CHEBYSHEV POLYNOMIALS BASED INTERVAL INVERSION APPROACH FOR THE ANALYSIS OF BOREHOLE GEOPHYSICAL DATA: A CASE STUDY FROM EGYPT

Abstract

In the last few years, the interval inversion approach has shown significant success in evaluating and characterizing the hydrocarbon-bearing zones, providing an optimal overdetermination ratio for more accurate and reliable solutions. In this study, the method is used with an alternative basis function to reveal the petrophysical properties of the reservoir rock in Komombo Basin, Upper Egypt. First, the depth-dependent response functions are utilized to formulate the forward problem. Then we expand the petrophysical parameters into a series by using Chebyshev polynomials as a basis function. The Marquardt algorithm is used to solve the inverse problem. Eventually, the petrophysical parameters – which include porosity, clay content, and water saturation in the invaded and uninvaded zone of W. Al Baraka-2 well – are derived from a relatively small number of expansion coefficients. The results are evaluated by computing the errors of the estimated parameters and measuring the misfit between the observed and calculated data. The reliable estimation of the petrophysical parameters assisted in figuring the hydrocarbon potentiality of the reservoir formation in the investigated area.