Technical Notes - The Application of Electrical Transients to Well Logging

The transient response of earth formations may be tlcter.171ined by means of four electrodes mounted coli-rienrly on n sonde. Exponentially decaying current pules are applied to one pair of electrodes and the re.rrrlting voltage transient at the other pair is recorded. It is shown by theoreticol analysis and verified by laboratory experiments that this arrangement readily yields the direct resistivity of the formation and provides valrrable additional information as well. INTRODUCTION Although electrical transients have been employed with moderate success in geophysical prospecting, their application to well logging has received virtually no attention in technical literature. In the conventional direct resistivity logging methods only the zero frequency impedance of the formation under study is measured, and no information is obtained regarding its reactive characteristics. Since the use of certain transients appears to offer some advantages in this respect, experiments were performed on a laboratory scale to investigate this possibility. This investigation was limited to a study of a four-electrode array where both the receiving and transmitting electrode pairs are mounted on a logging sonde, and decaying exponential pulses are applied to the transmitting electrodes. THEORY Given an electrode configuration as shown in Fig. I, located in a homogenous medium of resistivity p, if each electrode has an effective radius, r, which is small compared to the spacing, s and a, it is easy to show by integrating the volume resistivity that the input resistance, Rrw, of the transmitting electrodes is Rxw=p/2pr If a capacitor of capacity C, charged to a voltage Em, is suddenly connected to these electrodes, the resulting current, I(t), will then be The voltage transient, E(t), at the receiving electrodes may then be found by substracting the resulting potential at electrode Y from that appearing at electrode Z. and by inserting Eqs. 1 and 2 Integrating Eq. 4 with respect to tim