Petrophysical Inversion of Multifrequency Resistivity and Permittivity Logs and Laboratory Measurements

Abstract

In this thesis, we develop a unified inversion scheme that can be coupled to various type of relaxation models to process multi-frequency measurement of varied electromagnetic (EM) properties for purposes of improved EM-based geomaterial characterization. The proposed inversion scheme is firstly tested in few synthetic cases in which different relaxation models are coupled with the inversion scheme. Then, the inversion is applied to multi-frequency complex resistivity and complex permittivity measurements acquired in laboratory and in subsurface borehole environments. For purposes of inversion of laboratory-based EM measurements, the unified inversion scheme estimates up to seven relaxation-model parameters exhibiting convergence and accuracy for random initializations of the relaxation-model parameters within up to 3-orders of magnitude variation around the true parameter values. The inversion-derived estimates of relaxation-model parameters can be used for materials characterization. The inversion scheme is then improved for purposes of joint petrophysical inversion of multifrequency effective electrical conductivity and dielectric permittivity logs derived from various combinations of downhole EM logs acquired in clay- and pyrite-rich shale formations at multiple frequencies. The proposed joint interpretation method uses a single mechanistic model that accounts for the IP effect arising from clay and conductive mineral grains; thereby generating physically consistent water saturation estimates in shales. The proposed inversion-based interpretation also generates estimates of formation water salinity, surface conductance of clay, and average radius of clay and conductive mineral grains. The proposed method is firstly applied to three synthetic geological formations, with varying clay type, conductive mineral properties, and water saturation. Then the joint petrophysical inversion algorithm is applied to field broadband dispersion EM data acquired in a European Lower Paleozoic organic-rich shale formation. Finally, the inversion-based joint petrophysical interpretation is implemented for processing dielectric dispersion logs acquired in Bakken Petroleum System acquired at four discrete frequencies in the range of 10 MHz – 1 GHz. The newly developed interpretation method is applied to process the dielectric dispersion log acquired in Bakken formation to estimate water saturation, formation salinity, cementation index and homogeneity index. Water saturation estimates for a specific depth obtained using the proposed interpretation method is not one single value but a range of possible values within a desired accuracy. These water saturation estimates were compared against those obtained from resistivity induction log, NMR log, Quanti-ELAN solver, service company’s dielectric inversion, and Dean-Stark core measurements. Our estimates of water saturation and those obtained using the service company’s dielectric inversion exhibit best match with Dean-Stark’s core water saturation in Middle Bakken and Three Forks formations. The estimated water salinity is very high which agrees with core measurements. Homogeneity index obtained using our method indicates the presence of layering and heterogeneity in Lower Three Forks and Middle Bakken. The cementation index indicates high tortuosity and cementation in Upper and Lower Bakken.