An accurate determination of initial oil in place in the early life of reservoirs or an evaluation of a developed reservoir is required to well estimate the hydrocarbon volumes. Modified Archie formula (Sw = (a Rw / ϕm Rt)1/n) is the basic equation to compute water saturation in clean formation or suitable shaly water saturation model in shaly formation. The accuracy of water saturation value for given reservoir conditions depends on the accuracy of Archie parameters a, m and n. The terms of Archie relationship have been subjected to many laboratory investigations and even more speculations. There are many factors affecting porosity exponent, m, saturation exponent, n and tortousity factor, a. Therefore, it is very difficult to fix Archie parameters and neglecting reservoir characteristics; rock wettability, formation water salinity, permeability, porosity and fluids distribution. This paper presents a new technique to determine Archie parameters a, m and n. The developed technique is based on the concept of three dimensional- regression (3-D) plot of water saturation, formation resistivity and porosity. This 3D technique provides simultaneous values of Archie parameters. Also, the 3D technique overcomes the uncertainty problems due to the separate use of formation resistivity factor- porosity and water saturation equations to get a, m and n parameters.
Two field examples are given to show the applicability of the 3-D technique in comparison with three other techniques: 1) common values of Archie parameters, 2) conventional technique and 3) core Archie parameter estimation (CAPE) technique. The comparison among the four techniques has shown that 3-D technique provides an accurate and physically meaningful way to get Archie parameters a, m and n for given core samples. Water saturation profiles, using Archie parameters obtained from the four techniques, have been obtained for the studied section in the wells. These profiles have shown a significant difference in water saturation values. This difference could be mainly attributed to the uncertainty level for Archie parameters from each technique. The effect of saturation exponent on the accuracy of water saturation computation was tested using Archie's parameters derived from conventional technique and 3-D technique in the two wells.