The Kieper and MOISTWALL Moisture Analysis Methods for Walls

Transcription

1 SessionXI No. 2 The Kieper and MOISTWALL Moisture Analysis Methods for Walls A. Tenwolde ABSTRACT Few methods are available to predict water vapor migration through walls and to assess the potential for condensation. The moisture profile method, described in the ASHRAE Handbook Fundamentals, is the most widely accepted. In 1976 the Kieper method was introduced as an alternative. It attracted relatively little attention, however, and has remained practically unknown. This paper describes the Kieper method in detail and discusses its advantages and limitations. The major advantage is the relative ease of determining the most likely location for condensation in a wall and comparing the performance of different wall designs under identical environmental conditions. The Kieper method is graphical and, like the moisture profile method, based on one-dimensional steady-state vapor diffusion theory. The MOISTWALL program is an adaptation by the author of the Kieper method for a programable calculator. Neither the original moisture profile method nor the methods presented in this paper account for the effects of air leakage, hygroscopicity, and capillary action. Moreover, reliable input data for permeability of building materials are often not available. The methods do not provide a direct prediction of moisture damage, because damage also depends on initial moisture content, the types of material involved, temperatures, and the duration of condensation. Despite these limitations, analysis with the Kieper or MOISTWALL methods can provide valuable qualitative insights into the moisture performance of wall assemblies. INTRODUCTION Until recently, the use of vapor retarders together with appropriate ventilation was thought to provide adequate protection against moisture accumulation in walls. Now higher insulation requirements and higher indoor humidity levels due to reduced air infiltration have rekindled interest in moisture management. Anton TenWolde is a physicist at the Forest Products Laboratory, Forest Service, U.S. Department of Agriculture. The laboratory is maintained at Madison, WI, in cooperation with the University of Wisconsin. This manuscript was written and prepared by U.S. government employees on official time, and it is therefore in the public domain. 1033

2 Only a few available methods can analyze water vapor migration in walls and determine where and how much moisture is accumulating if condensation is occurring. The most widely accepted is the dew point or moisture profile method, described in the ASHRAE Handbook Fundamentals. 1 It is based on steady-state linear diffusion theory and ignores the effects of air convection and condensation-drying cycles. In spite of ita obvious limitations, the moisture profile method may serve to give the user an indication if moisture accumulation is likely. However, this method can be very time-consuming to use and often leads to errors when the condensation plane is not assumed in the correct location. An attempt to make this method more accessible resulted in a program developed by Lewis et al. for the a programmable calculator. 2 Although using that program, named WETWALL, is considerably less complicated or time-consuming than using the moisture profile method, WETWALL may not always correctly identify where in the wall condensation is taking place and how much moisture is accumulating. An alternative to the moisture profile method was introduced by Kieper et al. 3,4 Like the moisture profile method, it is based on one-dimensional steady-state diffusion equations. It is a graphical method, which allows rapid evaluation of different wall designs under the same environmental conditions. Unfortunately, this method has not yet found widespread acceptance, partly because it has not been clearly described an$ partly because blank Kieper diagrams are not readily available. This paper contains a description of the method and the mathematical basis for it. To facilitate the use of the Kieper method, the authorhas developedmoistwall-1, a program for the calculator, based on the same mathematical principles as the Kieper method. A simple algorithm estimating the effect of latent heat release was added and is described in this paper. Although a more comprehensive analytical tool is needed that includes convection and transient effects, such a method has yet to be developed. Until it is available the Kieper and MOISTWALL methods may serve as improved alternatives to the moisture profile method. THE KIEPER ANALYSIS METHOD The Kieper method is a graphical method used to (1) determine if condensation is occurring, (2) locate the point of maximum moisture accumulation, and (3) estimate the rate of accumulation. It is based on an adaptation of conventional one-dimensional steady-state diffusion and heat-conduction equations. This adaptation involves the definition of parameter x, representing the thermal properties of the wall, and parameter y, representing the vapor flow properties. These definitions of x and y not only simplify the heat and vapor flow equations but find their most important use in the Kieper diagram. Steady-State Heat Conduction The one-dimensional steady-state conductive heat flow rate through a layer of material is 1 proportional to the temperature difference across the material: (1) where q = heat flow rate (Btu/hr ft 2 [W/m 2 ]) R t = thermal resistance (hr ft2 F/Btu[m2 K/W]) = temperature difference ( F[ C]) 1034

3 A typical wall may be thought of as a combination of flat layers of materials. Under steady-state conditions with continuity of heat flow (no accumulation of heat in the wall), the temperature difference across each layer is proportional to its thermal resistance. It is possible to determine temperatures within the wall (Fig. 1A) with the following equation: (2) where t n = temperature at surface between layer n and next layer ( F[ C]) t i = indoor temperature ( F[ C]) t o = outdoor temperature ( F[ C]) R tk = thermal resistance of layer k (hr*ft 2 F/Btu[m2 * K/W]) = total thermal resistance of all layers (hr ft2 F/Btu[m2 K/W]) R t Layers usually include inner and outer air films and the numbering of layers is from inside to outside. If the parameter x is defined as: (3) the temperatures in the wall become a simple linear function of x with continuity of flow (Fig. 1B): Values of parameter x are between 0 and 1. Steady-State Vapor Diffusion Similarly to heat conduction, the water-vapor flow rate through a layer of material is approximately proportional to the vapor pressure difference across the layer: 1 where* w = vapor flow rate (grain/ft2 hr[kg/m2 s]) = vapor diffusion resistance (Rep[m/s]) = vapor pressure difference (in.hg[pa]) R v Eq 5 approximates water vapor flow by diffusion only. Flow of liquid water by capillary action in hygroscopic materials is not included. At higher relative humidities (70% or higher) capillarity can significantly change moisture flow. 5-7 Capillary flow is caused by differences in relative humidities and may therefore augment or counteract the vapor diffusion flow. 5,7 The exact relationship between the gradient in relative humidity and liquid moisture movement has not been established. Capillary flow is not included in the Kieper and MOISTWALL methods. (4) (5) *7000 grains = 1 lb (1 Rep = 1 ft 2 hr in. Hg/grain[1.74 x m/s]). Vapor diffusion resistance is the reciprocal of permeance, which is expressed in perms (1 perm = 1 gram/ft 2 hr in. Hg[5.75 x s/m]). 1035

4 If one assumes steady-state vapor flow with no moisture accumulation or evaporation anywhere in the wall, vapor pressures in the wall may be calculated with an equation similar to Eq 2: (6) where p n = vapor pressure at surface between layer n and the next layer (in. Hg[Pa]) p i = indoor vapor pressure (in. Hg[Pa]) p o = outdoor vapor pressure (in. Hg[Pa]) R vk = vapor diffusion resistance, layer k (Rep[m/s]) R v = total vapor diffusion resistance of all layers (Rep[m/sJ). If the parameter y n is defined as: Eq 6 may be written as: Vapor pressures in the wall are a linear function of y if continuity of flow is assumed. Values of y are between 0 and 1. Condensation The previous discussion and equations apply only if no coodensation takes place anywhere in the wall. When water vapor moves through the wall from the warm side to the colder side, the vapor present may exceed the capacity of the air to contain water vapor. This capacity is greatly reduced at lower temperatures. Condensation begins to occur when the vapor pressure reaches saturation. With Eq 8, the condensation boundary condition can be defined as: where p s (t) = saturation vapor pressure at location (x,y) This equation, however, does not define the location of the condensation plane, because vapor pressures throughout the wall are effected by the occurrence of condensation, and Eq 8 is no longer valid. If one assumes condensation at one point (plane) in the wall, vapor pressure at this point must be at saturation (Fig. 2). It is then obvious from Fig. 2 that the vapor pressure is no longer a simple linear function of y. Vapor pressures throughout the wall are lowered with the occurrence of condensation, and this increases the rate at which water vapor enters the wall. The condensation rate is the net vapor flow rate to the condensation plane. If condensation occurs only at the one location, the flows to and from the condensation plane can be characterized by: (7) (8) (9) (10a) 1036

5 (10b) where The net accumulation rate is: = flow rates to and from condensation plane (grain/ft2 hr[kg/m2 s]) = saturation vapor pressure at condensation plane (in. Hg[Pa]) = temperature at condensation plane ( F[ C]) = y coordinate of condensation plane. (11) Of course, condensation actually may occur simultaneously at two or more locations in the wall. These locations are all within the condensation "danger zone" defined by the condensation boundary equation. However, because damage from condensation is related to the amount of moisture present, the primary concern is with that location where potential moisture accumulation is the highest. Moreover, condensation at that location tends to cause the greatest reduction of vapor pressures throughout, the "danger zone," diminishing or eliminating the potential tor condensation at other locations an the zone. The Kieper and MOISTWALL methods locate only this one location, ignoring possible secondary points of condensation. The point of maximum potential accumulation is usually at one of the interfaces between two different layers of materials. The Kieper Diagram The Kieper diagram is used to determine graphically the potential location and rate of moisture accumulation. It is composed of a horizontal x-axis representing thermal properties (values 0 to 1), a vertical y-axis representing vapor flow properties (values 0 to 1), and a family of curves based on Eqs 9 and 11. The condensation boundary curve and auxiliary curves are dependent exclusively on the indoor and outdoor environmental conditions. An example of a Kieper diagram is shown in Fig. 3. Finally, a wall design profile can be drawn in this diagram that represents the thermal and vapor diffusion characteristics of the wall and depends only on material properties. Condensation Boundary Curve. The condensation boundary curve demarcates the condensation danger zone (Fig. 3). This zone, which consists of those x,y combinations for which condensation might occur, is defined only by indoor and outdoor temperatures and humidities and is independent of the design of the wall (Eq 9). For winter heating conditions when the indoor temperature is above the outdoor temperature, the condensation danger zone is under the condensation boundary curve in the lower right corner of the diagram. For summer cooling conditions, it is located in the upper left corner above the boundary curve. Auxiliary Curves. The most likely location for condensation (i.e., where potential moisture accumulation is the highest) and an estimate of the accumulation rate may be determined with the help of auxiliary curves defined in Eq 11. The curves, which can be drawn in the condensation danger zone in the Kieper diagram, connect those x,y combinations for which the potential moisture accumulation rate would be the same. To make these curves independent of the 1037

6 wall design, it is necessary to redefine the auxiliary curves as those x,y combinations for which the product of moisture accumulation rate and total vapor diffusion resistance. w c R v, is constant. As Eq 11 shows, w cr v is a function only of y (indoor and outdoor vapor pressuros and the saturation pressure), which is a function of x and indoor and outdoor temperatures. The boundary curve can be thought of as the auxiliary line for which w c R v = 0. Fig. 3 shows these curves for a specific combination of winter indoor and outdoor conditions. Lower auxiliary curves represent higher rates of moisture accumulation. Wall Design Profile. The thermal and vapor diffusion characteristics of the wall can be represented simply and simultaneously in the Kieper diagram. By using the definition equations of x and y (Eqs 3 and 7), each interface between two layers can be assigned a point in the diagram. The wall design profile is the line that connects these points. The profile always starts in the origin (0.0) and ends in the upper right corner (1,1). Each straight-line segment represents a layer of material. A wall consisting of one homogeneous layer of material would be represented by a single straight line between these two points, if the effects of the surface air films are ignored. An example of a wall profile is shown in Fig. 4 Finding the Location and Rate of Condensation If the wall profile does not intersect the condensation boundary curve, condensation is not occurring. If the wall profile penetrates the condensation danger zone (e.g., Fig. 5, a combination of Figs. 3 and 4). condensation is taking place. The location can be found by determining the auxiliary curve for the highest value of w cr v that still touches the wall profile. This is the point of maximum moisture accumulation. As Fig. 5 shows, this point is usually at one of the discontinuities in the wall profile, representing the interfaces between layers. Only in the unlikely event that a linear section of the wall profile would touch the auxiliary curve tangentially would this point be located within a layer. Such a location, however, would be very sensitive to changes in weather conditions. Thus, condensation within a homogeneous material layer tends to be transient in nature, unless the layer is "locked in" between two condensation planes at both surfaces. Persistent condensation within permeable cavity insulation is especially unlikely, because this layer would usually be represented by a long, almost-horizontal section in the wall design profile, reducing the likelihood of tangentially touching an auxiliary curve. Once the location is found, the corresponding value of w cr v for the auxiliary curve directly yields the moisture accumulation rate, w c. This is possible because the total vapor diffusion resistance (R v) of the wall is known. Example In the example, outdoor conditions are assumed at 20 F(-6.7 C), 50% relative humidity (RH), and indoor conditions at 70 F(21.1 C), 40% RH. The example wall is of typical wood-frame construction with no vapor retarder other than a layer of paint on the gypsum board. Thermal and vapor diffusion resistances of each layer and for the wall are listed in Tab. 1. The x and y coordinates can be calculated easily. For instance, the x coordinate for the interface between the insulation and sheathing is: 1038

7 Similarly, the y coordinate is: Coordinates for all interfaces are listed in Tab. 2 and plotted in Fig. 4. Part of the wall profile in Fig. 5 falls below the condensation boundary curve, indicating that condensation is occurring. The auxiliary curve with the highest accumulation rate that touches the wall profile is approximately the one for w cr v = 0.2;** it touches at x = 0.93, y = These x and y coordinates correspond with the sheathing-siding interface, and the moisture accumulation rate is: Analysis with the more time-consuming ASHRAE moisture profile method 1 yields approximately the same total value (0.11 grain/ft 2 hr[2.1 x 10-8 kg/m 2 s]) but indicates that condensation is occurring throughout the siding, with 80% of the accumulation on the inside surface of the siding and most of the other 20% immediately behind the exterior paint layer. This is an example of the general case previously discussed, in which the siding is "locked in" between two condensation planes. (The Kieper method does not yield the same locations, because the method is limited to one single location.) It is difficult to assess the seriousness of rate of accumulation. Under the given conditions it would take approximately 1000 hours to raise the moisture content of the siding by 1%, but in this case the moisture is accumulating as frost on the inner surface and could produce streaking of the siding when the frost melts. Summary of Kieper Method The Kieper method consists of the following steps: 1. Select or measure indoor and outdoor temperatures and relative humidities. 2. Select or create the corresponding Kieper diagram using Eqs 9 and Determine thermal and vapor diffusion resistances of each wall layer. 4. Calculate x,y coordinates of the interfaces between layers. 5. Graph wall profile in Kieper diagram. 6. Determine if any part of the wall profile is in the "condensation danger zone." 7. If so, determine the likely location for condensation and the moisture accumulation rate, using the auxiliary curves. THE MOISTWALL-1 PROGRAM The MOISTWALL-I program was developed for a programable calculator with printer. Like the Kieper method, it is based on the same one-dimensional steady-state diffusion equations described earlier and selects the location where moisture accumulation is the greatest. In addition, the program estimates the first-order effect of latent heat release on temperature and moisture accumulation. **The actual auxiliary curve touching the wall curve is approximately w cr v = 0.23, which can be estimated by interpolation between the curves for 0.2 and 0.5. The corresponding moisture accumulation rate is 0.23/2.26 = 0.1 grain/ft 2 hr(1.9 x 10-8 kg/m 2 s). 1039

8 The program is easier to use than the Kieper diagram and does not require any calculations or use of psychrometric charts or tables. The only initial inputs required are indoor and outdoor temperatures, relative humidities, and the thermal and vapor diffusion resistance of each layer in the wall. The program calculates and prints the indoor and outdoor vapor pressures and the total resistance values. It then computes with Eq 11 temperature and potential moisture accumulation at each interface between layers. The temperatures and initial values for accumulation w are printed. Negative numbers for accumulation indicate drying conditions. The program then identifies the maximum value of w and the corresponding location in the wall. If no condensation is occurring, the program prints a negative number for w and a zero as location identification. If condensation is detected, the change in temperature due to latent heat release and the consequent change in accumulation is calculated as outlined in the next sect ion. Effect of Latent Heat Release When water vapor condenses as liquid water, latent heat is released at a rate of approximately 0.15 Btu/grain (2440kJ/kg) or 0.17 Btu/grain (2770kJ/kg) when it condenses as frost. The effect of this on the temperature can be described in a simple manner, similar to the effect of condensation on vapor pressures. The rate of latent heat release is: where ql = latent heat release (Btu/ft 2 hr[w/m2 ]) c L = 0.15 Btu/grain (2440 kj/kg) (liquid condensation) = 0.17 Btu/grain (2770 kj/kg) (frost formation) w c = moisture accumulation rate (grain/ft2 hr[kg/m2 s]). The value used for c L is 0.16 Btu/grain(2600kJ/kg), which is an average value and causes a slight overestimation of heat release during liquid accumulation. Heat release during frost accumulation is slightly underestimated. The release of latent heat raises the temperature at the condensation plane (Fig. 6). Under steady-state conditions, heat flow to the condensation plene must equal heat flow from the condensation plane: (12) (13) With Eqs 12 and 13 the steady-state temperature at the condensation plane may be written as: The first term on the right-hand side represents the increase in t c as a result of latent heat release. This increase not only depends on the moisture accumulation rate but also on the thermal resistance of the wall and the location of the condensation plane. Eq 14 cannot be solved analytically because w depends on the saturation pressure p s(t c) (Eq 11), which is a nonlinear function of t. The accumulation rate decreases with higher temperatures, which in turn lowers the rate of latent heat release. Consequently, Eqs 11 and 14 would lend themselves well to an iterative numerical solution. However, program space limitations on the calculator precluded the use of such an iterative loop, and MOISTWALL therefore only calculates the correction once. In most applications, latent heat plays a minor role, and this approximation is 1040 (14)

9 sufficiently accurate; but in selected cases, a better approximation may be desirable. Problems occur when the adjusted temperature is above the dew point temperature, causing the adjusted value of w to be negative. Obviously, in reality, latent heat release cannot raise the temperature past the dew point. Although such cases can be identifiedwithmoistwall, other methods of analysis, not discussed in this paper, are needed to determine the correct values of t c and w c. A program listing is given in the appendix. Example The wall design (Tab. 1) is again used as an example. Indoor conditions are again assumed to be 70 F(21.1 C), 40% RH. and outdoor conditions 20 F(-6.7 C), 50% RH. Fig. 7 shows the MOISTWALL worksheet with the appropriate values. Resistance values of zero for the first and last layer have to be entered as to avoid division by zero during program execution. Fig. 8 presents the input and output for this example with an explanation of individual items. The results indicate condensation8 between layers 4 and 5, the sheathing and siding, at the rate of grains/ft 2 hr(2.07 x 10-8 kg/m 2 s). Printed positive initial values of moisture accumulation indicate that condensation potential exists at two other locations (locations 3 and 5), but it is not possible to determine from these results if condensation is indeed occurring simultaneously at these locations. As discussed previously, analysis with the ASHRAE moisture profile method 1 showed that simultaneous condensation is taking place throughout the siding but not at the sheathing-insulation interface (location 3). DISCUSSION The two methods of analysis arc both introduced as improvements on the ASHRAE moisture profile method. The major advantage of the Kieper and MOISTWALL methods is that they are less timeconsuming to use. As with the ASHRAE method, both methods should be used with caution because of the following limitations: The effects of air leakage, hygroscopicity, and capillary action are not considered. The method is one-dimensional; corners, tears, cracks, and holes in materials cannot be modeled. The net effect of condensation-drying cycles cannot be determined adequately with these methods. Reliable input values for vapor flow resistance are often not available, but this problem is generic to any moisture analysis method. The adjustment method for latent heat release in the MOISTWALL program is only approximate. If this effect appears to be of major importance, other calculation methods should be used. Because of these limitations and uncertainties in input values, results obtained with the Kieper, MOISTWALL, or moisture profile methods should generally be treated as qualitative, rather than quantitative. Users should be aware that these are methods for calculating condensation rates and not for predicting potential moisture damage. Damage depends on materials, duration of condensation, initial moisture contents, and temperatures. SUMMARY This report describes two alternative methods for analysis of moisture movement and accumulation in walls. Both are based on the same principles of one-dimensional steady-state diffusion theory and are offered as improved alternatives to the moisture profile analysis method in the ASHRAEHandbook--1981Fundamentals. Their main advantage is that they are easier to use. The Kieper method, a graphical method, was first introduced in 1976, but never gained widespread recognition. The major advantage is the relative ease of determining the most 1041

10 NOMENCLATURE

11 likely location for condensation and comparing the performance of different wall designs under identical conditions. Application provides evidence that condensation primarily occurs on surfaces between layers of different wall materials. Condensation within layers, especially within permeable cavity insulation, is far less likely and more transient in nature. The MOISTWALL method was developed by the author for use on a programmable calculator. The program calculates temperatures and potential moisture accumulation rate. It selects the location of maximum accumulation rate and adjusts for the effect of latent heat release. The latent heat effect greatly depends on the thermal properties of the wall and the location of the accumulating moisture. APPENDIX.--Program listing for MOISTWALL

12 1044

13 1045

14 Example Design: TABLE 1 Thermal Resibtanre and Vapor Diffusion Resistance of Insulated Frame Wall Example Wall: TABLE 2 x,y Coordinates for Kieper Diagram 1046

15 Figure 1. Multilayered wall (A) temperature profile, (B) temperature as a function of x Figure 2. Vapor pressures in a wall with and Figure 3. Kieper diagram with condensation without condensation boundary curve and auxiliary curves 1047

16 Figure 4. Kieper diagram with wall cirve Figure 5. Kieper diagram with condensation boundary curve, auxiliary curves, and wall curve Figure 6. Temperatures in a wall with and without condensation 1048

17 MOISTWALL-1 WORKSHEET Figure 7. MOISTWALL-1 worksheet with sample input values 1049

18 Figure 8. Example input and output for MOISTWALL

19 Discussion S.N. Flanders, U.S. Army CRREL, Hanover, NH: You cite the interfaces between materials as being the points of maximum condensation rates. Is moisture condensation taking place at other locations not at an interface within the "danger zone"? Would you expect condensation within the thickness of insulation in a ventilated attic without a vapor retarder? TenWolde: The theory suggests that condensation at an interface reduces the chance for condensation elsewhere in the "danger zone." Occasionally condensation may occur within layers, especially if the material is not homogeneous, but my calculations show that the moisture accumulation rate will be low in comparison. This need: to be verified in the laboratory. On the basis of theory, I do not expect significant condensation within the thickness of attic insulation. Of course. condensation or a surface above the insulation (floor, roof sheathing) may drip or "wick" back into the insulation. J.D. Verschcor. Consultant, Denver, CO: This paper presents an interesting way of portraying the potential condensation problem in a wall. Has the author considered how the potential condensation curves are modified when the wall cavity qis ventilated from the outside (infiltration) or from the inside (exfiltration)? A. TenWolde: The Kieper and MOISTWALL methods do not take air movement into account. Incorporating the effects of airflow into the Kieper method is complicate and I have not tried to do this. We are expanding the MOISTWALL method to include uniform airflow through a wall. TenWolde, Anton. The Kieper and MOISTWALL moisture analysis methods for walls. In: Thermal Performance of the Exterior Envelopes of Buildings 11: Proceedings of the ASHRAE/DOE Conference; 1982 December 6-9; Las Vegas, NV. Atlanta, GA: American Society of Heating Refrigerating and Air- conditioning Engineers, Inc.; 1983: