Dual Pore Network Model of Electrical Resistivity for Carbonate Rocks

Abstract

Extreme variability of carbonate depositional environments and susceptibility of carbonate sediments to a host of post-depositional (diagenetic) processes involving mineral dissolution and precipitation, result in complex pore structures comprising length scales from less than a micron and up to several millimeters in the form of vugs and solution channels of varying degree of connectedness. Significant deviations from Archie’s law relating the average water saturation to the average electrical resistivity are observed in carbonates. This behavior is a direct, but difficult to interpret or predict, consequence of the complexity of their microstructure. Considering that carbonate reservoirs hold a large fraction of the remaining world oil resources, the need to develop and validate efficient models of carbonate rock resistivity is pressing. There is now mounting consensus that interpretation of the petro-physical properties of carbonate rocks requires the consideration of dual pore network models (D-PNM). In this context, non- Archie behavior in carbonate rocks is qualitatively related to the degree of connectedness (percolation) of different water fractions, namely water residing in networks comprising pores of significantly disparate scales (micro-porosity and macro-porosity). What is presently lacking is a flexible D-PNM that could be calibrated to core laboratory data (micro-tomography, capillary pressure and resistivity). Availability of such a model would represent a useful advance in the practice of resistivity log interpretation for carbonate reservoirs. To this end, we investigate here a previously reported D-PNM which allows for heterogeneous matrix (micro-porosity) properties and variably-connected macro-porosity. By varying the relative amounts, geometric properties and degree of connectedness of micro-porosity and macro-porosity, we are able to stylistically reproduce all documented deviations of the resistivity index from Archie behavior.