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, to gether 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 both linguistic and numeric predictions based on qualitative knowledge and/ or quantitative data. Thus, fuzzy modelling is not only appropriate for the problem discussed here, but is also desirable for many geological problems characterized by non-numerical knowledge and imprecise information.