Wen H. Chen

A Comparison Study on Experimental Design and Response Surface Methodologies

Experimental design method is an alternative to traditional sensitivity analysis. The basic idea behind this methodology is to vary multiple parameters at the same time so that maximum inference can be attained with minimum cost. Once the appropriate design is established and the corresponding experiments (simulations) are performed, the results can be investigated by fitting them to a response surface. This surface is usually an analytical or a simple numerical function which is cheap to sample. Therefore it can be used as a proxy to reservoir simulation to quantify the uncertainties. Designing an efficient sensitivity study poses two main issues: • Designing a parameter space sampling strategy and carrying out experiments. • Analyzing the results of the experiments. (Response surface generation)

Real-Time Reservoir Model Updating Using Ensemble Kalman Filter

The ensemble Kalman Filter technique (EnKF) has been reported to be very efficient for real-time updating of reservoir models to match the most current production data. Using EnKF, an ensemble of reservoir models assimilating the most current observations of production data are always available. Thus the estimations of reservoir model parameters, and their associated uncertainty, as well as the forecasts are always upto-date. In this paper, we apply the EnKF for continuously updating an ensemble of permeability models to match realtime multiphase production data. We improve the previous EnKF by resolving the flow equations after Kalman filter updating so that the updated static and dynamic parameters are always consistent. By doing so, we show that the production data are also better matched for some cases. We investigate the sensitivity of using different number of realizations in the EnKF. Our results show that a relatively large number of realizations are needed to obtain stable results, particularly for the reliable assessment of uncertainty. The sensitivity of using different covariance functions is also investigated.