Use of reduced-order models in well control optimization

Abstract

Many aspects of reservoir management can be expected to benefit from the application of computational optimization procedures. The focus of this review paper is on well control optimization, which entails the determination of well settings, such as flow rates or bottom hole pressures, that maximize a particular objective function. As is the case with most reservoir-related optimizations, this problem is in general computationally demanding since function evaluations require reservoir simulation runs. Here we describe reduced-order modeling procedures, which act to accelerate these simulation runs, and discuss their use within the context of well control optimization. The techniques considered apply proper orthogonal decomposition (POD), which enables the representation of reservoir states (e.g., pressure and saturation in every grid block) in terms of a highly reduced set of variables. Two basic approaches are described-the direct application of POD-based reduction at each Newton iteration, and a trajectory piecewise linearization (POD-TPWL) procedure that applies POD to a linearized representation of the governing equations. Both procedures require one or more pre-processing 'training' simulation runs using the original full-order model. The use of both gradient-based optimization methods (including adjoint procedures) and direct search approaches with reduced-order models is described. Several concepts relevant to the general topic, including adjoint formulations and controllability, are also reviewed. Numerical results are presented for both approaches. In particular, the POD-TPWL procedure is applied to a computationally demanding bi-objective optimization problem, where it is shown to provide reasonable accuracy and a high degree of speedup.

Accelerating Physics-Based Simulations Using End-to-End Neural Network Proxies: An Application in Oil Reservoir Modeling

“…Accelerating reservoir simulations has a wide literature. State of the art techniques can be classified in two categories: 1) reducing the complexity of the PDEs while providing an acceptable loss of prediction accuracy (e.g., reduced order modeling [9] can accelerate the simulations by factors of 10 2 and has been found useful in optimization and control [12], and upscaling which achieves acceleration with coarser reservoir models [6]), and (2) simple polynomial interpolation techniques computing the objective function (e.g. Net Present Value, or NPV) or to characterize the uncertainty [23].…”

A State-of-the-Art Literature Review on Capacitance Resistance Models for Reservoir Characterization and Performance Forecasting

“…They work with the full underlying physics of the flow in porous media, and approximations are done in the context of matrices and solvers. The methodologies applied to reservoir simulation are vast, but the main algorithms in the nonlinear spectrum of models are: the proper orthogonal decomposition (POD) method [122,123], trajectory piecewise linearization (TPWL) technique [124,125], discrete empirical interpolation method (DEIM) [123,126], and quadratic-bilinear-model order reduction [127]. Many of these technologies are, indeed, part of the larger umbrella of approximation of dynamical systems, whereby the physical phenomena is recast into an input-output transfer function.…”

Well control optimization using a two-step surrogate treatment

“…Surrogate treatments for well control optimization, based on reduced-order modeling with proper orthogonal decomposition, have been developed by a number of researchers; see, e.g., [22,23,24], along with the review by Jansen and Durlofsky [25]. Reduced-physics models based on streamline methods were shown to provide useful surrogates in water injection optimization [26].…”