Modeling Salt Behavior with ECOS/RUNSALT: Terminology, Methodology, Limitations, and Solutions

Abstract

Damage to porous materials in heritage buildings caused by salt mixture crystallization is driven by the surrounding environmental conditions. To understand the crystallization behavior of a mixed salt solution as a function of changing climatic conditions (i.e., relative humidity and temperature), excluding factors such as the internal pore structure, the thermodynamic model ECOS/RUNSALT is the only freeware available that requires simple input and includes the most relevant ions for heritage buildings and solids. We suggest the use of specific terminology and describe how to use the model and how to interpret the output, with emphasis on key limitations for which solutions are provided. When used correctly, the model output can be trusted, specifically when it is used to inform preventive conservation (e.g., environmental conditions in which salt crystallization cycles should not occur). However, salt mixture kinetics and the internal pore structure remain crucial parameters that are not considered in the model. These aspects need further attention to develop a better understanding and correctly model salt damage in relation to climatic changes.

1. Introduction

Salt deterioration is a common issue when dealing with the conservation of porous materials in built heritage [1,2,3,4,5,6]. However, understanding salt behavior is a complex subject due to the presence of a wide variety of ions [7], which are often the result of groundwater infiltration by capillary rising damp, rainwater infiltration, and atmospheric, biological, or internal material contamination. Over time, these result in an accumulation of salts in the first few millimeters or centimeters of a material’s drying front. Damage to the material occurs when salts fill a porous material and crystallization cycles are provoked by changing environmental conditions. The individual mixture composition found in the material determines the crystallization behavior of each possible solid that can occur, as described by Price and Brimblecombe [8] in the context of porous materials. This behavior is further influenced by a wide range of internal and external factors of the salt-bearing porous material and salt solution properties, such as supersaturation, viscosity, pore characteristics, inner pore processes [9,10,11,12,13,14,15], and ambient environment. The sheer scope of all the parameters involved limits our current understanding of the real-world processes that underpin the damage potential of salts over time. However, the outcomes of specific scientific projects contribute to the understanding of complex salt behavior, as described in Price (Ed.) [16]. This has resulted in a thermodynamic model, Environmental Control of Salts (ECOS), used to determine the environmental conditions needed to reduce salt damage in porous materials. Based on the ECOS model, Bionda [17] developed RUNSALT, which is a graphical user interface (GUI) that takes care of the data pre-/postprocessing and the visualization of outputs. The freeware and published work [18,19,20,21,22,23,24,25,26,27,28,29,30,31] of the first use cases can be found on the RUNSALT website [32].

Since its development, the model has been used extensively to aid management decisions for the preservation of built heritage worldwide. Although a limited amount of literature is available [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50], it is important to note that its use is mostly undocumented in peer-reviewed literature; for example, in Belgium the software has been used for over 300 heritage sites [51]. Like any model, ECOS and RUNSALT have limitations and pitfalls, with ineffective or non-existent transfer from research to practice, a challenge faced more widely in heritage science, as recently explored by Richards and Brimblecombe [52]. Some of these limitations are linked to data processing and issues with the input parameters and outputs. Several of the limitations are reported on and addressed in this paper with the aim to advance the conservation field when considered or adjusted in future versions of the software. Additionally, when dealing with salt crystallization, an ambiguous use of terminology and discrepancies can be found in the literature; thus, specific terminology and abbreviations are suggested for salt mixtures.

2. Models and Theory

When dealing with salt mixtures, there are several models available that output, amongst others, specific saturation, crystallization, dissolution, and transition relative humidity points, that allow a deeper understanding of the mixture behavior under changing climatic conditions. However, most programs or models are designed for specific purposes, such as atmospheric, industrial (brines) or (sea) water chemistry, e.g., FREEZCHEM [53], E-AIM [54,55], and [56,57,58,59,60,61]. Since these programs and models have been developed primarily to address specific applications, they exclude relevant ions and data for salts typically found in building materials [7]. The computer program PHREEQC [62] and the ECOS/RUNSALT model [16,17] are the most cited in literature for this purpose. PHREEQC includes a variety of options and incorporations of ions, such as those described by, e.g., Benavente et al. [63] and Pérez-Diez et al. [64]. However, an important limitation in the aqueous model is the lack of internal consistency in the databases [62]. PHREEQC has a limited pre-installed dataset of solids and non-validated parameters, which the user needs to update. Moreover, experimental data are often lacking or contain inconsistencies in the literature [65]; it is thus a complicated and tedious task to complete the datasets and derive reliable results, particularly for systems containing nitrate. However, the program has potential in stone conservation, as it permits the implementation of, e.g., kinetics and in-pore situations.

ECOS/RUNSALT is currently the only model with simple inputs that include the most relevant salt phases found in the built environment, and can handle more complex systems when compared to PHREEQC. ECOS (Environmental Control of Salts) is a chemical equilibrium model initially developed on the molality-based thermodynamic approach of the ion interaction model of Pitzer [66]. There, the solubilities of the included mineral phases, as well as the water vapor–salt solution equilibrium, are considered. It is based on a molality-dependent expression for excess Gibbs energy which includes empirically determined interaction parameters and, by its minimization, allows the iterative determination of the activity and osmotic coefficient. While the latter coefficient is related to the water activity of the electrolyte solution, the activity coefficient corrects for the non-ideal behavior of ions in the solution. During the development of ECOS, it turned out that the parameterization of the model was well suited for the calculation of solubilities in mixed electrolyte solutions in the desired range, but in combination with the algorithm used for the calculation of the amounts of crystallized salts and solution, partly incorrect results were obtained. Especially in cases of high concentrations, the algorithm based on the original Pitzer molality-based model passed unrealistic conditions in ranges where the model was already invalid. It was possible to overcome this hurdle by using equations in terms of mole fractions [55,67,68,69], which was implemented in Fortran [70]. Having equivalent principles to the molality-based model, the mole fraction one, generally known as the Pitzer–Simonson–Clegg model, includes ion concentrations expressed as mole fractions [71]. Nevertheless, the original molality-based approach was later improved, as described by Steiger et al. [72], and should be considered as a valid alternative. In either case, it must be noted that ECOS always considers equilibrium conditions, neglecting kinetic aspects. Thus, certain metastable pathways are possible, and salt damage is linked to the kinetically driven supersaturation of the salt solution.

To further understand the ECOS calculations, we refer to the literature, e.g., [16,73,74,75,76,77,78], including data related to activity coefficients and (solubility) phase diagrams (solution concentration as molality (number of moles of dissolved salt per kilogram water) (m(salt)/mol·kg⁻¹), volume (V), relative humidity (RH), or water activity (a_w) over temperature (T)). Phase diagrams are best suited for binary or ternary systems to illustrate the crystallization pathways at given concentrations. However, the graphical representation of quaternary or higher systems becomes more complicated. If all data from such phase diagrams should be derived, x-y-z plots are required with, for example, x as RH, y as the number of moles of crystalline salt (n) or volume (V), and z as temperature (T). Such a plot is, in principle, the same as a combination of RUNSALT plots derived from calculations at different T or RH and presented with three axes, as shown by Menéndez [33].

Equilibrium conditions also mean that at each RH, ECOS considers an equilibration with the surroundings. In reality, RH changes are generally faster where non-equilibrium dynamic RH changes occur, so there are larger gradients between the vapor pressure of the solution and the surrounding air influencing evaporation.

When looking at phase diagrams in the context of ions found in building materials, at least senary or septenary systems should be considered that include the most important ions (CO₃²⁻, Cl⁻, NO₃⁻, SO₄²⁻, Na⁺, K⁺, Mg²⁺, and Ca²⁺) while excluding less common ions such as fluoride, phosphate, oxalate, ammonium, acetate, or formate, as previously described [79,80]. Since the least soluble salts will rapidly crystallize from a mixed salt system, carbonates and gypsum can be excluded in most cases. Thus, a senary system of more soluble salts will remain, including Cl⁻, NO₃⁻, Na⁺, K⁺, and Mg²⁺ with either SO₄²⁻ or Ca²⁺, as further described in [7], which is implemented in ECOS.

3. Terminology for Mixed Salt Systems and Methodology for Using RUNSALT

Understanding salt mixture behavior in porous media under changing climatic conditions is not a straightforward task and requires in-depth knowledge of the mixture composition and material characteristics, as well as internal and external factors. A first step, however, is knowing the correct salt mixture present, which requires data input preparation for the model, as described further in Steiger and Heritage [79] and recently verified by applying the method to a large dataset including several additional steps in Godts et al. [7].

Before moving forward with the methodology for using RUNSALT,

Table 1. Overview of terminology and suggested symbols to describe RUNSALT plots showing the crystallization pathway of mixed salt systems under changing RH. Refer also to Figure 1, the legend of Figure 1, and Table 2.

	Meaning	Base Symbol	Species-Specific Symbol 1
	Explanation following RUNSALT plots (example Figure 1)
1.	Mutual crystallization relative humidity	$R{H}_{\mathrm{cry}}^{\mathrm{m}}$	$R{H}_{{\mathrm{cry}}_1}^{\mathrm{m}}$
	RH point at the onset of any line shown in a plot corresponding to the start of crystallization; the number shown in the specific symbol refers to the species/solid in order of appearance from a humid to a dry environment. The use of the number (e.g., 1) in relation to the solids can be useful to understand the sequence of crystallization. The solution at this point is saturated with respect to a specific solid. When available, the first letters of the mineral name or chemical formula can used to replace the number, e.g., $R{H}_{{\mathrm{cry}}_1}^{\mathrm{m}}$ is aphthitalite = aph and thus $R{H}_{{\mathrm{cry}}_{\mathrm{aph}}}^{\mathrm{m}}$ (letter A in Figure 1). Aphthitalite is the first that crystallizes in the mixture and the same base symbol is used for the mutual crystallization relative humidity of all solids that crystallize (indicated with the letter B in Figure 1). This is only relevant when solution is still available before crystallization takes place (reactions in solution in Table 2).
2.	Mutual dissolution relative humidity	$R{H}_{\mathrm{dis}}^{\mathrm{m}}$	$R{H}_{{\mathrm{dis}}_1}^{\mathrm{m}}$
	RH point at the end of a horizontal line in a plot, looking from a dry to a humid environment, equals the start of dissolution; e.g., in Figure 1 this is illustrated by the RH points indicated with the letter C, and thus when solution becomes available.
3.	Mutual deliquescence relative humidity	$R{H}_{\mathrm{del}}^{\mathrm{m}}$	$R{H}_{{\mathrm{del}}_1}^{\mathrm{m}}$
	RH point at the end of a horizontal line in a plot when no more solution is available, looking from a dry to a humid environment, e.g., indicated as letter D in Figure 1. Here, the last solid that crystallizes is darapskite, and afterwards no more solution is available. Thus, $R{H}_{{\mathrm{del}}_{ \mathrm{dar}}}^{\mathrm{m}}$, as further illustrated by reaction number 2 shown in Table 2.
4.	Mutual transition relative humidity	$R{H}_{\mathrm{tra}}^{\mathrm{m}}$	$R{H}_{{\mathrm{tra}}_{[3-5]}}^{\mathrm{m}}$
	RH point at which salt transitions occur. The numbers refer to the solids involved in the transition, starting with solids before the dash (e.g., 3 in [3–5]) at more humid conditions transitioning to solids after the dash (e.g., 5 in [3–5]) at dryer conditions. Either a phase change (hydration, dehydration), decomposition, or the formation (addition) of solids occur under both wetting and drying conditions. For example, the transition of mirabilite to thenardite is $R{H}_{{\mathrm{tra}}_{[\mathrm{mir}-\mathrm{the}]}}^{\mathrm{m}}$, or is more complicated, as shown by reaction 3 in Table 2 (letter E in Figure 1).
	Additional terms that are useful when calculating water activities or concentrations. Values that are not included in the RUNSALT output data yet could be derived from the ECOS calculations.
5.	Mutual equilibrium relative humidity	$R{H}_{\mathrm{eq}}^{\mathrm{m}}$
	Any RH point at which a solution is in equilibrium with its environment = water activity at any concentration if solution is available, e.g., in Figure 1 any RH point above D, and thus $R{H}_{{\mathrm{del}}_{\mathrm{dar}}}^{\mathrm{m}}$.
6.	Mutual saturation relative humidity	$R{H}_{\mathrm{sat}}^{\mathrm{m}}$
	Any RH point at which a solution is saturated (points on the curves, e.g., in Figure 1, all RH points between A and C on the curve of aphthitalite crystallization), equal to the $R{H}_{\mathrm{eq}}^{\mathrm{m}}$ points during crystallization (when solid and solution are available).

¹ For practical considerations, double subscripts can be replaced by a comma between subscripts, e.g., RH^m_cry,aph.

is given to overcome the ambiguous use of terminology found in the literature and to clarify the crystallization pathways of mixed salt systems shown in RUNSALT plots (see example Figure 1). Specific RH points of interest are linked to the suggested symbols presented in the table, and the letters A to F are further detailed in the legend of Figure 1. Note how RH points of interest overlap depending on how a plot is read from a humid to a dry environment or vice versa. The term mutual (m) is chosen as the behavior of each solid is influenced by the mixture composition, and m is removed when dealing with single salts. The symbols are recommended for future use to make scientific information comparable.

The reactions presented in the RUNSALT plot shown in Figure 1 are further detailed in

Table 2. Summary of the reactions under drying conditions shown in the RUNSALT plot (Figure 1, noted as # 1, 2 and 3 above the figure).

Start Composition of the Solution (mol): 2Na+ + 2K+ + 1Cl− + 1NO3− + 1SO42−
#	Reactions in solution
1.	2Na+ + 6K+ + 4SO42− → Na2SO4∙3K2SO4 (cr)
2.	Na2SO4∙3K2SO4 (cr) + 11Na+ + Cl− + 10NO3− + 4H2O → NaCl (cr) + 6KNO3 (cr) + 4NaNO3∙Na2SO4∙H2O (cr)
	Solid-state reactions
3.	6NaNO3∙Na2SO4∙H2O (cr) + Na2K SO4)4 (cr) → 6KNO3 (cr) + 10Na2SO4 (cr)

.

Legend by Figure 1, with the letters A to F indicating specific RH points of interest:

A.

The first mutual crystallization relative humidity of the mixture ($R{H}_{{\mathrm{cry}}_1}^{\mathrm{m}}$) represents the RH at which crystallization initiates for the first solid that appears under drying conditions (aphthitalite here, and thus $R{H}_{{\mathrm{cry}}_{\mathrm{aph}}}^{\mathrm{m}}$). The solution is saturated with respect to aphthitalite, and above this RH all solids are dissolved.

B.

The mutual crystallization relative humidity of all the following solids that crystallize from the solution in the mixture, and thus is the RH at which crystallization first begins for $R{H}_{{\mathrm{cry}}_{\mathrm{hal}}}^{\mathrm{m}}, R{H}_{{\mathrm{cry}}_{\mathrm{nit}}}^{\mathrm{m}} \mathrm{and} R{H}_{{\mathrm{cry}}_{\mathrm{dar}}}^{\mathrm{m}}$.

C.

The mutual dissolution relative humidity of all solids in the mixture when solution becomes available is equal to the RH points when a crystal starts to dissolve for $R{H}_{{\mathrm{dis}}_{\mathrm{aph}}}^{\mathrm{m}}, R{H}_{{\mathrm{dis}}_{\mathrm{hal}}}^{\mathrm{m}}, R{H}_{{\mathrm{dis}}_{\mathrm{nit}}}^{\mathrm{m}} \mathrm{and} R{H}_{{\mathrm{dis}}_{\mathrm{dar}}}^{\mathrm{m}}$. B and C are often at the same RH; here, the resolution of the plot distorts the position for halite and niter, a phenomenon explained further on.

D.

The mutual deliquescence relative humidity of the mixture is the RH determined by the solids in the mixture at which the first dissolution starts to occur and solution becomes available; here, $R{H}_{{\mathrm{del}}_{\mathrm{dar}}}^{\mathrm{m}}$ also equals the dissolution relative humidity of $R{H}_{{\mathrm{dis}}_{\mathrm{aph}}}^{\mathrm{m}}, R{H}_{{\mathrm{dis}}_{\mathrm{hal}}}^{\mathrm{m}} \mathrm{and} R{H}_{{\mathrm{dis}}_{\mathrm{nit}}}^{\mathrm{m}}$.

E.

The mutual transition relative humidity $R{H}_{{\mathrm{tra}}_{[\mathrm{dar}/\mathrm{aph}]-[\mathrm{nit}/\mathrm{the}]}}^{\mathrm{m}}$. Here, under drying conditions, thenardite is formed and the amount of niter increases from the decomposition of darapskite and aphthitalite in a solid-state reaction.

F.

Plot stacking artifact caused by transition reactions, herein identified by chloride that is not available in other solids.

As described in the previous section, the ions used for the model input are Cl⁻, NO₃⁻, Na⁺, K⁺, and Mg²⁺, with either SO₄²⁻ or Ca²⁺. This excludes, amongst others, carbonates and the equimolar contents of calcium and sulfate, with the latter considered as the gypsum content. Hence, the model primarily calculates a maximum of six ions. The system composition is entered into the RUNSALT interface as mol or weight, with the selection of either a RH range between 15% and 98%, or a T range between −30 and +50 °C, after which either the T or RH value is fixed. The RUNSALT interface generates a temporary .DAT file that includes the inputs required by the model. These inputs are read in by the batch executable .EXE file which then initiates the model. In another temporary file, ECOS outputs the equilibrium composition at 50 equally spaced intervals for either the specific temperature or humidity range, and is then read by RUNSALT to produce a graphical representation of the crystallization behavior. The output can be exported in graphical and textual (.CSV) formats for further analysis through RUNSALT.

The crystallization behavior of the mixture is graphically represented by RUNSALT with the specified relative humidity (RH) or temperature (T) range on the x-axis, while the y-axis returns the amount of substance (mol) (Figure 1). After the plot is generated, one can choose to show the y-axis as volume (V) in cm³ (molar volume of salt, that is, equilibrium crystal volume) (Figure 2), which gives a more realistic visualization of the salt content in the pores. For example, aphthitalite is present in approximately one tenth of the total mol content (Figure 1), and at least a third of the total solid volume (Figure 2). The latter is thus more indicative of risk in the pore structure and will determine the overall interpretation and conservation advice. The use of volume in the outputs was recently illustrated in relation to climatic conditions by Costa et al. [81]. Expressing the results as volume is additionally useful to estimate pore filling, as the molar volume (V_m) can be used as an input value in the calculation, as described in Gulotta et al. [82]. All values on the y-axis are cumulative (stacked), meaning that the amount of the first solid should be deducted from the second to know the absolute value of each individual solid. The individual amount of salt is illustrated for halite (NaCl) at the given RH with the arrow in Figure 1.

As the data points are systematically calculated for 50 points within the chosen range of environmental parameters (RH or T), the smaller the range the higher the resolution. Hence, data related to smaller successive intervals can be stitched together to obtain a more detailed output. However, changes in stacking order in the detailed plots can occur at higher resolution. This process can be an important step to correct certain artifacts caused by the resolution of the chosen environmental parameters. For example, in Figure 3, if the RH range between 60 and 70% is entered into RUNSALT, the resolution of the plot increases to 0.2% RH, as opposed to 1.6% RH when generating a plot from 15 to 95% RH (Figure 1). Thus, the thermodynamically calculated mutual relative humidity points of interest, for example, $R{H}_{{\mathrm{cry}}_{\mathrm{nit}}}^{\mathrm{m}}$ and $R{H}_{{\mathrm{cry}}_{\mathrm{hal}}}^{\mathrm{m}}$, are more accurate. The plot also shows that $R{H}_{{\mathrm{cry}}_{\mathrm{dar}}}^{\mathrm{m}}$ or $R{H}_{{\mathrm{del}}_{\mathrm{dar}}}^{\mathrm{m}}$ is equal to $R{H}_{{\mathrm{dis}}_{\mathrm{nit}}}^{\mathrm{m}}$, $R{H}_{{\mathrm{dis}}_{\mathrm{hal}}}^{\mathrm{m}}$, and $R{H}_{{\mathrm{tra}}_{\left[\mathrm{aph}\right]-\left[\mathrm{hal}/\mathrm{nit}/\mathrm{dar}\right]}}^{\mathrm{m}}$. The resolution makes little to no difference to the final conservation advice given to the field in terms of the risk assessment of RH ranges of crystallization/dissolution. However, selecting a narrower range in the environmental parameters can clarify certain artifacts and uncertainties in the plot. In particular, the slightly non-vertical lines of aphthitalite, halite, and niter are caused by the resolution 0.2% RH, and these lines are in fact to be read as vertical (location shown by the dashed rectangles in Figure 2 and Figure 3). The same is true for the gap (transition $R{H}_{{\mathrm{tra} }_{\left[\mathrm{dar}/\mathrm{aph}\right]-\left[\mathrm{nit}/\mathrm{the}\right]}}^{\mathrm{m}}$) and all non-vertical lines at lower RH at approximately 43% (shown in Figure 2).

When reading the complete RUNSALT plot, we can start looking at the x-axis from a more humid environment on the far right (95% RH) to a dry environment on the far left (15% RH). Under more humid conditions, and before the first line appears, all salts are in solution. The solution has a certain concentration corresponding to the given RH; the further away from the first solid, the more the solution is diluted, which is theoretically infinite until pure water is reached at 100% RH. Just before the RH at which the first solid crystallizes (for example, in Figure 1, aphthitalite (Na₂SO₄∙3K₂SO₄)), the solution is at its highest degree of saturation. The solution is saturated and in equilibrium with the environment, and is referred to as mutual saturation relative humidity ($R{H}_{\mathrm{sat}}^{\mathrm{m}}$). In a mixture, this can be defined at any RH point where curved lines are visible in the RUNSALT outputs. The lines indicate the crystallization of a solid. Looking further at Figure 1, aphthitalite starts to crystallize at approximately 92% (20 °C); this point is the mutual crystallization relative humidity of the solution ($R{H}_{\mathrm{cry}}^{\mathrm{m}}$). Following the crystallization of aphthitalite to dryer conditions, the remaining ions are still in solution and become more concentrated until halite starts to crystallize, followed by niter and darapskite. Each solid has a crystallization relative humidity ($R{H}_{\mathrm{cry}}^{\mathrm{m}}$) of 67, 66, and 64% (±0.1), respectively. Similar to aphthitalite, for both halite and niter, the solid amount increases over a RH range, while all darapskite crystallizes at a specific RH point, as shown in Figure 3. This RH of 64% is also the point at which no more solution is available. This is the mutual deliquescence relative humidity ($R{H}_{\mathrm{del}}^{\mathrm{m}}$) of the mixture.

Looking further down the remaining crystallization pathway at dryer conditions below $R{H}_{{\mathrm{cry}}_{\mathrm{dar}}}^{\mathrm{m}}$ (=$R{H}_{\mathrm{del}}^{\mathrm{m}}$ of the mixture), while keeping in mind that no solution is available, the following solid-state reactions can be observed. First, a small amount of aphthitalite decomposes at the same RH as $R{H}_{{\mathrm{cry}}_{\mathrm{dar}}}^{\mathrm{m}}$, and from 64% to 43% RH all solids remain crystallized. For this mixture, the RH of 64% is the most important to avoid crystallization cycles and damage to porous materials. In practice, it would be common to advise a stable RH between 50% and 60% RH at 20 °C; that is, if all water sources are eliminated, other artifacts in the area remain well preserved under these conditions, the mixture compositions are representative for the entire salt risk assessment, and the location allows such a narrow range of RH to be maintained. However, some flexibility should be considered, specifically toward the lower RH range as the solid-state reactions might have limited effect on the substrates. Additionally, an RH increase over a limited time should be acceptable due to the kinetics considering dissolution/crystallization rates [43]. However, more research is needed to further understand these processes.

As shown in Table 2, the formation of thenardite is the result of the decomposition of aphthitalite and darapskite, which also explains the increase in niter at the same RH of approximately 43%. The decrease in halite at the same RH is an artifact of plot stacking (amount of substance or volume) on the y-axis. This can be derived from the fact that no other salt is formed with Cl⁻. In drier conditions (below 43%), all salts remain crystallized.

Looking back at higher RH in the figures, it is important to understand that, for example, aphthitalite in the system will only start to dissolve if all other salts have gone into solution and the solution has reached the specific dilution above 64% RH. Specifically, the dissolution of aphthitalite is dependent on the concentration of the surrounding solution. The solution will accumulate moisture, which can cause discoloration, moisture stains, the peeling of paint layers, and attract biological growth. At $R{H}_{{\mathrm{cry}}_{\mathrm{aph}}}^{\mathrm{m}}$ of 92%, the solution is saturated with respect to aphthitalite. Above this RH point, the solution becomes further diluted (until infinity at 100%). The amount of water vapor absorbed by the solution at a given RH can be calculated with ECOS; however, the data are currently not given in RUNSALT. Details on the backend calculations of the model are extensively described in Price et al. [16].

The above example shows the value of the model to derive specific advice for environmental salt risk assessment. The model has proven extremely valuable for the field and certain aspects have been verified with four ion mixtures by Rörig-Dalgaard [83]; however, several limitations and issues should be taken into consideration before application. In the following, the most common limitations and solutions are provided, while we abstain from considering deviations in the crystallization pathways if a solid becomes isolated from the remaining solution.

4. ECOS/RUNSALT Limitations and Solutions

Comparable to any model, ECOS/RUNSALT has limitations and pitfalls. An important obstacle in the calculations is caused when there are extremely high concentrations or supersaturation in hygroscopic mixtures, including calcium nitrate and calcium chloride, resulting in water activities higher than expected from thermodynamics. This obstacle was overcome by the incorporation of certain assumptions and non-verified solids, such as MgCa(NO₃)₄∙10H₂O, which rarely appears in the outputs. However, it is as yet unclear whether extreme hygroscopic solids crystallize in these conditions.

Concerning the input data, an issue occurs with the autobalance option in RUNSALT. When using theoretical charge input data with integer numbers (e.g., 1Cl⁻ and 1Na⁺), the autobalance works correctly. However, with experimental output of ion analyses, values with several decimal places are common and the autobalance only corrects the chloride content, rendering the output incorrect. It is thus recommended to abstain from using the ‘autobalance’ feature and consider the use of charge balance calculations as described in [7], including the downloadable calculation sheet and R script (.R and .xlsx) at [51]. Furthermore, an error message can occur due to rounding issues produced by the thermodynamic calculations, which is caused by the number of decimals of each ion value entered. This can be resolved by changing the place values of all ions equally to ones, tens, hundreds, or thousands, depending on the initial concentration; although the total amount on the y-axis (mol or volume) varies, the output remains identical.

In certain cases, an error message appears when either entering the full RH range from 15 to 98% as input in the environmental parameters, or under certain temperatures, depending on the mixture composition. Both errors are easily overcome by limiting the RH to 95% or increasing or decreasing the temperature by one to five degrees. In either case, the results obtained from the model for the limitations of output values are considered more than sufficient. Another issue in the environmental parameters is the possibility to use values below 0 °C, although the formation of ice is not incorporated in the outputs. It is thus advised not to use a temperature input values below 0 °C in RUNSALT.

Moving forward to complications specifically related to single salts in the ECOS calculations and RUNSALT outputs, inconsistencies are seen with more recent studies related to Ca(NO₃)₂, K₂SO₄, and MgSO₄ hydrates [84]. The critical RH values calculated by the ECOS of Ca(NO₃)₂, K₂SO₄, and MgSO₄ are presented in the RUNSALT output in Figure 4 and Figure 5, respectively. The crystallization behaviors of Ca²⁺ and NO₃⁻ show two critical RH values (Figure 4, left), the first at 51.82% for tetrahydrate (nitrocalcite) and the second at 37.98% for anhydrous calcium nitrate (at 20 °C RH resolution = 0.02%; resolution not represented in the figure). However, it is known that dehydration of the tetrahydrate only occurs over extended periods of time and at extreme low RH with transition values between the anhydrous di-, tri-, and tetrahydrate at 8.3%, 12.4%, and 20.5%, respectively [75]. Thus, considering that the dehydration of nitrocalcite is kinetically hindered, one can expect that the crystallization RH of the tetrahydrate is the only one to be considered, keeping in mind that more research is needed to understand the in-pore effects under realistic climatic conditions.

The RUNSALT outputs of K⁺ and SO₄²⁻ (calculated at 20 °C) show two critical RH values (Figure 4, right) with a relative humidity crystallization of potassium sulfate monohydrate starting at 97.7%, followed by dehydration to form arcanite at 89.7%. However, as detailed further by Archer and Kirklin [85], it has been found in several studies that the monohydrate phase does not occur below 9 °C, and if stable at all this is less probable at higher temperatures. Furthermore, the RH_cry should decrease with decreasing temperature; currently, the outputs show the opposite at lower temperatures, with a decreasing amount of the monohydrate (not illustrated). Thus, caution should be taken when looking at the critical RH values of potassium sulfate. Here, at 20 °C, K₂SO₄ is likely to start at 97.7% and the monohydrate can be ignored.

For magnesium sulfate (Figure 5), four critical RH values are shown at 20 °C, starting with the crystallization relative humidity, $R{H}_{{\mathrm{cry}}_{\mathrm{eps}}}^{}$ at 91.54% for MgSO₄∙7H₂O (epsomite), followed by the transition to MgSO₄∙6H₂O (hexahydrite), $R{H}_{{\mathrm{tra}}_{[\mathrm{eps}-\mathrm{hex}]}}^{}$ at 81.94%, and to MgSO₄∙4H₂O (starkeyite) and MgSO₄∙1H₂O (kieserite), with $R{H}_{{\mathrm{tra}}_{[\mathrm{hex}-\mathrm{sta}]}}^{}$ and $R{H}_{{\mathrm{tra}}_{[\mathrm{sta}-\mathrm{kie}]}}^{}$ at 62.3% and 27.16%, respectively. However, from experimental results and improved thermodynamic calculations (see [72,84]), important deviations specifically concerning starkeyite are derived. The data show that the values used in ECOS for this phase are inaccurate and no change in the mixtures from one to the other hydrate should be taken into consideration within the range of 5–40 °C. The original data from the ECOS/RUNSALT outputs are shown in Figure 5, while the corrected data are given in Figure 6. Here, at 20 °C, the RH_del of MgSO₄∙7H₂O (epsomite) is 91.2% RH with a transition to MgSO₄∙1H₂O (kieserite) at 46.6% RH; the hexahydrate only occurs at higher temperatures. The latter figure illustrates how ECOS/RUNSALT outputs with a wide RH range calculated in a variety of temperatures will correspond to the phase diagram, following the transition between kieserite, hexahydrite, and epsomite, and the RH_del at different temperatures. In addition to the described issues that should be considered in the model outputs, it remains important to understand that certain phases can be metastable and kinetically hindered, as further described for magnesium sulfates in Steiger et al. [84].

Several solids are missing in ECOS/RUNSALT, although they can play a role in the crystallization pathways and deterioration processes, such as Ca-K-NO₃ double salts [86]. The efflorescence found on monuments [80,87,88,89,90,91,92,93] reveals salts that are currently not available or not consistently incorporated in the model outputs, for example, humberstonite (Na₇K₃Mg₂(SO₄)₆(NO₃)₂∙6H₂O). Moreover, the removal of equimolar contents of calcium and sulfate (gypsum) can alter the RUNSALT outputs, including double salts such as glauberite (Na₂Ca(SO₄)₂), gorgeyite (K₂Ca₅(SO₄)₆∙H₂O), and syngenite (K₂Ca(SO₄)₂∙H₂O). However, the formation of the latter three might be kinetically hindered or occur as solid-state reactions over longer periods of time.

As detailed in [35], the model is not capable of systematically integrating the presence of an equimolar amount of calcium and sulfate ions. In rare cases, when the model allows calculations with calcium and sulfate, the crystallization pathway can change. In these cases, it is often observed that the common salt darapskite (NaNO₃∙Na₂SO₄∙H₂O) is replaced by glauberite (Na₂SO₄∙CaSO₄), as illustrated in Figure 7. As mentioned earlier, several issues are visible in the plot on the right, such as the kinetically hindered solid-state phase change between gypsum and anhydrite. Additionally, due to the stacking of the solids and the RH resolution, the vertical lines for glauberite and nitratine should remain horizontal; thus, the latter is simply an artifact of the gap between the transition $R{H}_{{\mathrm{tra}}_{[\mathrm{gyp}-\mathrm{anh}]}}^{\mathrm{m}}$. Further research is needed to understand the formation of double salts containing calcium and sulfate.

Furthermore, relevant carbonate salts such as thermonatrite (Na₂CO₃∙H₂O), natron (Na₂CO₃∙10H₂O), trona (Na₃CO₃HCO₃∙2H₂O), and kalicinite (KHCO₃) are absent from the model outputs. However, these soluble carbonates are rare and only seen in approximately 2% of samples taken in Belgium heritage [7]. Other rare anions not included but contributing to the total charge balance and crystallization pathway are fluoride, phosphate, oxalate, acetate, ammonium, and formate [79].

5. Discussion and Conclusions

ECOS/RUNSALT is currently the only model that includes the most relevant salt phases found in built heritage. We provide an overview to further the understanding of its use and suggest specific terminology for salt mixture behavior to simplify and clarify the model, and make scientific information comparable. Furthermore, as several limitations and pitfalls exist when using the model, possible incorrect interpretations of the derived outputs can occur. However, when the presented issues and solutions are taken into consideration, the RUNSALT outputs can be considered highly accurate. The most important issues described concern calcium nitrate, potassium sulfate, and magnesium sulfate phases (hydrates), and the possible influence of calcium sulfate on the formation of different solids under specific conditions.

It also remains important to examine the variety of factors that can cause deviations from the modeled crystallization behavior. Some of these factors include the in-pore situation, the material characteristics, impurities in the system, and salt kinetics. The latter is specifically relevant to environmental conditions, the separation of solids from the solution, gradients in solution concentrations, kinetically hindered salt crystallization, and rates of crystallization/dissolution, including long-term solid-state reactions. In any case, if a specific range of RH is considered safe when interpreting RUNSALT outputs, meaning salt crystallization/transition cycles are less likely to occur in the specific environment, the model outputs can be trusted, keeping in mind that different crystallization pathways are possible when certain salts are separated from the solution. Overall, more research is needed considering salt mixture kinetics in the pore system. An important aspect to focus on is the rate at which phase transitions occur, as this can guide conservation scientists towards a better prediction of salt damage in relation to climatic changes over time. Thereby, updates of the current model and wider accessibility of the source codes are important for the future.