# Quantitative geometric model of connected carbonaceous material in mudrocks

## Abstract

Unconventional gas resources have become important as an environment- friendly source of fuel. It is important to understand the pore level geometries of grains and voids in mudrocks in order to understand the flow potential of gas from these rocks.

Recent observations of nanopores within carbonaceous material in mudrocks have led to the hypothesis that such material provides conduits for gas migration within the mudrock matrix. This hypothesis requires that the carbonaceous material exist not as isolated grains but as connected clusters of grains within the mudrock. To examine this hypothesis, we develop an algorithm for the grain-scale modeling of the spatial distribution of grains of carbonaceous matter in a matrix of non-carbonaceous material (silt, clay). The algorithm produces a grain-scale model of the sediment which is precursor to a mudrock, then a sequence of models of the grain arrangement as burial compacts the sediment into mudrock.

The carbonaceous material is approximated by the simplest possible geometric model of spherical grains. These grains are distributed randomly within a population of other spheres that represent silt and clay grains. A cooperative rearrangement algorithm is used to generate a disordered packing of the grain mixture having a prescribed initial porosity. This model represents the sediment precursor of the shale in its original depositional setting. Periodic boundary conditions are imposed on the packing to eliminate wall-induced artifacts in the grain arrangement; in effect the packing extends infinitely in all three coordinate directions. We simulate compaction of the model sediment by incrementally rescaling the vertical coordinate axis, repeating the cooperative rearrangement calculation with periodic boundaries after each increment.

We determine the size distribution of clusters of touching carbonaceous grains, focusing particularly upon the approach toward percolation (when a cluster spans the entire packing). The model allows estimation of threshold fraction of carbonaceous material for significantly connected clusters to form. Beyond a threshold degree of compaction, connected clusters become much more prevalent. Other factors affecting the threshold fraction such as ductility of the carbonaceous material is also evaluated. Ductility is modeled by taking a grain consisting inner rigid core covered by the outer soft shell which can be penetrated and deformed during geometrical transformation.

The emergence of large numbers of clusters, or of a few large clusters, increases the probability that nanoporous conduits within the clusters would intersect a fracture in the mudrock. This should correlate with greater producibility of gas from the mudrock. Thus the dependence of the statistics of the clusters upon other parameters, such as the fraction of carbonaceous material, porosity, degree of compaction, etc., could be useful for estimating resource quality. For example, it is observed that the threshold concentration of carbonaceous material in the initial sediments for “significant clustering” enough to approach percolation is about 20 percent of the volume fraction. The degree of compaction needed to get “significant clustering” is 50%.