The well-loss function, CQ 2 , and the effective wellbore radius constitute two very important ideas in Jacob’s classic study (1947). Both ideas were accorded extreme importance in the petroleum engineering field. Swift and Kiel published results of their award-winning study on non-Darcy flow in 1962, and the skin-effect concept (related to effective wellbore radius) was presented independently by both Hurst and van Everdingen in 1953. Jacob’s well-loss function has been generalized to the form CQ n in the current literature, although this form seems to work well only over the range of flow rates used in testing. The petroleum engineering approach suggests that the form should be C(S T + DQ)Q, where S T is the skin effect, a constant, and D is the non-Darcy flow coefficient, often a constant also. The new form contains CQ n as a special case for a limited range of flow; however, n values would lie between 1 and 2. Field experience in water-well testing indicates n values from 2.5 to 2.7. Fetkovich (1973) presented information on oil and gas flow indicating that transmissivity depends upon pressure (thus also upon flow rate) for solution gas-drive oil production. There appears to be an analogy possible for high-rate production of gas-saturated water.

7.1 CONVERSION OF IMPEDANCE TO A FORM USEFUL FOR INTERPRETATION The difficulty in interpreting MT data consists of the fact that the inverse magnetotelluric problem is ill-posed, and its operator cannot be written in a closed form. Therefore, the basic method of interpretation is iterative optimization using regularizing operators. The optimization is carried out within the class of parametric solutions forming an interpretation model. This model is conceived from a priori concepts about the geology of the area under study and the physical properties of the rocks, as well as from the results of magnetotelluric observations. Thus, it is important to present the results of the magnetotelluric observations in a form that is convenient for direct geoelectric evaluations and conclusions. The frequency curve for the impedance (or the admittance) does not meet this need, since it is not particularly expressive and gives only a rough qualitative picture. However, a considerable improvement can be made by transformations using reasonably simple continuous operators. The transformed magnetotelluric data are expressed in geoelectric terms, such as “resistivity,” “conductivity,” and “depth.” The analysis of these data helps us to determine the type of geoelectric structure, to construct an interpretation model, and to evaluate some of its parameters. In this chapter, we will describe several interesting impedance and admittance transformations that are used more or less widely in magnetotelluric practice. Before developing these transformations, we would like to gain a better insight into the skin effect in layered media.

Abstract Resistivity logs use electrode arrays or coil arrays for focusing. The accuracy of the measurement is enhanced by designing the array to focus into the zone of interest. The most significant difference between laterolog and induction devices is that laterologs put the borehole fluid, the invaded zone, and the undisturbed zone in series in the radial direction of the borehole as regards current flow, whereas the induction devices put these regions in parallel. If the injected currents are constant, the measured potentials for laterolog tools increase proportionally with resistivity. The eddy current induced in the formation and the electric potential measured by induction devices will increase as the conductivity increases (i.e., as the resistivity decreases). This chapter briefly describes laterolog and induction tool response theories.