Constructing Reservoir Flow Simulator Proxies Using Genetic Programming for History Matching and Production Forecast Uncertainty Analysis

In current practice history matching is often performed on upscaled reservoir models without updating the original geological model. Taking into account new production data in an existing model is often problematic because of the lack of appropriate techniques. This problem becomes crucial when using geostatistical models. In such a case, the integration of new static and dynamic constraints requires the modification of an initial realization without destroying the initial history match and the overall geostatistical properties. This paper presents a new methodology based on advanced history matching techniques for updating dynamically 3D stochastic reservoir models to account for new production data. The proposed approach is based on the gradual deformation method. It allows local or global smooth transformations of the model while conserving the overall statistical characteristics. History matching is performed by coupling this method with an optimization process which integrates geostatistical modeling, upscaling, and fluid flow simulation in the same loop. This approach provides great flexibility in history matching various types of production data. In addition, inversion parameters can be selected throughout the entire modeling loop, from the facies spatial distribution, to petrochemical parameters and fluid flow parameters. Finally, local transformations may be performed to account for new wells or to update the reservoir model with new dynamic information. A successful application to a 3D stochastic reservoir model inspired from a real field is presented. The first step was to perform a history match using the production history available from an initial group of production wells. Then, new dynamic information is acquired from infill wells and over one year of additional production data. The heterogeneity distribution is locally modified by gradual deformation to update the model with this new information. The benefit of the proposed approach for improving the model characterization and reducing uncertainty on production forecasts is demonstrated.

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.

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.

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The aim of this work is to present the effectiveness of a fully integrated approach for ensemble-based history matching on a complex real field application. We show that the predictive ability of the ensemble of models is greatly enhanced through an integrated workflow promoting multidisciplinary collaboration between all subsurface disciplines. Consistent integration of geological and engineering understanding within the dynamic data conditioning phase of a reservoir study is a challenging task. The ensemble-based approach offers an efficient solution to this challenge, especially when it is tied in with an appropriate reservoir modeling approach, suitable parameterization and repeatable workflows. All these are key factors to ensure geological consistency while improving the match quality and reliability of the generated reservoir models. One key feature of the ensemble-based method is that it overcomes the typical limitation of the traditional approaches where the number of uncertainty parameters often has to be reduced resulting from practical or algorithm constraints. This is especially important on complex reservoirs, where the subsurface uncertainties cannot be represented in a handful of scalar multipliers while honoring the static and dynamic data measurements. We organize the proposed methodology in four main steps: firstly, an initial ensemble of models able to capture the model uncertainties in all parts of the modeling processes are generated. Next, the match level for different observed data specifying the likelihood error is assigned. Then the uncertainty parameters that should be modified in the history matching process are identified. Finally, we perform a computational intensive step on large-scale computing facilities, where a state-of-art iterative ensemble algorithm, tightly connected with standard geo-modeling tools, is used to consistently update the full set of models. The result is an ensemble of reservoir models where we can quantify both the uncertainty in the production forecast and in the reservoir model parameters. The methodology has been applied on a challenging History Matching problem for a turbiditic channel complex reservoir. We demonstrate the efficiency of the method, by generating an ensemble of reservoir models that offer geologically consistent explanations of the currently measured static and dynamic data. The model forecasts reliability is confirmed through a validation process using dynamic data that have been left out of the history matching process. More importantly, however, is that the proposed workflow, and resulting models provides a good starting point for a more efficient update of the reservoir models as new static and dynamic data become available. With the proposed approach is possible to move from sporadic updates of reservoir models towards frequent model updates when the new data arrive. Utilizing all available data in a consistent manner - when the data are collected - is the key to making more robust reservoir management decisions, especially for complex reservoirs.

In the production history matching process, the reservoir simulation model is modified in a way that it becomes consistent with production data, keeping the observed restrictions of the geological characterization phase. This technique is limited, mainly in mature fields, when the production history is not reliable, or in the beginning of production, when there are only a few observed data and uncertainties are higher. The development of new saturation data acquisition tools, such as 4D seismic and TDT/TDM logging tools helped to overcome some difficulties in the geologic model construction phase but the great challenge is how to use this data in a way to improve the petroleum production. History matching methodologies integrated with saturation data from 4D seismic are available in literature but no publications that utilize saturation data obtained from well logging were found. The advantage of the logging tools is the data accuracy but, on the other hand, it is limited to a few feet around the wells. The main objective of this project is to integrate the traditional history matching process with logging saturation data, developing more reliable simulation models and production forecasts. The saturation data is utilized as a new parameter to be matched as well as an auxiliary tool to help to determine critical regions which will be modified. An assisted history matching methodology, utilizing saturation data, streamlines and an optimization algorithm is proposed. The proposed methodology is applied to a synthetic reservoir model. Parameters of the process are studied and detailed, finding the best way to use the data. The model is also history matched with no saturation information and predictions of the matched models are compared, showing the benefits and restrictions of the new methodology.

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.

As the role of reservoir flow simulation increasingly impacts existing operations and field development decisions, it follows that rigor, fitness and consistency should be imposed on the calibration of reservoir flow models to dynamic data through history matching. Although a wealth of history matching techniques exist in the petroleum literature that propose novel algorithms or share case studies, seldom does the content guide the modeler in fit-for-purpose reservoir model calibration for an operating asset. To evaluate the applicability of these diverse techniques against standards required for reservoir management, an internal study was performed to benchmark four assisted history matching (AHM) techniques commonly promoted in the oil and gas industry. The techniques were vetted against a comprehensive suite of modeling requirements for multiple asset classes, integrating a variety of historical dynamic data types through the calibration of reservoir properties that control flow behavior from the field to inter-well scale. The methods benchmarked were: (1) Design of Experiments (DoE)-based, (2) Ensemble Kalman Filter and Ensemble Smoother, (3) Genetic Algorithm and (4) Generalized Travel Time Inversion. This manuscript focuses solely on the DoE-based technique.In order to consistently benchmark the techniques, a set of standards was defined against which each was evaluated to determine its suitability for widespread history matching applications. The standards involve: the capacity to parameterize (and therefore calibrate) a diversity of reservoir flow model attributes, the capacity to integrate different types of dynamic data, the level of independence from the flow simulator and the capability to provide probabilistic outcomes for predictive uncertainty assessment. Of the four techniques, the DoE-based approach uniquely satisfied all requirements. Its history matching workflow has the flexibility to incorporate any form of reservoir model parameter and to assimilate a history matching error metric for any individual or group of historical data types; therefore, benchmarking established DoE-based techniques as unambiguously the most compliant with generic asset modeling requirements. The approach was also identified as the most straightforward, both theoretically and in practical computation, and therefore applicable to the broadest range of practitioners. Perhaps most importantly, the approach demonstrated the capacity for accurate quantification of uncertainty (or non-uniqueness) in reservoir quality resulting from an exhaustive, although approximate, exploration of model parameter space and the associated history matching error metric(s).This manuscript compiles the results and insights gained from benchmarking of the DoE-based techniques through the proposal of a comprehensive assisted history matching workflow. The workflow is designed for generality while providing best practices that guide the modeler in fit-for-purpose application. Limitations of the workflow are also recognized. Key components include: selection and screening of calibration parameters based on statistical significance, development of surrogate models to characterize the relationship between parameters and the simulated historical data being integrated into the reservoir model, use of the surrogate models for exhaustive yet efficient exploration of parameter space to identify (non-unique) history matched models, and (deterministic or probabilistic) discrete reservoir model selection for use in forecast-based decision making. Each step of the AHM workflow is presented from a conceptual and applied perspective, and field applications are provided to demonstrate key concepts. Although the applications presented include two deepwater Gulf of Mexico assets, the workflow and insights provided are developed from benchmarking across a diverse suite of asset types.

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.

The current trend for history matching is to find multiple calibrated models instead of a single set of model parameters that match the historical data. The advantage of several current workflows involving assisted history matching techniques, particularly those based on heuristic optimizers or direct search, is that they lead to a number of calibrated models that partially address the problem of the non-uniqueness of the solutions. The importance of achieving multiple solutions is that calibrated models can be used for a true quantification of the uncertainty affecting the production forecasts, which represent the basis for technical and economic risk analysis.In this paper, the importance of incorporating the geological uncertainties in a reservoir study is demonstrated. A workflow, which includes the analysis of the uncertainty associated with the facies distribution for a fluvial depositional environment in the calibration of the numerical dynamic models and, consequently, in the production forecast, is presented. The first step in the workflow was to generate a set of facies realizations starting from different conceptual models. After facies modeling, the petrophysical properties were assigned to the simulation domains. Then, each facies realization was calibrated separately by varying permeability and porosity fields. Data assimilation techniques were used to calibrate the models in a reasonable span of time. Results showed that even the adoption of a conceptual model for facies distribution clearly representative of the reservoir internal geometry might not guarantee reliable results in terms of production forecast. Furthermore, results also showed that realizations which seem fully acceptable after calibration were not representative of the true reservoir internal configuration and provided wrong production forecasts; conversely, realizations which did not show a good fit of the production data could reliably predict the reservoir behavior. Thus a statistical approach was confirmed to be the only way to reduce the uncertainty inherent to reservoir modeling and should be adopted as a standard in reservoir studies.

Time-lapse seismic changes can be compared with pressure and/or saturation changes derived from a flow simulator by using petro-elastic model. As the number of seismic data is huge and it has a 3D character, it is expected to be a great help to condition the reservoir model. An (automated) history matching loop comprises the following four stages: 1) parameterization, 2) objective function definition, 3) optimization and 4) loop-stopping criterion. Focusing the objective function, the brief explanation of some element technology is done. With the introduction of time-lapse seismic as an additional constraint, history matching is performed to construct a more reliable reservoir model, which can be used to predict a future oil production.The impact of data integration on production forecasting uncertainty is analyzed. The synthetic model used representative for a gravity fault system, such as East flank of Statfjord field. By changing the constraining data, i. e. time-lapse seismic and production data, its impact on the probability density function (pdf) of the future cumulative oil production (FCOP) can be quantified. The variance of FCOP-pdf is reduced and the maximum pdf value is increased by adding extra information to the reservoir model. For this specific synthetic model, the seismic data gives a reservoir model with a higher probability than the production data. The most probable models are obtained when conditioning the reservoir model with both types of data.

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.

Relative permeability is one of the most important properties in Coal bed methane/gas (CBM/CBG) fields for reliable reservoir modelling due to two-phase fluid flow. In CBM reservoirs, one of the biggest challenges remains with the high unreliability of laboratory experimental relative permeability data due to the inherent nature of coal. The scope of this study is to define the shape of the relative permeability curve using available production data analysis. The interplay between water and gas within the coal cleats affects the mobility of both water and gas. In Sohagpur CBM blocks of India, there is enough production data associated with wells. In this study, a comprehensive production data analysis (PDA) was done on wells to quantify the relative permeability curve. Though gas and water rates are available from the production history, it becomes essential to determine the well static pressure at different times so that the pressure-dependent gas and water properties can be evaluated. Conventional Z function is modified by King (1990) for CBM to include sorption behaviour and known as Z* function which, when used with pressure and plotted with cumulative gas production (Gp), gives a straight line like conventional gas reservoir behaviour. The plot gives static well pressure for any known Gp in the production history of the well and gas water properties can be determined at every pressure using standard correlations. Thus, the relative permeability ratio of gas and water krg/krw can be obtained at every pressure using the relationship described above. It is found that the application of material balance study which, when combined with Production Data Analysis (PDA), gives useful information on relative permeability. This helped quantifying relative permeability which is used for reservoir modelling and simulation. History matching exercises are carried out for the wells for part of the available production data and forecasts are generated for rest of the production history. The forecasts of both gas and water are matching with the history which acts as validation points and provides good confidence on reliability of the generated relative permeability curve. Further, forecast period of the existing wells are extended to more years and sensitivities are carried out with additional infill and/or new to optimize further development planning. The present study brings uniqueness in the form of two innovative workflows integrating production data, compositional data, and pressure. This has been used along with existing conventional knowledge of material balance with some modification for coal reservoir adsorption phenomena which adds considerable value to the existing knowledge. These workflows can be applied in other reservoirs or basins for more reliable reservoir modelling and forecasting which may help both CBM evaluation and exploitation time and cost effective and optimize the field development.

Karachaganak field is one of the largest accumulations of gas-condensate in the world in production since 1985. Located in the northern Pricaspian Basin (Kazakhstan) the field is a Permo-Carboniferous isolated carbonate platform with a hydrocarbon column that resides within different environments of deposition. The distribution of reservoir properties has been largely debated because of both the depositional heterogeneity and the diagenetic overprint.These uncertainties were assessed by analyzing and integrating the vast amount of geological and production data to build a predictive history matched reservoir model.Seismic facies analysis, with support from outcrop analogues and integrated with field core and log data, reveals, within stratigraphic intervals, "Depositional Regions" (DRs) that ranges from platform interior bedded deposits to aggrading/prograding mounds, clinoforms, slopes and basin sediments. These DRs were first seismically mapped, identifying field scale heterogeneity, and then petrophysically characterized using geologic and dynamic data.A sequence of progressively optimized models was built according to geologically meaningful concepts that make use of DRs and critical petrophysical issues (such as enhanced/matrix permeability, sealing barriers and dolomitization) were in parallel addressed. A reference model has been so defined and a history match of remarkable quality has been achieved for this complex heterogeneous reservoir.The uncertainty was investigated in a pragmatic manner using HM as benchmark. The reservoir uncertainty decreases closer and closer to the wells, hence alternative models scenarios were built by gradually changing DRs petrophysical properties going away from the production wells. Using the distance and the magnitude of the perturbations as control parameters and the quality of history match as selection criterion, we could identify two "end members??. These cases represent possible alternative scenarios both consistent with the geological data and still endorsed by a high quality history match, two reservoir models capable to give a significant spread in the production forecast.

This paper presents a comparison study in which several partners have applied methods to quantify uncertainty on production forecasts for reservoir models conditioned to both static and dynamic well data. A synthetic case study was set up, based on a real field case. All partners received well porosity/permeability data and ‘historic’ production data. Noise was added to both data types. A geological description was given to guide the parameterization of the reservoir model. Partners were asked to condition their reservoir models to these data and estimate the probability distribution of total field production at the end of the forecast period. The various approaches taken by the partners were categorized. Results showed that for a significant number of approaches the truth case was outside the predicted range. The choice of parameterization and initial reservoir models gave the largest influence on the prediction range, whereas the choice of reservoir simulator introduced a bias in the predicted range.