AN INVERTED PETROPHYSICAL MODEL FOR SHALY SANDS

The mathematics of a generalized Maxwell-Wagner model for shaly sands have been inverted to reciprocate six vital rock parameters from frequ ency-dependent complex impedance data. These parameters are porosity, clay volume fraction, cation exchange capacity, average rock grain siz e and water saturations in both the flushed zone and the virgin format ion. The direct model, which incorporates the double-layer dielectric enhancement of clays, uses these rock properties to simulate the real and imaginary parts of the complex impedance of shaly sands as a funct ion of frequency. The inversion theory led to a coupled nonlinear syst em of equations. When physical constraints were enforced on the system unknown variables, the inverted model output showed reasonable agreem ent with the measured data. The model has been tested with a suite of shaly-sand core data covering a range of approximately 50 feet into a tight gas sand formation. The inverted model allows to estimate severa l important rock properties from either a sole frequency sweep of nond estructive laboratory complex impedance data, or from a combination of dielectric and resistivity log data.