57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

We have made considerable progress in furthering our understanding of the impact of a porous, elastic medium on the transport behavior of a fluid contained in the medium. This coupling of fluid transport with elasticity is relevant in many physical situations including, for example, flow through gels and earth subsidence associated with oil recovery. Building upon our earlier continuum models of poroelastic transport and biased diffusion, published in the Journal of Applied Physics and Physica A, respectively, we are developing an atomistic model of fluid imbibition in a deformable solid. This model will highlight non-Fickian behavior associated with elastic deformation and is described below.We employ both Monte Carlo (MC) and molecular dynamics (MD) simulations to describe the diffusive behavior of small atoms through a solid lattice comprising larger atoms. In our model, we construct a fluid reservoir containing the small atoms using grand-canonical MC simulation to fix the chemical potential in the reservoir. The reservoir is, therefore, a source of fluid atoms, and the difference in chemical potential between the reservoir and the crystal provides a driving force for diffusion. The dynamics of both the small and the large atoms are simulated using MD, and we use a hybrid algorithm consisting of both MC and MD updates to equilibrate the reservoir and to move the atoms according to Newtonian dynamics. This is a challenging task as we wish to construct a relatively open crystal structure in equilibrium with a liquid at relatively high temperature so that liquid atoms will penetrate into the crystal. We have now found a range of parameter space (i.e., temperature, chemical potential) and atomic radii so that the fluid reservoir coexists with the crystal and are examining the mean-squared displacement of fluid atoms within the crystal.Our goal here is to describe fluid uptake in a deformable medium, namely the crystal lattice. It is expected that we will be able to identify two distinct regimes, a Fickian regime associated with the flow of relatively small spheres that create little distortion of the crystalline medium, and a non-Fickian regime in which relatively large spheres generate stresses within the crystal. In this latter regime one expects that atomic mobility will be relatively small and that diffusive behavior may be spatially nonlocal given the coupling of the concentration field of the diffusing species to the elastic field in the solid. The underlying assumption here is that the elastic fields relax quickly on the time scale of fluid atom motion, and therefore the diffusive driving force depends on the spatial distribution of the smaller atoms.In this final year of the project, we expect to obtain uptake curves for fluid atoms and to compare these curves with those expected from Fickian diffusion. In addition, by changing the system temperature, the atomic radii and the solid density we will be able to effectively tune the elastic response of the solid and, hence, the observed diffusive behavior. Future work will involve the construction of porous networks with a desired distribution of pore sizes and connectivities to investigate the impact of pore network geometry on diffusive transport.