Updating Stochastic Reservoir Models With New Production Data

Summary Reconciling multiscale data for reservoir characterization is a crucial issue, because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as well-test and production data. In this paper, we present a new methodology to directly update fine-scale geostatistically-based reservoir models by combining gradual deformation parameterization for the fine-scale geostatistical model, and an upscaling technique for the coarse-scale flow simulation model. As consequence, both fine- and coarse-scale models are updated by dynamic data during the history matching process. The proposed methodology includes: Perturbation of the fine-scale geostatistical model using the gradual deformation parameterization. Gradual deformation ensures the preservation of the overall geostatistical properties of the fine model. Generation of the coarse-scale flow simulation model by upscaling the fine-scale geostatistical model. Fluid-flow simulation and sensitivity computation of the flow simulation results with respect to the fine-scale parameterization. This sensitivity computation is analytical and takes into account the upscaling process. Direct updating of the fine-scale geostatistical model using classical optimization process. Direct updating ensures consistency between the fine- and coarse-scale models. The accuracy of the proposed methodology was improved by calibrating the flow simulation model. The objective of this calibration is to reduce the error introduced by the upscaling step during the flow simulation. We applied successfully our methodology for fine-scale reservoir characterization process by integrating permanent downhole gauge measurements directly into a 3D-geostatistical model containing about two million gridblocks. This test is designed to highlight several key issues of the proposed methodology: Efficiency of the upscaling step, coupled with gradient-based optimization to speed up history matching. Usefulness of the calibration step for a correct integration of upscaling techniques in history matching. Capability of the methodology for maintaining consistency and coherency between fine-scale and coarse-scale models. Improvement of the reservoir characterization process by integrating dynamic data at both fine geostatistical scale and coarse simulation scale.

The aim of the study is to condition stochastic generated realizations on well test data in order to improve simulation of fades and petrophysics in fluvial reservoirs. First we have used the pressure data to estimate the shortest distance from the well to a possible channel boundary and thereby simulate the channel structures. The well test also provides the permeability average in the part of the channel intersected by the well. Together with core/log data and general knowledge of the reservoir this have been used to simulate permeability. These permeability realizations is input to a numerical flow simulator and compared with experimental results of the well test.

This paper presents a new methodology for constraining 3-D stochastic reservoir models to well and historical production data. Based on the inversion framework, this methodology is mainly composed of a new algorithm for gradually deforming continuous geostatistical models and of an efficient optimization algorithm. The gradual deformation algorithm generates a process of realizations which evolve smoothly while preserving the overall statistical characteristics of the stochastic model. Deformation control by a limited number of parameters improves the efficiency of the process. In comparison with other approaches, the number of iterations is significantly reduced. The deformation procedure can be coupled with an optimization algorithm to obtain automatic history matching capability. The inversion of several model parameters and the gradual selection of a new constrained realization can be performed simultaneously. The analytical gradient method as well as approximated gradients are used to improve the convergence rate of the procedure. The successful application to a 3-D synthetic case, derived from an actual field case, is described in the paper. The shape of the top structure of the reservoir and the activity coefficient of an aquifer are simultaneously constrained to the historical data recorded for 5 wells. The structural uncertainties are described by a geostatistical model. The definition of the top structure is improved by gradual deformation to ensure the geostatistical consistency of the model during the match of production data. An interference well test case is also presented to illustrate the decrease in uncertainties obtained by integrating a geological description and pressure data. P. 221

Reservoir modeling is a critical step in the planning and development of oil fields. Before a reservoir model can be accepted for forecasting future production, the model has to be updated with historical production data. This process is called history matching. History matching requires computer flow simulation, which is very time‐consuming. As a result, only a small number of simulation runs are conducted and the history‐matching results are normally unsatisfactory. This is particularly evident when the reservoir has a long production history and the quality of production data is poor. The inadequacy of the history‐matching results frequently leads to high uncertainty of production forecasting. To enhance the quality of the history‐matching results and improve the confidence of production forecasts, we introduce a methodology using genetic programming (GP) to construct proxies for reservoir simulators. Acting as surrogates for the computer simulators, the “cheap” GP proxies can evaluate a large number (millions) of reservoir models within a very short time frame. With such a large sampling size, the reservoir history‐matching results are more informative and the production forecasts are more reliable than those based on a small number of simulation models. We have developed a workflow which incorporates the two GP proxies into the history matching and production forecast process. Additionally, we conducted a case study to demonstrate the effectiveness of this approach. The study has revealed useful reservoir information and delivered more reliable production forecasts. All of these were accomplished without introducing new computer simulation runs.

Using commercial numerical reservoir simulators to build a full field reservoir model and simultaneously history match multiple dynamic variables for a highly complex, offshore mature field in Malaysia, had proven to be challenging, manpower intensive, highly expensive, and not very successful. This field includes almost two hundred wells that have been completed in more than 60 different, non-continuous reservoir layers. The field has been producing oil, gas and water for decades. The objective of this article is to demonstrate how Artificial Intelligence (AI) and Machine Learning is used to build a purely data-driven reservoir simulation model that successfully history match all the dynamic variables for all the wells in this field and subsequently used for production forecast. The model has been validated in space and time. The AI and Machine Learning technology that was used to build the dynamic reservoir simulation and modeling is called spatio-temporal learning. Spatio-temporal learning is a machine-learning algorithm specifically developed for data-driven modeling of the physics of fluid flow through porous media. Spatio-temporal learning is used in the context of Deconvolutional Neural Networks. In this article Spatio-temporal Learning and Deconvolutional Neural Networks will be explained. This new technology is the result of more than 20 years of research and development in the application of AI and Machine Learning in reservoir modeling. This technology develops a coupled reservoir and wellbore model that for this particular oil & gas field in Malaysia uses choke setting, well-head pressure and well-head temperature as input and simultaneously history matches Oil production, GOR, WC, reservoir pressure, and water saturation for more than a hundred wells through a completely automated process. Once the data-driven reservoir model is developed and history matched, it is blind validated in space and time in order to establish a reliable and robust reservoir model to be used for decision making purposes and opportunity generation to maximise the field value. The concepts and the methodology of history match of multiple wells, individual offshore platforms, and the entire field will be presented in this article along with the results of blind validation and production forecasting. Results of using this model to perform uncertainty quantification will also be presented. A case study of a highly complex mature field with large number of wells and years of production has been used to be studied and simulated by this data-driven approach. Time, efforts, and resources required for the development of the dynamic reservoir simulation models using AI and Machine Learning is considerably less than time and resources required using the commercial numerical simulators. It is validated that the TDM developed model can make very reasonable prediction of field behavior and production from the existing wells based on modification of operational constraints and can be a prudent complementary tool to conventional numerical simulators for such complex assets.

Time-lapse seismic data has been widely used for the detailed reservoir characterization, and data assimilation algorithms are commonly used for petroleum reservoir history matching of production data. However, hardly any seismic data has been integrated into the reservoir inverse modeling workflow, due to the large data size, finer gridding, and especially the scarcity in time of the seismic data. Popular ensemble-based reservoir inverse modeling methods such as ensemble Kalman filter (EnKF) also face the problems of high computational cost due to the storage of the intermediate variables, restarting the reservoir simulating process and the inconsistency of the full-step and step-wise simulations. The intrinsic sequential data assimilations characteristics of the EnKF set obstacles to assimilate 4D seismic data. The alternative method can be the ensemble smoother (ES), which is an ensemble based method for data assimilation. The ES is based on a Bayesian updating scheme of the reservoir model to match the production history and improve the production forecast. To improve the algorithm convergence, a multiple data assimilation (MDA) method was proposed by Emerick and Reynolds (2012a). The algorithm we used is called ensemble smoother with multiple data assimilation (ESMDA), we modified the ESMDA to integrate the geophysical data, and created the new workflow to history match both the production and geophysical data. The available production data is well measurements, including oil production rate, well water cut and bottom-hole pressure, as well as time-lapse geophysical data, including P-wave impedance. In this paper, we first formulated the mathematical descriptions of ESMDA, we then down-scaled the seismic data, and modified the data assimilation algorithms, illustrated the history matching workflow for both production and geophysical data, finally, we showed how it works with a case study on a water flooding operation in a synthetic reservoir. In comparison, we also showed the history matching only on the production data, which yields an inferior results than the one matches both production and seismic data.

This paper presents an integrated methodology (using versatile history matching software) for constraining 3D stochastic reservoir models to well data and production history and its application to a real case (a tight-gas reservoir in the Southern North Sea). The approach is to formulate the history matching problem as a minimization problem where the objective function to be minimized is the squared difference of the real production data values and the corresponding simulated data. To resolve this inverse problem, we use gradient based optimization techniques to update the entire simulation workflow, thanks to advanced parametrization techniques. The set of model parameters characterizes the stochastic geological model (including the diagenetic modeling) and the fluid flow simulator, which allows the facies distributions (and their associated petrophysical properties), diagenetic overprint and well properties (such as skin) to be modified until an acceptable match is obtained. The parametrization technique is coupled to constrained optimization algorithms to ensure that model parameters remain within realistic bounds of the geological settings and ensures that the geologically derived stochastic properties of the initial reservoir are preserved throughout the history matching process. This application shows how the combination of a versatile history matching tool with efficient parametrization techniques can improve the quality and efficiency of a geologically driven history matching process. The speed of this process will be valuable when analyzing a set of history matched models allowing a better assessment to be made of the risk and uncertainty associated with predictions of future performance.

An increasing number of field development projects include rigorous uncertainty quantification workflows based on parameterized subsurface uncertainties. Reservoir model calibration workflows for reservoir simulation models including historical production data, also called history matching, deliver non-unique solutions and remain technically challenging. In addition, the validation process of the reservoir simulation model often introduces a break of the conceptual connection to the geological model. This raises questions on how to quantify the deviation between the calibrated simulation model and the original geological model. Workflow designs for history matching require scalable and efficient optimization techniques to address project needs. Derivative-free techniques like Markov Chain Monte Carlo (MCMC) are used for optimization and uncertainty quantification. Adjoint techniques derive analytical sensitivities directly from the flow equations. For history matching those sensitivities are efficiently used for property updates on grid block level. Both techniques have different characteristics and support alternative history matching strategies like global vs. local, stochastic vs. deterministic. In this work both techniques will be applied in an integrated workflow design to the Norne field. The Norne field is a North Sea oil-and-gas reservoir with approximately 30 wells, with one third being used for WAG injection for pressure support. Field data was previously released by Statoil and made available for a public benchmark study (NTNU Norway) testing history matching techniques including production and time-lapsed seismic data. We focus on well production data for history matching. MCMC is used for global parameter updates and uncertainty quantification in a Bayesian context. An implementation of an adjoint technique is applied for analytical sensitivity calculations and local parameter adjustments of rock properties. History matching results are presented for field wide and well-by-well production data. Consistency checks between updated and original geological model are presented for rock property distribution maps. Geostatistical measures including spatial correlations are used to quantify deviations between updated and original geological model. In conclusion scalability and performance efficiency of the practical workflow implementation is discussed with a perspective of a consistent feedback loop from history matching to geological modeling.

Assisted history matching (AHM) using Design of Experiments (DoE) is one of the most commonly applied history matching techniques in the oil and gas industry. When applied properly, this stochastic method finds a representative ensemble of history-matched reservoir models for probabilistic uncertainty analysis of production forecast. Although DoE-based AHM is straightforward in concept, it can be misused in practice because the workflow involves many statistical and modeling principles that should be followed rigorously. In this paper, the entire DoE-based AHM workflow is demonstrated in a coherent and comprehensive case study that is divided in seven key stages: problem framing, sensitivity analysis, proxy building, Monte-Carlo simulation, history-match filtering, production forecast, and representative model selection. Best practices of each stage are summarized to help reservoir management (RM) engineers understand and apply this powerful workflow for reliable history matching and probabilistic production forecasting. One major difficulty in any history matching method is to define the history-match tolerance, which reflects the engineer's comfort level of calling a reservoir model "history-matched" even though the difference between simulated and observed production data is not zero. It is a compromise to the intrinsic and unavoidable imperfectness of reservoir model construction, data measurement, and proxy creation. A practical procedure is provided to help engineers define the history-match tolerance considering the model, data-measurement, and proxy errors.

Full-physics models in history matching and optimization can be computationally expensive since these problems usually require hundreds of simulations or more. We have previously implemented a physics-based data-driven network model with a commercial simulator that serves as a surrogate without the need to build the 3-D geological model. In this paper, we reconstruct the network model to account for complex reservoir conditions of mature fields and successfully apply it to a diatomite reservoir in the San Joaquin Valley (SJV) for rapid history matching and optimization. The reservoir is simplified into a network of 1-D connections between well perforations. These connections are discretized into grid blocks and the grid properties are calibrated to historical production data. Elevation change, saturation distribution, capillary pressure, and relative permeability are accounted for to best represent the mature field conditions. To simulate this physics-based network model through a commercial simulator, an equivalent 2-D Cartesian model is designed where rows correspond to the above-mentioned connections. Thereafter, the history matching can be performed with the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm under a sequential iterative process. A representative model after history matching is then employed for well control optimization. The network model methodology has been successfully applied to the waterflood optimization for a 56-well sector model of a diatomite reservoir in the SJV. History matching result shows that the network model honors field-level production history and gives reasonable matches for most of the wells, including pressure and flow rate. The calibrated ensemble from the last iteration of history matching yields a satisfactory production prediction, which is verified by the remaining historical data. For well control optimization, we select the P50 model to maximize the Net Present Value (NPV) in 5 years under provided well/field constraints. This confirms that the calibrated network model is accurate enough for production forecasts and optimization. The use of a commercial simulator in the network model provided flexibility to account for complex physics, such as elevation difference between wells, saturation non-equilibrium, and strong capillary pressure. Unlike traditional big-loop workflow that relies on a detailed characterization of geological models, the proposed network model only requires production data and can be built and updated rapidly. The model also runs much faster (tens of seconds) than a full-physics model due to the employment of much fewer grid blocks. To our knowledge, this is the first time this physics-based data-driven network model is applied with a commercial simulator on a field waterflood case. Unlike approaches developed with analytic solutions, the use of commercial simulator makes it feasible to be further extended for complex processes, e.g., thermal or compositional flow. It serves as an useful surrogate model for both fast and reliable decision-making in reservoir management.

Traditional reconciliation of geomodels with production data is one of the most laborious tasks in reservoir engineering. The uncertainty associated with the great majority of model variables only adds to the overall complexity. This paper describes the conceptualization, implementation, and visualization characteristics of the multilevel assisted history matching (AHM) technique that captures inherent model uncertainty and allows for better quantification of production forecasts. The workflow is applied to history matching of the pilot area in a major, structurally complex Middle East (ME) carbonate reservoir. The simulation model combines 49 wells in five waterflood patterns to match 50 years of oil production and 12 years of water injection and to predict eight years of production. Initially, the reservoir model was calibrated to match oil production by modifying permeability and/or porosity at well locations and by fine-tuning rock-type properties and water saturation. The second level history match implemented two-stage Markov chain Monte Carlo (McMC) stochastic optimization to minimize the misfit in water cut on a well-by-well basis. The inversion process is dramatically accelerated by the efficient parameterization of permeability, constraining the proxy model using streamline-based sensitivities and using parallel and cluster computing. The optimal number of representative history-matched models was identified to capture the uncertainty in reservoir spatial connectivity using rigorous optimization and dynamic model ranking based on forecasted oil recovery factors (ORFs). The reduced set of models minimized the computational load for forecast-based analysis, while retaining the knowledge of the uncertainty in the recovery factor. The comprehensive probabilistic AHM workflow was implemented at the operator's North Kuwait Integrated Digital Oilfield (KwIDF) collaboration center. It delivers an optimized reservoir model for waterflood management and automatically updates the model quarterly with geological, production, and completion information. This allows engineers to improve the reservoir characterization and identify the areas that require more data capture.

Significant uncertainty exists in the detailed 3-D distribution of lithofacies, porosity, and permeability in every reservoir. Understanding and modeling the heterogeneous 3-D distribution of these rock properties is critical for improved oil recovery and reservoir management. Geostatistical techniques are being increasingly used to generate alternative heterogeneous 3-D reservoir models that are consistent with the available data. Although a large number of stochastic reservoir models or realizations may be available, a small number of realizations are considered in practice. Due to computer limitations, it is only possible to visualize and perform fine-scale full-field flow simulation on a limited number of realizations. Techniques are reviewed in this paper for ranking a suite of geostatistical realizations so that low-side, expected, and high-side realizations may be reliably chosen. Detailed analysis/flow simulation may then be performed on these realizations that somehow bound the uncertainty in the reservoir. Reservoir management is improved when expected and bounding cases are considered rather than using a limited number of "random" realizations. This paper reviews a number of methods for ranking geostatistical reservoir models. These methods may be classified into three categories. The first category includes statistical methods such as simple statistics, 3-D measures of connectivity, and connectivity to specific well locations. Methods in the second class are based on approximations to flow simulation, e.g., random walk-type results. The third category is for flow-simulation based methods for a simpler process than that being considered for improved oil recovery, e.g., tracer simulation and flow simulation with coarsened models. The applicability of a number of ranking methods is illustrated with a small example. There is no unique ranking index when there are multiple flow response variables and no ranking measure is perfect. Nevertheless, the value of ranking realizations will be quantified by examining the expected loss knowing an economic loss function and the true distribution of uncertainty. Introduction The primary objective of the application of geostatistical tools for reservoir modeling is to create realistic numerical geological models or realizations of the 3-D spatial distribution of lithofacies, porosity. and permeability. An often disturbing fact of geological reservoir modeling is that there are alternative realizations that honor all of the available data equally well and yet yield different reservoir performance predictions. In fact, it is often advertised that "a different realization can be obtained by simply changing a random number seed". A fundamental principle of geostatistics is that of data integration, i.e., all known data should be honored "by construction" and not left to chance. Of course, this is not always possible; it is difficult to constrain detailed 3-D geological realizations to seismic and historical production data. We are restricting ourselves to plausible realizations. There are times when certain realizations would be rejected on the basis of familiarity with the reservoir or data not used in the geostatistical modeling such as production-related historical observations. We are not considering the rejects; only those realizations that meet all basic requirements of reasonableness are considered. Exact prediction / decision making would require exhaustive knowledge of the spatial distribution of porosity and permeability. At any specific instant in time, there is such a single true distribution of petrophysical properties. This true distribution was created by the complex interaction of many different chemical, physical. and biological processes over geological time and would be accessible only through exhaustive sampling. In all practical situations, the unique true distribution will remain unknown. This paper addresses the uncertainty due to incomplete information. We do not consider uncertainty due tothe volume support or scale difference between core measurements and geological modeling cells,the limited flexibility of our geostatistical modeling techniques to reproduce complex nonlinear features, ornumerical approximations in the subsequent flow simulator. P. 105

The application of elastic stress simulation for fracture modeling provides a more realistic description of fracture distribution than conventional statistical and geostatistical techniques, allowing the integration of geomechanical data and models into reservoir characterization. The geomechanical prediction of the fracture distribution accounts for the propagation of fracture caused by stress perturbation associated with faults. However, the challenge lies in estimating the past remote stress conditions which induced structural deformation and fracturing, the limited applicability of the elasticity assumption, and the latent uncertainty in the structural geometry of faults. The integration of historical production data and welltest permeability into geomechanical fracture modeling is a practical way to reduce such uncertainty. We propose to combine geostatistical algorithms for history matching with geomechanical elastic simulation model for developing an integrated yet efficient fracture modeling tool. This paper presents an integrated approach to history matching of naturally fractured reservoirs which includes 1) fracture trend prediction through elastic stress simulation, 2) geostatistical population of fracture density based on fracture trend map, 3) fracture permeability modeling integrating fracture density, matrix permeability and welltest permeability, and 4) numerical flow simulation and history matching. All of these implementations are incorporated into a single forward modeling process and iterated in the automatic history matching scheme. To obtain a history match on a reservoir model, we jointly perturb the large-scale fracture trend and local-scale geostatistical fluctuations of fracture densities rather than perturbing permeability calibrated from fractures. This strategy enables us to preserve the geological/geomechanical consistency throughout the history matching process. The geomechanically simulated fracture trend model is calibrated to both production data and geological structure map (faults and horizons) by finding the optimum remote stress condition for elastic stress-field simulation. The latter is achieved by matching the actually observed structural deformation trend with the simulated one. The smaller-scale fluctuation of fracture density is simultaneously history matched through the probability perturbation method of Caers (2003)1,2. The result of synthetic reservoir application is presented.

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The Fleming gas‐condensate field, located on the eastern flank of the Central Graben, UK North Sea, is an elongate stratigraphic pinch‐out whose reservoir is composed of stacked turbidite sandstones of the lower Palaeogene Maureen Formation. The sandstones have a sheet‐like geometry with each sandstone lobe being partially offset into the swales of the preceding lobes. In such depositional environments, the understanding of lateral and vertical sandstone connectivity, a major uncertainty in reservoir modelling and well planning and production strategies, depends upon the choice of depositional model that is applied and the lateral continuity of pelagic mudstones.Previously published work defined a model, based on variations in the composition of agglutinated foraminiferal populations, that could be used to derive a qualitative measure of the level of pelagic influence within mudstones interbedded with turbidite sandstones. It was considered that mudstones with a high pelagic influence are likely to be more laterally extensive than those with a low pelagic index. A fuzzy logic workflow was constructed using this model and was applied to the Fleming field in order to identify laterally persistent mudstones. This approach was combined with high‐resolution correlation of bioevents using graphic correlation. A detailed layering scheme for the Fleming field was defined and this predicted the presence of a field‐wide mudstone.Initial attempts at history matching during reservoir simulation using a simple six‐layer lithostratigraphical scheme were not successful. A revised layering scheme defined by biofacies modelling and graphic correlation was used to produce a 13‐layer model; this was later simplified by combination with the six‐layer model to produce a ten‐layer model. This layering scheme is shown to provide a better understanding of both net‐to‐gross distribution and the dynamic behaviour of the field, and also improved history matching against production data. The biostratigraphical model applied using a fuzzy logic approach is authenticated by the reservoir simulation (fluid flow) and pre‐ and post‐maintenance well pressure tests of well 22/5b‐A3 which showed that the perforated interval in that well is isolated from the perforated intervals in the other producing wells. While history matching during reservoir simulation is important, the predictive capability of the fuzzy logic model proved to be critical to our understanding of the field.