Understanding the impact of subsurface uncertainties on production responses is an integral part of the decision making process. A more accurate quantification of the uncertainty band around production forecasts contributes to better business decisions. Traditional experimental design workflows, where a limited set of models represent the key uncertainties in subsurface parameters, might be well suited for new field developments. However, when a field has been produced for several years, all models have to be conditioned to available production data in order to obtain meaningful predictions. Data integration and uncertainty assessment of future performance of the reservoir are indivisible processes that cannot be generally addressed by simple techniques.
In this paper we present a method to tackle such complex inverse problems where highly non-linear responses are involved. The goal is to minimize an objective function that stands for the goodness-of-fit of the history-match. The key idea is to use high quality proxies of the objective function to accelerate the search for solutions. An efficient experimental design stage allow for the selection of key parameters while an optimization routine involving Genetic Algorithms (GA) is used to determine the best combinations of parameters. The models that reasonably honor the historical data are selected and provide an estimate of future production. The final distribution of the prediction variables defines the range of uncertainty conditioned to production history. The practicality of the methodology is demonstrated with a study of an off-shore field in West Africa that has several years of complex production history.
Quantifying uncertainty in production forecast for a real field with complex history is a difficult task. Monte Carlo simulations coupled with probabilistic inverse theory is in general not practical due to the large number of simulations required. Efficient alternatives involving proxies and various optimization algorithms have been investigated. The fitness of the model to the observed data (history-match error function) is modeled using response surfaces of various nature, polynomial, kriging or spline for instance.