“Dual laterolog response in 3-D environments,” Petrophysics, Vol. 41, No. 3, pp. 234-241, 2000.
Computer codes based on the finite element method (FEM) have been developed to model dual laterolog responses in 3-D environments. Validation of the 3-D FEM codes is carried out by showing that results of the codes agree with those obtained by an analytic solution, and by 2-D FEM codes. Using the 3-D FEM codes, dual laterolog responses in highly deviated wells, horizontal wells, dipping anisotropic formations, and fractured carbonate formations are studied . For a laterolog instrument in a formation consisting of a resistive bed between two conductive shoulder beds, one tends to believe that the greater the dip angle is, the lower the reading of the apparent resistivity at the center of the bed will be. However, such a behavior is not always true. The resistivity reading also depends on the bed thickness and on the resistivity contrast between the resistive bed and the shoulder beds. In some cases, it is seen that when the dip angle varies from 0 to 75 degrees, readings at the center of the resistive bed actually increase with the dip angle. Therefore in thin dipping beds, the response of both the deep and the shallow laterolog instrument is difficult to predict without carrying out computer modeling. The study also illustrates the dual laterolog response in a horizontal well in a formation containing a resistive bed. The readings of both the shallow and the deep arrays are strongly affected by the shoulder beds when the arrays are in the resistive bed. Even when the bed thickness is as thick as three meters, shoulder beds still have strong influence on the deep laterolog. The effect of anisotropy on the dual laterolog is small even at large dip angles. The apparent resistivity responses of the dual laterolog are determined mainly by the horizontal resistivity of the anisotropic formation. As expected, in a fractured formation the apparent resistivity response decreases as the fracture opening width is increased, or as the resistivity of the fluid in the fracture is decreased. It is shown that in some cases the fracture with a five-meter extent has the same effect as the one with an infinite extent; and a 100 micrometer fracture opening has an apparent thickness of one meter. When there are five or more fractures per meter along the borehole axis, then the fractured formation can be modeled as an anisotropic formation.