# Effective Moisture Penetration Depth (EMPD) Model[LINK]

The EMPD (Effective Moisture Penetration Depth) model is a simplified, lumped approach to simulate surface moisture adsorption and desorption. It estimates moisture adsorption and desorption from building surfaces and calculates the effect this adsorption/desorption has on the humidity in each zone. There are two fictitious layers of material with uniform moisture content: a surface layer, which accounts for short-term moisture buffering, and a deep layer, which accounts for more slowly responding moisture buffering. The model calculates the moisture transfer between the air and the surface layer and between the surface layer and the deep layer. This moisture transfer impacts the zone humidity, and also impacts the zone temperature through latent-to-sensible conversion from the heat of adsorption.

## EMPD Model Description[LINK]

The EMPD concept is based on the assumption of cyclical variations in humidity, and therefore material moisture content, u. In other words, the following constraint must be met:

∫t2t1dudtdt=0

This is generally a reasonable assumption for buildings, with daily internal latent gains. The EMPD model uses a thin material layer of constant thickness at each material surface. The moisture content is assumed constant across this thickness, termed the *surface penetration depth*. For most building materials, the equilibrium moisture sorption isotherm can be defined by the following general equation (Kerestecioglu et al. 1988):

u=aϕb+cϕd

where a, b, c, and d are fitting parameters and ϕ is relative humidity.

This surface layer (labeled with subscript 1 below) exchanges moisture with the zone air based on the difference between the zone air vapor density and the material vapor density. The model converts the surface layer moisture content to a vapor density ρv through the material’s sorption curve:

ρv1=0.622ρairu1dudϕPPsat−u1

where

dudϕ = slope of the moisture sorption curve, kg/kg-RH

Psat = saturated vapor pressure

ρair = dry-air density

The moisture flux between the material and the zone air, jzone, is the difference in vapor densities divided by the overall mass transfer resistance, which is the sum of the diffusive resistance of the surface layer, the diffusive resistance of any coating, and the convective resistance of the air boundary layer:

jzone=ρv1−ρv,zoneRMT1+RMT,coating+RMT,BL

The surface layer resistance is calculated with:

RMT,1=dEMPD,12¯RwaterTδperm

where

dEMPD,1 = depth of surface layer, m

¯Rwater = universal gas constant for water (461.52 J/kg-K)

T = temperature, K

δperm = water vapor permeability of the material, kg/m-s-Pa

The coating resistance is:

RMT,coating=tcoatingPambientδperm,coating¯RwaterT

where

tcoating = coating thickness, m

Pambient = ambient pressure, Pa

δperm,coating = permeability of the coating, kg/m-s-Pa.

Finally, the boundary layer mass-transfer resistance is calculated by converting the heat-transfer coefficient to mass transfer with the Lewis relation:

RMT,BL=ρairCpairhconv

Behind the surface layer is a deep layer (labeled with subscipt 2 below) of thickness dEMPD,2. The surface layer accounts for buffering of high-frequency changes in the zone air humidity, while the deep layer accounts for the material’s response to longer term changes in the zone air humidity. The model calculates the moisture flux between the surface and deep layers with:

j2=ρv,1−ρv,2RMT,2

where RMT,2 is:

RMT,2=dEMPD,1+dEMPD,22¯RwaterTδperm

These moisture fluxes are used to update the moisture content (or equivalent RH, ϕ of each layer:

ϕ1(t)=ϕ1(t−δt)−(jzone+j2)⋅TimeStepρmatldEMPD,1dudϕ

ϕ2(t)=ϕ2(t−δt)+j2⋅TimeStepρmatldEMPD,2dudϕ

where

ρmatl = Material dry density, kg/m3

TimeStep = Simulation timestep, s

dudϕ = slope of moisture curve (change in moisture content / change in RH), kg/kg ⋅ RH

The equivalent RH and equivalent vapor density are related with:

ρv,1=ϕ1Psat(T)¯RwaterT

ρv,2=ϕ2Psat(T)¯RwaterT

The zone flux is used, along with the area of the particular surface, to update the zone humidity ratio, as discussed in [moisture-predictor-corrector].

The zone flux is also used to calculate the sensible heat released (during adsorption) or absorbed (during desorption) at the material surface:

Qflux=jzonehfg

where hfg is the enthalpy of vaporization of water, assumed to be 2500 kJ/kg. This is added to the heat balance calculations at the interior surface.

For further information on the EMPD model, see References below.

## EMPD Nomenclature[LINK]

A=surface area[m2]d=penetration depth[m]j=water mass flux[kgm2⋅s]¯Rwater=universal gas constant for water,461.52[Jkg⋅K]RMT=Mass transfer resistance[s/m]T=temperature[K]u=moisture content[kgkg]

### Greek letters[LINK]

δ=permeability[kgm⋅s⋅Pa]ϕ=relative humidityρ=density[kgm3]ρv=vapor density[kgm3]

1=surface layer node2=deep layer nodeBL=boundary layermatl=solid materialzone=zone air

Cunningham, M.J., *The moisture performance of framed structures - a mathematical model*, Build. Environ. 23 (1988) 123-35.

Kerestecioglu, A., M. Swami, R. Dabir, N. Razzaq, P. Fairey, *Theoretical and Computational Investigation of Algorithms for Simultaneous Heat and Moisture Transport in Buildings*. Florida Solar Energy Center, DOE/SF/16305-2, 1988.

Cunningham, M.J., *Effective penetration depth and effective resistance in moisture transfer*, Build. Environ. 27 (1992) 379-86

Janssen, H. and S. Roels, *Qualitative and quantitative assessment of interior moisture buffering by enclosures*, Energ. Buildings. 41 (2009) 382-94.

Abadie, M.O. and K.C. Mendonca, *Moisture performance of building materials: From material characterization to building simulation using the Moisture Buffer Value concept*, Build. Environ. 44 (2009) 388-401.

Vereecken, E., S. Roels, H. Janssen, *In situ determination of the moisture buffer potential of room enclosures*, J. Build. Phys. 34 (2011) 223-46.

Woods, J., Winkler, J, and Christensen, D. *Evaluation of the Effective Moisture Penetration Depth Model for Estimating Moisture Buffering in Buildings*, NREL/TP-5500-57441, 2013.

Woods, J., J. Winkler, D. Christensen, E. Hancock, *Using Whole-House Field Tests to Empirically Derive Moisture Buffering Model Inputs*. NREL/TP-5500-62456, 2014.

## Effective Moisture Penetration Depth (EMPD) Model[LINK]

## Overview[LINK]

The EMPD (Effective Moisture Penetration Depth) model is a simplified, lumped approach to simulate surface moisture adsorption and desorption. It estimates moisture adsorption and desorption from building surfaces and calculates the effect this adsorption/desorption has on the humidity in each zone. There are two fictitious layers of material with uniform moisture content: a surface layer, which accounts for short-term moisture buffering, and a deep layer, which accounts for more slowly responding moisture buffering. The model calculates the moisture transfer between the air and the surface layer and between the surface layer and the deep layer. This moisture transfer impacts the zone humidity, and also impacts the zone temperature through latent-to-sensible conversion from the heat of adsorption.

## EMPD Model Description[LINK]

The EMPD concept is based on the assumption of cyclical variations in humidity, and therefore material moisture content, u. In other words, the following constraint must be met:

∫t2t1dudtdt=0

This is generally a reasonable assumption for buildings, with daily internal latent gains. The EMPD model uses a thin material layer of constant thickness at each material surface. The moisture content is assumed constant across this thickness, termed the

surface penetration depth. For most building materials, the equilibrium moisture sorption isotherm can be defined by the following general equation (Kerestecioglu et al. 1988):u=aϕb+cϕd

where a, b, c, and d are fitting parameters and ϕ is relative humidity.

This surface layer (labeled with subscript 1 below) exchanges moisture with the zone air based on the difference between the zone air vapor density and the material vapor density. The model converts the surface layer moisture content to a vapor density ρv through the material’s sorption curve:

ρv1=0.622ρairu1dudϕPPsat−u1

where

dudϕ = slope of the moisture sorption curve, kg/kg-RH

Psat = saturated vapor pressure

ρair = dry-air density

The moisture flux between the material and the zone air, jzone, is the difference in vapor densities divided by the overall mass transfer resistance, which is the sum of the diffusive resistance of the surface layer, the diffusive resistance of any coating, and the convective resistance of the air boundary layer:

jzone=ρv1−ρv,zoneRMT1+RMT,coating+RMT,BL

Nodal network for effective moisture pentration depth model [fig:Nodal-network-for-effective-moisture-penetration-depth-model]

The surface layer resistance is calculated with:

RMT,1=dEMPD,12¯RwaterTδperm

where

dEMPD,1 = depth of surface layer, m

¯Rwater = universal gas constant for water (461.52 J/kg-K)

T = temperature, K

δperm = water vapor permeability of the material, kg/m-s-Pa

The coating resistance is:

RMT,coating=tcoatingPambientδperm,coating¯RwaterT

where

tcoating = coating thickness, m

Pambient = ambient pressure, Pa

δperm,coating = permeability of the coating, kg/m-s-Pa.

Finally, the boundary layer mass-transfer resistance is calculated by converting the heat-transfer coefficient to mass transfer with the Lewis relation:

RMT,BL=ρairCpairhconv

Behind the surface layer is a deep layer (labeled with subscipt 2 below) of thickness dEMPD,2. The surface layer accounts for buffering of high-frequency changes in the zone air humidity, while the deep layer accounts for the material’s response to longer term changes in the zone air humidity. The model calculates the moisture flux between the surface and deep layers with:

j2=ρv,1−ρv,2RMT,2

where RMT,2 is:

RMT,2=dEMPD,1+dEMPD,22¯RwaterTδperm

These moisture fluxes are used to update the moisture content (or equivalent RH, ϕ of each layer:

ϕ1(t)=ϕ1(t−δt)−(jzone+j2)⋅TimeStepρmatldEMPD,1dudϕ

ϕ2(t)=ϕ2(t−δt)+j2⋅TimeStepρmatldEMPD,2dudϕ

where

ρmatl = Material dry density, kg/m3

TimeStep = Simulation timestep, s

dudϕ = slope of moisture curve (change in moisture content / change in RH), kg/kg ⋅ RH

The equivalent RH and equivalent vapor density are related with:

ρv,1=ϕ1Psat(T)¯RwaterT

ρv,2=ϕ2Psat(T)¯RwaterT

The zone flux is used, along with the area of the particular surface, to update the zone humidity ratio, as discussed in [moisture-predictor-corrector].

The zone flux is also used to calculate the sensible heat released (during adsorption) or absorbed (during desorption) at the material surface:

Qflux=jzonehfg

where hfg is the enthalpy of vaporization of water, assumed to be 2500 kJ/kg. This is added to the heat balance calculations at the interior surface.

For further information on the EMPD model, see References below.

## EMPD Nomenclature[LINK]

A=surface area[m2]d=penetration depth[m]j=water mass flux[kgm2⋅s]¯Rwater=universal gas constant for water,461.52[Jkg⋅K]RMT=Mass transfer resistance[s/m]T=temperature[K]u=moisture content[kgkg]

## Greek letters[LINK]

δ=permeability[kgm⋅s⋅Pa]ϕ=relative humidityρ=density[kgm3]ρv=vapor density[kgm3]

## Subscripts[LINK]

1=surface layer node2=deep layer nodeBL=boundary layermatl=solid materialzone=zone air

## References[LINK]

Cunningham, M.J.,

The moisture performance of framed structures - a mathematical model, Build. Environ. 23 (1988) 123-35.Kerestecioglu, A., M. Swami, R. Dabir, N. Razzaq, P. Fairey,

Theoretical and Computational Investigation of Algorithms for Simultaneous Heat and Moisture Transport in Buildings. Florida Solar Energy Center, DOE/SF/16305-2, 1988.Cunningham, M.J.,

Effective penetration depth and effective resistance in moisture transfer, Build. Environ. 27 (1992) 379-86Janssen, H. and S. Roels,

Qualitative and quantitative assessment of interior moisture buffering by enclosures, Energ. Buildings. 41 (2009) 382-94.Abadie, M.O. and K.C. Mendonca,

Moisture performance of building materials: From material characterization to building simulation using the Moisture Buffer Value concept, Build. Environ. 44 (2009) 388-401.Vereecken, E., S. Roels, H. Janssen,

In situ determination of the moisture buffer potential of room enclosures, J. Build. Phys. 34 (2011) 223-46.Woods, J., Winkler, J, and Christensen, D.

Evaluation of the Effective Moisture Penetration Depth Model for Estimating Moisture Buffering in Buildings, NREL/TP-5500-57441, 2013.Woods, J., J. Winkler, D. Christensen, E. Hancock,

Using Whole-House Field Tests to Empirically Derive Moisture Buffering Model Inputs. NREL/TP-5500-62456, 2014.Documentation content copyright © 1996-2020 The Board of Trustees of the University of Illinois and the Regents of the University of California through the Ernest Orlando Lawrence Berkeley National Laboratory. All rights reserved. EnergyPlus is a trademark of the US Department of Energy.

This documentation is made available under the EnergyPlus Open Source License v1.0.