Electrical Modeling of the Inhomogeneous Invaded Zone

The ideal rock model in electrical well logging for prospecting hydrocarbon consists of three cylindrical layers characterized by homogeneous resistivities. The second layer of model represents the zone of invasion, where under real circumstances the resistivity is not constant but changes with the distance from the borehole. This condition could be taken into consideration, but the solution of the electrical direct problem for such a case is very complicated. Any kind of invasion resistivity profile can be approximated by many cylindrical layers of homogeneous resistivities. A recursive formula is derived by which the many-layer problem can be solved simply. Numerical calculations were made to study the effect of the inhomogeneity of the invaded zone. Apparent resistivities of different Laterolog and normal arrangements were calculated for several models having linearly increasing resistivity values. These were evaluated by least-squares fitting to determine the equivalent electrical parameters of the usual model of three homogeneous layers. The results show that there is practically no error in determination of the true resistivity, but the depth of invasion may be significantly smaller than that of the linear resistivity profile.