Robust Waterflooding Optimization of Multiple Geological Scenarios

Abstract

Dynamic optimization of waterflooding using optimal control theory has a significant potential to increase ultimate recovery, as has been shown in various studies. However, optimal control strategies often lack robustness to geological uncertainties. We present an approach to reduce the impact of geological uncertainties in the field development phase known as a robust optimization (RO). RO uses a set of realizations that reflect the range of possible geological structures honoring the statistics of the geological uncertainties. In our study we used 100 realizations of a 3-dimensional reservoir in a fluvial depositional environment with known main flow direction. We optimized the rates of the 8 injection and 4 production wells over the life of the reservoir, with the objective to maximize the average net present value (NPV). We used a gradient-based optimization method where the gradients are obtained with an adjoint formulation. We compared the results of the RO procedure to two alternative approaches: a nominal optimization and a reactive control approach. The nominal optimization is based on a single realization, while in the reactive approach each production well is shut in when production is no longer profitable. The three control strategies were applied to each realization, from which the average NPV's and three cumulative distribution functions were determined. The RO results displayed a much smaller variance than the alternatives, indicating the increased robustness to geological uncertainty. Moreover, the RO procedure significantly improved the average NPV, compared to the alternative methods: on average 9% higher than using reactive control and 3% higher than for the nominal case. Introduction Within this paper, we consider the secondary recovery phase of a petroleum reservoir using waterflooding. In this case a number of injection and production wells are drilled to preserve a steady reservoir pressure and sweep the reservoir. The use of smart wells expands the possibilities to manipulate and control fluid flow paths through the oil reservoir. The ability to manipulate (to some degree) the progression of the oil-water front provides the possibility to search for a control strategy that will result in maximization of ultimate oil recovery. Dynamic optimization of waterflooding using optimal control theory has a significant potential to increase ultimate recovery by delaying water breakthrough and increasing sweep, as has been shown in various studies1. However, optimal control strategies often lack robustness to geological uncertainties. By discarding these uncertainties, bounding the sensitivity to a possibly large system-model mismatch is not taken into account within the optimization procedure. As a result, the optimal control strategy may seize to be optimal or may even result into very poor performance. Dealing with uncertainty is a topic encountered in many fields related to modeling and control. It can essentially be divided into two different strategies, which are not mutually exclusive: reducing the uncertainty itself using measurements, i.e. history matching2,3 and reducing the sensitivity to the uncertainty. However, within this paper, we consider a situation in which no production data is assumed available, which rules out any history matching approach to reduce the geological uncertainty. Our study forms part of a larger research project to enable closed-loop model-based reservoir management4. A suggested approach from the downstream process industry, to optimization problems which suffer from vast uncertainty and limited measurement information, is the use of a so-called robust optimization technique5,6,7. In robust optimization, the optimization procedure is carried out over a set of realizations, in this way actively accounting for the influence of the uncertainty. The implementation of multiple realizations within the optimization process has been addressed by Yeten8, however this study deviates in way they are incorporated in the objective function and in the number of realizations. The goal of this paper is to present a robust optimization procedure based on a set of 100 realizations of a 3-dimensional oil-water reservoir, which leads to a control strategy that explicitly accounts for geological uncertainty.

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

“…This includes partial and sometimes heuristic approaches, valid for particular types of constraints [5,38,39,43], and more systematic approaches, valid for a broader range of constraint equations [9,14,22,33,37]. An important feature in simulations involving highly compressible fluids, which we have in the systems considered here since we inject gas, is the occurrence of transient peaks in the rate in response to changes in well bottom-hole pressure (bottom-hole pressure, or BHP, is the wellbore pressure at a specified depth within the reservoir).…”

“…Our third example uses the three-dimensional geological model introduced in [38]. We again consider CO 2 injection, though this model contains a total of six components, defined in Table 6.9.…”

Model-reduced gradient-based history matching

“…All other settings for model reduction and history matching stayed the same. For this case, we assumed, following Van Essen et al [39], that the main direction of the channels was known, e.g., from seismic measurements, but that no specific knowledge about the channel configuration was available. The set of 100 realizations of the reservoir were sketched by hand based on the geological insight, with a strong vertical correlation, and each realization displayed an alternative channel configuration.…”

“…The model, originally introduced by Van Essen et al [39], describes iso-thermal slightly compressible twophase (oil-water) flow, in a channelized reservoir with eight injection and four production wells; see Fig. 2.…”

Value of information in closed-loop reservoir management

“…Because of the inherent uncertainty in the geological characterization of the subsurface, a non-deterministic approach is necessary. Robust life-cycle optimization uses one or more ensembles of geological realizations (reservoir models) to account for uncertainties and to determine the production strategy that maximizes a given objective function over the ensemble (see, e.g., Yeten et al [21] or Van Essen et al [20]). …”