A pore space model for rock permeability and bulk modulus

Abstract

A simple network model of pore space in rocks has been developed with which permeability and bulk modulus as a function of confining pressure can be calculated. Pores are modeled as straight conduits with circular, elliptic, or tapered cross sections. The interconnection of these conduits is modeled by emplacing them in regular two‐dimensional hexagonal, square, or triangular networks. Flow through each conduit is modeled using Poiseuille's law. Flow through the network is calculated based upon the analogy of fluid flow in Darcy's law to current flow in Ohm's law. An estimate of the effective bulk modulus is obtained by summing the contributions of the individual pores. The effect of confining pressure on permeability and bulk modulus is determined by the solid properties and the shape of the pores. For appropriate aspect ratio distributions, the permeability and bulk modulus characteristics of the network model are similar to those found for laboratory rock samples. For rocks of moderate porosity, like sandstone, the model predicts that the bulk modulus is most affected by small, low aspect ratio pores. In contrast, for rocks like granite and tight sandstones (permeability less than 0.5 mdarcy) in which there are relatively few round pores, the bulk modulus and the permeability are both controlled by easily deformed pores. These types of responses are observed in experimental data. The success of the model in predicting these general bulk modulus and permeability responses indicates that while the models presented are too simple to represent a rock completely, the network theory approach is a promising method for modeling porous media.

Nonlinear effective pressure law for permeability

“…Gangi's and Walsh's models usually give comparable results, but Gangi's model is a little less practical because it requires knowledge of permeability at zero effective pressure, a quantity that may be difficult to estimate accurately (we did test Gangi's model but, since it always agrees with Walsh's model, the results are not reported in section 4). Seeburger and Nur [1984] and Yale [1984], among others, numerically investigated the effect of fracture connectivity and of variations in fracture geometry, but these studies did not lead to analytical expressions that could be used in our work. Another work worth mentioning is that of Gavrilenko and Gueguen [1989], who modeled the permeability of a heterogeneous population of smooth or rough microcracks, including percolation effects.…”

Permeability of illite‐bearing shale: 1. Anisotropy and effects of clay content and loading

“…They are readily distinguished from the large equant pores and tube-like intergranular spaces at grain triple junctions of sandstones that serve as nodes and critical linkages, respectively, in connected pore networks of reservoir rocks [Seeburger and Nu, 1984;Doyen, 1988;Bernabé, 1991;Fredrich et al, 1993]. Thus the geometries of pores in shales, the physical properties of host material surrounding pores, and the network of connected pores depend on clay mineral distribution and alignment.…”

Particle Scale Reservoir Mechanics

“…To predict the effect of stress change on permeability, Seeburger and Nur (1984) developed a network model with the consideration of a hydrostatic stress state present. The geometric parameters of the flow network are related to the hydrostatic stress.…”