A Modified Purcell/Burdine Model for Estimating Absolute Permeability from Mercury-Injection Capillary Pressure Data

Abstract

Abstract This paper presents the development and validation of a new semi-analytical, statistically-derived model for estimating absolute permeability from mercury-injection capillary pressure data. The foundations of our new model are the classic Purcell and Burdine equations which relate absolute permeability to capillary-pressure/wetting-phase-saturation properties. We also incorporate characteristic capillary pres-sure behavior using the Brooks-Corey power-law model. The final form of our proposed model allows us to compute absolute permeability as a function of effective porosity, irreducible wetting phase saturation, displacement or threshold pressure, and basic pore size characteristics. We tested and correlated our model using 89 sets of mercury-injection (Hg-air) capillary pressure data – including core samples from both carbonate and sandstone lithologies. In summary, we found that our model consistently yields accurate results for a wide range of rock properties. Introduction The fundamental relationships between pore size/geometry and basic rock properties (e.g., effective porosity, absolute permeability, etc.) are well-documented in the petroleum and petrophysics literature. Moreover, the literature is replete with models for estimating or predicting permeability from basic rock properties. Nelson4 has developed a comprehensive re-view of the literature, and he has identified five major categories of permeability models based on the physical rock attributes used in the model development:The five major model categories specified by Nelson are:Petrophysical models,Models based on grain size and mineralogy,Models based on surface area and water saturation,Well log models, andModels based on basic rock pore dimensions. In this paper, we focus on models that incorporate basic rock pore characteristics and dimensions, and specifically, pore characteristics as determined from capillary pressure data. Nelson has further classified these particular models as direct types since they not only relate rock permeability directly to the pore dimensions and connectivity, but also incorporate fundamental theories of fluid flow through porous media. Most of these direct methods – especially the early models developed in the 1940s and 1950s – use mercury-injection capillary pressure data to quantify the rock pore and pore throat characteristics.