A theoretical approach for water saturation estimation in shaly sandstones

Abstract

The process of quantitative reservoir characterization is a crucial component spanning from the initial estimation of in-place reserves to the optimization of production design. Water saturation is a critical parameter in quantitative reservoir characterization that directly impacts the in-place reserve estimates. In the case of shale-free sandstones, the computation of water saturation using Archie's equation yields fairly accurate results. However, in shaly sandstone reservoirs, the presence of multiple conductive entities in the rock poses additional complexities. Currently, various empirical, semi-empirical and theoretical equations are available in literature to estimate water saturation; nevertheless, none of these models is such that it is both theoretically sound and practically applicable.In this study, we present a novel approach that is both theoretically sound and practically applicable in computing water saturation in shaly sandstones. The fluid-saturated rocks are treated as a system consisting of two interlocked lattice-like structures, namely grains and fluid in the interconnected pores. The composite fluid comprising water and hydrocarbon is modeled using the general mixture rule, while the Hanai-Bruggeman equation is employed to model the electrical conductivity of this system. The resulting electrical conductivity equation is then utilized to compute water saturation in shaly sandstones.The proposed equation was effectively validated using the published core data. Furthermore, we compare the new model with other grain conductivity-based models such as Mixing model and Berg's model. Our findings show that while describing core data the proposed equation gives a lower average Relative Root Mean Squared Error (RRMSE) of 2.05% as compared to 7.56% and 5.58% for the Mixing and Berg's model available in literature, respectively. Moreover, the range of porosity and water conductivity for which the proposed model is applicable, surpasses that of the current models. We also suggest that this equation can be extended to other systems with a similar two interlocked lattice-like structure, such as carbonates.