Development of stochastically reconstructed 3D porous media micromodels using additive manufacturing: numerical and experimental validation.

We propose an integrated methodology for the design and fabrication of 3D micromodels that are suitable for the pore-scale study of transport processes in macroporous materials. The micromodels, that bear the pore-scale characteristics of sandstone, such as porosity, mean pore size, etc, are designed following a stochastic reconstruction algorithm that allows for fine-tuning the porosity and the correlation length of the spatial distribution of the solid material. We then construct a series of 3D micromodels at very fine resolution (i.e. 16 µ m) using a state-of-the-art 3D printing infrastructure, specifically a ProJet MJP3600 3D printer, that utilizes the Material Jetting technology. Within the technical constraints of the 3D printer resolution, the fabricated micromodels represent scaled-up replicas of natural sandstones, that are suitable for the study of the scaling between the permeability, the porosity and the mean pore size. The REV- and pore-scale characteristics of the resulting physical micromodels are recovered using a combination of X-ray micro-CT and microfluidic studies. The experimental results are then compared with single-phase flow simulations at pore-scale and geostatistic models in order to determine the effects of the design parameters on the intrinsic permeability and the spatial correlation of the velocity profile. Our numerical and experimental measurements reveal an excellent match between the properties of the designed and fabricated 3D domains, thus demonstrating the robustness of the proposed methodology for the construction of 3D micromodels with fine-tuned and well-controlled pore-scale characteristics. Furthermore, a pore-scale numerical study over a wider range of 3D digital domain realizations reveals a very good match of the measured permeabilities with the predictions of the Kozeny-Carman formulation based on a single control parameter, k 0 , that is found to have a practically constant value for porosities ϕ ≥ 0.2 . This, in turn, enables us to customize the sample size to meet REV constraints, including enlarging pore morphology while considering the Reynolds number. It is also found that at lower porosities there is a significant increase in the fraction of the non-percolating pores, thus leading to different k 0 , as the porosity approaches a numerically determined critical porosity value, ϕ c , where the domain is no longer percolating.

History effects on nonwetting fluid residuals during desaturation flow through disordered porous media.

We investigate experimentally the sweeping of a nonwetting fluid by a wetting one in a quasi-two-dimensional porous medium consisting of random obstacles. We focus primarily on the resulting phase distributions and the residual nonwetting phase saturation as a function of the normalized wetting fluid flow rate-the capillary number Ca-at steady state. The wetting liquid is then flowing in the medium partially saturated by immobile nonwetting liquid blobs. The decrease of the nonwetting saturation is an irreversible process that depends strongly on flow history and more specifically on the highest value of Ca reached in the past. At lower Ca values, when capillary forces are dominant, the residual steady state saturation depends significantly on the initial phase configuration. However, at higher Ca, the saturation becomes independent of the history and thus follows a master curve that converges to an asymptotic residual value. Blob sizes range over four orders of magnitude in our experimental domain, following a probability distribution function P that scales with the blob size s as P(s)∝s(-2) for blob sizes larger than the typical pore size. It also exhibits a maximum size cutoff s(max), that decreases as s(max)∝Ca(-1). To determine the flow properties, we have measured the pressure drop (B) versus the flow rate (Ca). In the ranges of low and high Ca values, the relationship between Ca and B is found to be linear, following Darcy's law (B∝Ca). In the intermediate regime, the progressive mobilization of blobs leads to a nonlinear dependence B∝Ca(0.65), due to an increase of the available flow paths.

Pore-network study of the characteristic periods in the drying of porous materials.

We study the periods that develop in the drying of capillary porous media, particularly the constant rate (CRP) and the falling rate (FRP) periods. Drying is simulated with a 3-D pore-network model that accounts for the effect of capillarity and buoyancy at the liquid-gas interface and for diffusion through the porous material and through a boundary layer over the external surface of the material. We focus on the stabilizing or destabilizing effects of gravity on the shape of the drying curve and the relative extent of the various drying periods. The extents of CRP and FRP are directly associated with various transition points of the percolation theory, such as the breakthrough point and the main liquid cluster disconnection point. Our study demonstrates that when an external diffusive layer is present, the constant rate period is longer.