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Book Population based Algorithms for Improved History Matching and Uncertainty Quantification of Petroleum Reservoirs

Download or read book Population based Algorithms for Improved History Matching and Uncertainty Quantification of Petroleum Reservoirs written by Yasin Hajizadeh and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality.

Book Novel Sampling Techniques for Reservoir History Matching Optimisation and Uncertainty Quantification in Flow Prediction

Download or read book Novel Sampling Techniques for Reservoir History Matching Optimisation and Uncertainty Quantification in Flow Prediction written by Lina Mahgoub Yahya Mohamed and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern reservoir management has an increasing focus on accurately predicting the likely range of field recoveries. A variety of assisted history matching techniques has been developed across the research community concerned with this topic. These techniques are based on obtaining multiple models that closely reproduce the historical flow behaviour of a reservoir. The set of resulted history matched models is then used to quantify uncertainty in predicting the future performance of the reservoir and providing economic evaluations for different field development strategies. The key step in this workflow is to employ algorithms that sample the parameter space in an efficient but appropriate manner. The algorithm choice has an impact on how fast a model is obtained and how well the model fits the production data. The sampling techniques that have been developed to date include, among others, gradient based methods, evolutionary algorithms, and ensemble Kalman filter (EnKF). This thesis has investigated and further developed the following sampling and inference techniques: Particle Swarm Optimisation (PSO), Hamiltonian Monte Carlo, and Population Markov Chain Monte Carlo. The inspected techniques have the capability of navigating the parameter space and producing history matched models that can be used to quantify the uncertainty in the forecasts in a faster and more reliable way. The analysis of these techniques, compared with Neighbourhood Algorithm (NA), has shown how the different techniques affect the predicted recovery from petroleum systems and the benefits of the developed methods over the NA. The history matching problem is multi-objective in nature, with the production data possibly consisting of multiple types, coming from different wells, and collected at different times. Multiple objectives can be constructed from these data and explicitly be optimised in the multi-objective scheme. The thesis has extended the PSO to handle multi-objective history matching problems in which a number of possible conflicting objectives must be satisfied simultaneously. The benefits and efficiency of innovative multi-objective particle swarm scheme (MOPSO) are demonstrated for synthetic reservoirs. It is demonstrated that the MOPSO procedure can provide a substantial improvement in finding a diverse set of good fitting models with a fewer number of very costly forward simulations runs than the standard single objective case, depending on how the objectives are constructed. The thesis has also shown how to tackle a large number of unknown parameters through the coupling of high performance global optimisation algorithms, such as PSO, with model reduction techniques such as kernel principal component analysis (PCA), for parameterising spatially correlated random fields. The results of the PSO-PCA coupling applied to a recent SPE benchmark history matching problem have demonstrated that the approach is indeed applicable for practical problems. A comparison of PSO with the EnKF data assimilation method has been carried out and has concluded that both methods have obtained comparable results on the example case. This point reinforces the need for using a range of assisted history matching algorithms for more confidence in predictions.

Book Intelligent Digital Oil and Gas Fields

Download or read book Intelligent Digital Oil and Gas Fields written by Gustavo Carvajal and published by Gulf Professional Publishing. This book was released on 2017-12-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intelligent Digital Oil and Gas Fields: Concepts, Collaboration, and Right-time Decisions delivers to the reader a roadmap through the fast-paced changes in the digital oil field landscape of technology in the form of new sensors, well mechanics such as downhole valves, data analytics and models for dealing with a barrage of data, and changes in the way professionals collaborate on decisions. The book introduces the new age of digital oil and gas technology and process components and provides a backdrop to the value and experience industry has achieved from these in the last few years. The book then takes the reader on a journey first at a well level through instrumentation and measurement for real-time data acquisition, and then provides practical information on analytics on the real-time data. Artificial intelligence techniques provide insights from the data. The road then travels to the "integrated asset" by detailing how companies utilize Integrated Asset Models to manage assets (reservoirs) within DOF context. From model to practice, new ways to operate smart wells enable optimizing the asset. Intelligent Digital Oil and Gas Fields is packed with examples and lessons learned from various case studies and provides extensive references for further reading and a final chapter on the "next generation digital oil field," e.g., cloud computing, big data analytics and advances in nanotechnology. This book is a reference that can help managers, engineers, operations, and IT experts understand specifics on how to filter data to create useful information, address analytics, and link workflows across the production value chain enabling teams to make better decisions with a higher degree of certainty and reduced risk. Covers multiple examples and lessons learned from a variety of reservoirs from around the world and production situations Includes techniques on change management and collaboration Delivers real and readily applicable knowledge on technical equipment, workflows and data challenges such as acquisition and quality control that make up the digital oil and gas field solutions of today Describes collaborative systems and ways of working and how companies are transitioning work force to use the technology and making more optimal decisions

Book Dictionary of Mathematical Geosciences

Download or read book Dictionary of Mathematical Geosciences written by Richard J. Howarth and published by Springer. This book was released on 2017-05-27 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dictionary includes a number of mathematical, statistical and computing terms and their definitions to assist geoscientists and provide guidance on the methods and terminology encountered in the literature. Each technical term used in the explanations can be found in the dictionary which also includes explanations of basics, such as trigonometric functions and logarithms. There are also citations from the relevant literature to show the term’s first use in mathematics, statistics, etc. and its subsequent usage in geosciences.

Book Parallel Problem Solving from Nature   PPSN XII

Download or read book Parallel Problem Solving from Nature PPSN XII written by Carlos Coello Coello and published by Springer. This book was released on 2012-08-27 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 7491 and 7492 constitutes the refereed proceedings of the 12th International Conference on Parallel Problem Solving from Nature, PPSN 2012, held in Taormina, Sicily, Italy, in September 2012. The total of 105 revised full papers were carefully reviewed and selected from 226 submissions. The meeting began with 6 workshops which offered an ideal opportunity to explore specific topics in evolutionary computation, bio-inspired computing and metaheuristics. PPSN 2012 also included 8 tutorials. The papers are organized in topical sections on evolutionary computation; machine learning, classifier systems, image processing; experimental analysis, encoding, EDA, GP; multiobjective optimization; swarm intelligence, collective behavior, coevolution and robotics; memetic algorithms, hybridized techniques, meta and hyperheuristics; and applications.

Book Introduction to Geological Uncertainty Management in Reservoir Characterization and Optimization

Download or read book Introduction to Geological Uncertainty Management in Reservoir Characterization and Optimization written by Reza Yousefzadeh and published by Springer Nature. This book was released on 2023-04-08 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores methods for managing uncertainty in reservoir characterization and optimization. It covers the fundamentals, challenges, and solutions to tackle the challenges made by geological uncertainty. The first chapter discusses types and sources of uncertainty and the challenges in different phases of reservoir management, along with general methods to manage it. The second chapter focuses on geological uncertainty, explaining its impact on field development and methods to handle it using prior information, seismic and petrophysical data, and geological parametrization. The third chapter deals with reducing geological uncertainty through history matching and the various methods used, including closed-loop management, ensemble assimilation, and stochastic optimization. The fourth chapter presents dimensionality reduction methods to tackle high-dimensional geological realizations. The fifth chapter covers field development optimization using robust optimization, including solutions for its challenges such as high computational cost and risk attitudes. The final chapter introduces different types of proxy models in history matching and robust optimization, discussing their pros and cons, and applications. The book will be of interest to researchers and professors, geologists and professionals in oil and gas production and exploration.

Book Reservoir Characterization and History Matching with Uncertainty Quantification Using Ensemble based Data Assimilation with Data Re parameterization

Download or read book Reservoir Characterization and History Matching with Uncertainty Quantification Using Ensemble based Data Assimilation with Data Re parameterization written by Mingliang Liu and published by . This book was released on 2021 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir characterization and history matching are essential steps in various subsurface applications, such as petroleum exploration and production and geological carbon sequestration, aiming to estimate the rock and fluid properties of the subsurface from geophysical measurements and borehole data. Mathematically, both tasks can be formulated as inverse problems, which attempt to find optimal earth models that are consistent with the true measurements. The objective of this dissertation is to develop a stochastic inversion method to improve the accuracy of predicted reservoir properties as well as quantification of the associated uncertainty by assimilating both the surface geophysical observations and the production data from borehole using Ensemble Smoother with Multiple Data Assimilation. To avoid the common phenomenon of ensemble collapse in which the model uncertainty would be underestimated, we propose to re-parameterize the high-dimensional geophysics data with data order reduction methods, for example, singular value decomposition and deep convolutional autoencoder, and then perform the models updating efficiently in the low-dimensional data space. We first apply the method to seismic and rock physics inversion for the joint estimation of elastic and petrophysical properties from the pre-stack seismic data. In the production or monitoring stage, we extend the proposed method to seismic history matching for the prediction of porosity and permeability models by integrating both the time-lapse seismic and production data. The proposed method is tested on synthetic examples and successfully applied in petroleum exploration and production and carbon dioxide sequestration.

Book Data Analytics in Reservoir Engineering

Download or read book Data Analytics in Reservoir Engineering written by Sathish Sankaran and published by . This book was released on 2020-10-29 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Analytics in Reservoir Engineering describes the relevance of data analytics for the oil and gas industry, with particular emphasis on reservoir engineering.

Book Modelling and Quantification of Structural Uncertainties in Petroleum Reservoirs Assisted by a Hybrid Cartesian Cut Cell

Download or read book Modelling and Quantification of Structural Uncertainties in Petroleum Reservoirs Assisted by a Hybrid Cartesian Cut Cell written by Mohammad Ahmadi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir distributed properties and reservoir structure calls for History Matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history-matched models which might result in different predictions of reservoir performance. Uncertainty Quantification restricts the raised model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of Uncertainty Quantification ignore large scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more intensely compared with petrophysical uncertainty. What makes the quantification of structural uncertainty impracticable is the need for global regridding at each step of History Matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian Cut Cell Method which decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of History Matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of class Locally Conservative Flux Continuous Methods (Extended Enriched Multipoint Flux Approximation Method abbreviated to extended EMPFA). The robustness and consistency of proposed Hybrid Cartesian Cut Cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. In this research, the general framework of Uncertainty Quantification is extended and well-equipped by proposed approach to tackle uncertainties of different structures such as reservoir horizons, bedding layers, faults and pinchouts. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic models of uncertain structures. Also this thesis provides a comparative study of structural uncertainty influence on reservoir forecasts among various geological structures.

Book DEVELOPMENT OF AN ASSISTED HISTORY MATCHING AND UNCERTAINTY QUANTIFICATION TOOL BASED ON GAUSSIAN PROCESSES PROXY MODELS AND VARIOGRAM BASED SENSITIVITY ANALYSIS

Download or read book DEVELOPMENT OF AN ASSISTED HISTORY MATCHING AND UNCERTAINTY QUANTIFICATION TOOL BASED ON GAUSSIAN PROCESSES PROXY MODELS AND VARIOGRAM BASED SENSITIVITY ANALYSIS written by Sachin Rana and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: History matching is an inverse solution process in which uncertain parameters of the numerical reservoir model are tuned in an eort to minimize the mismatch between simulated production and observed production data. History matching problem can be solved as an optimization or data assimilation problem. In this research, the history matching problem is solved from the optimization point of view. Currently, many commercial history matching tools use evolutionary strategy optimization algorithms such as dierential evolution, particle swarm optimization etc. to find solutions of history matching. However, these algorithms usually require a large number of numerical simulation runs in order to converge to acceptable solutions. If each numerical simulation takes an extensive time to complete, these algorithms become inecient. In this research, a new assisted history matching tool named as GP-VARS is presented that can provide multiple solutions of history matching fewer numerical simulations. GP-VARS uses Gaussian process (GP) based proxy models to provide fast approximate forward solutions which are used in Bayesian optimization to find history match solutions in an iterative manner. An application of VARS based sensitivity analysis is applied on forward GP model to calculate the sensitivity index for uncertain reservoir parameters. The results of sensitivity analysis are used to regulate the lower and upper bounds of dierent reservoir parameters in order to achieve faster convergence. A second GP model is used to provide an inverse solution which also provides temporary history match solutions. Since the history matching problem has non-unique solutions, the uncertainty in reservoir parameters is quantified using Markov Chain Monte Carlo (MCMC ) sampling from the trained forward GP model. The collected MCMC samples are then passed to a third GP model that is trained to predict the EUR values for any combination of reservoir parameters. The GP-VARS methodology is applied to three dierent heterogeneous reservoir case studies including a benchmark PUNQ-S3 reservoir located in north sea and the M4.1 reservoir located in Gulf of Mexico. The results show that history matching can be performed in approximately four times less number of numerical simulation runs as compared to the state of the art dierential evolution algorithm. In addition, it was found that the P50 estimates of EUR are in close agreement with truth values in the presented case studies.

Book Modelling and Quantification of Structural Uncertainties in Petroleum Reservoirs Assisted by a Hybrid Cartesian Cut Cell enriched Multipoint Flux Approximation Approach

Download or read book Modelling and Quantification of Structural Uncertainties in Petroleum Reservoirs Assisted by a Hybrid Cartesian Cut Cell enriched Multipoint Flux Approximation Approach written by Mohammad Ahmadi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir distributed properties and reservoir structure calls for History Matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history-matched models which might result in different predictions of reservoir performance. Uncertainty Quantification restricts the raised model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of Uncertainty Quantification ignore large scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more intensely compared with petrophysical uncertainty. What makes the quantification of structural uncertainty impracticable is the need for global regridding at each step of History Matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian Cut Cell Method which decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of History Matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of class Locally Conservative Flux Continuous Methods (Extended Enriched Multipoint Flux Approximation Method abbreviated to extended EMPFA). The robustness and consistency of proposed Hybrid Cartesian Cut Cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. In this research, the general framework of Uncertainty Quantification is extended and well-equipped by proposed approach to tackle uncertainties of different structures such as reservoir horizons, bedding layers, faults and pinchouts. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic models of uncertain structures. Also this thesis provides a comparative study of structural uncertainty influence on reservoir forecasts among various geological structures.

Book History Matching and Uncertainty Characterization

Download or read book History Matching and Uncertainty Characterization written by Alexandre Emerick and published by LAP Lambert Academic Publishing. This book was released on 2012-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. Among these methods, the ensemble Kalman filter (EnKF) is the most popular one for history-matching applications. The main advantages of EnKF are computational efficiency and easy implementation. Moreover, because EnKF generates multiple history-matched models, EnKF can provide a measure of the uncertainty in reservoir performance predictions. However, because of the inherent assumptions of linearity and Gaussianity and the use of limited ensemble sizes, EnKF does not always provide an acceptable history-match and does not provide an accurate characterization of uncertainty. In this work, we investigate the use of ensemble-based methods, with emphasis on the EnKF, and propose modifications that allow us to obtain a better history match and a more accurate characterization of the uncertainty in reservoir description and reservoir performance predictions.

Book Quantification of Uncertainty During History Matching

Download or read book Quantification of Uncertainty During History Matching written by Martin Guillermo Alvarado and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study proposes a new, easily applied method to quantify uncertainty in production forecasts based on reservoir simulation. The new method uses only observed data and mismatches between simulated values and observed values as history matches of observations progress to a final "best" match. The method is applicable even when only limited information is available from a field. Previous methods suggested in the literature require more information than our new method. Quantifying uncertainty in production forecasts (i.e., reserve estimates) is becoming increasingly important in the petroleum industry. Many current investment opportunities in reservoir development require large investments, many in harsh exploration environments, with intensive technology requirements and possibly marginal investment indicators. Our method of quantifying uncertainty uses a set of history-match runs and includes a method to determine the probability density function (pdf) of future oil production (reserves) while the history match is evolving. We applied our method to the lower-Pleistocene 8-Sand reservoir in the Green Canyon 18 field, Gulf of Mexico. This field was a challenge to model because of its complicated geometry and stratigraphy. We objectively computed the mismatch between observed and simulated data using an objective function and developed quantitative matching criteria that we used during history matching. We developed a method based on errors in the mismatches to assign likelihood to each run, and from these results, we determined the pdf of reservoir reserves and thus quantified the uncertainty in the forecast. In our approach, we assigned no preconceived likelihoods to the distribution of variables. Only the production data and history matching errors were used to assess uncertainty. Thus, our simple method enabled us to estimate uncertainty during the history-matching process using only dynamic behavior of a reservoir.

Book Fundamental Controls on Fluid Flow in Carbonates

Download or read book Fundamental Controls on Fluid Flow in Carbonates written by S.M. Agar and published by Geological Society of London. This book was released on 2015-02-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights key challenges for fluid-flow prediction in carbonate reservoirs, the approaches currently employed to address these challenges and developments in fundamental science and technology. The papers span methods and case studies that highlight workflows and emerging technologies in the fields of geology, geophysics, petrophysics, reservoir modelling and computer science. Topics include: detailed pore-scale studies that explore fundamental processes and applications of imaging and flow modelling at the pore scale; case studies of diagenetic processes with complementary perspectives from reactive transport modelling; novel methods for rock typing; petrophysical studies that investigate the impact of diagenesis and fault-rock properties on acoustic signatures; mechanical modelling and seismic imaging of faults in carbonate rocks; modelling geological influences on seismic anisotropy; novel approaches to geological modelling; methods to represent key geological details in reservoir simulations and advances in computer visualization, analytics and interactions for geoscience and engineering.

Book History matching of Petroleum Reservoir Models by the Ensemble Kalman Filter and Parameterization Methods

Download or read book History matching of Petroleum Reservoir Models by the Ensemble Kalman Filter and Parameterization Methods written by Leila Heidari and published by . This book was released on 2011 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: History-matching enables integration of data acquired after the production in the reservoir model building workflow. Ensemble Kalman Filter (EnKF) is a sequential assimilation or history-matching method capable of integrating the measured data as soon as they are obtained. This work is based on the EnKF application for History-matching purposes and is divided into two main sections. First section deals with the application of the EnKF to several case studies in order to better understand the merits and shortcomings of the method. These case studies include two synthetic case studies (a simple one and a rather complex one), a Facies model and a real reservoir model. In most cases the method is successful in reproducing the measured data. The encountered problems are explained and possible solutions are proposed. Second section deals with two newly proposed algorithms combining the EnKF with two parameterization methods: pilot point method and gradual deformation method, which are capable of preserving second order statistical properties (mean and covariance). Both developed algorithms are applied to the simple synthetic case study. For the pilot point method, the application was successful through an adequate number and proper positioning of pilot points. In case of the gradual deformation, the application can be successful provided the background ensemble is large enough. For both cases, some improvement scenarios are proposed and further applications to more complex scenarios are recommended.

Book History Matching and Uncertainty Quantification Using Sampling Method

Download or read book History Matching and Uncertainty Quantification Using Sampling Method written by Xianlin Ma and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty quantification involves sampling the reservoir parameters correctly from a posterior probability function that is conditioned to both static and dynamic data. Rigorous sampling methods like Markov Chain Monte Carlo (MCMC) are known to sample from the distribution but can be computationally prohibitive for high resolution reservoir models. Approximate sampling methods are more efficient but less rigorous for nonlinear inverse problems. There is a need for an efficient and rigorous approach to uncertainty quantification for the nonlinear inverse problems. First, we propose a two-stage MCMC approach using sensitivities for quantifying uncertainty in history matching geological models. In the first stage, we compute the acceptance probability for a proposed change in reservoir parameters based on a linearized approximation to flow simulation in a small neighborhood of the previously computed dynamic data. In the second stage, those proposals that passed a selected criterion of the first stage are assessed by running full flow simulations to assure the rigorousness. Second, we propose a two-stage MCMC approach using response surface models for quantifying uncertainty. The formulation allows us to history match three-phase flow simultaneously. The built response exists independently of expensive flow simulation, and provides efficient samples for the reservoir simulation and MCMC in the second stage. Third, we propose a two-stage MCMC approach using upscaling and non-parametric regressions for quantifying uncertainty. A coarse grid model acts as a surrogate for the fine grid model by flow-based upscaling. The response correction of the coarse-scale model is performed by error modeling via the non-parametric regression to approximate the response of the computationally expensive fine-scale model. Our proposed two-stage sampling approaches are computationally efficient and rigorous with a significantly higher acceptance rate compared to traditional MCMC algorithms. Finally, we developed a coarsening algorithm to determine an optimal reservoir simulation grid by grouping fine scale layers in such a way that the heterogeneity measure of a defined static property is minimized within the layers. The optimal number of layers is then selected based on a statistical analysis. The power and utility of our approaches have been demonstrated using both synthetic and field examples.