Interphase mass transfer in variable aperture fractures: Controlling parameters and proposed constitutive relationships

Interphase mass transfer in variable aperture fractures occurs in many problems where two immiscible fluids are present, such as dissolution of dense nonaqueous phase liquids into groundwater, dissolution of CO(2) in deep saline aquifers, and evaporation of trapped water by flowing gas during natural gas production. Typically, one fluid is entrapped by capillary forces and resides in immobilized regions whose distribution and geometry are controlled by the relative influence of capillary, gravitational, and viscous forces within the fracture. For the case of fractures bounded by a low porosity/permeability matrix, interphase mass transfer occurs predominantly owing to diffusive/advective transport from the entrapped phase interface into the phase flowing through the fracture. We explore the relative influence of the initial entrapped phase geometry and mean flowing phase velocities on the dissolution of the entrapped phase. Our systematic simulations use a percolation-based model of phase invasion and depth-averaged models of flow, transport, and mass transfer. The invasion model provides a physically based distribution of entrapped phase within the fracture and the mass transfer model implicitly calculates interphase mass transfer from discrete regions of entrapped phase without the need for empirical mass transfer relationships. Results demonstrate behavior across a wide range of initial entrapped phase distributions, with entrapped phase saturations ranging from zero to near the percolation threshold. Interfacial area evolves with a near-linear dependence on entrapped phase saturation during dissolution in each simulation, and fracture-scale intrinsic mass transfer rate coefficients exhibit a nonlinear dependence on Peclet number and a negligible dependence on entrapped phase saturation. These observations provide a basis for the development of constitutive relationships that quantify interphase mass transfer in variable aperture fractures as a function of entrapped phase saturation and flow rate; coarse-grid dissolution simulations using these constitutive relationships demonstrate good agreement with results from the high-resolution mechanistic simulations.