Surface-based modelling provides a computationally efficient approach for generating geometrically realistic representations of heterogeneity in reservoir models. However, conditioning Surface-Based Geological Models (SBGMs) to well data can be challenging because it is an ill-posed inverse problem with spatially distributed parameters. To aid fast and efficient conditioning, we use here SBGMs that

Domain decomposition methods are widely used as preconditioners for Krylov subspace linear solvers. In the simulation of porous media flow there has recently been a growing interest in nonlinear preconditioning methods for Newton’s method. In this work, we perform a numerical study of a spatial additive Schwarz preconditioned exact Newton (ASPEN) method as a nonlinear preconditioner for Newton’s method

Least-squares reverse time migration has proven to be the state-of-the-art for linear imaging technique of complex subsurface structures. Assuming a variable-density acoustic medium, least-squares iterations have the potential to compensate for the artifacts caused by finite frequency of the seismic source, limited acquisition aperture, uneven illumination and parameter cross-talk. The main drawback

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate

A Correction to this paper has been published: https://orcid.org/https://doi.org/10.1007/s10596-021-10093-8

This study presents a workflow to optimize the location of CO2 injectors in order to maximize stored volume and prevent fault reactivation due to increases of pore pressure. We combine coupled reservoir flow and geomechanics simulations with neural network surrogate models and find the best injector location based on net present environmental value (NPEV). The surrogate models can complement the numerical

In this paper we carry out numerical analysis for a family of simplified gas transport models with hydrate formation and dissociation in subsurface, in equilibrium and non-equilibrium conditions. These models are adequate for simulation of hydrate phase change at basin and at shorter time scales, but the analysis does not account directly for the related effects of evolving hydraulic properties. To

The exploratory phase of a hydrocarbon field is a period when decision-supporting information is scarce while the drilling stakes are high. Each new prospect drilled brings more knowledge about the area and might reveal reserves, hence choosing such prospect is essential for value creation. Drilling decisions must be made under uncertainty as the available geological information is limited and probability

In this paper, we formulate and test numerically a fully coupled fully implicit finite volume (FV) method for solving the nonlinear coupling between two-phase flows and geochemical reactions in porous media on a reservoir scale. The problem is modeled by a highly nonlinear system of degenerate partial differential equations (PDEs governing a compositional two-phase flow model) coupled to ordinary and/or

With the continuous depletion of oil and natural gas resources, the development of fluvial reservoirs has gradually become a key research direction, which makes the reconstruction of fluvial reservoirs a challenging problem due to the irregular shapes and complicated trends of fluvial facies. The traditional numerical simulation method obtains reconstruction results through the probability in training

We present a novel numerical upscaling technique for modeling the wave response of gas-hydrate bearing sediments composed of a rock frame, gas-hydrate and water, where the hydrate consists of ice-like lattice of water molecules with methane trapped inside. These sediments are highly heterogeneous at mesoscopic scales, much smaller than the wavelength but much larger than the pore size, inducing substantial

As a serious meteorological natural disaster, windstorm has caused great harm to people’s lives and property. The tracking and trending of the wind storm, as well as the spatio-temporal process changes of its key features, such as wind eye, eye-wall, and wind circle, have long been the researchers’ focuses. The use of visualization tools to help meteorologists analyze and understand the spatio-temporal

Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate

Shale oil and shale gas, as widely distributed unconventional resources, have attracted much attention at present due to the fast-increasing demands for energy. Since shale is the storage medium for shale oil and gas, its microscopic characteristics surely will influence its own storage ability and the difficulty of exploitation. The internal structures of shale can be studied based on establishing

A Correction to this paper has been published: https://doi.org/10.1007/s10596-021-10079-6

This paper presents a reduced-order finite element (ROFE) method with seldom degrees of freedom for the incompressible miscible displacement problem, where the proper orthogonal decomposition (POD) technique is used. The algorithm process for the ROFE method is provided. Some numerical experiments are presented to help us understand this method and verify the accuracy and efficiency of this method

In this work, we consider an online enrichment procedure in the context of the Generalized Multiscale Finite Element Method (GMsFEM) for the two-phase flow model in highly heterogeneous porous media. The coefficient of the pressure equation is referred to as the permeability and is the main source of heterogeneity within the model. The elliptic pressure equation is solved using online GMsFEM, which

In order to quantify the performance ranking of oil wells in high water cut reservoir, a quantitative evaluation method of oil wells is established from two perspectives of numerical simulation and machine learning respectively. The backward flight time of oil wells control area is obtained by numerical simulation. The flow heterogeneity of oil wells is evaluated based on Lorentz coefficient, and the

A method for infering bed topography beneath glaciers from surface measurements (elevation from altimetry and velocity from InSAR) and sparse thickness measurements is developed and evaluated. The method is based on an original non-isothermal Reduced Uncertainty (RU) version of the Shallow Ice Approximation (SIA) equation that natively incorporates the surface measurements. The flow model has a single

A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, which is consistent with the continuous model dynamics. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal

Dimensional reduction strategy is an effective approach to derive reliable conceptual models to describe flow in fractured porous media. The fracture aperture is several orders of magnitude smaller than the characteristic size (e.g., the length of the fracture) of the physical problem. We identify the aperture to length ratio as the small parameter 𝜖 with the fracture permeability scaled as an exponent

Anthropogenic land subsidence can be evaluated and predicted by numerical models, which are often built over deterministic analyses. However, uncertainties and approximations are present, as in any other modeling activity of real-world phenomena. This study aims at combining data assimilation techniques with a physically-based numerical model of anthropogenic land subsidence in a novel and comprehensive

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. J. Comput. Phys. 217(2), 627–641 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually solved with tight tolerances

In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and heterogeneous porous media. In the offline adaptive method, we first derive an a-posteriori error indicator based on one weighted L2-norm of the local residual operator

Explicit numerical schemes are popular in multiphysics and multiscale simulations, yet their use in stiff problems often requires time steps to be so small as to render simulations over large time horizons infeasible. Exponential time differencing (ETD) has proved to be an efficient scheme for tackling differential operators with linear stiff and nonlinear non-stiff parts. Such natural separation,

The Fast Marching Method (FMM) has been applied to characterize the transient drainage volume and to simulate flow as a function of time in porous media using the concept of the “diffusive time of flight” (DTOF). The DTOF (τ) provides a spatial coordinate which reduces the three dimensional pressure diffusivity equation to an equivalent one dimensional formulation. It is obtained from the solution

We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed

The observation and analyses of cores are the bases of various studies on oil and gas exploration and development. However, the real natural cores suffer from their own instability and constant weathering or erosion as well as experimental damages, leading to the changes of their physical and chemical characteristics. Digital cores can address the above issues by core digitalization and then reusing

Rapidly changing heterogeneous supercomputer architectures pose a great challenge to many scientific communities trying to leverage the latest technology in high-performance computing. Many existing projects with a long development history have resulted in a large amount of code that is not directly compatible with the latest accelerator architectures. Furthermore, due to limited resources of scientific

Seismic modeling plays an important role in geophysics and seismology for estimating the response of seismic sources in a given medium. In this work, we present a MATLAB-based package, FDwave3D, for synthetic wavefield and seismogram modeling in 3D anisotropic media. The seismic simulation is carried out using the finite-difference method over the staggered grid, and it is applicable to both active

Streamlines have been used for reservoir modeling and flow visualization in the petroleum industry and in computational fluid dynamics. When applied to the calculation of volumetric sweep and the identification of by-passed hydrocarbons for improved oil recovery, it is important that the velocity models that are used to trace trajectories across the cells of a grid are flux conservative. As such, the

The modeling of thermodynamic equilibria leads to complex nonlinear chemical systems which are often solved with the Newton-Raphson method. But this resolution can lead to a non convergence or an excessive number of iterations due to the very ill-conditioned nature of the problem. In this work, we combine a particular formulation of the equilibrium system called the Positive Continuous Fraction method

In the context of long-term degradation of porous media, the coupling between fracture mechanics and reactive transport is investigated. A reactive transport model in a cracked discontinuous and heterogeneous porous medium is proposed. The species transport through and along the crack network are taken into account in a multibody approach. A dedicated geochemistry solver is developed and allows to

Sophisticated modeling of the migration of sorbing radionuclides in compacted claystones is needed for supporting the safety analysis of deep geological repositories for radioactive waste, which requires robust modeling tools/codes. Here, a benchmark related to a long term laboratory scale diffusion experiment of cesium, a moderately sorbing radionuclide, through Opalinus clay is presented. The benchmark

A Correction to this paper has been published: https://doi.org/10.1007/s10596-020-10022-1

The identification of micropore systems in carbonate rocks is an important task of image processing because of the high impact these systems cause on fluid flow. Currently, one of the main tools used to characterize rock samples is computed tomography (CT). Such micro information poses the challenge associated with the limitation of the CT’s resolution. Therefore, we propose an alternative method of

Geological facies modeling has long been studied to predict subsurface resources. In recent years, generative adversarial networks (GANs) have been used as a new method for geological facies modeling with surprisingly good results. However, in conventional GANs, all layers are trained concurrently, and the scales of the geological features are not considered. In this study, we propose to train GANs

Seismic imaging faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Reverse time migration (RTM) is a high-resolution depth migration approach useful for extracting information such as reservoir localization and boundaries. RTM, however, is time-consuming and data-intensive as it requires

Iterative ensemble smoothers (IES) are among the state-of-the-art approaches to solving history matching problems. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-least-squares problems. In a broader picture, history matching is essentially an inverse problem, which is often ill-posed and may not possess a unique solution. To mitigate

While the mimetic finite-difference method shares many similarities with the finite-element and finite-volume methods, it has the advantage of naturally accommodating grids with arbitrary polyhedral elements. In this study, we use this attribute to develop an adaptive scheme for the solution of the geophysical electromagnetic modelling problem on unstructured grids. Starting with an initial tetrahedral

This Special Issue contains a series of fourteen papers that resulted from the Lorentz workshop in Leiden in the period of May 22–25 in 2018.

Sharp-front problems arising from equations that tend toward a hyperbolic limit occur routinely in modeling transport phenomena in porous medium systems. Numerical methods to approximate hyperbolic conservation equations are mature for finite volume methods. However, irregularly shaped domains make finite element methods (FEMs) an attractive approach for many subsurface problems. For conforming FEM

This paper presents a new mathematical representation of multiphase thermodynamic equilibrium using so-called repartition coefficients. Combined with a global mass formulation of multiphase Darcy flow in porous media, it allows the derivation of a computationally efficient family of time schemes. The model accounts for the mass conservation of an arbitrary number of components flowing through an arbitrary

The Stokes-Brinkman equations model fluid flow in highly heterogeneous porous media. In this paper, we consider the numerical solution of the Stokes-Brinkman equations with stochastic permeabilities, where the permeabilities in subdomains are assumed to be independent and uniformly distributed within a known interval. We employ a truncated anchored ANOVA decomposition alongside stochastic collocation

It is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, the conditional probability density function (pdf) of the uncertain model parameters is proportional to the prior pdf of the model parameters, multiplied by the likelihood of the measurements. The static model parameters are random variables characterizing the reservoir model while the observations include, e

Geologists and Reservoir Engineers routinely use time-domain nuclear magnetic resonance (NMR) to learn about the porous structure of rocks that hold underground fluids. In particular, two-dimensional NMR (2DNMR) technique is now gaining importance in a wide variety of applications. Crucial issue in 2DNMR analysis are the speed, robustness and accuracy of the data inversion process. This paper proposes

An ensemble-based method for seismic inversion to estimate elastic attributes is considered, namely the iterative ensemble Kalman smoother. The main focus of this work is the challenge associated with ensemble-based inversion of seismic waveform data. The amount of seismic data is large and, depending on ensemble size, it cannot be processed in a single batch. Instead a solution strategy of partitioning

Trajectory data can objectively reflect the moving law of moving objects. Therefore, trajectory prediction has high application value. Hurricanes often cause incalculable losses of life and property, trajectory prediction can be an effective means to mitigate damage caused by hurricanes. With the popularization and wide application of artificial intelligence technology, from the perspective of machine

Computational models of subsurface flow involve the coupling between fluid velocity and transport equations. While solving these problems independently can be challenging, we expose the additional complication associated with coupling them. We focus on numerical methods that can readily accommodate unstructured meshes, with emphasis on the mixed finite-element method for the velocity-pressure formulation

The representation of geological bodies is a difficult task, which involves a large number of parameters and assumptions that are commonly simplified in object-based modeling. A famous method that has been extensively applied for modeling geological bodies is the use of non-uniform rational B-Spline curves (NURBS) to delimit the boundaries of an object. Although NURBS provides highly detailed models

Investments in oil and gas projects are driven by critical field development decisions including well placement, which often significantly affect the projects’ economics. Due to their typically high cost and inherently insufficient data (especially in greenfields, or fields in their early stage of development), managing uncertainty is critical when optimizing a field development plan. The use of a

Ensemble data assimilation methods, particularly iterative forms of ensemble smoother, are very useful assisted history matching techniques. One of the main challenges in the application of these methods is the excessive variance loss due to sampling errors occasioned by the limited size ensembles used in practical cases. The standard procedure to mitigate this problem is called distance-based localization

Uranium In Situ Recovery (ISR) is based on the direct leaching of the uranium ore in the deposit by a mining solution. Fluid flow and geochemical reaction in the reservoir are difficult to predict due to geological, petrophysical and geochemical uncertainties. The reactive transport simulation code used to model ISR is very sensitive to the spatial distribution of physical and chemical properties of

In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our filter implementation combines information brought by an ensemble of model realizations, and that based on our prior knowledge about the dynamical system of interest. We perform the combination of both sources of information via optimal shrinkage factors

A Correction to this paper has been published: https://doi.org/10.1007/s10596-020-10024-z

In addition to the ongoing development, pre-salt carbonate reservoir characterization remains a challenge, primarily due to inherent geological particularities. These challenges stimulate the use of well-established technologies, such as artificial intelligence algorithms, for image classification tasks. Therefore, this work intends to present an application of deep learning techniques to identify

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective

Reservoir simulation is critically important for optimally managing petroleum reservoirs. Often, many of the parameters of the model are unknown and cannot be measured directly. These parameters must then be inferred from production data at the wells. This is an inverse problem which can be formulated within a Bayesian framework to integrate prior knowledge with observational data. Markov Chain Monte

Direct pore scale simulations of two-fluid flow on digital rock images provide a promising tool to understand the role of surface wetting phenomena on flow and transport in geologic reservoirs. We present computational protocols that mimic conventional special core analysis laboratory (SCAL) experiments, which are implemented within the open source LBPM software package. Protocols are described to

Land cover classification is one of the most important applications of POLSAR images. In this paper, a hybrid biogeography-based optimization support vector machine (HBBOSVM) has been introduced to classify POLSAR images of RADARSAT 2 in band C acquired from San Francisco, USA. The main purpose of this classification is to minimize the number of features and maximize classification accuracy. The proposed