Implementation strategies and uncertainties of moisture transport properties in heat,air and moisture (HAM) models: Comparative insights from WUFI and DELPHIN

Abstract

Heat, air and moisture (HAM) models are essential for predicting the hygrothermal behavior of building components. However, their outputs can vary significantly due to differences in how hygrothermal material properties are implemented. This study systematically examines the implementation strategies and related uncertainties of moisture transport properties in two widely applied HAM models, WUFI and DELPHIN, focusing on their parameterization logics governed by different driving potentials: relative humidity and capillary pressure. The first part of the study consolidates the characterization methods, data processing procedures and implementation strategies to bridge experimental data to model inputs. The second part applies this setup in two comparative simulation scenarios: one under “extreme” exposure, representing liquid-dominated transport beyond the hygroscopic range in a single loadbearing material with a finishing layer; and another under “service” conditions, involving an internally insulated concrete wall exposed to 50%–98% relative humidity (RH). Results show that simplified liquid transport formulations markedly distort predictions under over-hygroscopic conditions, while the choice between integral or separate representations of vapor and liquid transport significantly alters the coupled heat–moisture balance. This synthesis identifies inconsistencies between material characterization and its practical implementation and quantifies how these discrepancies affect hygrothermal predictions across different regimes. While the findings are specific to the tested regimes, they demonstrate how modeling assumptions and data-handling strategies shape prediction accuracy. By aligning the characterization–processing–implementation chain, the study offers a diagnostic showcase for assessing implementation uncertainty, supporting more robust and physically consistent HAM modeling.

Keywords

HAM models heat air and moisture hygrothermal response moisture transport material properties simulation implementation

Introduction

Heat, air, and moisture (HAM) models are widely applied to evaluate hygrothermal performance of building components. Developed from the steady-state Glaser (1958) method and the coupled transient hygrothermal equations introduced by Philip and Devries (1957) or Luikov (1964), these models have evolved into either commercial software or in-house codes. From theory to practice, their implementations have diverged in selecting driving potentials and describing material properties to resolve the discontinuity of moisture content potential at the materials’ interfaces (Burch and Chi, 1997; Cunningham, 1990; Kiessl, 1983; Kohonen, 1984; Künzel, 1995; Matsumoto, 1978; Pedersen, 1990; Salonvaara et al., 2011). Among the most established HAM models, WUFI and DELPHIN have become central to both academic research and engineering practice (Amorim et al., 2024; Gan et al., 2025; Klõšeiko and Kalamees, 2022; Palani et al., 2025; Vandemeulebroucke et al., 2024). While their governing equations are largely mathematically and physically equivalent (Dang et al., 2023), simulation outcomes often vary due to differences in how geometric configurations (Bottino-Leone, 2021; Vereecken and Roels, 2013), material properties (Roels et al., 2004, 2010), boundary conditions (Dang et al., 2024b; Zhou et al., 2023) or other factors are defined and implemented (Dang, 2025).

Recent intercomparison and validation exercises, such as the round robin “Empirical validation of HAM-models based on a dedicated HB-CB experiment” (Dang et al., 2025a), revealed that significant discrepancies can arise even when identical input datasets are used. These variations stem largely from differences in how hygric material properties are implemented as well as from user-dependent input decisions (Dang et al., 2025b). Follow-up analyses that minimized user variability showed limited deviations when simulations remained within the hygroscopic range (Dang et al., 2026a). However, as these findings are confined to vapor-dominated regimes, uncertainties under over-hygroscopic conditions remain insufficiently addressed—where the combined influence of vapor and liquid transport increases parameter sensitivity and may lead to greater divergence in hygrothermal predictions.

To extend the understanding of these effects, it is first necessary to clarify how uncertainties arise during the characterization and transformation of hygric material properties. Such uncertainties originate from three main sources: (1) intra-operator repeatability (on same samples performed by the same individual using the same equipment in the same lab; ISO 5725-1, 2023), (2) inter-operator reproducibility (on same samples performed by different individuals using different equipment or following different measurement protocols in different labs; Feng et al., 2020; López et al., 2017; Roels et al., 2004), and (3) material heterogeneity (including production-related inconsistencies, e.g., between manufacturers or between batches from the same manufacturer, in engineered materials and intrinsic variability particularly in natural materials; Aït Oumeziane et al., 2021; Hofheinz et al., 2025; Xu et al., 2023). Whereas the impact of repeatability is relatively restricted, material heterogeneity and inter-operator reproducibility are known to be significant (Feng et al., 2015). On one hand, these uncertainties are particularly pronounced for properties that cannot be directly measured and must be inferred through physical or mathematical transformations, such as deriving liquid diffusivity from moisture content profiles measured via Boltzmann transformation (Roels et al., 2003) or simplified alternatives (Ren et al., 2019). Translating such data into liquid permeability or other equivalent parameters introduces further complexities, as outcomes are influenced by other factors like the slope of the moisture retention curve. On the other hand, even more accessible properties like the moisture retention curve may differ depending on the selected characterization methods (Dang et al., 2024a; Feng and Janssen, 2021) or treatment of hysteresis behavior (Zhu et al., 2025). As a result, “identical” materials in model databases (ASHRAE, 2013; Kumaran, 1996; Materialdatensammlung für die energetische Altbausanierung) can display markedly different hygric properties, and the freedom granted to users in assigning these parameters further amplifies the variability in simulated results (Dang et al., 2025b; Yamamoto and Takada, 2022). While previous sensitivity analyses have highlighted these discrepancies (Panico et al., 2023; Vandemeulebroucke et al., 2023), systematic approaches to evaluate and manage such implementation uncertainties remain scarce.

This study addresses two related gaps: (1) the methodological complexity involved in transforming and implementing hygric material data and (2) the lack of comparative analyses that explicitly examine how the implementation strategies affect hygrothermal predictions under representative moisture regimes. It first synthesizes the characterization methods, data processing procedures and model-specific parameterization logics employed by WUFI and DELPHIN—each governed respectively by relative humidity and capillary pressure. Building on this structured overview, two complementary simulation regimes are introduced to examine regime-dependent sensitivities. Stage I focuses on over-hygroscopic exposures dominated by liquid transport, using the EU HAMSTAD Benchmark 4 (Adan et al., 2004; Hagentoft et al., 2004) and an extended real-climate evaluation with wind-driven rain (WDR). Stage II investigates typical service conditions (50%–98% RH), where vapor and liquid transport mechanisms coexist, through virtual wall configurations that isolate the effects of integral versus separate implementation strategies for vapor and liquid transport properties. Material properties are tailored to each model’s input format to ensure comparability. Beyond extending benchmark studies, this work consolidates methodological understanding by comparing implementation pathways in WUFI and DELPHIN, revealing how distinct parameterization logics interact with regime-dependent sensitivities across hygroscopic and over-hygroscopic domains. Through this comparative lens, it clarifies the limits of empirical versus physics-based transformations and translates these insights into practical diagnostics for improving modeling performance. By elucidating the full characterization–processing–implementation chain, the study bridges empirical validation with model transparency, advancing the treatment of material property uncertainty in HAM modeling.

Theoretical and experimental basis

Formulation of governing equations for hygrothermal transport

WUFI Pro 6.7 and DELPHIN 6.1 both deal with coupled heat and moisture transport through building components. Note that air transport as well as salt and VOC transfers are additionally considered in DELPHIN, but they are not comprised in this study. Regarding the moisture balance, the moisture mass change in each control volume over time should always equal the net sum of incoming and outgoing moisture flows. Vapor and liquid transport follow Fick’s (1995) law and Darcy’s law (Darcy, 1856) respectively. General formulations of one-dimensional moisture balance are formulated in equations (1) and (2), derived using two different driving potentials for liquid transport: relative humidity $φ$ [%] (WUFI’s choice) and capillary pressure $P_{c}$ [Pa] (DELPHIN’s choice).

\begin{matrix} \frac{\partial w}{\partial t} = - \nabla (g_{v} + g_{l}) \\ = \nabla (δ_{v} \nabla P_{v} + D_{w} \nabla w) \\ = \nabla (δ_{v} \nabla P_{v} + D_{w} \frac{\partial w}{\partial φ} \nabla φ) \\ = \nabla (δ_{v} (P_{vsat} \nabla φ + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) + D_{w} \frac{\partial w}{\partial φ} \nabla φ) [as P_{v} = φ \cdot P_{vsat} (T)] \\ = \nabla ([δ_{v} φ \frac{\partial P_{vsat}}{\partial T}] \nabla T + [δ_{v} P_{vsat} + D_{w} \frac{\partial w}{\partial φ}] \nabla φ) \end{matrix}

(1)

\begin{matrix} \frac{\partial w}{\partial t} = - \nabla (g_{v} + g_{l}) \\ = \nabla (δ_{v} \nabla P_{v} + K_{l} \nabla P_{c}) \\ = \nabla (δ_{v} (P_{vsat} \nabla φ + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) + K_{l} \nabla P_{c}) [as P_{v} = φ \cdot P_{vsat} (T)] \\ = \nabla (δ_{v} (P_{vsat} (\frac{\partial φ}{\partial P_{c}} \nabla P_{c} + \frac{\partial φ}{\partial T} \nabla T) + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) + K_{l} \nabla P_{c}) [as φ = f (P_{c}, T)] \\ = \nabla (δ_{v} (P_{vsat} ((\frac{φ}{ρ_{w} R_{v} T}) \nabla P_{c} + (\frac{- P_{c} φ}{ρ_{w} R_{v} T^{2}}) \nabla T) + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) + K_{l} \nabla P_{c}) \\ [as φ = e^{\frac{P_{c}}{ρ_{w} R_{v} T}}] \\ = \nabla ([δ_{v} φ \frac{\partial P_{vsat}}{\partial T} - \frac{δ_{v} P_{vsat} P_{c} φ}{ρ_{w} R_{v} T^{2}}] \nabla T + [K_{l} + \frac{δ_{v} φ P_{vsat}}{ρ_{w} R_{v} T}] \nabla P_{c}) \end{matrix}

(2)

where $w$ [kg/m³] is volumetric moisture content; $t$ [s] is time; $g_{v}$ and $g_{l}$ [kg/(m²·s)] are vapor and liquid fluxes respectively; $δ_{v}$ [s] is vapor permeability; $P_{v}$ , $P_{vsat}$ , and $P_{c}$ [Pa] are vapor pressure, saturation vapor pressure and capillary pressure respectively; $D_{w}$ [m²/s] is liquid diffusivity; $x$ [m] is distance; $T$ [K] is temperature; $K_{l}$ [s] is liquid permeability; $ρ_{w}$ [kg/m³] is water density; $R_{v}$ [J/(kg·K)] is water vapor gas constant.

For the heat balance, similarly, the enthalpy change in each control volume over time should always equal the net sum of incoming and outgoing heat flows. The conduction part is expressed by Fourier’s law (Baron Fourier, 1878), while the convection part consists of latent and sensible components, as shown in equation (3). By inserting the moisture flux expressions of equations (1) and (2), it can be further developed into equations (4) and (5), respectively.

\begin{matrix} \frac{\partial H}{\partial T} \frac{\partial T}{\partial t} + \frac{\partial H}{\partial w} \frac{\partial w}{\partial t} = (c_{dry} ρ_{dry} + c_{l} w_{l} + c_{v} w_{v}) \frac{\partial T}{\partial t} \\ = - \nabla (q_{cond} + q_{conv}) \\ = \nabla (λ \nabla T + (L_{v} + c_{v} T) g_{v} + c_{l} T g_{l}) \end{matrix}

(3)

where $c$ [J/(kg·K)] is specific heat capacity, with the subscripts $dry$ , $l$ , and $v$ corresponding to dry material, liquid water and water vapor respectively; $H$ [J/m³] is enthalpy density; $q_{cond}$ and $q_{conv}$ [J/(m²·s)] are conductive and convective heat fluxes respectively; $L_{v}$ [J/kg] is the latent heat of evaporation; $ρ$ [kg/m³] is density.

\begin{matrix} \nabla (λ \nabla T + (L_{v} + c_{v} T) g_{v} + c_{l} T g_{l}) \\ = \nabla (λ \nabla T + (L_{v} + c_{v} T) \cdot δ_{v} (P_{vsat} \nabla φ + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) + c_{l} T \cdot D_{w} \frac{\partial w}{\partial φ} \nabla φ) \\ = \nabla ([λ + δ_{v} φ (L_{v} + c_{v} T) \frac{\partial P_{vsat}}{\partial T}] \nabla T + [c_{l} T D_{w} \frac{\partial w}{\partial φ} + δ_{v} P_{vsat} (L_{v} + c_{v} T)] \nabla φ) \end{matrix}

(4)

\begin{matrix} \nabla (λ \nabla T + (L_{v} + c_{v} T) g_{v} + c_{l} T g_{l}) \\ = \nabla (λ \nabla T + (L_{v} + c_{v} T) \cdot δ_{v} (P_{vsat} ((\frac{φ}{ρ_{w} R_{v} T}) \nabla P_{c} + (\frac{- P_{c} φ}{ρ_{w} R_{v} T^{2}}) \nabla T) + φ \frac{\partial P_{vsat}}{\partial T} \nabla T) \\ + c_{l} T \cdot K_{l} \nabla P_{c}) \\ = \nabla ([λ - \frac{δ_{v} P_{c} φ (L_{v} + c_{v} T)}{ρ_{w} R_{v} T^{2}}] \nabla T + [c_{l} T K_{l} + \frac{δ_{v} P_{vsat} φ (L_{v} + c_{v} T)}{ρ_{w} R_{v} T}] \nabla P_{c}) \end{matrix}

(5)

On the right-hand sides of equations (1)–(5), the partial derivatives are the driving potential gradients, and the preceding parts, comprised in square brackets, are the corresponding material properties and related hygrothermal variables. The moisture balance equations, which involve vapor diffusion and liquid transport (equations (1) and (2)), are completely implemented in both WUFI and DELPHIN. The heat balance in DELPHIN is in line with equations (3) and (5). In WUFI, however, the advection of sensible heat due to liquid flow or vapor transport is neglected: specifically, the component “ $c_{v} {Tg}_{v} + c_{l} {Tg}_{l}$ ” on the right-hand side of equation 3 is omitted.

Determination and implementation of hygric material properties

Both WUFI and DELPHIN include built-in material property databases, while also allowing users to define custom entries—provided they comply with model requirements such as monotonicity and threshold constraints. As previous studies (Dang et al., 2025a, 2025b, 2026a) suggested, the thermal properties have much less influence on simulated hygrothermal responses than the hygric properties, so this study tackles the hygric properties only. Various approaches for determining and implementing hygric properties are outlined in this section. The variation of these properties as inputs (e.g., sorption isotherm (Salonvaara et al., 2001), vapor resistance factor (Zhao et al., 2011) and liquid permeability (Defraeye et al., 2013) has been shown to influence the hygrothermal response predictions.

Moisture transport properties

Apart from some budding pore-network-modeling techniques to numerically determine the moisture permeability $K_{l}$ [s] (Islahuddin and Janssen, 2019), the main approach is to determine the moisture diffusivity $D_{w}$ [m²/s] experimentally. It starts with the Boltzmann transformation of transient moisture profiles $w (x / \sqrt{t})$ obtained via X-ray attenuation (Roels and Carmeliet, 2006) or NMR (Wolter and Krus, 2005) during a capillary absorption process (equation 6; Carmeliet et al., 2004). While these imaging methods enable precise moisture profiling, they are not always accessible (Wolter and Krus, 2005). Alternative solutions include the ruler method (Evangelides et al., 2010), the multi-step method (Bianchi Janetti, 2018) and Künzel’s (1995) formula. Among them, the ruler method seems to provide results closest to X-ray attenuation but is limited to materials with a distinct waterfront, while the multi-step method is applicable to most porous materials but requires extensive sample conditioning and complex data processing (Ren et al., 2019). Künzel’s formula is the simplest approach but lacks consistent accuracy (Dang, 2025). As shown in equation (7), it is dependent on the capillary absorption coefficient $A_{w}$ [kg/(m·s^0.5)] and the free saturation moisture content $w_{f}$ [kg/m³] (equivalent to $w_{cap}$ obtained in a capillary absorption test (ISO 15148, 2002)).

Moisture diffusivity can be converted into permeability via the slope of the moisture retention curve (equation (8)). WUFI only supports $D_{w} (w)$ function and distinguishes between two variants: $D_{ws}$ for suction and $D_{ww}$ for redistribution. The former describes capillary water uptake when the imbibing surface is fully wetted, while the latter describes the redistribution of absorbed water once wetting ceases. WUFI requires inputs for both functions but dynamically selects which function to apply at each computational time step depending on whether the WDR boundary condition is non-zero. This activation applies to the entire material domain, disregarding spatial variations in moisture sorption (Künzel and Kiessl, 1996). WUFI treats the moisture diffusivity as liquid-dominated and activates it only when RH reaches 80 %. Künzel’s formula (equation (7)) is the default solution for $D_{ws} (w)$ function in WUFI, requiring two values calculated at 80% and 100% RH for logarithmic interpolation. The $D_{ww} (w)$ function is derived analogously, using interpolation between $D_{ws}$ at 80% and 0.1 times $D_{ws}$ at 100% RH, reflecting the assumption that moisture redistribution within the material is significantly slower than suction-driven moisture uptake. In DELPHIN, $K_{l} (w)$ function appears as the default function, while $D_{w} (w)$ function can be used alternatively. Unlike WUFI’s flexibility, DELPHIN requires both curves to be monotonic.

D_{w} (w) = - \frac{\int_{w (0)}^{w ((x \sqrt{t}))} (x \sqrt{t}) dw}{2 \frac{\partial w}{\partial (x \sqrt{t})}}

(6)

D_{w} (w) = 3.8 \cdot {(\frac{A_{w}}{w_{f}})}^{2} \cdot 1000^{\frac{w}{w_{f}} - 1}

(7)

K_{l} = D_{w} \cdot \frac{\partial w}{\partial P_{c}}

(8)

Note that the aforementioned approaches typically capture the entire absorption process, but moisture diffusivity is uncertain in lower moisture content range and must be supplemented with other tests to account for vapor transport contribution—just as WUFI’s bivariate approach to liquid diffusivity. Dry (or wet) cup tests (ISO 12572, 2016) are commonly used to determine vapor-dominated moisture transport properties under specific RH conditions. These properties are expressed as vapor diffusion coefficient $δ_{v}$ [s] (under the gradient of vapor pressure $P_{v}$ ) or vapor diffusion resistance factor $μ$ [−] (defined as the ratio of vapor diffusion coefficient in air $δ_{a}$ [s] and that in material $δ_{v}$ [s]). In WUFI, a $μ (φ)$ function is applicable; in DELPHIN, either $μ (φ)$ function or the vapor permeability $K_{v} (w)$ function can be assigned. Specifically, $K_{v}$ [s] (under the gradient of capillary pressure $P_{c}$ ) can be mathematically converted from vapor diffusion coefficient $δ_{v}$ [s] (under the gradient of vapor pressure $P_{v})$ . The vapor diffusion coefficient in air $δ_{a}$ [s] is determined by the ratio of vapor diffusivity in air $D_{va}$ [m²/s] and the product of water vapor constant $R_{v}$ [J/(kg·K)] and temperature $T$ [K]. The three parameters are fixed as constants in DELPHIN (Vogelsang et al., 2013): $T$ = 293.15 K, $R_{v}$ = 462 J/(kg K), $D_{va}$ = 26.1 × 10⁻⁶ m²/s. Since liquid water partially fills the pores in the wet cup test, vapor transport is affected by the saturation and air entrapment (Fukui and Takada, 2024). To account for this, a reduction in vapor transport properties can be considered, for instance, using a non-linear reduction approach as adopted in the HAMSTAD benchmark exercise (Hagentoft et al., 2004). Equation (9) formulates vapor permeability as a function of capillary pressure (since it is the actual driving potential in DELPHIN), $K_{v} (P_{c})$ , incorporating this reduction approach. In this case, the vapor resistance factor measured in the dry cup test, $μ_{dry}$ [−], is utilized, under the assumption that only pure vapor transport occurs during the test.

Another key uncertainty is whether to treat vapor and liquid transport terms separately or integrally. Vapor transport is dominant in the low moisture content range, and therefore the dry cup test result is assumed to represent the pure vapor transport term. In contrast, wet cup tests comprise also the contribution of liquid water transport, which can be quantified as the difference between the total and the vapor transport terms (equation (10)). When applying the reduction in the vapor transport term, such as the factor $\frac{1 - \frac{w}{w_{sat}}}{0.503 \cdot {(1 - \frac{w}{w_{sat}})}^{2} + 0.497}$ in equation (9), the vapor transport term $\frac{δ_{a}}{μ_{dry}}$ in equation (10) should likewise be reduced to ensure consistency. However, cup tests do not cover the over-hygroscopic range, where liquid-dominant moisture transport properties must be characterized via alternative approaches. Therefore, one approach is to separately implement the obtained vapor and liquid transport properties from different sources. For instance, WUFI’s developers suggest using a constant $μ_{dry}$ value, paired with an $D_{w} (w)$ function (WUFI forum). An alternative approach, particularly when liquid water transport is not dominant, is to treat vapor and liquid water transport terms integrally purely based on the cup tests. This involves using a $μ (φ)$ function without explicitly implementing liquid diffusivity. For DELPHIN, since the $K_{v} (w)$ function is based on $μ_{dry}$ as obtained from the dry cup test, the vapor transport term is exclusively characterized, while the $K_{l} (w)$ function solely represent the liquid transport term.

There are two major errors commonly made in the implementation of moisture transport properties. The first is “redundant consideration,” where both a $μ (φ)$ function and a $D_{w} (w)$ function are implemented that incorporate liquid transport term repeatedly in the low moisture range. The second is “insufficient consideration,” where only a $μ (φ)$ function is assigned particularly when simulating an over-hygroscopic sorption process. Even when a fitting curve of the cup test results may be extrapolated into the over-hygroscopic range, the reliability remains uncertain (Dang et al., 2026a). The impact of these errors is reported by Dang et al. (2025a).

\begin{matrix} K_{v} (P_{c}) = (δ_{v} \cdot \frac{1 - \frac{w}{w_{sat}}}{0.503 \cdot {(1 - \frac{w}{w_{sat}})}^{2} + 0.497}) \cdot \frac{\nabla P_{c}}{\nabla P_{v}} \\ = (\frac{D_{va}}{μ_{dry} R_{v} T} \cdot \frac{1 - \frac{w}{w_{sat}}}{0.503 \cdot {(1 - \frac{w}{w_{sat}})}^{2} + 0.497}) \cdot \frac{P_{v}}{ρ_{w} R_{v} T} \end{matrix}

(9)

K_{l} (P_{c}) = (\frac{δ_{a}}{μ (φ)} - \frac{δ_{a}}{μ_{dry}}) \cdot \frac{P_{v}}{ρ_{w} R_{v} T}

(10)

Moisture storage properties

The moisture storage property, expressed as sorption isotherm $w (φ)$ in WUFI or as moisture retention curve $w (P_{c})$ in DELPHIN (where $w (φ)$ function can be alternatively used), describes the equilibrium between moisture saturation and moisture potential in porous media. Within the hygroscopic range, it is commonly characterized using the gravimetric desiccator method (ISO 12571, 2000), which involves exposing samples to different RH conditions and recording their weights. In the over-hygroscopic range, the storage function can be determined by the pressure plate test (ISO 11274, 1998), mercury intrusion porosimetry (MIP; ISO 15901-1, 2016), etc. Sorption isotherms and moisture retention curves are typically used to describe the hygroscopic and over-hygroscopic ranges respectively (Feng and Janssen, 2021), with conversions between the two enabled via Kelvin’s law (equation (11)). Regardless of format, these storage functions must be strictly monotonic, as required by both WUFI and DELPHIN.

P_{c} = ρ_{w} \cdot R_{v} \cdot T \cdot \ln (φ)

(11)

Methods and results

To assess how specific implementation strategies for moisture transport properties affect hygrothermal predictions across distinct moisture regimes, this study conducts targeted simulations using WUFI Pro and DELPHIN, the most widely used HAM models. The assessment is structured in two stages, each addressing a different regime. Stage I focuses on liquid transport under over-hygroscopic conditions, using EU HAMSTAD Benchmark 4 (Hagentoft et al., 2004). The wall configuration, comprising an external load-bearing layer and an internal finishing layer, is subjected to “extreme” moisture exposures featured by WDR loads. An additional evaluation is conducted under measured real-world climate conditions using the same setup. Simulations compare liquid diffusivity $D_{w} (w)$ estimated via Künzel’s formula (equation (7)) as recommended by WUFI, against the experimentally derived liquid permeabilities $K_{l} (w)$ . Where feasible, all relevant property formats are implemented in both models to isolate the impact of implementation strategies and the intrinsic model differences. Stage II examines how different strategies for integrating or separating vapor and liquid transport properties influence simulation outcomes. Two virtual configurations, a concrete wall internally insulated with either autoclaved aerated concrete (AAC) or calcium silicate (CS), are subjected to either a wetting–drying cycle or continuous wetting, representing as typical “service” exposures. All simulations are conducted in DELPHIN due to its broader support for property formats, including those approaches compatible with WUFI.

Table 1 summarizes the scenarios and analytical objectives for the two stages. To maintain clarity and better reflect the close alignment between methods and results, each stage is presented as a selfcontained unit in which the setup, modeling approaches and simulation outcomes are discussed together.

Table 1.

Overview of simulation scenarios and analytical objectives.

DetailsStages	Configurations and boundary conditions	Simulation models	Key questions addressed
Stage 1	HAMSTAD Benchmark 4, under “extreme” or “real climate” conditions	WUFI and DELPHIN	• Reliability of Künzel’s formula (equation (7)) for $D_{w} (w)$ estimation
			• Equivalence between $D_{w} (w)$ and $K_{l} (w)$ derived via different methods/models
Stage II	Concrete-AAC or concrete-CS, under “service” conditions	DELPHIN	Equivalence between integral and separate implementation of vapor and liquid transport properties

Stage I: Impact of implementation approaches for liquid transport properties

Stage I uses the HAMSTAD Benchmark 4 as a controlled setting. All necessary simulation inputs—including material properties, boundary conditions and initial conditions—are explicitly specified in the instruction document (Hagentoft et al., 2004). As shown in Figure 1, the airtight wall consists of a 0.1 m thick external load-bearing material layer and a 0.02 m thick internal finishing layer, both exposed to heat and moisture loads. Table 2 provides the single-valued properties of these materials. In accordance with the validation publication provided by DELPHIN’s developers (Sontag et al., 2013), this study adheres to their implementation procedures and parameter assignments. Although WUFI has not published a corresponding validation document, its simulations also comply with the input requirements outlined in the HAMSTAD instruction. Additionally, the grid discretization is further refined to ensure that the results are not influenced by numerical precision.

Table 2.

Single-valued material properties implemented in stage I.

Materialsproperties	Load-bearing material	Internal finishing material
Density $ρ$ [kg/m³]	2005	790
Specific heat capacity $c$ [J/(kg·K)]	840	870
Thermal conductivity $λ$ [W/(m·K)]	0.5	0.2
Vapor resistance factor at dry state $μ_{dry}$ [−]	30	3
Vacuum saturation moisture content $w_{sat}$ [kg/m³]	157	209

In this study, the only modification pertains to the implementation approaches for the liquid transport property of the load-bearing material. On the one hand, the default approach, referred to as approach K1.0, is precisely represented by the provided data series of the $K_{l} (P_{c})$ function. By linking this with the slope of the moisture retention curve (see equation (8)), a theoretically equivalent $D_{w} (w)$ function can be derived, leading to the approach D1.0. The approaches K1.0 and D1.0 are simulated in DELPHIN and WUFI respectively. Note that DELPHIN only supports strictly monotonic material property functions. Therefore, the original D1.0 curve—whose liquid diffusivity exhibits a peak in the low moisture content range—must be modified by excluding certain data points to meet this criterion and yield a modified approach, D1.1. Approach D1.1 is applied in both WUFI and DELPHIN to enable inter-model comparison. On the other hand, an alternative solution is to estimate the liquid diffusivity via logarithmic interpolation between values at 80% and 100% RH based on Künzel’s formula (equation (7)). This method forms the basis of approach D2.0. The required capillary absorption coefficient $A_{w}$ [kg/(m·s^0.5)] and capillary moisture content $w_{cap}$ [kg/m³] are obtained by a preceding capillary absorption simulation, in which the original $K_{l} (P_{c})$ function is implemented. Since the D2.0 approach is compatible with both WUFI and DELPHIN, it is also selected for inter-model comparison to assess differences under identical input conditions. Expanding on this, another approach D2.1 involving the two liquid diffusivities, $D_{ws} (w)$ and $D_{ww} (w)$ , is simulated in WUFI. Since DELPHIN only supports single moisture diffusivity function, the result of $D_{ws} (w)$ is implemented in approach D2.0, while the translated $K_{l} (P_{c})$ function leads to a separate approach, K2.0. This configuration generates four scenarios in DELPHIN (K1.0, D1.1, K2.0, and D2.0) and four scenarios in WUFI (D1.0, D1.1, D2.0, and D2.1). Table 3 and Figure 2 present the implementation approaches and the resulting liquid transport properties.

Table 3.

Implementation approaches for liquid transport properties of stage I.

Approaches and models	Data resources and processing methods
K1.0 (DELPHIN)	Provided in the HAMSTAD instruction document
D1.0 (WUFI)	Theoretically equivalent to K1.0(DELPHIN) (translated via equation (8)), subject to inter-model differences
D1.1 (DELPHIN)	Adapted from D1.0(WUFI) by excluding certain data in low moisture content range to ensure monotonicity
D1.1 (WUFI)	Theoretically equivalent to D1.1(DELPHIN), subject to inter-model differences
D2.0 (WUFI)	Estimated using Künzel’s formula (equation (7))
K2.0 (DELPHIN)	Theoretically equivalent to D2.0(WUFI), subject to inter-model differences
D2.0 (DELPHIN)	Theoretically equivalent to D2.0(WUFI), subject to inter-model differences
D2.1 (WUFI)	Adapted from D2.0(WUFI) by distinguishing $D_{ww} (w)$ from $D_{ws} (w)$ with the default reduction

An additional remark concerns the implementation of the moisture storage properties in WUFI (Dang et al., 2026b), though it is not the primary focus of this section. The data series of the $w (P_{c})$ function is provided in the HAMSTAD instruction document (Hagentoft et al., 2004). Since WUFI only supports the $w (φ)$ function, a conversion via Kelvin’s law (equation (11)) is applied. Simulations start with manually input moisture contents at default RH values, progressing in increments of 10% from 0% to 50%, 5% from 50% to 90%, and 1% from 90% to 99%, with additional points at 99.5% and 100%. However, abrupt boundary condition transitions, particularly rain events accompanied with low temperatures, make the moisture storage highly sensitive to the $w (φ)$ function in the over-hygroscopic range, causing sudden saturation jumps on the exterior surface. To smooth the curve, additional manually input data points, converted from $w (P_{c})$ function via Kelvin’s law, are inserted between 99.5% and 100% RH. Results indicate that the more interpolation points are provided for the $w (φ)$ function, the more accurate WUFI’s predictions become. In contrast, DELPHIN appears more robust: even with sparse input data that would lead to inaccuracies in WUFI, it still yields results consistent with those derived from the $w (P_{c})$ function. This suggests that DELPHIN performs more refined internal interpolation without user intervention, whereas WUFI’s accuracy remains highly dependent on the resolution of the user’s inputs.

The comparative simulations among these approaches are conducted in two steps. In the first step, different implementation approaches are applied to the liquid transport properties of the load-bearing material while all other inputs remain consistent with those specified in the instruction (Hagentoft et al., 2004). The simulated hygrothermal responses are then compared against predictions from the HAMSTAD project participants (Hagentoft et al., 2004). Although experimental evidence is unavailable, inter-model comparison provides an effective demonstration of model consistency still. In the second step, the boundary conditions are changed into a full-year in-situ experimental dataset of the VLIET building (Leuven, Belgium; Dang et al., 2024b, 2025c; Vereecken and Roels, 2021; see Figure 3), which includes WDR imposed to the wall, thereby making the differences more pronounced under real-life weather conditions. All other inputs remain unchanged from the first step.

Figure 4 illustrates the simulated moisture contents at both surfaces and moisture content profiles in the first step of stage I, compared with the predictions from HAMSTAD participants (Hagentoft et al., 2004; indicated by the gray band). Overall, the outcomes from various scenarios exhibit a consistent trend with the reference results, although differences exist in the fluctuation amplitudes and the variation rates. The liquid transport properties of the load-bearing material differ across implementation strategies in each scenario, influencing moisture dynamics. As its outer boundary is sensitive to rain exposures, certain discrepancies are observed in the moisture content fluctuations, as illustrated in Figure 4(a). In general, the approaches K1.0 and D1.0, which either fully implement or completely transform the material properties as instructed, produce outcomes that align most closely with the reference results. Although D1.1 incorporates simplifications in the low-humidity range to comply with the monotonicity requirement, it still maintains good consistency. Conversely, K2.0 and D2.0, based on the liquid diffusivity curve derived from the simplified formula (equation (7)), exhibit significant deviations from the given curve in the high-humidity range. These discrepancies result in distinct variations in peak moisture levels and waveform shifts during extreme transitions between dry and wet conditions. The D2.1 approach, which applies dual moisture diffusivities depending on rainy or non-rainy conditions, yields predictions that generally fall between the 1.0-series and 2.0-series scenarios. Despite the consistent implementation of material properties of the internal finishing layer across scenarios, its moisture content remains influenced by the variations in the moisture dynamics of the load-bearing material (Figure 4(b)). The distinction between “curves,” 1.0-series versus 2.0-series, appears to exert a slightly greater impact than the inherent differences between models. This can be largely attributed to the overall higher liquid permeability and diffusivity in the capillary range associated with the 2.0-series, resulting from the use of Künzel’s simplified formula (equation (7)). The moisture content profiles (Figure 4(c)–(h)) further highlight the influence of various strategies for modeling the liquid transfer properties. For the load-bearing material, the 1.0-series and 2.0-series scenarios form distinct groups, with the former aligning more closely with the reference results. Model-related differences are also evident: approach D1.1 produces divergent results in the two models; the discrepancy between D2.0 (DELPHIN) and D2.0 (WUFI) almost exceeds that between D2.0 (DELPHIN) and K2.0 (DELPHIN), despite their theoretical equivalence. This could stem from differences in internal algorithms, although precise attribution is challenging due to the non-disclosure of both software codes.

Figure 5 illustrates the simulated moisture masses (MM) of the load-bearing material during the second step of stage I. Although displayed in logarithmic scale, the differences among simulation results of various scenarios are not readily distinguishable. To enhance interpretability, the main plot overlays the overall range (the light blue area) with the mean curve (the bright blue line), while the red shading indicates the standard deviation, capturing the variability across scenarios. Periods of heightened material moisture content and larger standard deviations, specifically the 10-day spans in February, March, and October, underscore the potentially greater influence of varying moisture transport property implementations, as clearly illustrated by the magnified intervals in the upper subplot. Overall, the discrepancies between the models may exceed those introduced by parameter conversion. For example, D2.0 (DELPHIN) almost entirely overlaps K2.0 (DELPHIN) but exhibits some deviation from D2.0 (WUFI). In contrast, K1.0 (DELPHIN) and D1.0 (WUFI) demonstrate better agreement, generally predicting lower moisture mass than D1.1 (DELPHIN and WUFI), which underestimates moisture transport in low-humidity regions due to monotonicity constraints, potentially leading to slower evaporation predictions. Furthermore, since D2.0 (WUFI) and D2.1 (WUFI) employ identical implementations for moisture transport properties except during rain events, their localized magnifications appear nearly identical.

However, when examining cumulative annual outcomes in Table 4, D2.1 (WUFI) produces overall the highest moisture mass, likely due to its suction characteristics being identical to D2.0 (WUFI) but exhibiting slower redistribution. The liquid diffusivity applied for redistribution is intended to represent reduced moisture transfer; however, the assignment criteria for both types of liquid diffusivities in WUFI depend solely on rainfall occurrence. This simplified approach fails to account for spatial variations in moisture transfer rates within the structure, leading to significant overestimations or, in some cases, potential underestimations. Given the inherent difficulty of direct measurements, it remains challenging to determine which model is closer to actual conditions. Nevertheless, the rationale behind distinguishing the two methods solely based on the presence or absence of rainfall warrants further scrutiny—particularly considering that, in high-humidity conditions, the numerical discrepancy between the two methods can differ by an order of magnitude. More critically, the computational bias introduced by this distinction far exceeds both intrinsic model differences and parameter conversion-induced deviations.

Table 4.

Data characteristics of simulation moisture contents of the loading-bearing material in the second step of stage I.

MetricsScenarios	Minimum	25% percentile	Median	75% percentile	Maximum	Average
K1.0 (DELPHIN)	0.0300	0.0537	0.0653	0.0861	1.6068	0.0902
D1.0 (WUFI)	0.0284	0.0533	0.0660	0.0961	2.0331	0.1032
D1.1 (DELPHIN)	0.0300	0.0543	0.0654	0.0835	1.5996	0.0976
D1.1 (WUFI)	0.0284	0.0537	0.0653	0.0908	2.0211	0.1075
K2.0 (DELPHIN)	0.0300	0.0537	0.0649	0.0907	1.6169	0.1045
D2.0 (DELPHIN)	0.0300	0.0539	0.0651	0.0897	1.6143	0.1043
D2.0 (WUFI)	0.0284	0.0542	0.0657	0.1072	2.0605	0.1267
D2.1 (WUFI)	0.0284	0.0543	0.0657	0.1081	2.0606	0.1274

Stage II: Impact of integral versus separate implementation approaches for vapor and liquid transport properties

Stage II primarily investigates different formulations of vapor and liquid transport properties, evaluating their influence on predicted hygrothermal responses, particularly under boundary conditions that may drive materials partially into the over-hygroscopic regime. While the integral and separate implementations of vapor and liquid transport terms are often equivalent, notable questions remain. A key concern is whether supplementary data for liquid transport properties, obtained with Boltzmann transformation or Künzel’s formula, should complement the data derived solely from cup test results. As preliminarily discussed by Dang et al. (2026a), this “supplement” becomes particularly significant in the over-hygroscopic range. However, for (extremely) low moisture contents in the hygroscopic range, such supplementary approaches frequently lack accuracy and may even lead to risks of overestimation (Klõšeiko et al., 2023). Moreover, the impact of integrally or separately implementing the vapor and liquid transport properties on hygrothermal response prediction is case-dependent. While both approaches may prove to be “viable” in specific scenarios (Dang et al., 2026a), the underlying complexities require further exploration to determine which approach, if any, represents the most “accurate” solution.

Two virtual scenarios are developed to explore the complimentary liquid transport during hygroscopic moisture absorption and redistribution. These scenarios also force the transport process into the over-hygroscopic range, hence highlighting the significance of integral versus separate implementations of vapor and liquid transport properties. As shown in Figure 6, the wall configuration consists of a 300 mm concrete layer internally insulated with 100 mm of either AAC or CS. The two scenarios differ in their sorption processes, corresponding to “wetting-drying” (WD) and “pure wetting” (WW). In both configurations, the concrete layer acts as vapor-tight, effectively blocking vapor diffusion through its thickness, whereas the CS and AAC layers are highly capillary-active, enabling significant liquid water transport. Under the imposed boundary conditions, representing either pure wetting or combined wetting and drying, the system experiences not only vapor-phase migration but also liquid water condensation and evaporation within the capillary-active insulation. This creates distinct combinations of moisture transfer mechanisms in each scenario, allowing the influence of vapor–liquid transport interactions to be examined under contrasting sorption regimes. In the WD scenario, the boundary conditions are set to 3°C and 50% RH on the left (“outdoor”) and 28°C and 98% RH on the right (“indoor”) for the first 480 hours, enabling wetting of the AAC or CS layer. For the subsequent 480 hours, the conditions are reversed to introduce a drying process. In the WW scenario, the boundary conditions are set oppositely, ensuring a continued wetting. During the first 480 hours, the left side is set to 28°C and 98% RH, and the right side to 3°C and 50% RH. In the subsequent 480 hours, the conditions are reversed. This configuration ensures a continuous wetting process. In all scenarios, initial conditions are set to 15°C and 75% RH. The surface transport coefficients follow the specifications in HAMSTAD instruction document (Hagentoft et al., 2004): $α_{e}$ = 25 W/m²K and $β_{e}$ = 2 × 10⁻⁷ s/m for the “outdoor” side, while $α_{i}$ = 8 W/m²K and $β_{i}$ = 3 × 10⁻⁸ s/m for the “indoor” side. These scenarios involve vapor–liquid interactions under conditions where both transport mechanisms are active, examining how integrated versus separated modeling approaches affect hygrothermal predictions. To eliminate model-specific discrepancies, all simulations are performed in DELPHIN, which supports multiple formats of material properties.

The properties of material “ConcreteB25_411” in DELPHIN’s database are assigned to concrete. For AAC and CS, the hygric properties are derived from Feng and Janssen (2021), whereas their thermal properties are assigned based on comparable entries in DELPHIN’s material database. Table 5 provides an overview of the single-valued material properties. The moisture storage properties are implemented using a piecewise function (Dang et al., 2025a): only the portion of the sorption isotherm below 97.4% RH (derived from the desiccator test) and the portion of the moisture retention curve above 97.4% RH (derived from the MIP) are used.

Table 5.

Single-valued material properties implemented in stage II.

MaterialsProperties	Concrete	AAC	CS
Density $ρ$ [kg/m³]	2320.2	461.2	271.0
Porosity $Ψ$ [m³/m³]	0.143	0.814	0.891
Specific heat capacity $c$ [J/(kg·K)]	850	1081	1160
Thermal conductivity $λ$ [W/(m·K)]	2.100	0.095	0.065
Vapor resistance factor at dry state $μ_{dry}$ [−]	110.00	7.35	1.97
Capillary saturation moisture content $w_{cap}$ [kg/m³]	136.0	313.4	755.8
Vacuum saturation moisture content $w_{sat}$ [kg/m³]	143.0	812.6	888.8
Capillary absorption coefficient $A_{w}$ [kg/(m·s^0.5)]	0.008	0.046	1.010

The only variable relates to the processing and implementation of the moisture transport properties for CS and AAC. From Feng and Janssen (2021), the following data can be extracted or derived: the measured $μ (φ)$ function from the cup test, the measured $D_{w} (w)$ and $K_{l} (w)$ functions from the Boltzmann-transformed X-ray attenuation test, and the estimated $D_{w} (w)$ and $K_{l} (w)$ functions using Künzel’s formula (equation (7)). The integral approach, denoted as V0L0, is derived entirely from the $μ (φ)$ function from the cup test. Its separate version, incorporating a constant vapor transport term and a liquid transport term as outlined in equation (10), is designated as V1L1 to evaluate equivalence.

Beyond this straightforward implementation, additional subapproaches are introduced to account for reduction strategies in vapor transport behavior in high humidity range and alternative methods for specifying liquid transport behavior, either through independent liquid transport measurements or simplified formulations. For vapor transport, two strategies are examined to represent the reduced vapor flow in increasingly saturated pores: a non-linear reduction following equation (9) (subapproach V2) and a linear reduction used as a reference (subapproach V3). For liquid transport, two approaches are considered: one based on the X-ray attenuation test with Boltzmann transformation (subapproach L2) and the other derived from Künzel’s formula (subapproach L3). As vapor transport dominates in the lowhumidity range, the L2 and L3 formulations become unreliable there, and the corresponding parts of both curves are therefore replaced with permeabilities derived from the cup test (equivalent to L1). For L2, this substitution is applied at roughly 90% RH, below which the cup test measurements are available and considered reliable. For L3, in accordance with Künzel’s assumption that $D_{w}$ becomes relevant only from 80% RH onward (Künzel, 1995), the portions of the $K_{l} (w)$ curve corresponding to RH below 80% are likewise replaced with cup-test-derived permeabilities while the formulation based on Künzel’s formula is retained from this threshold onward. For AAC, however, the liquid permeability predicted by Künzel’s formula at 80% RH is lower than the cuptestderived permeability up to approximately 95% RH; therefore, the cuptestbased values are smoothly extrapolated over this interval to ensure a continuous transition. Combining these vapor and liquid transport subapproaches yields four paired scenarios—V2L2, V2L3, V3L2, and V3L3—complementing the baseline V0L0 and V1L1 cases. All six scenarios are simulated in DELPHIN, which accommodates all required property formats. In the simulations, vapor and liquid transport properties are introduced as $K_{v}$ and $K_{l}$ functions respectively. The corresponding implementation approaches are summarized in Table 6.

Table 6.

Implementation approaches for moisture transport properties in stage II.

Approaches	Descriptions
V0L0	The $μ (φ)$ function as directly obtained from the cup test is implemented
V1L1	Vapor and liquid transport terms are separated from the cup test results (equation (10)). The constant value, $μ_{dry}$ , is assigned to the $μ (φ)$ function or converted to the $K_{v} (w)$ function, assuming vapor transport is constant without reduction. The $K_{l} (w)$ function subtracting the vapor contribution from the total is implemented
V2L2	The non-linear reduction (equation (9)) is applied for the $\log [K_{v} (w)]$ function separated from the cup test results. The $K_{l} (w)$ function derived from X-ray attenuation test is implemented, with the portion of the curve corresponding to RH below around 90% replaced by the permeabilities derived from the cup test (equivalent to L1)
V2L3	The non-linear reduction (equation (9)) is applied for the $\log [K_{v} (w)]$ function separated from the cup test results. The $K_{l} (w)$ function using Künzel’s formula (equation (7)) is implemented, with the portion of the curve corresponding to RH below 80% replaced by the permeabilities derived from the cup test (equivalent to L1)
V3L2	The linear reduction is applied for the $\log [K_{v} (w)]$ function separated from the cup test results. The $K_{l} (w)$ function derived from X-ray attenuation test is implemented, with the portion of the curve corresponding to RH below around 90% replaced by the permeabilities derived from the cup test (equivalent to L1)
V3L3	The linear reduction is applied for the $\log [K_{v} (w)]$ function separated from the cup test results. The $K_{l} (w)$ function using Künzel’s formula (equation (7)) is implemented, with the portion of the curve corresponding to RH below 80% replaced by the permeabilities derived from the cup test (equivalent to L1)

Figure 7 illustrates the resulting vapor and liquid transport properties corresponding to these approaches. Overall, V2 remains close to V1 except near saturation whereas V3 exhibits pronounced decreases. For liquid permeabilities, the differences among approaches converge in the high moisture content range. While the discrepancies between L2 and L3 generally remain within one order of magnitude, L1 clearly underestimates liquid transport in this range. The distinct scales of the vapor and liquid transport functions reflect a modeling assumption embedded in DELPHIN: vapor transport is assumed to extend up to vacuum saturation, whereas liquid transport is limited by capillary saturation.

The “equivalent vapor and liquid permeability” $K_{v + l}$ [s] is employed to harmonize the properties in different gradients in Figure 8 (Dang et al., 2025a). The equivalent permeabilities derived from the various approaches differ by roughly one order of magnitude in the hygroscopic range. From 80% RH, the threshold at which Künzel’s formula assumes the onset of liquid transport, the L3 series curves show a sharp increase for CS. In contrast, the AAC curves exhibit only a gradual rise, owing to the data processing applied to ensure a smooth transition up to 95% RH between the portions derived from Künzel’s formula and those based on the cup test results. From approximately 90% RH onward for CS or 95% RH for AAC, the permeabilities associated with L2 and L3, both of which incorporate an independent liquidtransport component, display a pronounced increase.

Figures 9 and 10 present the simulated RH profiles and moisture mass (MM) time series for stage II. The 480th and 960th hours are visualized as they mark the transition in boundary conditions and the termination of the numerical simulation. From the RH perspective, the simulated results for concrete remain nearly identical across all scenarios, whereas the CS or AAC layer enters the over-hygroscopic range to varying extents. Different combinations of implementation subapproaches for vapor and liquidtransport properties yield moisture conditions that differ slightly toward drier or wetter states (Figure 9(c) and (g)). Regarding the MM time series for the two sorption processes across the two wall configurations, no clear pattern emerges. The differences between V0L0 and V1L1 are pronounced, even surpassing those observed in scenarios where additional liquid transport terms are incorporated. In the concrete-AAC wall, similar trends appear among materials assigned to the same implementation approaches for liquid transport properties; conversely, the impact of vapor transport property implementation on the concrete-CS wall seems non-negligible (Figure 10(b), (d), (f), (h)).

While incorporating or omitting additional liquid transport terms has an impact, the more noteworthy discrepancies occur between scenarios V0L0 and V1L1. Both scenarios implement moisture transport properties derived from the cup test, either integrally or separately, and are theoretically equivalent. However, these differences suggest underlying implementation nuances. In fact, the default reduction applied to the $μ (φ)$ function in DELPHIN (as described in equation (12)) is only identified after unexpected deviations are observed in the simulation results and subsequently clarified through direct communication with the model developers—information not disclosed in the user manual or published literature. This reduction, however, does not apply if users pre-convert the data to the default $K_{v} (w)$ function, thereby avoiding the unexpected internal adjustment. To assess whether this internal reduction accounts for these discrepancies in outcomes, an additional simulation is conducted using an adjusted $μ (φ)$ function divided by the reduction factor, aiming to restore the original cup test results as expected to be implemented in the integral implementation approach shown in Figure 7. Interestingly, this adjusted V0L0 scenario did not yield significant differences compared to the previously reduced V0L0 version. Nevertheless, this observation does not preclude the possibility that such reductions may lead to substantial deviations under different boundary conditions or with other material configurations. Therefore, it is recommended to convert parameters into DELPHIN’s default formats prior to simulation, to avoid uncertainties from this undocumented internal reduction.

μ {(φ)}_{reduction} = μ {(φ)}_{user - input} \cdot (1 - \frac{w}{w_{sat}})

(12)

Despite these efforts, the discrepancies between V0L0 and V1L1 remain unresolved. An alternative hypothesis is that the two implementation approaches treat moisture fluxes differently, which may affect the advection of sensible and latent heat within the heat balance equation (equation (3)), thereby influencing the overall moisture transport behavior. Specifically, V1L1 considers a portion of moisture flow as liquid flow for the calculation of sensible heat advection, while V0L0 treats the entire moisture flux as vapor flow, thereby accounting for the full latent heat transport associated with $L_{v}$ in equation (3). As latent heat transport plays a far more significant role than sensible heat transport, this fundamental difference likely contributes more substantially to the observed discrepancies. To validate this hypothesis, two additional implementation approaches are introduced: (1) V0L0_Kv, where the $μ (φ)$ function is converted into the $K_{v} (w)$ function via equation (13) (similar to equation (9) but without reduction and utilizing varied $μ$ values; designed to verify the equivalence of different parameters for material properties and should be identical to V0L0) and (2) V0L0_Kl, where the $μ (φ)$ function is transformed into the $K_{l} (w)$ function for implementation, as described in equation (14); following the derivation in equation (2). These approaches are compared with the existing V0L0, which implements only the fitted $μ (φ)$ function from the cup test without liquid water transport, and V1L1. In sum, V0L0 and V0L0_Kv rely entirely on vapor transport while V0L0_Kl employs only liquid transport. In contrast, V1L1 incorporates both vapor and liquid mechanisms. The WD scenario of the concrete-CS wall is used for the supplementary comparisons among the four approaches.

K_{v} (P_{c}) = \frac{D_{va}}{μ (φ) \cdot R_{v} T} \cdot \frac{\nabla P_{c}}{\nabla P_{v}}

(13)

K_{l} (P_{c}) = δ_{v} \cdot \frac{φ P_{vsat}}{ρ_{w} R_{v} T} = \frac{D_{va}}{μ (φ) \cdot R_{v} T} \cdot \frac{φ P_{vsat}}{ρ_{w} R_{v} T}

(14)

Figure 11 presents the detailed outputs of the WD scenario for the concrete-CS wall, implemented using four different approaches for liquid transport properties: V0L0, V0L0_Kv, V0L0_Kl, and V1L1. Overall, the results of V0L0 and V0L0_Kv exhibit strong similarity, though slight discrepancies exist, potentially due to fitting variations and numerical precision. Nevertheless, the findings largely support the equivalence of different material property parameters. As expected, V1L1, which incorporates both vapor and liquid transport, falls between the results of V0L0 and V0L0_Kv (relying solely on vapor transport) and V0L0_Kl (exclusively employing liquid transport). The cumulative total heat flux (HF) is shown in Figure 11(d), with its two contributing components—enthalpy flux due to vapor diffusion and conductive heat flux at the interior surface—presented in Figure 11(e) and (f), respectively. These correspond to the terms $(L_{v} + c_{v} T) g_{v}$ and $λ \nabla T$ in equation (3). Note that the enthalpy flux due to liquid advection (the term $c_{l} {Tg}_{l}$ in equation (3)), remains zero across all simulation cases, including V0L0_Kl, which is explicitly configured to represent moisture transport exclusively via the liquid phase. This contradicts the intended modeling assumption and suggests that DELPHIN may still internally resolve moisture transport through vapor diffusion, even under configurations designed to suppress it. However, no explanation for this behavior is provided by the model developers.

To verify this assumption, an additional comparative scenario WD + WDR is applied to V0L0_Kl, imposing a liquid source of 1 L/(m² s) at both interior and exterior surfaces. Figure 12(a) displays the enthalpy heat flux due to liquid advection at the exterior boundary (se.), the concrete/CS interface (it.) and the interior boundary (si.). While the liquid advection at the interior surface remains zero, both the concrete/CS interface and the exterior surface exhibit the effects of liquid water transfer. Figure 12(b) presents the RH profiles under the WD + WDR scenario, further confirming that liquid migration at the concrete/CS interface originates from the exterior liquid source. Meanwhile, the interior surface, despite being in a prolonged near-saturation state, still exhibits zero liquid advection. This behavior suggests that DELPHIN may only activate liquid transport mechanisms when an imposed liquid source is present at the exterior boundary. Since rare materials are both capillary-active and vapor-tight, the approach V0L0_Kl is unlikely to be adopted in practice. Nevertheless, computational discrepancies in hygric predictions may still arise among integral and separate approaches for implementing vapor and liquid transport properties, including V0L0, V0L0_Kv and V1L1. These deviations are generated through their impact on heat transfer.

Conclusion

Reliable hygrothermal prediction hinges on the accurate implementation of hygric material properties. Although HAM models such as WUFI and DELPHIN are built on theoretically equivalent formulations, differences in how these properties are characterized, processed and implemented can produce substantial variations in simulation outcomes. This study adopts a structured, simulation-based approach to examine the strategies and uncertainties associated with the implementation of hygric material data across two representative moisture regimes. Rather than proposing new physical formulations, it advances transparency in HAM modeling by exposing how internal algorithms, data-handling routines and embedded simplifications shape hygrothermal predictions. The proposed scheme provides a diagnostic basis for evaluating reliability across moisture regimes and supports consistent implementation practices to improve reproducibility and model comparability.

Implementation of liquid transport coefficients.

Comparative simulations reveal that Künzel’s empirical formula introduces systematic bias compared with the measurement-based data. Its assumption that liquid transport becomes active only above 80% RH is particularly restrictive: the resulting permeabilities can fall below those inferred from cup test measurements, and in the high moisture range they may deviate from X-ray – derived values by up to an order of magnitude. In WUFI, the binary distinction between liquid diffusivities for suction and redistribution based solely on WDR presence overlooks the continuous nature of liquid transport, leading to potential over- or underestimations under real climatic conditions. DELPHIN, conversely, enforces strict monotonicity of material property curves; this ensures numerical robustness but may underestimate liquid diffusivity in the low moisture range where experimental data often show non-monotonic behavior.

Coupling of vapor and liquid transport mechanisms.

Under typical service conditions within the hygroscopic range, both vapor and liquid transport act simultaneously. While previous studies have suggested that a vapor-dependent transport function, $μ (φ)$ or $K_{v} (w)$ , may suffice for purely hygroscopic processes (Dang et al., 2026a), the present results show that in the over-hygroscopic range, liquid transport contributes significantly and require explicit representation via $D_{w} (w)$ or $K_{l} (w)$ functions. Additionally, although DELPHIN provides extensive documentation, the internal criteria governing the separation of vapor and liquid transport and their influence on heat transfer remain unclear, as the simulated behavior does not fully match the published descriptions.

Implementation of moisture storage properties.

Beyond transport mechanisms, notable differences emerge in the handling of moisture storage. WUFI’s accuracy is highly sensitive to the resolution of user-defined storage curves; finer input improves precision but increases user burden and risk of inconsistency. DELPHIN is assumed to mitigate this through robust internal interpolation of sorption isotherms and moisture-retention curves, enhancing stability and reducing reliance on high-resolution data.

Implications for model users and developers.

For users, the findings underscore the critical role of implementation choices in shaping simulation outcomes. Even mathematically consistent formulations can diverge due to model-specific assumptions, with deviations strongly influenced by moisture regime and boundary conditions. Users should identify the dominant sorption regime for their application, assess the reliability of alternative implementation strategies with inter-model comparison and experimental validation. Building on the comparative simulations presented in this article and related companion studies (Dang, 2025; Dang et al., 2023, 2025a, 2026a, 2026b), the following practical guidance for model application can be formulated for implementing moisture transport coefficients.

For simulations confined (primarily) to the hygroscopic range, users should prioritize the accurate specification of vapor transport properties, as reliable predictions can generally be achieved without further refinement of liquid transport properties.

For simulations that extend toward or into the over-hygroscopic range, users should obtain liquid transport properties from independent measurements or simplified approaches and evaluate their performance through comparison with experimental data and/or with simulation results generated using alternative implementation approaches.

For scenarios characterized by pronounced wetting or capillarydriven processes, users should systematically evaluate the sensitivity of the predicted responses to modelspecific assumptions by testing multiple representations of liquid transport properties, and, in the absence of measurement data, treat the simulated results more as indicative trends than as numerically reliable predictions.

Moreover, sensitivity analyses are indispensable, as both the intrinsic variability in the moisturetransport behavior of different materials and the uncertainties inherent in HAM models can influence simulation accuracy to different extents across sorption regimes (Dang, 2025), making such analyses essential for identifying the assumptions and parameter choices to which the simulated results are most responsive.

For developers, the findings underline the need for greater methodological transparency. Limited access to source codes leaves users reliant on default settings that may conceal algorithmic simplifications. Such “hidden” uncertainties undermine reproducibility and user confidence. Developers are thus encouraged to document internal assumptions, re-examine default configurations and provide regime-specific guidance balancing numerical efficiency with physical validity.

Footnotes

Acknowledgements

The authors would express gratitude to Thomas Schmidt, Christian Bludau and Daniel Zirkelbach of the WUFI team and Heiko Fechner and John Grunewald of the DELPHIN team for explaining the implementation of material properties in their models.

Author note

Xinyuan Dang is now affiliated with School of Architecture, Planning and Environmental Policy, University College Dublin, Dublin, Ireland.

ORCID iDs

Xinyuan Dang

Hans Janssen

Author contributions

Xinyuan Dang: conceptualization, methodology, experiments, data processing and visualization, writing – original draft, funding acquisition; Hans Janssen: supervision, conceptualization, methodology, writing – review & editing; Staf Roels: supervision, conceptualization, methodology, experiments, writing – review & editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research is supported by China Scholarship Council (grant number: 202006090005).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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