Authors:Véronique Gervais; Mickaële Le Ravalec Pages: 3 - 28 Abstract: Numerical representations of a target reservoir can help to assess the potential of different development plans. To be as predictive as possible, these representations or models must reproduce the data (static, dynamic) collected on the field. However, constraining reservoir models to dynamic data – the history-matching process – can be very time consuming. Many uncertain parameters need to be taken into account, such as the spatial distribution of petrophysical properties. This distribution is mostly unknown and usually represented by millions of values populating the reservoir grid. Dedicated parameterization techniques make it possible to investigate many spatial distributions from a small number of parameters. The efficiency of the matching process can be improved from the perturbation of specific regions of the reservoir. Distinct approaches can be considered to define such regions. For instance, one can refer to streamlines. The leading idea is to identify areas that influence the production behavior where the data are poorly reproduced. Here, we propose alternative methods based on connectivity analysis to easily provide approximate influence areas for any fluid-flow simulation. The reservoir is viewed as a set of nodes connected by weighted links that characterize the distance between two nodes. The path between nodes (or grid blocks) with the lowest cumulative weight yields an approximate flow path used to define influence areas. The potential of the approach is demonstrated on the basis of 2D synthetic cases for the joint integration of production and 4D saturation data, considering several formulations for the weights attributed to the links. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9663-y Issue No:Vol. 22, No. 1 (2018)

Authors:M. Baumann; R. Astudillo; Y. Qiu; E. Y. M. Ang; M. B. van Gijzen; R.-É. Plessix Pages: 43 - 61 Abstract: In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently using the preconditioned IDR(s) method. We present an efficient and robust way to apply a single preconditioner using MSSS matrix computations. For 3D problems, we present a memory-efficient implementation that exploits the solution of a sequence of 2D problems. Realistic examples in two and three spatial dimensions demonstrate the performance of the new algorithm. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9667-7 Issue No:Vol. 22, No. 1 (2018)

Authors:Abiola D. Obembe; M. Enamul Hossain; Ben-Mansour Rached Pages: 63 - 80 Abstract: The Oberbeck-Boussinesq (OB) approximation is widely employed as a simplifying assumption for density-dependent flow problems. It reduces the governing differential equations to simpler forms, which can be handled analytically or numerically. In this study, a modified OB model is formulated to account for the variation of rock permeability and porosity with temperature during the hot fluid injection process in an oil-saturated porous medium under the assumption of local thermal equilibrium (LTE). The mathematical model is solved numerically using a fully implicit control volume finite difference discretization with the successive over relaxation (SOR) method to handle the non-linearity. Subsequently, the numerical model is validated with the analytical solution of the simplified problem successfully. Through detailed sensitivity analyses, the simulation results reveal the hot fluid injection rate as the most important operational parameter to be optimized for a successful thermal flood. The numerical runs show that that for single-phase core-flood simulation, the effect of temperature on the rock absolute permeability and porosity can be neglected without introducing any significant errors in the estimated recovery and temperature profile. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9670-z Issue No:Vol. 22, No. 1 (2018)

Authors:Sujit K Bose Pages: 81 - 86 Abstract: Free surface flow of an incompressible fluid over a shallow plane/undulating horizontal bed is characteristically turbulent due to disturbances generated by the bed resistance and other causes. The governing equations of such flows in one dimension, for finite amplitude of surface elevation over the bed, are the Continuity Equation and a highly nonlinear Momentum Equation of order three. The method developed in this paper introduces the “discharge” variable q = η U, where η = elevation of the free surface above the bed level, and U = average stream-wise forward velocity. By this substitution, the continuity equation becomes a linear first-order PDE and the momentum equation is transformed after introduction of a small approximation in the fifth term. Next, it is shown by an invertibility argument that q can be a function of η: q = F(η), rendering the momentum equation as a first order, second degree ODE for F(η), that can be be integrated by the Runge-Kutta method. The continuity equation then takes the form of a first order evolutionary PDE that can be integrated by a Lax-Wendroff type of scheme for the temporal evolution of the surface elevation η. The method is implemented for two particular cases: when the initial elevation is triangular with vertical angle of 120 ∘ and when it has a sinusoidal form. The computations exhibit the physically interesting feature that the frontal portion of the propagating wave undergoes a sharp jump followed by tumbling over as a breaker. Compared to other discretization methods, the application of the Runge-Kutta and an extended version of the Lax-Wendroff scheme is much easier. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9671-y Issue No:Vol. 22, No. 1 (2018)

Authors:Ahmad Jan; Ethan T. Coon; Scott L. Painter; Rao Garimella; J. David Moulton Pages: 163 - 177 Abstract: Integrated surface/subsurface models for simulating the thermal hydrology of permafrost-affected regions in a warming climate have recently become available, but computational demands of those new process-rich simu- lation tools have thus far limited their applications to one-dimensional or small two-dimensional simulations. We present a mixed-dimensional model structure for efficiently simulating surface/subsurface thermal hydrology in low-relief permafrost regions at watershed scales. The approach replaces a full three-dimensional system with a two-dimensional overland thermal hydrology system and a family of one-dimensional vertical columns, where each column represents a fully coupled surface/subsurface thermal hydrology system without lateral flow. The system is then operator split, sequentially updating the overland flow system without sources and the one-dimensional columns without lateral flows. We show that the app- roach is highly scalable, supports subcycling of different processes, and compares well with the corresponding fully three-dimensional representation at significantly less computational cost. Those advances enable recently developed representations of freezing soil physics to be coupled with thermal overland flow and surface energy balance at scales of 100s of meters. Although developed and demonstrated for permafrost thermal hydrology, the mixed-dimensional model structure is applicable to integrated surface/subsurface thermal hydrology in general. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9679-3 Issue No:Vol. 22, No. 1 (2018)

Authors:Shahid Manzoor; Michael G. Edwards; Ali H. Dogru; Tareq M. Al-Shaalan Pages: 195 - 230 Abstract: Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cell-centred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundary conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9686-4 Issue No:Vol. 22, No. 1 (2018)

Authors:Shahid Manzoor; Michael G. Edwards; Ali H. Dogru; Tareq M. Al-Shaalan Pages: 231 - 231 Abstract: Due to an oversight, some author’s corrections were not carried out during Performing proof corrections stage. The Publisher apologizes for these mistakes. The original article was corrected. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9699-z Issue No:Vol. 22, No. 1 (2018)

Authors:Niloofar Misaghian; Mehdi Assareh; MohammadTaqi Sadeghi Pages: 261 - 282 Abstract: The upscaling process of a high-resolution geostatistical reservoir model to a dynamic simulation grid model plays an important role in a reservoir study. Several upscaling methods have been proposed in order to create balance between the result accuracy and computation speed. Usually, a high-resolution grid model is upscaled according to the heterogeneities assuming single phase flow. However, during injection processes, the relative permeability adjustment is required. The so-called pseudo-relative permeability curves are accepted, if their corresponding coarse model is a good representation of the fine-grid model. In this study, an upscaling method based on discrete wavelet transform (WT) is developed for single-phase upscaling based on the multi-resolution analysis (MRA) concepts. Afterwards, an automated optimization method is used in which evolutionary genetic algorithm is applied to estimate the pseudo-relative permeability curves described with B-spline formulation. In this regard, the formulation of B-spline is modified in order to describe the relative permeability curves. The proposed procedure is evaluated in the gas injection case study from the SPE 10th comparative solution project’s data set which provides a benchmark for upscaling problems [1]. The comparisons of the wavelet-based upscaled model to the high-resolution model and uniformly coarsened model show considerable speedup relative to the fine-grid model and better accuracy relative to the uniformly coarsened model. In addition, the run time of the wavelet-based coarsened model is comparable with the run time of the uniformly upscaled model. The optimized coarse models increase the speed of simulation up to 90% while presenting similar results as fine-grid models. Besides, using two different production/injection scenarios, the superiority of WT upscaling plus relative permeability adjustment over uniform upscaling and relative permeability adjustment is presented. This study demonstrates the proposed upscaling workflow as an effective tool for a reservoir simulation study to reduce the required computational time. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9688-2 Issue No:Vol. 22, No. 1 (2018)

Authors:Calogero B. Rizzo; Felipe P. J. de Barros; Simona Perotto; Luca Oldani; Alberto Guadagnini Pages: 297 - 308 Abstract: We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (P e), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing P e. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9693-5 Issue No:Vol. 22, No. 1 (2018)

Authors:Maziar Veyskarami; Amir Hossein Hassani; Mohammad Hossein Ghazanfari Pages: 329 - 346 Abstract: The network modeling approach is applied to provide a new insight into the onset of non-Darcy flow through porous media. The analytical solutions of one-dimensional Navier-Stokes equation in sinusoidal and conical converging/diverging throats are used to calculate the pressure drop/flow rate responses in the capillaries of the network. The analysis of flow in a single pore revealed that there are two different regions for the flow coefficient ratio as a function of the aspect ratio. It is found that the critical Reynolds number strongly depends on the pore geometrical properties including throat length, average aspect ratio, and average coordination number of the porous media, and an estimation of such properties is required to achieve more reliable predictions. New criteria for the onset of non-Darcy flow are also proposed to overcome the lack of geometrical data. Although the average aspect ratio is the main parameter which controls the inertia effects, the effect of tortuosity on the onset of non-Darcy flow increases when the coordination number of media decreases. In addition, the higher non-Darcy coefficient does not essentially accelerate the onset of inertial flow. The results of this work can help to better understand how the onset of inertial flow may be controlled/changed by the pore architecture of porous media. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9695-3 Issue No:Vol. 22, No. 1 (2018)

Authors:Fayadhoi Ibrahima; Hamdi A. Tchelepi; Daniel W. Meyer Pages: 389 - 412 Abstract: In the context of stochastic two-phase flow in porous media, we introduce a novel and efficient method to estimate the probability distribution of the wetting saturation field under uncertain rock properties in highly heterogeneous porous systems, where streamline patterns are dominated by permeability heterogeneity, and for slow displacement processes (viscosity ratio close to unity). Our method, referred to as the frozen streamline distribution method (FROST), is based on a physical understanding of the stochastic problem. Indeed, we identify key random fields that guide the wetting saturation variability, namely fluid particle times of flight and injection times. By comparing saturation statistics against full-physics Monte Carlo simulations, we illustrate how this simple, yet accurate FROST method performs under the preliminary approximation of frozen streamlines. Further, we inspect the performance of an accelerated FROST variant that relies on a simplification about injection time statistics. Finally, we introduce how quantiles of saturation can be efficiently computed within the FROST framework, hence leading to robust uncertainty assessment. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9698-0 Issue No:Vol. 22, No. 1 (2018)

Authors:Mohamed Hayek; Anis Younes; Jabran Zouali; Noura Fajraoui; Marwan Fahs Pages: 413 - 421 Abstract: A new analytical solution is developed for interference hydraulic pumping tests in fractal fractured porous media using the dual-porosity concept. Heterogeneous fractured reservoirs are considered with hydrodynamic parameters assumed to follow power-law functions in radial distance. The developed analytical solution is verified by comparison against a finite volume numerical solution. The comparison shows that the numerical solution converges toward the analytical one when the size of the time step decreases. The applicability of the fractal dual-porosity model is then assessed by investigating the identifiability of the parameters from a synthetic interference pumping test with a set of noisy data using Bayesian parameter inference. The results show that if the storage coefficient in the matrix is fixed, the rest of the parameters can be appropriately inferred; otherwise, the identification of the parameters is faced with convergence problems because of equifinality issues. PubDate: 2018-02-01 DOI: 10.1007/s10596-017-9701-9 Issue No:Vol. 22, No. 1 (2018)

Authors:Xufei Hu; Yiren Fan; Hui Sun; Lei Wang; Zhenguan Wu Abstract: A three-dimensional (3D) nuclear magnetic resonance (NMR) spectrum can simultaneously provide distributions of longitudinal relaxation time (T1), transverse relaxation time (T2), and diffusivity (D); thus, it greatly improves the capacity of fluid identification, typing, and quantitative evaluations. However, several challenges that significantly hinder the widespread application of this technique remain. The primary challenges are the high time and memory costs associated with the current 3D NMR inversion algorithms. In addition, an activation sequence optimization method for 3D NMR inversions has not been developed. In this paper, a novel inversion method for 3D NMR spectra and a detailed optimization method for activation sequences and acquisition parameters were proposed. The novel method, namely randomized singular value decomposition (RSVD) inversion algorithm, can reduce memory requirements and ensure computational efficiency and accuracy. Window averaging (WA) technique was also adopted in this study to further increase computational speed. The optimized method for pulse sequences is mainly based on projections of the 3D NMR spectra in the two-dimensional (2D) and one-dimensional (1D) domains. These projections can identify missing NMR properties of different fluids. Because of the efficiency and stability of this novel algorithm and the optimized strategy, the proposed methods presented in this paper could further promote the widespread application of 3D NMR. PubDate: 2018-02-22 DOI: 10.1007/s10596-018-9730-z

Authors:A. Mostafaie; E. Forootan; A. Safari; M. Schumacher Abstract: Hydrological models are necessary tools for simulating the water cycle and for understanding changes in water resources. To achieve realistic model simulation results, real-world observations are used to determine model parameters within a “calibration” procedure. Optimization techniques are usually applied in the model calibration step, which assures a maximum similarity between model outputs and observations. Practical experiences of hydrological model calibration have shown that single-objective approaches might not be adequate to tune different aspects of model simulations. These limitations can be as a result of (i) using observations that do not sufficiently represent the dynamics of the water cycle, and/or (ii) due to restricted efficiency of the applied calibration techniques. To address (i), we assess how adding daily Total Water Storage (dTWS) changes derived from the Gravity Recovery And Climate Experiment (GRACE) as an extra observations, besides the traditionally used runoff data, improves calibration of a simple 4-parameter conceptual hydrological model (GR4J, in French: modèle du Génie Rural à 4 paramètres Journalier) within the Danube River Basin. As selecting a proper calibration approach (in ii) is a challenging task and might have significant influence on the quality of model simulations, for the first time, four evolutionary optimization techniques, including the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-objective Particle Swarm Optimization (MPSO), the Pareto Envelope-Based Selection Algorithm II (PESA-II), and the Strength Pareto Evolutionary Algorithm II (SPEA-II) along with the Combined objective function and Genetic Algorithm (CGA) are tested to calibrate the model in (i). A number of quality measures are applied to assess cardinality, accuracy, and diversity of solutions, which include the Number of Pareto Solutions (NPS), Generation Distance (GD), Spacing (SP), and Maximum Spread (MS). Our results indicate that according to MS and SP, NSGA-II performs better than other techniques for calibrating GR4J using GRACE dTWS and in situ runoff data. Considering GD as a measure of efficiency, MPSO is found to be the best technique. CGA is found to be an efficient method, while considering the statistics of the GR4J’s 4 calibrated parameters to rank the optimization techniques. The Nash-Sutcliffe model efficiency coefficient is also used to assess the predictive power of the calibrated hydrological models, for which our results indicate satisfactory performance of the assessed calibration experiments. PubDate: 2018-02-20 DOI: 10.1007/s10596-018-9726-8

Authors:Katerina Georgiou; John Harte; Ali Mesbah; William J. Riley Abstract: We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling. PubDate: 2018-02-20 DOI: 10.1007/s10596-018-9729-5

Authors:Swathi Boddula; Eldho T. I. Abstract: To develop sustainable groundwater management strategies, generally coupled simulation-optimization (SO) models are used. In this study, a new SO model is developed by coupling moving least squares (MLS)-based meshless local Petrov-Galerkin (MLPG) method and modified artificial bee colony (MABC) algorithm. The MLPG simulation model utilizes the advantages of meshless methods over the grid-based techniques such as finite difference (FDM) and finite element method (FEM). For optimization, the basic artificial bee colony algorithm is modified to balance the exploration and exploitation capacity of the model more effectively. The performance of the developed MLPG-MABC model is investigated by applying it to hypothetical and field problems with three different management scenarios. The model results are compared with other available SO model solutions for its accuracy. Further, sensitivity analyses of various model parameters are carried out to check the robustness of the SO model. The proposed model gave quite promising results, showing the applicability of the present approach. PubDate: 2018-02-13 DOI: 10.1007/s10596-018-9718-8

Authors:Eric Chung; Yalchin Efendiev; Wing Tat Leung Abstract: This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast. PubDate: 2018-02-12 DOI: 10.1007/s10596-018-9719-7

Authors:Sanghyun Lee; Baehyun Min; Mary F. Wheeler Abstract: We present a framework for the coupling of fluid-filled fracture propagation and a genetic inverse algorithm for optimizing hydraulic fracturing scenarios in porous media. Fracture propagations are described by employing a phase field approach, which treats fracture surfaces as diffusive zones rather than of interfaces. Performance of the coupled approach is provided with applications to numerical experiments related to maximizing production or reservoir history matching for emphasizing the capability of the framework. PubDate: 2018-02-10 DOI: 10.1007/s10596-018-9728-6

Authors:S. A. Abdul Hamid; A. H. Muggeridge Abstract: We present an analytical solution to estimate the minimum polymer slug size needed to ensure that viscous fingering of chase water does not cause its breakdown during secondary oil recovery. Polymer flooding is typically used to improve oil recovery from more viscous oil reservoirs. The polymer is injected as a slug followed by chase water to reduce costs; however, the water is less viscous than the oil. This can result in miscible viscous fingering of the water into the polymer, breaking down the slug and reducing recovery. The solution assumes that the average effect of fingering can be represented by the empirical Todd and Longstaff model. The analytical calculation of minimum slug size is compared against numerical solutions using the Todd and Longstaff model as well as high resolution first contact miscible simulation of the fingering. The ability to rapidly determine the minimum polymer slug size is potentially very useful during enhanced oil recovery (EOR) screening studies. PubDate: 2018-02-08 DOI: 10.1007/s10596-018-9721-0