Study On Forward Modeling Method Of Charts Correction In Normal Resistivity Logging With Complicated Borehole Environment

Borehole correction in normal resistivity logging is of great significance to the reevaluation of the old hydrocarbon exploration,the purpose of this paper is to figure out a rapid and efficient pseudo analytical method for computing electric potential and electric field values excited from a DC point in cylindrically multilayered media,which is helpful to the complicated calculation of borehole environment correction charts in normal resistivity logging and also gives enough evidence in analyzing the effect of different parameters on well-logging response.At first,this paper introduces the principle of normal resistivity logging and the ways of borehole environment correction.To mark out the importance of borehole environment correction,some examples are also discussed.The borehole environment is divided into centric type and eccentric type.Afterwards,starting with poisson equation,we obtain the solution through the algorithms of Dirac function expansion and variables separation.In order to consolidate the boundary definition,the current element is assumed to be equivalent to a kind of special boundary condition,which simpfies the treatment on DC point,then we also talk about how to gain the equation of reflection coefficient and transmission coefficient through this algorithm.To solve the overflow and underflow problems in modified Bessel function,an efficient rescaled formulation is introduced later.Moreover,challenges arise in the numerical computation because of the high frequency of modified Bessel function,a rapidly convergent spatial spectral integral path is presented,and this paper chooses fast integration of rapidly oscillatory functions by David Levin to improve the accuracy and stability of programming.Finally,based on the above algorithms,the software program using C++ language is designed for calculating electric potential,electric field values and apparent resistivity due to DC point exciation in cylindrically multilayered medium.The computation results indicate that a variety of factors including diameter of borehole,eccentricity,ratio of layers resistivity to mud resistivity,anisotropy coefficient and different electrode systems,play different roles in influencing the measurement of borehole environment correction.To sum up,the experimental results show that psuedo analytical method together with separation of variables does have incredibly fast and accurate property in forward model calculating of template correction in normal resistivity logging wth complicated borehole environment.What's more,the calculation of apparent resistivity curves in complicated borehole environment is related to both the ratio of electrode spacing to the diament of wells and layers resistivity to mud resistivity rather than the specific values of electrode spacing distance and diament of wells.However,the impact of eccentricity difference can be neglected,while anisotropy coefficient with small values has to be considered carefully.