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 introduces an engineering workflow for probabilistic assisted history matching 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. While relative to evolutionary algorithms or the ensemble Kalman filter (EnKF), the McMC methods provide a statistically rigorous alternative for sampling posterior distribution; when deployed in direct simulation, they impose a high computational cost. The approach presented here accelerates the process by parameterizing the permeability using discrete cosine transform (DCT), constraining the proxy model using streamline-based sensitivities and utilizing parallel and cluster computing. While probabilistic assisted history matching (AHM) successfully reduced the misfit for most producing wells, the computational convergence was sensitive to the level of preserved geological detail. 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 well-treatment program is an important part of the fielddevelopment plan, and certain variables, such as job-pause time (JPT) and fracture screenout, can affect its efficiency. JPT is the time during which pumping is paused between subsequent treatments of a job. Screenout occurs because of a sudden restriction of fluid flow inside the fracture and through the perforation. The objectives of this work are to investigate whether, from existing data, it is possible to find patterns in significant variables that affect the extreme values of JPT in a particular region, and what is the most critical variable causing screenout. The answers are sought by applying a classification-and-regression tree (CART) to both categorical and continuous variables in the database. The practical application of CART is presented by use of case studies containing JPT and screenout. Significant variables are found that affect the response variables, and predictor variables are ranked in the hierarchal order of their importance. Such information can be used to control predictor variables that cause high JPT or screenout.The results are outlined in an intuitive way, including categorical, continuous, and missing values. Because CART is a datadriven, deterministic model, one cannot calculate the confidence interval of the predicted response. The confidence in results is purely because of historical values, and the accuracy of the result produced by a tree model depends on the quality of recorded data measured in terms of volume, reliability, and consistency. The prediction capability of CART is enhanced by use of the normalscore transform and by dividing the data set into smaller groups by use of clustering. The approach presented in this paper analyzes a data set under limited information and high uncertainty and should lead to developing methodology for generating proxy models to find future success indices (e.g., one for drilling efficiency or production from a fracture). This could standardize stimulation and generate decision practices to save costs in field development and the optimization process.
History matching processes for complex and large reservoirs have always posed difficulties to reservoir engineers. To help reservoir engineers during history matching, various assisted history matching (AHM) algorithms have been developed. While AHM can help automate various aspects of history matching, oftentimes, algorithms suffer from slow convergence. This work proposes an ensemble based markov-chain Monte Carlo (MCMC) based algorithm with efficient sampling from the given distribution of properties. For efficient sampling properties during AHM, streamline trajectories are used to find the connection between source(s) and producer well. Streamline tracking based on output of the full-physics simulator is used as a guideline to capture the fluid flow patterns, and only properties of grid cells along the streamline trajectories are considered prime candidates for history matching. The proposed algorithm was applied to a sector model of a reservoir as a test case study to history match water cut on a well-by-well basis.
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