A Comparative Study of Capillary-Pressure-Based Empirical Models for Estimating Absolute Permeability in Tight Gas Sands

Abstract

Abstract This paper presents the results of a laboratory study where we compare permeability estimates obtained from several mercury-injection capillary-pressure-based models to a set of measured (steady-state), Klinkenberg1-corrected permeability in tight gas sands. We evaluated 63 core samples from several prolific tight gas reservoirs in the U.S. Steady-state permeability and mercury-injection capillary pressure tests were completed on each sample. The permeability samples range is from 0.0001 mD to 0.2 mD. We review a variety of currently-employed models that are classified as belonging to either Poiseuille or Percolation/ Characteristic Length models. We identify those correlations that are best applied in tight gas sands by quantifying each method's accuracy and precision and force rank each based on error analysis score. Introduction The petroleum and geoscience literature are replete with models for estimating both air and absolute permeability from basic rock properties. The most widespread models are those which incorporate pore dimensions and length characteristics quantified from mercury-injection capillary pressure (MICP) measurements. Moreover, most capillary-pressure-based models developed prior to the mid-1980s were derived for more conventional reservoirs with permeability greater than 1.0 mD. Except for the Walls-Amaefule2 modification to the Swanson3 model and the more recent Huet-Blasingame4 model, none of the current models were developed specifically for tight gas sands with permeability in the micro-Darcy range. Therefore, the objective of our study is to compare the applicability of several widely-used, MICP-based empirical models for estimating absolute permeability in tight gas sands. We evaluated 63 core samples obtained from nine tight gas sand sands in five basins within the U.S and one in Argentina. We compare absolute permeability calculated using several MICP-based models to measured the Klinkenberg-corrected permeability using a steady-state technique. Effective porosity in the test samples range from 2 to 15 percent, while permeability ranges from 0.0001 to 0.20 mD. Models evaluated in our study include the Purcell5, Swanson3, WallsAmaefule2, Katz-Thompson6,-8, Pittman9, Kamath10, HuetBlasingame4 and Dastidar11 methods (the Dastidar method is subsequently referred to in this work as the OU method). Permeameters used by commercial laboratories require regularly-shaped samples for accurate measurements. Consequently, the most important application of our study will be for estimating absolute permeability from cuttings and irregularly-shaped sidewall core samples on which we can measure mercury-injection capillary pressures. We identify the applicability of common industry models for estimating absolute permeability in low-permeability sands. We not only identify the most accurate models, but we also quantify the errors associated with other models. Overview of Existing Permeability Models As we noted earlier, the majority of permeability estimates obtained from capillary pressures curves are derived from two fundamental theories:12Percolation/Characteristic Length Models: Percolation theory describes the spreading a fluid though a statistically random porous medium with a variable pore throat distribution whose flow properties are overwhelmingly controlled by a single or multiple characteristic length scales.13Poiseuille Models. Poiseuille theory attempts to treat the flow paths of rocks as a bundle of tubes with various pore diameters. The complexity of a rock system does not necessarily lend itself to the bundle of tubes model. However, many authors have introduced scaling factors into Poiseuille Theory that treat variable pore throat distributions and tortuosity as a calibration constants.12