A COMPARATIVE STUDY OF VARIOUS VOLUMETRIC APPROACHES TO INTERPRET ELECTRICAL LOG DATA FROM SHALY SAND RESERVOIR

Abstract

For electrical conductivity response of shaly-sand reservoir, in the case of 100% water saturation, three popular volumetric models: 1) Bussian (1983), 2) Mixing (Tenchov, 1998), 3) Glover et al. (2000) and another proposed by Notiyal (2002) are evaluated. Lima et al. (2005) have pointed out that plot of bulk conductivity versus water conductivity for Bussian model shows inconsistency with the trend of experimental data for water conductivity (o.) less than matrix conductivity (cry). Notiyal's model is a modification of Bussian model to be used for that very case. Consistency of Notiyal's model is tested for two cases: 1) matrix conductivity - fluid conductivity, leads to bulk conductivity fluid conductivity - matrix conductivity (called isoconductivity point) irrespective of values of other reservoir parameters because the system virtually turns to a single phase system and 2) for very small value of porosity, bulk conductivity tends to matrix conductivity for low salinity range. Bulk conductivity versus water conductivity plot is also now consistent with the trend of experimental data. Since, all the three models result in non-linear equations, so, feeling a need of some robust non-linear scheme, genetic algorithm (GA) has been implemented inculcating a temperature parameter similar to that of simulated annealing (Stoffa and Sen, 1991) to solve and fit corresponding equations to the experimental data available in literature. When the three equations corresponding to the three models are fitted to the data of the sample C-26 taken by Waxman and Smits (1968) using GA with a relative root mean squared error (rRMSE) of 2.47% for Bussian model and 3.92% for mixing model, it shows a great improvement over the one worked out by Lima et al. (2005) using the grid search method by minimizing the chi-square error with an rRMSE of 10.11% for Bussian model and 14.03% for mixing model. Further, for partial saturation, a proposed extension of Bussian model (we call it extended Bussian model), Tenchov's model (Tenchov, 1998) and Berg's model (1995) are evaluated. In the proposed model, water conductivity is replaced by the conductivity of a composite fluid which is taken as a bi-component mixture of formation water and hydrocarbon. Theory of mixture yields the conductivity of this composite fluid. Only Berg's model passes all the consistency and validation tests.