SPE Journal is receiving an increasing number of papers for review. This year, we have therefore increased the number of papers that appear in each of the six bimonthly issues. The December issue of
SPE Journal consists of 30 papers, which I have divided into six categories that reflect the type of experimental and/or numerical method used and not the physical process studied.
Pore-Scale Analysis and Modeling. This section contains six papers discussing studies of multiphase flow on the pore scale. In the first paper, Iglauer et al. use micro-CT to study 3D three-phase flow occurring in gasflood-assisted EOR in intermediate-wet core plugs. The authors demonstrate a large variation in fluid configuration, fluid-fluid curvature, and capillary pressures, which testifies to the complexity of the corresponding multiphase systems.
The second paper by Chen and Heidari uses pore-scale simulation to study measurements of electrical resistivity and dielectric permittivity. On the basis of the new understanding, the authors propose a new method that combines interpretation of these two measurements to improve assessment of hydrocarbon saturation and enable assembly of spatial distribution of rock components (pore, kerogen, and pyrite networks) in conventional models. Then, in the next paper, Argüelles-Vivas and Badadagli study gravity-driven steam-displacement of heavy oil inside a glass-bead sandpack model to explain the formation of residual oil saturation.
In the fourth paper, Riewchotisakul and Akkutlu use nonequilibrium molecular-dynamics simulations to study steady-state methane flow in carbon nanotubes. It is shown that these tubes contain an adsorbed phase that may significantly influence gas transport. Using a bundle-of-capillaries approach, the authors estimate a permeability increase of at least 50% for the organic micropores of Marcellus shale.
The fifth paper by Yassin et al. proposes new relative-permeability models for dual-wettability systems in unconventional rocks. In these systems, the oleic phase will act as the wetting phase in the hydrophobic pore network in the organic part of the system and the aqueous phase will act as a wetting phase in the hydrophilic pore network in the inorganic part.
In the last paper, Wang et al. investigate the effect of pore-size distribution on phase transitions during depressurization of a light oil and a retrograde gas confined inside nanoporous media.
Reservoir Characterization/Uncertainty Quantification. To quantify uncertainty in reservoir characterization, it is common to generate an ensemble of reservoir models that may include hundreds of individual realizations that each need to be simulated. The first paper by Suzuki et al. presents a new approach that makes use of association-rule mining, a common technique from data mining, together with high dimensional visualization to analyze simulation results from massive model ensembles. This is exemplified by 9072 models generated in the previous SAIGUP study, which was an interdisciplinary reservoir-modeling project aiming to investigate the influence of geological features on the oil recovery from shallow-marine reservoirs.
The focus of the second paper is on generating geostatistical realizations of continuous variables such as porosity and permeability, water and oil saturation, and shale volumes within each geological facies. Here, Barnett et al. propose the use of a projection-pursuit multivariate transform method to improve the reproduction of multivariate properties existing between the continuous variables inside each facies.
The next two papers focus on various aspects of Monte Carlo methods for uncertainty quantification. The multilevel Monte Carlo method was recently introduced to reduce the computational costs associated with Monte Carlo simulations. Here, the idea is to perform simulations on a hierarchy of grids, so that parts of the sampling can be performed on coarser grids, where the solution of the forward flow problem is less costly. This gives rise to two errors, a sampling error and a discretization error. Müller et al. address how to balance these two errors and present a parallelization strategy. Then, the fourth paper, by Yu et al., discusses how to combine a Markov-chain Monte Carlo method with a fractional decline-curve model to improve uncertainty quantification in well-performance forecasts for shale-gas reservoirs.
Multiscale Methods, Upscaling, and Model Reduction. The first three papers in this section discuss methods aiming to accelerate the computation of pressures and flow velocities on field and sector models. The methods operate on two nested grids—a fine grid describing the geological heterogeneity and a coarse grid used to evolve the flow equations—and are referred to as multiscale methods because they try to correctly resolve the effect of the full variety of spatial correlations represented in fine-grid geological models. Kozlova et al. present the first implementation of a multiscale finite-volume (MsFV) method inside a commercial simulator. Manea et al. discuss the design and implementation of the same method on multi- and many-core computer architectures. The MsFV method is robust and has computational performance comparable to state-of-the-art multigrid methods on rectilinear grids, but may exhibit instabilities for highly heterogeneous media and is difficult to formulate robustly for the types of grids seen in contemporary geocellular models. Finally, Møyner and Lie present a validation study for an alternative multiscale method on reservoir models with black-oil type flow physics. Their MsRSB method is more robust with respect to strong heterogeneities, is easily formulated on highly complex grids, and has recently become the method of choice in the commercial implementation discussed by Kozlova et al.
The next two papers discuss multiscale simulation of in-situ conversion, a process in which tightly spaced electrical heaters are inserted into oil-shale resources to heat solid kerogen and turn it into recoverable hydrocarbons. To make simulations more computationally tractable, Li et al. introduce a dual-grid model in which thermal-reactive, compositional flow equations are solved on a coarse grid, using kinetic parameters and a heater-well model derived from fine-scale computations. Then, Alpak and Vink present an alternative adaptive, two-scale method in which a global coarse-scale model and multiple local fine-scale near-heater models are sequentially time stepped. The global model gives boundary conditions to the fine-scale models, which subsequently are upscaled to provide effective properties for the global equation. If necessary, this process is repeated iteratively.
The last two papers by Yoon et al. and Yang et al. discuss model-reduction methods. Here, the key idea is that although the dynamics of a multiphase simulation takes place in a high-dimensional vector space, it is possible to reproduce the essential features of the simulation by use of a reduced set of variables lying in a lower-dimensional vector space. The overall approach consists of an offline stage that computes representative solutions (snapshots), which are then reduced to a small-dimensional space, and an online stage, in which the reduced offline space is used to approximate the multiphase flow behavior for particular parameter combinations. Both papers use proper orthogonal decomposition (POD) to generate the offline space, but differ in the way they reduce the nonlinear part of the online system. Yoon et al. use a hyper-reduction procedure, whereas Yang et al. use discrete empirical interpolation (DEIM) combined with a generalized multiscale finite-element method for inexpensive computation of POD snapshots. By including velocity as an auxiliary variable, Yang et al. ensure that the POD-DEIM method is mass conservative.
History Matching and Optimization. The first paper by Gao et al. discusses assisted history-matching of discrete facies models. To overcome the problem of irregular and nonsmooth data-mismatch functions, the authors propose a new algorithm that combines a noise-insensitive and parallelized direct-pattern-search algorithm (with auto-adaptive pattern-size updates) with a trust-region type Gauss-Newton or a quasi-Newton minimization method. In the next paper, Zhao et al. describe the interwell-numerical-simulation (INSIM) model, which approximates the performance of a reservoir under waterflooding and calculates oil and water rates so that these can be used to history-match water-cut data. The key idea of INSIM is to replace the reservoir by a network of inter-well control units, each having an associated pore volume and transmissibility, and then use material balance (derived from two-phase flow equations) combined with Buckley-Leverett theory to track saturation fronts.
The third paper by Le et al. proposes two automatic procedures for choosing the inflation factors to avoid ensemble collapse in the ensemble-smoother with multiple data assimilation (ES-MDA) method. The fourth paper by Lu and Chen explains how to use the exact analytical solution for pseudo-steady flow of a vertically fractured well to optimize the performance of the well by means of optimal fracture design.
Griding and Discretization. The first three papers in this section discuss use of dynamic gridding for simulating advanced recovery processes. Hoteit and Chawathé report the implementation of a dynamic-gridding approach in an in-house simulator to accelerate the computation of chemically-enhanced oil recovery. In particular, the authors discuss how to eliminate dynamic grid remapping and recalculation of transmissibilities, how to capture heterogeneity at all grid levels, how to represent complex geology with adapted grids, and how to dynamically track multiple fronts associated with surfactant-polymer and chase-water slugs. Perez-Perez et al. consider simulation of steam-assisted gravity-drainage processes with steam/solvent coinjection and study the appropriate choice of grid size to represent the near-edge zone of the resulting steam/solvent chamber. Insight from this initial sensitivity study is then used to devise an adaptive gridding method that follows and resolves details of the steam/solvent front. Finally, Mostaghimi et al. present an adaptive mesh method for simulating viscous fingering by use of unstructured control-volume finite-element methods. In the method, the local element size is determined using a metric tensor field that depends on estimates of solution-interpolation errors, giving finer meshes where the flow properties change rapidly and coarser meshes elsewhere.
The last paper by Sun et al. compares and contrasts various approaches to generate unstructured grids for modeling complex fracture networks arising around multiple horizontal wells. The authors present a new gridding and discretization workflow to handle nonorthogonal and low-angle intersections of clustered fractures with nonuniform apertures, and also discuss how to reduce the number of grid cells to give improved computational performance.
Simplified Models and Analytical Solutions. The first two papers in the last section use the concept of diffusive time-of-flight (DTOF) to study fractured reservoirs. DTOF measures the propagation time of a pressure front and is obtained by solving an Eikonal-type equation. This equation is derived by transforming the diffusivity equation describing transient pressure evolution in a heterogeneous medium to Fourier coordinates by use of an asymptotic approach to write the solution as an inverse power series, and retaining only the zeroth-order term. Fujita et al. propose to use DTOF to transform the fracture-flow equation of a multidimensional dual-porosity model into a family of 1D transport equations. By solving the 1D equations numerically, the authors obtain a 3D simulation method that is analogous to conventional streamline simulation. The authors also discuss a similar triple-continuum approach for shale gas modeling. In the second paper, Cui et al. use what is essentially the same idea to transform the transient pressure and energy-balance equations of a thermal model into two 1D equations with DTOF acting as spatial coordinate and then use numerically computed solutions of these 1D equations to quantitatively interpret temperature measurements to fracture profiles in horizontal wells.
In the third paper, Johansen et al. extend the classical 1D Buckley-Leverett solution for constant flow rate to a system governed by constant inlet and outlet pressures. The fourth paper by Schmid et al. derives the analytic solution of capillary-controlled displacement in 1D using fractional-flow theory (i.e., thereby developing the capillary analogue of the classical Buckley-Leverett solution for viscous-dominated flow). The last paper by Yuan et al. applies the method of characteristics to develop semi-analytical solutions describing particulate flows in porous media. The authors then use these solutions to evaluate to what extent nanoparticles can be used to mitigate fines migration in porous media.
Recently, Amy Kan and Peter Valko retired from the editorial board. I hereby thank them for the service they have provided to SPE and the readers of the journal. Likewise, let me welcome our new Associate Editors: Cheng Chen (Virginia Tech), Kun Ma (Total), and Joachim Moortgat (Ohio State University). Last, but not least, I wish to thank all those who have contributed to write and review the 30 papers in this issue.
Knut-Andreas Lie, Executive Editor
SINTEF ICT / NTNU