Estimation of Permeability from Porosity, Specific Surface Area, and Irreducible Water Saturation using an Artificial Neural Network

Abstract

Abstract An Artificial Neural Network (ANN) was designed and tested in the present study to examine the correlation between permeability estimations and porous medium properties, such as porosity, specific surface area, and irreducible water saturation. The network developed in this work is a predictive tool that uses soft computing techniques to estimate absolute permeability of carbonate reservoirs. The Artificial Neural Network toolbox of MATLAB® R2006b and the Feed Forward Error Back Propagation methodology were used in the construction of the network. Carbonate reservoir field data presented in the literature were utilized in the training, testing, and validation of the proposed model. The present study indicates that ANN generated permeability values are consistent with those obtained from core analysis. Results from this study confirm the complex relationship among permeability, porosity, specific surface area and irreducible water saturation of carbonate reservoirs, and suggest that variations in specific surface area affect the magnitude of irreducible water saturations, thus creating an apparent dependence of permeability on irreducible water saturation. Additional observations support a direct relationship between porosity and permeability, and an inverse relationship between specific surface area and permeability. Introduction Porosity-permeability relationships are of great importance for the reservoir engineer because of the difficulties and uncertainties associated with direct permeability interpretations from well-log data. Accurate permeability predictions provide engineers with the ability to design and manage efficient processes in the development of oil and gas fields. Although it is generally accepted that permeability is closely related to porosity, their relationship cannot be captured by a simple expression. Absolute permeability is a dynamic flow property, while porosity is a measure of the storage capacity of a rock, a static rock property. The absolute permeability of a porous medium varies with grain size, sorting, cementing, direction, and location; thus the scatter quality of permeability plots. A wide range of permeability correlations using pore- and field-scale models are presented in the literature 1–3. Starting with the seminal works by Kozeny 4 and Carman 5, many different correlations have been proposed between porosity and permeability. The Kozeny-Carman equation was developed for a porous medium represented by a bundle of uniform capillary tubes and introduces a direct dependence between porosity and permeability, while accounting for specific surface area and tortuosity as a measure of flow resistance. eq. (1) For unconsolidated porous media with variable particle size, Panda and Lake 6 propose a modification of the Kozeny-Carman equation to express permeability in terms of particle-size distribution characteristics and the bulk physical rock properties. They found reasonable agreement between predicted and experimental permeability, relying on appropriate estimations of surface area, and demonstrated the modest impact of sorting on the quality of their predictions. With respect to sorting, porosity tends to increase for perfectly sorted media and decrease as sorting becomes poorer 7, thus affecting permeability.