Evaporation in Capillary Porous Media at the Perfect Piston‐Like Invasion Limit: Evidence of Nonlocal Equilibrium Effects

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure‐saturation relationship classically introduced to obtain the one‐equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two‐equation model must be considered for improving the continuum modeling of evaporation.

[1]  P. Crausse,et al.  Etude fondamentale des transferts couples chaleur-masse en milieu poreux , 1981 .

[2]  V. S. Vaidhyanathan,et al.  Transport phenomena , 2005, Experientia.

[3]  Pejman Tahmasebi,et al.  Pore-scale simulation of flow of CO2 and brine in reconstructed and actual 3D rock cores , 2017 .

[4]  Stig Bakke,et al.  Extending Predictive Capabilities to Network Models , 1998 .

[5]  Vahid Joekar-Niasar,et al.  Effect of fluids properties on non-equilibrium capillarity effects: Dynamic pore-network modeling , 2011 .

[6]  Veerle Cnudde,et al.  Imaging and image-based fluid transport modeling at the pore scale in geological materials : a practical introduction to the current state-of-the-art , 2016 .

[7]  Regular regimes in sorption processes : calculation of drying rates and determination of concentration dependent diffusion coefficients , 1976 .

[8]  M. Prat.  2D MODELLING OF DRYING OF POROUS MEDIA: INFLUENCE OF EDGE EFFECTS AT THE INTERFACE. , 1991 .

[9]  S. Whitaker.  Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying , 1977 .

[10]  M. Prat,et al.  Numerical and experimental network study of evaporation in capillary porous media. Phase distributions , 1996 .

[11]  Y. Yortsos,et al.  Effect of Liquid Films on the Drying of Porous Media , 2004 .

[12]  J. R. Philip,et al.  Moisture movement in porous materials under temperature gradients , 1957 .

[13]  Ian Turner,et al.  A 3-D version of TransPore: a comprehensive heat and mass transfer computational model for simulating the drying of porous media , 1999 .

[14]  S. Nowicki,et al.  MICROSCOPIC DETERMINATION OF TRANSPORT PARAHETERS IN DRYING POROUS MEDIA , 1992 .

[15]  Marc Prat,et al.  Three-dimensional pore network simulation of drying in capillary porous media , 1999 .

[16]  E. Tsotsas,et al.  Drying with Formation of Capillary Rings in a Model Porous Medium , 2015, Transport in Porous Media.

[17]  Michel Quintard,et al.  Convection, dispersion, and interfacial transport of contaminants: Homogeneous porous media , 1994 .

[18]  R. Schrage.  A theoretical study of interphase mass transfer , 1953 .

[19]  Y. Yortsos,et al.  Drying in porous media with gravity-stabilized fronts: experimental results. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Jean-Louis Auriault,et al.  Transport in Porous Media: Upscaling by Multiscale Asymptotic Expansions , 2005 .

[21]  Shmuel Assouline,et al.  Characteristic lengths affecting evaporative drying of porous media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  E. F. Kaasschieter,et al.  Analytic solution for the non-linear drying problem , 2002 .

[23]  E. Tsotsas,et al.  Influence of pore structure on drying kinetics: A pore network study , 2007 .

[24]  D. Or,et al.  Drainage mechanisms in porous media: From piston‐like invasion to formation of corner flow networks , 2016 .

[25]  J. Barrett,et al.  Kinetic evaporation and condensation rates and their coefficients , 1992 .

[26]  Hjp Harold Brocken,et al.  Determination of moisture diffusivity in porous media using moisture concentration profiles , 1996 .

[27]  Marc Prat,et al.  Recent advances in pore-scale models for drying of porous media , 2002 .

[28]  Roger G. Marchand,et al.  Moisture Diffusivity of Cellulose Insulation , 1994 .

[29]  E. Tsotsas,et al.  Pore Network Drying Model for Particle Aggregates: Assessment by X-Ray Microtomography , 2012 .

[30]  S. M. Hassanizadeh,et al.  Insights into the Relationships Among Capillary Pressure, Saturation, Interfacial Area and Relative Permeability Using Pore-Network Modeling , 2008 .

[31]  E. Tsotsas,et al.  Kinematics in a slowly drying porous medium: Reconciliation of pore network simulations and continuum modeling , 2017 .

[32]  Marc Prat,et al.  Pore‐Network Models: A Powerful Tool to Study Drying at the Pore Level and Understand the Influence of Structure on Drying Kinetics , 2011 .

[33]  F. Büchi,et al.  Validation of pore network simulations of ex-situ water distributions in a gas diffusion layer of proton exchange membrane fuel cells with X-ray tomographic images , 2016 .

[34]  Marc Prat,et al.  On the influence of pore shape, contact angle and film flows on drying of capillary porous media , 2007 .

[35]  Stig Bakke,et al.  A Predictive Network Model for Three-Phase Flow in Porous Media , 2000 .

[36]  A. Luikov.  SYSTEMS OF DIFFERENTIAL EQUATIONS OF HEAT AND MASS TRANSFER IN CAPILLARY-POROUS BODIES (REVIEW) , 1975 .

[37]  M. Prat,et al.  Three periods of drying of a single square capillary tube. , 2009, Physical review letters.

[39]  E. Tsotsas,et al.  Remarks on the paper “Extension of Hoshen–Kopelman algorithm to non-lattice environments” by A. Al-Futaisi and T.W. Patzek, Physica A 321 (2003) 665–678 , 2006 .

[40]  S. Whitaker,et al.  One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems , 1993 .

[41]  T. Nguyen,et al.  Two-phase flow model of the cathode of PEM fuel cells using interdigitated flow fields , 2000 .

[42]  Matthew D. Jackson,et al.  Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. , 2002 .

[43]  Marc Prat,et al.  Numerical and experimental network study of evaporation in capillary porous media. Drying rates , 1998 .

[44]  José María Sala,et al.  Characterization of Moisture Transport Properties for Lightened Clay Brick — Comparison Between Two Manufacturers , 2007 .