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

Subsurface models are central pieces of information in different earth-related disciplines such as groundwater management and hydrocarbon reservoir characterization. These models are normally obtained using geostatistical simulation methods. Recently, methods based on deep learning algorithms have been applied as subsurface model generators. However, there are still challenges on how to include conditioning

Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. A common way to describe the foam displacement is by using population balance models, which consider the foam texture as part of the gas phase. Numerical simulation of such equations presents serious difficulties connected to the high non-linearity in the fractional flow. The linear kinetic model

The Groningen gas field in the Netherlands is experiencing induced seismicity as a result of ongoing depletion. The physical mechanisms that control seismicity have been studied through rock mechanical experiments and combined physical-statistical models to support development of a framework to forecast induced-seismicity risks. To investigate whether machine learning techniques such as Random Forests

Aiming at the infeasibility of using quadrilateral-prisms to describe sharp shapes, an improved vertical stretch algorithm was proposed to generate three-dimensional (3D) hybrid meshes based on the quadrilateral mesh converted from triangles to discretize the geometric models with pinch-out features. A robust and automatic mesh generator was developed, which served as a preprocessing tool for simulating

Iterative ensemble smoothers have been widely used for calibrating simulators of various physical systems due to the relatively low computational cost and the parallel nature of the algorithm. However, iterative ensemble smoothers have been designed for perfect models under the main assumption that the specified physical models and subsequent discretized mathematical models have the capability to model

Ensemble methods are remarkably powerful for quantifying geological uncertainty. However, the use of the ensemble of reservoir models for robust optimization (RO) can be computationally demanding. The straightforward computation of the expected net present value (NPV) requires many expensive simulations. To reduce the computational burden without sacrificing accuracy, we present a fast and effective

Ensemble smoothers are among the most successful and efficient techniques currently available for history matching. However, because these methods rely on Gaussian assumptions, their performance is severely degraded when the prior geology is described in terms of complex facies distributions. Inspired by the impressive results obtained by deep generative networks in areas such as image and video generation

Quasi-implicit schemes for treating velocity-dependent mobilities in underground porous media flow simulation, occurring when modeling non-Newtonian and non-Darcy effects as well as capillary desaturation, are presented. With low-order finite-volume discretizations, the principle is to evaluate mobilities at cell edges using normal velocity components calculated implicitly, and transverse velocity

This paper presents a numerical simulator for solving compositional multiphase flow and reactive transport. The simulator was developed by effectively linking IC-FERST (Imperial College Finite Element Reservoir SimulaTor) with PHREEQCRM. IC-FERST is a next-generation three-dimensional reservoir simulator based on the double control volume finite element method and dynamic unstructured mesh optimization

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from usual model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number (O(500–1000)) of flow simulations

In this work, a method for well log data classification is presented. The method relies on a coordinate transformation to restructure the data in an optimal way and a quasi-probabilistic interpolation technique capable of smoothing noisy data. The approach does not require case-specific design, is computationally efficient and provides a statistical characterization of the classification problem. Consequently

Studying model uncertainty and identifying the parameter uncertainty in the modeling of water flow through the soil is useful to improve water and soil management. This research aimed to assess the uncertainty of tshe parameters soil water retention curve (SWRC) models using an efficient hybrid of the Monte Carlo technique e.g. generalized likelihood uncertainty estimation (GLUE). GLUE estimates the

A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion

We have developed and tested a new Eikonal first-arrival forward model scheme by combining a fast marching method (FMM) algorithm (Sethian et al. Proc. SPIE 2726 optical microlithography IX 1996); Sethian et al. Geophys., pp. 17781781 1997); Sethian et al. SIAM Rev. 41(2), 199235 1999), an upwind Eikonal solver scheme first described by Sethian and Popovici in 1996, with a more accurate but less robust

In this work, we use the method of volume averaging to upscale the pore-scale diffusion equation on the Sierpiński carpet. Based on the isotropy condition in the fractal structure and the fact that the ratio of length scales in the Sierpiński carpet is constant, a general expression for the effective diffusion coefficient regarding the iteration of the fractal structure is suggested. Additionally,

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of hierarchically connected manifolds is formed which we refer to as mixed-dimensional. The governing equations with respect to linear elasticity are then defined on this mixed-dimensional

In this paper, we present the results of benchmark simulations for plume spreading during CO2 geo-sequestration conducted with the newly developed Australian CO2 Geo-Sequestration Simulator (ACGSS). The simulator uses a hybrid finite element–finite volume (FEFVM) simulation framework, integrating an asynchronous local time stepping method for multi-phase multi-component transport and a novel non-iterative

The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the discrete fracture network (DFN) model. A Darcy problem is solved to compute the advective field, then used in a subsequent time-dependent transport-diffusion-reaction problem. The numerical schemes are benchmarked in terms of flexibility in handling

Complex dynamical systems are an integral part of predictive analysis that model diverse phenomena. As these models improve, they become more complex and depend on an increasing number of model or driver inputs. Uncertainty plagues these inputs (initial conditions, boundary conditions, key model parameters, signal noise, etc.), thereby introducing errors into the forecast of the model and significantly

A multiphase-field approach for elasto-plastic and anisotropic brittle crack propagation in geological systems consisting of different regions of brittle and ductile materials is presented and employed to computationally study crack propagation. Plastic deformation in elasto-plastic materials such as frictional, granular or porous materials is modelled with the pressure-sensitive Drucker-Prager plasticity

Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes

Two efficient and scalable numerical solution methods will be compared using exact Jacobians to solve the fully coupled Newton systems arising during fully implicit discretization of the equations for two-phase flow in porous media. These methods use algebraic multigrid (AMG) to solve the linear systems in every Newton step. The algebraic multigrid methods rely on (i) a Schur Complement Reduction (SCR-AMG)

Horizontal wells have been used for water flooding operations for the purpose of pressure maintenance and improved oil recovery, e.g., in tight oil reservoirs. Injection profiling along the well lateral is required to determine the effectiveness of water flooding operations and to maintain high sweep efficiency. Recent improvements in downhole temperature monitoring tools allow monitoring the transient

High-order discretizations have become increasingly popular across a wide range of applications, including reservoir simulation. However, the lack of stability and robustness of these discretizations for advection-dominant problems prevent them from being widely adopted. This paper presents work towards improving the stability and robustness of the discontinuous Galerkin (DG) finite element scheme

Resistivity and acoustic logs are widely used to estimate gas hydrate saturation in various sedimentary systems using one of the two popular methods ((1) acoustic velocity and (2) electrical resistivity), but the limitations of these two methods are often overlooked, which include (i) well-specific calibration of empirical exponents in the electrical resistivity method, (ii) assumption of known pore

Water coning is one of the common issues in subsurface systems in which water flows into the production well through perforated zones. This phenomenon can cause severe problems in wellbore and surface facilities. Thus, accurate prediction of water breakthrough can help to adapt to the production mode and avoid such issues. Conducting flow simulations, as a conventional approach, can be very time demanding

The correct choice of interface conditions and effective parameters for coupled macroscale free-flow and porous-medium models is crucial for a complete mathematical description of the problem under consideration and for accurate numerical simulation of applications. We consider single-fluid-phase systems described by the Stokes–Darcy model. Different sets of coupling conditions for this model are available

Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermo-hydraulic interaction between tightly

Field development optimization, in which well configuration, well types, and well controls are determined, represents a computationally demanding mixed integer nonlinear programming problem. Such problems may require very large numbers of function evaluations, and if each of these corresponds to a detailed flow simulation, the optimization can become intractable. In this paper, we incorporate a set

1D water oil displacement in porous media is usually described by the Buckley-Leverett equation or the Rapoport-Leas equation when capillary diffusion is included. The rectilinear geometry is not representative for near well oil displacement problems. It is therefore of interest to describe the radially symmetric Buckley-Leverett or Rapoport-Leas equation in cylindrical geometry (radial Buckley-Leverett

Microbially mediated sulfate reduction is a ubiquitous process in many subsurface systems. Isotopic fractionation is characteristic of this anaerobic process, since sulfate-reducing bacteria (SRB) favor the reduction of the lighter sulfate isotopologue (S32O42−) over the heavier isotopologue (S34O42−). Detection of isotopic shifts has been utilized as a proxy for the onset of sulfate reduction in subsurface

An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat’s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach

In unconventional reservoir rocks, pore anisotropy and gas high Knudsen number (Kn) effect are prominent, while gas slippage factor is a crucial parameter to evaluate their apparent permeability. To analyze the correlation of gas slippage factor with pore anisotropy of porous media and Kn, two-dimensional bundle models and anisotropic porous media with same characteristic length were skillfully constructed

In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which combines a piecewise constant interpolation and the restriction operator by Wesseling/Khalil with a line-wise relaxation procedure. A local Fourier analysis is performed