We present the projection-based embedded discrete fracture model (pEDFM) for hexahedral corner-point grid (CPG) geometries, for the simulation of hydrothermal processes in fractured porous media. ...Unlike the previously-developed pEDFM for structured box grids, our new development allows for the modeling of complex geometries defined with hexahedral CPG cells. It also advances the pEDFM method to include coupled flow and heat transfer systems. Mass and energy conservation equations are simulated in a fully-coupled manner using a fully-implicit (FIM) integration scheme. This allows for stable simulations, specially when large time steps are taken. Independent corner-point grids are imposed on the rock matrix and all fractures, with conductivities ranging from highly permeable to flow barriers. The connectivities between the non-neighboring grid cells are described such that a consistent discrete representation of the embedded fractures occurs within the corner-point grid geometry, specially as the quadrilateral interfaces are allowed to be fully flexible. Various numerical tests including geologically-relevant and real-field models, which are established in the literature, are conducted to demonstrate the applicability of the developed method. It is shown that pEDFM can accurately capture the physical influence of both highly conductive fractures and flow barriers on the flow and heat transfer fields in complex reservoir geometries. This development is promising for flow simulations of real-field geo-models, increasing the discretization flexibility and enhancing the computational performance for capturing explicit fractures accurately.
•Projection-based embedded discrete fracture model (pEDFM) for hexahedral corner-point Grid (CPG) geometries.•Accurate and explicit representation of fractures with generic conductivity contrasts.•Fully coupled mass and heat transport in fractured porous media.•Accurate modeling of geologically-relevant and real field-scale formations.
This paper deals with pore-scale two-phase flow simulations in carbonate rock using the pore network method (PNM). This method was used to determine the rock and flow properties of three different ...rock samples, such as porosity, capillary pressure, absolute permeabilities, and oil–water relative permeabilities. The pore network method was further used to determine the properties of rock matrices, such as pore size distribution, topological structure, aspect ratio, pore throat shape factor, connected porosity, total porosity, and absolute permeability. The predicted simulation for the network-connected porosity, total porosity, and absolute permeability agree well with those measured experimentally when the image resolution is appropriate to resolve the relevant pore and throat sizes. This paper also explores the effect of the wettability and fraction of oil-wet pores on relative permeabilities, both in uniform and mixed wet systems.
•In this work, we present a novel TSFVM discretization scheme for underground fluid flow problems.•The method reduces the well-known MPFA flux expressions to a strictly TPFA with the added benefit of ...accuracy and efficiency.•This is a major development in cases where heterogeneity and unstructured grids result in a tensorial flow behavior.
A novel Two-Step cell-centered Finite Volume Method (TSFVM) is developed in this work to discretize the heterogeneous and anisotropic pressure equation on triangular and quadrilateral grids in 2D and hexahedral and tetrahedral grids in 3D. Physical properties such as permeability and porosity are piece-wise constant on each grid cell. In the first step, the Galerkin Finite Element Method (FEM) is utilized to compute pressure solutions at all cell vertices. In the second step, pressure values at cell vertices are used to derive continuous two-point flux stencils for cell faces. Mass conservation equations are then written for each cell to obtain a system of linear equations that can be solved for pressure at cell centers. Extensive numerical experiments are carried out to test the performance of our TSFVM. In particular, we compare TSFVM with the classical Multipoint Flux Approximation (MPFA-O) method as well as a more recently developed MPFA method with full pressure support called enhanced MPFA (eMPFA). The results show that the TSFVM compares well with eMPFA for challenging test cases for which MPFA-O breaks down. Specifically, and as a significant step forward, our TSFVM is quite robust for challenging problems involving heterogeneous and highly anisotropic permeability tensors when both MPFA-O and eMPFA suffer from unphysical oscillations. Finally, the numerical convergence study demonstrates that TSFVM has comparable convergence behavior to MPFA-O method for both homogeneous and discontinuous permeability fields.
Physics-informed neural network (PINN) models are developed in this work for solving highly anisotropic diffusion equations. Compared to traditional numerical discretization schemes such as the ...finite volume method and finite element method, PINN models are meshless and, therefore, have the advantage of imposing no constraint on the orientations of the diffusion tensors or the grid orthogonality conditions. To impose solution positivity, we tested PINN models with positivity-preserving activation functions for the last layer and found that the accuracy of the corresponding PINN solutions is quite poor compared to the vanilla PINN model. Therefore, to improve the monotonicity properties of PINN models, we propose a new loss function that incorporates additional terms which penalize negative solutions, in addition to the usual partial differential equation (PDE) residuals and boundary mismatch. Various numerical experiments show that the PINN models can accurately capture the tensorial effect of the diffusion tensor, and the PINN model utilizing the new loss function can reduce the degree of violations of monotonicity and improve the accuracy of solutions compared to the vanilla PINN model, while the computational expenses remain comparable. Moreover, we further developed PINN models that are composed of multiple neural networks to deal with discontinuous diffusion tensors. Pressure and flux continuity conditions on the discontinuity line are used to stitch the multiple networks into a single model by adding another loss term in the loss function. The resulting PINN models were shown to successfully solve the diffusion equation when the principal directions of the diffusion tensor change abruptly across the discontinuity line. The results demonstrate that the PINN models represent an attractive option for solving difficult anisotropic diffusion problems compared to traditional numerical discretization methods.
Low salinity waterflooding (LSW) has shown promising results in terms of increasing oil recovery at laboratory scale. In this work, we study the LSW effect, at laboratory scale, and provide a basis ...for quantifying the effect at field scale by extracting reliable relative permeability curves. These were achieved by experimental and numerical interpretation of laboratory core studies. Carbonate rock samples were used to conduct secondary and tertiary unsteady-state coreflooding experiments at reservoir conditions. A mathematical model was developed as a research tool to interpret and further validate the physical plausibility of the coreflooding experiments. At core scale and a typical field rate of ~1 ft/day, low salinity water (LS) resulted in not only ~20% higher oil recovery compared to formation water (FW) but also recovered oil sooner. LS water also showed capability of reducing the residual oil saturation when flooded in tertiary mode. The greater oil recovery caused by LSW can be attributed to altering the wettability of the rock to less oil-wet as confirmed by the numerically extracted relative permeability curves.
Despite the significant advancements in geomodelling techniques over the past few decades, it is still quite challenging to obtain accurate assessments of hydraulic fracture propagation. This work ...investigates the effect of fluid leak-off in a dual-porosity system on the hydraulic fracture propagation geometry, which, in turn, affects hydrocarbon recovery from tight and unconventional reservoirs. Fracture propagation within tight reservoirs was analyzed using the Pseudo Three-Dimensional-Carter II model for single- (P3D-C) and dual-porosity systems (P3D-C-DP). Previous studies have accounted for leak-off in single-porosity models; however, studies within dual-porosity systems are still quite limited. We present a novel approach to coupling fluid leak-off in a dual-porosity system along with a fracture-height growth mechanism. Our findings provide important insights into the complexities within hydraulic fracturing treatment design using our new and pragmatic modeling approach. The simulation results illustrate that fluid leak-off in dual-porosity systems contributes to a confined fracture half-length (xf), that is 31% smaller using the P3D-C-DP model as opposed to the single-porosity model (P3D-C). As for the fracture height growth (hf), the P3D-C-DP model resulted in a 40% shorter fracture height compared to the single-porosity model.
Physics-informed neural networks (PINNs) are an emerging technology in the scientific computing domain. Contrary to data-driven methods, PINNs have been shown to be able to approximate and generalize ...well a wide range of partial differential equations (PDEs) by imbedding the underlying physical laws describing the PDE. PINNs, however, can struggle with the modeling of hyperbolic conservation laws that develop shocks, and a classic example of this is the Buckley–Leverett problem for fluid flow in porous media. In this work, we explore specialized neural network architectures for modeling the Buckley–Leverett shock front. We present extensions of the standard multilayer perceptron (MLP) that are inspired by the attention mechanism. The attention-based model was, compared to the multilayer perceptron model, and the results show that the attention-based architecture is more robust in solving the hyperbolic Buckley–Leverett problem, more data-efficient, and more accurate. Moreover, by utilizing distance functions, we can obtain truly data-free solutions to the Buckley–Leverett problem. In this approach, the initial and boundary conditions (I/BCs) are imposed in a hard manner as opposed to a soft manner, where labeled data are provided on the I/BCs. This allows us to use a substantially smaller NN to approximate the solution to the PDE.
Modeling flow and transport in fractured porous media has been a topic of intensive research for a number of energy- and environment-related industries. The presence of multiscale fractures makes it ...an extremely challenging task to resolve accurately and efficiently the flow dynamics at both the local and global scales. To tackle this challenge, we developed a computational workflow that adopts a two-level hierarchical strategy based on fracture length partitioning. This was achieved by specifying a partition length to split the discrete fracture network (DFN) into small-scale fractures and large-scale fractures. Flow-based numerical upscaling was then employed to homogenize the small-scale fractures and the porous matrix into an equivalent/effective single medium, whereas the large-scale fractures were modeled explicitly. As the effective medium properties can be fully tensorial, the developed hierarchical framework constructed the discrete systems for the explicit fracture–matrix sub-domains using the nonlinear two-point flux approximation (NTPFA) scheme. This led to a significant reduction of grid orientation effects, thus developing a robust, applicable, and field-relevant framework. To assess the efficacy of the proposed hierarchical workflow, several numerical simulations were carried out to systematically analyze the effects of the homogenized explicit cutoff length scale, as well as the fracture length and orientation distributions. The effect of different boundary conditions, namely, the constant pressure drop boundary condition and the linear pressure boundary condition, for the numerical upscaling on the accuracy of the workflow was investigated. The results show that when the partition length is much larger than the characteristic length of the grid block, and when the DFN has a predominant orientation that is often the case in practical simulations, the workflow employing linear pressure boundary conditions for numerical upscaling give closer results to the full-model reference solutions. Our findings shed new light on the development of meaningful computational frameworks for highly fractured, heterogeneous geological media where fractures are present at multiple scales.
Use of nanoparticles as a method for enhancing oil recoveries has become an attractive prospect. Experimental evidence has shown that this technique possesses the ability to improve recoveries via ...wettability alteration and interfacial tension reduction amongst other strategies. In this study, we analyze the potential of nanoparticles employed in coreflood experiments. Low concentration acid was added to aid in the dispersion of the nanoparticles in the brine by protecting them from being aggregated, while enhancing the stimulation of the tight porous media. Electrokinetics was also implemented following a sequential as well as a simultaneous approach to further stimulate the fluids injected, controlling their mobility, and therefore, increasing the depth of penetration within the porous media. Several coreflood experiments were carried out on highly heterogeneous carbonate samples of Middle Eastern origin with permeabilities of around 0.1 mD. Zeta potential measurements were conducted on the inlet side of the preserved core-plugs after the conclusion of each coreflood. The findings indicated a close connection between the rate of wettability alteration observed over the duration of nano-acid fluid injection and mode of electrokinetic application. The best performing nano-acid fluids correlated with the highest shift in the magnitude of the zeta potential across all tested strategies. Results show that oil recovered via this hybrid technique was mostly 10–15% higher than that derived when only smart brine was employed.
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