A two scale analysis of tight sandstones
Abstract:Tight sandstones have a low porosity and a very small permeability K. Available models for K do not compare well with measurements. These sandstones are made of SiO_2 grains, with a typical size of several hundreds of micron. These grains are separated by a network of micro-cracks, with sizes ranging between microns down to tens of nm. Therefore, the structure can be schematized by Voronoi polyhedra separated by plane and permeable polygonal micro-cracks.
Our goal is to estimate K based on a two scale analysis and to compare the results to measurements.
For a particular sample , local measurements on several scales include FIB/SEM , CMT and 2D SEM. FIB/SEM is selected because the peak pore size given by Mercury Intrusion Porosimetry is of 350nm. FIB/SEM imaging (with 50 nm voxel size) identifies an individual crack of 180nm average opening, whereas CMT provides a connected porosity (individual crack) for 60 nm voxel size, of 4 micron average opening.
Numerical modelling is performed by combining the micro-crack network scale (given by 2D SEM) and the 3D micro-crack scale (given by either FIB/SEM or CMT). Estimates of the micro-crack density are derived from 2D SEM trace maps by counting the intersections with scanlines, the surface density of traces, and the number of fracture intersections. K is deduced by using a semi empirical formula valid for identical, isotropic and uniformly distributed fractures . This value is proportional to the micro-crack transmissivity sigma.
Sigma is determined by solving the Stokes equation in the micro-cracks measured by FIB/SEM or CMT.
K is obtained by combining the two previous results. Good correlation with measured values on centimetric plugs is found when using sigma from CMT data. The results are discussed and further research is proposed.
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