Kopia Session3-5.pdf

MODELLING OF VOLATILE ORGANIC COMPOUNDS EMISSION FROM

DRY BUILDING MATERIALS

Hongyu Huang Fariborz Haghighat

Department of Building, Civil and Environmental Engineering

Concordia University, Montreal, Canada

hongyu_h@ cbs-engr.concordia.ca

haghi@ cbs-engr.concordia.ca

ABSTRACT

A numerical model was developed to predict volatile

organic compound (VOC) emission rate from dry

building materials. The model considers mass diffusion

process within the material and mass convection &

diffusion processes in the boundary layer. All the

parameters, mass diffusion coefficient of the material,

material/air partition coefficient, and mass transfer

coefficient of the air can be either found in the

literature or calculated using known principles.

modeling.

Physical models are based on the fundamentals of mass

transfer processes [1] ; diffusion within the material as

results of concentration, pressure, or temperature

gradient, and surface emission between the material

and the overlying air as a consequence of evaporation,

convection and diffusion. Fick's second law describes

the diffusion within the materials. For wet materials

such as paints or wood stain, the diffusion coefficient

within the material is very difficult to determine, and

studies show that the surface emission usually

dominates the emission processes. Therefore, most of

the emission models for wet building materials are

concentrated on the VOC transport in the air [2-4] . For

dry building materials, the diffusion within the material

cannot be ignored and the internal diffusion is more

likely to be the dominating resistance. Recent review of

existing emission models for dry material reveals some

of their shortcomings. For example, the diffusion

controlled emission models only consider the internal

diffusion and ignore the surface convection process [5,6] .

This simplification causes the model to underestimate

VOC emission at the early stage when the surface

concentration is relatively high. The conjugate mass

transfer model assumes the VOC concentration at the

material bottom is constant and ignores the sorption

factor [7] . Those assumptions are not appropriate for real

building material, since the concentration distribution

inside the material is time dependent and the sorption

factor cannot be ignored. Further, the model developed

for the semi-infinite materials [ 8 ] are not suitable for thin

building materials.

The predictions of the model was validated at two

levels: with experimental results from the specially

designed test and with the prediction made by a CFD

model. The results indicate that there is generally a

good agreement between the model predictions, the

experimental results, and the CFD results.

Keywords: dry building material, VOC emission,

diffusion, and numerical model

INTRODUCTION

Volatile Organic Compounds emitted by building

materials are recognized as major problems affecting

human comfort, health and productivity. Therefore,

accurate modeling of the material emission rate in

buildings is important for predicting the contaminant

concentration, occupant exposure and for the design of

mechanical ventilation systems. Recently, there has

been a growing interest in the development of

mathematical models to predict the quality of indoor

air.

Emission models include empirical models and

physical models. The parameters of empirical models

are determined by fitting experimental data to a

predefined model. The main drawback of these models

are that nonlinear regression curve fitting might lead to

multiple solutions and the resulting empirical

parameters may not be scaled up for use in actual

buildings. Therefore, physical models based on the

mass transfer processes are more attractive to most

researchers for building material emission rate

Therefore, some researchers turn to CFD to study

emission from dry building materials and their concern

is mainly on contaminant distributions in the air.

Recently developed CFD models consider both the

surface emission and the internal diffusion [9,10] . The

critical problem of these models is the solution

convergence, and the main inherent drawback of this

technique is that the CFD simulation would be too

expensive and time consuming to be used as a routine

procedure for long term VOC emission prediction.

VOC concentration in the air phase and the VOC

concentration in the material phase can be described by

Henry’s law [12] :

Although there are a lot of achievements in the

development of mathematical models for dry building

materials, a model which could overcome the existing

shortcomings is not yet available. This paper describes

the development of a numerical model.

()

(2)

Where C m (b,t) is VOC concentration at the material

surface (ug/m 3 ) and C as is the VOC concentration in the

air near material surface (ug/m 3 ), k is the material/air

partition coefficient, b is the thickness of the material

(m), and t is the time (s).

THE EMISSION MODEL

The physical system considered here is a dry building

material (carpet, vinyl flooring, particleboard, etc.) and

has its one surface exposed to the air. The VOC

emission from this material is composed of three main

processes as shown in Figure 1.

Mass transfer in the material

For a dry material with homogeneous diffusivity, the

transient VOC diffusion in the material can be

described by the one-dimensional diffusion equation:

Air

Boundary

Layer

Interface

∂

() ()

∂

(3)

∂

Material

Where C m is the VOC concentration in the material

(ug/m 3 ), D m is the VOC diffusion coefficient of the

material (m 2 /s) and y is the coordinate in which the

VOC diffusion in the material takes place (m).

Figure 1: Physical configuration of VOC emission from

the dry building material. 1: Internal diffusion; 2:

Material /air interface; 3. External advection.

Mass balance in the room or chamber

Assuming that the VOC is totally mixed in the room

air. The transient mass balance in the room or chamber

can be expressed by:

Mass transfer in the boundary layer

When air passes over the material surface, a mass

boundary layer exists between the surface material and

the main flow. The VOC mass transfer in this mass

boundary layer is determined by diffusion and

convection. The rate of VOC mass transfer in the

boundary layer can be expressed as:

∂

() () b

−

∂

(4)

∂

(

−

)

(1)

Where C a is the VOC concentration in the room air

(ug/m 3 ), C in is the VOC concentration in the supply air

(ug/m 3 ), N is the air exchange rate (h -1 ) and L is the

material loading factor (m 2 /m 3 ).

Where h is the mean mass transfer coefficient (m/s), C as

is the VOC concentration in the air near material

surface (ug/m 3 ) and C a is the VOC concentration

outside the mass boundary layer (ug/m 3 ).

Boundary conditions and solutions

Some initial conditions and boundary conditions are

needed to close the above equations.

Material /air interface

At the material/air interface, the material is the

adsorbent and the VOC gas is the adsorbate. The

material exerts an attractive force normal to the surface

plane. Consequently, the concentration of VOC at the

material phase exceeds that in the gas phase. Langmuir

and BET are the most common isotherm models which

may be used to describe this process [11] . At

atmospheric pressure, for low VOC concentration and

isothermal conditions, equilibrium relation between the

a) Initial conditions:

A homogeneous new material with initial VOC

concentration of

C m

( )

(5)

The initial VOC concentration in the room air (C a0 ) is:

()

(6)

estimate the VOC diffusion coefficient in the air [15] :

Fuller, Schettler and Giddings (FSG) method and

Wilke and Lee (WL) method. FSG method is the most

accurate for non-polar gasses at low to moderate

temperatures. In this study, the FGS method was used

to estimate VOC diffusion coefficient in the air. This

method is based on the following correlation:

b) Boundary conditions:

At the material bottom, there is no VOC passing

through this surface.

∂

() 0

−

0 =

(7)

∂

−

(12)

(

)

At the material surface and room air interface, the mass

balance can be written as:

VOC

(

)

Where

VOC

, T is the absolute

∂

() (

()

(8)

)

−

VOC

∂

temperature (K), P is the pressure (atm), V a is the air

molar volume (cm 3 /mol), V VOC is the VOC molar

volume (cm 3 /mol), M a is the air molecular weight

(g/mol) and M VOC is the VOC molecular weight

(g/mol).

There are four key parameters which need to be

determined: the mass transfer coefficient in the air, h,

the partition coefficient, k, the mass diffusion

coefficient in the material, D m , and the VOC initial

concentration, C 0 .

Therefore, the mass transfer coefficient can be

estimated using Equations 9-12. Those correlations are

only valid when the concentration at the bottom of

mass boundary layer is constant. Since the VOC

concentration at the material surface is very low and

the VOC diffusion through the material is very slow:

the VOC concentration near the material surface will be

relatively stable. Thus, we may assume that the

concentration near the material surface is constant in a

given time step.

Mass transfer coefficient in the air, h

In the mass boundary layer, the following relationships

exist [ 13 ] :

a) For laminar flow, (Re l <500,000):

664

(9)

b) For turbulent flow, (Re l >500,000):

Material/air partition coefficient, k

The material/air partition coefficient describes the

relationship between the concentration in the gas phase

and the concentration in the material phase. It is a

material property and is obtained experimentally [5,16] .

037

(10)

c) Combined laminar /turbulent flow, (Re l <10 7 ,

Re tr =500,000):

Mass diffusion coefficient in the material, D m

The diffusion coefficient in the material is usually a

function of many factors, such as the pore structure, the

material type, compound properties and temperature, as

well as VOC concentration. The dependence of the

diffusion coefficient on the VOC concentration can be

ignored considering that the VOC concentration in the

material is usually very low. The diffusion coefficient

is usually determined experimentally [5,16] .

(

037

−

8700

)

(11)

Where,

is the

kinematic viscosity of the air (m 2 /s), u is the mean air

velocity over the material (m/s), l is the characteristic

length of material (m) and D a is the VOC diffusion

coefficient in the air (m 2 /s).

Initial concentration, C 0

Initial concentration in the material can be obtained

through solvent extraction, high temperature thermal

desorption or direct analysis [17] . Recently a cryogenic

grinding/ fluidized bed desorption method was

The VOC diffusion coefficient (D a ) can be directly

obtained from literature [14] or can be estimated through

other methods. Two main methods have been used to

developed to measure the initial concentration [6] . The

VOC concentration in the material, VOC emission rate

and the VOC concentration in the room are a function

of the initial concentration, thus a small error in initial

concentration estimation may cause a significant error

in prediction results.

THE MODEL VALIDATION

The model's prediction was compared with the

experimental results of two particleboard tests as well

as the predictions made by a CFD model [ 9] .

The model predictions were compared with

experimental data obtained at Massachusetts Institute

of Technology [9] . The experiments were carried out in

a small-scale chamber of 0.5

SOLUTION TECHNIQUES

A numerical finite difference method was used to

simultaneously solve equations 1-4 using the initial

conditions, Equations 5 and 6, and boundary

conditions, Equations 7 and 8. The outcomes are:

0.4

0.25 m 3 at a

temperature of 23

0.5 0 C, relative humidity 50

0.5%,

0.05h -1 . Two different

specimens of particleboard were tested. Major

compounds identified for the tested particleboards were

the same: hexanal,

a) The VOC concentration at the material surface

C m (b,t):

-pinene, camphene, and limonene.

The particleboard properties (D m , k, and C 0 ) were

estimated by using the chamber emission data

(concentration vs. time) to fit the CFD model [9] . The

physical properties of the particleboard were supplied

by the experimenter and they are given in Table 1. The

airflow inside the chamber is treated as laminar flow

over a flat plate.

∆

) ()

−

(

∆

(

−

∆

)

∆

(

−

∆

)

∆

(

−

∆

)

(

)

Table 1 Physical properties of particleboard emissions

Compound

TVOC

Hexanal

-Pinene

(

∆

)

Particleboard 1

D m (m 2 /s)

7.65

10 -11

7.65

10 -11

1.2

10 -10

b) The VOC concentration in the room air, C a (t):

C 0 (ug/m 3 )

5.28

10 7

1.15

10 7

3.45

10 6

3289

5602

Particleboard 2

D m (m 3 /s)

7.65

10 -11

7.65

10 -11

1.2

10 -10

∆

()

) ()

C 0 (ug/m 3 )

9.86

10 7

2.96

10 7

7.89

10 6

(

∆

3289

5602

(14)

(

−

∆

)

(

∆

)

Figures 2 to 7 show the comparison of the predicted

TVOC, hexanal and

-pinene concentrations with the

experimental results for particleboard 1. The

experiment was carried out for 96 hours. There is good

agreement between predicted concentrations and

experimental measurements. There are some

discrepancies between predicted results (both with the

proposed numerical model and the CFD model) and

experimental results during the initial hours. This might

be due to instability and partial mixing in the chamber

at the beginning of the tests.

c) The VOC emission rate, R(t):

()

() ()

−

(15)

d) The normalized emitted mass, M/M 0 :

()

∆

Figures 5 to 7 compare the model predicted TVOC,

hexanal and

(16)

-pinene concentrations with the

experimental ones for particleboard 2. The experiment

was carried out for 840h in the chamber. As shown in

the figures the predictions of the TVOC, hexanal and

Where y

∆

is the space grid distance (m), t

∆

is the

calculation time step (s).

-pinene made by the proposed model fit the

experimental data very well. The predicted results and

and air exchange rate 1.0

experimental results closely follow the same trend,

especially for the long term; see Figures 5b, 6b and 7b.

12,000

Measured Data

CFD Model

numerical Model

9,000

The model predictions were also compared with the

prediction of a CFD model [9] . Figures 2 to 7 also

compare the model predicted TVOC, hexanal and

6,000

pinene concentrations with the results predicted by a

CFD model. In general, there is excellent agreement

between predicted numerical results, measurement data

and CFD predictions. As shown in Figures 2 and 3, for

short term, the predictions made by CFD for sample 1

(PB1) fit the experimental data better than the proposed

numerical model. While, for long term, Figures 5, 6

and 7 show that the prediction made by the proposed

model fit the experimental data better than the

prediction made by CFD. However, over all, the

predicted curves of the two models follow the

experimental results closely.

3,000

120

150

Time (h)

Figure 5 (a) Comparison of TVOC concentrations

(PB2)

12,000

Measured Data

CFD Model

numerical Model

9,000

6000

6,000

5000

Measured Data

CFD Model

Numerical model

3,000

4000

3000

200

400

600

800

2000

Time (h)

1000

Figure 5 (b) Comparison of TVOC concentrations

(PB2)

100

Time (h)

Figure 2 Comparison of TVOC concentrations (PB1)

4,000

Measured Data

CFD Model

numerical Model

1600

3,000

Measured data

CFD Model

Numerical Model

1200

2,000

800

1,000

400

120

150

Time (h)

100

Figure 6 (a) Comparison of hexanal concentrations

(PB2)

Time (h)

Figure 3 Comparison of hexanal concentrations (PB1)

4,000

800

Measured Data

M easured Data

CFD M odel

Numerical M o del

3,000

CFD Model

numerical Model

600

2,000

400

1,000

200

400

600

800

100

Time (h)

Figure 6 (b) Comparison of hexanal concentrations

(PB2)

Figure 4 Comparison of

-pinene concentrations (PB1)

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