Prediction under Uncertainty in Reservoir Modeling

Reservoir simulation is routinely employed in the prediction of reservoir performance under different depletion and operating scenarios. Usually, a single history matched model, conditioned to production data, is obtained. The model is then used to forecast future production profiles. Since the history match is non-unique, this is essentially an inverse problem. Hence the forecast production profiles are uncertain, although this uncertainty is not usually quantified. This paper presents a new approach for generating uncertain reservoir performance predictions and quantifying the uncertainty associated with forecasting future performance. Firstly, we generate multiple reservoir realizations using a new stochastic algorithm. This involves adaptively sampling the model parameter space using an algorithm, which biases the sampling towards regions of good fit. Using the complete ensemble of models generated, we resample from the posterior distribution and quantify the uncertainty associated with forecasting reservoir performance, in a Bayesian framework. To demonstrate the strength of the method in performance prediction, we use an upscaled model to history match fine scale data. We then forecast the fine grid performance using the maximum likelihood model and quantify the uncertainty associated with the predictions. We demonstrate that the maximum likelihood model is highly accurate in reservoir performance prediction. This method differs from other methods for generating multiple reservoir realizations in the following way. Rather than seeking a single global optimum, the algorithm selectively samples parameter space to derive an ensemble of models. These models share the common property of fitting the observed data to some degree of accuracy. This approach is reasonable since the inverse problem is ill-posed. In contrast to other stochastic methods, the algorithm performs a guided search in parameter space by using information derived from the complete ensemble of previously generated models. Hence no external directionality is imposed on the search process. In Bayesian analysis, the posterior probability distribution characterizes the uncertainty in the model parameters estimated from an ensemble of models. Correctly sampling from this distribution is therefore essential for accurate quantification of forecasted reservoir performance. The Neigbourhood algorithm utilizes the nearest neighbor property of the Voronoi cells, together with a Markov Chain Monte Carlo algorithm, in correctly sampling from the posterior probability distribution. Introduction Petroleum reservoir data is inherently uncertain. The field information is usually sparse and noisy. Part of the data is obtained from cores (~10 of the reservoir volume) collected at a finite