Modeling evaporation processes in a saline soil from saturation to oven dry conditions

HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Hydrol. Earth Syst. Sci. Discuss., 8, 529–554, 2011 www.hydrol-earth-syst-sci-discuss.net/8/529/2011/ doi:10.5194/hessd-8-529-2011 © Author(s) 2011. CC Attribution 3.0 License. Hydrology and Earth System Sciences Discussions This discussion paper is/has been under review for the journal Hydrology and Earth System Sciences (HESS). Please refer to the corresponding final paper in HESS if available. Modeling evaporation processes in a saline soil from saturation to oven dry conditions M. Gran1,2, J. Carrera1, S. Olivella2, and M. W. Saaltink2 1GHS, Institute of Enviromental Assessment and Water Research (IDAEA), CSIC, Barcelona, Spain 2Dept. Geotechnical Engineering and Geosciences, Universitat Politecnica de Catalunya, UPC-BarcelonaTech, Barcelona, Spain Received: 16 December 2010 – Accepted: 18 December 2010 – Published: 18 January 2011 Correspondence to: M. Gran (meritx[email protected]) Published by Copernicus Publications on behalf of the European Geosciences Union. 529 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Abstract Thermal, suction and osmotic gradients interact during evaporation from a salty soil. Vapor fluxes become the main water flow mechanism under very dry conditions. A coupled nonisothermal multiphase flow and a reactive transport model of a salty sand soil was developed to study such an intricate system. The model was calibrated with data5 from an evaporation experiment (volumetric water content, temperature and concentration). The retention curve and relative permeability functions were modified to simulate oven dry conditions. Experimental observations were satisfactorily reproduced, which suggests that the model can be used to assess the underlying processes. Results show that evaporation is controlled by heat, and limited by salinity and liquid and va-10 por fluxes. Below evaporation front vapor flows downwards controlled by temperature gradient and thus generates a dilution. Vapor diffusion and dilution are strongly influenced by heat boundary conditions. Gas diffusion plays a major role in the magnitude of vapor fluxes. 1 Introduction15 Understanding evaporation is necesary in many fields of earth system sciences (Shuttleworth, 2007). In fact, soil evaporation is crucial in controlling the balance of soilsurface water and energy in arid and semiarid areas (Saito et al., 2006). The actual mechanisms controlling evaporation are intricate (Sakai et al., 2009). Soil evaporation may be controlled by the soil-atmosphere boundary layer when the soil is moist20 or by hydraulic conditions when it is dry (Schneider-Zapp et al., 2010). In the latter case, evaporation causes the soil to dry and heat up causing liquid, vapor and heat fluxes to interact. The presence of solutes increases the complexity of the system and exacerbates the consequences leading to salinization. A number of researchers have analyzed this problem from an experimental perspec-25 tive (Wheeting, 1925; Scotter, 1974; Nassar and Horton, 1989; Scanlon, 1992). These 530 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | authors concluded that water flux in dry and salinized soils is controlled by salinity and temperature gradients. Salinity causes water activity to drop, thus reducing vapor pressure in equilibrium with liquid water and driving vapor towards the saltier zone. Evaporation depends also on temperature and absorbs energy. Thus, evaporation is affected by water flow and energy and solutes transport. The interaction of matric po-5 tential, temperature and salinity gradients under very dry conditions was studied by Gran et al. (2010), who observed a salinity decrease below the evaporation front owing to condensation of downward vapor flux. Although experimental studies are critical, they do not yield direct measurements of flow and phase change processes, which must be indirectly inferred from state variable measurements. This is not easy when10 the phenomena are complex and coupled. Therefore, quantitative understanding of the above processes requires numerical modeling. Most models of evaporation focus on the interactions between water and heat flow (Jackson et al., 1974; Scanlon and Milly, 1994; Boulet et al., 1997). These authors conclude that vapor flux is dominant near the surface where the soil is dry, and that15 water flows in the liquid phase below the evaporation front. A good approximation to water table evaporation under isothermal conditions was obtained by Gowing et al. (2006), who divided the soil into liquid flow and vapor flow zones separated by the evaporation front. The nature of the evaporation front is unclear: Gran et al. (2010) observed a sharp front, whereas Konucku et al. (2004) concluded that a sharp phase20 transformation could not be expected. Notwithstanding, these models do not consider the role of salinity. The effect of high salinities was modeled by Nassar and Horton (1989), who simulated water transport in unsaturated nonisothermal salty soil on the basis of steadystate heat and mass transfer. Ironically, salinity effects have commonly been predicted25 assuming dilute solutions, which is not sufficient to compute vapor and liquid pressures (Burns et al., 2006). This explains the difficulties encountered by Nassar et al. (1992) when modeling evaporation from salty solutions. 531 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Two additional factors must be borne in mind when modeling evaporation from high salinity solutions. First, salt precipitates tend to form a low permeability crust that should be modeled (Yakirevich et al., 1997). Crust formation was modeled but not compared with experimental data by Olivella et al. (1996a). Second, under hot conditions, the residual saturation can no longer be considered a lower bound for saturation5 (Milly and Eagleson, 1982; Rossi and Nimmo, 1994; Prunty, 2003). A modification of the retention curve and relative permeability function must therefore be considered. A nonisothermal multiphase flow model is necessary to simulate the processes under these very dry conditions. Advective and diffusive vapor flows must be allowed, and high concentration values and oven dry conditions near the surface must be ac-10 knowledged. Mass balances of water, air, heat and solutes are necessary and effects of thermal, suction and salinity gradients must be simulated interacting simultaneously. The present work seeks to model the experiments of Gran et al. (2010) in order to (a) evaluate the magnitude and direction of the water fluxes and gain a greater understanding of the downward vapor flow mechanism, (b) describe the evolution and15 location of condensation-evaporation, and (c) to assess the relevance of the matric potential, temperature and osmotic gradients in controlling the aforementioned water separation process. 2 Evaporation experiment and conceptual model Laboratory experiments consisted of open sand columns initially saturated with an ep-20 somite (MgSO4·7H2O) solution. Evaporation was forced by an infrared lamp so that radiation at the soil surface was similar to the summer radiation at mid-latitudes. The experiment continued until the overall saturation fell to 0.32. At this stage, the columns were dismounted to measure vertical profiles of temperature, volumetric water content and solute concentration. Some identical columns were dismounted at different times25 to obtain the time evolution of those profiles. These columns were dismantled sequentially after reaching saturation degrees of 74% (after 2 days of evaporation), 50% (after 4 days), 40% (5 days) and 32% (12 days). 532 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Both column experiments and results are described in Gran et al. (2010) and a diagram is shown in Fig. 1. Results displayed a coupled phenomenon. Capillarity brings about an upward liquid flux and soil drying. The liquid flux transports solutes by advection towards the top, where evaporation leads to a dramatic increase in concentration. Evaporation also5 reduces the water content and the unsaturated hydraulic conductivity causing the evaporation front to move downwards. Measurements suggest that this front is very narrow. A water separation process occurs at the front. On the one hand, concentrations are high above the front, where water flow is restricted to the vapor phase. On the other hand, underneath the evaporation front, concentrations are diluted below initial values.10 That is, vapor flows not only upwards from the evaporation front but also downwards. Condensation of this downward vapor flux causes dilution. 3 Processes and governing equations The system is governed by thermohydraulic and geochemical processes. To simulate them, it is necessary to study water flow and heat and reactive transport. Changes15 in porosity, thermal conductivity, permeability and water activity caused by water content reduction and salt precipitation should be simulated as well as vapor pressure variations in response to changes in water activity. Moreover, the precipitates present in the system (epsomite MgSO4·7H2O, hexahydrite MgSO4·6H2O, pentahydrite MgSO4·5H2O and starkeyite MgSO4·4H2O) are highly hygroscopic. Therefore,20 hydratation-dehydratation of the mineral phases must be considered in the mass water balance. 3.1 Thermohydraulic processes The thermohydraulic model focuses on the mass balance of water (liquid water and vapor) and air (dissolved in water and in the gas phase) in terms of pressure, and the25 533 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | energy balance in terms of temperature. The equations of water and air mass balance are: ∂ ∂t(ωw lρlSlφ+ωw gρgSgφ)+∇·(jw l+jw g)=fw(1) ∂ ∂t(ωa lρlSlφ+ωa gρgSgφ)+∇·(ja l+ja g)=fa(2) where subscripts l and g refer to liquid and gas and superscript w and a refer to water5 and air, ωis the mass fraction (kg kg −1) of a component in a phase, ρis the density (kg m−3) of a phase, Sis the hydraulic saturation (m3m−3), φis the porosity (m3m−3), j(kg m−2s−1) is the total flux (advective, diffusive and dispersive) and fis an external source/sink term (kg m−3s−1). The energy mass balance is written as:10 ∂ ∂t(Esρs(1−φ)+ElρlSlφ+EgρgSgφ)+ +∇·(ic+jEl +jEg)=fQ(3) where icis the energy flux (J m−2s−1) owing to conduction through the porous medium, the other fluxes (jEl,jEg) are advective fluxes of energy (J m−2s−1) caused by mass motions and fQis an internal/external supply (J m−3s−1). A state variable is associated with each mass balance: liquid pressure (Pl), gas15 pressure (Pg) and temperature (T). Constitutive laws must be used to express the mass balance equations as a function of the state variables. The constitutive laws that control these balances are shown in Table 1. 3.2 Oven dry conditions As discussed above, under oven-dry conditions, the residual saturation can no longer20 be considered a lower bound for saturation, and a modification of the retention curve and relative permeability functions must be considered. Milly and Eagleson (1982) simply considered the residual saturation to be zero; Rossi and Nimmo (1994) proposed 534 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a different function to extend the capillary curve towards fully dry conditions; and Prunty (2003) used the zero value in standard retention curve models but modified the relative permeability function for the dry range. The van Genuchten (1980) model is widely used under moist conditions but requires modification to represent the very dry ones. The assumption is that soil can reach full5 drying, i.e. if evaporation takes place in an oven at 105 ◦C or near the surface under a dry or hot atmosphere (Ross et al., 1991). The van Genuchten retention curve is: Se=1+(Pc/P0)1 1−λ−λ(4) where Pcis capillary pressure, P0is related to the capillary pressure required to de-10 saturate the soil and λis a shape parameter of the function. This equation permits to calculate the effective saturation (Se) as a function of a minimum saturation Siand the actual saturation (Sl): Se=(Sl−Si)/(1−Si) or Sl=Si+(1−Si)Se(5) In order to extend this curve for high suctions (i.e. conditions of drying by evaporation),15 the minimum degree of saturation is expressed as follows: Si=S0 minαln(Pdry c/Pc) (6) The parameter Pdry ccan be identified with the capillary pressure for the dry material and can be considered equal to Poven dryness c=1000 MPa. However, lower values may be considered if dryness is induced by atmospheric conditions that are less extreme20 than oven dryness. Finally, αmodifies somewhat the transition point and S0 min is used in the permeability function below. This proposed retention curve is a continuous function with continuous derivatives. A similar form was already proposed by Fayer and Simmons (1995). 535 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | The following relative permeability function is proposed for the new retention curve Krl =0, Sl≤S0 min Krl =qSep1−1−S1/λ ep λ2 , Sl> S0 min (7) Sep =(Sl−S0 min)/(1−S0 min) Note that for saturations below S0 min the capillary pressure can be calculated from the5 retention curve, but the relative permeability is zero. This allows representing water isolated in the meniscus that can not flow as a liquid phase but can still evaporate. Figure 2 compares the proposed model and the original van Genuchten model, in terms of retention curve and relative permeability. The parameters used here (see Table 1) are obtained by calibration. Based on these results, the incorporation of a branch for10 the drying process of the residual water of the soil becomes necessary. 3.3 Reactive transport The mass balance used for the reactive transport can be written as ∂φSlρlca ∂t =LI(ca)+R(8) Ll() =−∇·(qlρl())+∇·(DlφSlρl∇())+ml 15 R=reps +rhex +rpent +rstark rmin =σmink(Ωmin −1) where vector ca(mol/kg) is the concentration of aqueous species and Llis the linear operator for the advection, dispersion/diffusion, mlis the non-chemical source-sink (mol m−3s−1) and Dlis the dispersion/diffusion tensor (m2s−1). Rcontains the rates of20 the kinetic reactions (rmin) for all the different mineral phases (reps,rhex,rpent and rstark), σmin is the mineral reactive surface and Ωmin is the ratio between the ion activity product and the equilibrium constant. The reaction rates enable us to estimate the liquid 536 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | water provided by mineral hydratation-dehydratation. This amount of water is added to the water mass balance as a source/sink term (fw l) in Eq. 1. fw l=(7reps +6rhex +5rpent +4rstark)mw(9) where mwis the water molecular weight. 4 Numerical model5 The problem is considered one dimensional in a vertical direction. The grid is made up of 240 elements (for 24 cm column length) consisting of two materials: the first covers the top 1.5 cm, and the second the rest. The gas diffusion enhancement factor (τ0) (see Table 1) was calibrated to be 1.2 in the upper material and 8 below. Accordingly, we reduce the vapor diffusion near the column surface, simulating more salt precipitates10 (salt crust formation), thereby reproducing more accurately the experimental results. Different boundary conditions (BC) for liquid, vapor and heat were chosen to reproduce the laboratory conditions (see Table 2). The top boundary is a mixed condition representing gas (air and vapor) and heat inflow-outflows. A radiative heat flux (from the lamp) was added at the top boundary condition. The lateral and bottom BC were15 of no-flow for water and solutes, but some loss of energy was permitted to dissipate across the boundary. Initial conditions are also applied: initial porosity (φ=0.4), initial gas and liquid pressures (Pg=Pl=0.101325 MPa) and initial temperature (T0=25 ◦C). Numerical simulations were carried out using the RETRASO-CODE BRIGHT (RCB)20 code, which couples the thermohydraulic model CODE BRIGHT (CB) of Olivella et al. (1996b) with the reactive transport model RETRASO of Saaltink et al. (2004). Furthermore, geochemical calculations are performed with the object-oriented chemical module CHEPROO (Bea et al., 2009, 2010), which includes high salinity solutions using the equations of Pitzer (1973). The feedback of reactive transport in thermohydraulics25 is performed by a time lag approach. The code solves the thermohydraulic equations 537 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Fayer, M. J. and Simmons, C. S.: Modified soil-water retention functions for all matric suctions, Water Resourc. Res., 31, 1233–1238, 1995. 535 Gowing, J. W., Konukcu, F., and Rose, D. A.: Evaporative flux from a shallow watertable: the influence of a vapour-liquid phase transition, J. Hydrol., 321, 77–89, 2006. 531 Gran, M., Carrera, J., Massana, J., W. Saaltink, M., Olivella, S., Ayora, C., and Lloret, A.:5 Dynamics of water vapor flux and water separation processes during evaporation from a salty dry soil, J. Hydrol., 396, 215–220, doi:10.1016/j.jhydrol.2010.11.011, 2011. 531, 532, 533 Jackson, R. D., Reginato, R. J., Kimball, B. A., and Nakayama, F. S.: Diurnal soil-water evaporation – comparison of measured and calculated soil-water fluxes, Soil Sci. Soc. Am. J., 38, 861–866, 1974. 53110 Konucku, F., Istanbulluoglu, A., and Kocaman, I.: Determination of water content in drying soils: incorporating transition from liquid phase to vapour phase, Aust. J. Soil Res., 42, 1–8, 2004. 531, 542 Milly, P. and Eagleson, P.: Parameterization of moisture and heat fluxes across the land surface for use in atmospheric general circulation models, Tech. Rep. 279, R. M. Parsons Laboratory,15 Dept. of Civil Eng., Massachusetts Institute of Technology, Cambridge, 1982. 532, 534 Nassar, I. N. and Horton, R.: Water transport in unsaturated non-isothermal salty soil. 2. Theoretical development, Soil Sci. Soc. Am. J., 53, 1330–1337, 1989. 530, 531 Nassar, I. N., Horton, R., and Globus, A. M.: Simultaneous transfer of heat, water, and solute in porous-media. 2. Experiment and analysis, Soil Sci. Soc. Am. J., 56, 1357–1365, 1992.20 531 Olivella, S., Carrera, J., Gens, A., and Alonso, E. E.: Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation, Transp. Porous Media, 25, 1–25, 1996a. 532 Olivella, S., Gens, A., Carrera, J., and Alonso, E. E.: Numerical formulation for a simulator25 (CODE BRIGHT) for the coupled analysis of saline media, Engin. Comput., 13, 87–112, 1996b. 537 Pitzer, K. S.: Thermodynamics of electrolytes. 1. Theoretical basis and general equations, J. Phys. Chem., 77, 268–277, 1973. 537 Prunty, L.: Soil water retention and conductivity when vapor flow is important, J. Irrig. Drain.30 Eng.-ASCE, 129, 201–207, 2003. 532, 535 Ross, P. J., Williams, J., and Bristow, K. L.: Equation for extending water-retention curves to dryness, Soil Sci. Soc. Am. J., 55, 923–927, 1991. 535 544 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Rossi, C. and Nimmo, J. R.: Modeling of soil-water retention from saturation to oven dryness, Water Resour. Res., 30, 701–708, 1994. 532, 534 Saaltink, M. W., Batlle, F., Ayora, C., Carrera, J., and Olivella, S.: RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media, Geol. Acta, 2(3), 235–251, 2004. 5375 Saito, H., Simunek, J., and Mohanty, B. P.: Numerical analysis of coupled water, vapor, and heat transport in the vadose zone, Vadose Zone J., 5, 784–800, 2006. 530 Sakai, M., Toride, N., and Simunek, J.: Water and vapor movement with condensation and evaporation in a sandy column, Soil Sci. Soc. Am. J., 73, 707–717, 2009. 530 Scanlon, B. R.: Evaluation of liquid and vapor water-flow in desert soils based on Cl-36 and10 tritium tracers and nonisothermal flow simulations, Water Resour. Res., 28, 285–297, 1992. 530 Scanlon, B. R. and Milly, P. C. D.: Water and heat fluxes in desert soils. 2. Numerical simulations, Water Resour. Res., 30, 721–733, 1994. 531, 542 Schneider-Zapp, K., Ippisch, O., and Roth, K.: Numerical study of the evaporation process and15 parameter estimation analysis of an evaporation experiment, Hydrol. Earth Syst. Sci., 14, 765–781, doi:10.5194/hess-14-765-2010, 2010. 530 Scotter, D. R.: Salt and water movement in relatively dry soil, Aust. J. Soil Res., 12, 27–35, 1974. 530 Shokri, N., Lehmann, P., and Or, D.: Critical evaluation of enhancement factors for va-20 por transport through unsaturated porous media, Water Resourc. Res., 45, W10433, doi:10.1029/2009WR007769, 2009. 543 Shuttleworth, W. J.: Putting the “vap” into evaporation, Hydrol. Earth Syst. Sci., 11, 210–244, doi:10.5194/hess-11-210-2007, 2007. 530 van Genuchten, M.: A closed-form equation for predicting the hydraulic conductivity of unsatu-25 rated soils, Soil Sci. Soc. Am. J., 44, 892–898, 1980. 535 Wheeting, L. C.: Certain relationships between added salts and the moisture of soils, Soil Sci., 19, 287–299, 1925. 530 Yakirevich, A., Berliner, P., and Sorek, S.: A model for numerical simulating of evaporation from bare saline soil, Water Resour. Res., 33, 1021–1033, 1997. 53230 545 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1. Constitutive laws, parameters and values used in the numerical model. Constitutive laws Parameters and values Water saturation for Sl=Si+(1−Si)SeS0 min=0.08, α=0.1 ret. curve in modified Se=1+(Pc/P0)1 1−λ−λλ=0.93, P0=0.0025 MPa van Genuchten model Si=S0 minαlnPdry c/PcPdry c=650 MPa Relative permeability function Krl =qSep1−1−S1/λ ep λ2 λ=0.93 (for a new ret. curve) Sep=Sl−S0 min/1−S0 min Intrinsic permeability for qα=−kkrα µα(∇Pα−ραg)k0=2.8×10−11 m2 Darcy’s Law k=k0exp(b(φ−φ0)) b=40, φ0=0.4 Diffusive flux of vapor iα=−(τφραSαDmI)∇wαD=5.9×10−6m2s−1K−nPa (Fick’s Law) Dm=τD(273.15+T)n Pgn=2.3 τ=τ0Sm gτ0=8, m=3 Conductive flux of heat λdry=(1−φ)nλsolid+φnλgas λsol=2 W mK−1,n=2 (Fourier’s Law) λsat=(1−φ)nλsolid+φnλliq λgas=0.01 W mK−1 λ=pSlλsat+1−pSlλdry λliq=0.6 W mK−1 Psychrometric Law Pv=136075awexp−5239.7 273.15+TMPa Where awis the molar mass fraction of water in liquid calculated by the reactive transport from aqueous concentrations. 546 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 2. Liquid, vapor and heat boundary conditions and corresponding parameters. Boundary conditions Top Lateral Bottom Liquid flux jl=0jl=0jl=0 Vapor flux (ωw g)0=0.020 kg/kg jw g=(ωw g)0j0 g+(Pg)0=0.101325 MPa +(ωw g)0γg(P0 g−Pg)+γg=50 kg/s/MPa/m2 +βg((ρgωw g)0−(ρgωw g)) βg=0.03 m/s ρg=1.12 kg/m3 Energy flux j0 e=750 J/sj0 e=0j0 e=0 je=j0 e+γe(T0−T)+Ew g(jw g)T0=25 ◦CT0=26 ◦CT0=26 ◦C γe=24 J/s/C/m2γe=25 J/s/C/m2γe=1 J/s/C/m2 547 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 3. Studied parameters for the sensitivity analysis: boundary heat dissipation (at the walls and at the bottom) and gas diffusion enhancement factor (τ0). Compared to the base model (BM): the boundary heat dissipation, by means of γvalue, has been doubled and increased by an order of magnitude alternatively and τ0value for the upper material (firsts 1.5 cm) has been increased from 1.2 to 8 to equal the value for all the column. Model Parameter BM 2γbot 10γbot 2γwall 10γwall τ0 γwall 11 1 2 10 1 γbottom 25 50 250 25 25 25 τ01.2 1.2 1.2 1.2 1.2 8 548 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Lamp WATER SALT ENERGY Radiant heat Vapor flux Liquid flux Evaporation front Min. Advection Dispersion Diffusion Crust Cond. Latent heat adv. Sensible heat adv. conc. Evap. Fig. 1. Diagram of the design of the evaporation column experiments and their conceptual model. The water fluxes are on the left, the salt fluxes are on the centre and the energy ones on the right. 549 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Relative permeability 1E-8 1E-6 1E-4 1E-2 1E+0 0 0.2 0.4 0.6 0.8 1 Saturation Rel. Perm. Van Genuchten (Mualem method) Oven dry (proposed) Retention curve 1E-4 1E-2 1E+0 1E+2 0 0.2 0.4 0.6 0.8 1 Saturation Cap. Press. (MPa) Van Genuchten Oven dry (proposed) Fig. 2. Retention and relative permeability curves (original van Genuchten and oven dry proposed models) for the sand used in the column experiments. 550 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Saturation 0 4 8 12 16 20 24 0.0 0.2 0.4 0.6 0.8 1.0 Depth (cm) 12d 6.6d 1.1d 3.3d Salinity(mol/kg) 0.01 0.1 1 10 12d 6.6d 3.3d Init. Conc. 1.1d Temp. (ºC) 26 30 34 38 42 46 50 12d 6.6d 3.3d 1.1d Fig. 3. Profiles of saturation, temperature and salinity measured at the end of the experiment (symbols) and computed (lines). The time evolution is shown for four different times (after 1.1 days, 3.3 days, 6.6 days and, at the end of the experiment, 12 days). 551 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Liquid water flux (mm/day) 0 4 8 12 16 20 24 -2 2 6 10 14 18 Depth (cm) 12d 6.6d 3.3d 1.1d Vapor flux (mm/day) -202468 1.1d 12d 6.6d 3.3d -120 -90 -60 -30 0 Total (cond+adv) heat flux (J/ms) 1.1d 3.3d 6.6d 12d -2-101234 Water flux (mm/day) at 12 days Vapor Liquid Total Vapor (adv) (diff) 0 4 8 12 16 20 24 -250 -200 -150 -100 -50 0 Conductive heat flux (J/ms) Depth (cm) 1.1d 3.3d 6.6d 12d Fig. 4. Computed profiles of liquid, vapor and total water fluxes (above), and conductive and total (conductive plus advective) heat fluxes (below). Positive and negative values stand for upward and downward flows, respectively. The simulation results are shown for four different times (after 1.1 days, 3.3 days, 6.6 days and 12 days). The difference between the diffusive vapor flux and the total water flux, displayed in the top 4 cm of the above graph on the right, is equal to the advective vapor flux. 552 HESSD 8, 529–554, 2011 Modeling evaporation processes in a saline soil M. Gran et al. Title Page Abstract Introduction Conclusions References Tables Figures J I J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Cond-Evap (10^2 Kg/s/m3) -9 -7 -5 -3 -1 1 1.1d 12d 6.6d 3.3d Mass fraction of vapor (%) 0 4 8 12 16 20 24 1234567 Depth (cm) 12d 6.6d 3.3d 1.1d 0 4 8 12 16 20 24 -0.01 0 0.01 0.02 0.03 Depth (cm) 1.1d 12d 6.6d 3.3d Condensation Fig. 5. Computed profiles of vapor mass fraction and evaporation (negative)/condensation (positive) rates for four different times. Note the change in the vapor mass fraction slope at 1.5 cm depth owing to the imposition of the reduction in vapor diffusivity on the salt crust. 553