bluuebunny/crossref_metadata_2025 huggingface dataset:
Parallel Computation for Complex Wells Modeling in Full-Field Reservoir Simulation
Authors: Al-Shaalan T. M. , Dogru A. H. , Al-Youbi A. H. , Ismail H.
Published: February 2017

This paper discusses the parallel implementation of complex wells modeling in a large-scale simulation. Due to intensive computational requirements of giant reservoirs with hundreds of these complex wells, parallel implementation is essential for practical simulation studies. In this work, a distributed memory approach using message passing interface (MPI) is employed for parallelization where each processor is responsible for the computation of one or more complex wells. For inter-processor communication, a non-blocking technique is utilized to increase the parallel efficiency. Parallel implementation is not the only challenge for large-scale simulation. For instance, full-field simulation with hundreds of complex wells increases the probability of a nonconvergence solution for at least one or more complex wells during reservoir simulation. Robust algorithms are needed to guarantee convergence and improve performance. Therefore, in this paper, we propose treating complex wells as a subsurface network where it can be represented using graph theory. In addition, simulation results for a full-field with hundreds of intelligent complex wells are included. This will show the importance of well coupling with rigorous treatment of downhole controls and devices on accurately modeling large-scale and complex reservoir.
An Improved Boundary Element Method for Modeling Fluid Flow through Fractured Porous Medium
Authors: Cao Yang , Killough John E.
Published: February 2017

To accurately capture the flow behavior and dynamics in fractured reservoirs, a theoretically sound, and practically robust boundary element method (BEM) numerical algorithm has been developed and successfully implemented. Explicit and discrete fracture description is adopted in this approach, and the complex fracture settings and interactions can be effectively simulated. Modules characterizing the transient flow dynamics and the flow dependence on matrix heterogeneity, which are seldom studied by previous researchers through a BEM approach, have also been established and investigated.

Specifically, our model starts from two simplifications: the flow inside the fractures is treated as twodimensional, and the fractures can be equivalently seen as planar source or sink entities interacting with the matrix. In our approach, only the matrix boundaries and fractures are discretized into small elements, and each element associates with either one or two unknowns. Two sets of equations generated from the above two simplifications are used to relate these unknowns and solve the problem. And when the flow transientness and matrix heterogeneity are concerned, additional internal matrix points are selected and taken into computation, following the procedure of the dual reciprocity boundary element method (DRBEM).

Several case studies have been conducted, and result comparison indicates the validity of this approach. Finally the strength and weakness of our approach are also discussed in this paper.
A Physics-Based Data-Driven Model for History-Matching, Prediction and Characterization of Waterflooding Performance
Authors: Guo Zhenyu , Reynolds Albert C. , Zhao Hui
Published: February 2017

We develop a new data-driven model for the assisted history matching of production data from a reservoir under waterflood. Although the model is developed from production data and requires no prior knowledge of rock property fields, it incorporates far more fundamental physics than that of the popular capacitance-resistance model (CRM). The new model also represents a substantial improvement on an interwell numerical simulation model (INSIM) which was presented previously in a paper co-authored by the last two authors of the current paper. The new model, which is referred to as INSIM-FT, eliminates the three deficiencies of the original INSIM data-driven model. (1) For some complex cases, e.g., when a producer is converted to an injector or when injected water from more than one injector passes through an intermediate well node, the INSIM procedure for calculation of water saturation degrades to an ad hoc calculation which introduces inaccuracies. Our new model uses an accurate front-tracking procedure to calculate water saturation, hence the name INSIM-FT. (2) The original INSIM formulation assumes relative permeabilities are known a priori which defeats the objective of finding a model without requiring knowledge of petrophysical properties; INSIM-FT estimates relative permeabilities by historymatching. (3) Unlike CRM, the original INSIM model does not provide a reasonable characterization of how water from an injector is allocated among producers and thus does not reliably identify large-scale geological features such as faults. INSIM-FT remedies this INSIM deficiency.

The reliability of INSIM-FT for history-matching, future reservoir performance prediction and reservoir characterization is validated with two synthetic models, and its performance is compared with that of CRM. Finally, INSIM-FT is applied to a field case.
GPU-Offloaded General Purpose Simulator for Multiphase Flow in Porous Media
Authors: Khait Mark , Voskov Denis
Published: February 2017

Reservoir simulation plays an important role in the petroleum industry. Today, there is a specific demand to run ensembles of megaand even giga-cell models. The iterative solution of the large systems of nonlinear governing equations, which describe the multiphase mass transfer in the subsurface, takes the most of the simulation time. The linearization part of the solution process occupies a significant fraction of that time, especially in compositional models. Moreover, the implementation of the linearization step usually embodies the most substantial, complex, and specific part of the computational loop in modern simulators, defining which physical mechanisms and assumptions are employed. This significantly complicates the implementation of simulation codes for heterogeneous computing hardware, which promises significant improvements in simulation time. In this work, we use the recently proposed Operator-Based Linearization (OBL) approach to develop a general purpose reservoir simulation code aiming to substantially decrease the simulation time. OBL offers a simplified linearization method, enhancing the computational performance of simulation and providing an opportunity of a painless porting to heterogeneous computing architectures. To distinct the contribution of both factors, we developed two versions of the compositional simulation prototype code: for traditional CPU and GPU-accelerated hardware architectures. While the former allowed us to speed the linearization stage up by an order of magnitude in comparison with the conventional approach, based on Automatic Differentiation (AD), the latter improved it further by another order of magnitude. The developed prototype realizes the potential of the OBL approach and GPU computing architecture, proving significant improvement in general purpose simulation performance.
The Order of Accuracy of the Fixed-Stress Type Two-Pass and Deferred Correction Methods for Poromechanics
Authors: Yoon H. C. , Kim J.
Published: February 2017

We study the order of accuracy in time discretization for poromechanics, applying the fixed-stress split scheme. High-order methods in time are often used, for example, in order to match high-order schemes in space. We consider two operator splitting methods motivated from the fixed-stress split: a two-pass algorithm and a spectral deferred correction (SDC) method. The two-pass algorithm, known for a symmetric operator splitting scheme as Strang's splitting, is typically employed for a high-order method of non-stiff ordinary differential equations (ODEs). The SDC method is also a structure conserving efficient scheme for an arbitrary high-order of accuracy. However, poromechanics yields the governing equations that have a form of differential algebraic equations (DAEs), where typical high-order time integration schemes for non-stiff ODEs are not appropriate. Performing mathematical analysis, we find that both methods do not achieve high-order accuracy in poromechanics, although both methods can reduce the errors in their time discretizations. From numerical experiments, we find that the mathematic estimates are consistent with the numerical results of the fixed-stress type two-pass and SDC methods, which still provide the first-order accuracy in time.
Unstructured Gridding and Consistent Discretizations for Reservoirs with Faults and Complex Wells
Authors: Klemetsdal Ø. S. , Berge R. L. , Lie K.-A. , Nilsen H. M. , Møyner O.
Published: February 2017

This work consists of two parts. In the first part, we present new methods for generating unstructured polyhedral grids that align to prescribed geometric objects. Control-point alignment of cell centroids is introduced to accurately represent horizontal and multilateral wells, but can also be used to create volumetric representations of fracture networks. Boundary alignment of cell faces is introduced to accurately preserve geological features such as layers, fractures, faults, and/or pinchouts. Prescribed geometric objects will often intersect each other. To handle such cases, we propose a conflict-point handling scheme that creates conforming cells even at intersections. We also discuss how to generalize this method to 3D. Here, our method honors control-point alignment of cell centroids and boundary alignment of cell faces away from object intersections.

The predominant discretization method for multiphase flow in reservoir simulation is the two-point flux-approximation (TPFA) method. This finite-volume method is mass conservative, but only conditionally consistent and hence susceptible to grid-orientation effects. In the second part of the paper, we review a series of consistent methods and compare and contrast these methods both with respect to accuracy and monotonicity. Our comparisons include a multipoint flux-approximation (MPFA-O) method, the nonlinear TPFA method, mimetic methods, and the more recent virtual element methods. To limit the discussion, we focus on incompressible flow, for which we study the effects of deformed cell geometries, anisotropic permeability, and robustness with respect to various approaches to grid near wells and adapt it to lower-dimensional objects like faults and fractures.
Compositional Reservoir Flow Simulation for Organic-Rich Gas Shale
Authors: Olorode O. M. , Akkutlu I. Y. , Efendiev Y.
Published: February 2017

A new-generation compositional reservoir flow simulation model is presented for organic-rich shale gas formations including convective-diffusive mass balance equations for hydrocarbon components in organic (kerogen), inorganic and fracture continua. The model presented accounts for the presence of dispersed kerogen with sorbed-gas corrected dynamic porosity. Maxwell-Stefan theory is used to predict pressureand composition-dependence of molecular diffusion in the formation. The equations are discretized and solved numerically using control volume finite element method.

The simulation is based on a new multi-scale conceptual flow model. We consider that kerogen is dispersed at a fine scale in the inorganic matrix and that it will be the discontinuous component of total porosity at the reservoir simulation scale, which could be up to six orders of magnitude larger. A simple mass balance equation is introduced to enable kerogen to transfer gas to the inorganic matrix that is collocated in the same grid-block. The convective-diffusive transport takes place between neighboring grid blocks only in the inorganic matrix.

The simulation results show that the multi-scale nature of the rock is important and should not be ignored because this could result in an overestimation of the contribution of the discontinuous kerogen. We also observe that although adsorbed fluid could contribute significantly to storage in the shale formation, its contribution to production could be severely limited by the lack of kerogen continuity at the reservoir scale and by a low degree of coupling between the organic and inorganic pores. The contribution of Maxwell-Stefan diffusion to the overall transport in the shale formation increases as the inorganic matrix permeability is reduced due to pressure decline during production.
Multiphase Thermal Compositional Wellbore Modeling in Hybrid Steam/Solvent Injection
Authors: Almeida Rafael Valladares , Rahnema Hamid
Published: February 2017

Solvent aided steam injection is one of the most promising enhanced oil recovery methods for recovering heavy oil and oil sands. Experiments, simulations, and some field pilots have demonstrated that a hybrid steam and solvent injection can result in better production rates and higher ultimate oil recovery. However, the simulation studies assume that the steam and solvent mixture will be at the sandface in pre-determined pressure, temperature, and steam/solvent gas molar ratios, neglecting the pressure gradients, heat losses, and condensations that occur along the wellbore, which will affect the thermodynamic condition of the mixture at the perforation zones. This paper provides important background information regarding the wellbore numerical modeling in hybrid steam/solvent injection. Detailed formulations of pressure gradient and enthalpy calculations are described, and we investigate the effect of partial pressure on the condensation behavior of steam and solvent. The benefits of the model on the steam and solvent co-injection process optimization are examined with three case studies, where steam is co-injected with a) gas condensate, b) medium weight solvent, and c) heavy weight solvent. Gas condensate is unlikely to condense in the wellbore. However, medium and heavy weight solvents might condense depending on the steam and solvent ratios. To avoid solvent condensation, it is suggested to reduce the solvent ratio compared to steam, or to increase the steam quality at the wellhead. As a result, the solvent partial pressure will be reduced.
Uncertainty Quantification for Foam Flooding in Fractured Carbonate Reservoirs
Authors: Almaqbali A. , Spooner V. E. , Geiger S. , Arnold D. , Mackay E.
Published: February 2017

When simulating foam floods, uncertainties exist in both the foam and reservoir parameters however the combination of these uncertainties are rarely incorporated in forecasting. Foam flooding is an effective enhanced oil recovery method that controls mobility, reduces gas relative permeability, delays gas breakthrough and helps improve sweep efficiency. Thus it is often used in highly heterogeneous reservoirs where significant subsurface uncertainties exist. Foam uncertainties exist as (a) foam stability is controlled by a number of factors such as critical water and surfactant concentrations, brine salinity, and oil saturation which are unknown in the subsurface spatially and (b) foam flood simulation requires the accurate description of multiple parameters used in the foam flood models which are unknown.

This study quantifies and compares the impact of uncertainties associated with foam model parameters with the heterogeneity of a fractured carbonate reservoir, an analogue to the highly prolific Arab D formation. Foam model parameters are not known a-priori but can be tuned to experimental data, which ideally represent a range of foam regimes and reservoir conditions. Geological heterogeneities in fractured carbonate reservoirs are complex and include, matrix wettability, fracture density/orientation and initial saturation distribution.

To quantify uncertainties geological uncertainties in fractured carbonate reservoirs, an automated framework was used to history match the production response of a fractured carbonate field by varying geological parameters. This accounts for the geological uncertainties during a waterflood, which are then combined with foam uncertainties from experimental analysis in the optimisation step, by optimising the mean response of the model to foam flooding across a range of geological and foam scenarios. Our workflow used a combination of Particle Swarm Optimisation for history matching and manual optimisation, the final results of which show a wide range of possible impacts of foam flooding from different but equally well matched reservoirs.

The novelty of our work is that it demonstrates how parameters that control foam stability and hence effectiveness in mobility control are related to both foam properties and geological uncertainty. Carrying these uncertainties into foam model properties from core to field scale will translate into considerably more robust estimates of uncertainty when predicting field-scale recovery compared to simulations that only consider uncertainty in the reservoir model.
A Non-Orthodox MPFA Method Coupled to a High Order Modified Flow Oriented Scheme for the Simulation of Two-Phase Flows in Heterogeneous and Anisotropic Reservoirs
Authors: Contreras F. R. , Souza M. R. , Lyra P. R. , Carvalho D. K.
Published: February 2017

In this paper, we propose a full finite volume approach to simulate two-phase flows of oil and water in heterogeneous and anisotropic petroleum reservoirs in 2-D. The IMPES procedure is used to solve the coupling between the pressure and the saturation equations. The eliptic pressure equation is discretized by a non-orthodox linear Multi-Point Flux Approximation (MPFA-HD) method capable to handle heterogeneous and highly anisotropic media. Following the MPFA-D (MPFA-Diamond) scheme and some existent non-linear cell centered strategies, the key point in the construction of our scheme is the discretization of the flux across each cell face. First, we construct the one-sided fluxes on each cell independently and then, we integrate both one-sided fluxes over the control surface and finally we express the cell edge fluxes as a convex combination of the one side fluxes, to obtain a unique flux expression. On the other hand, differently from the MPFA-D, in our scheme, fluxes on each cell face are explicitly expressed by one cell centered unknown defined on the cells sharing that face and two auxiliary unknowns defined at two face endpoints that do not necessarily belong to the same face shared by the adjacent cells. These auxiliary vertex unknowns are eliminated by a proper interpolation. To solve the saturation equation, we propose a Modified Flow Oriented Scheme (M-FOS). This flow oriented variant explicitly computes the multidimensional numerical fluxes by using higher order accuracy in space. Besides, for problems with distorted meshes, the proposed formulation takes into account the angular distortion of the computational mesh by means of an adaptive weight, that tunes the multidimensional character of the formulation according to the grid distortion. This strategy diminishes the occurrence of Grid Orientation Effects (GOE). In order to avoid spurious oscillations in higher-order approximations, a recently devised Multidimensional Limiting Process (MLP) is adopted. This strategy guarantees monotone solutions and can be used with any polygonal mesh. Finally, an entropy fix strategy is also employed in order to produce convergent solutions. The performance of our numerical formulation is evaluated by solving some benchmark problems.
A Multiscale Restriction-Smoothed Basis Method for Compositional Models
Authors: Møyner O. , Tchelepi H.
Published: February 2017

Compositional simulation is attractive for a wide variety of applications in reservoir simulation and it is especially valuable when modeling gas injection for enhanced oil recovery. Since the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the gas front and the pressure propagation. Unfortunately, discretizing a compositional flow system with many components on a high-resolution geological model leads to very large and poorly conditioned linear systems, and the high computational cost of solving these systems tends to render field- scale simulations infeasible. An additional challenge is the need for phase-equilibrium calculations, which often represent a large fraction of the computational time when both gas and liquid are present.

We present a multiscale solver for compositional three-phase flow problems in which the behavior of the liquid and vapor phases are described by generalized cubic equations of state. The solver relies on a total-mass and overall composition based sequential solution strategy for the flow and transport equations and uses restricted smoothing to compute multiscale basis functions on unstructured grids with general polyhedral cell geometries. The resulting method computes approximate pressure solutions (to within a prescribed residual tolerance) that have conservative fluxes on the reduced computational grid, the original fine-scale grid, or any intermediate partition.

The new method is verified against existing compositional simulators on conceptual models and validated on more complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, pinched and eroded cells, etc.

The resulting implementation is the first demonstrated multiscale method applicable to general compositional problems relevant for the petroleum industry, which includes a cubic equation of state and stratigraphic grids.
A General Non-Uniform Coarsening and Upscaling Framework for Reduced-Order Modeling
Authors: Lie K.-A. , Kedia K. , Skaflestad B. , Wang X. , Yang Y. , Wu X.-H. , Hoda N.
Published: February 2017

This paper presents a general framework for constructing effective reduced-order models from an existing high-fidelity reservoir model, irrespective of grid topology. We employ a flexible hierarchical grid coarsening strategy that is designed to preserve geologic features and structures in the underlying model such as environments of deposition and faults. The strategy supports selecting and combining coarsening methods that are targeted to the flow patterns in different parts of the reservoir. This includes, but is not limited to, explicit user-imposed boundaries, using efficient field-wide flow indicators, topological and geometric partitioning and methods for amalgamating and splitting clusters of cells.

Collectively, these schemes enable an automatic strategy that separates a model into flow-dependent compartments that are respectively close to, far away from, or in between regions of sharp flow transients such as wells. These compartments may then be coarsened using different tailored techniques and target grid resolutions providing much more flexibility compared to traditional coarsening methods. We demonstrate that various techniques for flow-based transmissibility upscaling can be deployed on the resulting coarsened model to compute effective model properties. The hierarchical construction strategy allows efficient exploration of the geologic features of a reservoir that most impact flow patterns and well communication. The coarsened models are shown to be rank and trend accurate, enabling a more exhaustive sensitivity analysis if needed. We study the accuracy of the reduced-order model with a particular emphasis on the upscaled model's ability to capture effects of multiple phases in simulation runs compared to the full high-fidelity model.
Online Adaptive POD-DEIM Model Reduction for Fast Simulation of Flows in Heterogeneous Media
Authors: Yang Yanfang , Gildin Eduardo , Efendiev Yalchin , Calo Victor
Published: February 2017

In the paper, we propose an online adaptive POD-DEIM model reduction method for fast multiscale reservoir simulations in highly heterogeneous porous media. The approach uses Proper Orthogonal Decomposition (POD) Galerkin projection to construct a global reduced system. The nonlinear terms are approximated by the Discrete Empirical Interpolation Method (DEIM). To adapt at the online stage the states (velocity, pressure and saturation) of the system, we incorporate new data, as it becomes available. Once the criterion for updates is satisfied, we adapt the reduced system online by updating the POD subspace and the DEIM approximation of the nonlinear functions. These global online basis function updates improve the accuracy of snapshot approximation. Since the adaption is performed infrequently, the new methodology does not add a significant computational overhead due to the adaptation of the reduced bases. Our approach is particularly useful for situations where one needs to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method is able to construct a robust reduced system even if an initial poor choice of snapshots is used. We demonstrate with a numerical experiment to demonstrate the efficiency of our method.
Data-Driven Metric Learning for History Matching
Authors: Miller Jacob , Thiagarajan Jayaraman J. , Bremer Peer-Timo , Hoda Nazish , Stern Dave , Mifflin Rick
Published: February 2017

History matching, a highly non-unique inverse problem, is critical to calibrate model parameters in many scientific applications. A typical approach to history matching is to start with a uniform sampling of the high-dimensional parameter space and employ a surrogate modeling based black-box optimization to perform sequential sampling. Though this general workflow has been well studied, the problem of choosing an appropriate merit function to compare time-varying simulation outputs has been overlooked. Instead, convenient metrics such as the L2 or the LI-norm are employed. In this paper, we show that choosing an appropriate metric can significantly improve the solutions of sequential sampling. To this end, we propose a metric learning technique, develop a sequential sampling pipleline with the metric, and demonstrate its superiority to the conventional L2-norm metric.
Generation of a Proposal Distribution for Efficient MCMC Characterization of Uncertainty in Reservoir Description and Forecasting
Authors: Li Xin , Reynolds Albert C.
Published: February 2017

Generating an estimate of uncertainty in production forecasts has become almost standard in the oil industry but is often done with procedures that yield at best a highly approximate uncertainty quantification. Formally, the uncertainty quantification of a production forecast can be achieved by generating a correct characterization of the posterior probability density function (pdf) of reservoir model parameters conditional to dynamic data and sampling this pdf correctly. While Markov chain Monte Carlo (MCMC) provides a theoretically rigorous method for sampling any target pdf that is known up to a normalizing constant, in reservoir engineering applications, researchers have found that it may require extraordinarily long chains containing millions to hundreds of million of states to obtain a a correct characterization of the target pdf. When the target pdf has a single mode or has multiple modes concentrated in a small region, it is possible to implement a proposal distribution based essentially on random walk so that the resulting Markov chain Monte Carlo algorithm based on the Metropolis-Hastings acceptance probability can yield a good characterization of the posterior pdf. However, such a method may still require the generation of millions of states in the chain in order to obtain a proper sampling of the posterior pdf. For a high-dimensional multimodal pdf with modes separated by large regions of low or zero probability, characterizing the pdf with MCMC based on random walk is not feasible. While methods such as population MCMC exist for characterizing a multimodal pdf, their computational cost generally makes the application of these algorithm far too costly for field application. In this paper, we design a new proposal distribution based on a Gaussian mixture pdf for use in MCMC where the posterior pdf can be a multimodal pdf, possibly with the modes spread far apart. Simply put, the method generates modes using a gradient-based optimization method and constructs a Gaussian mixture model to use as the basic proposal distribution. Tests on three simple problems are presented to establish the validity of the method. The performance of the new MCMC algorithm is compared with random walk MCMC and is also compared with population MCMC for a target pdf which is multimodal.
Adaptive Coarsening in Physical Representation for the Robust Thermal-Compositional Simulation
Authors: Voskov Denis , Khait Mark
Published: February 2017

The nonlinear nature of flow and transport in porous media requires a linearization of the governing numerical model equations. We propose a new linearization approach and apply it to complex thermal-compositional problems of practical interest. The approach approximates exact physics of a simulation problem, which is similar to an approximate representation of space and time discretization performed in conventional simulation. Maintaining control of the error in approximate physics, we perform an adaptive parametrization to improve the performance of the method and adaptive coarsening to identify the major nonlinearities in the physical description. The global under-relaxation based on inflection points detection in parameterized space of the state variables provides a highly robust strategy to obtain nonlinear solution. This strategy was applied to several challenging compositional problems. In all cases, the proposed strategy improves the robustness and efficiency of the nonlinear solution.
Dual Grid Method for Aquifer Acceleration in Parallel Implicit Field-Scale Reservoir Simulation
Authors: Du Shouhong , Fung Larry S. , Dogru Ali H.
Published: February 2017

For many field-scale reservoir simulation models, aquifer regions (both peripheral and bottom) can represent a large percentage of total active grid blocks. The objective of this work is to build an accurate method respecting the fine-scale heterogeneities, but significantly reduce the computational cost of keeping the aquifer grids in the model, where they are deemed necessary to better describe the variable strength of water influx.

The present method can be considered a specialized two-level grid coarsening or upscaling method. Within the aquifer regions, each column of fine cells are coarsened vertically based on fine-scale z-transmissibility. A coarsened column may consist of a single amalgamated aquifer cell or multiple vertically disconnected aquifer cells separated by flow barriers. The pore volume (PV), compressibility, and lateral flow terms of the coarse cell are restricted from the fine-grid cell. The lateral connectivities within the aquifer regions and between the aquifer and the reservoir are honored, inclusive of the fine-scale description of faults, pinchouts, and null cells. Reservoir regions are not coarsened. Two alternatives exist for the fine-scale pressure reconstruction from the coarse-grid solution. The first method uses the vertical equilibrium concept. The second method performs a 1D solution for the fine-scale pressure. A spatially variable multi-porosity permeability model can also be accommodated. In parallel implementation, besides the load balancing method, the memory balancing method is also necessary. All these aspects will be explained in the paper.

The method has been applied successfully to several complex full-field simulation models where the transient aquifer water influx has been identified as a key factor. These models include dual porosity, dual permeability models with a complex geologic description. We compare simulation results using the accelerated aquifer calculation method against the original fine-grid simulation model without acceleration and demonstrate the efficacy of the new method. For the models tested, the actual speedup factors achieved are also compared against the theoretically computed improvement factors.

The dual grid method strives to significantly reduce computational cost but retain the fine-scale heterogeneity data to accurately represent the water movement within the water zones of the simulation model. The method differs from the standard upscaling and grid coarsening method where the coarse-grid properties are computed a priori. Instead, the fine-scale information is restricted to the coarse grid during Newton's iteration to represent the fine-scale flow behavior. This is analogous to the multiscale method, but we apply this only vertically within the aquifer regions.
A Novel Method for Multi-Resolution Earth Model Gridding
Authors: Suter Erich , Friis Helmer André , Vefring Erlend H. , Kårstad Terje , Escalona Alejandro
Published: February 2017

Earth models are important tools for support of decision making processes for optimal exploitation of subsurface resources. In earth modelling applications, massive amounts of information result from collecting and interpreting measurements and simulating physical scenarios at various scales and resolutions. The size of an earth model grid is a consequence of its scale and resolution. The grid size is a major factor for the computational efficiency when managing the model and performing various model based simulations. The grid is controlled by the geological structure, and the resolution of the grid is therefore controlled by the resolution of the geological structure (the number of structural elements).

We discuss principles for a multi-resolution framework for earth model gridding where the aim is to allow automatic, local control of the resolution of a populated grid by locally controlling the resolution of the geological structure. The structure is ordered in a hierarchical manner, and splits the subsurface into a nested set of regions that are ordered in a corresponding hierarchical fashion. Each region can be separately gridded. The method is based on a recent method for local updates of the connectivity (topology) of the geological structure and of the resolution of a populated grid. Similar to existing strategies for multi-resolution modelling in other sciences and applications, the proposed method allows local control with the trade-off between numerical accuracy and grid size. The method should allow to locally change the model resolution even during a modelling exercise; subsurface volumes of high interest can be represented at fine resolution, whereas in volumes of less interest, details can be omitted. The method also enables local updates and local scale uncertainty management of the geological structure.

The aim of the proposed method is to develop an effective methodology that supports real-time earth model based workflows such as geosteering where multiple grid realizations are never fixed and always updated with the most recent measurements and interpretations, and where each realization is always kept at an optimal resolution.
Coupled Geomechanics and Flow Simulation on Corner-Point and Polyhedral Grids
Authors: Andersen Odd , Nilsen Halvor MøII , Raynaud Xavier
Published: February 2017

Reservoir geology has traditionally been described using corner-point grids. For such grid and general polyhedral grids, two-point flux-approximation (TPFA) schemes, or modifications thereof, are simple and robust methods which, despite grid-orientation errors and a general lack of consistency, have been considered sufficient for simulation in light of the inherent geological uncertainty. However, there is no equivalent methods to simulate elasticity, and this has hampered flexible coupling between grids made for flow simulations and grids made for geomechanical calculations.

Using the newly developed virtual element method (VEM) for mechanics on polyhedral grids, we show how geomechanics simulations on corner-point grids can be coupled with traditional discretizations (and solvers) used in black-oil and compositional simulators. The new VEM method can be seen as an extension of finite element methods to general grids. In a first order VEM method, the energy of the non-linear basis functions is not computed exactly, as in FEM, but approximated by introducing a regularisation term. This may result in large error, especially for grids with high aspect ratio. We discuss the implications of the use of VEM for applications to reservoir modeling.

We will primarily use Biots type coupling restricted to linear elasticity. However, we also discuss how nonlinear coupling can be practically introduced using Automatic Differentiation (AD), which is the numerical technique of choice in several modern research simulators. The AD framework typically enables automatic evaluations of the derivative of vector functions. The difficulty in the case of nonlinear couplings with mechanics is that many of the important physical quantities involved, such as the mechanical properties and the stress, naturally live on cells, so that the discretization operators themselves becomes nonlinear quantities that have to be differentiated. Accurate and robust treatment of these challenges are discussed.

Computational cost is a major challenge when coupling geomechanical effects with flow simulation. First of all, the mechanical system needs to include the overburden and the rocks surrounding the reservoir. Secondly, mechanics in its simplest form is described by a vector-Laplace equation, which results in an additional elliptic system that is approximately three times larger than the pressure part of the flow equations. Several decoupling techniques have been introduced to overcome this challenge. We show how such methods can easily be implemented directly on the corner-point or polyhedral grids with the proposed VEM discretization. To showcase the coupling of geomechanics and flow simulation, we use a flexible open-source prototyping framework, which has been benchmarked against state-of-the-art commercial and research simulators.
A Robust Iterative Ensemble Smoother Method for Efficient History Matching and Uncertainty Quantification
Authors: Ma Xiang , Hetz Gill , Wang Xiaochen , Bi Linfeng , Stern Dave , Hoda Nazish
Published: February 2017

Many recent developments in generating history matched reservoir models that approximately characterize subsurface uncertainty are associated with the ensemble smoother (ES) method. It is much better suited for practical history matching applications because it does not require updating of the dynamical variables and thus the frequent simulation restarts required by ensemble kalman filter (EnKF) are avoided. However, the performance of original single update scheme of ES is poor for strongly nonlinear problems and therefore iterations may be needed. Several iterative forms of ES were proposed in the past few years, most of which combine ideas from random maximum likelihood (RML) and ensemble-based techniques. Unlike previous implementations, we pose the history matching problem as a full nonlinear least squares optimization problem and classical Levenberg-Marquardt (LM) algorithm is used as the optimization solver. By showing the that solution of the linearized least squares subproblems arising from each iteration has similar structure to that of standard ES update equation, we propose to use ES as the linear least squares solver to avoid the expensive adjoint calculation. In this way, the proposed algorithm can be considered as an iterative ES and the regularization parameter can be updated following the standard LM rule. Furthermore, because it is casted as an optimization problem, it is straightforward to extend it to robust nonlinear least squares method that can automatically estimate the measurement noise level and reduce the effect of outliers in the data that is essential for field applications. Two synthetic reservoir models are used to showcase the effectiveness and robustness of the newly developed algorithm.
Parallel Enriched Algebraic Multiscale Solver
Authors: Manea A. M. , Hajibeygi H. , Vassilevski P. , Tchelepi H. A.
Published: February 2017

A Parallel Enriched Algebraic Multiscale Solver (PEAMS) for simulation of flow in heterogeneous formations with high contrasts is introduced. Built on the recently developed enrichment strategy for single processing algorithms, i.e., EAMS of Manea et al. (2016), the PEAMS describes an efficient parallel implementation procedure as to how to enrich a given multiscale formulation with additional local basis functions. These additional basis functions, constructed in parallel computational platform, aim to resolve large error components for a generic fine-scale system with no right-hand-side term. The design and computational overhead of the enrichment kernels in shared-memory parallel environments are discussed in detail. The robustness and scalability of PEAMS are then illustrated for highly heterogeneous and anisotropic 3D multi-milion-cell reservoir models. The presented results show that, by adding only a few locally- supported complementary basis functions, the convergence of the original multiscale method is significantly enhanced. This is achieved with incurring a marginal overhead in the complexity to the coarse-scale operator. Moreover, in shared-memory parallel environments, it is shown that both of the enrichment procedure and the resulting enriched solver are scalable. Therefore, PEAMS casts a promising framework for robust iterative multiscale formulations for real-field applications, where parallel processing architectures are essential.
C1-Continuous PPU Schemes for Efficient Simulation of Fully-Coupled Multi-Phase Flow with Gravity
Authors: Jiang Jiamin , Younis Rami M.
Published: February 2017

In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iteration. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases.

Several complex heterogeneous multi-dimensional numerical examples under the three-phase black-oil formulation are presented. The examples include a miscible gas injection problem that involves significant variations in the total-velocity field over time. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that our C1-PPU scheme is both entropy-satisfying, and exhibits superior convergence properties for large time steps compared to the other alternatives.
Using Machine Learning to Predict Production at a Peace River Thermal EOR Site
Authors: Martin Eileen , Wills Peter , Hohl Detlef , Lopez Jorge L.
Published: February 2017

When many daily measurements of a thermal EOR field are taken throughout production, it is not cost effective to manually interpret trends to update reservoir models, so we developed an automated data-driven approach for production prediction using machine learning techniques. This is a two-step scheme that first predicts auxilary field measurements from directly-controlled field settings, then uses these predicted field measurements to predict production. The full two-step prediction process needs further refinement, but the second step alone shows promise for aiding in automated interpretation of data. Time shifts from daily seismic surveys improved production predictions.
A Feature-Enriched Multiscale Method for Simulating Complex Geomodels
Authors: Lie K.-A. , Møyner O. , Natvig J. R.
Published: February 2017

Multiscale methods have been shown to offer an order-of-magnitude increase in the speed of reservoir simulators. This may enable users to model complex fluid flow and geology with greater speed and flexibility than is available with the current computational technologies. Contemporary multiscale methods typically use a restriction operator to construct a reduced system of flow equations and a prolongation operator to map pressure unknowns from the reduced flow equations back to the original simulation grid. When combined with a local smoother, this gives an iterative solver that can efficiently compute approximate pressures to within a prescribed accuracy and still provide mass-conservative fluxes. We present an adaptive and flexible framework for combining multiple sets of such multiscale approximations. Each multiscale approximation can target a certain scale; geological features like faults, fractures, facies, or other geobodies; or a particular computational challenge like propagating displacement and chemical fronts, wells being turned on or off, etc. Multiscale methods that fit the framework are characterized by three features. First, the prolongation and restriction operators are constructed using a non-overlapping partition of the fine grid. Second, the prolongation operator is composed of a set of basis functions, each of which has compact support within a support region that contains a coarse grid block. Finally, the basis functions form a partition of unity.

Through a series of numerical examples that include idealized geology and flow physics as well as geological models of real assets, we demonstrate that the new framework increases the accuracy and efficiency of multiscale technology. In particular, we show how it is possible to combine multiscale approximations with different resolution as well as multiscale approximations targeting, among others, high-contrast fluvial sands; fractured carbonate reservoirs; challenging grids including faults, pinchouts and inactive cells; and complex wells.