Oil Reservoir Production Forecasting with Uncertainty Estimation Using Genetic Algorithms

A genetic algorithm is applied to the problem of conditioning the petrophysical rock properties of a reservoir model on historic production data. This is a difficult optimization problem where each evaluation of the objective function implies a flow simulation of the whole reservoir. Due to the high computing cost of this function, it is imperative to make use of an efficient optimization method to find a near optimal solution using as few iterations as possible. In this study we have applied a genetic algorithm to this problem. Ten independent runs are used to give a prediction with an uncertainty estimate for the total future oil production using two different production strategies. 1 Oil production history matching In order to be able to forecast the oil production using different production strategies, one needs realistic geological models of the oil reservoir. The geological models are formulated on grids with thousands or millions of grid cells. Each grid cell has several physical variables, and hence, the number of unknown parametres in a realistic reservoir characterization is formidable. The history matching problem is the problem of finding geological models which are consistent with both static data—such as permeabilities and porosities as measured in wellbore plugs—and with dynamic data such as production rates, bottom hole pressures, and gas oil ratios throughout the production history of the field. In general, the history matching problem is a non-unique inverse problem; several combinations of parametre values representing the geology could give the same production performance. In a full scale heterogeneous reservoir, the number of unknown parametres is often as high as several millions while the number of observables is much smaller. The task is to find a set of parametres so that the difference between the results of flow simulations and the true production history is as small as possible. This is a hard optimization problem. Since the computational cost of differentiation within a flow simulator is very high, we have chosen to experiment with a genetic algorithm (GA) [1, 2] as an optimization tool. For any realistic case one expect that there are many local optima in the history matching problem. Since production parametres to a large extent are determined by the geology near the wells, regions far from wells are not very well determined by this kind of inverse modelling. This induces large uncertainties in the predicted production, especially if new wells are drilled. In order to estimate this prediction uncertainty, we have generated a population of history matched models where each individual is generated by an independent GA optimization. In this way it is hoped that we span a significant part of the parametre space compatible with the known production history and thus, that we can estimate the prediction uncertainty. 2 The PUNQ S3 case The method is tested on a synthetic oil field prepared as part of the PUNQ (production forecasting with uncertainty quantification) project sponsored by the European Community. In the PUNQ project ten partners from industry, research institutes and universities are collaborating on research on uncertainty quantification methods for oil production forecasting [3]. The ‘historic data’ of the case studied in this paper were generated using the Eclipse oil simulator. Gaussian noise was added to both the historic data and the well observations before the data sets with uncertainties were presented to the partners. At the time the history matching was carried out, the true reservoir was not known to the partners. In the present work we used the More simulator for history matching. Figure 1: A reservoir model optimized with GA.