Improved Simultaneous Determination of Formation Properties from Well Logs

Abstract

A well log computation technique, similar to one developed earlier, can be used to differentiate the separate contributions of many possible minerals. The scheme may be extended to include the possible minerals. The scheme may be extended to include the effects of resistivity tools as they relate to porosity and saturation. Introduction The successful application of computer log analysis to the Chaveroo field by Burke, Curts, and Cox stimulated our interest in this method. The modification of their method, which is presented here, has been used successfully by Getty Oil Co. in the analysis of logs from several fields. For both methods a set of simultaneous equations relating log response to formation composition is solved for the fractions of each component present. The method presented here allows inclusion of geological information and an arbitrary number of logs. As will be shown, the present method allows greater flexibility and control than the previous method of Burke et al. To assist in visualizing, the mathematical relationships are supplemented by a graphical analogy. In the text of the paper, the solution process is discussed in terms of this graphical analogy. Computational aspects of the solution are described in the Appendix. Basis of Computation The basic assumption employed by Burke et al. was that logged values can be represented as a linear equation of the form: where Xa is the logged or measured value of some property of a mixture containing n components. i property of a mixture containing n components. i is the fraction of component i in the mixture, and Xi is the property value assigned to a pure component i. For example, if a formation is water-filled dolomite, the logged sonic transit time may be represented by where w + D = 1. If the sonic transit times in water ( tw) and dolomite ( tD) are known, the fractions of water ( w) and dolomite (0D) can be calculated. If the solid matrix is a mixture of dolomite and gypsum, and if sonic and neutron-porosity logs are available, the fractions of water, dolomite, and gypsum can be obtained by solving the following set of simultaneous equations: Na = Nw w + ND 0D + NG 0G ta = tw 0w + tD 0D + tG 0G with the added restriction that all 0's must be positive. In these equations Na is the logged neutron positive. In these equations Na is the logged neutron porosity. porosity. The requirement of positive 's can be expressed conveniently in graphical form. In Fig. 1, pure component points are labeled W, D, and G, representing water, dolomite, and gypsum, respectively. JPT P. 827