Film flow dominated simultaneous flow of two viscous incompressible fluids through a porous medium

Abstract

We present an experimental study of two-phase flow in a quasi-two-dimensional porous medium. The two phases, a water-glycerol solution and a commercial food grade rapeseed/canola oil, having an oil to water-glycerol viscosity ratio M = 1.3, are injected simultaneously into a Hele-Shaw cell with a mono-layer of randomly distributed glass beads. The two liquids are injected into the model from alternating point inlets. Initially, the porous model is filled with the water-glycerol solution. We observe that after an initial transient state, an overall static cluster configuration is obtained. While the oil is found to create a connected system spanning cluster, a large part of the water-glycerol clusters left behind the initial invasion front is observed to remain immobile throughout the rest of the experiment. This could suggest that the water-glycerol flow-dynamics is largely dominated by film flow. The flow pathways are thus given through the dynamics of the initial invasion. This behavior is quite different from that observed in systems with large viscosity differences between the two fluids, and where compressibility plays an important part of the process.

Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

“…In a similar experiment by Aursjø et al. (2014) with different fluids, a food grade oil and water–glycerol as the two phases, the oil was found to make films in the pores, making a connected system of flowing pathways throughout the whole system, and a large part of the water–glycerol clusters were left behind. The pore-level dynamics is therefore very different in that case, and correspondingly different power law exponents were found for the film-flow system.…”

Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow-Dependent Relative Permeability Scaling

“…At steady-state conditions in one-dimensional flow, the flow rate ratio, r, is equal to the mobility ratio, . The equivalence, expressed in the first part of eqn (5), is a conjecture resulting from direct flow analysis (see Appendix I in [9]).…”

“…Because of the common pressure gradient [eqn (1)] and the equivalence between flow rate ratio and mobility ratio [eqn (5)], relative permeability curves intersect at a fixed value of the flow rate ratio, the so-called cross-over flow rate ratio value, rx. The latter is reciprocal to the viscosity ratio, = (1⁄ ), as provided by eqn (5). This inherent characteristic of steady-state flows is universally observed in all relative permeability vs flow rate ratio diagrams ( [9], [15] and Fig.…”

“…In those cases the disconnected NWP fluidic elements block part of the available flow cross-section by a fraction analogous to the average saturation and effect a relative reduction of the permeability of both the NWP and the wetting phase (WP). Nevertheless, there is ample experimental evidence that disconnected flow is a substantial and sometimes prevailing flow pattern [1][2][3][4][5][6][7][8].…”

“…However, at moderate/low velocities, when capillary forces are comparable to viscous forces, the macroscopic pressure gradient does not scale linearly with the flow rate. Experimental studies on steady-state two-phase flows in glass beads [3,5,6], in glass bead columns [11], as well as in sand-pack columns [12], revealed that the non-linear relation between pressure gradient and flow rate can be described by generic power laws with different exponent values. The discrepancy between the values of the scaling exponents is attributed to differences associated with dimensionality of the pertinent variables, measurements pertaining to different flow conditions, dimensionality of the NWP/WP/PM system etc.…”