bluuebunny/crossref_metadata_2025_split huggingface dataset:
Use of Approximate Dynamic Programming for Production Optimization
Authors: Wen Zheng , Durlofsky Louis J. , Van Roy Benjamin , Aziz Khalid 
Published: February 2011

Abstract
In production optimization, we seek to determine the well settings (bottomhole pressures, flow rates) that maximize an objective function such as net present value. In this paper we introduce and apply a new approximate dynamic programming (ADP) algorithm for this optimization problem. ADP aims to approximate the global optimum using limited computational resources via a systematic set of procedures that approximate exact dynamic programming algorithms. The method is able to satisfy general constraints such as maximum watercut and maximum liquid production rate in addition to bound constraints. ADP has been used in many application areas, but it does not appear to have been implemented previously for production optimization. The ADP algorithm is applied to two-dimensional problems involving primary production and water injection. We demonstrate that the algorithm is able to provide clear improvement in the objective function compared to baseline strategies. It is also observed that, in cases where the global optimum is known (or surmised), ADP provides a result within 1-2% of the global optimum. Thus the ADP procedure may be appropriate for practical production optimization problems.
New Phase Behavior Algorithm for Simulation of CO2 Storage
Authors: Lazaro-Vallejo L. , Leahy M. , Dance T. , LaForce T. 
Published: February 2011

Abstract
Trapping carbon dioxide underground is considered a key technology to mitigate climate change on a large scale. Numerous studies have shown how injection strategies and geological uncertainty have an impact on how much CO2 can be trapped as residual saturation (Qi, 2009a; Qi, 2008 and Obi, 2004). In cases of large uncertainty such as deep saline aquifers, simulations are run on a high number of possible geological realisations to compensate for the lack of data. Consequenty, computation times can become prohibitive. As a result, it is necessary to develop fast and more physically accurate methods for CO2 storage simulations. Streamline-based simulations are a good tool for this as they divide the 3D field into a set of multiple 1D problems that are easier and quicker to solve. Typical streamline-based simulators perform advective-flow transport on the streamlines while the rest of the physical processes are calculated on the underlying grid. This makes the simulation dependent on the number of pressure time-steps. This paper shows that the number of pressure time-steps can affect the convergence of results due to phase behavior errors. We propose two new phase behavior algorithms that assume thermodynamic equilibrium along the streamlines and use them to extend our existing in-house 3-component 2-phase streamline simulator. In order to validate our new algorithm, a 1D simulation was compared against 1D analytical Buckley-Leverett solution. All the algorithms were validated on 2D and 3D sections of the SPE 10th Comparative Model using water alternating gas (WAG) injection followed by chase brine. Results show that both new thermodynamic algorithms were faster in terms of CPU cost and had a faster convergence of results. Based on the validated model, we performed simulations on a geological model of the stage 2 CO2CRC Otway Project to test residual trapping. The injection strategy followed was similar to that described in Zhang et al. (2010) and the aim was to compare our results to TOUGH2 results. Streamline and TOUGH2 predicted similar CO2 profiles. The results indicate that more than 79% of the CO2 injected can be trapped as residual saturation in the deep saline aquifer.
Application and Variance Based Sensitivity Analysis of Surfactant-Polymer Flood
Authors: Mollaei Alireza , Lake Larry W. , Delshad Mojdeh 
Published: February 2011

Abstract
We study the performance and behavior of surfactant-polymer (SP or micellar-polymer, MP) flooding enhanced oil recovery (EOR) using an analytical chemical flood predictive model (CFPM). The research has two parts based on the deterministic and the stochastic nature of the problem.
In a deterministic study, the SP flood performance (ultimate recovery efficiency and oil-rate vs. time) of TORIS reservoir database (theTertiary Oil Recovery Information System) was predicted using the modified CFPM. Results helped to determine the best candidates for SP flooding based on each reservoir's rock and fluid properties. From there we can determine the effect of different parameters (reservoir rock and fluid properties, injection design variables) on ultimate recovery efficiency and peak oil rate of an SP flood, which gives good clues about the sensitivity of output results to different input parameters.
To recognize the behavior of the model under for uncertain inputs we used a variance-based sensitivity analysis (SA) method known as Winding Stairs (WS), which needs much fewer runs than traditional Monte-Carlo (MC) and Latin Hypercube methods. The results of the SA method helped us to identify the most important sources of uncertainty of SP floods either through direct influences or interactions with other parameters. Based on these results we can reduce the uncertainty of output results of SP flood significantly by reducing the uncertainty of the input parameters that cause the largest uncertainty.
Numerical Experiments with AMG Solver in Reservoir Simulation
Authors: Mishev Ilya , Shaw Jason , Lu Pengbo 
Published: February 2011

Abstract
AMG (Algebraic Multi-Grid) solver proved to be one of the most efficient solvers handling linear systems from discretization of the pressure equation in IMPES and Sequential Implicit formulations. We share our experience in using it in production simulations. We also discuss how AMG solver can be used as a component in composite solvers for other formulations or in parallel algorithms.
Classical AMG (Ruge-Stuben) approach is very well suited for monotone matrices from finite volume discretizations, but cannot solve efficiently linear systems with the facility unknowns included because of the different nature of these equations. We have chosen to alleviate this problem by using the multiplicative Schwarz framework. One application of this preconditioner consists of solving the facility system to a relatively loose tolerance followed by one AMG V-cycle on the pressure system. Our experiments confirm there is no loss of efficiency due to the facility unknowns. Moreover, the same approach can be extended naturally to Adaptive Implicit (AIM) formulation with different parts of the matrix handled by different linear solvers. AMG is also very efficient when used as a sub-domain solver in the overlapping additive Schwarz domain decomposition algorithm. The straightforward generalization of the serial algorithm produced unexpected results with respect to the robustness of the algorithm. The theoretical analysis provided valuable insight on the interplay of the multiplicative and additive Schwarz methods and showed us how to reorganize the algorithm to correct the problems. We also report our new findings on the influence of the overlap size between the sub-domains on the convergence of additive Schwarz method.
Interior-Point Formulation for the Constrained Ensemble Kalman Filter
Authors: Phale Hemant A. , Oliver Dean S. 
Published: February 2011

Abstract
The standard formulation of the ensemble Kalman filter (EnKF) does not take into account the physical constraints on state variables during the data assimilation step so constraint violations are often handled heuristically. The physical constraints often contain valuable information about the system which are critical for the valid initialization and forecast. A successful enforcing of these constraints during the data assimilation step of the EnKF is necessary for valid estimation of reservoir properties.
A number of solutions to the problem of constraint violation have been proposed in the past including the constrained EnKF (CEnKF), iterative EnKF, transformation of state variables, reparameterization, and truncation. In this paper, we present an interior-point method for incorporating the inequality constraints into the EnKF methodology (IPCEnKF). In this approach, the objective function for data assimilation is reformulated by adding a barrier function to penalize proximity of the state variables to the boundaries of the feasible region and to set a barrier on the state variables against leaving the feasible region. The proposed method is efficient compared to the CEnKF as it does not require the identification of the active constraints. Although the method is iterative to reduce the effect of the barrier term at each assimilation step, the iterations do not require running the simulator.
The method is successfully tested first on a 1D linear example to illustrate the performance when nonlinearity is not an issue, then on a more realistic 3D, three-phase reservoir flow assimilation problem based on the modified SPE9 model. Results from the reservoir problem show the effectiveness of the newly proposed IPCEnKF method in matching the observations and honoring the inequality constraints on phase saturations. The proposed method is able to achieve a better estimate of reservoir properties than is obtained using only truncation with the standard EnKF.
Multiscale parameterization with adaptive localization for improved assimilation of time-lapse data
Authors: Chen Yan , Nourazari Sara , Oliver Dean S. 
Published: February 2011

Abstract
Time-lapse seismic or electromagnetic data are similar to production data in that they are generally strongly sensitive to averages of porosity and permeability over extended regions, but only weakly sensitive to the properties of individual gridblocks. Consequently, updates of model parameters from the ensemble Kalman filter (EnKF) will be subject to substantial error due to spurious correlations when the size of the ensemble is small. Adaptive localization methods will reduce the magnitude of the spurious correlations, but may also eliminate the true, but weak, correlations. For this type of data, there appears to be a relationship between the spatial scale of the model variables and the sensitivity of observations to the variables. By introducing a multiscale expansion with adaptive localization, we are able to increase the sensitivity to the larger scale variables and more accurately compute their magnitudes, while eliminating updates of the small scale variables with weak correlations.
In this paper we compare three approaches to data assimilation for observation operators with weak, nonlocal sensitivity to model variables. The first approach is the EnKF without localization of any kind. The second approach is the EnKF with adaptive bootstrap localization or screening of the Kalman gain. In the third approach, we apply the EnKF with adaptive bootstrap localization to the problem of updating a multiscale expansion of the model variables. These approaches are illustrated through application to several spatially distributed data assimilation problems. The first application is a one-dimensional vector of correlated random variables for which the observations are averages over intervals. The second example is a two-dimensional correlated array of permeability values for which the data are observations of pressure in an observation well at two times. The final example is also a two-dimensional flow problem, but one in which the concentration of an injectant is observed at several times. In the first two examples, the ensemble Kalman filter approach with a multiscale expansion and adaptive localization gave the best results. In the final example, results from adaptive localization with and without the multiscale expansion are essentially equivalent because the correlation of data limits the scale of the features in the Kalman gain matrix.
Multiblock methods for coupled flow-transport and compositional flow through porous media - Applications to the simulation of transport of reactive species and carbon sequestration
Authors: Thomas S. G. , Wheeler M. F. 
Published: February 2011

Abstract
This paper presents multiblock methods for coupled multiphase flow and species transport modeling in porous media applications. These methods provide local mass conservation and a continuous approximation of fluxes across inter-element faces and sub-domain (inter-block) interfaces and can treat non-matching grids, allowing for a flexible choice of grid refinements. Furthermore, they lend themselves naturally to parallel implementations of multiphysics, multinumerics, multiscale applications of porous media flow and transport.
The paper briefly introduces mortar mixed finite element methods (MMFEM) [1] for coupled porous media flow and transport applications, followed by the main emphasis of the paper which is a novel extension of an enhanced velocity mixed finite element method (EVMFEM) [2] to similar problems flow and reactive transport. The paper also presents the formulation of a recent application of EVMFEM to such challenging problems as compositional flow simulations of CO2 sequestration, that is now widely accepted as the most feasible solution to address the growing environmental concerns due to global warming, as well as a very effective means for enhanced oil and gas recovery.
Computational experiments with EVMFEM suggest that it is advantageous to apply grid refinements around wells and where plumes of chemical species are expected to be transported. Allowing for variable grid refinements greatly reduces the simulation cost (wall clock times), compared with single block fine-grid everywhere strategies, while preserving overall accuracy of the solution. Furthermore, initial studies indicate that the implementation is scalable in parallel simulations. For completeness, a few significant analytic results on convergence of the method are stated and referenced, omitting proof.
This work is significant in advancing the understanding and application of multiblock methods in reservoir simulation development. Problems such as transport of chemical species in multiphase flow and CO2 sequestration have begun to assume significant importance in decisions regarding the preservation of our environment and in the safe and reliable means of delivering energy. This paper offers useful methods and some innovative future directions to address the huge computational costs involved in solving such complex problems.
History Matching for Non-Gaussian Random Fields Using the Probabilistic Collocation Based Kalman Filter
Authors: Zhang Dongxiao , Li Heng , Chang Haibin 
Published: February 2011

Abstract
In this work, an approach for estimating non-Gaussian permeability field is developed, through a probabilistic collocation based Kalman filter (PCKF). In this approach, the polynomial chaos expansion is used to parameterize the non-Gaussian permeability field. The state variables are expressed by the polynomial chaos expansion whose coefficients are sequentially updated when observations are available. The probabilistic collocation method is employed to solve for the coefficients of the polynomial chaos expansion. The probabilistic collocation method is non-intrusive to the reservoir model, thus it allows the forward simulations to be performed independently with existing reservoir simulators, as in the Monte Carlo simulation.
The applicability of the approach is demonstrated with black oil problems in spatially heterogeneous reservoirs. Continuous production data are used as observations for sequentially updating the permeability field. The PCKF approach is also compared with the ensemble Kalman filter (EnKF) for investigating the accuracy, efficiency and applicability. It reveals that the PCKF other than the EnKF can be used to efficiently estimate the non-Gaussian permeability field. While keeping the advantages of EnKF, such as the sequential updating and parallelism, the PCKF is more suitable for permeability fields characterized by non-Gaussian random fields.
Three-Phase Compositional Modeling of CO2 Injection by Higher-Order Finite Element Methods with CPA Equation of State
Authors: Moortgat Joachim , Li Zhidong , Firoozabadi Abbas 
Published: February 2011

Abstract
Injection of CO2 in water-flooded hydrocarbon reservoirs and in saline aquifers may require models based on high-order accurate numerical methods. For such applications, cubic equations of state (EOS) and Henry's law may not be sufficiently accurate. The association of water molecules and cross-association of water and CO2 molecules affects the phase behavior of CO2-water mixtures and requires a cubic-plus-association (CPA) equation of state (EOS). In this work, we present a new higher-order three-phase compositional model with the following features: 1) species transfer among the three phases, in particular CO2 solubility in water, 2) an implicit-pressure, explicit-composition scheme that uses the mixed hybrid finite element method to simultaneously solve for the pressure and the total volumetric flux, and a discontinuous Galerkin approximation to update mass transport, 3) Fickian diffusion, 4) efficient solution of the CPA-EOS, 5) advancement in the two-dimensional bisection method for robust phase amount computation, and 6) consistent boundary conditions for the three-phase fractional flow formalism. We present a number of numerical examples with broad applications in improved oil recovery in water-flooded oil reservoirs, and CO2 sequestration.
Fast Reservoir Parameter Estimation by Using Effect of Principal Components Sensitivities and Discrete Cosine Transform
Authors: Dadashpour M. , Rwechungura R. , Kleppe J. 
Published: February 2011

Abstract
Estimation of reservoir parameters such as porosity and permeability from production history and time-lapse seismic data is still challenging. When the object is a large hydrocarbon reservoir with a large number of unknown parameters, the problem will be even more difficult and needs to have geologically realistic solutions especially in adjoint-free gradient-based methods.
Replacing the original set of unknown parameters with a lower dimension group that captures the most important features of the field will be a proper procedure to speed-up the optimization procedure. This work proposes a method for parameter reduction by using sensitivity of principal components (PC's) to the observation data and combination of principal component analysis (PCA) and discrete cosine transform (DCT).
DCT is a robust, fast and efficient method that does not require heavy computing. However, the difficulty of including geological as well as bound constraints in some optimization algorithms can lead to solutions that are geologically unacceptable. PCA has the facility to implement both types of constraints. Then it can reduce the number of parameters and geologically acceptable results may be ensured. Reduction of the number of parameters will be done in two steps, first by PCA and then by DCT. Resulting in much fewer parameters and still provide solutions with the high number of accuracy from a geological point of view.
This paper evaluates the performance and advantages of combining these methods and choosing most sensitive components for parameter reduction in parameter estimation. The methodology is applied in noise-free and noisy semi-synthetic models inspired by real field data, based on data from the Norne Field offshore Norway. The results show that using most sensitive principal components to the observation data and combining it with DCT can be a useful tool for speeding-up this type of optimization routines.
Optimal Well Placement under Uncertainty using a Retrospective Optimization Framework
Authors: Wang Honggang , Ciaurri David Echeverría , Durlofsky Louis J. , Cominelli Alberto 
Published: February 2011

Abstract
Subsurface geology is highly uncertain, and it is necessary to account for this uncertainty when optimizing the location of new wells. This can be accomplished by evaluating reservoir performance, for a particular well configuration, over multiple realizations of the reservoir and then optimizing based on, for example, expected net present value or expected cumulative oil production. A direct (exhaustive) procedure for such an optimization would entail the simulation of all realizations at each iteration of the optimization algorithm. This could be prohibitively expensive when it is necessary to use a large number of realizations to capture geological uncertainty. In this work we apply a procedure that is new within the context of reservoir management, retrospective optimization (RO), to address this problem. RO solves a sequence of optimization subproblems that contain increasing numbers of realizations. We introduce the use of k-means clustering for selecting these realizations. Three example cases are presented that demonstrate the performance of the RO procedure. These examples use particle swarm optimization and simplex linear interpolation based line search as the core optimizers (the RO framework can be used with any underlying optimization algorithm, either stochastic or deterministic). In the first example, we achieve essentially the same optimum using RO as we do using an exhaustive optimization approach, but RO requires an order of magnitude fewer simulations. The results clearly demonstrate the advantages of cluster-based sampling over random sampling for the examples considered. Taken in total, our findings indicate that RO using cluster sampling represents a very promising approach for optimizing well locations under geological uncertainty.
Accurate and Efficient Simulation of Multiphase Flow in a Heterogeneous Reservoir by Using Error Estimate and Control in the Multiscale Finite-Volume Framework
Authors: Hajibeygi H. , Lunati I. , Lee S. H. 
Published: February 2011

Abstract
The Multiscale Finite-Volume (MSFV) method is designed to reduce the computational cost by splitting the original global problem into a set of localized problems (with approximate local boundary conditions) coupled by a coarse global problem. The MSFV error can be reduced iteratively (i-MSFV) using an improved (smoothed) multiscale solution to enhance the localization conditions or by using a Krylov subspace method (e.g. GMRES) preconditioned by the MSFV system. In a multiphase flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure) that are necessary to achieve the desired accuracy of the saturation solution.
In this work, we extend the i-MSFV method to sequential implicit simulations of time dependent problems. To control the error of the coupled saturation-pressure system, we analyze the transport error due to approximate flux fields. We then propose a-priori error estimate based on the residual of the pressure equation. At the beginning of the simulation we iterate until the specified pressure accuracy is achieved. To minimize the required iterations in time-dependent multiphase flow problems, this initial solution is also utilized to improve the localization assumption at later time steps. Additional iterations are employed only when the residual becomes larger than a specified threshold value. The saturation equation error in presence of an approximate conservative MSFV velocity field is anlayzed. Finally, a saturation error expression is derived, and a residual based strategy is introduced to control numerical errors. Numerical results show that the proposed strategy results in efficient and accurate simulation of multiphase flow in heterogeneous porous media.