State-Of-The-Art in Permeability Determination From Well Log Data: Part 1- A Comparative Study, Model Development

This study discusses and compares, from a practical point of view, three different approaches for permeability determination from logs. These are empirical, statistical, and the recently introduced “virtual measurement” methods. They respectively make use of empirically determined models, multiple variable regression, and artificial neural networks. All three methods are applied to well log data from a heterogeneous formation and the results are compared with core permeability, which is considered to be the standard. In this first part of the paper we present only the model development phase in which we are testing the capability of each method to match the presented data. Based on this, the best two methods are to be analyzed in terms of prediction performance in the second part of this paper. Introduction Reservoir characterization is a very important domain of petroleum engineering. An effective management strategy can be applied only after obtaining a detailed and close-to-reality ”image” of spatial distribution of rock properties. Among these, the most difficult to determine and predict is permeability. A great amount of work was done by several investigators in the 1-10 attempt to grasp the complexity of permeability function into a model with general applicability (Table 1). All these studies give a better understanding of the factors controlling permeability, but they also show that it is an illusion to look for a “universal” relation between permeability and other variables. The regression approach, using statistical instead of “stiff” deterministic formalism, tries to predict a conditional average, or expectation of permeability, corresponding to a given set of parameters . However, the previous empirical studies give the 12-14 guidelines for selecting the dependent variables which are to be used in the predictor development. A different predictive equation must be established for each new area or new field. The main drawback of this method is that the distribution of the predicted values is more narrow than that of the original data set. The newest method, called “virtual measurement ,” makes use 18,19 of the artificial neural networks, that are model-free function estimators. Because of this characteristic, they are very flexible tools. A back propagation neural network is trained with all the available data, including the measured permeability from cores. This is the “learning” process, during which the network recognizes the pattern of permeability distribution and “adapts” itself in order to be able to predict that pattern. All three methods mentioned above are applied to log data from a heterogeneous oil-bearing formation and the results are compared with core-determined permeability, which is considered to be not the reality, but the standard. 1. Empirical Models Empirical models are based on the correlation between permeability, porosity, and irreducible water saturation. K o z e n y , 1 9 2 7 . The first equation relating measurable rock properties with permeability was proposed in 1927 by Kozeny: