Network models of porous media incorporates microscopic characteristics of the pore space, as well as determine the evolution of the macroscopic transport properties of such systems from changes in pore structure and from chemical and physical interactions of particles, porous media and water phase, at the pore scale(1). There are many degrees of similarity to which a network model can represent the actual medium pore space. The criteria adopted for particle generation, motion and capture also differ in the published network models.
Compared to previous similar works(2,3,4), the main improvement of the present model is that it deals with realistic velocities at the pore scale, a fundamental concern to particle transport processes(5). This is accomplished thanks to the incorporation of morphologic (pore space geometry, pore and pore throat sizes distributions) and topologic (pore interconnectivity, quantified by an average coordination number) medium characteristics relevant to fluid flow, particle motion and capture. These attributes are established either by applying Image Analysis associated with Stochastic Virtual Reconstruction techniques, or by using Capillary Driven Porosimetry data (e. g. mercury porosimetry), associated with some empirical correlations.
As a basis for the particulate fluid flow simulations, a 3-D network model of nodes and bonds, as proposed by Ioannidis and Chatzis(6), and latter modified by Ioannidis et al.(7), was employed. For the sake of this work, some alterations were made(8). The absolute permeability of thenetwork model is calculated by solving a system of linear mass balance equations for the sites, along with equations of hydraulic conductivity for the bonds. Realistic permeability estimates are obtained.
Stochastic criteria adopted to simulate the generation, motion and capture of the particles are also physically meaningful. Both physical-chemical interception and size exclusion mechanisms of particle retention are modeled, the former with the aid of two empirical parameters, as originally proposed by Rege and Fogler(2). Particlecapture modifies the flow field in the network, that is recurrently calculated, resulting in permeability decline as more particles are retained.
The permeability vs. time curve, obtained from an unique laboratory test, by injecting a particulate water in a representative core sample, is used to calibrate the simulation results, determining the two empirical parameters used to model the particle interception capture mechanism. Afterwards, the same values of the empirical parameters can be used to estimate the injectivity performance when modifications are imposed to the original medium connectivity, pore and pore throat size distributions and/or to the particle size distributions (provided that the chemical/mineralogical compositions of porous medium, water phase and particles are preserved).
Sensitivity analysis shows that, besides the particle to pore throat size ratio, concentration and flow velocity, other important factors governing the permeability impairment are the medium average coordination number and the shape of the pore throats(8).
SAHIMI, M., GAVALAS, G.R. and TSOTSIS, T.T., Statistical and Continuum Models of Fluid-Solid Reactions in Porous Media, Chemical Engineering Science, Vol. 45, No. 6, pp. 1443–1502, 1990. REGE, S. D., FOGLER, H. S., A Network Model for Deep Bed Filtration of Solid Particles and Emulsion Drops, AIChE Journal, Vol. 34, No. 11, pp. 1761–1772, 1988.