Theory of microwave dielectric constant logging using the electromagnetic wave propagation method

Abstract

The composite dielectric constants of earth formations at microwave frequencies are strongly dependent on formation water saturations and relatively independent of water salinities. Therefore, microwave frequency dielectric constant logging offers an attractive new electromagnetic (EM) method of formation evaluation. The EM wave propagation method of dielectric constant logging attempts to deduce the dielectric properties of earth formations from phase shift and attenuation measurements of EM field, which have been propagated in the formation. A device which utilizes this method of well logging has been proposed by Calvert (1974) and Rau (1976) in two recent U.S. patents. We discuss the basic physics underlying the operation of a device of this type and describe the plane wave procedure discussed by these authors for relating the phase shift and attenuation measurements made by such a device to the formation dielectric properties. This procedure is suspect, since it is based on an unrealistic plane wave model which fails to treat the radiation field correctly and ignores the presence of a layer of mud cake which separates the antenna pad from the formation. To determine the errors likely to be inherent in using this procedure in practice, we consider several simple theoretical models of an EM wave propagation tool. Computer experiments performed on these theoretical models indicate that the apparent formation traveltimes obtained by using this procedure are semiquantitatively accurate with relative errors less than five percent in most cases. For our theoretical models, correction plots or departure curves are demonstrated which enable one to deduce the true formation traveltimes, given the apparent values and a knowledge of the dielectric properties and thickness of the mud cake. The problems which remain if this new method of logging is to attain its full potential (e.g., the accurate determination of formation fluid saturations) are discussed.