Modelling of hysteresis influence on mass transfer in building ...

GRUPO CYTED311RT0417- PPCONTROLOPTIMOInforme de la Primera reunión mantenida los días 28, 29 y 30 de Junio de 2011 en el hotelSARAY de Granada, España.1. Asistentes:Argentina:Enrique VallésBrasil:Griselda BarreraChile:Raúl QuijadaHumberto PalzaFelipe OsorioEspaña:Rosario BenaventeJosé Manuel PereñaAntonio BelloMaría Luisa CerradaJavier Arranz-AndrésVicente LorenzoJosé Manuel Gómez-ElviraBegoña PeñaLaura Alonso HermiraPortugal:Rosário G. RibeiroVenezuela:Arquímedes Karam1

ARTICLE IN PRESS636J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642Relative humidity [%]757065605550454035302506Relative humidity pr<strong>of</strong>ile for Test 1121824Time [h]30RH (%) x=12,5mmRH (%) x=25mmRH (%) x=12,5mm EXP.RH (%) x=25mm EXP.Fig. 2. Calculated and measured relative humidity pr<strong>of</strong>iles <strong>of</strong> the material atdifferent depths, for test 1.364248Table 3Mean deviation between calculated results and measured dataDepth (mm)DeviationSorption (%) Desorption (%)Test 112.5 6.29 6.2725 10.29 10.97Test 212.5 6.42 10.3725 10.92 17.59Test 412.5 3.65 7.3525 5.58 10.29Relative humidity [%]757065605550454035302506Relative humidity pr<strong>of</strong>ile for Test 31218 24Time [h]30RH (%) x=12,5mmRH (%) x=25mmRH (%) x=12,5mm EXP.RH (%) x=25mm EXP.364248butes to higher differences. The higher error for the deeper layercan be <strong>influence</strong>d by uncertainty in the material properties. It isobvious that material properties are characterised with experimentaluncertainty and in calculation the impact is moresignificant for the deeper layers. The differences betweenexperimental measurements and calculation are not so high andquite good agreement can be seen. For all cases, a good agreementwith the results from others codes has also been found [24]. Itmust be noticed that for most <strong>of</strong> the codes the results <strong>of</strong>simulations are almost the same but quite different from theexperimental measurements. None <strong>of</strong> the numerical model gaveexactly the same results as the measurements. One <strong>of</strong> the reasonsmight be that some <strong>of</strong> the moisture transport phenomena in theporous material were not taken into consideration.Fig. 3. Calculated and measured relative humidity pr<strong>of</strong>iles in material at differentdepths, for test 3.4. Sensitivity studyRelative humidity [%]656055504540353006Relative humidity pr<strong>of</strong>ile for Test 41218 24Time [h]RH (%) x=12,5mmRH (%) x=25mmRH (%) x=12,5mm EXP.RH (%) x=25mm EXP.Fig. 4. Calculated and measured relative humidity pr<strong>of</strong>iles in material at differentdepths, for test 4.the moisture was absorbed by the material and higher in thesecond part where moisture was desorbed out <strong>of</strong> the material.Also, smaller differences can be noticed for the depth <strong>of</strong> 12.5 mmand higher for the deeper layer. The mean values <strong>of</strong> relative errorfor each case and process are presented in Table 3.The higher values <strong>of</strong> the error in desorption are connected withthe <strong>hysteresis</strong> phenomenon. At the beginning <strong>of</strong> calculation, theRH condition in the material is uniform for simulation andmeasurement. But when the desorption process starts, thedifference between the RH condition in the sample in thecalculation and the measurement already exists, which contri-30364248In order to check the <strong>influence</strong> <strong>of</strong> some <strong>of</strong> the materialproperties and <strong>of</strong> the calculation parameters on model results, asensitivity study was performed for two thicknesses <strong>of</strong> sample37.5 and 150.0 mm. Two <strong>of</strong> the material properties (sorptionisotherm and vapour permeability) and two <strong>of</strong> the calculationparameters (time step and number <strong>of</strong> layers) were taken intoconsideration. Each parameter has been changed to a lower and ahigher value and compared with the original ‘‘reference’’ resultsfor corresponding thickness. Test 1 from Table 1 was taken as thereference case for samples <strong>of</strong> 37.5 mm. Finally, eight additionalcases were simulated for each thickness. For each additional caseonly one parameter/material property was changed, the otherswere kept constant. The comparison <strong>of</strong> results between eachvariant and the reference case was made by checking the relativehumidity pr<strong>of</strong>iles at depths <strong>of</strong> 12.5 and 25.0 mm for the 37.5 mmspecimen and at depths <strong>of</strong> 50.0 and 100.0 mm for the four-timesthicker material.4.1. Influence <strong>of</strong> numbers <strong>of</strong> layers and time stepThe reference number <strong>of</strong> layers (15, see Table 1) was increasedto 18 and decreased to 12 (for the 150-mm-thick sample 48, 60and 72 layers were tested). The time step has been changed fromthe reference value <strong>of</strong> 60–120 and 30 s. The calculation showedthat none <strong>of</strong> those changes <strong>influence</strong>d the simulation resultfor either the thinner or the thicker material. The relative errorfor the highest value <strong>of</strong> the RH pr<strong>of</strong>ile (after 24 h) on the depth<strong>of</strong> 12.5/50.0 and 25.0/100.0 (mm) is presented in Tables 3 and 4.All calculations for the 12, 15 and 18 layers gave very similarresults. The difference was less than 0.1%, showing good precision

ARTICLE IN PRESS638J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642A similar chart was obtained for the relative humidity pr<strong>of</strong>ile atdepth 25.0 mm. The changes <strong>of</strong> the vapour permeability <strong>influence</strong>also the vapour transfer and its accumulation in the material.Hereafter, in Table 6 the relative deviation for the highest value<strong>of</strong> the RH pr<strong>of</strong>ile (after 24 h) at depths <strong>of</strong> 12.5 and 25.0 mm ispresented.The same analysis has been done for the thicker material, andthe deviations <strong>of</strong> relative humidity at depths <strong>of</strong> 50.0 and100.0 mm are presented in Table 7.Again, the errors are bigger and deeper in the thinner material,but this time, for the thicker sample the deviations are lower anddeeper in the material. For both thicknesses <strong>of</strong> the material in thesimulation with lower values <strong>of</strong> water vapour permeability thanin the reference case, the problem with divergence occur. It mightbe connected with a too long time step and too thin layers used inthe numerical simulations.Some uncertainty is always associated with the experimentalcharacterization <strong>of</strong> materials. The variations used in the sensitivitystudy above seem reasonable approximation <strong>of</strong> experimentaluncertainty. Therefore it must be remembered that the calculatedvalues are also within a limit <strong>of</strong> several percent; here about 6% asshown in the results in the table above.5. <strong>Modelling</strong> <strong>hysteresis</strong> <strong>of</strong> the sorption isothermSorption <strong>hysteresis</strong> <strong>influence</strong>s the water vapour transport inthe material. To describe the effect <strong>of</strong> <strong>hysteresis</strong>, the empiricalmodel proposed by Pedersen [11] in MATCH s<strong>of</strong>tware was used inHumi-mur. Eq. (4) is used for desorption and Eq. (5) is used in thecase <strong>of</strong> adsorptionx d;h ¼ ðu u aÞ A x d þ Bðu u d Þ A x aðu d u a Þ A (4)x a;h ¼ Bðu u aÞ A x d þðu u d Þ A x a(5)ðu d u a Þ Awhere u a and u d are moisture contents in kg/kg, x a and x d are themoisture capacities (kg/kg) <strong>of</strong>, respectively, adsorption anddesorption isotherms for a given relative humidity, and u is theactual moisture content in kg/kg.Computed moisture capacity x d,h or x a,h is used in Eq. (3). Thefunction (4) is used for desorption if in the previous two timesteps the water content was decreasing, the function (5) is usedfor adsorption if in the previous two time steps the water contentwas increasing. Pedersen proposed the values <strong>of</strong> A and Bcoefficients as follows: A ¼ 2 and B ¼ 0.1. Although, like the otherresearchers showed [21,25], it is better to fit those coefficients foreach material. For fitting the experimental data, primary sorptionand desorption isotherm and secondary sorption or desorptionisotherm are needed.5.1. Setting A and B coefficientThe coefficients A and B from Eqs. (4) and (5) were chosenusing experimental data <strong>of</strong> primary adsorption and desorptionisotherm and secondary desorption isotherm, as plotted in Fig. 9.Finally, coefficient A was found to be equal to 1.6 and B to 0.68.Those values were used in Eqs. (4) and (5), implemented in Humimur,for simulations <strong>of</strong> mass flow in the material with the effect <strong>of</strong><strong>hysteresis</strong>.Even if the values <strong>of</strong> A and B coefficients fit well theexperimental data, the fully empirical procedure <strong>of</strong> selection isnot satisfactory from the theoretical point <strong>of</strong> view. It is still apresent challenge to enhance understanding and modelling <strong>of</strong>Water content [kg/kg]0.0180desorption 79.5-33%0.0160adsorption0.0140desorption0.01200.01000.00800.00600.00400.00200.00000.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80<strong>hysteresis</strong>. It seems interesting to exploit micro-structural properties,such as pore-size distribution.5.2. Simulations and resultsIn this part <strong>of</strong> the paper the results <strong>of</strong> mass flow calculation forthe model with the <strong>hysteresis</strong> effect are presented. The simulationswere done for gypsum board from Test 1 (Table 1), withthickness <strong>of</strong> the sample l ¼ 12.5 mm, number <strong>of</strong> layers z ¼ 5, timestep ¼ 60 s, and period <strong>of</strong> calculation ¼ 360 h. The boundarycondition, ambient relative humidity, was described by asinusoidal function with a 24-h period, oscillating between 30%and 50%. The initial relative humidity in the material was equal to40%. In Fig. 10, water content in the middle layer <strong>of</strong> the material isplotted.The darker line describes the process <strong>of</strong> change in watercontent when at the beginning the desorption process appears.The lighter line depicts the process starting with adsorption. Alarge difference can be seen during several initial cycles betweenthe two situations. However, after several cycles (approximately12 here), the material water content is predictably at the samelevel in both situations.Additional simulations <strong>of</strong> the mass flow in the material wereperformed with different levels <strong>of</strong> relative humidity: for the first 7days it was varying sinusoidaly between 55% and 45% and for thenext week between 50% and 40%. Fig. 11 shows that moisturecontent in the material, as expected, is situated in between thecurves <strong>of</strong> adsorption and desorption, and the shape <strong>of</strong> the curve issimilar to previous results from the literature [12].6. Impact <strong>of</strong> <strong>hysteresis</strong>Relative humidity [-]0.901.00Fig. 9. Curves <strong>of</strong> primary sorption and desorption isotherms, and seconddesorption isotherm from [24].To demonstrate the <strong>influence</strong> <strong>of</strong> sorption <strong>hysteresis</strong> effect onwater vapour transport in building materials, series <strong>of</strong> simulations<strong>of</strong> the 12.5-mm-thick gypsum board were performed. The samematerial and same boundary conditions were used with twomodels: with and without <strong>hysteresis</strong> effect. The convection masstransfer coefficient b and temperature were the same as thoseused in Test 1 (Tables 1 and 2), but the relative humidity in the airwas changing sinusoidally between 45% and 55%. The calculationswere made for four variants (see Fig. 12): Hysteresis: The model with <strong>hysteresis</strong> effect. Adsorption: Model without the <strong>hysteresis</strong> effect. The dependencybetween the relative humidity and the water content isdescribed by the adsorption isotherm.

ARTICLE IN PRESSJ. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642 6390.00600.0055Water content [kg/kg]0.00500.00450.00400.00350.00300.0025layer 3 desorptionlayer 3 adsorption0.00200 24 4872 96120144 168 192Time [h]216240264288312336360Fig. 10. Moisture mass content at the depth <strong>of</strong> 6.25 mm.Water content [kg/kg]0.0080.0070.0060.0050.0040.0030.0020.25<strong>hysteresis</strong>sorption isothermdesorption isotherm0.350.45 0.55Relative humidity [-]0.65Fig. 11. Pr<strong>of</strong>ile <strong>of</strong> water content at the depth <strong>of</strong> 6.25 mm, as a function <strong>of</strong> periodicalchanges <strong>of</strong> air relative humidity.Water content [kg/kg]0.0080.0070.0060.0050.0040.0030.002240252264<strong>hysteresis</strong>adsorptiondesorptionaverage276Time [h]Fig. 12. Moisture mass content in the gypsum board at the depth <strong>of</strong> 6.25 mm, forfour calculation variants.288300312 Desorption: Model without the <strong>hysteresis</strong> effect. The dependencybetween the relative humidity and the water content isdescribed by the desorption isotherm. Average: Model without the <strong>hysteresis</strong> effect. The dependencybetween the relative humidity and the water content isdescribed by the average from adsorption and desorptionisotherms.In Fig. 15 the pr<strong>of</strong>iles <strong>of</strong> moisture content in the gypsum boardafter stabilization are presented. A significant difference can beseen between the model with <strong>hysteresis</strong> effect and the modelsusing only adsorption or desorption equations. However, whenthe average curve between adsorption and desorption is used, theresults can approximate correctly the behaviour with <strong>hysteresis</strong>effect.The results <strong>of</strong> simulations for the changing humidity conditionsin the air (for the first week the relative humidity was changing from45% to 55% and for the next week from 40% to 50%) are presented inFig. 13. It can be seen that achieving the equilibrium state in thematerial takes approximately 1 week, in case <strong>of</strong> <strong>hysteresis</strong>. Here,significant differences in the level <strong>of</strong> moisture content between themodel with <strong>hysteresis</strong> and all other variants can be seen. The effect<strong>of</strong> sorption <strong>hysteresis</strong> is more important in the case <strong>of</strong> stronglydynamic changes <strong>of</strong> the boundary relative humidity than in the case<strong>of</strong> steady-state conditions.7. Practical use <strong>of</strong> the Humi-mur model7.1. Implementation in an energy performance simulation toolIn order to demonstrate the practical use <strong>of</strong> the developedmodel, the first module <strong>of</strong> Humi-mur was implemented into awell-known building simulation tool called TRNSYS [26]. TRNSYSwas designed to solve complex energy system problems but thevariation <strong>of</strong> the indoor parameters like temperature or relativehumidity can be also simulated. Thanks to the modular structure<strong>of</strong> the TRNSYS programme, the Humi-mur model was translatedinto FORTRAN and implemented in TRNSYS Studio as a new typeresponsible for the moisture buffering <strong>of</strong> the materials. Humi-murcalculates moisture flow exchanged between indoor air andmoisture buffering materials. This moisture flow is also includedin the water vapour mass balance <strong>of</strong> the indoor air, as shown inFig. 14.

ARTICLE IN PRESS640J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–6420.0080.007<strong>hysteresis</strong>adsorptiondesorptionaverageWater content [kg/kg]0.0060.0050.0040.0030.0020 24 48 72 96 120 144 168 192 216 240 264 288 312 336Time [h]Fig. 13. Moisture mass content in the gypsum board at the depth <strong>of</strong> 6.25 mm, for four calculation variants, with changes in air relative humidity.Fig. 14. Scheme <strong>of</strong> the Humi-mur implementation into the TRNSYS simulation tool.It has been shown that the Humi-mur model implemented intoTRNSYS environment allows to predict indoor relative humidity <strong>of</strong>the considered zone [27]. Also, the model <strong>of</strong> moisture bufferingwas used to examine the <strong>influence</strong> <strong>of</strong> materials water vapourstorage on moulds growth risk on the internal wall surfaces. It wasshown that materials that buffer water vapour can significantlydecrease the risk <strong>of</strong> mould growth [28].In order to check if <strong>hysteresis</strong> effect <strong>influence</strong>s moisturebuffering <strong>of</strong> the materials at the building level, some additionalcalculations in the TRNSYS programme have been performed.In the simulations two models have been used: the firstwithout <strong>hysteresis</strong> and with average sorption isotherm, and thesecond with <strong>hysteresis</strong> <strong>of</strong> sorption curves. The calculations <strong>of</strong>indoor absolute humidity were made for a small room(2.5 3.5 2.6 m 3 ) with the gypsum board (30 m 2 ) as a bufferingmaterial. The considered room had two external walls and onewindow. It was assumed that the rest <strong>of</strong> the zone’s envelopes wereadiabatic. Additional gains <strong>of</strong> heat and water vapour were alsoadded. The periods with heat and humidity production wereestablished each morning (from 6 to 8 a.m.), afternoon (from 12 to14 p.m.) and evening (from 18 to 21 p.m.). Also a ventilation rate<strong>of</strong> 22.75 m 3 /h was assumed. The simulations were performed for 1year, using weather file Warsaw (Poland). In order to avoid too lowtemperatures in the zone, the heating season with a constanttemperature <strong>of</strong> 20 1C was set from the 1 October till 15 May. In thesimulation the time step <strong>of</strong> 600 s was used for the model without<strong>hysteresis</strong> effect and <strong>of</strong> 72 s for the model with <strong>hysteresis</strong> effect.Hourly results were compared.7.2. Results and discussionIn Fig. 15 the relative difference <strong>of</strong> water content <strong>of</strong> the indoorair between the models is presented. Although most <strong>of</strong> the timethe difference is smaller than 5% and the mean difference equals3.1%, it can be noticed that sometimes the difference reaches highvalues. It was calculated that for 23% <strong>of</strong> the time, the differencepasses the limit <strong>of</strong> 5% and for 6% <strong>of</strong> the time is higher than 10%.The difference between results <strong>of</strong> the absolute humidity obtainedusing the model without <strong>hysteresis</strong> and with <strong>hysteresis</strong> can reachas much as 20%. The highest values <strong>of</strong> the difference wereobtained when the absolute humidity in the zone had the highestor the lowest values. It was also noticed that for the maximumvalues <strong>of</strong> the zone absolute humidity, the model without<strong>hysteresis</strong> was decreasing water content in the air moresignificantly than the model with the <strong>hysteresis</strong> effect. Similarsituations occurred for the minimum values <strong>of</strong> the zone absolutehumidity. The model only with the average sorption curve wasincreasing the water content <strong>of</strong> the air more significantly than themodel with <strong>hysteresis</strong>. This phenomenon shows that using in thecalculation model only with the average sorption curve reducesthe amplitude <strong>of</strong> indoor absolute humidity more than the morerealistic model with <strong>hysteresis</strong>. Neglecting <strong>hysteresis</strong> in thesorption curve leads to overestimations <strong>of</strong> the moisture bufferingcapacity <strong>of</strong> materials. For some materials those differences willnot provide significant errors but for others (such as wood) theymay lead to underestimations <strong>of</strong> risk <strong>of</strong> condensation or <strong>of</strong> mouldgrowth.

ARTICLE IN PRESSJ. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642 64110000Number <strong>of</strong> hours10001001012.512.5 7.517.522.5Relative difference in water content between two models [%]Fig. 15. Relative difference in water content <strong>of</strong> the air between results obtained using the model without <strong>hysteresis</strong> and with <strong>hysteresis</strong>.Table 5Sensitivity <strong>of</strong> relative humidity calculations for different number <strong>of</strong> layers and timestep for the 150 mm thick sampleParameter Value Deviation(depth 50.0 mm)8. Conclusions and perspectivesDeviation(depth 100.0 mm)Number <strong>of</strong> layers 48 0.01% 0.00%72 Divergence DivergenceTime step (s) 30 0.01% 0.01%120 Divergence DivergenceTable 6Sensitivity <strong>of</strong> relative humidity calculations for changes in sorption isotherm andvapour permeability for the 37.5 mm thick sampleProperty Adjusted Deviation(depth 12.5 mm)Sorption isotherm ( ) 3.50% 6.15%(+) 3.61% 6.19%Deviation(depth 25.0 mm)Vapour permeability ( ) Divergence Divergence(+) 2.70% 4.94%Table 7Sensitivity <strong>of</strong> relative humidity calculations for changes in sorption isotherm andvapour permeability for the 150 mm thick sampleProperty Adjusted Deviation(depth 50.0 mm)Sorption isotherm ( ) 0.48% 3.42%(+) 12.11% 10.67%Deviation(depth 100.0 mm)Vapour permeability ( ) Divergence Divergence(+) 4.37% 3.49%A new module for the precise representation <strong>of</strong> mass transferin materials in contact with indoor air, called Humi-mur, waselaborated and validated in this work. It was then applied toestimate the sensitivity <strong>of</strong> the results to uncertainty in measuredmaterial properties and the impact <strong>of</strong> <strong>hysteresis</strong> effect. Humi-murwas also successfully implemented in a whole-building simulationcode, TRNSYS. The new model allows considering severaldifferent materials, and for precise definition <strong>of</strong> properties formoisture transfer.Reasonable estimation <strong>of</strong> experimental uncertainty resulted inthe deviation <strong>of</strong> approximately 6% in calculated results. It isimportant to know better the accuracy <strong>of</strong> predictions. The simulationtool cannot give results more precisely than the input data. Somekind <strong>of</strong> uncertainty or error-bar should then complement thesimulation results. For some variation <strong>of</strong> parameters the divergenceproblems occur (see Tables 5–7). The difficulty in obtaining resultsfrom numerical calculation is related mainly with too long time stepor too thin layer in the material. The stability <strong>of</strong> numericalsimulation will be investigated in the near future.Concerning <strong>hysteresis</strong> in the sorption isotherm, we showedthat using only one <strong>of</strong> the sorption isotherm equations (adsorptionor desorption) leads to significant differences. More preciseresults were achieved if the average <strong>of</strong> the adsorption anddesorption equations was used in the model. For less-precisecalculations it appeared to be a reasonable approximation <strong>of</strong>mean behaviour. However, for strong variations in boundaryconditions, it is not well suited. Indeed, convergence to some kind<strong>of</strong> quasi-permanent state is much slower if <strong>hysteresis</strong> isconsidered. This effect <strong>influence</strong>s the dynamic behaviour <strong>of</strong>materials. It was also shown that in realistic conditions (a roomunder variable climate and hygrothermal loads), neglecting<strong>hysteresis</strong> leads to overestimation <strong>of</strong> moisture buffering properties<strong>of</strong> materials in contact with the indoor air. In some cases suchoverestimation may conduct to the underestimation <strong>of</strong> risks <strong>of</strong>mould growth and/or condensation.References[1] Padfield T. Humidity buffering <strong>of</strong> the indoor climate by absorbent walls [online]. In: Proceedings <strong>of</strong> the fifth symposium on building physics inNordic countries, vol. 2. Goteborg: Chalmers University <strong>of</strong> Technology;1999. p. 637–44 Pdf available at: /http://www.padfield.org/tim/cfys/appx/pubs.phpS.[2] Osanyintola OF, Simonson CJ. Moisture buffering capacity <strong>of</strong> hygroscopicbuilding materials: experimental facilities and energy impact. Energy andBuildings 2006;38:1270–82.[3] Hens H. Final report, vol. 1, Task 1: modelling, IEA Annex 24. ACCO Leuven;1996.[4] Canada Mortgage and Housing Corporation (CMHC). Review <strong>of</strong>hygrothermal models for building envelope retr<strong>of</strong>it analysis. Researchhighlights, technical series 03-128./http://www.cmhc-schl.gc.ca/publication/en/rh-pr/tech/03-128-e.htlmS.[5] Künzel HM. Simultaneous heat and moisture transport in building components.One- and two-dimensional calculation using simple parameters. IRBVerlag; 1995.

ARTICLE IN PRESS642J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642[6] WUFI. PC-program for calculating coupled heat and moisture transfer inbuilding components. /http://www.wufi.de/index_e.htlmS.[7] Holm A, Künzel HM. Two-dimensional transient heat and moisture simulations<strong>of</strong> rising damp with WUFI 2D. 12th international brick/block masonryconference, Madrid, 25–28 June 2000.[8] Burch DM, Chi J. MOIST. A PC program for predicting heat and moisturetransfer in buildings envelopes. Release 3.0, 1997.[9] Hagent<strong>of</strong>t CE, Blomberg T. 1D-HAM. Coupled heat, air and moisture transfer inmulti-layered wall structures. Manual with brief theory and an example,version 2.0, 2000. /http://www.buildingphysics.com/manuals/1dham.pdfS.[10] MATCH—Moisture and temperature calculation for constructions <strong>of</strong> hygroscopicmaterials, /http://www.match-box.dkS.[11] Pedersen CR. Combined heat and moisture transfer in building constructions.Ph.D. thesis. Report 214. Thermal Insulation Laboratory, Technical University<strong>of</strong> Denmark, 1990.[12] Pedersen CR. Transient calculation on moisture migration using a simplifieddescription <strong>of</strong> <strong>hysteresis</strong> in the sorption isotherms. The second symposium onbuilding physics in the Nordic Countries, Trondheim, 20–22 August 1990.[13] Geving S, Karagiozis A, Salonvaara M. Measurements and two-dimensionalcomputer simulations <strong>of</strong> the hygrothermal performance <strong>of</strong> a wood frame wall.Journal <strong>of</strong> Thermal Insulation and Building Envelopes 1997;20(April 1):301–19.[14] Geving S. A systematic method for hygrothermal analysis <strong>of</strong> buildingconstructions using computer models. In: Proceedings <strong>of</strong> the buildingsimulation, vol. 2; 1997. p. 355–61.[15] Mukhopadhyaya P, Goudreau P, Kumaran MK, van Reenen D. Influence <strong>of</strong>material properties on the moisture response <strong>of</strong> an ideal stucco wall: resultsfrom hygrothermal simulation. In: Sixth Nordic Building Physics Symposium,Trondheim, Norway, 17–19 June 2002.[16] Salonvaara M, Karagiozis A, Holm A. Stochastic building envelope modeling—the<strong>influence</strong> <strong>of</strong> material properties. Performance <strong>of</strong> exterior envelopes<strong>of</strong> whole buildings VIII: integration <strong>of</strong> building envelopes, CD-ROM (2001),December 2–7 2001. 8pp.[17] Kumaran MK. Final Report, vol.3. Task 3: Material properties, Acco Leuven,1996.[18] Sereda PJ, Feldman RF. CBD-130.Wetting and drying <strong>of</strong> porous materials, 1970.[19] Mualem Y. A conceptual model <strong>of</strong> <strong>hysteresis</strong>. Water Resources Research1974;10(3).[20] Time B. Studies on hygroscopic moisture transport in Norway spruce (Piceaabies). Part 2: <strong>Modelling</strong> <strong>of</strong> transient moisture transport and <strong>hysteresis</strong> inwood. Holz Als Roh-und Werkst<strong>of</strong>f 2002;60(6).[21] Carmelit J, de Wit M, Jansen H. Hysteresis and moisture buffering <strong>of</strong> wood. In:Seventh Nordic symposium on building physics, Reykjavik, 12–15 June 2005.[22] Peralta PN. <strong>Modelling</strong> wood moisture sorption <strong>hysteresis</strong> using theindependent-domain theory. Wood Fiber Science 1995;27:250–7.[23] Crausse P, Laurent JP, Perrin B. Influence des phenomenes d’<strong>hysteresis</strong> sur lesproprietes hydriques de materiaux poreux: Comparaison de deux modeles desimulation du comportement thermohydrique de parois de batiment. RevenuGenerale de Thermique 1996;35(410).[24] James C, Simonson CJ, Talukdar P. Annex 41 report for common exercisesubtask 2, IEA annex 41, June 2007. 89pp.[25] Frandsen HL. <strong>Modelling</strong> <strong>of</strong> moisture transport in wood. Wood science andtimber engineering, Paper no. 1, 2nd ed. Department <strong>of</strong> Building Technologyand Structural Engineering, Aalborg University, March 2005.ISSN:1395-7953R0502.[26] Klein SA, Beckman WA, Mitchell JW, et al. TRNSYS 16, a transient systemsimulation program, Solar Energy Laboratory, University <strong>of</strong> Wisconsin,Madison, USA, 2004.[27] Kwiatkowski J, Feret K, Woloszyn M, Roux J-J. Predicting indoor relativehumidity using building energy simulation tools. In: The sixth internationalconference on indoor air quality, ventilation & energy conservation inbuilding, Sendai, Japan, 28–31 October 2007.[28] Kwiatkowski J, Woloszyn M, Roux J-J. The <strong>influence</strong> <strong>of</strong> material moisturebuffering on moulds growth risk on the internal wall surfaces (Wplywbuforowania wilgoci przez materialy na ryzyko rozwoju plesni na powierzchniprzegrod wewnetrznych), IX Polish conference ‘‘The problems <strong>of</strong> indoor airquality in Poland’’ (IX Ogolnopolska Konferencja ‘‘Problemy jakosci powietrzawewnetrznego w Polsce’’), Warsaw, Poland, 22–23 November 2007 [inpolish].