bluuebunny/crossref_metadata_2025 huggingface dataset:
Model-Based Well Location Optimization – A Robust Approach
Authors: Ramirez B. A. , Joosten G. J. , Kaleta M. P. , Gelderblom P. P.
Published: February 2017

Well Location Optimization (WLO) plays a critical role in maximizing recovery from hydrocarbon reservoirs. Identification of well locations typically relies on expert subsurface knowledge and ad-hoc flow simulation scenarios. Such approaches, due to the complexity and uncertainty of subsurface descriptions, can easily miss highly profitable possibilities. This situation has motivated the development of model-based optimization workflows that can assist subsurface specialists in choosing improved well locations. In practice, model-based optimization workflows are implemented in a deterministic fashion and applied to low, mid and high simulation scenarios. The workflow proposed in this paper takes into account model uncertainty in the optimization outcomes.

Deterministic WLO entails optimizing the easting and northing coordinates of wells with respect to an objective function (e.g. net present value or ultimate recovery). The workflow applies to fixed well trajectories. For each new proposed well location, there is a mapping of the new well connections to the reservoir simulation grid. The approach has shown resilience in handling realistic scenarios including non-uniform areal gridding, pinch out features, local grid refinements or tartan gridding, and non-uniform layering dimensions.

Deterministic optimization techniques may anchor the results to particular portions of the uncertainty space, while robust optimization techniques propagate the effect of uncertain parameters on the optimization outcomes. The trade-off between the investigated span of uncertainty space and available computational capability needs to be made. Due to the continuous growth in computational capabilities, it is ever more attainable.

Robust optimization incorporates the effect of uncertain parameters in the optimization process. It is a natural extension of the history matching process in brownfields, but it is also applicable to green fields where dynamic data is yet to be received. For such cases, a robust optimization workflow will yield outcomes that take into account the uncertainty of parameters described by a prior distribution, e.g. only conditioned to static data.

The WLO workflow involves (i) executing deterministic WLO, (ii) examining the deterministic WLO results on a set of reservoir simulation models that capture the uncertainty space, and (iii) executing robust WLO. This workflow was tested with gradient-based optimization methods, derivative-free methods, and hybrid methods, the latter being the most optimal of the three.

The robust implementation of this workflow handles realistic reservoir simulation scenarios by exploiting coarse-grained parallelism and has been applied successfully to field cases with up to fifty wells. In this paper, WLO is showcased on one synthetic case and one field case to illustrate the capabilities of the workflow.
Nonlinear Convergence for Near-Miscible Problem: A Mystery Unveiled for Natural Variable Simulator
Authors: Cao Hui , Zaydullin Rustem , Obi Eguono
Published: February 2017

In reservoir simulation, the nonlinear solver is used to solve the nonlinear system of conservation and phase-equilibrium equations at each time step. The convergence behavior of this solver is vital for the robustness and performance of any reservoir simulator.

Based on the basic solution variables used in a reservoir simulator, we have natural variable based simulators with phase-dependent solution variables (e.g. phase saturations), and mass/overall variable based simulators without phase-dependent solution variables. The nonlinear convergence behavior between these two types of simulators has been compared previously. It has been found that natural variable based simulator works well for immiscible and miscible flow, while sometimes it has apparent convergence issues for near-miscible flow.

In this paper, we analyze the fundamental physical and numerical causes for the nonlinear convergence difficulty encountered for near-miscible flow for a natural variable based simulator and study why the same issues do not appear in both immiscible and miscible flow. Based on our analysis, some carefully designed user tuning parameters can be applied to partially alleviate the convergence issue for near-miscible flow. Unfortunately this is neither general nor good enough. To fundamentally solve this issue, we propose a straightforward nonlinear solver modification which is applicable for all types of displacements (immiscible/miscible/near-miscible/mixed). We demonstrate improvements on the real field cases with different types of flow. For near-miscible and mixed type of displacements, the improvements in Newton iterations can be significant, while for the other types, our nonlinear solver modification does not show the adverse effect. For reference, we also compared the convergence behavior of the proposed solver with that from a standard mass variable based commercial simulator.
Dynamic Mesh Adaptivity for Immiscible Viscous Fingering
Authors: Adam A. , Pavlidis D. , Percival J. R. , Salinas P. , Loubens R. De , Pain C. C. , Muggeridge A. H. , Jackson M. D.
Published: February 2017

The unstable displacement of one fluid by another in a porous medium occurs frequently in various branches of enhanced oil recovery. It is now well known that when the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive, particularly in 3D. We use IC-FERST, a novel control volume finite element (CVFE) code that uses dynamic mesh adaptivity on unstructured meshes to simulate 2D and 3D viscous fingering with higher accuracy and lower computational cost than conventional methods. We provide evidence that these unstructured mesh simulations in fact yield better results that are less influenced by grid orientation error than their structured counterparts. We also include the effect of capillary pressure and show three examples that are very challenging to simulate using more conventional approaches.
Integration of Distributed Gauss-Newton with Randomized Maximum Likelihood Method for Uncertainty Quantification of Reservoir Performance
Authors: Chen Chaohui , Gao Guohua , Li Ruijian , Cao Richard , Chen Tianhong , Vink Jeroen C. , Gelderblom Paul
Published: February 2017

Although it is possible to apply traditional optimization algorithms together with the Randomized Maximum Likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method that integrates the Distributed Gauss-Newton (DGN) method with the RML method to generate multiple realizations conditioned to production data synchronously.

RML generates samples from an approximate posterior by finding a large ensemble of maximum posteriori points, from a distribution function in which the data and prior mean values have been perturbed with Gaussian noise. Rather than performing these optimizations in isolation, using large sets of simulations to evaluate the finite difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation, in which simulation results are shared among optimizations whenever these results are helping to converge a specific optimization. In order to improve sharing of results, we relax the accuracy of the finite difference approximations for the gradients, by using more widely spaced simulation results. To avoid trapping in local optima, a novel global search algorithm integrated with DGN and RML is applied. In this way we can significantly increase the number of conditional realizations that sample the approximate posterior, while reducing the total number of simulations needed to converge the optimization processes needed to obtain these realizations.

The proposed workflow has been applied to field examples on liquid rich shale or tight oil reservoirs developed with hydraulically fractured horizontal wells. The uncertain parameters include stimulated rock volume (SRV) and matrix properties, such as permeability and porosity, and hydraulic-fracture properties, such as conductivity, height, and half length. The case studies involve a sensitivity analysis to identify key parameters, a history matching study to generate history-matched realizations with the proposed method, and an uncertainty quantification of production forecasting based on those conditioned models. The new approach is able to enhance the confidence level of the Estimated Ultimate Recovery (EUR) assessment by accounting for production forecasting results generated from all history-matched realizations. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of history-matched, or rather data-conditioned, realizations can be generated in parallel within 20-40 iterations. The computational cost (CPU usage) is reduced by a factor of 10 to 25 when compared to the traditional RML approach.
Parallel Multiobjective Optimization for the Coupled Compositional /Geomechanical Modeling of Pulse Testing
Authors: Min Baehyun , Wheeler Mary F. , Sun Alexander Y.
Published: February 2017

This paper presents numerical simulation results of pulse testing experiments carried out at a test site of a carbon capture and geological storage project in Mississippi, USA. The primary objective of this study is to validate the effectiveness of pulse testing as a monitoring tool for detecting potential CO2 leakage pathways with application to the test site. Detrending followed by Fourier transform is adopted to decompose sinusoidal pressure anomalies induced by a periodic injection of CO2 into frequencies used as target parameters of history matching. The secondary objective is to calibrate the geologic model of the test site by reducing the discrepancy between observed and simulated Fourier parameters and assess uncertainties associated with the compositional brine-CO2 flow. An assisted history matching tool that mounts global- and multi-objective evolutionary algorithms is developed, integrated with an in-house flow-geomechanics simulator, and employed to manage pulse testing simulations with a low computational cost in high-performance parallel computing environments. Grid cells in the test site are locally refined using enhanced-velocity that allows nonmatching grids on interfaces between subdomains. Experiments performed with one pulser well and two monitoring wells under steady-state conditions are considered baselines for subsequent experiments that convert one monitoring well into a production well as an artificial CO2 leakage pathway. The difference between the pressure anomalies obtained from the baseline and leak experiments are captured as a signal of CO2 leakage detection with reliability in the simulation results. A trade-off relationship between the matching qualities at the two monitoring wells is revealed more clearly by invoking multi-objective history matching than conventional global-objective history matching. This comparative study to investigate the significance of multi-objective optimization in subsurface characterization represents that diversity-preservation in the ensemble composed of qualified geologic models has the advantage of reducing bias for uncertainty quantification.
Pore Size Variability and Sieving Effect in Liquid Shale—A Multiple Permeability Approach and Eagle Ford Case Study
Authors: Alfi Masoud , An Cheng , Cao Yang , Yan Bicheng , Barrufet Maria A. , Killough John E.
Published: February 2017

We propose a robust multiple permeability model to account for pore size variability and filtration effects in shale reservoirs and to explain the behavior of unconventional resources such as anomalous gas oil ratios. Recent developments in technology transformed unconventional low-permeability shales into reliable energy sources. With regard to capacity, unconventional resources are found to be more abundant than conventional ones. These resources have opened new challenges and technical difficulties along with enhanced capacities. Recent advances in high precision analytical tools have revealed that pore size distribution in shale reservoirs cover a wide range. Molecules in pores with different sizes may exhibit significantly different thermodynamic behavior. Rock fluid interactions and space hindrance effects play an important role when pore sizes become close to species' molecular dimeters. This effect can result in a composition difference between pores with large and small diameters in shale reservoirs (sieving effect), with small pores mostly filled with smaller hydrocarbon molecules and large molecules residing in larger pores. To account for such a diverse behavior, this paper proposes a multiple permeability model, which divides shale media into three different permeability/porosity systems: fracture, matrix with large pores and matrix with small pores. We use a modified version of the Peng Robinson equation of state to model the equilibrium hydrocarbon distribution in large and small pores. Our thermodynamics calculations show that as pore dimeter decreases, the concentration of larger hydrocarbon molecules in those pores decreases because of size filtration. A synthetic reservoir model is used along with the multiple permeability model to analyze reservoir production behavior at different conditions. The so-called sieving effect is believed to be responsible for the anomalous production behavior (lower-than-expected or constant gas oil ratios for extended production periods). Our model is then applied to a real Eagle Ford case to history-match production data with the stimulated reservoir volume built upon the fracture microseismic data. The results show that our multiple permeability model provides a powerful tool to evaluate the complicated flow dynamics in liquid shales.
Algebraic Dynamic Multilevel Method for Compositional Simulations
Authors: Cusini M. , Fryer B. , Kruijsdijk C. P. , Hajibeygi H.
Published: February 2017

A dynamic multilevel compositional solver (C-ADM) is introduced for fully(and sequentially-) implicit systems arising from compositional displacements in natural porous media. The fully (or sequential) implicit system is first described at a fine-scale resolution, where phases are allowed to consist of different components (based on thermodynamics equilibrium). In addition, heterogeneous capillary functions (defined based on Leverett's J-function) and gravitational effects are both considered, adding significantly to the non-linear complexity of the processes. Given this complex fine-scale system for a heterogeneous reservoir, C-ADM defines a dynamic multilevel system, based on an error criterion, where the grid resolution is defined based on the physics of the process as well as geological complexities and location of wells. Once this multilevel grid is defined, sequences of prolongation and restriction operators are employed to obtain an accurate and efficient multilevel system. CADM allows for a general set of prolongation operators, e.g., constant, bilinear (or polynomial), and multiscale basis functions. The restriction operators, however, are constructed based on a mass-conservative finite-volume formulation at all levels. For several challenging test cases it is shown that C-ADM employs only a small fraction of the fine-scale grids to provide an accurate description of the process. C-ADM casts a promising approach in the application of dynamic grid refinement methods for real-field applications.
Simulation of Deviated Wells Using 3D Unstructured Grids of Flexible Resolution
Authors: Artus Vincent , Fructus Dorian , Houzé Olivier
Published: February 2017

A method is presented for the numerical simulation of wells with arbitrary trajectories using 3D unstructured grids, with a resolution that automatically adjusts to the simulation context: for pressure transient analysis (logarithmic time steps) or low permeability reservoirs a very fine grid is used. The grid is progressively coarsened when early-time transients can be ignored and/or mobility increases. Different discretization controls are applied for full late time consistency between the various resolutions.

A criterion is derived to determine the optimum grid resolution based on the mobility of the fluid in the vicinity of the wellbore and the smallest time step to simulate.

The finest grid uses a full 3D voronoi module around the wellbore, with cells of progressively increasing size away. This module is connected to a coarser background 2.5D voronoi grid for the bulk of the reservoir. Generalized transmissibility derivations accurately account for the well trajectory and estimate the fluxes across potentially non-orthogonal connections.

Progressively coarsened grids are then used to adapt to the problem. For relatively fine grids, generalized derivations of transmissibility and well index values capture the radial effects and avoid the numerical pseudo-skin typically observed with 2.5D grids.

As illustrated with various cases, such approach accurately and consistently simulates wells of complex geometries for all resolutions. The outcome is a new method for generating 3D unstructured grids that automatically adapt to the expected time resolution of the simulation, while ensuring consistency between transient and long-term simulations via original discretization controls.
Accurate Dual-Porosity Modeling of CO2 Storage in Fractured Reservoirs
Authors: March Rafael , Elder Herwald , Doster Florian , Geiger Sebastian
Published: February 2017

Naturally fractured reservoirs are currently being considered as potential candidates for geological storage of CO2. Simulations of fractured reservoirs are notoriously challenging. Dual-porosity models are a cost-effective way of representing fractured reservoirs whose fundamental ingredient are transfer functions that represent fracture-matrix interaction in an up-scaled manner. In order to develop accurate transfer functions, it is essential to capture the underlying physics of the fluid transfer. Material properties and dominant processes in CO2 storage differ from the ones in conventional production environments. In this contribution we develop a novel transfer function that accounts for these differences. We first analyse the simplifying hypotheses that are commonly made in the current existing transfer functions. Those simplifications lead to inaccurate results in the context of CO2 storage. We then develop a transfer function for buoyancy displacement based on the timescale of the one-dimensional equation for immiscible two-phase flow in porous media. We analyse how the newly developed transfer functions improve over the current existing ones in simple matrix-block geometries. The results are evaluated against high-resolution numerical simulations of matrix blocks considering realistic physical properties of CO2/Brine systems and fractured rocks. Our results show that the developed transfer functions are able to represent accurately the basic physics of the process, and improve over other existing transfer functions in the literature. The transfer functions are also implemented in a dual-porosity simulator and different CO2 injection scenarios are tested. We show that a careful design of the injection schedule may increase the mass of CO2 that is stored in the matrix block.
Simulation Capability Development for Four-Phase Flow through Porous Media
Authors: Fang Chen , Li Zhidong , Guo Weidong , Chempath Shaji , Selvam Balki , Lu Pengbo
Published: February 2017

Historically, numerical reservoir simulators have been mainly used to model three distinct phases, i.e., hydrocarbon liquid, vapor, and aqueous phases. Not surprisingly, most simulator architectures are designed and implemented within a three-phase framework, for both phase-equilibrium calculations and solving dynamic flow through porous media. Recently, many reservoir recovery processes involve more than one hydrocarbon liquid phase in subsurface, e.g., second hydrocarbon liquid phase forming in CO2 miscible / near-miscible injection, asphaltene deposition induced by gas injection, solvent-based Enhanced Oil Recovery (EOR) processes. Therefore, it is critical to accurately model the formation and flow of four separate phases in the reservoir, namely, heavy hydrocarbon liquid, light hydrocarbon liquid, vapor, and aqueous, or LLVA. Modeling the four-phase flow poses a series of significant numerical modeling challenges that most existing commercial simulators cannot address effectively and reliably. There have been numerous research and development efforts on this topic in both industry and academia. However, most of the proposed approaches require major architecture redesign and significant implementation revamp.

This paper highlights our simulation capability development for modeling four-phase flow in a computationally efficient and numerically stable manner while capturing the essential physics. First of all, we incorporate a newly-developed robust flash algorithm into the phase equilibrium calculations for the three hydrocarbon phases (LLV). Several algorithm improvements have been made to ensure stability and robustness of the flash engine over the full range of pressure and composition variation, without sacrificing computational efficiency. Secondly, a novel fit-for-purpose algorithm has been derived and implemented to model the four-phase (LLVA) flow within the conventional three-phase reservoir simulation framework, avoiding a major code rewrite. The particular algorithm is analytically rigorous and physically sound, suitable for multiple enhanced oil recovery (EOR) processes, for both heavy oil and light oil.

These unique modeling capability enhancements enable us to model complex recovery processes efficiently and effectively and provide the ability to understand the physical processes, design / optimize operating strategy, as well as predict reservoir performance.
Equation-of-State Approach to Model Relative Permeability Including Hysteresis and Wettability Alteration
Authors: Khorsandi Saeid , Li Liwei , Johns Russell T.
Published: February 2017

Commercial compositional simulators commonly apply correlations or empirical relations based on tuned experimental data to calculate phase relative permeabilities. These relations cannot adequately capture effects of hysteresis, fluid compositional variations and rock wettability alteration. Furthermore, these relations require phases to be labeled, which is not accurate for complex miscible or near miscible displacements with multiple hydrocarbon phases. Therefore, these relations can be discontinuous for miscible and near-miscible displacements causing inaccuracies and numerical problems in simulation.

This paper develops an equation-of-state (EoS) to model robustly and continuously the relative permeability as functions of phase saturations and distributions, fluid compositions, rock surface properties, and rock structure. Phases are not labelled; instead, the phases in each grid block are ordered based on their compositional similarity. Phase compositions and rock surface properties are used to calculate wettability and contact angles. The model is tuned to measured two-phase relative permeability curves with few tuning parameters and then used to predict relative permeability away from the measured experimental data. The model is applicable to all flow in porous media processes, but is especially important for low salinity polymer, surfactant, miscible gas and water-alternating-gas flooding. The results show excellent ability to match measured data, and to predict observed trends in hysteresis and oil saturation trapping including those from Land's model and for a wide range in wettability. The results also show that relative permeabilities are continuous at critical points and yields a physically correct numerical solution when incorporated within a compositional simulator (PennSim). The model has very few tuning parameters, and the parameters are directly related to physical properties of rock and fluid, which can be measured. The new model also offers the potential for incorporating results from CT-scans and pore-network models to determine some input parameters for the new EoS.
An Automated Adaptive Scheme for Asynchronous Coupled Flow and Geomechanics Simulation
Authors: Ita Joel , Malekzadeh Farshad , White Deandra
Published: February 2017

In a coupled reservoir fluid flow-Geomechanics simulation, the rate of change in the pore compressibility can be orders of magnitude different from pressure diffusion rate. The significant contrast between characteristic times of the two physical processes presents opportunities to optimize the amount of coupling required during the time evolution of the simulation via asynchronous (aka loose) coupling.

Examination of the governing equations for flow in a deformable porous medium reveals that the variation of the Lagrangian porosity (δφ) depends implicitly on the variation in pore pressure (δp) and also on the variation of the bulk strain (δε). However, the pore compressibility used in reservoir simulation supposes that (δφ) is a function of (δp) only. To accomplish this, past studies have employed chain-ruling where ∂ε/∂p is substituted to find an expression for (δφ) that is a function of (δp) only. In most cases, ∂ε/∂p is not known analytically and must be derived numerically using changes in strain and pressure seen at previous coupling stages during the time evolution of the simulation. Because of the reliance on previous history, the determination of when to take the next coupling step is usually based on an arbitrary condition like requiring a fixed number of time steps to occur in the flow simulation between coupling steps.

When a coupling step occurs, a posteriori error estimate of the pore volume change is made. The simulation continues if the error is sufficiently small. If the error is large, the simulation reverts to the state at the previously coupling step and a smaller time interval elapses before the next step is taken. Obviously, reverting to a previous step is inefficient and should be avoided. Given that the error is governed by how closely the numerical determination of ∂ε/∂p is to its actual value over the time period considered and that the actual value of ∂ε/∂p depends on the heterogeneity in the subsurface as well as the rate of hydrocarbon production, a physically based coupling criterion is required for maximal efficiency.

Here, results are shown from simulations where the error in ∂ε/∂p is estimated a priori based on the rate of change of pressure. This information is then used to estimate when a significant error in porosity has accumulated which triggers a coupling step. Additionally, in each coupled time step, the actual error is calculated and use of this information results in an automated coupling method that is self-corrective and unconditionally stable. This scheme also exhibits a significant performance gain compared to other common schemes utilizing arbitrary or time based conditions for coupling when accuracy is taken into consideration.
Influence of Foam on the Stability Characteristics of Immiscible Flow in Porous Media
Authors: van der Meer J. M. , Farajzadeh R. , Jansen J. D.
Published: February 2017

Accurate field-scale simulations of foam enhanced oil recovery are challenging, due to the sharp transition between gas and foam. Hence, unpredictable numerical and physical behavior is often observed, casting doubt on the validity of the simulation results. In this paper a thorough stability analysis of the foam model is presented, to validate the simulation results and lay a foundation for a tailor-made solver, which can both handle large-scale reservoir simulations and accurately resolve front instabilities. We study the effect of a strongly non-monotonous total mobility function arising from foam models on the stability characteristics of the flow. To this end, we generalize the linear stability analysis of Riaz and Tchelepi (2004–2007) to nearly discontinuous relative permeability functions, and compare the results with those of highly accurate numerical simulations. In addition, we present a qualitative analysis for the effect of different reservoir and fluid properties on the foam fingering behavior. In particular, we consider the effect of heterogeneity of the reservoir, injection rates, and foam quality. Relative permeability functions play an important role in the onset of fingering behavior of the injected fluid (Riaz and Tchelepi, 2006a). Hence, we can deduce that stability properties are highly dependent on the nonlinearity of the foam transition. The foam-water interface is governed by a very small total mobility ratio, implying a stable front. The transition between gas and foam, however, exhibits a huge total mobility ratio, leading to instabilities in the form of viscous fingering. This implies that there is an unstable pattern behind the front. An indication of this behavior was shown in (Farajzadeh et al., 2016) for a similar foam model, but the authors did not provide a satisfying explanation for the cause of these instabilities. Here we closely study the influence of the foam on instabilities at and behind the front, and are able to predict the flow stability for different foam qualities. We deduce that instabilities are indeed able to grow behind the front, but are later absorbed by the expanding wave. The stability analysis, validated by numerical simulations, provides valuable insights about the important scales and wavelengths of the foam model. In this way we remove any ambiguity regarding the effect of grid resolution on the convergence of the solutions. This makes it possible to design a suitable computational solver that captures all the appropriate scales, while retaining computational efficiency.
Inexact Hierarchical Scale Separation: An Efficient Linear Solver for Discontinuous Galerkin Discretizations
Authors: Thiele Christopher , Araya-Polo Mauricio , Alpak Faruk O. , Riviere Beatrice , Frank Florian
Published: February 2017

Hierarchical scale separation (HSS) is a new approach to solve large sparse systems of linear equations arising from discontinuous Galerkin (DG) discretizations. We investigate its applicability to systems stemming from the nonsymmetric interior penalty DG discretization of the Cahn-Hilliard equation, discuss its hybrid parallel implementation for large-scale simulations, and compare its performance to a widely used iterative solver. The solution of the linear systems, in particular in massively parallel applications, is a known performance bottleneck in direct numerical approaches.

HSS splits the linear system into a coarse-scale system of reduced size corresponding to the local mean values of the DG solution, and a set of decoupled local fine-scale systems corresponding to the higher order components of the DG solution. The scheme then alternates between coarse-scale and fine-scale system solves until both components converge, employing a standard iterative solver for the coarse-scale system and direct solves for the set of small fine-scale systems, which allow for an optimal parallelization. The motivation of HSS is to increase parallelism by decoupling the linear systems, therefore reducing the communication overhead within sparse matrix-vector multiplications of classical iterative solvers. Providing some mild assumptions on the underlying DG basis functions, the above-mentioned splitting can be done on the resulting linear systems (i. e. without knowledge of the numerical scheme), which further motivates the development of the HSS scheme as a blackbox solver for DG discretizations.

We propose a modified HSS algorithm ("inexact HSS," IHSS") that shifts computation to the highly parallel fine-scale solver, and thus reduces global synchronization. The key result is that the IHSS scheme significantly speeds up the linear system solves and outperforms a standard GMRES solver (up to 9x speedup for some configurations). A hybrid parallel IHSS solver has been implemented using the Trilinos package. Its convergence for linear systems from the Cahn-Hilliard problem is verified, and its performance is compared to a standard iterative solver from the same package. In the future, IHSS may possibly be used as a blackbox solver to speed up DG based simulations, e.g., of reservoir flow or multicomponent transport.
Well Trajectory Optimization Constrained to Structural Uncertainties
Authors: Hanea R. G. , Casanova P. , Wilschut F. Hustoft , Fonseca R. M.
Published: February 2017

A key objective in any reservoir development plan is to achieve maximum reservoir exploitation which is usually quantified using an economic objective such as net present value (NPV). A key element of such an optimized development plan is an optimized well planning scheme (number, placement and trajectories of the wells). In the well planning phase, it is important to quantify the geological uncertainty. In this study, a new approach is presented in which the targets and thereby the trajectories of the wells are optimized while the geological uncertainties are taken into account. The latter is achieved by using an ensemble of updated reservoir models resulting from assisted history matching (AHM) as the input for the optimization of the field development plan. For the case presented in this study, the reservoir structure, more specific the top and bottom of the reservoir, is assumed to be the main source of uncertainty. To optimize the well targets and trajectories, the Stochastic Simplex Approximate Gradients (StoSAG) methodology is used. A parameterization of the well path is proposed, in which the angles, azimuths and measured depths of the targets are used as controls to optimize the trajectories of the horizontal wells. With this parameterization, the horizontal section is not always straight, in contrast to the approaches presented in many previous publications. The proposed workflow has been applied successfully on a realistic synthetic case inspired from a real field case. The results show that significant increases in objective function can be achieved when well trajectories are optimized constrained to uncertainties in the structural model.
Localized Solvers for General Full-Resolution Implicit Reservoir Simulation
Authors: Sheth Soham M. , Younis Rami M.
Published: February 2017

In the solution of implicit reservoir simulation timesteps, the Newton iteration updates are often very sparse; this sparsity can be as high as 95% and can vary dramatically from one iteration to the next. We develop, implement and demonstrate a mathematically sound adaptive framework to predict this sparsity pattern before the system is solved. The development first mathematically relates the Newton update in functional space to that of the discrete system. Next, the Newton update formula in functional space is homogenized and solved in such a way that it results in conservative estimates of the numerical Newton update. The cost of evaluating the estimates is linear in the number of nonzero components. The estimates are used to label the components of the solution vector that will be nonzero, and the corresponding submatrix is solved. The computed result is guaranteed to be identical to the one obtained by solving the entire system.

When applied to various simulations of three-phase flow recovery processes in the SPE 10 geological model, the observed reduction in computational effort ranges between four to tenfold depending on the level of total compressibility in the system, the time step size and on the degree of complexity in the underlying physics. We show the extensions to the case of flow and multicomponent transport where the reduction in computation effort ranges between four to tenfold. The improvement in computational speed scales strongly with the number of transport components, and to a lesser degree with problem size. The results of the localized and full simulations are identical, as is the nonlinear convergence behavior.
A Multi-Porosity, Multi-Physics Model to Simulate Fluid Flow in Unconventional Reservoirs
Authors: Wang Cong , Xiong Yi , Huang Zhaoqin , Winterfeld Philip , Ding Didier , Wu Yu-Shu
Published: February 2017

Gas flow in shales is complicated by the highly heterogeneous and hierarchical rock structures (i.e., ranging from organic nanopores, inorganic nanopores, less permeable micro-fractures, more permeable macro-fractures, to hydraulic fractures). The dominant fluid flow mechanism varies in these different flow regimes, and properties of these rock structures are sensitive to stress changes with different levels. Although traditional single-porosity and double-porosity models can simulate certain time range of reservoir performance with acceptable accuracy, they are not generally applicable for the prediction of long-term performance and have limitations to improve our understandings of enhanced hydrocarbon recovery. In this paper, we present a multi-domain, multi-physics model, aiming to accurately simulate the fluid flow in shale gas reservoirs with more physics-based formulations.

An idealized model has been developed for the purpose of studying the characteristic behavior of a fractured nanopore medium, which contains five regions: organic nanopores, inorganic nanopores, local micro-fractures, global natural fractures, and hydraulic fractures. Fluid flow governing equations in this model vary according to the different dominant fluid flow mechanisms in different regions. For example, the apparent permeability, which is the intrinsic permeability multiplied by a correction factor, is used to account for the gas slippage through nanopores of shale matrix; while the organic and inorganic nanopores in this matrix have different capacities for gas adsorption. On the other hand, for fluids flow in natural fractures and hydraulic fractures with high velocity, the non-Darcy flow model is used to capture the strong inertia when is comparable to viscous force.

Numerical studies with practical interests are discussed. Several synthetic, but realistic test cases are simulated. Input parameters in these cases are evaluated using either the laboratory or theoretical work. Our results demonstrate that this model is able to capture the typical production behavior of unconventional reservoirs: a great initial peak, the sharp decline in the first few months, followed by a long flat production tail. A series of sensitivity analyses, which address the organic matter content, organic matter connectivity, natural fracture density, and hydraulic fracture spacing, will also be conducted.
Pressure Coupling for Geomechanical Multi-Phase Flow Simulation Using Vertex Centered Flow Elements and Unstructured Grids
Authors: SAMIER Pierre
Published: February 2017

Significant work has been done for generating unstructured grids. Coupled geomechanics simulation and hydraulic fracture flow for gas shale simulation have given a new impulse for unstructured gridding.

The objective of the paper is to couple flow and geomechanics using unstructured grid models, to demonstrate the ability to apply a more efficient pressure coupling using discretization at vertices on both sides (mechanical and flow equations).

Coupled equations are discretized and solved on an unstructured flow grid and a geomechanical finite element grid which are composed of various types of elements such as tetrahedrons and hexahedrons. On the flow side, a recent multi-point flux method, the Vertex Approximate Gradient (VAG) (Eymard 2012) is investigated for solving the reservoir equations on such unstructured grid. SPE paper 173309 (Samier, Masson 2015) presented the implementation of VAG scheme inside a next generation reservoir simulator designed for handling unstructured grids. This paper proposes an iterative coupling scheme with full pressure coupling at vertices. The geo-mechanics equations fully coupled to a single phase flow are solved using global pressure.

Then the resulting deformations are iteratively coupled to the multi-phase flow simulator.

Since most geo-mechanic simulators propose fully coupled single phase flow features, the main advantage of this method is the ability to use a full pressure coupling method with industrial simulators.

The convergence of this new scheme is discussed and results are presented for two cases described below. The two cases are validation cases used by other SPE papers. Faults are modeled using specific cohesive elements. Results are compared with standard loose iterative coupling method using TPFA cell centered elements.

SPE paper 173232 (RSS 2015, Doster et al) presented a full pressure coupling method using cell centered elements. The aim of the paper is to extend the method to unstructured grids and to vertex centered elements which are more adequate for a coupled problem since the multi-phase flow pressures, component masses and displacements unknowns are now discretized at the same location.
Optimization Based Isenthalpic Flash for Thermal Reservoir Simulations
Authors: Chempath Shaji , Sun Huafei , Haugen Kjetil
Published: February 2017

We present an algorithm for multiphase isenthalpic phase-equilibrium calculations. The algorithm addresses issues related to robustness and performance of isenthalpic flash, which sometimes get aggravated due to narrow boiling conditions. The isenthalpic flash is posed as an optimization of total system entropy for the given input conditions: pressure, system enthalpy, and composition of the mixture. We use a second-order optimization method to maximize entropy, with the individual phase-compositions and phase-enthalpies as the independent variables. At any point during the iterative solution procedure, the direction of the iterative step can be checked by ensuring an increase in entropy. During the iterations we allow phases to be split further into sub-phases to tackle the issue of a phase having multiple roots for the specified enthalpy (the phase is at boiling point temperature). We successfully apply the method to calculate the phase diagrams for many hydrocarbon mixtures. We have shown that the isenthalpic flash with entropy maximization works robustly in all the cases tested, including the narrow-boiling examples. Result of applying the flash to fluids with two hydrocarbon phases and a simplified water and rock phase is also presented.
A Mixed Natural and Concentration Variable Formulation for Chemical Flood Simulation
Authors: Shi Xundan , Han Choongyong , Wolfsteiner Christian , Chang Yih-Bor , Schrader Mark
Published: February 2017

Correlations for PVT properties used in chemical flood simulation are frequently written in concentration variables. Therefore, a mixed variable formulation has been proposed to implement chemical flooding option in an existing natural variable simulator. The new formulation results in a straightforward and efficient implementation of published PVT correlations as well as fast convergence.

A new three-layer pseudo component framework (i.e., phase – pseudo component – pure component) has been adopted to effectively model a group of pure components that can have the same composition and properties in each phase where it exists while allowing the flexibility of using different variable types on the pure component level, such as phase mole fraction and molar concentration. This ensures the same composition for pseudo component in different phases without introducing extra constraint equations.

In our implementation, we use a symmetric binodal curve and tie lines to describe the liquid phase behavior based on the pseudo-component concept. Phase densities and viscosities are computed using correlations with corresponding pseudo-component values and volumetric concentrations. A Corey-type relative permeability model and shear thinning effect on viscosity are also implemented. Furthermore, both cation exchange on surfactant/clay and adsorption of polymer/surfactant on rock are efficiently implemented.

Our algorithms have been validated against other state-of-the-art chemical flood simulators with both small conceptual test cases and large scale models. A very good agreement in results and a high nonlinear performance have been observed.

Mixed natural and concentration variable formulation proposed in this paper is a novel method to implement chemical flood capability in an existing natural variable simulator. The combination of mass and natural variables for surfactant flood simulation into a single formulation is an industry first. Its extensibility and robustness give us confidence for further extensions along these lines.
New Formulations for Isothermal Multiphase Flash
Authors: Paterson D. , Michelsen M. L. , Stenby E. H. , Yan W.
Published: February 2017

Two algorithms are proposed for isothermal multiphase flash. These are referred to as modified RAND and vol-RAND. The former uses the chemical potentials and phase amounts as the iteration variables while the latter uses chemical potentials and phase volumes to co-solve a pressure explicit equation of state with the equilibrium equations. When compared to the conventional approach of treating a single phase as dependent, these methods are more structured with all components in all phases treated in the same way. Both have been derived to include chemical reactions for any number of phases along with the possible simplifications for purely phase equilibria.
Numerical Modelling of Hybrid Steam and In-Situ Combustion Performance for Oil Sands
Authors: Yang Min , Harding Thomas G. , Chen Zhangxin , Yu Kuizheng , Liu Hui , Yang Bo , He Ruijian
Published: February 2017

Steam injection is a widely used thermal technology to recover heavy oil and oil sands resources, while high operating costs have made it vulnerable to low crude oil prices. In-Situ Combustion (ISC) provides an alternative to steam injection with the advantage of low operating costs and high energy efficiency. Hybrid steam and ISC has great potential in oil sands recovery because it combines the advantages of both steam injection and ISC. Before design of this hybrid process, it is important to understand the displacement mechanisms during this hybrid process.

In this study, numerical simulation has been performed to investigate the performance of co-injection of an air and steam process at the experimental scale. A three-dimensional radial numerical model has been developed using CMG STARS to simulate a steam flood test and a combustion tube test. The co-injection of enriched air and steam was performed after a period of hot water flooding in the combustion tube test. Simulated temperature profiles and combustion front velocities were matched with experimental measured results, indicating that the high temeprautre oxidation (HTO) reactions were captured in the simulation. In order to understand displacement mechnisms, simulation results obtained from both tests have been compared and analyzed, including temperature profiles, a steam front velocity, residual oil saturation, and oil recovery.

It is found that co-injection of steam and enriched air has the potential to improve oil recovery. An ultimate recovery factor of around 90% is achieved for the co-injection of the steam and enriched air process, while the recovery factor is around 60% for the steam flooding test. This is because ISC is able to recover residual oil left behind by the steam flooding. However, steam still plays a dominant role in displacement of bitumen. The steam front propagates faster than the combustion front. Also, the steam front travels faster with the presence of the combustion front, indicating that the combustion front behaves as a heat source for steam front propagation. This work greatly increases the understanding of displacement mechanisms in a hybrid steam and combustion process.