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Results
A New Look at Conflicting Multiple Objectives Optimization using Fuzzy Rules-Based System
Mirzabozorg, Arash (University of Calgary/Computer Modelling Group Ltd.) | Nghiem, Long (Computer Modelling Group Ltd.) | Li, Heng (Computer Modelling Group Ltd.) | Yang, Chaodong (Computer Modelling Group Ltd.) | Chen, Zhangxin (University of Calgary)
Abstract Population-based stochastic optimization algorithms have increasingly been used by history matching and optimization research groups because of their ability to find an ensemble of optimal solutions when compared with gradient-based optimizers. The most common approach used by the existing algorithms in history matching and optimization workflows is to minimize or maximize a single global objective function (GOF), which is an aggregated summation of all individual objective functions, to find optimal solutions. There are many situations, however, where individual objective functions compete with one another in such a way that to get an optimal solution, improving one objective function may come at the cost of degrading the other. To address this problem, a multi-objective optimization (MOO) method has recently been shown to be an excellent approach. One of the main algorithms used in this context is multi-objective particle swarm optimization (MO-PSO) which has been applied in many real applications to tackle the conflicting nature of objective functions in history matching and optimization studies. The question that needs to be answered is whether the above method is the only option for handling multi-objective optimization problems or if there is an alternative approach to find optimal solutions in the form of a Pareto front. In other words, how can engineering knowledge about the nature of competing individual objective functions (in the form of fuzzy IF-THEN rules) guide population-based optimization algorithms toward a Pareto optimal solutions front in an optimization context? We propose a framework whereby a Fuzzy Inference System (FIS) is coupled with Differential Evolution (DE) to provide a means (FIS + DE) for reservoir engineers to incorporate their expertise in multi-objective optimization of a reservoir model under study. We demonstrate the power of the above approach using two Steam Assisted Gravity Drainage (SAGD) case studies. In the first study, the objective is to simultaneously maximize the net present value (NPV) and minimize the cumulative steam oil ratio (CSOR). In the second one, we present the merits of the proposed workflow using a numerical tuning case study in which the goal is to find models that run faster and with minimum material balance errors. The results showed that the application of FIS + DE was successful in providing the same quality trade-off optimal solutions as those obtained by MO-PSO in the first test case; however, the second scenario demonstrated the superiority of the suggested framework in finding a better Pareto front than MO-PSO.
- Europe (1.00)
- North America > United States > Texas (0.28)
- Overview (0.46)
- Research Report > New Finding (0.34)
Abstract We consider an application of hierarchical multiscale techniques previously developed by the authors for the long-term production optimization of a real field offshore Brazil. This field has been produced for several years and it represents a significant share of the overall oil production for that country. A life-cycle production optimization is considered, to estimate the optimal well rates for producers and injectors at a sequence of control steps under certain facility constraints. The production optimization step is preceded by a ten-year historical period, where seismic and production data were history-matched using ensemble-based approaches. The well controls are optimized for the next ten years of production using the multiscale techniques Hi-MO and RHi-MO. Our approaches are successfully compared against a reference case, which applies the well rates used to forecast production of the real field, as well as a standard optimization procedure with a fixed set of well controls and a successive splitting procedure.
- South America > Brazil (0.67)
- North America > United States > Texas (0.47)
- North America > United States > Oklahoma (0.46)
- South America > Brazil > Rio de Janeiro > South Atlantic Ocean > Campos Basin > Marlim Field > Macae Formation (0.99)
- South America > Brazil > Rio de Janeiro > South Atlantic Ocean > Campos Basin > Marlim Field > Lago Feia Formation (0.99)
- South America > Brazil > Campos Basin (0.99)
- Europe > United Kingdom > North Sea > Central North Sea > Moray Firth > Central Graben > P 111 (0.93)
Ensemble-Based Multi-Objective Optimization of On-Off Control Devices Under Geological Uncertainty
Fonseca, R.M.. M. (Delft University of Technology) | Leeuwenburgh, O.. (TNO) | Rossa, E. Della (ENI) | Hof, P.M.J. Van (Eindhoven University of Technology) | Jansen, J.D.. D. (Delft University of Technology)
Abstract We consider robust ensemble-based (EnOpt) multi-objective production optimization of on-off inflow control devices (ICDs) for a sector model inspired on a real-field case. The use of on-off valves as optimization variables leads to a discrete control problem. We propose a re-parameterization of such discrete controls in terms of switching times, i.e. we optimize the time at which a particular valve is either open or closed. This transforms the discrete control problem into a continuous control problem which can be efficiently handled with the EnOpt method. Additionally this leads to a significant reduction in the number of controls which is expected to be beneficial for gradient quality when using approximate gradients. We consider an ensemble of sector models where the uncertainty is described by different permeability, porosity, net-to-gross and initial water saturation fields. The controls are the ICD settings over time in the three horizontal injection wells, with approximately 15 ICDs per well. Different optimized strategies resulting from different initial strategies were compared. We achieved a mean 4.2% increase in expected NPV at a 10% discount rate compared to a traditional pressure maintenance strategy. Next, we performed a sequential bi-objective optimization, and achieved an increase of 9.2% in the secondary objective (25% discounted NPV to emphasize short-term production gains) for a minimal decrease of 1% in the primary objective (0% discounted NPV to emphasize long-term recovery gains), as averaged over the 100 geological realizations. The workflow was repeated for alternative numbers of ICDs showing that having fewer control options lowers the expected value for this particular case. The results demonstrate that ensemble-based optimization workflows are able to produce improved robust recovery strategies for realistic field sector models against acceptable computational cost.
- Europe (1.00)
- North America > United States > Texas (0.68)
- Research Report > New Finding (0.66)
- Research Report > Experimental Study (0.48)
Abstract Inference of spatially distributed reservoir properties from production data in scattered wells poses an under-constrained inverse problem that has nonunique solutions. One major contributor to problem ill-posedness is over-parameterization of spatially distributed reservoir properties. We recently introduced sparse representations of unknown reservoir properties for history matching by exploiting the correlation in their spatial distribution. In this approach, during history matching, instead of estimating reservoir properties for each model grid cell, the sparse representation of the reservoir properties are estimated from production data. The resulting history-matching problem can be solved using recent developments in sparse signal processing, widely known as compressed sensing. This novel sparse formulation of history matching effectively searches for relevant geologic patterns in a diverse collection of geologic elements, known as a sparse geologic dictionary, to explain the production data. We demonstrate the effectiveness of sparse history matching and illustrate its suitability for field-scale application. We discuss efficient reduced-order methods to speed up the computational aspect of constructing sparse geologic dictionaries for large-scale applications. We present history matching results with an adapted version of the Brugge benchmark model in which sparse geologic dictionaries are learned from a collection of uncertain prior model realizations. The proposed framework has several important properties that make it desirable for history matching application, including reconciling the disparity in data and model resolutions, respecting the expected geologic continuity, and accounting for uncertainty in geologic scenario.
- North America > United States > Texas (0.28)
- North America > United States > California (0.28)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (3 more...)
An Efficient Optimisation Technique Using Adaptive Spectral High-Dimensional Model Representation: Application to CO2 Sequestration Strategies
Petvipusit, Kurt R. (Department of Earth Science and Engineering, Imperial College London) | Elsheikh, Ahmed H. (Institute of Petroleum Engineering, Heriot-Watt university, UK) | King, Peter R. (Department of Earth Science and Engineering, Imperial College London) | Blunt, Martin J. (Department of Earth Science and Engineering, Imperial College London)
Abstract The successful operation of CO2 sequestration relies on designing optimal injection strategies that maximise economic performance while guaranteeing long-term storage security. Solving this optimisation problem is computationally demanding. Hence, we propose an efficient surrogate-assisted optimisation technique with three novel aspects: (1) it relies on an ANOVA-like decomposition termed High-Dimensional Model Representation; (2) component-wise interactions are approximated with adaptive sparse grid interpolation; and (3) the surrogate is adaptively partitioned closer to the optimal solution within the optimisation iteration. A High-Dimensional Model Representation (HDMR) represents the model output as a hierarchical sum of component functions with different input variables. This structure enables us to select influential lower-order functions that impact the model output for efficient reduced-order representation of the model. In this work, we build the surrogate based on the HDMR expansion and make use of Sobol indices to adaptively select the significant terms. Then, the selected lower-order terms are approximated by using the Adaptive Sparse Grid Interpolation (ASGI) approach. Once the HDMR is built, a global optimizer is run to decide: 1) the domain shrinking criteria; and 2) the centre point for the next HDMR building. Therefore, this proposed technique is called a walking Cut-AHDMR as it shrinks the search domain while balancing the trade-off between exploration and exploitation of the optimisation algorithm. The proposed technique is evaluated on a benchmark function and on the PUNQ-S3 reservoir model. Based on our numerical results, the walking Cut-AHDMR is a promising approach: not only does it require substantially fewer forward runs in building the surrogate of high dimension but it also effectively guides the search towards the optimal solution. The proposed method provides an efficient tool to find optimal injection schedules that maximise economic values of CO2 injection in deep saline aquifers.
Abstract Algebraic multigrid (AMG) methods for directly solving coupled systems of partial differential equations (PDEs) have been extensively used in various types of numerical simulations in engineering. A necessary condition for its efficient applicability is the simulation process being driven by elliptic components. In reservoir simulation the pressure, described by Darcy's law, is known to drive the process and hence System-AMG should be applicable and outperform classical solvers. In the context of adaptive and fully implicit reservoir simulations, the linearization of balance equations results in linear systems of equations that can be challenging. This makes it crucial to exploit all physical information from the full system to construct a robust AMG strategy and to extend it to more complex simulations than Black-Oil. At the same time, the full set of information helps to get the best out of AMG. Just as with multigrid in general, System- AMG provides a framework for combining algorithmic modules rather than a fixed solution algorithm. The adaptation of the solution strategy to the concrete class of applications is the key to obtain the best performance. Finally, System-AMG does not only allow for choosing more efficient algorithmic strategies, but also for exploiting parallelism in an optimized way, regardless of the simulation code being parallelized or not. Because the linear solver time is typically far dominating, even serial simulators can immediately and substantially benefit from MPI parallelism.
Abstract Reliable early characterization of global reservoir connectivity is critical for improving field development plans. A main difficulty in identification of field-scale reservoir connectivity is the discrepancy between the low resolution of available field-scale pressure data and the high resolution of geologic models. In this paper, we propose a workflow for integration of pressure data for estimating large-scale reservoir connectivity. Since pressure variation represents a smooth function, we adopt an extremely low resolution (coarse scale) grid system for reservoir simulation. We generate the grid system through Delaunay triangulation by using the location of the static pressure measurements as control points and distribute the unstructured grid blocks according to the spatial resolution of the observations. Using flow-based upscaling, we create the initial coarse scale static simulation model from fine-scale geological model. Then, we use the ensemble Kalman filter to automatically adjust the global parameters such as aquifer strength, global continuity/discontinuity of reservoir properties, and fault transmissibilities to match the static pressure. The important advantages of the proposed workflow for characterization of field-scale reservoir connectivity from pressure data include very fast connectivity estimation with a low-order model and effective parameterization to reduce the number of unknowns to a level commensurate with the available static pressure measurements. We successfully apply our framework to data from real fields to illustrate its suitability and application to realistic reservoirs. To verify the performance of our method we demonstrate the compatibility of the estimation results with the existing geological evidence.
- North America > United States > Texas (1.00)
- Asia (0.68)
- Geology > Geological Subdiscipline (0.68)
- Geology > Structural Geology > Fault (0.34)
Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Reservoir Simulation Symposium held in The Woodlands, Texas USA, 18-20 February 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract The treatment of chemical reactions is required for many simulation applications including in-situ conversion and geological carbon storage. In this work we present a strategy for incorporating chemical reaction modeling into an existing EOS-based compositional simulator. Both kinetic and equilibrium, as well as heterogeneous and homogeneous chemical reactions are included in the implementation. As a first step, the method entails the construction of the Jacobian matrix for a compositional system that does not include any chemical reactions. Then, linear transformations are applied at the level of the Jacobian matrix to account for reaction terms. These transformations act to convert the initial component-based Jacobian matrix to a matrix based on element balances. In so doing, they eliminate all equilibrium reaction rates and reduce the number of kinetic reaction terms that appear.
- Geology > Rock Type (0.68)
- Geology > Geological Subdiscipline > Geochemistry (0.46)
Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations
Gries, Sebastian (Fraunhofer Institute for Algorithms and Scientific Computing SCAI) | Stüben, Klaus (Fraunhofer Institute for Algorithms and Scientific Computing SCAI) | Brown, Geoffrey L. (Computer Modelling Group Ltd.) | Chen, Dingjun (Computer Modelling Group Ltd.) | Collins, David A. (Computer Modelling Group Ltd.)
Abstract Fully implicit petroleum reservoir simulations result in huge, often very ill-conditioned linear systems of equations to solve for different unknowns, for example, pressure and saturations. It is well known that the full system matrix contains both hyperbolic as well as nearly elliptic sub-systems. Since the solution of the coupled system is mainly determined by the solution of their elliptic (typically pressure) components, (CPR-type) two-stage preconditioning methods still belong to the most popular approaches to tackle such coupled systems. After a suitable extraction and decoupling, the numerically most costly step in such two-stage methods consists in solving these elliptic sub-systems. It is known that algebraic multigrid (AMG) provides a technique to solve elliptic linear equations very efficiently. The main advantage of AMG-based solvers – their numerical scalability – makes them particularly efficient for solving huge linear systems. Depending on the application, the system’s properties range from simple to highly indefinite. Unfortunately decoupling pressure and saturation related parts may introduce further difficulties. Consequently, in complex industrial simulations, the application of AMG to elliptic sub-systems might not be straightforward. In fact, an important goal in defining an efficient two-stage preconditioning strategy consists in extracting elliptic sub-systems that are suitable for an efficient AMG solution and, at the same time, ensure a fast overall convergence of the two-stage approach. The importance of this will be demonstrated for several industrial cases. In particular, some of these cases are very hard to solve by AMG if applied in a standard way. Preliminary results for a CPR-type coupling of SAMG to CMG’s PARASOL, a variable degree variable ordering ILU preconditioner using FGMRES, are compared to using PARASOL by itself. Alternative preconditioning operators will be presented giving elliptic sub-systems which are not only more suitable for applying AMG efficiently but also help accelerate the CPR-type process. Comparisons with one-level iterative methods will show the acceleration by AMG is highly superior. Finally, a strategy is presented that combines all linear solver parts in one single AMG-iteration. In this sense CPR can be seen as a special case of AMG for systems. This, in turn, yields a – formally – very simple but simultaneously very flexible solution approach.
Abstract Unconventional reservoirs are characterized by sufficiently low permeabilities so that the pressure depletion from a producing well may not propagate far from the well during the life of a development. This is in contrast to conventional plays where the pressure transients may probe the entire reservoir in weeks to months. The concept of depth of investigation and its application to unconventional reservoirs provide the understanding necessary to describe and optimize the interaction between complex multi-stage fractured wells, reservoir heterogeneity, drainage volumes, pressure depletion, well rates, and the estimated ultimate recovery. Previous studies have performed unconventional reservoir analysis using more conventional reservoir simulation techniques. High resolution local PEBI grids and global corner point grids have been used to represent complex fracture geometry and conductivity and estimate subsequent well performance. However, these techniques do not provide the more geometric understanding provided by the depth of investigation and drainage volumes. The application of the depth of investigation to heterogeneous reservoirs can be obtained from an asymptotic expansion of the diffusivity equation leading to the Eikonal equation which describes the propagation of the pressure front. This equation is solved using a Fast Marching Method to calculate a diffusive time of flight at every location within the domain. The diffusive time of flight is directly related to pressure front propagation. Unlike in a reservoir simulator, this frontal propagation is determined in a single non-iterative calculation, which is extremely fast. Once the pressure fronts are determined spatially, we may apply a pseudo-steady state pressure approximation within the moving front to determine pressure depletion and well rates. In the current study, we extend the Fast Marching Method for solution of the Eikonal equation to complex simulation grids including corner point and unstructured grids. This allows the rapid approximation of reservoir simulation results without the need for flow simulation, and also provides the time-evolution of the well drainage volume for visualization. Understanding the drainage volume alone is useful for well spacing and multi-stage fracture spacing optimization. Additional potential applications include well trajectory and hydraulic fracture location optimization, reservoir model screening and ranking, matrix/fracture parameter estimation, uncertainty analysis and production data integration.
- Europe (1.00)
- North America > United States > Texas (0.47)
- North America > United States > Texas > Haynesville Shale Formation (0.99)
- North America > United States > Louisiana > Haynesville Shale Formation (0.99)
- North America > United States > Arkansas > Haynesville Shale Formation (0.99)