Using Spatial Constraints in Clustering for Electrofacies Calculation

Abstract

Petroleum reservoir geological models are usually built in two steps. First, a 3-D model of geological bodies is computed, within which rock properties are expected to be stationary and to have low variability. Such geological domains are referred to as “facies” and are often “electrofacies” obtained by clustering petrophysical log curves and calibrating the results with core data. It can happen that log responses of different types of rock are too similar to enable satisfactory estimation of the facies. In such situations, taking into account the spatial aspect of the data might help the discriminative process. Since the clustering algorithms that are used in this context usually fail to do so, we propose a method to overcome such limitations. It consists in post-calibrating the estimated probabilities of the presence of each facies in the samples, using geological trends determined by experts. The final facies probability is estimated by a simple kriging of the initial ones. Measurement errors reflecting the confidence in the clustering algorithms are added to the model, and the target mean is taken as the aforementioned geological trend. Assets and liabilities of this approach are reviewed; in particular, theoretical and practical issues about stationarity, neighborhood choice, and possible generalizations are discussed. The estimation of the variance to be assigned to each data point is also analyzed. As the class probabilities sum up to one, the classes are not independent; solutions are proposed in each context. This approach can be applied for extending class probabilities in 3-D.