Simulation of laterolog by the 3D finite-element method

We have developed a modeling code using the finite element method (FEM) to simulate laterolog responses in three-dimensional inhomogeneous formation models. The code has been benchmarked against analytical solutions and the numerical mode-match method (NMM) for subsets of the 3D geometry. The differences between our results and two others are within 5%. We have further employed the code to simulate the laterolog responses in horizontal and highly deviated wells. The results show that the apparent resistivity decreases with the degree of well deviation from vertical, given the formation model is unchanged. The decreasing ratio also increases with the increase of deviation angle. This becomes significant when the deviation angles are between 40 and 90 degrees. When the angle is close to 90 degrees, the response closes to the average resistivity of shoulder and mud. Finally, we have studied the response of laterolog in formations containing a vertical fracture. The results demonstrate that it is not possible to detect a single vertical fracture with such a laterolog when the fracture width is less than 0.001 m. However, the vertical fracture has significant effects on the apparent resistivity when its width is above 0.01 m. The resistivity of the fluids in the fracture is another important parameter to control the changes of the apparent resistivity. The relative influence of fractures on the apparent resistivity increases with the increase of the contrast between the fluid resistivity and the background formation resistivity.