex fracture network. Natural or induced fractures are typically present in subsurface geological formations. Therefore, they need to be carefully studied for reliable estimation of the long-term carbon dioxide storage. Instinctively, flow-conductive fractures may undermine storage security as they increase the risk of CO 2 leakage if they intersect the CO 2 plume. In addition, fractures may act as flow barriers, causing significant pressure gradients over relatively small regions near fractures. Nevertheless, despite their high sensitivities, the impact of fractures on the full-cycle storage process has not been fully quantified and understood. In this study, a numerical model is developed and applied to analyze the role of discrete fractures on the flow and transport mechanism of CO 2 plumes in simple and complex fracture geometries. A unified framework is developed to model the essential hydrogeological trapping mechanisms. Importantly, the projection-based embedded discrete fracture model is incorporated into the framework to describe fractures with varying conductivities. Impacts of fracture location, inclination angle, and fracture-matrix permeability ratio are systemically studied for a single fracture system. Moreover, the interplay between viscous and gravity forces in such fractured systems is analyzed. Results indicate that the fracture exhibits differing effects regarding different trapping mechanisms. Generally speaking, highly-conductive fractures facilitate dissolution trapping while weakening residual trapping, and flow barriers can assist dissolution trapping for systems with a relatively low gravity number. The findings from the test cases for single fracture geometries are found applicable to a larger-scale domain with complex fracture networks. This indicates the scalability of the study for field-relevant applications. [ABSTRACT FROM AUTHOR]

Abstract: An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media. [Copyright &y& Elsevier]

Abstract: The multiscale finite volume (MSFV) method is a computationally efficient numerical method for the solution of elliptic and parabolic problems with heterogeneous coefficients. It has been shown for a wide range of test cases that the MSFV results are in close agreement with those obtained with a classical (computationally expensive) technique. The method, however, fails to give accurate results for highly anisotropic heterogeneous problems due to weak localization assumptions. Recently, a convergent iterative MSFV (i-MSFV) method was developed to enhance the quality of the multiscale results by improving the localization conditions. Although the i-MSFV method proved to be efficient for most practical problems, it is still favorable to improve the localization condition adaptively, i.e. only for a sub-domain where the original MSFV localization conditions are not acceptable, e.g. near shale layers and long coherent structures with high permeability contrasts. In this paper, a space–time adaptive i-MSFV (ai-MSFV) method is introduced. It is shown how to improve the MSFV results adaptively in space and simulation time. The fine-scale smoother, which is necessary for convergence of the i-MSFV method, is also applied locally. Finally, for multiphase flow problems, two criteria are investigated for adaptively updating the MSFV interpolation functions: (1) a criterion based on the total mobility change for the transient coefficients and (2) a criterion based on the pressure equation residual for the accuracy of the results. For various challenging test cases it is demonstrated that iterations in order to obtain accurate results even for highly anisotropic heterogeneous problems are required only in small sub-domains and not everywhere. The findings show that the error introduced in the MSFV framework can be controlled and improved very efficiently with very little additional computational cost compared to the original, non-iterative MSFV method. [ABSTRACT FROM AUTHOR]

Abstract: The multiscale finite-volume (MSFV) method was originally developed for the solution of heterogeneous elliptic problems with reduced computational cost. Recently, some extensions of this method for parabolic problems have been proposed. These extensions proved effective for many cases, however, they are neither general nor completely satisfactory. For instance, they are not suitable for correctly capturing the transient behavior described by the parabolic pressure equation. In this paper, we present a general multiscale finite-volume method for parabolic problems arising, for example, from compressible multiphase flow in porous media. Opposed to previous methods, here, the basis and correction functions are solutions of full parabolic governing equations in localized domains. At the same time, to enhance the computational efficiency of the scheme, the basis functions are kept pressure independent and do not have to be recalculated as pressure evolves. This general approach requires no additional assumptions and its good efficiency and high accuracy is demonstrated for various challenging test cases. Finally, to improve the quality of the results and also to extend the scheme for highly anisotropic heterogeneous problems, it is combined with the iterative MSFV (i-MSFV) method for parabolic problems. As one iterates, the i-MSFV solutions of compressible multiphase problems (parabolic problems) converge to the corresponding fine-scale reference solutions in the same way as demonstrated recently for incompressible cases (elliptic problems). Therefore, the proposed MSFV method can also be regarded as an efficient linear solver for parabolic problems and studies of its efficiency are presented for many test cases. [Copyright &y& Elsevier]

Abstract: The multiscale finite-volume (MSFV) method for the solution of elliptic problems is extended to an efficient iterative algorithm that converges to the fine-scale numerical solution. The localization errors in the MSFV method are systematically reduced by updating the local boundary conditions with global information. This iterative multiscale finite-volume (i-MSFV) method allows the conservative reconstruction of the velocity field after any iteration, and the MSFV method is recovered, if the velocity field is reconstructed after the first iteration. Both the i-MSFV and the MSFV methods lead to substantial computational savings, where an approximate but locally conservative solution of an elliptic problem is required. In contrast to the MSFV method, the i-MSFV method allows a systematic reduction of the error in the multiscale approximation. Line relaxation in each direction is used as an efficient smoother at each iteration. This smoother is essential to obtain convergence in complex, highly anisotropic, heterogeneous domains. Numerical convergence of the method is verified for different test cases ranging from a standard Poisson equation to highly heterogeneous, anisotropic elliptic problems. Finally, to demonstrate the efficiency of the method for multiphase transport in porous media, it is shown that it is sufficient to apply the iterative smoothing procedure for the improvement of the localization assumptions only infrequently, i.e. not every time step. This result is crucial, since it shows that the overall efficiency of the i-MSFV algorithm is comparable with the original MSFV method. At the same time, the solutions are significantly improved, especially for very challenging cases. [Copyright &y& Elsevier]

• The paper presents the first benchmarking study between homogenization and multiscale methods. • Developments are done in a unified adaptive dynamic multilevel (ADM) framework. • Both methods are employed to simulate multiphase flow in highly heterogeneous porous media. • Fully implicit coupling with finite volume scheme is used at all spatial scales. Accurate simulation of multiphase flow in subsurface formations is challenging, as the formations span large length scales (km) with high-resolution heterogeneous properties. To deal with this challenge, different multiscale methods have been developed. Such methods construct coarse-scale systems, based on a given high-resolution fine-scale system. Furthermore, they are amenable to parallel computing and allow for a-posteriori error control. The multiscale methods differ from each other in the way the transition between the different scales is made. Multiscale (finite element and finite volume) methods compute local basis functions to map the solutions (e.g. pressure) between coarse and fine scales. Instead, homogenization methods solve local periodic problems to determine effective models and parameters (e.g. permeability) at a coarser scale. It is yet unknown how these two methods compare with each other, especially when applied to complex geological formations, with no clear scale separation in the property fields. This paper develops the first comparison benchmark study of these two methods and extends their applicability to fully implicit simulations using the algebraic dynamic multilevel (ADM) method. At each time step, on the given fine-scale mesh and based on an error analysis, the fully implicit system is solved on a dynamic multilevel grid. The entries of this system are obtained by using multiscale local basis functions (ADM-MS), and, respectively, by homogenization over local domains (ADM-HO). Both sets of local basis functions (ADM-MS) and local effective parameters (ADM-HO) are computed at the beginning of the simulation, with no further updates during the multiphase flow simulation. The two methods are extended and implemented in the same open-source DARSim2 simulator (https://gitlab.com/darsim2simulator), to provide fair quality comparisons. The results reveal insightful understanding of the two approaches, and qualitatively benchmark their performance. It is re-emphasized that the test cases considered here include permeability fields with no clear scale separation. The development of this paper sheds new lights on advanced multiscale methods for simulation of coupled processes in porous media. [ABSTRACT FROM AUTHOR]

This paper presents the development of an algebraic dynamic multilevel method (ADM) for fully implicit simulations of multiphase flow in homogeneous and heterogeneous porous media. Built on the fine-scale fully implicit (FIM) discrete system, ADM constructs a multilevel FIM system describing the coupled process on a dynamically defined grid of hierarchical nested topology. The multilevel adaptive resolution is determined at each time step on the basis of an error criterion. Once the grid resolution is established, ADM employs sequences of restriction and prolongation operators in order to map the FIM system across the considered resolutions. Several choices can be considered for prolongation (interpolation) operators, e.g., constant, bilinear and multiscale basis functions, all of which form partition of unity. The adaptive multilevel restriction operators, on the other hand, are constructed using a finite-volume scheme. This ensures mass conservation of the ADM solutions, and as such, the stability and accuracy of the simulations with multiphase transport. For several homogeneous and heterogeneous test cases, it is shown that ADM applies only a small fraction of the full FIM fine-scale grid cells in order to provide accurate solutions. The sensitivity of the solutions with respect to the employed fraction of grid cells (determined automatically based on the threshold value of the error criterion) is investigated for all test cases. ADM is a significant step forward in the application of dynamic local grid refinement methods, in the sense that it is algebraic, allows for systematic mapping across different scales, and applicable to heterogeneous test cases without any upscaling of fine-scale high resolution quantities. It also develops a novel multilevel multiscale method for FIM multiphase flow simulations in natural subsurface formations. [ABSTRACT FROM AUTHOR]

Highlights • Algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM) is developed. • F-ADM generates an automatic framework to accurately represent discrete fractures at multiple scales, based on multilevel operators. • F-ADM develops multi-level embedded discrete fracture model, i.e., independent grids are used at all levels for fractures and matrix. • F-ADM is directly applicable to heterogeneous fractured media with no dependency on upscaled quantities. • F-ADM is a scalable and stable (fully-implicit) multiscale method for multiphase flow simulations in large-scale fractured media. Abstract We present an algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM), where fractures are resolved at fine scale with an embedded discrete modelling approach. This fine-scale discrete system employs independent fine-scale computational grids for heterogeneous matrix and discrete fractures, which results in linear system sizes out of the scope of the classical simulation approaches. To reduce the computational costs, yet provide accurate solutions, on this highly resolved fine-scale mesh, F-ADM imposes independent dynamic multilevel coarse grids for both matrix and lower-dimensional discrete fractures. The fully-implicit discrete system is then mapped into this adaptive dynamic multilevel resolution for all unknowns (i.e., pressure and phase saturation). The dynamic resolution aims for resolving sharp fronts for the transport unknowns, thus constant interpolators are used to map the saturation from coarse to fine grids both in matrix and fractures. However, due to the global nature of the pressure unknowns, local multilevel basis functions for both matrix and fractures with flexible matrix-fracture coupling treatment are introduced for the pressure. The assembly of the full sets of basis functions allows for mapping the solutions up and down between any resolutions. Due to its adaptive multilevel resolution, F-ADM develops an automatic integrated framework to homogenise or explicitly represent a fracture network at a coarser level by selection of the multilevel coarse nodes in each sub-domain. Various test cases, including multiphase flow in 2D and 3D media, are studied, where only a fraction of the fine-scale grids is employed to obtain accurate nonlinear multiphase solutions. F-ADM casts a promising approach for large-scale simulation of multiphase flow in fractured media. [ABSTRACT FROM AUTHOR]

A novel multiscale method for multiphase flow in heterogeneous fractured porous media is devised. The discrete fine-scale system is described using an embedded fracture modeling approach, in which the heterogeneous rock (matrix) and highly-conductive fractures are represented on independent grids. Given this fine-scale discrete system, the method first partitions the fine-scale volumetric grid representing the matrix and the lower-dimensional grids representing fractures into independent coarse grids. Then, basis functions for matrix and fractures are constructed by restricted smoothing, which gives a flexible and robust treatment of complex geometrical features and heterogeneous coefficients. From the basis functions one constructs a prolongation operator that maps between the coarse- and fine-scale systems. The resulting method allows for general coupling of matrix and fracture basis functions, giving efficient treatment of a large variety of fracture conductivities. In addition, basis functions can be adaptively updated using efficient global smoothing strategies to account for multiphase flow effects. The method is conservative and because it is described and implemented in algebraic form, it is straightforward to employ it to both rectilinear and unstructured grids. Through a series of challenging test cases for single and multiphase flow, in which synthetic and realistic fracture maps are combined with heterogeneous petrophysical matrix properties, we validate the method and conclude that it is an efficient and accurate approach for simulating flow in complex, large-scale, fractured media. [ABSTRACT FROM AUTHOR]

We develop the first multiscale method for fully implicit (FIM) simulations of multiphase flow in porous media, namely CPR-MS method. Built on the FIM Jacobian matrix, the pressure system is obtained by employing a Constrained Pressure Residual (CPR) operator. Multiscale Finite Element (MSFE) and Finite Volume (MSFV) methods are then formulated algebraically to obtain efficient and accurate solutions of this pressure equation. The multiscale prediction stage (first-stage) is coupled with a corrector stage (second-stage) employed on the full system residual. The converged solution is enhanced through outer GMRES iterations preconditioned by these first and second stage operators. While the second-stage FIM stage is solved using a classical iterative solver, the multiscale stage is investigated in full detail. Several choices for fine-scale pre- and post-smoothing along with different choices of coarse-scale solvers are considered for a range of heterogeneous three-dimensional cases with capillarity and three-phase systems. The CPR-MS method is the first of its kind, and extends the applicability of the so-far developed multiscale methods (both MSFE and MSFV) to displacements with strong coupling terms. [ABSTRACT FROM AUTHOR]

Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The time-dependent saturation profile, on the other hand, may exhibit sharp local gradients or discontinuities (fronts) where the solution accuracy is highly sensitive to the time-step size. Therefore, accurate flow solvers need to address the multiscale spatial scales, while advanced transport solvers need to also tackle multiple time scales. This paper presents the first multirate multiscale method for space-time conservative multiscale simulation of sequentially coupled flow and transport equations. The method computes the pressure equation at the coarse spatial scale with a multiscale finite volume technique, while the transport equation is solved by taking variable time-step sizes at different locations of the domain. At each coarse time step, the developed local time-stepping technique employs an adaptive recursive time step refinement to capture the fronts accurately. The applicability (accuracy and efficiency) of the method is investigated for a wide range of two-phase flow simulations in heterogeneous porous media. For the studied cases, the proposed method is found to provide 3 to 4 times faster simulations. Therefore, it provides a promising strategy to minimize the tradeoff between accuracy and efficiency for field-scale applications. • The pressure is solved at coarse-scale in space. • The approximate fine-scale pressure solution is found via multiscale basis functions. • The saturation is solved by developing a conservative multiscale in time method. • The saturation is solved using different time steps at different locations. • The approach casts efficient and accurate simulations for large-scale porous media. [ABSTRACT FROM AUTHOR]