Pore-scale percolation modeling of two-phase flow in granular porous media

A modified invasion percolation (MIP) model of two-phase flow is implemented at the pore scale and applied to a range of immiscible displacement processes. Simulation results quantify the relationship between the statistical properties of the void space and the immiscible displacement structure.; A dimensional analysis of two-phase flow in porous is presented, demonstrating the role of the pore scale and characterizing the immiscible displacement process in terms of thirteen dimensionless parameters. Difficulties associated with implementing scaled physical model of two-phase flow processes are identified, and similitude criteria are developed for a scaled physical model of air sparging.; Separate MIP simulations of gradient stabilized drainage and imbibition to equilibrium demonstrate that the controlling parameters are the (appropriate) Bond number, Bo (ratio of buoyancy forces evaluated over the grain scale to capillary forces evaluated over an appropriate pore scale, depending on whether drainage or imbibition), and the coefficient of variation of the appropriate length scale distribution. The equilibrium height is demonstrated to scale as the inverse of the Bo (per Jurin's law) and the width of the equilibrium fringe to scale as the combined parameter Bo/cov. MIP simulations of gradient stabilized displacement are also used to quantify residual saturations and constrain estimates of the mean coordination number.; Results of simulations of gradient destabilized drainage results demonstrate that finger sizes depend on the effective Bond number (consisting of buoyancy and possibly viscous components) and the (nonwetting) coefficient of variation. Experimental results are used to examine the interactions among advancing fingers, and identify future directions of MIP modeling. Based on a scale analysis, criteria are presented that quantify the conditions under which finger generation and disconnection are expected to occur.; The coupled percolation/continuum model of drying in granular porous media builds on work by Prat (1993) and Prat (2002). Primary contributions include detailed analyses of the effects of changes in boundary conditions and medium properties on drying times and phase distribution, as well as an investigation of the observed secondary drying front. In addition, results provide evidence of the ability of the MIP model at estimating interface areas and mass transfer rates.