Combining Hydraulic and Electrical Conductivity for Pore-Space Characterization in Carbonate Rocks

Abstract

Pore-space characteristics are of fundamental importance for production forecasting and reservoir management, especially in complex carbonate reservoirs, as they influence both electrical and hydraulic processes taking place in the interconnected, fluid-filled pore space. For theoretical model calculations of permeability and formation factor, capillary-channel models describing a straight tube with a constant circular cross-sectional area are frequently used. This assumption, however, does not reflect the variability of the pore radius in natural rocks.

Therefore, a modified capillary model for interconnected pore space in water-saturated, water-wet carbonate rocks is presented in this study. It describes a rotated pore channel with a radius varying between its two extreme values r_t (pore throat) and r_b (pore body), and is applicable to both electrical and hydraulic conductivity. Theoretical model calculations indicate that the most critical influences on permeability are exerted by the r_b /r_t ratio, followed by radius r_b, tortuosity and finally porosity. Formation factor, in contrast, is controlled by the r_b /r_t ratio, tortuosity, and porosity, but radius r_b has no influence.

The model expressions for permeability and formation factor are combined to achieve two aims: (1) exclude tortuosity from a new permeability prediction method based on electrical resistivity, radius r_b and a function covering the effect of pore-space geometry; and (2) derive pore-space characteristics (radius r_b or r_t combined with the r_b /r_t ratio) from a crossplot of permeability vs. formation factor. A carbonate database including routine core analysis data and radii r_t and r_b derived from mercury injection capillary pressure (MICP) measurements and backscattered electron image (BSE) analysis is used to predict the permeabilities of different carbonate fabric types. A comparison of predicted to measured parameters indicates that their agreement is generally very satisfying. Overestimates of permeability and underestimates of pore-body size only occur in samples with a high amount of large pores.