In traditional history matching, it is common practice to perturb either a single prior model or a suite of models that share a variogram model or a training image. As a result, the posterior model(s) reflect the residual uncertainty only in terms of stochastic variations in the random seed. In contrast a procedure is presented that can accommodate uncertainty in prior geological models. The production data in response to polymer flooding is used to select a subset of models from the initial set. The residual uncertainty in the reservoir model and the accompanying flow response as visualized over the posterior set is used to formulate the future control strategy. Model selection as well as the formulation of the optimal control strategy is facilitated through the use of an efficient proxy. That proxy is continually updated and refined as the feedback control process is progresses.
A major change from current modeling approaches is that the entire prior model is taken as a single entity and processed through a fast proxy for the polymer flooding process. The ?distance? between any two models is calculated on the basis of their proxy responses. Reservoir models with similar proxy responses are grouped using PCA and K-means clustering. Subsequently, the posterior probability of each cluster is computed using a Bayesian inversion process, a cluster is drawn and the process is continued at the next level of the selected cluster. Incremental production data is rapidly assimilated since it is used only for further refinement of the previously identified clusters. |
