BOREHOLE DE RESISTIVITY RESPONSE FOR A TRANSITIONAL INVADED ZONE

A borehole direct-current resistivity boundary value problem for norma l and lateral electrode configurations is solved assuming axial symmet ry. The borehole mud, a flushed zone, an invaded zone, and an uncontam inated zone are all assumed to be present. A linear transition in resi stivity is assumed for the invaded zone. Frobenius extended power seri es and the method of separation of variables are used to solve the 1-D problem. Single-run borehole resistivity sounding and solution of the inverse problem are suggested for estimating the resistivity of the u ncontaminated zone and the radius of invasion. Finite-difference model ing is done to estimate the effect of shoulder beds in borehole soundi ng. Some of the computed 1-D and 2-D model apparent resistivity curves are compared with the existing scale model data. The analysis reveals that the mud cake effect is negligible for normal and lateral electro de array and the invasion zone thickness is reflected in the forward m odels. Apparent resistivity curves with and without a transitional inv aded zone are well separated. Resistivity departure curves are well se parated for fixed resistivity and variable resistivity invaded zone mo dels. A normal electrode configuration can feel the presence of the sh oulder bed in a 2-D model when the bed thickness is about 12 times the electrode separation. One-dimensional ridge regression inversion with synthetic forward model data is presented to suggest an alternative a pproach for determining the resistivity of the uncontaminated zone (R( t)) and the radius of invasion (r(i)). We conclude that (1) a single r un borehole sounding with 10 or 12 data points from a normal or latera l log may be used, rather than 3 points from a dual laterolog R(xo) to ol, for better estimation of R(t), and (2) a borehole forward model sh ould include a transitional invaded zone. Finally, an alternative appr oach for the estimation of the radius of invasion is proposed.