The porosity exponent m represents an important parameter in Archie’s equation; it is routinely used in well logging interpretation and formation evaluation. It reflects some petrophysical rock properties, such as the petrofabrics, pore fabrics, and overburden pressure (OBP). Data measured at ambient conditions for a total of 55 sandstone core samples were obtained from 8 wells varying in depositional facies, geologic age, degree of consolidation, and cementation material and then measured again at OBP, similar to the actual reservoir conditions, to check the effect of OBP on Archie’s parameters and to introduce a model of high reliability. Other published data sets were also used to confirm the study results. Based on the best-fit regression analysis, several empirical relationships were introduced to relate the porosity exponent to pore volume, lithology factor, and permeability. The effect of OBP on the porosity exponent was also investigated in relation to the petrophysical parameters. Given the above, a new statistical model is proposed to relate the porosity exponent to the permeability of the studied sandstone samples in the Gulf of Suez, Egypt. The effect of confining pressure on the studied porosity exponent m and the lithology factor a is significant when porosity ϕ is less than or equal to 10%.
From the present study, categorization of the studied samples into flow units and rock types using the hydraulic flow unit and the discrete rock types increased the reliability of the obtained relationships and increased the applicability of the obtained equations. In addition, the value of the lithology factor a fluctuates around 1 (0.92–1.04, regardless of the applied processing method), whereas the value of the porosity exponent m fluctuates around 1.83. The obtained relationships between the formation resistivity factor and porosity have a very high reliability (−0.949 ≥ correlation coefficient ≥ −0.969).