Simulation of the Electrical Resistivity of Dual-Porosity Carbonate Formations Saturated with Fluid Mixtures

摘要

For carbonate formations characterized by a complex pore structure, traditional methods for estimating water saturation from resistivity logs can lead to significant errors. In this paper we present the results of simulations of the effective electrical conductivity of dual-porosity carbonate formations saturated with fluid mixtures. For the calculations we have applied the Effective Medium Approximation method. Carbonate rocks are represented is media composed of (1) a matrix with solid grains and small-scale primary pores, and (2) large-scale secondary pores embedded in this matrix. In this model, all components are approximated by tri-axial ellipsoids. We consider different distributions of water and non-conductive fluid in the primary and secondary pores. The matrix pore system has been represented by a mixture of pores that are completely saturated either with water or with non-conductive fluids, by pores approximated by layered ellipsoids where the outer layer is water (water-wet formations), and by a combination of these two models. Water distribution in the secondary pore system has been modeled by layered ellipsoids where water occupies the outer layer. We have obtained dependences of the effective electrical resistivity as a function of saturation of the primary and secondary pores for different secondary-pore concentrations and types. The calculations have shown that the application of Archie's expression for a single-pore system results in under- or over-estimation of the water saturation in dual-porosity carbonates. Depending on the secondary-pore shapes and concentrations, the relative errors in the determination of water saturation can reach 25-30 percent for formations with a matrix porosity of 0.08-0.10 and a secondary porosity of 0.01-0.02. Based on the simulations performed, we propose an approach for determining water saturation in dual-porosity water-wet carbonate formations. The approach includes (1) the estimation of the type and concentration of the secondary pores using joint inversion of micro-electrical and acoustic data, and (2) the assessment of water saturation by adjusting the model parameters so that the calculated resistivity agrees with that measured by laterologs. The feasibility of evaluating water saturation using this approach is demonstrated with experimental data.