Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone)
Authors: Javadpour F. 
Published: March 2010

Abstract
Gas-producing mudrock systems are playing an important role in the volatile energy industry in North America and will soon play an equally important role in Europe. Mudrocks are composed of very fine grained particles, and their pores are very small, at the scale of nanometers. Gas production from these strata is much greater than what is anticipated given their very low Darcy permeability. In this paper, images of nanopores obtained by Atomic Force Microscopy (AFM) are presented for the first time. Gas flow in nanopores cannot be described simply by the Darcy equation. Processes such as Knudsen diffusion and slip flow at the solid matrix separate gas flow behaviour from Darcy-type flow. We present a formulation for gas flow in the nanopores of mudrocks based on Knudsen diffusion and slip flow. By comparing this new gas flow formulation and Darcy flow for compressible gas, we introduce an apparent permeability term that includes the complexity of flow in nanopores, and it takes the form of the Darcy equation so that it can easily be implemented in reservoir simulators. Results show that the ratio of apparent permeability to Darcy permeability increases sharply as pore sizes reduce to smaller than 100 nm. Also, Knudsen diffusion's contributions to flow increase as pores become smaller. Unlike Darcy permeability, which is a characteristic of the rock only, permeation of gas in nanopores of mudrocks depends on rock, gas type and operating conditions.

Introduction
In general, very fine grained sediments (&lt;62.5 µm) are collectively referred to as mudrocks, which show no fissility (paperlike parting) and are commonly classified as mudstones; those that show fissility are commonly classified as shales. The reader is referred to Folk(1), who developed a simple classification of mudrocks. The term mudrocks, rather than shales, for unconventional gas-producing strata is used in this paper to be in line with the scientific classification acceptable in the geosciences.
The existence of nanopores in mudrocks has been revealed recently by ultra-high pressure mercury injection(2, 3) and back-scattered scanning electron microscopy(4). In this paper, for the first time we show nanopores and nanogrooves detected in mudrocks using atomic force microscopy (AFM)(5). Now that we are confident that such small pores exist in mudrocks, the challenge is to understand and develop governing equations to describe gas flow in these small pores. We present new formulations for gas flow that include some complexities that were ignored in developing the Darcy equation.
At equilibrium, gas molecules are distributed throughout strata, as illustrated in Figure 1. Gas molecules occupy pores as compressed gas, cover the surface of the kerogen materials as adsorbed gas and disperse in the kerogen materials as dissolved gas. Drilling a well or inducing a fracture disturbs the equilibrium, and gas molecules start flowing toward the low pressure zone. First, the freely compressed gas in the pores is produced. Then, the gas molecules on the surface of the kerogen walls desorb and increase pore pressure(2). Gas desorption changes the concentration equilibrium between the bulk of the kerogen and its surface, as illustrated in Figure 1.