bluuebunny/crossref_metadata_2025_split huggingface dataset:
Using Model Error With the Ensemble Kalman Filter for More Accurate Model Updates and Predictions
Authors: Aanonsen Sigurd Ivar 
Published: February 2009

Abstract
The EnKF has become increasingly popular for updating and history matching reservoir simulation models. Originally the filter was developed for sequential conditioning of state variables to dynamic data. It was later extended to solve the combined state and parameter estimation problem. Within petroleum, the focus has been mainly on parameter estimation, and although an unknown model error is present in all real reservoir studies, model error is commonly neglected, assuming that all error is due to uncertainty in the estimated parameters. In this paper we investigate the effect of a model error on the EnKF behaviour for a single-phase permeability estimation problem, and whether it is possible to improve the solution and predictions by including an unknown model error in the EnKF procedure. Numerical upscaling errors are chosen for the test case. However, the procedure should be applicable for any type of unknown model errors. It is demonstrated that with model error present, but not included in the analysis, it is not possible to match the data. The permeability estimate becomes unstable, and the predictions are very bad. However, by adding an unknown model error, data can be matched, and the parameter estimates may be significantly improved. Both uncorrelated and correlated errors are tested. Correlated errors are included as additional unknowns in the EnKF state vector. Predictions, and short term predictions in particular, are significantly improved.
Front-Tracking Methods for Use in Streamline Simulation of Compressible Flow
Authors: Nilsen Halvor Møll , Lie Knut-Andreas 
Published: February 2009

Abstract
Streamline methods are gaining popularity in the industry by providing fast desktop simulation of large reservoir models or multiple realizations. Traditionally, streamline simulation has been associated with simplified physics. but recent advances have demonstrated its potential also for compressible three-phase or component flaws. However, streamline simulation is still most efficient for two-phase incompressible flow, for which one can utilize a particularly efficient front-tracking method to solve 1-D transport equations along streamlines that is unconditionally stable and independent of the strongly irregular time-of-flight grid. In a recent paper (Nilson and Lie 2008), we presented, for the first time, front-tracking methods for simulating 1-D compressible two-phase flow. We also developed two methods that were particularly efficient for solving compressible flow in which one phase is incompressible, motivated by the simulation of CO2 injection. Here we apply these methods to streamline simulation of 3-D models, including a real-life model of a North Sea formation, which is under consideration as a potential target for CO2 deposition. Our numerical results demonstrate that streamlines and front tracking together give very efficient simulation of compressible flow. Similar ideas can also be applied for dual-porosity models, but this is not investigated in great detail herein.
A Multiscale Mixed Finite Element Method For Vuggy and Naturally Fractured Reservoirs
Authors: Gulbransen Astrid Fossum , Hauge Vera Louise , Lie Knut-Andreas 
Published: February 2009

Abstract
Vugs, caves, and fracture can significantly alter the effective permeability of carbonate reservoirs and should be accurately accounted for in a geomodel. Accurate modeling of the interaction between free-flow and porous regions is essential for flow simulations and detailed production engineering calculations. However, flow simulation of such reservoirs is very challenging because of the co-existence of porous and free-flow regions on multiple scales that need to be coupled.
Multiscale methods are conceptually well-suited for this type of modeling as they allow varying resolution and provide a systematic procedure for coarsening and refinement. However, to date there are hardly no multiscale methods developed for problems with both free-flow and porous regions. Our work is a first step to make a uniform multiscale framework, where we develop a multiscale mixed finite-element (MsMFE) method for detailed modeling of vuggy and naturally-fractured reservoirs. The MsMFE method uses a standard Darcy model to approximate pressure and fluxes on a coarse grid, but capatures fine-scale effects through basis functions determined from numerical solutions of local Stokes-Brinkman flow problems on the underlying fine-scale geocellular grid. The Stokes-Brinkman equations give a unified approach to simulating free-flow and porous regions using a single system of equations, avoid explicit interface modeling, and reduce to Darcy or Stokes flow by appropriate choices of parameters.
In the paper, the MsMFE solutions are compared with fine-scale Stokes-Brinkman solutions for test cases including both short- and long-range fractures. The results demonstrate how fine-scale flow in fracture networks can be represented within a coarse-scale Darcy flow model by using multiscale elements computed solving the Stokes-Brinkman equations. The results indicate that the MsMFE method is a promising path toward direct simulation of highly detailed geocellular models of vuggy and naturally-fractured reservoirs.
Adjoint Multiscale Mixed Finite Elements
Authors: Krogstad S. , Hauge V. L. , Gulbransen A. F. 
Published: February 2009

Abstract
We develop an adjoint model for a simulator consisting of a multiscale pressure solver and a saturation solver that works on flow adapted grids. The multiscale method solves the pressure on a coarse grid that is close to uniform in index space and incorporates fine-grid effects through numerically computed basis functions. The transport solver works on a coarse grid adapted by a fine-grid velocity field obtained by the multiscale solver. Both the multiscale solver for pressure and the flow-based coarsening approach for transport have earlier shown the ability to produce accurate results for high degree of coarsening. We present results for a complex realistic model to demonstrate that control settings based on optimization of our multiscale flow-based model closely matches or even outperforms those found by using a fine-grid model. For additional speed-up, we develop mappings used for rapid system updates during the time-stepping procedure. As a result, no fine-grid quantities are required during simulations and all fine grid computations (multiscale basis functions, generation of coarse transport grid and coarse mappings) become a preprocessing step. The combined methodology enables optimization of water flooding on a complex model with 45,000 grid-cells in a few minutes.
Interpretation of Partitioning Interwell Tracer Tests Using EnKF with Coarse Scale Constraints
Authors: Devegowda Deepak , Akella Santha , Datta-Gupta Akhil , Efendiev Yalchin 
Published: February 2009

Abstract
The success of enhanced recovery processes depends largely on the accurate characterization of the location and distribution of the target oil. The Partitioning Interwell Tracer Test (PITT) is designed to identify the residual oil saturation during waterflooding. In this test a conservative and a partitioning tracer are injected into the reservoir. The conservative tracer travels with the water phase whereas the partitioning tracer dissolves in both water and oil. The separation between the conservative and the partitioning tracer at the producer can be used to infer the residual oil saturation distribution.
The interpretation of partitioning tracer tests in the presence of mobile oil is considerably more difficult because the separation of the tracer response depends not only on the partitioning coefficients but also on the spatial distribution of the saturation itself. We propose a two-stage Ensemble Kalman Filter (EnKF) that utilizes the tracer data in conjunction with coarse-scale saturation constraints to identify the fine-scale saturation distribution and associated uncertainties. The coarse-scale saturation distribution can be conveniently obtained via an inversion of the waterflood response, for example water-cut data at the producers. The tracer data are first used to condition the ensemble of fine scale model realizations which are further improved via the coarse-scale constraint. The scale-decomposition of the inverse problem significantly improves the performance of the EnKF and prevents filter divergence as more data are assimilated.
We demonstrate the effectiveness of our approach using two and three-dimensional examples. First, we derive the coarse-scale saturation from a streamline-based inversion of the waterflood response. Next, the two-stage EnKF is used to interpret the PITT using the coarse-scale saturation constraint. A performance comparison of our proposed approach with the standard EnKF clearly indicates better characterization of the reservoir heterogeneities and improved estimates of the spatial distribution of bypassed oil.
Partitioners for Parallelizing Reservoir Simulations
Authors: Shuttleworth Robert , Maliassov Serguei , Zhou Hui 
Published: February 2009

Abstract
Computer simulations of oil and gas reservoirs require the construction and solution of large, sparse linear systems with millions or even tens of millions of unknowns at each time step or Newton iteration. For efficiency, these tasks are often parallelized. While the parallel construction of the Jacobian matrix and right hand side vectors mainly depends on the load balance between the processors, the parallel solution of the resulting linear system is sensitive to the way the system is partitioned amongst processors during the solution process. We evaluate several different strategies to parallelize the solution of the linear system on both shared and distributed memory architectures, using a strategy to optimize both the load balance of processors and the convergence of the linear solver. We discuss partitioning strategies based on multi-level graph partitioning using an approach for optimal vertex/edge weighting for reservoir simulation models based on unstructured, 2½D finite volume spatial discretization. We present parallel scalability and timing results obtained from field studies, using ExxonMobil's proprietary reservoir simulator, EMpower.
Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs
Authors: Natvig J. , Skaflestad B. , Bratvedt F. , Bratvedt K. , Lie K.-A. , Laptev V. , Khataniar S. K. 
Published: February 2009

Abstract
Advances in reservoir characterization and modeling have given the industry improved ability to build detailed geological models of petroleum reservoirs. These models are characterized by complex shapes and structures with discontinuous material properties that span many orders of magnitude. Models that represent fractures explicitly as volumetric objects pose a particular challenge to standard simulation technology with regard to accuracy and computational efficiency.
We present a new simulation approach based on streamlines in combination with a new multiscale mimetic pressure solver with improved capabilities for complex fractured reservoirs. The multiscale solver approximates the flux as a linear combination of numerically computed basis functions defined over a coarsened simulation grid consisting of collections of cells from the geological model. Here, we use a mimetic multipoint flux approximation to compute the multiscale basis functions. This method has limited sensitivity to grid distortions. The multiscale technology is very robust with respect to fine-scale models containing geological objects such as fractures and fracture corridors. The methodology is very flexible in the choice of the coarse grids introduced to reduce the computational cost of each pressure solve. This can have a large impact on iterative modeling workflows.
Energy Minimizing Bases for Efficient Multiscale Modeling and Linear Solvers in Reservoir Simulation
Authors: Dubois Olivier , Mishev Ilya D. , Zikatanov Ludmil 
Published: February 2009

Abstract
We demonstrate the applicability of energy minimizing bases for two-phase flow simulations, and we highlight several advantageous properties that they possess. We show how they can be implemented to obtain efficient serial (algebraic multigrid) and parallel (Additive Schwarz with coarse space correction) linear solvers for large-scale heterogeneous problems. We also confirm with experiments that using such bases for coarsening a problem produces a numerical solution of quality comparable to that of other available multiscale techniques. Finally, we also indicate how different coarsening levels can be used in different regions, in order to keep a finer resolution near certain areas of interest and significantly coarser resolution elsewhere. A multilevel approach is adopted to efficiently construct the basis functions for the coarser resolution.
Dynamic Data Integration and Quantification of Prediction Uncertainty Using Statistical Moment Equations
Authors: Likanapaisal P. , Li L. , Tchelepi H. A. 
Published: February 2009

Abstract
A probabilistic framework for dynamic data integration (history matching) has become accepted practice. The idea is to build an ensemble of reservoir models, all of which being consistent with the geologic scenario and also honoring all available (static and dynamic) information. In addition to data assimilation, the probabilistic framework provides an assessment of the prediction uncertainty due to incomplete knowledge of the reservoir description. Methods based on Monte Carlo Simulation (MCS) are widely used. This is driven by the generality and simplicity of MCS. As a black-box approach, only pre/post-processing of conventional flow simulations is needed. To achieve reasonable accuracy in estimating the statistical moments of flow performance predictions, however, large numbers of realizations are usually necessary. Here, we use an alternative direct approach for model calibration and uncertainty quantification. Specifically, we describe a Statistical Moment Equations (SME) framework for both the forward and inverse problems. In the SME method, the equations governing the statistical moments of the quantities of interest (e.g., pressure, saturation) are derived and solved directly. Immiscible two-phase flow problems are investigated, where we assume that in addition to statistical information (and a few measurements) about the permeability field, measurements of pressure, saturation, and flow rate are available at a few locations and several times. For the forward problem, the flow (pressure and total-velocity) equations are solved on regular grid, while a streamline-based strategy is used to solve the transport moments. A Kriging-based inversion algorithm, in which the statistical moments of permeability are conditioned directly based on available dynamic data, is used. We analyze the behaviors of the saturation moments and their evolution as they are conditioned on measurements, in both space and time. Moreover, we compare the SME inversion scheme with Kalman filter approaches (an MCS inversion approach) for dynamic data integration, from a mathematical framework perspective.
Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification
Authors: Mohamed L. , Christie M. , Demyanov V. 
Published: February 2009

Abstract
History matching and uncertainty quantification are two important research topics in reservoir simulation currently. In the Bayesian approach, we start with prior information about a reservoir – for example from analogue outcrop data – and update our reservoir models with observations, for example from production data or time lapse seismic. The goal of this activity is often to generate multiple models that match the history and use the models to quantify uncertainties in predictions of reservoir performance. A critical aspect of generating multiple history matched models is the sampling algorithm used to generate the models. Algorithms that have been studied include gradient methods, genetic algorithms, the Ensemble Kalman Filter, and others.
This paper investigates the efficiency of three stochastic sampling algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm Optimization (PSO) algorithm and the Neighborhood Algorithm (NA). HMC is a Markov Chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to achieve larger jumps than are possible with other MCMC techniques. PSO is a swarm intelligence algorithm that uses similar dynamics to HMC to guide the search, but incorporates acceleration and damping parameters to provide rapid convergence to possible multiple minima. The Neighbourhood Algorithm is a sampling technique that uses the properties of Voronoi cells in high dimensions to achieve multiple history matched models.
The algorithms are compared by generating multiple history matched reservoir models, and comparing the p10 – p50 – p90 uncertainty bounds produced by each algorithm. We show that all the algorithms are able to find equivalent match qualities for this example, but that some algorithms are able to find good fitting results quickly, whereas others are able to find a more diverse set of models in parameter space. The effects of the different sampling of model parameter space are compared in terms of the p10 - p50 - p90 uncertainty bounds in forecast oil rate.
These results show that algorithms based on Hamiltonian dynamics and swarm intelligence concepts have the potential to be effective tools in uncertainty quantification in the oil industry.
Adaptively-Localized-Continuation-Newton: Reservoir Simulation Nonlinear Solvers That Converge All the Time
Authors: Younis R. M. , Tchelepi H. A. , Aziz K. 
Published: February 2009

Abstract
Growing interest in understanding, predicting, and controlling advanced oil recovery methods emphasizes the importance of numerical methods that exploit the nature of the underlying physics. The Fully Implicit Method offers unconditional stability in the sense of discrete approximations. This stability comes at the expense of transferring the inherent physical stiffness onto the coupled nonlinear residual equations which need to be solved at each time-step. Current reservoir simulators apply safe-guarded variants of Newton's method, and often can neither guarantee convergence, nor provide estimates of the relation between convergence rate and time-step size. In practice, time-step chops become necessary, and are guided heuristically. With growing complexity, such as in thermally reactive compositional models, this can lead to substantial losses in computational effort, and prohibitively small time-steps. We establish an alternate class of nonlinear iteration that both converges, and associates a time-step to each iteration. Moreover, the linear solution process within each iteration is performed locally.
By casting the nonlinear residual for a given time-step as an initial-value-problem, we formulate a solution process that associates a time-step size with each iteration. Subsequently, no iterations are wasted, and a solution is always attainable. Moreover, we show that the rate of progression is as rapid as a standard Newton counterpart whenever it does converge. Finally, by exploiting the local nature of nonlinear waves that is typical to all multi-phase problems, we establish a linear solution process that performs computation only where necessary. That is, given a linear convergence tolerance, we identify the minimal subset of solution components that will change by more than the specified tolerance. Using this a priori criterion, each linear step solves a reduced system of equations. Several challenging examples are presented, and the results demonstrate the robustness of the proposed method as well as its performance.
Geomechanics of Heterogeneous Bitumen Carbonates
Authors: Freeman T. T. , Chalaturnyk R. J. , Bogdanov I. I. 
Published: February 2009

Abstract
Around 26% of Alberta's bitumen resources are held in carbonate formations. Due to the lack of efficient technologies to extract bitumen from carbonates these resources are currently classified as "inaccessible". Among possible technologies, thermal recovery methods will be a strong option for recovery of bitumen from carbonates. Amongst thermal recovery methods, Steam Assisted Gravity Drainage (SAGD) is one of the best methods originally developed and successfully used for oil sands in Alberta. However, because of heterogeneity, lower permeability and deeper position of bitumen carbonates, steam injection method may not be as effective in bitumen carbonate reservoirs as they are in oil sands. Alternate heating methods such as electrical ohmic heating and higher frequency (radio frequency and microwave) electromagnetic methods are strong alternative options.
During a thermal recovery process, stress state within the reservoir is significantly altered due the thermal stresses and steam pressure. The new stress state can impact the multiphase flow of steam and bitumen by enhanced permeability or stimulated fractures. All the previous studies on geomechanics of thermal recovery methods have been focused on SAGD and that only for oil sands and because of fundamental differences between bitumen carbonates and oil sands the results are not applicable for carbonates. Change of permeability in carbonates under elevated stresses would not necessarily be caused by shear failure and it could emerge by connecting the isolated vugs or stimulation of the existing fractures.
A fully coupled electro-thermo-hydro-mechanical (ETHM) model based on multiphysics platform is used to study the simultaneous interaction between non-isothermal multiphase flow in the carbonates and stresses and strains in the reservoir. The advantage of multiphysics modeling by COMSOL Multiphysics is that being a general-purpose simulator it offers a possibility for multi-physical coupling via the wide choice of application modes such as electrical or chemical. Heterogeneity of the carbonate is modeled through a probabilistic distribution of mechanical and hydraulic properties to account for inherent variability in carbonate properties.