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# porosity exponent

1. n. [Formation Evaluation]

The exponent, m, in the relation of formation factor (F) to porosity (phi). For a single sample, F is related to phi using the Archie equation F = 1 / phim, with m being the only coefficient needed. In this case, m has been related to many physical parameters, but above all to the tortuosity of the pore space. In theory, it can range from 1 for a bundle of tubes to infinity for porosity that is completely unconnected. For a simple packing of equal spheres, m = 1.5. With a more tortuous pore space or more isolated pores, m increases, while with fractures or conductive solids, m decreases. As a general average for typical reservoir rocks, m is often taken as 2. For a group of rock samples, it is common practice to find a relationship between F and phi that uses two coefficients (F = a / phim). In this case m, like a, becomes an empirical constant of best fit between F and phi, and may take a wide range of values. In complex formations, such as shaly sands or carbonates with multiple pore types, a constant m does not give good results. One solution is to vary m, with the variability related to parameters such as porosity, shaliness, or rock texture, or else determined directly from logs in zones where the water saturation is known or can be computed from a nonresistivity measurement such as electromagnetic propagation. In shaly sands, the preferred solution is to use a saturation equation, such as Waxman-Smits, dual water, SGS or CRMM, in which m is defined as the intrinsic m, determined from the intrinsic formation factor at high salinities or after correction for the effect of shale. In carbonates with multiple pore types, such as fractures, vugs, interparticle porosity and microporosity, one solution is to use equations with different porosity exponents for each pore type. The volume of each pore type must then be determined from logs or borehole images.