Modeling Kinetic Interphase Mass Transfer for Two-Phase Flow in Porous Media Including Fluid–Fluid Interfacial Area

Abstract

Interphase mass transfer in porous media takes place across fluid-fluid interfaces. At the field scale, this is almost always a kinetic process and its rate is highly dependent on the amount of fluid-fluid interfacial area. Having no means to determine the interfacial area, modelers usually either neglect kinetics of mass transfer and assume local equilibrium between phases or they estimate interfacial area using lumped parameter approaches (in DNAPL pool dissolution) or a dual domain approach (for air sparging). However, none of these approaches include a physical determination of interfacial area or accounts for its role for interphase mass transfer. In this work, we propose a new formulation of two-phase flow with interphase mass transfer, which is based on thermodynamic principles. This approach comprises a mass balance for each component in each phase and a mass balance for specific interfacial area. The system is closed by a relationship among capillary pressure, interfacial area, and saturation. We compare our approach to an equilibrium model by showing simulation results for an air-water system. We show that the new approach is capable of modeling kinetic interphase mass exchange for a two-phase system and that mass transfer correlates with the specific interfacial area. By non-dimensionalization of the equations and variation of Peclet and Damköhler number, we make statements about when kinetic interphase mass transfer has to be taken into account by using the new physically based kinetic approach and when the equilibrium model is a reasonable simplification.

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling

“…This allows for the conclusion that the inclusion of fluid-fluid interfacial area into the capillary pressure-saturation relationship makes hysteresis disappear or, at least, reduces it down to a very small value. Niessner & Hassanizadeh (2008;2009a;b) have modeled two-phase flow-using the thermodynamically-based set of equations developed by Hassanizadeh & Gray (1990)-and showed that this interfacial-area-based model is indeed able to model hysteresis as well as kinetic interphase mass and also energy transfer in a physically-based way.…”

“…In order to do numerical modeling, simplifying assumptions need to be made. In the following, we present such a simplified equation system as was derived in Niessner & Hassanizadeh (2009a). This set of balance equations can be described by six mass and three momentum balance equations.…”

“…If so, then it may not be sufficient to use a classical local equilibrium model instead of the more complex interfacial-area-based model. To allow for a decision, Niessner & Hassanizadeh (2009a) make the system of equations (16) through (28) dimensionless and study the dependence of kinetics on Damköhler number and Peclet number. To do so, they define dimensionless variables:…”

Capillary-Driven Transport of Dissolved Salt to the Drying Zone During $$\hbox {CO}_{2}$$ CO 2 Injection in Homogeneous and Layered Porous Media

“…Evaporation of water from the formation brine into the injected CO 2 is a complex phenomenon: It occurs due to the mutual solubility of CO 2 and water Pruess 2005, 2010). The rate of evaporation depends on factors including interfacial area between brine and CO 2 (Niessner and Hassanizadeh 2009), persistence of liquid pathways to supply brine to the drying front (Lehmann et al 2008;Nachshon et al 2011;Shokri et al 2010), CO 2 flow velocity (Zuluaga et al 2001) and thermodynamic properties which determine the vapor pressure. The efficiency of evaporation determines the steepness of the gradient in brine saturation inside the porous medium and therefore the significance of capillary-driven flow.…”

Non-equilibrium interphase heat and mass transfer during two-phase flow in porous media—Theoretical considerations and modeling

“…In fact, one would expect physical approaches to modeling kinetic interphase mass and heat transfer to contain the interfacial area between the phases as a variable. Recently, a two-phase flow and solute transport model was developed that included interfacial area as a state variable [36]. In that model, interphase mass transfer was modeled as a kinetic process.…”