A deterministic/stochastic model to predict the variation in bulk modulus of chalk

Ekofisk, located 200 km west of the Norwegian coast, is one of the main oilfields in the North Sea. Since the early 1980s severe compaction of chalk reservoir layers has been observed as a consequence of reservoir depletion during oil production. Subsequently, this compaction has been amplified by assisted oil recovery using seawater flooding. The development of our understanding of the inherent mechanisms of this phenomenon has been the objective of extensive experimental investigations in the last two decades. Owing to the very high cost of cored material from the reservoir, experiments are usually performed on chalk samples from an outcrop in Belgium lying at the same stratigraphic level as the Ekofisk reservoir chalks. However, even at the laboratory sample scale,. experimental variability of material response is observed. From a theoretical and numerical point of view, the determination of the mechanical properties of the material is of utmost importance for accurate modelling at both sample scale (laboratory tests) and reservoir scale. The aim of this paper is to introduce a stochastic approach within a deterministic constitutive model of chalk to enable the influence of material heterogeneity to be included in analyses for the range of observed mechanical responses. In modelling the random distribution of material parameters, the time-consuming Monte Carlo simulation method is replaced by a more efficient stochastic modelling technique. The results are given in the form of statistical parameters for the experimental laboratory test responses. The parameters of the distribution law (mean value, range of variation, spatial correlation structure) are fitted to reproduce the range of experimental responses observed at sample scale. Interest is focused on the variability of the chalk bulk modulus, as observed during isotropic compression tests. The proposed methodology provides a satisfactory explanation for the variability of response observed at the sample scale. The potential for extending the proposed approach to reservoir scale is briefly discussed.