Hybrid modelling of fractured reservoirs using the effective medium theory

Abstract

Naturally Fractured Reservoirs usually exhibit power law length distributions which do not possess any characteristic length scale, rendering the use of continuum methods difficult. This necessitates the adoption of hybrid models that represent a subset of the fractures as continua and the remainder as discrete fractures. However, the appropriate partitioning of fractures into these two subsets is an unresolved issue. In this regard, we propose a workflow which utilizes the Effective Medium Theory (EMT) by Sævik et al. (2013) as both an upscaling tool and a partitioning guide for single porosity hybrid modelling. EMT is used to find the largest nonpercolating subset of small fractures which will be upscaled into a single porosity background. The remaining fractures will be represented explicitly. This workflow allows reservoir engineers to systematically design an appropriate partitioning strategy for hybrid modelling. The paper explores this workflow via a two-part study. Part one validates the accuracy of EMT. Part two compares simulation results generated from different partitioning choices. The results show that the output of EMT matches that of numerical upscaling and that the workflow proposed leads to a hybrid model that is fit-for-purpose with a reduction in computational costs.