Flow diagnostics, as referred to herein, are computational tools derived from controlled numerical flow experiments that yield quantitative information regarding the flow behavior of a reservoir model in settings much simpler than would be encountered in the actual field. In contrast to output from traditional reservoir simulators, flow-diagnostic measures can be obtained within seconds. The methodology can be used to evaluate, rank, and/or compare realizations or strategies, and the computational speed makes it ideal for interactive visualization output. We also consider application of flow diagnostics as proxies in optimization of reservoirmanagement work flows. In particular, by use of finite-volume discretizations for pressure, time of flight (TOF), and stationary tracers, we efficiently compute general Lorenz coefficients (and variants) that are shown to correlate well with simulated recovery. For efficient optimization, we develop an adjoint code for gradient computations of the considered flow-diagnostic measures. We present several numerical examples, including optimization of rates, well placements, and drilling sequences for two-and threephase synthetic and real field models. Overall, optimizing the diagnostic measures implies substantial improvement in simulation-based objectives. IntroductionComputational tools for reservoir modeling play a critical role in the development of strategies for optimal recovery of hydrocarbon resources. These tools can be simply viewed as a means of forecasting recovery given a set of data, assumptions, and operating constraints; (e.g., to validate alternative hypotheses about the reservoir or systematically explore different strategies for optimal recovery).By nature, reservoir modeling is an interdisciplinary exercise, and reservoir-modeling tools must be well-integrated to promote collaboration between scientists and engineers with different backgrounds. New work flows are emerging because of recent advances in static reservoir characterization and dynamic flow simulation. Modern numerical flow simulators have evolved to include more-general grids, complex fluid descriptions, flow physics, well controls, and couplings to surface facilities. These generalizations have helped to more realistically describe fluid flow in the reservoir on the time scales associated with reservoir management. Meanwhile, modern reservoir-characterization techniques have shifted away from traditional variogram-based models toward object-and feature-based models that more accurately describe real geologic structures. To quantify uncertainty in the characterization, it is necessary to generate an ensemble of reservoir models that may include one thousand or more individual realizations. Reservoir simulation is computationally demanding, and a single simulation on a full reservoir model may require from some minutes to hours or even days. Direct evaluation of multiple production scenarios on large ensembles of Earth models is therefore impractical with full-featured flow simulators, and the comp...

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We present MRST-AD, a free, open-source framework written as part of the Matlab Reservoir Simulation Toolbox and designed to provide researchers with the means for rapid prototyping and experimentation for problems in reservoir simulation. The article outlines the design principles and programming techniques used and explains in detail the implementation of a full-featured, industry-standard black-oil model on unstructured grids. The resulting simulator has been thoroughly validated against a leading commercial simulator on benchmarks from the SPE Comparative Solution Projects, as well as on a real-field model (Voador, Brazil). We also show in detail how practitioners can easily extend the black-oil model with new constitutive relationships, or additional features such as polymer flooding, thermal and reactive effects, and immediately benefit from existing functionality such as constrained-pressure-residual (CPR) type preconditioning, sensitivities and adjoint-based gradients. Technically, MRST-AD combines three key features: (i) a highly vectorized scripting language that enables the user to work with high-level mathematical objects and continue to develop a program while it runs; (ii) a flexible grid structure that enables simple construction of discrete differential operators; and (iii) automatic differentiation that ensures that no analytical derivatives have to be programmed explicitly as long as the discrete flow equations and constitutive relationships are implemented as a sequence of algebraic operations. We have implemented a modular, efficient framework for implementing and comparing different physical models, discretizations, and solution strategies by combining imperative and object-oriented paradigms with functional programming. The toolbox also offers additional features such as upscaling and grid coarsening, consistent discretizations, multiscale solvers, flow diagnostics and interactive visualization.

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