Summary In nonlinear model order reduction, hyper reduction designates the process of approximating a projection‐based reduced‐order operator on a reduced mesh, using a numerical algorithm whose computational complexity scales with the small size of the projection‐based reduced‐order model. Usually, the reduced mesh is constructed by sampling the large‐scale mesh associated with the high‐dimensional model underlying the projection‐based reduced‐order model. The sampling process itself is governed by the minimization of the size of the reduced mesh for which the hyper reduction method of interest delivers the desired accuracy for a chosen set of training reduced‐order quantities. Because such a construction procedure is combinatorially hard, its key objective function is conveniently substituted with a convex approximation. Nevertheless, for large‐scale meshes, the resulting mesh sampling procedure remains computationally intensive. In this paper, three different convex approximations that promote sparsity in the solution are considered for constructing reduced meshes that are suitable for hyper reduction and paired with appropriate active set algorithms for solving the resulting minimization problems. These algorithms are equipped with carefully designed parallel computational kernels in order to accelerate the overall process of mesh sampling for hyper reduction, and therefore achieve practicality for realistic, large‐scale, nonlinear structural dynamics problems. Conclusions are also offered as to what algorithm is most suitable for constructing a reduced mesh for the purpose of hyper reduction. Copyright © 2016 John Wiley & Sons, Ltd.

Model-based production analysis using analytical or numerical models is not a new phenomenon and is considered a robust technique for analyzing and forecasting production data; however, its application to unconventional reservoir systems often proves problematic due to model non-uniqueness resulting from long-term transient flow regimes. This non-uniqueness, an unavoidable fact when analyzing inverse problems, is worsened by the uncertainty surrounding input model parameters when attempting to describe reservoir systems with a great deal of complexity (e.g. very low permeability, geomechanical effects, near-critical fluids, natural fracturing, etc.). The problem facing the engineer presents itself when different combinations of input parameters yield nearly identical history matches but very different time-rate profiles and estimated ultimate recovery (EUR) values when forecasting future production for a particular well.A systematic framework that covers the full range of uncertainty for all relevant input parameters would clearly mitigate the ambiguity of production analysis and forecasting under uncertain conditions. In this work it is proposed that experimental design, which is a statistical technique used to describe or optimize a process by systematically analyzing the effect of the various controllable and uncontrollable factors of a system on an output (e.g. EUR), can provide such a framework. In this work, a methodology combining model-based production analysis with experimental design is used to history match and forecast fractured vertical and multi-fractured horizontal oil wells in the Vaca Muerta Shale with high-frequency time-rate-pressure data. The primary objectives of this work are to provide a comprehensive overview of the Vaca Muerta shale, outline experimental design as it relates to model-based production analysis, quantify uncertainties in model input parameters, and finally history match and forecast two wells that are producing in the Vaca Muerta Shale.

Production forecasting in unconventional reservoir systems is not an easy task and should not be soley accomplished using empirical decline curve analysis. Advanced analytical and numerical models have facilitated the analysis of unconventional systems; however, it is almost always impractical to analyze and forecast hundreds of wells using these techniques. The focus of this work is to demonstrate a practical and timely methodology using model based production analysis as the foundation for the analysis and forecasting of each producing well in a particular area/field in an unconventional reservoir. The methodology is founded on a thorough diagnostic assessment of all available data, thorough production analysis of key wells, and extension to the remaining wells using key information from the diagnostic analysis. The methodology includes three main components: production diagnostics, model-based analysis for representative wells, and production forecasting. Production diagnostics is performed on a single well basis to identify flow regimes and performance metrics of each well, and performed on a multi-well basis to compare performance and identify characteristic behavior which can lead to well groupings and the selection of representative wells for analysis. Representative well(s) from each group are analyzed using model-based analysis incorporating non-linear behaviors associated with the production performance. A systematic analysis procedure is followed to account for the uncertainty on well/reservoir parameters affecting production behavior by utilizing an experimental design methodology. Multiple history matches are obtained accounting for uncertainties such as drainage area, permeability, etc. Following model-based analysis, production forecasts are developed for the corresponding history matches. Based on either a statistical distribution of EUR values or a deterministic approach, characteristic low/mid/high time-rate profiles can be derived. These profiles are extended to other wells via scaling factors to determine EUR values. Coming full circle, the scaling factors are then compared to well/reservoir data using maps and cross plots of performance metrics obtained from diagnostics to aid in the performance based analysis of the group.