This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 182617, “Field-Scale Assisted History Matching Using a Systematic, Massively Parallel Ensemble-Kalman-Smoother Procedure,” by Binghuai Lin, Paul I. Crumpton, SPE, and Ali H. Dogru, SPE, Saudi Aramco, prepared for the 2017 SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20–22 February. The paper has not been peer reviewed. This work presents a systematic and rigorous approach of reservoir decomposition combined with the ensemble Kalman smoother to overcome the complexity and computational burden associated with history matching field-scale reservoirs in the Middle East. The paper provides the formulation of the iterative regularizing ensemble Kalman smoother, introduces the use of streamline maps to facilitate domain decomposition, and presents a discussion on covariance localization. Computational-efficiency problems are addressed by three levels of parallelization. Introduction History matching, in which uncertain parameters are chosen so the reservoir model can reproduce the historical field performance, plays a key role in field development. Several techniques have been developed in the past decades to address the history-matching problem. It is widely acknowledged that a single deterministic reservoir model is not sufficient to represent a reservoir’s complex characteristics along with its uncertainty. The underlying reason is that history matching is an ill-posed inverse problem with nonunique solutions that can match the historical data. To overcome the nonuniqueness problem in the history-matching process, the ensemble Kalman filter (EnKF) has been introduced to the petroleum industry with many successful applications. The EnKF can be characterized as a Monte Carlo version of the classic Kalman filter in the sense that it uses an ensemble of samples to represent necessary statistics, such as covariance of model parameters and the correlations between model parameters and observations. An important feature of the EnKF method is that it sequentially assimilates observations when available to update the realizations in the ensemble, which includes the un-certain model parameters and primary model state variables. Hence, the EnKF is suitable for real-time data assimilation to update the ensemble continuously when new data are available. The joint update of the model parameters and state variables, however, can result in physically implausible dynamic states. Alternatively, the ensemble-smoother (ES) method updates only the model parameters with all observations simultaneously and thus avoids inconsistent dynamic-state updates. The comparison of the performance of the EnKF and ES methods has revealed that the EnKF normally outperforms the ES method. This is because the ES method purely depends on the prior ensemble and avail-able data. For highly nonlinear dynamic systems, it is not sufficient to achieve desirable performance by only one update. Also, by assimilating all observations at once, the ES is prone to overshooting and divergence. An iterative ES was developed on the basis of the Levenberg-Marquardt method of regularizing the update direction and choosing the step length. This method normally requires a significant number of iterations to converge and, thus, becomes computationally prohibitive for large-scale models. An approach was later proposed to improve the performance of the ES by assimilating the same data sets multiple times. In this iterative ES procedure, the measurement-error covariance matrix is inflated to obtain suitable updates for each iteration.

Summary We propose a feature-oriented ensemble history-matching workflow with a focus on the integration of time-lapse seismic and electromagnetic (EM) data. The developed workflow consists of two main steps. First, the rock cross-properties, such as water saturation and porosity relating to both seismic and EM attributes, are estimated by joint inversion of seismic and EM data using an iterative ensemble smoother (ES). Second, the remaining model parameters of interest, such as permeability, are calibrated using the updated cross-properties. To assimilate the inverted-saturation information efficiently, we take a feature-oriented integration approach in which front positions are identified from the inverted-saturation field. Related model parameters are then conditioned to the interpreted fronts using the iterative ES with a distance parameterization. The novelty of the proposed approach consists of combining the feature-oriented history matching with ensemble-based geophysical inversion to achieve an efficient joint integration of multiple sources of geophysical data. The performance of the proposed history-matching workflow is examined using a 2D channelized reservoir model and a more-realistic 3D reservoir model with a crosswell configuration for seismic and EM surveys. It is demonstrated that the developed workflow provides a novel and effective way to calibrate reservoir models with multiple sources of geophysical data. The experimental results show a positive synergy effect on the characterization of model variables by jointly assimilating seismic and EM data.

Summary Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.

Summary Recently, Emerick and Reynolds ( 2012 ) introduced the ensemble smoother with multiple data assimilations (ES-MDA) for assisted history matching. With computational examples, they demonstrated that ES-MDA provides both a better data match and a better quantification of uncertainty than is obtained with the ensemble Kalman filter (EnKF). However, similar to EnKF, ES-MDA can experience near ensemble collapse and results in too many extreme values of rock-property fields for complex problems. These negative effects can be avoided by a judicious choice of the ES-MDA inflation factors, but, before this work, the optimal inflation factors could only be determined by trial and error. Here, we provide two automatic procedures for choosing the inflation factor for the next data-assimilation step adaptively as the history match proceeds. Both methods are motivated by knowledge of regularization procedures—the first is intuitive and heuristical; the second is motivated by existing theory on the regularization of least-squares inverse problems. We illustrate that the adaptive ES-MDA algorithms are superior to the original ES-MDA algorithm by history matching three-phase-flow production data for a complicated synthetic problem in which the reservoir-model parameters include the porosity, horizontal and vertical permeability fields, depths of the initial fluid contacts, and the parameters of power-law permeability curves.

Summary Time-lapse-seismic-data assimilation has been drawing the reservoir-engineering community's attention over the past few years. One of the advantages of including this kind of data to improve the reservoir-flow models is that it provides complementary information compared with the wells' production data. Ensemble-based methods are some of the standard tools used to calibrate reservoir models using time-lapse seismic data. One of the drawbacks of assimilating time-lapse seismic data involves the large data sets, mainly for large reservoir models. This situation leads to high-dimensional problems that demand significant computational resources to process and store the matrices when using conventional and straightforward methods. Another known issue associated with the ensemble-based methods is the limited ensemble sizes, which cause spurious correlations between the data and the parameters and limit the degrees of freedom. In this work, we propose a data-assimilation scheme using an efficient implementation of the subspace ensemble randomized maximum likelihood (SEnRML) method with local analysis. This method reduces the computational requirements for assimilating large data sets because the number of operations scales linearly with the number of observed data points. Furthermore, by implementing it with local analysis, we reduce the memory requirements at each update step and mitigate the effects of the limited ensemble sizes. We test two local analysis approaches: one distance-based approach and one correlation-based approach. We apply these implementations to two synthetic time-lapse-seismic-data-assimilation cases, one 2D example, and one field-scale application that mimics some of the real-field challenges. We compare the results with reference solutions and with the known ensemble smoother with multiple data assimilation (ES-MDA) using Kalman gain distance-based localization. The results show that our method can efficiently assimilate time-lapse seismic data, leading to updated models that are comparable with other straightforward methods. The correlation-based local analysis approach provided results similar to the distance-based approach, with the advantage that the former can be applied to data and parameters that do not have specific spatial positions.

Summary In general, a probabilistic framework for a modeling process involves two uncertainty spaces: model parameters and state variables (or predictions). The two uncertainty spaces in reservoir simulation are connected by the governing equations of flow and transport in porous media in the form of a reservoir simulator. In a forward problem (or a predictive run), the reservoir simulator directly maps the uncertainty space of the model parameters to the uncertainty space of the state variables. Conversely, an inverse problem (or history matching) aims to improve the descriptions of the model parameters by using the measurements of state variables. However, we cannot solve the inverse problem directly in practice. Numerous algorithms, including Kriging‐based inversion and the ensemble Kalman filter (EnKF) and its many variants, simplify the system by using a linear assumption. The purpose of this paper is to improve the integration of measurement errors in the history‐matching algorithms that rely on the linear assumption. The statistical moment equation (SME) approach with the Kriging‐based inversion algorithm is used to illustrate several practical examples. In the Motivation section, an example of pressure conditioning has a measurement that contains no additional information because of its significant measurement error. This example highlights the inadequacy of the current method that underestimates the conditional uncertainty for both model parameters and predictions. Accordingly, we derive a new formula that recognizes the absence of additional information and preserves the unconditional uncertainty. We believe this to be the consistent behavior to integrate measurement errors. Other examples are used to validate the new formula with both linear and nonlinear (i.e., the saturation equation) problems, with single and multiple measurements, and with different configurations of measurement errors. For broader applications, we also develop an equivalent formula for algorithms in the Monte Carlo simulation (MCS) approach, such as EnKF and ensemble smoother (ES).