ExTra: A FORTRAN program to calculate resistivity departure curves with a quasi-exponential transition zone

Abstract

In borehole geophysics it is important to determine accurately the physical parameters of the formation. For electrical methods in oil exploration one of the most important being the true resistivity of the formation. This information helps to assess the recoverability of the oil and the economic viability of the oil field. An interactive computer program ExTra is presented in the paper. The source code is written in standard FORTRAN 77. ExTra computes the forward model response for borehole resistivity sounding for two electrode (normal) configuration. The earth model consists of three cylindrical layers of infinite extent, which is an ideal setup for response computation in one-dimension (1-D). These layers consist of borehole mud, the innermost layer, the flushed zone, and invaded zone. The outermost layer is of infinite radial extent and termed an uncontaminated zone. The dc (direct current) boundary value problem is solved analytically. Resistivity values in the different zones are considered to be uniform except in the invaded zone where the value changes radially. Analytical derivation has been cited for a quasi-exponential transition in resistivity in the invaded zone. Gauss quadrature is used for numerical evaluation of the infinite integral. To achieve higher efficiency, 1-D spline interpolation is introduced for computation of the kernel function at desired values of the integration variable. All the results are expressed as dimensionless quantities. Apparent resistivity response for other known arrays (electrode configurations) can be computed using this program with minor and necessary changes in the code. Solution for infinite bed thickness is shown which can be extended for finite bed thickness where the effect from the vertical inhomogeneity is negligible. The invasion profile presented here is realistic from the point of the actual borehole environment and physical model studies.