The growth in the application of optimization in reservoir management has placed greater demands on the application of history matching to produce models that not only reproduce the historical production behavior, but also preserve geological realism and quantify forecast uncertainty. Geological complexity and limited access to the subsurface typically result in a large uncertainty in reservoir properties and forecasts. There is, however, a systematic tendency to underestimate such uncertainty, especially when rock properties are modeled using Gaussian random fields. In this paper, we address two sources of uncertainty: uncertainty in regional trends by introducing stochastic trend coefficients and uncertainty in variogram model by treating correlation length or range as a stochastic variable instead of a well-determined variogram parameter. The hierarchical parameters including trend coefficients and heterogeneities can be estimated using ensemble Kalman filter (EnKF) for history matching.
Hierarchical or multi-scale heterogeneities are generally poorly represented, especially in deepwater reservoirs. We developed a hierarchical description of heterogeneities that introduced new variables into the reservoir description. We tested our method for updating these variables using production data from a deepwater field whose reservoir model has over 200,000 unknown parameters. The match of reservoir simulator forecasts to real field data using a standard application of EnKF had not been entirely satisfactory, as it was difficult to match water cut in one of the wells. None of the realizations of the reservoir exhibited water breakthrough using the standard method. By adding uncertainty in trends of reservoir properties, the ability to match the water cut and other production data was improved substantially.
The results indicate that an improvement in the generation of the initial ensemble and in the variables describing the property fields give an improved history match with plausible geology. It reduces the tendency to underestimate uncertainty while still providing reservoir models that match data.