Abstract

The microgeometry of the pore space influences the membrane potential E m and the dc electrical conductivity sigma of a shaly sand in a similar manner, independent of the details of the geometry. E m and sigma are related via the conductivities of cations and anions sigma cation and sigma anion ; sigma = sigma cation + sigma anion , and E m varies as sigma cation /(sigma cation + sigma anion ). This explicit relationship is used to investigate the role of the geometrical factors that influence both E m and sigma in a related manner. The dependence of sigma on water conductivity sigma w can be well approximated with four geometrical parameters, which can be obtained from the slopes and the inter -cepts of curves of sigma versus sigma w at high and low salinities. I show how these geometrical factors appear in the expression for E m as well. The geometrical parameters, one of them being the formation factor, vary from rock to rock; and any trend in the parameters depends on the local geology. For the data on a group of 140 different cores, the geometrical factors could be well approximated by functions of porosity, cementation exponent, and charge density, to give a simple conductivity formula analogous to the empirical formulas that are most widely used in formation evaluation. These empirical factors are used to obtain an approximate formula for E m .

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