Nonequilibrium thermomechanical modeling of liquid drainage/imbibition in trickle beds

Abstract

We extend the macroscopic nonequilibrium thermomechanical multiphase flow theory proposed by Hassanizadeh and Gray for porous media to analyze a set of drainage and imbibition experiments in trickle beds. The nonequilibrium model rests on inclusion of mass and momentum conservations for the gas‐liquid interface, nonequilibrium capillary pressure, Helmholtz free energy gradients in the body supply of momentum for fluid bulk phases and gas‐liquid interface, and mass exchange rates between interface and fluid bulks accounting for production and destruction of gas‐liquid interfacial area. To solve the nonequilibrium model, entropy‐consistent constitutive relationships are derived and calibrated using liquid holdup and bed pressure drop measurements in drainage and imbibition. The model captures very well the decay (drainage), and breakthrough (imbibition) curvatures of liquid holdup and pressure drop kinetics, while model closer inspection allows assessing the role of nonequilibrium capillary pressure and of dynamic interfacial mass exchanges for the production/destruction of interfacial area. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3123–3134, 2012

Three‐dimensional simulations of gas‐liquid cocurrent downflow in vertical, inclined, and oscillating packed beds

“…Such physics is incomplete because it insufficiently describes the role and presence of interfaces and their thermodynamic properties. 13 Recently, Iliuta et al 13 studied the dynamics of trickle bed reactors under liquid-induced pulsing operation conditions via a nonequilibrium model, based on the macroscopic nonequilibrium thermomechanical theory of Hassanizadeh and Gray 14 for multiphase flows in porous media, which includes the mass and momentum conservations for the gas-liquid interface, nonequilibrium capillary pressure, Helmholtz free energy gradients in the body supply of momentum for fluid bulk phases and gas-liquid interface, and mass exchange rates between interface and fluid bulks accounting for production and destruction of gas-liquid interfacial area.…”

Flooding limit in countercurrent gas–liquid structured packed beds—Prediction from a linear stability analysis of an Eulerian two-fluid model

“…In countercurrent gas-liquid structured packed-bed columns, preflooding conditions entail ∂h ℓ =∂t 4 0 and dynamic capillary pressure becomes lower than its equilibrium capillary pressure (Iliuta et al, 2012). As result, it is impossible for the dynamic capillary forces to counterbalance the inertial forces, especially under large flow channel conditions which characterize structured packed-bed columns precluding the existence of stability regions (Dankworth and Sundaresan, 1989).…”

“…Gray and Hassanizadeh (1991) and Iliuta et al (2012) formulated the pressure difference between the phases (non-equilibrium or dynamic capillary pressure, P g À P ℓ ) as a sum between an equilibrium (or static) capillary pressure term and a nonequilibrium term…”

Hydrodynamics of Trickle Bed Reactors with Catalyst Support Particle Size Distributions

“…For trickle-bed reactors, characterization of the hydrodynamics facilitates the engineering of the uniform distribution of flow, efficient wetting of the catalyst, operation in the desired flow-regime, and adequate heat and mass transfer. The CFD models describing these phenomena and models of transient imbibition/drainage have been reported in the literature, while the ideal of a predictive and generally applicable model for maldistribution has yet to be developed. Precedent and foundational to these endeavors is the study and modeling of the hydrodynamics under uniform trickling flow.…”