Explanation of the mould and lifetime calculators

Disclaimer

The information in this document is based on the current understanding of the issues presented. It does not necessarily apply in all situations, nor do any represented activities ensure complete protection as described. Although reasonable efforts have been made to ensure that the information is accurate and up to date, the publisher, Canadian Conservation Institute (CCI), does not provide any guarantee with respect to this information, nor does it assume any liability for any loss, claim or demand arising directly or indirectly from any use of or reliance upon the information. CCI does not endorse or make any representations about any products, services or materials detailed in this document or on external websites referenced in this document; these products, services or materials are, therefore, used at your own risk.

On this page

• List of abbreviations
• Explanation of the Mould Calculator
  • Sources of data and derivation of the equations
  • Static versus dynamic relative humidity
  • Multiple tactics for practical prevention of mould
  • Health issues
• Explanation of the Lifetime Calculator
  • To begin, two simple rules of thumb
  • The idea of object lifetime
  • Historical evidence for benchmark lifetimes
  • Logarithmic categories for material lifetimes
  • Plotting the effect of temperature on lifetime
  • Plotting the effect of relative humidity on lifetime
  • Plotting the effect of temperature and relative humidity on lifetime
  • ClimaSpec allows complex scenarios
  • Equations for lifetimes
    • Model #1
    • Model #2
    • Model #3
    • Model #4
    • Model #5
• Bibliography

List of abbreviations

ASHRAE

American Society of Heating, Refrigerating and Air-Conditioning Engineers

CCI

Canadian Conservation Institute

ICOM-CC

International Council of Museums, Committee for Conservation

IPI

Image Permanence Institute

ISO

International Organization for Standardization

RH

relative humidity

Explanation of the Mould Calculator

Stefan Michalski and Tom Strang

Sources of data and derivation of the equations

Figure 1 collects several authors’ data on the time required for mould growth. The solid blue line is a curve fitted by Michalski (1993) to data by Snow et al. (1944) on the time required for visible mycelia to appear on dried grass, linseed cake and bone meal (black points). Of the foodstuffs Snow et al. studied, these were the most representative of a broad class of museum objects, cellulosic and proteinaceous. These data and the fitted curve (solid blue) appear in previous Canadian Conservation Institute (CCI) publications, such as Figure 4 in Agent of deterioration: incorrect relative humidity and Technical Bulletin 23 Guidelines for Humidity and Temperature for Canadian Archives. Figure 1 is also a figure in the 1999 to 2023 editions of the chapter “Museums, Galleries, Archives, and Libraries” in the ASHRAE Handbook: Heating, Ventilating, and Air-Conditioning Applications. The relative humidity (RH) equation for this curve (shown in the legend at the top right) is used to calculate the “probable time for noticeable mould” in the Mould Calculator of ClimaSpec found in the left-hand menu.

More recently, Strang (2012) compiled more data from research that used media designed to maximize mould growth, especially gelatin. Gelatin is the mould-sensitive layer in photographic materials, the sized canvas of paintings and their linings and glue-sized papers. Figure 1 summarizes the key parts of his compilation. The black vertical lines span the range of times reported at each RH for fructification. These are consistent with the double red line for visible mycelia, inasmuch as fructification would occur after growth of mycelia, that is, would take slightly longer (be higher than the double red line). The germination data (a large cloud in Strang’s original graphs) is represented here by just the outer edge of that cloud, indicating the shortest times reported for germination at each RH (the white crosses). The dashed blue line is fitted so as to just skirt outside these white crosses. The calculator uses the equation for this dashed blue line (shown in the legend in the top right corner) to provide the shortest probable time for germination of spores.

Note: Numbers in Table 1 have been rounded to one or two significant digits.

Static versus dynamic relative humidity

Sedlbauer (2001) developed a dynamic model for mould growth during fluctuating conditions that has been incorporated into the building performance software known as WUFI (Wärme Und Feuchte Instationär / transient heat and moisture transport). Such dynamic models are beyond the scope of the Mould Calculator in ClimaSpec. Instead, we consider static conditions, using data from numerous studies that maintained constant RH, as plotted in Figure 1, and temperature.

Conservatively, you can apply the calculator to two fluctuating conditions. If RH is fluctuating but always above 65% RH, then enter the RH of the most humid periods into the calculator. (This provides a precautionary value: the shortest possible time for growth.) If and when RH drops below 65% and does so long enough for the materials to reach equilibrium with this lower RH, then any mould that was growing can be considered dead. (The cycle of growth must begin again from spores when RH goes above 65%.)

Multiple tactics for practical prevention of mould

Preventive conservation against mould is multifaceted. It is unusual (though not impossible) for high RH (damp) to occur uniformly and in a stable manner throughout a room. Mould is usually a localized event, triggered by external sources of water, condensation, poor ventilation, inappropriate packaging, temperature gradients, etc. (consult figures 5 and 6 in Agent of deterioration: incorrect relative humidity). Cleanliness of the objects also plays a role, not just in terms of spores but also in terms of nutrients that sustain mould growth. Methods for controlling these factors and many more are described in detail in Technical Bulletin 26 Mould Prevention and Collection Recovery: Guidelines for Heritage Collections.

Health issues

Mould is a great risk to occupants of the space, not just to the collections. When confronting mould events, please refer as soon as possible to Technical Bulletin 26 Mould Prevention and Collection Recovery: Guidelines for Heritage Collections. For a more detailed text on health issues with mould, as well as the numerous situations that support mould in buildings, consult Adan and Samson (2011).

Explanation of the Lifetime Calculator

Stefan Michalski

This section provides technical background to the Lifetime Calculator that is part of ClimaSpec. This calculator provides estimates of the lifetime of organic objects that decay rapidly by chemical processes at moderate temperatures and RH as well as the improvements possible by various patterns of colder or drier conditions. (Some of the content of the following sections appeared first in the 2019 edition of the American Society of Heating, Refrigerating, and Air-Conditioning Engineers [ASHRAE] chapter, prepared by the author as a member of the committee responsible for that chapter. It has been revised here.)

Estimates of object lifetimes at room temperature, as listed in Table 2 and provided in ClimaSpec, can vary. The lifetimes may be up to three times shorter or longer than those stated for each object. Likewise, when choosing a lower temperature and lower RH, using the best available models and data, the subsequent lifetime improvement may vary from the prediction. This is due primarily to uncertainty in the activation energy, as illustrated by the shaded areas in Figure 2. Despite these uncertainties, calculators of the lifetime benefits of cold and dry storage are considered useful by the authors cited as well as the research institutions that they represent.

To begin, two simple rules of thumb

Before engaging with charts, calculators and equations, a simple rule of thumb quantifies what is at stake: a drop in temperature of 5°C (for example, from 21°C to 16°C) doubles the object’s lifetime. This is true for materials that decay rapidly by chemical processes at normal storage conditions (for example, poor-quality paper, many photographic films and magnetic tapes and discs). Another drop of 5°C doubles the object’s lifetime again. Thus, a drop from 21°C to 11°C quadruples lifetime. And so on. Conversely, each rise of 5°C cuts lifetime in half.

A second rule of thumb is that a reduction in RH by one half (for example, 50% to 25%) doubles (or more) the object’s lifetime (Michalski 2002).

These rules of thumb can set the stage for the consideration of temperature-controlled storage. However, calculating complex seasonal scenarios for energy savings is necessary when fine-tuning the balance between preservation costs and sustainability or when considering the impact of intermittent exposure to warm conditions or thermal pest control events. The Lifetime Calculator in ClimaSpec serves this need.

The idea of object lifetime

There are three outputs from the Lifetime Calculator:

• a benchmark lifetime for the selected object at moderate temperature (about 20°C) and moderate RH (about 50%);
• the lifetime multiplier at a selected temperature and RH scenario; and
• the product of the first and second, that is, the predicted lifetime at the selected scenario.

“Lifetime” has a clear and unambiguous meaning (more or less) when applied to humans. For deteriorating objects, however, “lifetime” becomes ambiguous. To specify it, we must make three difficult judgments:

• What is the cultural value or utility of the object, such as art objects with aesthetic value or documents kept as records of information?
• Are there measurable characteristics that affect value, such as yellowing, loss of strength or loss of readability?
• What is the criterion for unacceptable loss of a particular characteristic, for example, unacceptable yellowing for use on display or insufficient document strength for direct access by researchers?

These definitions are unambiguous for only a few types of heritage objects. For example, when digital media or magnetic media become unreadable, it is clear that their archival utility as information carriers has “died.” The Lifetime Calculator in ClimaSpec always provides a description of the characteristic that is being assigned to the lifetime estimate and, if possible, of the impact on the object’s utility. However, you should always interpret the loss of utility and value within your own context. An unreadable videotape may be dead to an archive and partially dead for a video installation in an art gallery but still useful in a room that displays the technology of a 1980s home.

In order to justify and design cold storage, you might avoid all the uncertainty of these cultural judgments and simply consider the relative improvement in collection lifetime provided by colder and drier conditions, such as “10 times longer” (which the Lifetime Calculator provides). However, given the costs of colder and drier storage, you still need to establish that, without such storage, the lifetimes of the objects in question are somehow too short when considering the institution’s preservation mandate. In another instance, you might need to establish whether the lifetime of some materials will be significantly shortened by undergoing a high-temperature pest control treatment.

In archives, it has become common practice to use cold storage for entire collections (photographic films is one example). This is not the practice in museums and art galleries, which can lead to the decay of many 20th-century objects within a curator’s lifetime. These objects include rubber, celluloid, acetates, polyurethane foams, colour photographs, etc. (consult Table 2, right-hand column).

Historical evidence for benchmark lifetimes

Benchmark information in Table 2 was first compiled in Technical Bulletin 23 Guidelines for Humidity and Temperature for Canadian Archives. Extensive notes and references for most of the materials in the table are contained in that publication. When the table was next prepared for the CCI resource Agent of deterioration: incorrect temperature, non-archival materials were added. However, optical disc entries were deleted because more specific lifetime estimates had become available in CCI Note 19/1 Longevity of Recordable CDs, DVDs and Blu-rays. Lifetimes range from 5 years to over 100 years, depending on the manufacturing process.

The final version of the table is used elsewhere on the CCI website and was also included in the 2019 and 2023 editions of the ASHRAE chapter “Museums, Galleries, Archives, and Libraries.”

In ClimaSpec, these and other sources are used to provide benchmark lifetimes.

Logarithmic categories for material lifetimes

Timelines for our own lives or for historical events usually consist of uniform, linear steps of years or decades. This does not work well for the categories of chemical lifetimes of materials, which are best spaced as multiples. For example, each category can be several times more durable than its neighbour. The question becomes: how precisely can we segregate such categories? CCI has found that the categories used in Table 2 (30 years, 100 years, 300 years and 1000 years) are sufficient to capture practical generalizations. In technical terms, these categories follow a logarithmic scale (base 10), with two steps for each log unit. The midway point between 1 and 10 is 10^½ = 3.16, which is rounded to 3 for simplicity.

For a few well-studied materials, such as paper and photographic film, assuming you know the acidity and have a precise definition of end of life, you might be able to make more precise predictions than implied by these logarithmic categories. In general, to say that a material such as acidic paper is in the 100-year group of Table 2 means that its lifetime is probably around 100 years; however, it might be anywhere from a factor of three smaller to a factor of three larger. Thus, each category has an uncertainty extending to its adjacent categories.

Plotting the effect of temperature on lifetime

The key chemical parameter for predicting the effect of temperature change on the lifetime multiplier is the activation energy (E_a). A compilation of activation energies for organic materials in heritage collections (Reilly et al. 1995; Nishimura 1996; Michalski 2002), such as paper, film, photographic dyes, magnetic media and resin varnishes, shows that the activation energy of more than three quarters of the materials studied falls within the range of 80 to 120 kJ/mol. A recent study of the thermal decay of the strength of wood yields E_a = 85 kJ/mol, so also within this range (Froidevaux and Navi 2013). Most recently, values ranging from 93 kJ/mol to 130 kJ/mol were measured in different modern printing papers. In Figure 2, this total range of 80 kJ/mol to 130 kJ/mol is shown by the grey shaded area.

This range of activation energy can also be derived theoretically with no consideration of specific materials other than stipulating that the chemical process takes at least several decades to approach completion at room temperatures (Michalski 2002). Thus, both the empirical data and the theory suggest that this range of activation energy can be used as a universal value for heritage materials, such as those listed in Table 3. The middle value of this range, 100 kJ/mol, a convenient round number, was selected for the graphs of lifetime multipliers in Technical Bulletin 23 Guidelines for Humidity and Temperature for Canadian Archives.

Note: Numbers in Table 3 have been rounded to one or two significant digits.

For materials that decay significantly within a few decades or less, such as polyester polyurethane that can turn to powder (the weak link in magnetic media and a material popular with artists in the late 20th century) or natural resin varnishes that yellow unacceptably, activation energies fall into a lower range of 60 to 80 kJ/mol (Michalski 2000), indicated by the striped zone in Figure 2.

Plotting the effect of relative humidity on lifetime

Although all authors agree on the role of temperature and activation energy in calculating the lifetime multiplier, a variety of models exist for calculating the effect of RH. All agree that lower RH decreases the rate of decay, but by exactly how much remains uncertain, simply because there is not enough experimental data to confirm one model over another.

The five most widely known models, in chronological order, are as follows (the technical basis of each model is discussed in a later section, Equations for lifetimes):

1. Sebera (1994) popularized his earlier pioneering work in a report for the Commission on Preservation and Access. He coined the term “isoperms” for lines of equal lifetime in charts, such as in Figure 4.
2. The Image Permanence Institute’s preservation index, originally provided as a preservation wheel, is now available in a web app, eClimateNotebook. The tool is based on the table of multipliers published by Reilly et al. (1995).
3. Equations and charts were published in Technical Bulletin 23 Guidelines for Humidity and Temperature for Canadian Archives.
4. Equations and charts were published in journal articles by researchers from University College London and the National Archives, London (Strlič et al. 2015).
5. Equations and charts were published for specific types of printing paper by researchers from CCI and the Centre de recherche sur la conservation (Paris) (Tétreault et al. 2023). These are also available as a calculator (Paper Permanence Calculator) on the Preventive conservation tools page.

The predictions of the five models for the effect of RH on lifetime relative to lifetime at 50% RH are plotted in Figure 3. In the region from 30% RH to 60% RH, the models overlap with no practical differences in their predictions. Dropping from 50% RH to 25% RH increases lifetime by two or slightly more for all models, as suggested earlier in the rule of thumb. Conditions above 60% RH should be avoided anyway to reduce the risk of gelatin layers in photographs sticking to adjacent surfaces and the risk of mould, which begins at 65% RH (consult the Mould Calculator in ClimaSpec). Generally, conditions below 25% RH should be avoided to reduce the risk of deformation or fracture.

In summary, the five models give similar predictions in the region that is considered practical for most collections. That said, the possible mass desiccation of collections, such as newspaper stacks, that can tolerate RH below 25% (which would be much less energy intensive than equivalent cold storage) depends very much on which model is best at predicting lifetime multipliers below 25% RH.

Plotting the effect of temperature and relative humidity on lifetime

Sebera (1994), the first author to propose a graphical representation of the relationship between lifetime, temperature and RH, used a rectangular graph as shown in Figure 4 and called the lines of constant lifetime “isoperms.” Strlič et al. (2015) proposed the term “isochrones.” Figure 4 plots current models #2, #3, #4 and #5. Although the authors of model #5 propose different E_a for different types of printing papers, their model is plotted for E_a = 101 kJ/mol. According to the authors, this is consistent with the E_a for acidic newsprint.

These four models give almost identical results in the practical range of RH (60% down to 30%) and in the majority of the practical range of temperatures. The IPI model does predict that one needs temperatures that are up to 3 degrees less then the other two models suggest for the same lifetime, but this is not a significant difference when deciding to adopt cool or cold storage.

Rather than one CCI model, all four current models (#2, #3, #4 and #5) are presented in Figures 4 and 5 and associated tables and in the section Equations for lifetimes. This is done for two reasons: to provide the reader with an impartial comparison of current models; and to demonstrate that, while the differences are interesting to the researchers, the practical advice is identical: use cool or cold storage for rapidly decaying objects whenever possible.

Figure 5, a psychrometric chart, is an alternative graphical representation of lifetime multipliers (isoperms, isochrones). This chart shows the conventional way that engineers map temperature and RH when designing systems. The horizontal axis is temperature, and the vertical axis is the weight of water vapour in the air (absolute humidity). RH becomes a set of curved lines (from 10% up to the maximum of 100% RH).

If, for example, you want to find combinations of temperature and RH to give materials lifetimes that are 10 times longer than shown in Table 2, look for the plots labelled “×10” in Figures 4 or 5 (or in Table 5, the column labelled “×10”), and you will find that for 50% RH, the three models range between 3°C and 5°C, so about 4°C. If you choose 30% RH, then the ×10 multiplier is at 7°C to 9°C, so about 8°C.

Notes:

1. Some values shown in Table 5 go beyond the scale in Figures 4 and 5.
2. Model #5 is calculated based on the newsprint that the authors analyzed and whose E_a = 101 kJ/mol.

ClimaSpec allows complex scenarios

The Lifetime Calculator in ClimaSpec has several advantages over charts and tables:

• It allows you to enter complex scenarios with seasonal setbacks month by month for energy savings.
• It allows the calculation of the effect of occasional removal from storage to warmer or more humid conditions.
• Where available, it uses specific values of activation energy for the material.

The Lifetime Calculator defaults to model #3, consistent with other CCI publications.

Equations for lifetimes

All lifetime calculators proposed in the conservation science literature recognize that for organic materials that decay rapidly due to chemical instability (such as materials listed in the right-hand column of Table 2), the mechanism is acid hydrolysis. It increases with the acidity of the material, RH and temperature. The lifetime can be expressed as the product of three functions (f): one function dependent on the acidity of the material, one dependent on temperature and one dependent on RH or, for some authors, the related parameter, moisture content.

Equation 1: t_L = C * f(pH) * f(T) * f(RH, MC)

Where

C = a constant for each material, units of time

pH = acidity of the material

t_L = lifetime, units of time

T = temperature, K

RH = relative humidity, dimensionless

MC = moisture content (of the material), dimensionless

The equation for the dependence of lifetime on temperature (the second term in Equation 1), named after its discoverer, Svante Arrhenius, has been used for practical chemical engineering for over a century. In terms of lifetime (rather than the reciprocal, rate of reaction), the Arrhenius equation becomes:

Equation 2: f(T) = exp(E_a/(R*T))

Where

R = Gas (Boltzmann) constant, 8.314 J/(mol·K)

E_a = activation energy, J/mol

For ease of comparison, the five authors’ proposals for the dependence of lifetime on RH and temperature have been rearranged into the same general form of Equation 1. The purpose of presenting these five proposals is not to imply any preference, nor to offer any critique of their respective validity. Each has been published in peer-reviewed publications over the last 30 years. Rather, the purpose is to show that, despite the differences in their derivation and their sample materials, their predictions of the benefit of cool and cold storage converge in ranges practical for collections managers.

In each of the following equations, the constant (C) has been set so that the equation gives the lifetime multiplier (t_LM) in comparison to the lifetime at 20°C and 50% RH. For clarity, the activation energy term has been placed in curly brackets { }.

Model #1

Although not plotted in Figures 4 or 5, Sebera’s (1994) model for isoperms is noted here for its historical significance in the field of archive preservation. Sebera used a modified form of the Arrhenius equation; it includes a second dependence on temperature placed outside the exponential. Subsequent authors omitted this since it has a relatively minor effect. For activation energy, Sebera reviewed available data on paper and proposed a range between two values: 125 and 146 kJ/mol (25 and 35 in his original units of kCal/mol). His estimates of E_a are above the currently accepted values (from later studies), so his isoperms exaggerate the benefit of cold storage. In the absence of any data to the contrary, he assumed that lifetime was simply proportional to RH. Sebera’s equation becomes:

Equation 3: t_LM = C * 1/T * exp[{125 or 146}/(R*T)] * (1/RH)

Where

t_LM = lifetime multiplier, relative to a value of 1 at 20°C and 50% RH

Model #2

The authors (Reilly et al. 1995) derived parameters from extensive data on acetate film. The equations were not published verbatim, but the authors’ published table of lifetime multipliers can be fitted to the following equation. The RH term has a small temperature correction. The equation of Reilly et al. becomes:

Equation 4: t_LM = 4.69E–17 * exp[{94.9}/(R*T)] * exp[RH * (0.02087 *T – 8.79)]

Model #3

The author (Michalski 2000) derived activation energy from a large review of data on paper, film and dyes. The dependence on RH was derived from a re-analysis (Michalski 1993) of extensive paper-aging data at several relative humidities produced by Graminski et al. (1978). Michalski’s equation becomes:

Equation 5: t_LM = 6.17E–19 * exp[{100}/(R*T)] * (1/RH)^1.3

Model #4

The authors (Strlič et al. 2015) derived equations from their extensive data on new as well as old papers. The RH term has a small temperature correction. The equation of Strlič et al. becomes:

Equation 6: t_LM = 9.468E–21 * exp[{119}/(R*T)]

* exp[−36.72 * {ln(1 − RH)/(1.67*T − 741.82)}^{(1/(5.7622 − 0.012*T))]}

Although the full Equation 6 is used for Figures 4 and 5, it is informative to see what model #4 looks like if fitted to an equation of the same form as the one for models #1, #2 and #3. Throughout the practical range of relative humidities (20% to 60%) and the practical range of temperatures (20°C down to −10°C), the following equation gives results within 10% of that of Equation 6 when using an activation energy (E_a) of 100 kJ/mol:

Equation 7: t_LM = 1.00E–17 * exp[{100}/(R*T)] * exp[–3.7*RH]

Model #5

The authors (Tétreault et al. 2023) derived an equation from a study of modern printing papers. Although acidity (pH) played a key role in the lifetime of the types of paper they analyzed, they found that an equation for lifetime multipliers could be independent of acidity. Their primary conclusion was that different groups of modern printing papers had sufficiently different E_a (97 kJ/mol to 130 kJ/mol) such that it was useful to consider those differences, as can be done with the Paper Permanence Calculator that is based on their model and that can be found on the Preventive conservation tools page. Their equation for isoperms, that is, relative lifetime, is as follows (Tétreault et al. 2023; equation 14):

Equation 8: t_LM = 2.46 * exp[(0.572-0.00822*T)RH] * exp[({E_a}]/R)*(1/T – 1/293.15)

For the figures and tables in this document, and for the sake of generalized comparison among models, their model is calculated for E_a = 101 kJ/mol, their value for acidic newsprint.

In summary, when using an equation of the same form as Equation 1, models #2, #3, #4 and #5 all suggest very similar activation energy (E_a), around 95 kJ/mol to 101 kJ/mol. Model #5 does suggest higher values for some types of printing paper.

For the effect of RH, however, there are significant differences between models below 20% RH and above 60% RH. There is not enough data at these extremes of RH to establish which is correct. Among the different models, the RH term differs in two ways. First, authors Reilly et al. (1995), Strlič et al. (2015) and Tétreault et al. (2023) assume that the fundamental variable is moisture content, which does depend in turn on RH, but only when adjusted for different temperatures. Then, authors Sebera (1994) and Michalski (2000) assume that RH is the fundamental parameter. A more important difference, however, is the choice of function: some authors use an exponential function (Reilly et al. 1995; Strlič et al. 2015, Tétreault et al. 2023); others (Michalski 1993, 2000, 2002; Sebera 1994; Erhardt and Mecklenburg 1995; Zou et al. 1996) use a power law, (which includes Sebera’s use of index 1, linear dependence). Models using an exponential function have the odd aspect of implying that hydrolysis continues at 0% RH (that is, without moisture), whereas a power law implies that hydrolysis stops when moisture is absent. Hence, the rapid divergence of the models at RH below 20% (as well as above 60%) in Figures 4 and 5. As noted earlier, this divergence is not of practical impact since no one is currently recommending storage at such low relative humidities (or at high humidities), but it does become relevant when explaining how much the low RH of unhumidified buildings in winter has benefited acidic collections in the past and can again in the future.

Bibliography

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© Government of Canada, Canadian Conservation Institute, 2025

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