The Numerical Simulation Of The Dielectric Constant Detector

Dielectric logging is a set of well logging method that use the dielectric constant todistinguish the different layers of rock. Because the dielectric constant of oil or most rockforming minerals is very difference with that of water, dielectric constant of the formationdepends largely on the water content of in unit volume of the inland.Therefore dielectriclogging instrument can accurately measure water content in formation and rock structure.Firstly, according to the dielectric polarization mechanism we determine that thedielectric logging tool’s working frequencies are in the range of a few MHz to1GHz; Wehave studied the waveform of electromagnetic wave in this spectrum in the actual loggingenvironment, then determine improved-plane wave model and spherical wave model todescribes the electromagnetic wave propagationin actual stratum.And from maxwell’sequations mediation, we deduce different dielectrical response expression about the instrumentparameters and formation parameters in different model.Then, using the numerical analysis method we discuss the specific numericalchangeswith dielectric response and frequency, spacing in typical formation.According to thespecific requirements to made instrument,We determine the working frequency of theinstrument is20MHZ to300MHZ and1GHZ,andthe20MHz to300MHz band is suitablefor the spherical wave model, the frequency of1GHz is suitable for the plane wavemodel;T-R space is in the range of45mm to120mm;spacing is25mm.Finally, we inverse solution for the improved plane wave model directly and use of theproperties of the Lambert W function to simplify the spherical wave model.we obtain theanalytical expression about the dielectric parameters on logging parameters.Programmingcalculation, the result shows that the error of numerical solution can be controlled within oneover one thousand.