A Stochastic Simplex Approximate Gradient (StoSAG) for optimization under uncertainty

Abstract

SUMMARYWe consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical models contain uncertain parameters because of geological uncertainties. In that case, 'robust optimization' is performed by optimizing the expected value of the objective function over an ensemble of geological models. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capable of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as 'modified robust EnOpt') and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoretical arguments to show why StoSAG is superior to EnOpt.

Improved CRM Model for Inter-Well Connectivity Estimation and Production Optimization: Case Study for Karst Reservoirs

“…For our study, it was a stochastic search direction. The StoSAG algorithm proposed by Fonseca et al [33] with the stochastic search direction, described as following, was used to maximize the augmented Lagrange objective function L a (u, λ, µ):…”

“…The results indicated that CRM models have high potential to serve as a cogent proxy model for waterflooding related decision-making and obtain robust results that result in a near-optimal solution. Recently, a novel ensemble-based technique, stochastic-simplex-approximate-gradient (StoSAG), was developed by Fonseca et al [33,34]. The StoSAG deals with reservoir simulator as a black box and approximates gradient through the inputs and outputs of all the ensemble runs.…”

Ensemble-based optimization of interwell connectivity in heterogeneous waterflooding reservoirs

“…At each iteration of the so-called inner loop, the newly developed StoSAG optimization algorithm (Fonseca et al, 2016) is applied to solve the above-mentioned augmented Lagrangian function by considering hybrid nonlinear constraints.…”

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

“…For the use in robust optimization, see van Essen et al (2009); for a general overview, see Jansen (2011). Alternative, less codeintrusive, robust methods use approximate gradient and/or stochastic methods (Chen et al 2009;Chen and Oliver, 2010;Li et al 2013;Fonseca et al 2015Fonseca et al , 2016 or 'non-classical' methods such as, e.g., streamline methods (Alhutali et al 2008), evolutionary strategies (Pajonk et al 2011), or polynomial chaos expansions in combination with response surfaces (Babaei et al 2015), with further references given in Echeverrıa Ciaurri et al (2011).…”