A genetic algorithm approach to evaluate models for electrical conductivity response of shaly sand reservoir, based on volumetric approach.

摘要

This paper focuses on evaluation of three models; 1) Bussian (1983), 2) Mixture (Korvin, 1982; Technov, 1998) and 3) Glover et al. (2000) for electrical conductivity response of shaly sand reservoir based on volumetric approach and looking for some scheme to solve corresponding equations better than the used schemes so far in literature. As all the models result in non-linear equations, so, there was a need of non-linear scheme to solve these equations. Genetic algorithm (GA), implementing the concept of stretching (Stoffa and Sen, 1991) has been applied to solve non-linear equations and to interpret experimental data of the sample C-26 from Waxman and Smits (1968) paper. The same job has been done by Lima et al. (1995), using the grid search method by minimizing the chi-square error (Bevington, 1969) with a relative RMS error 10.11% for Bussian model and 14.03% for Mixture model. A great improvement is obtained using GA with a relative RMS error 2.47% for Bussian model and 3.92% for mixture model. For Glover's model which was not evaluated by Lima et al., it was difficult to obtain a relative RMS error less than 13% using GA. Lima et al. (2005) have pointed out that Bussian model shows anomalous behaviour in low salinity range, so, a modified Bussian equation is proposed for low salinity range which is tested for two cases; 1) matrix conductivity - fluid conductivity, leads to bulk conductivity ~ fluid conductivity ~ matrix conductivity irrespective of values of other parameters because the system turns to a single phase system and 2) For very small value of porosity, bulk density tends to matrix conductivity for low salinity range.