A Computer-Oriented Generalized Porosity-Lithology Interpretation of Neutron, Density and Sonic Logs
Authors: Harris Martin H. , McCammon R.B. 
Published: December 2007

A Computer-Oriented Generalized Porosity-Lithology Interpretation of Porosity-Lithology Interpretation of Neutron, Density and Sonic Logs
Linear bulk volume response equations for neutron, density and sonic logs in carbonates can be generalized for any lithologic sequence. Specific formulations of these equations are presented here for simultaneously computing porosity and lithology in sand and shale, as well as in carbonates.

Introduction
Within recent years, the simultaneous determination of porosity and lithology from combinations of neutron, density and sonic logs has gained wide recognition as a log interpretation technique in areas where the heterogeneity of carbonate reservoir rocks poses serious problems. More recently, the same technique has been applied to sand-shale interpretations where the lithology problems are more subtle but as critical. The earliest attempts to apply this technique were based on graphic solutions involving cross-plots of observed log data. This approach proved restrictive, however, becausethree logs could not be simultaneously evaluated,digital computer solutions could not be applied directly, andsand-shale interpretation problems were ignored.
Recently, some computer solutions have been obtained. Simultaneous evaluation of porosity-lithology relationships based on the three porosity logs were reported first by Savre." This was an iterative technique employing charts. A log response equation was defined for each of the three porosity logs; then the porosity and lithology were evaluated by finding an porosity and lithology were evaluated by finding an exact solution to a set of given equations. The calculations were performed with a digital computer. The work of Savre was extended by Burke et al. to include computation of negative fractions of porosity or lithology. Burke et al. dealt with this by selectively adding silica to the solution until the negative fractions disappeared. Thus, up to five lithologic and porosity fractions could be considered, rather than the maximum of four considered by Savre. The nonunique character of the solutions obtained by Burke et al. was recognized by Roper and Jones. They partially alleviated this problem by investigating several mineral combinations, allowing the user to specify his preference of mineral group solution. Negative solutions were replaced by solutions deemed closest in a geometric sense. The problem of nonunique solutions was also considered by Dawson-Grove and Palmer. As many as 70 possible solutions obtained from a family of eight lithologic and porosity elements were evaluated four at a time. The solution containing the elements most frequently occurring in all of the other solutions was accepted. These investigations all dealt with log interpretation in carbonates. One particularly noteworthy application of porosity-lithology solutions for sand-shale interpretations porosity-lithology solutions for sand-shale interpretations was reported by Tixier et al. Rather than interpreting each log in terms of its bulk volume response, as is common, they represented the response in terms of apparent sandstone porosity. The equations were solved by successive approximation, with a limit on gas saturation and a variable gas transit time. This approach, however, means the method cannot be generally applied to a wide range of problems.
JPT
P. 239