We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the wellknown problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.
In spite of large uncertainties in the actual reservoir structure, structural parameters of a reservoir model are usually fixed during history matching and only the flow properties of the model are allowed to vary. This often leads to unlikely or even unfeasible property updates and possibly to a poor predictive capability of the model. In those cases it may be expected that updating of the structural parameters will improve the quality of the history match. Preferably such structural updates should be implemented in the static (geological) model, and not just in the dynamic (flow) model. In this paper we use a gradientbased history matching method to update structural properties of the static model. We use an adjoint method to efficiently compute the derivatives of the data mismatch with respect to grid block porosities in the dynamic model and convert the corresponding volume changes to structural updates (layer thicknesses) in the static model. This method is suitable for structural updating of large scale reservoir models using production data and/or time-lapse seismics or other spatially distributed data. The method is tested on a 3D synthetic model, where time-lapse as well as production data have been used to update depth of the reservoir's bottom horizon. We obtained significant improvements in the history match quality and the predictive capability of the model.
Abstract-Over the recent years a variety of new developments have been introduced within the field of oil recovery, with the aim to maximize production of oil and gas from petroleum reservoirs. One of these new developments is the introduction of so-called "smart wells", which are equipped with control valves to actively control the oil production. The optimal operational strategy of these control valves can be found using a dynamic optimization procedure. However, due to geological uncertainty inherent to reservoir modelling, the mismatch between the reservoir model and the real reservoir may become considerable. As a result, a model-based optimal solution may seize to be the optimal, but will yield sub-optimal or even worse results. Within this work a robust optimization approach is presented that takes the possibly large impact of the mismatch between model and reservoir into account using a set of multiple reservoir realizations.
Abstract-Over the recent years a variety of new developments have been introduced within the field of oil recovery, with the aim to maximize production of oil and gas from petroleum reservoirs. One of these new developments is the introduction of so-called "smart wells", which are equipped with control valves to actively control the oil production. The optimal operational strategy of these control valves can be found using a dynamic optimization procedure. However, due to geological uncertainty inherent to reservoir modelling, the mismatch between the reservoir model and the real reservoir may become considerable. As a result, a model-based optimal solution may seize to be the optimal, but will yield sub-optimal or even worse results. Within this work a robust optimization approach is presented that takes the possibly large impact of the mismatch between model and reservoir into account using a set of multiple reservoir realizations.
In oil production waterflooding is a popular recovery technology, which involves the injection of water into an oil reservoir. Studies on model-based dynamic optimization of waterflooding strategies have demonstrated that there is a significant potential to increase lifecycle performance, measured in Net Present Value. However, in these studies the complementary desire of oil companies to maximize daily production is generally neglected. To resolve this, a hierarchical optimization structure is proposed that regards economic life-cycle performance as primary objective and daily production as secondary objective. The existence of redundant degrees of freedom allows for the optimization of the secondary objective without compromising optimality of the primary objective.
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