MODELING COUPLED MOISTURE AND SALT TRANSPORT IN POROUS MATERIALS Robert Černý, Zbyšek Pavlík, Milena Jiřičková, Lukáš Fiala, Jiří Maděra INTRODUCTION

Size: px

Start display at page:

Download "MODELING COUPLED MOISTURE AND SALT TRANSPORT IN POROUS MATERIALS Robert Černý, Zbyšek Pavlík, Milena Jiřičková, Lukáš Fiala, Jiří Maděra INTRODUCTION"

Nickolas White
5 years ago
Views:

1 THERMOPHYSICS 26 Proceedings o the seminar October 26 2 MODELING COUPLED MOISTURE AND SALT TRANSPORT IN POROUS MATERIALS Robert Černý, Zbyšek Pavlík, Milena Jiřičková, Lukáš Fiala, Jiří Maděra Department o Mechanics, Faculty o Civil Engineering, Cech Technical University in Prague, Thákurova 7, Prague 6, Cech Republic, cernyr@sv.cvut.c, pavlik@sv.cvut.c, jiricko@sv.cvut.c, ialal@sv.cvut.c, madera@sv.cvut.c Abstract: Basic models o coupled moisture and salt transport in porous materials are discussed rom the point o view o their suitability to the solution o practical problems o salt damage. A modiied diusion-advection model is identiied as the most suitable or this purpose which is illustrated on an example o its practical application. Keywords: Moisture transport, salt transport, porous materials, modeling INTRODUCTION Practically all deterioration mechanisms in porous materials are related to transport processes o heat, momentum, various phases o water, and chemical compounds. For example, a chemical substance rom the surroundings contacts irst the surace o a porous material, and concentrates in the surace region. Then, it can be dissolved in water and transported in the orm o a solution into the bulk. The rate o penetration o this substance into the bulk depends on a variety o physical and chemical quantities, or instance on temperature, moisture content in the material, the level o stress in the material element, on the structure o the porous matrix and the level o its deterioration, etc. Also, the external conditions are very important, or instance the supply o the particular substance in the surroundings, temperature and moisture variations in the surroundings. An accurate description o all these eects requires an application o a proper model o transport processes, because the mechanisms governing the heat, momentum, moisture and chemical compounds transport are coupled. In many cases, these mechanisms cannot be completely separated rom each other and treated individually without a signiicant loss o accuracy. Also, the mathematical models o heat, momentum, water and chemical compounds transport contain a variety o storage and transport material parameters, which have to be determined in a wide range o ield quantities, such as temperature, moisture content and concentration o the particular chemical compound. A choice o a mathematical model or describing a speciic problem o material degradation is always a compromise between the required physical-chemical suitability and the accuracy on one side, and the availability o material data or perorming the calculations on the other. The models should be simple enough to allow obtaining the required data with a minimum o necessary measured transport and storage material parameters. On the other hand, application o oversimpliied models could lead to serious errors, which might harm the service lie prediction process and results in unrealistic service lie estimates. Water-soluble salts in the porous system can present a serious threat to the material deterioration. The harmul eects o such salts consist in the act that ater possible water evaporation salt crystals and crystal-hydrates are ormed that oten have crystalliation pressures

2 THERMOPHYSICS 26 Proceedings o the seminar October higher than the strength o the particular porous material. The pressure exerted on pore walls can then lead to material destruction. However, the problem with salt ingress in porous building materials is not restricted only to the materials o load bearing structures. Renders can be aected as well. Salts can crystallie either in the porous system o renders or on their surace. Crystalliation on the surace does not lead to damage o render material but salt elorescence appears on the surace, which is a serious aesthetic law. In this paper, basic models o coupled moisture and salt transport in porous materials are discussed rom the point o view o their suitability to the solution o practical problems o salt damage. BASIC MODELS OF MOISTURE AND SALT TRANSPORT Most models applied in current research practice or the description o salt transport in porous materials are very simple. These employ Fick's diusion equation or the salt concentration with a constant diusion coeicient and constant initial and boundary conditions: C 2 C = D 2 (1) C (, t) = C (2) C (, t) = (3) C ( x,) =, (4) where D is the salt diusion coeicient, C the salt concentration, C the salt concentration at the exposed boundary, x the distance rom the exposed boundary, t the time. The problem (1) - (4) has a very simple mathematical solution (e.g., Carslaw and Jaeger [1]): x C( x, t) = C 1 er, (5) 2 Dt and this is the main reason or its high application requency. This model was employed or instance by Tuutti [2], Funahashi [3], Cady and Weyers [4], Weyers [5], Zemajtis et al. [6], Costa and Appleton [7] and many others. The model (1)-(4), which can be considered as the simplest choice ever in modeling salt transport contains several serious laws that have to be taken into account in any practical application o it. The main problems with the model consist in the assumption o constant diusion coeicient and in the act that it neglects the inluence o water transport on the transport o chemical compounds. As a consequence, a single value o the diusion coeicient can never be obtained rom the measured concentration proiles, particularly i the measurements are perormed over longer time periods. The diusion coeicient then appears as a unction o time. Nevertheless, this model proved to be useul in many practical applications because the calculated diusion coeicients have at least a relative value, i.e., it is possible to compare diusion coeicients in dierent types o materials and dierent environments. Another extreme in describing salt transport in porous materials is a consideration o ully coupled heat, moisture and chemical compounds transport phenomena. Among the most advanced models o this type, the model by Grunewald [8], [9] belongs to very promising (see e.g. the comments by Černý and Rovnaníková [1] or more details).

3 THERMOPHYSICS 26 Proceedings o the seminar October However, it should be pointed out that nor this model is an ideal solution. The main problem o the model [8], [9] consists in its complexity and particularly in the act that it requires too many parameters to be determined in advance. The measurements o some o them are very time consuming so that or instance determination o liquid convection coeicients can take several months i static methods are used. In addition, all coeicients should be measured as unctions o all state variables, which means at least a dependence on temperature, moisture content and salt concentration. Thereore, this model can be reasonably used only in the case that a database o necessary material parameters is already available. A possible way out rom the problems arising due to either oversimpliication or too high complexity is to choose a reasonable compromise, i.e. a model that is somewhere in between these two extremes. Unortunately, such models were only rarely used in the research practice until now. An example o application o a model o this type was introduced by Boddy et al. [11] where an attempt o including moisture transport in the salt transport equation was done. However, Boddy et al. [11] still assumed a linear salt diusion problem with the diusion coeicient as a unction o time and temperature, and in addition, the problem o coupling moisture transport and salt transport was not solved at all. A more successul attempt in this direction was done or the transport o NaCl solution in calcium silicate brick by Pel et al. [12] who used the Bear and Bachmat diusion-advection model [13] in the orm: ( wc ) r Cb = div( wd gradc ) div( C v) (6) w r = div v, (7) where C is the concentration o ree salt in water (in kg/m 3 o the solution), C b the concentration o bonded salt in the whole porous body (in kg/m 3 o the sample), D the salt diusion coeicient (in m 2 /s), v r the Darcy s velocity (in m/s), w the volumetric moisture content (in m 3 /m 3 ), and κ the moisture diusivity (in m 2 /s). Expressing Darcy s velocity in terms o moisture diusivity, r v = κ grad w, (8) they arrived to a system o two parabolic partially coupled partial dierential equations with three principal material parameters, namely D, κ and the ion binding isotherm C b = C b (C ). In a practical application o the model, Pel et al. [12] neglected the dispersion term in Eq. (6) so that they aced just the determination o κ and C b = C b (C ). This was done using NMR measurements o moisture content and Na + ions concentration. However, the agreement between the experimental and computational Na + ions concentration proiles was not very good. Thereore, either the model was too simple or possibly the choice or the way o determination o the necessary material parameters was not ideal. DIFFUSION-ADVECTION MODEL OF MOISTURE AND SALT TRANSPORT INCLUDING SALT BONDING AND CRYSTALLIZATION In this paper, the moisture and salt transport modeling treatment chosen by Pel et al. [12] is modiied and extended in order to avoid the apparent mistakes in the original model. The basic idea that the mechanism o salt solution transport is described by Bear and Bachmat diusion-advection model [13] taking into account not only the inluence o moisture low on salt transport but also the eect o salt bonding on pore walls is preserved. In addition to the eects taken into account in the

4 THERMOPHYSICS 26 Proceedings o the seminar October original model rom [12], salt crystalliation and water vapor transport are introduced into the model in order to acilitate modeling o drying experiments. Also, contrary to the model rom [12], the dispersion eects in the liquid phase are considered as signiicant and included into the parameter identiication process. The modiied mathematical model can then be written as ollows: ( wc ) C w Cb Cc H ( C, sat C ) = ( wd ) + ( C κ ) (9) C c w w δ p v = κ + (1) ρ w [ w( C = C, sat )] H ( C where C c is the amount o crystallied salt (in kg/m 3 o the sample), C,sat is the saturated ree salt concentration (in kg/m 3 o the solution), H is the Heaviside step unit unction, H(x )=1, H(x<)=, δ the water vapor diusion permeability (in s), p v the partial pressure o water vapor (Pa), and ρ w the density o water (in kg/m 3 ). C, sat } (11) PARAMETER IDENTIFICATION OF THE DIFFUSION-ADVECTION MODEL OF MOISTURE AND SALT TRANSPORT For the determination o moisture diusivity as a unction o moisture content and salt diusion coeicient as a unction o salt concentration, a salt solution suction experiment rom a ree salt solution level into a dry specimen is proposed. This makes it possible to neglect salt crystalliation and water vapor transport so that the model is simpliied as ( wc ) C w Cb = ( wd ) + ( C κ ) (12) w w = κ. (13) The arrangement o the experiment is analogous to standard water suction experiments. The samples are irst dried at 8 C and.1 mbar and water and vapor-proo insulated by epoxy resin on all lateral sides. Then, they are exposed by one o their aces to the penetrating salt solution. Duration o the experiment is chosen dierent or three dierent groups o samples. Ater this time, the samples are cut into several pieces and in each piece water content and salt concentration are measured. Moisture content is determined by the gravimetric method using weighing the moist and dried specimens so that the moisture proiles are obtained. In the determination o salt concentration, the particular samples are ater drying irst ground by a vibration mill so that grains smaller than.63 mm are obtained. Then the ground samples are overlowed by 8 C warm distilled water and leached. The salt contents in particular leaches are measured using the ion selective electrode. On the basis o measured ion binding isotherm, C b = C b (C ), the proiles o bound and ree salts are determined. The measured moisture and salt concentration proiles is then subject o inverse analysis, using Eqs. (12) and (13). The conditions o the experimental setup described above allow or a

5 THERMOPHYSICS 26 Proceedings o the seminar October signiicant simpliication o the generally quite complicated inverse problem. The constant initial conditions and Dirichlet boundary conditions on both ends o the specimen or both moisture content and salt concentration where one o the Dirichlet boundary conditions is equal to the initial condition make it possible to consider the inverse problem as a semi-ininite one, and an extension o the standard Boltmann-Matano treatment can be applied. Ater applying Boltmann transormation to equations (12), (13) and perorming some straightorward algebraic operations in a similar way as with the solution o the inverse problem to one parabolic equation (see [1] or details), the ollowing ormulas or the determination o κ and D are obtained: 1 dw κ ( ) = d, (14) dw d 2t d D( ) = dw C ( ) κ ( ) d dc w( ) d + 2t 1 dc w( ) d d( wc d ) dc + dc b dc d d, (15) where is the space variable, t is the time corresponding to the chosen moisture and salt concentration proiles w = w(,t ), C = C (,t ), the chosen values o moisture and salt concentration are w = w(, t ), C = C (, t ), and the corresponding moisture diusivity and salt diusion coeicient κ( ) = κ(w, C ), D( ) = D(w, C ). In a practical calculation o κ and D, a set o values is chosen,, the corresponding [w i, κ(w i, C i )], [C i, D(w i, C i )] points calculated, and κ(w) and D(C ) unctions constructed. VERIFICATION OF THE COMPUTATIONAL MODEL IN A WETTING EXPERIMENT For the veriication o the diusion-advection model o coupled moisture and salt transport, 1M-NaCl solution suction into sandstone samples was chosen. The chloride binding isotherm o sandstone was measured irst. The samples o sandstone with the dimensions o 2 x 4 x 16 mm were then subjected to 1-D chloride solution penetration and moisture proiles and chloride concentration proiles were determined or the suction times o 3, 6 and 9 minutes using the method described in the previous Section. Moisture diusivity and chloride diusion coeicient were then calculated using Eqs. (14), (15). Fig. 1 shows the moisture diusivity o sandstone as unction o moisture content. We can see that obtained results correspond to the values typical or highly capillary active materials.

6 THERMOPHYSICS 26 Proceedings o the seminar October ,E-4 1,E-5 κ [m 2 /s] 1,E-6 1,E-7 1,E-8,,5,1,15,2,25,3,35 w [m 3 /m 3 ] Fig. 1 Moisture diusivity o sandstone 1,E-3 1,E-4 D [m 2 /s] 1,E-5 1,E-6, 2, 4, 6, 8, C [kg/m 3 solution] Fig. 2 Chloride diusion coeicient o sandstone Fig. 2 shows the chloride diusion coeicient o sandstone in dependence on ree ion concentration calculated using the κ(w) unction in Fig. 1. We can see that rom the quantitative point o view, the calculated diusion coeicient is quite high, about our orders o magnitude higher than the diusion coeicients o most ions in ree water. Thereore, the common diusion mechanism was probably not the only driving orce or the chloride transport within the liquid phase and some other driving orces were taking place here. The acceleration o chloride transport can be attributed most easily to dispersion eects in the liquid phase or to surace diusion on pore walls.

7 THERMOPHYSICS 26 Proceedings o the seminar October 26 26,4,35,3 measured calculated w [m 3 /m 3 ],25,2,15,1,5,,,5,1,15,2,25,3,35 x/ t [m/s 1/2 ] Fig. 3 Comparison o measured and calculated moisture proiles 1, 9, 8, C [kg/m 3 solution] 7, 6, 5, 4, 3, 2, 1, measured calculate,,,5,1,15,2,25,3,35 x/ t [m/s 1/2 ] Fig. 4 Comparison o measured and calculated chloride concentration proiles For the veriication o the numerical stability o the parameter identiication process o the applied coupled moisture and salt transport model, a orward analysis was perormed. The moisture diusivity and chloride diusion coeicient given in Figs. 1, 2 were substituted into the computational implementation o the model (12), (13) and moisture and ree chloride concentration proiles were calculated or the suction times o 3, 6 and 9 minutes exactly as in the experiments. The results in Figs. 3, 4 show that the calculated moisture and chloride concentration

8 THERMOPHYSICS 26 Proceedings o the seminar October proiles agreed reasonably well with the measured proiles, the dierences were well within the error range o the measuring methods. CONCLUSIONS A modiied diusion-advection model was identiied as the most suitable option or modeling coupled moisture and salt transport in porous materials at present. It can avoid both the oversimpliications such as the assumption o linear salt diusion problem without water low eect which application could result in signiicant distortion o physical reality and the too high complexities connected with an application o ully coupled heat, moisture, salt and momentum transport models which could ace almost irresolvable problems with the accuracy o necessary input parameters. The basic condition or the applicability o the diusion-advection model in this paper in scientiic and technical practice which is the stability o the parameter identiication process was met very well. The computational implementation o the model was also ound to be suiciently accurate, which makes good prerequisites or the successul uture practical applications o the model. ACKNOWLEDGEMENTS This research was supported by Cech Science Foundation, under grant No. 13/6/31. REFERENCES [1] Carslaw HS, Jaeger JC.: Conduction o Heat in Solids. Clarendon Press, Oxord, [2] Tuuti K.: Corrosion o Steel in Concrete. Swedish Cement and Concrete Research Institute, Stockholm, [3] Funahashi M.: Predicting corrosion-ree service lie o a concrete structure in a chloride environment. ACI Material Journal, Vol. 87, pp , [4] Cady P. D., Weyers R. E.: Predicting service lie o concrete bridge decks subject to reinorcement corrosion. Corrosion Forms and Control or Inrastructure, ASTM STP 1137, American Society or Testing and Materials, pp , [5] Weyers R. E.: Service lie model or concrete structures in chloride laden environments. ACI Materials Journal, Vol. 95, pp , [6] Zemajtis J., Weyers R. E., Sprinkel M. M.: Corrosion protection service lie o lowpermeable concretes and low-permeable concrete with a corrosion inhibitor. Transportation Research Report 1642, National Research Council, Washington, 1998, pp [7] Costa A, Appleton J.: Chloride penetration into concrete in marine environment Part II: Prediction o long term chloride penetration. Materials and Structures, Vol. 32, pp , [8] Grunewald, J. Diusiver und konvektiver Sto- und Energietransport in kapillarporösen Baustoen, PhD Thesis, TU Dresden: Dresden, [9] Grunewald, J.: DELPHIN Documentation, Theoretical Fundamentals, TU Dresden: Dresden, 2. [1] Černý R., Rovnaníková P.: Transport Processes in Concrete. Spon Press, London 22. [11] Boddy A., Bent E., Thomas M. D. A., Hooton R.D.: An overview and sensitivity study o a multimechanistic chloride transport model. Cement and Concrete Research, Vol. 29, pp , [12] L. Pel, Kopinga K., Kaasschieter E. F.: Saline absorption in calcium-silicate brick observed by NMR scanning. J. Phys. D: Appl. Phys, Vol.. 33, 2, [13] Bear J. and Bachmat Y.: Introduction to Modelling o Transport Phenomena in Porous Media, Vol 4. Kluwer, Dordrecht 199.

Determination of water and salt transport parameters of porous materials using methods of inverse modelling

Computational Methods and Experimental Measurements XIII 349 Determination of water and salt transport parameters of porous materials using methods of inverse modelling L. Fiala, Z. Pavlík, M. Pavlíková