Abstract

Modeling of in-situ energy extraction processes (e.g., coal gasification and oil shale retorting) has been examined by assuming the affected zones may be described by oblate or prolate spheroids of lowered electrical resistivity. The purpose of the model study is to determine if such subsurface bodies may be monitored and defined by electrical resistivity measurements made in boreholes away from the reaction zone.Solutions of the Laplace equation in (1) oblate and (2) prolate spheroidal coordinate systems enable theoretical determination of the electrical potential distribution as would be measured in a borehole near an anomalous body of oblate or prolate shape. The body is assumed to be enclosed within an infinite, homogeneous mass. Normal (pole-pole) type curves of (1) electrical resistivity for various electrode spacings (sounding curves) and (2) electrical resistivity for various positions in the borehole (vertical profiling) are developed for both oblate and prolate spheroidal models using spheroids of increasing size as a sensitivity parameter.Modeling results verify that an oblate body of the same cross-sectional shape as a prolate body produces the larger anomaly. For the various size and resistivity parameters specified in this study, deviations from the homogeneous case (i.e., no spheroid) range from 3 percent for the smallest oblate and prolate bodies up to 60 percent for the largest modeled oblate body. If a + or -5 percent uncertainty because of instrumentation, field technique, or random noise may be assumed, this implies a lower limit to the size of a detectable body. On this basis, the smaller spheroids of this study would not be detectable. However, both sounding and profiling type measurements offer promise as effective monitoring tools, and, if repeated over the period of process time, may enable process growth estimates. Further, because the oblate case is independent of azimuth while the prolate is not, measurements made in a series of borings surrounding the process center may describe the shape tendency (oblate versus prolate) of the process and determine directivity (azimuth of prolate major axis) of the process if existent.

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