Fuzzy modelling and the prediction of porosity and permeability from the compositional and textural attributes of sandstone

A new method is presented here for predicting porosity and permeability from the compositional and textural characteristics of sandstones. The method employs fuzzy modelling which is a linguistic paradigm based on fuzzy logic, rooted in the theory of fuzzy sets. The essentials of fuzzy modelling are explained using an example in which porosity and permeability values of a sandstone are predicted from five compositional and textural attributes. Fuzzy modelling can be accomplished in five steps: (i) Identification of input and output variables. In this paper, the inputs are five compositional and textural parameters, namely: relative amounts of ductile grains, rigid grains and detrital matrix, together with grain size, and the Trask sorting coefficient. The output is either porosity or permeability. (ii) Fuzzy clustering of output values. (iii) Formation of membership grades of input data. (iv) Generation of fuzzy rules; and (v) Prediction via fuzzy inference. Compared to statistical modelling (i.e. multiple regression analysis), fuzzy modelling is not only assumption-free but is also tolerant of outliers. Fuzzy modelling is capable of making bath linguistic and numeric predictions based on qualitative knowledge and/ or quantitative data. Thus, fuzzy modelling is not only appropriate for the problem discussed here, brit is also desirable for many geological problems characterized by nonnumerical knowledge and imprecise information.