TRANS4 - A FORTRAN PROGRAM FOR COMPUTING APPARENT RESISTIVITY DEPARTURE CURVES FOR AN INFINITELY THICK BED WITH TRANSITIONAL INVADED ZONE IN BOREHOLE GEOPHYSICS

In petroleum exploration it is necessary to measure the resistivities of the formation units along the borehole wall once a well is drilled. It is necessary to estimate the true resistivity of the formation (R( t)) away from the borehole wall for assessment of movable oil and life of the oil field. In this paper the program TRANS4 is presented as a forward model for borehole resistivity sounding for a two electrode (n ormal) configuration. The source code is written in FORTRAN 77. The ea rth model consists of a cylinder of borehole mud surrounded by coaxial cylinders of flushed zone, invaded zone, and uncontaminated zone. The direct current potential boundary value problem is solved using the m ethods of separation of variables and Frobenius extended power series. In this problem invaded zone resistivity (or conductivity) is assumed to differ linearly with radial distance. To avoid algebraic singulari ty the problem was divided into two different parts. Resistivity (when R(t) < R(xo)) and conductivity (when sigma(t) < sigma(xo)) models are solved separately. Here R(t) and sigma(t), are the true resistivity a nd conductivity of the uncontaminated zone and R(xo) and sigma(xo) are the resistivity and conductivity of the flushed zone respectively. Ap parent resistivity is computed using 7 point Gauss quadrature. Spline interpolation is introduced for calculation of the kernel function at desired values of the integration variable which are used in numerical integration. Computed apparent resistivity with and without applicati on of spline interpolation are presented to show the reduction in comp utation time. Results are expressed in a nondimensional form. The prog ram can be used for computation of apparent resistivities for other el ectrode configurations with minor and necessary modifications. This fo rward model is solved for infinite bed thickness. This solution will b e valid for finite bed thickness where shoulder bed effect is negligib le. The forward model algorithm could be used as a subroutine for 1-D inversion where a realistic transitional invaded zone model is assumed .