History Matching Of Reservoir Models Research Articles

Inclusion of seismic attributes in reservoir ensemble coverage analysis

There is a lack of quality-control (QC) methods to ensure measured seismic data are within the span of modeled seismic data in the context of ensemble-based seismic history matching of reservoir models. The dimensionality of seismic data makes it difficult to visualize the data and further compare them to the large number of ensembles in an efficient manner. Two attributes called coverage and importance are introduced to incorporate the key elements of reviewing an ensemble. The coverage attribute delineates where the set of models replicates the measured data, and the importance attribute identifies where it is important to fit the data above the noise threshold. The two attributes are then combined to highlight in which spatial area our reservoir model ensemble appropriately models the data and where a significant discrepancy exists between our ensemble of models and the measured data. The attributes are closely connected to noise, as coverage always must be analyzed in terms of the noise level. Although noise may not be explicitly corrected for, the methodology corrects the attributes for the noise assessed. The method is applied on two data examples from field seismic data: a 4D absolute difference amplitude map and a 4D relative impedance difference cube. The first example shows how changing the oil-water contact of the ensemble can improve the coverage without any history matching, and the second shows how it is more difficult to get a good coverage using 3D seismic attributes rather than using 2D maps of seismic data. The proposed QC attributes provide tools to better manage coverage of seismic data in the ensemble.

Managing Uncertainty in Geological CO2 Storage Using Bayesian Evidential Learning

Carbon capture and storage (CCS) has been increasingly looking like a promising strategy to reduce CO2 emissions and meet the Paris agreement’s climate target. To ensure that CCS is safe and successful, an efficient monitoring program that will prevent storage reservoir leakage and drinking water contamination in groundwater aquifers must be implemented. However, geologic CO2 sequestration (GCS) sites are not completely certain about the geological properties, which makes it difficult to predict the behavior of the injected gases, CO2 brine leakage rates through wellbores, and CO2 plume migration. Significant effort is required to observe how CO2 behaves in reservoirs. A key question is: Will the CO2 injection and storage behave as expected, and can we anticipate leakages? History matching of reservoir models can mitigate uncertainty towards a predictive strategy. It could prove challenging to develop a set of history matching models that preserve geological realism. A new Bayesian evidential learning (BEL) protocol for uncertainty quantification was released through literature, as an alternative to the model-space inversion in the history-matching approach. Consequently, an ensemble of previous geological models was developed using a prior distribution’s Monte Carlo simulation, followed by direct forecasting (DF) for joint uncertainty quantification. The goal of this work is to use prior models to identify a statistical relationship between data prediction, ensemble models, and data variables, without any explicit model inversion. The paper also introduces a new DF implementation using an ensemble smoother and shows that the new implementation can make the computation more robust than the standard method. The Utsira saline aquifer west of Norway is used to exemplify BEL’s ability to predict the CO2 mass and leakages and improve decision support regarding CO2 storage projects.

Выбор математического выражения и компонентного состава целевой функции для автоматизированной адаптации геолого-гидродинамических моделей

Выбор математического выражения и компонентного состава целевой функции для автоматизированной адаптации геолого-гидродинамических моделей

A multiobjective dominance and decomposition algorithm for reservoir model history matching

Reservoir model history matching is a multiobjective optimization problem. It involves the adjustment of relevant reservoir model input parameters, to minimize the mismatch between simulated and observed reservoir responses and to obtain a diverse set of geologically plausible reservoir simulation models. Typically, single objective optimization methods are adopted during history matching. This requires weighted sum scalarization. However, scalarization biases the optimization search, limiting the diversity of the recovered solutions. In this work, a computer assisted history matching procedure based on transform parameterization and a multiobjective evolutionary algorithm with dominance and decomposition (MOEA/DD) is proposed. In the procedure, history matching is treated as a multiobjective optimization problem, parameterized in terms of a small number of kernel principal component analysis (KPCA) variables. KPCA provides efficient parameterization of the reservoir model input property fields. Concurrently, MOEA/DD provides robust and unbiased optimization over multiple objectives. The effectiveness of the proposed procedure is demonstrated with the UNISIM-I-H history matching benchmark problem.

Sensitivity-based upscaling for history matching of reservoir models

Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical. Consequently, upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs. This is because as the number of grid blocks increases, the number of flow equations increases and this increases, in large proportion, the time required for solving flow problems. Although we can adopt parallel computation to share the load, a large number of grid blocks still pose significant computational challenges. Thus, upscaling acts as a bridge between the reservoir scale and the simulation scale. However as the upscaling ratio is increased, the accuracy of the numerical simulation is reduced; hence, there is a need to keep a balance between the two. In this work, we present a sensitivity-based upscaling technique that is applicable during history matching. This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix. The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp–wk approach. In the 2Dwp–wk approach, a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression. The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix. The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled. In essence, neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model, thus integrating upscaling with wavelet multiscale inverse modeling. We apply the method to estimate the parameters of two synthetic reservoirs. The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis. The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results. The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.

Technology Focus: History Matching and Forecasting (April 2015)

Technology Focus Production forecasting is one of the main tasks of engineers involved in reservoir management. To perform it, they resort to models, which vary from simple decline curves to complex numerical simulations. Regardless of the model’s level of complexity, uncertainty will always exist in the forecasts. Therefore, reservoir engineers devote significant efforts trying to incorporate data in these models (history matching), aiming to mitigate uncertainty and improve the reliability of the predictions. The reservoir-history-matching literature is quite extensive. The first works on automatic history matching were published in the 1960s. Nowadays, there is a wealth of history-matching methods. As a result, we observe that it is becoming a common industrial practice to generate multiple history-matched models, even for fairly complex problems with thousands of uncertainty variables and a large amount of data. However, we are still far from a definitive solution. Actually, it seems that there will be no single best history-matching technique. Instead, what we may have is the best method for the specific problem. Moreover, there are many challenges that are not completely addressed. In particular, most of the approaches seem overly simplistic to handle complex geology and structural uncertainties. Also, the computational demand for uncertainty quantification remains an issue. Therefore, industry and academia still have much work to do. Another point I want to mention is that, back in 2009, SPE promoted a forum meeting titled “Getting to Robust Production Forecasts.” This meeting became the startup of a Global Integrated Workshop Series on production forecasting. To date, there have been six meetings; the latest was held this year in Malaysia. These workshops have the ambitious goal of developing a production-forecasting guideline. I think we will hear more about this in the coming years. The papers summarized in this feature and the ones indicated in the additional-reading list are good examples of recent developments and field applications of history matching and forecasting. I hope you enjoy them. JPT Recommended additional reading at OnePetro: www.onepetro.org. SPE 163582 An Ensemble-Based Nonlinear Orthogonal Matching Pursuit Algorithm for Sparse History Matching of Reservoir Models by Ahmed H. Elsheikh, The University of Texas at Austin, et al. SPE 170622 Integrated Subsurface Uncertainty Study and Application—A Case Study of a Chalk Reservoir, Greater Ekofisk Area, North Sea by H.J. Yu, ConocoPhillips, et al. SPE 170945 Practical Considerations for Forecasting Production Data in Unconventional Reservoirs—Variable- Pressure Drop Case by P.W. Collins, Texas A&M University, et al.

Characterization of Non-Gaussian Geologic Facies Distribution Using Ensemble Kalman Filter with Probability Weighted Re-Sampling

The Ensemble Kalman Filter (EnKF) is a Monte Carlo-based technique for assisted history matching and real-time updating of reservoir models. However, it often fails to detect precise locations of distinct facies boundaries and their proportions, as the facies distributions are non-Gaussian, while geologic data for reservoir modeling is usually insufficient. In this paper, a new re-sampling step is introduced to the conventional EnKF formulation; after certain number of assimilation steps, the updated ensemble is used to generate a new ensemble with a novel probability weighted re-sampling scheme. The new ensemble samples from a probability density function that is conditional to both the geological information and the early production data. After the re-sampling step, the forecast model is applied to the new ensemble from the beginning up to the last update step (without any intermediate Kalman updates). Full EnKF is again applied on the ensemble members to assimilate the remaining production history. Combination of EnKF and regenerating new members using the re-sampling method demonstrates reasonable improvement and reduction of uncertainty in history matching of reservoir models with multiple facies. The histogram and the experimental variogram of the updated ensemble members are more consistent with the static geologic information. Moreover, the technique helps maintaining ensemble variance which is essential for uncertainty estimation in the posterior probability distribution of facies proportions.

A multiresolution adjoint sensitivity analysis of time-lapse saturation maps

Improvements in seismic data acquisition and processing have made seismic technology a viable source of information for locating hydrocarbon deposits and also for describing the spatial variability of reservoir parameters. While three-dimensional seismic technology is already a well-established means of locating hydrocarbon deposits, the 4D (or time-lapse) seismic is gradually becoming a source of reservoir parameter description. In particular, time-lapse seismic is increasingly becoming a useful source of information about fluid migration and pressure changes in the reservoir. In recent years, time-lapse seismic data or saturation maps derived from such data have been used to estimate spatial distribution of reservoir parameters through history matching. However, successful application of the method to accurate description of reservoir parameter variability remains a challenge. Some major challenges in the application of time-lapse seismic data in reservoir model history match are the poor resolution of the seismic data, uncertainty associated with the maps of changes in saturation derived from the seismic data, and the massiveness of the data or the associated saturation maps. Repeat seismic data are blurred or low-resolution maps of trends in reservoir responses to production and injection activities. These trends are influenced by reservoir property distribution and when used judiciously, constitute a good source of information that can help in reducing the uncertainty associated with reservoir parameter estimates. The maps of changes in reservoir saturation or pressure obtained from repeat seismic data are themselves fraught with uncertainties and care must be taken when using these maps to estimate reservoir parameters. Furthermore, obtaining the most useful information from a voluminous seismic data set is challenging and is still an active area of research. In this work, we present the use of the wavelet transform to integrate maps of changes in reservoir saturation derived from time-lapse seismic data into reservoir model history matching. The work involves transforming the saturation-change map into a wavelet space and then history matching some carefully selected wavelets to obtain estimates of reservoir parameters. Three sample applications based on synthetic data are used to show the suitability of the approach. Comparison is made to conventional approach in which the saturation-change map is not transformed into wavelets before matching.

Sparse History Matching: Nonlinear-Orthogonal-Matching-Pursuit Algorithm

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 163582, ’An Ensemble-Based Nonlinear-Orthogonal-Matching-Pursuit Algorithm for Sparse History Matching of Reservoir Models,’ by Ahmed H. Elsheikh, University of Texas at Austin, King Abdullah University of Science and Technology; Mary F. Wheeler, SPE, University of Texas at Austin; and Ibrahim Hoteit, King Abdullah University of Science and Technology, prepared for the 2013 SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18-20 February. The paper has not been peer reviewed. A nonlinear orthogonal-matching pursuit (NOMP) for sparse calibration of reservoir models has been proposed. Sparse calibration is a challenging problem because the unknowns are the nonzero components of the solution and their associated weights. NOMP is a greedy algorithm that, at each iteration, discovers components of the basis functions that are most correlated with the residual. The proposed algorithm relies on approximate-gradient estimation by use of an iterative-stochastic-ensemble method (ISEM). ISEM uses an ensemble of directional derivatives to approximate gradients efficiently. Introduction Subsurface-flow models rely on many parameters that cannot be measured directly. Instead, a sparse set of measurements may exist at well locations. The complete distributions of these unknown fields commonly are inferred by a model-calibration process that takes into account historical re-cords of the input/output of the model. However, the amount of data available to constrain the models often is limited in quantity and quality. The result is an ill-posed inverse problem that might allow many different solutions. Parameter-estimation techniques that can be applied to this problem can be classified into Bayesian methods based on Markov-chain Monte Carlo methods, gradient-based-optimization methods, and ensemble-Kalman-filter methods. An important step in the automatic-calibration process is to define a proper parameterization of these unknown fields. Most of the parameterization methods depend on a previous model’s assumptions that define the spatial correlations of the unknown fields implicitly with a parameter-covariance matrix. Karhunen-Loève expansion (KLE) can be used for parameterizing spatially distributed fields. KLE, also known as proper orthogonal decomposition or principal-component analysis in the finite-dimensional case, is widely used for parameterizing the permeability field in subsurface-flow models. KLE is an effective method that is simple to implement; however, it preserves only the second-order moments of the distribution. For complex continuous geological structures such as a channelized domain, KLE fails to preserve higher-order moments. Sparse calibration and compressed sensing are active research areas in the signal-processing community. Standard reconstruction methods rely on defining a set of basis functions that are orthogonal, as in KLE methods, and then an attempt is made to find the optimal set of weights to reconstruct the measurements. This reconstruction problem is an ill-posed problem, and regularization techniques (i.e., Tikhonov regularization) that constrain the ℓ2 norm of the solution are applied commonly. The quality of the solution depends on the class of basis functions used to parameterize the search space. In sparse-calibration methods, a large collection of basis functions is included in a dictionary, and the solution process consists of picking the best basis functions for accurate reconstruction of the unknown field and finding the associated weights.

Estimating Facies Fields by Use of the Ensemble Kalman Filter and Distance Functions—Applied to Shallow-Marine Environments

Summary The ensemble Kalman filter (EnKF) is one of the most promising tools for assisted history matching of reservoir models, but challenges remain for applications on complex geological structures (facies fields). In this paper, we propose a method that uses distance functions to estimate such fields. The definition of a distance function is “the shortest distance between a given position in the field and the boundary separating facies types.” The idea behind this approach is that distances have smooth properties, and the distribution of the ensemble in a given gridblock is without multimodality and in better agreement with the EnKF Gaussianity assumptions. The distances are then updated by use of the EnKF and converted to petrophysical parameters when the reservoir simulator is run to the next assimilation time. The approach is flexible and simple and possesses several advantages compared with other existing methods: The input items for the method are facies realizations that can be generated with any preferred geostatistical tool; we ensure that the updated fields always are facies realizations; we ensure the conditioning of the correct facies types at the well location, both initially and during the assimilation steps; and the method does not involve complex modifications of the standard EnKF equations. The approach presented here is based on an extension of previous work performed by the authors. The novelty of the extension is summarized by the following: Any number of specified facies types can be estimated; one distance function is used for each facies type—at each gridblock, the facies type that corresponds to the distance function with maximal value is selected; there are no restrictions on the structure of the facies field to be estimated; and the methodology is extended to update variations in the petrophysical parameters within each facies type. The first of these extensions is considered the most important because the flexibility regarding the number of facies types is necessary for every real industrial application. We demonstrate the methodology on a field with shallow-marine-environment characteristics. The conclusions from the example are that the history match is improved, uncertainty is reduced, and the method always returns facies realizations with geological authenticity.

Estimating Facies Fields Using the Ensemble Kalman Filter and Distance Functions

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 143031, ’Estimating Facies Fields Using the Ensemble Kalman Filter and Distance Functions - Applied to Shallow Marine Environments,’ by Rolf J. Lorentzen, SPE, Geir Nevdal, SPE, and Ali Shafieirad, SPE, International Research Institute of Stavanger, prepared for the 2011 SPE Europec/EAGE Annual Conference and Exhibition, Vienna, Austria, 23-26 May 2011. The paper has not been peer reviewed. The ensemble Kalman filter (EnKF) is a promising tool for assisted history matching of reservoir models, and it works well for cases in which petrophysical properties are modeled by use of Gaussian random fields with variogram models. Many reservoirs have complex geological structures, which can have rapid spatial variations in the petrophysical properties (e.g., permeability and porosity). Applying the EnKF directly on such reservoirs can lose characteristics of the fields (i.e., sharp gradients are smeared). A method is proposed in which distance functions are used to estimate an arbitrary number of facies types. Introduction The goal for using the EnKF on complex reservoirs is to ensure that the updated fields are facies realizations, or at least approximations, and that a good history match is obtained. Truncated pluri-Gaussian methods are used for updating facies fields. Here, two Gaussian random fields are defined on the model grid. These fields then are updated by use of the EnKF, instead of updating the petrophysical properties directly. A truncation map then is used to assign specific combinations of the two Gaussian fields to a particular facies type. A different approach is to extend the EnKF to sample from Gaussian mixture models. The Gaussian mixture models can have multimodal distributions and are, thereby, more suited for facies fields. The distributions are obtained by computing a weighted sum of standard Gaussian distributions. The extension of the EnKF involves computation of the weights, conditional mean, and conditional covariances. The method presented here introduces one level-set function for each facies type. The result is several distances at each gridblock with the same sign; therefore, the maximum of the distances in a given gridblock is used to determine the facies type. This method presents no restrictions on the structure of the facies field to be estimated, and any type of facies field may be estimated. A problem with this approach is that it is unlikely that the two functions change sign in the same gridblock, which makes it difficult to estimate fields if all types of transitions between facies types occur (i.e., it is difficult to estimate fields in which Facies 1 borders against Facies 4, or Facies 2 borders against Facies 3).