COMBINED INVERSION OF BOREHOLE RESISTIVITY AND SONIC MEASUREMENTS TO ESTIMATE WATER SATURATION, POROSITY AND DRY-ROCK ELASTIC MODULI IN THE PRESENCE OF INVASION

摘要

Water saturation, porosity and dry-rock (skeleton) elastic moduli are often evaluated independently using measurements that obey different physical principles. Such an interpretation methodology does not take into account possible deterministic or statistical relationships between different physical measurements when probing the same rock formation. We describe a new inversion-based method that combines resistivity and sonic borehole measurements to estimate the four properties simultaneously. The objective of the combined inversion is to suppress ambiguity in the estimation of in-situ properties thereby improving the accuracy and reliability of the results over traditional methods. We assume a radial one-dimensional model to develop the numerical simulation and inversion components of the study. Moreover, for simplicity we assume invasion in the form of a single piston-like fluid saturation front with one invaded and one virgin zone. The inversion is driven by array-induction and sonic waveform measurements. We use the numerical-mode-matching method and the frequency-wavenumber domain method to simulate induction and sonic measurements, respectively. Induction measurements are related to water saturation and porosity via Archie’s equations. For sonic measurements, we resort to Biot-Gassmann’s equation to relate the saturated rock’s elastic moduli to porosity and fluid saturation. The distorted Born iterative method and a modified preconditioned conjugate gradient method are used for the inversion of induction and sonic measurements, respectively Results confirm that the combined use of resistivity and sonic measurements considerably reduces ambiguity in the inversion and provides reliable estimates of saturation in both the invaded and virgin zones. Moreover, inclusion of the dry-rock elastic moduli as independent variables avoids enforcing a lithologyspecific relationship to porosity.