We consider L-scheme and Newton-based solvers for Biot model under large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthermore, the fluid compressibility is assumed to be non-linear. A Lagrangian frame of reference is used to keep track of the deformation. We perform an implicit discretization in time (backward Euler) and propose two linearization schemes

In this paper, a novel computational framework is introduced for simulation of multiphase flow, geomechanics, and fracture propagation in porous media based on Biot’s model for poroelasticity by focusing on interactions between hydraulic and natural fractures. Since realistic porous media contain many natural fractures, it is important not only to stimulate hydraulic fractures but also to study the

In numerical simulations of multiphase flow and transport in fractured porous media, the estimation of the hydrocarbon recovery requires accurately predicting the capillary-driven imbibition rate of the wetting phase initially present in the fracture into the low-permeability matrix. In the fully implicit finite-volume scheme, this entails a robust methodology that captures the capillary flux at the

Conventional diffusion equations for fluid flow through porous media do not consider the effects of the history of rock, fluid, and flow. This limitation can be overcome by the incorporation of “memory” in the model, using fractional-order derivatives. Inclusion of fractional-order derivatives in the diffusion equation, however, adds complexity to both the equation and its numerical approximation.

Subsurface flow and geomechanics are often modeled with sequential approaches. This can be computationally beneficial compared with fully coupled schemes, while it requires usually compromises in numerical accuracy, at least when the sequential scheme is non-iterative. We discuss the influence of the choice of scheme on the numerical accuracy and the expected computational effort based on a comparison

A major part of world hydrocarbon resources is located in fractured reservoirs. The identification of fractured reservoir parameters is essential for their optimal production. The Warren-Root model is one of the most fundamental models for fluid flow in fractured reservoirs. The simplified assumption of the Warren-Root model is not applicable for a finite reservoir, and transition zone cannot be detected

Three-dimensional magnetotelluric modeling algorithm of high accuracy and high efficiency is required for data interpretation and inversion. In this paper, edge-based finite element method with unstructured mesh is used to solve 3D magnetotelluric problem. Two boundary conditions—Dirichlet boundary condition and Neumann boundary condition—are set for cross-validation and comparison. We propose an efficient

In this work, we consider a hybrid mixed finite element method for Biot’s model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy’s velocity system of Biot’s model presented by Niu et al. (Appl. Math. Comput. 347: 767–784, 2019) is not uniformly stable with respect to the physical parameters, resulting in some issues in numerical simulations. To alleviate such problems, following

In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of

In this paper, it is proposed an enhanced sequential fully implicit (ESFI) algorithm with a fixed stress split to approximate robustly poro-elastoplastic solutions related to reservoir geomechanics. The constitutive model considers the total strain effect on porosity/permeability variation and associative plasticity. The sequential fully implicit (SFI) algorithm is a popular solution to approximate

We are concerned with stochastic methods for predictive simulations of flows in the subsurface that can incorporate dynamical data (such as pressure data and production curves in field-scale operations) to reduce uncertainty in determining time-dependent subsurface properties such as absolute permeability, porosity and Young’s modulus in the context of poroelasticity. There exists a considerable amount

Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity

This paper presents convolutional neural network architectures for integration of dynamic flow response data to reduce the uncertainty in geologic scenarios and calibrate subsurface flow models. The workflow consists of two steps, where in the first step the solution search space is reduced by eliminating unlikely geologic scenarios using distinguishing salient flow data trends. The first step serves

Strong coupling between geomechanical deformation and multiphase fluid flow appears in a variety of geoscience applications. A common discretization strategy for these problems is a continuous Galerkin finite element scheme for the momentum balance equation and a finite volume scheme for the mass balance equations. When applied within a fully implicit solution strategy, however, this discretization

Fate and transport of heavy metals is controlled by the biogeochemical processes in the environment. Reactive transport modeling is particularly important for capturing the complex interplay between the microbial community dynamics and redox-stratified environments. The focus of this study is to investigate the impacts of (i) multicomponent diffusion (MCD) and (ii) electrical double layer (EDL) on

In geosciences, generative adversarial networks have been successfully applied to generate multiple realizations of rock properties from geological priors described by training images, within probabilistic seismic inversion and history matching methods. Here, the use of generative adversarial networks is proposed not as a model generator but as a model reconstruction technique for subsurface models

In this work, we consider the transport of a surfactant in variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard, and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence

One way to quantify the uncertainty in Bayesian inverse problems arising in the engineering domain is to generate samples from the posterior distribution using Markov chain Monte Carlo (MCMC) algorithms. The basic MCMC methods tend to explore the parameter space slowly, which makes them inefficient for practical problems. On the other hand, enhanced MCMC approaches, like Hamiltonian Monte Carlo (HMC)

The numerical modelling of flows in geologic porous media, accounting for plastic behaviour of rocks at high temperatures and hydrofracturing at high fluid pressures, is required for a better understanding of hydrothermal and volcanic systems. The investigation of these systems is limited given the lack of reliable and available reservoir simulation software that accounts for complicated rock behaviour

This paper describes miscible displacement upon air injection in a porous medium saturated with oil corresponding to conditions of high-pressure air injection (HPAI). We assume that injection fluids and produced fluids are fully miscible with the oil at the prevailing high pressure. We use three pseudo-components, viz., oxygen, oil, and an inert component, which includes nitrogen, carbon dioxide, etc

Efficient and safe production of hydraulically fractured reservoirs benefits from the prediction of their geometrical attributes. Geophysical methods have the potential to provide data that are sensitive to fracture geometries, alleviating the typically sparse nature of in situ reservoir observations. Moreover, surface-based methods can be logistically and economically attractive since they avoid operational

Though geologic carbon storage (GCS) is widely recognized as a promising strategy to reduce emissions of greenhouse gas (GHG), the potential for mobilization of radioactive uranium (U) from U-bearing minerals in deep subsurface due to CO2 injection remains a concern. In this study, supercritical CO2 and brine flowing through a fracture surrounded by reservoir rock containing uranium is simulated so

Permeability and its anisotropy are of central importance for groundwater and hydrocarbon migration. Existing fluid dynamics methods for computing permeability have common shortcomings, i.e., high computational complexity and long computational time, reducing the potential of these methods in practical applications. In view of this, a 3D CNN-based approach for rapidly estimating permeability in anisotropic

We develop a staggered finite element procedure for the coupling of a free viscous flow with a deformable porous medium, in which interface phenomena related to the skin effect can be incorporated. The basis of the developed simulation procedure is the coupled Stokes-Biot model, which is supplemented with interface conditions to mimic interface-related phenomena. Specifically, the fluid entry resistance

Geostatistical seismic inversion methods use stochastic sequential simulation as the model generation and perturbation technique. These stochastic simulation methods use a global variogram model to express the expected spatial continuity pattern of the subsurface elastic properties of interest. The conditioning to a single variogram model is not suitable for complex and non-stationary geological environments

Predicting the petrophysical properties of rock samples using micro-CT images has gained significant attention recently. However, an accurate and an efficient numerical tool is still lacking. After investigating three numerical techniques, (i) pore network modeling (PNM), (ii) the finite volume method (FVM), and (iii) the lattice Boltzmann method (LBM), a workflow based on machine learning is established

The general field development optimization problem is complex due to the potentially large number of controls of mixed type and discontinuities in the objective function related to varying numbers and types of wells being placed in a discretized grid. This may make the problem challenging or even unsuitable for certain types of optimization methods that rely on, e.g., the availability of (adjoint)

Numerical modeling of geochemistry associated with geologic CO2 storage involves many conceptual and quantitative uncertainties. In this study, a time efficient arbitrary polynomial chaos (aPC) expansion approach was proposed to do global sensitivity analysis of mineral dissolution and precipitation modeling in geologic carbon storage scenarios. To demonstrate the workflow of the aPC approach, a numerical

In this study, a 3D coupled FEM-DEM method was adopted to study the influence of thermal-induced damage on the mechanical properties of fractured rock mass. In this method, the rock matrix was discretized into bulk elements bridged by cohesive elements, and the preexisting fractures were represented by cohesive elements. The thermal-induced damage process was modeled through two parts, i.e., thermal

The phenomenon of flow-channeling, or the existence of preferential pathways for flow in fracture networks, is well known. Identification of the channels (“backbone”) allows for system reduction and computational efficiency in simulation of flow and transport through fracture networks. However, the purpose of machine learning techniques for backbone identification in fractured media is two-pronged

This paper presents a numerical simulation tool for the analysis of coupled processes related to subsurface operations. The tool combines the open-source scientific code OpenGeoSys with the reservoir simulator Eclipse enabling the coupling of thermal, hydraulic, mechanical and geochemical processes. While the coupling of multiphase flow with heat and reactive geochemical component transport has been

Model-based production optimization relies on a dynamic model that simulates the fluid flow in the oil reservoirs, and an economic objective function that assigns an economic measure to the recoverable oil reserves. An optimization algorithm utilizes the dynamic model to find the production scenario which maximizes the economic measure of profit. However, due to incompleteness and doubtfulness of available

We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the

Poroelasticity theory can be used to analyse the coupled interaction between fluid flow and porous media (matrix) deformation. The classical theory of linear poroelasticity captures this coupling by combining Terzaghi’s effective stress with a linear continuity equation. Linear poroelasticity is a good model for very small deformations; however, it becomes less accurate for moderate to large deformations

In this study, imbibition process is investigated in heterogeneous hydrocarbon reservoir using the non-classical (effective viscous finger) model equations proposed by Luo et al. (SPE Res. Eval. Engineering, 20(4), 1–16 2017). Counter-current spontaneous imbibition is analyzed in different heterogeneous porous media. The heterogeneity is mainly due to the spatial variation of the porosity and absolute

Modeling of hydraulic fracturing processes is of great importance in computational geosciences. In this paper, a phase-field model is developed and applied for investigating the hydraulic fracturing propagation in saturated poroelastic rocks with pre-existing fractures. The phase-field model replaces discrete, discontinuous fractures by continuous diffused damage field, and thus is capable of simulating

We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential

Borehole resistivity measurements are routinely employed to measure the electrical properties of rocks penetrated by a well and to quantify the hydrocarbon pore volume of a reservoir. Depending on the degree of geometrical complexity, inversion techniques are often used to estimate layer-by-layer electrical properties from measurements. When used for well geosteering purposes, it becomes essential

Prior to the estimation process of channelized reservoirs, in the context of any Assisted History Matching method, the parameterization of facies field is a necessary task. The parameterization of the facies field consists of defining a numerical field (parameter field) on the reservoir domain so that, using a projection function, we are able to recover the facies field from the values of parameter

The fully implicit method is the most commonly used approach to solve black-oil problems in reservoir simulation. The method requires repeated linearization of large nonlinear systems and produces ill-conditioned linear systems. We present a strategy to reduce computational time that relies on two key ideas: (i) a sequential formulation that decouples flow and transport into separate subproblems, and

A novel upscaling approach was previously introduced using pressure transient concepts which allowed us to distinguish between well-connected, weakly connected, and disconnected pay in the local upscaling region. The current work applies these same concepts to benchmark the upscaling formulation against existing upscaling techniques to test the impact of localization. The local flow field generated

Subsurface reservoir models have a high degree of uncertainty regarding reservoir geometry and structure. A range of conceptual models should therefore be generated to explore how fluids-in-place, reservoir dynamics, and development decisions are affected by such uncertainty. The rapid reservoir modelling (RRM) workflow has been developed to prototype reservoir models across scales and test their dynamic

For most history matching problems, the posterior probability density function (PDF) may have multiple local maxima, and it is extremely challenging to quantify uncertainty of model parameters and production forecasts by conditioning to production data. In this paper, a novel method is proposed to improve the accuracy of Gaussian mixture model (GMM) approximation of the complex posterior PDF by adding

We present a novel nonlinear formulation for modeling reactive-compositional flow and transport in the presence of complex phase behavior due to a combination of thermodynamic and chemical equilibria in multi-phase systems. We apply this formulation to model precipitation/dissolution of minerals in reactive multiphase flow in subsurface reservoirs. The proposed formulation is based on the consistent

In cases with significant density difference between the injection mixture and the reservoir fluids, segregation can take place on short temporal scales relative to the typical time-step lengths of the simulation. A fully resolved 3D description is computationally demanding and is often difficult to achieve with buoyancy segregated flow. Vertical equilibrium (VE) is one possible technique for effective

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D–3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well

Distributed Gauss-Newton (DGN) optimization method has been proved very efficient and robust for history matching and uncertainty quantification (HM&UQ). The major bottleneck for performance enhancement is the expensive computational cost of solving hundreds of Gauss-Newton trust-region (GNTR) subproblems in each iteration. The original GNTR solver applies the less efficient iterative Newton-Raphson

There is strong interest to design sequential fully implicit (SFI) methods for compositional flow simulations with convergence properties that are comparable to fully implicit (FI) methods. SFI methods decompose the fully coupled system into a pressure equation and a transport system of the components. During the pressure update, the compositions are frozen, and during the transport calculations, both

Algebraic multiscale (AMS) is a recent development for the construction of efficient linear solvers in reservoir simulations. It employs upscaling ideas to coarsen the respective linear system and provides a high amount of inherent parallelism. However, it has the drawback that it can so far only be applied to scalar problems, e.g., a pressure sub-problem. Moreover, AMS relies on the availability of

The fluid injection in sedimentary formations may generate geochemical interactions between the fluids and the rock minerals, e.g., CO2 storage in a depleted reservoir or a saline aquifer. To simulate such reactive transfer processes, geochemical equations (equilibrium and kinetics equations) are coupled with compositional flows in porous media in order to represent, for example, precipitation/dissolution

Transient well test analysis provides valuable information about reservoir characteristics such as permeability and the hydraulic diffusivity coefficient. It is based on the solution of diffusivity equation, which describes mass transfer in porous media. On the whole, analytical solutions are used for interpreting well test data. However, all these solutions were obtained under the condition of reservoir

Multiphase flow simulation in fractured reservoirs at field scale is a significant challenge. Despite recent advances and a wide range of applications in both hydrology and hydrocarbon reservoir engineering, discussing efficient methods that cover computational complexity, accuracy, and flexibility aspects is still of paramount importance for a better understanding of these complex media. In this work

Abstract Relating the attenuation and velocity dispersion of seismic waves to fluid pressure diffusion (FDP) by means of numerical simulations is essential for constraining the mechanical and hydraulic properties of heterogeneous porous rocks. This, in turn, is of significant importance for a wide range of prominent applications throughout the Earth, environmental, and engineering sciences, such as

Abstract The coupled THMC model, interface for pressure solution analysis under coupled conditions, IPSACC, that was proposed by the authors and can describe the long-term evolution in rock permeability due to mineral reactions (i.e., pressure solution and free-face dissolution/precipitation) within rock fractures, was upgraded in the present study by incorporating the processes of fracture initiation/propagation

Abstract A common method of imaging with seismic data is reverse time migration (RTM) in which recorded data are back-propagated to form an image of the subsurface. Least-squares RTM (LSRTM) extends this method to an iterative method that minimizes a data misfit term. An appropriate regularization term such as a sparsity-promoting functional (e.g., total variation (TV)) is required to stabilize the

Abstract This paper focuses on the modeling of heat transfer between fluid flowing in a well and the surrounding rock mass and proposes an efficient domain decomposition approach to solve this problem. The importance of such a method is illustrated by the study of the modeling of underground gas storage in salt caverns.

Abstract Reservoir engineers use large-scale numerical models to predict the production performance in oil and gas fields. However, these models are constructed based on scarce and often inaccurate data, making their predictions highly uncertain. On the other hand, measurements of pressure and flow rates are constantly collected during the operation of the field. The assimilation of these data into

Abstract Fluid flow in rough fractures and the coupling with the mechanical behaviour of the fractures pose great difficulties for numerical modeling approaches due to complex fracture surface topographies, the non-linearity of hydro-mechanical processes and their tightly coupled nature. To this end, we have adapted a fictitious domain method to enable the simulation of hydro-mechanical processes in

Abstract The disposal of heat-generating nuclear waste in salt host rock generates a thermal gradient around the waste package that may cause brine inclusions in the salt grains to migrate toward the waste package. In this study, a dual-continuum model is developed to analyze such a phenomenon. In this model, fluid flow in terms of advective and diffusive fluxes in the interconnected pore space and