Multi-Exponential Inversion and Laboratory Study of Induced Polarization Relaxation Time Spectra of Shaly Sands
Authors: Tong M.S. , Li L. , Wang W.N. , Jiang Y.Z. , Shi D.Q. , Du G.T. 
Published: March 2010

Abstract
According to the traditional Induced Polarization (IP) logging method, the IP relaxation time spectrum can give much more information about a reservoir, such as the pore structure, permeability, formation water resistivity, and shaliness. In this paper, the Singular Value Decomposition (SVD) algorithm is used to inverse the IP multi-relaxation data of the rock samples. The appropriate number of relaxation arrangement points in the relaxation data inversion is from 32 to 64. All of the relaxation spectra show a multi-peak shape.
IP decay curve measurements have been performed on 30 samples from the Daqing Oil Field using the four-electrode technique. The effects of charging current, charging and discharging time, brine salinity, and water saturation on the relaxation spectra of the rock were analyzed qualitatively, so that we could develop a new IP spectra logging tool that could be used successfully in practice. When we discussed the effect of one parameter on the relaxation time spectra, the others remained fixed. The results show that the relaxation spectrum relates with the charging time, discharging time, and depends strongly on water saturation. The salinity of NaCl brine and the charging current density are shown to have a small influence on the relaxation spectra in the special ranges.

Introduction
Induced polarization (IP) phenomena were observed more than 80 years ago, which may be caused by metallic minerals or clay Content(1–8). The detection of IP in the time-domain is made by measuring both the maximum voltage during the charging period of a dc current flow, and the transient decay of the electrical potential as a function of time, after the current is turned off. IP logging is traditionally used to determine the formation water resistivity and shaliness parameter (Qv), which is defined as the cation exchange capacity of the shaly sands per unit pore volume(9–12). But up to now, no IP logging has successfully been used commercially to evaluate or locate petroleum reservoirs.
The theory analysis shows that the IP relaxation characteristics relate to the pore structure of the rock and the IP decay curve is a superposition of signals coming from all pores with different sizes(13). So, the curve can be fitted with multi-exponential decay function and a relaxation spectrum can be obtained. The spectrum contains much more information than the traditional IP method. The IP spectra of full water-saturated rock gives a quick, easy, and nondestructive way to characterize the rock, such as the pore structure, permeability, and Qv. On the other hand, we can develop a new time-domain IP spectra logging tool. This kind of IP spectra logging can be also used to obtain the formation water resistivity and shaliness parameter, Qv, as the traditional time-domain IP logging tool. In order to transfer the lab results downhole, the borehole effects, such as rugosity and mud, should also be considered. This can be achieved by using focusing technology as well as technologies used in traditional lateral logging tools.