Understanding and controlling airborne organic compounds in the indoor environment

22 Pages·2015·0.99 MB·English

IndoorAir2016;26:39–60 ©2015JohnWiley&SonsA/S.PublishedbyJohnWiley&SonsLtd
wileyonlinelibrary.com/journal/ina
PrintedinSingapore.Allrightsreserved INDOORAIR
doi:10.1111/ina.12198
Keynote: Indoor Air 2014
Understanding and controlling airborne organic compounds in the
indoor environment: mass transfer analysis and applications
Abstract Mass transfer is key to understanding and controlling indoor Y.Zhang1,J.Xiong2,J.Mo1,
airborne organic chemical contaminants (e.g., VVOCs, VOCs, and SVOCs). M.Gong1,J.Cao1
In this study, we first introduce the fundamentals of mass transfer and then
present a series of representative works from the past two decades, focusing 1InstituteofBuiltEnvironment,TsinghuaUniversity,
on the most recent years. These works cover: (i) predicting and controlling Beijing,China,2SchoolofMechanicalEngineering,
emissions from indoor sources, (ii) determining concentrations of indoor air BeijingInstituteofTechnology,Beijing,China
pollutants, (iii) estimating dermal exposure for some indoor gas-phase
Key words: Indoor Air Quality (IAQ); Exposure; Health
SVOCs, and (iv) optimizing air-purifying approaches. The mass transfer
risk;Aircleaning;Builtenvironment;Masstransfer.
analysis spans the micro-, meso-, and macroscales and includes normal mass
transfer modeling, inverse problem solving, and dimensionless analysis.
These representative works have reported some novel approaches to mass Y.Zhang
transfer. Additionally, new dimensionless parameters such as the Little InstituteofBuiltEnvironment
number and the normalized volume of clean air being completely cleaned in TsinghuaUniversity100084Beijing,China
a given time period were proposed to better describe the general process Tel.:[phone]
characteristics in emissions and control of airborne organic compounds in Fax:[phone]
e-mail:[email protected]
the indoor environment. Finally, important problems that need further study
are presented, reflecting the authors’ perspective on the research
opportunities in this area. Receivedforreview29November2014.Acceptedfor
publication28February2015.
PracticalImplications
New man-made materials developed in the past few decades that are extensively used in indoor environments may
emit an array of hazardousairborne organic compounds.It has been found that certain ‘modern diseases’ arelinked
to ‘modern exposures’, that is, exposure to these chemicals. To effectively reduce such exposures, it is necessary to
quantitativelyunderstandthepathwayofpollutantsfromsourcetoexposure.Thisstudyprovidesanoverviewofthe
basicknowledgeofmasstransfer andintroducessomerecent representativeworks inwhichmasstransferknowledge
was applied or newly developed to understand and control indoor airborne organic compounds. The authors hope
that the knowledge and methods presented in this study will be helpful for future research in broad areas of Indoor
AirQualitycontrol.
been called ‘modern exposure’. Certain ‘modern dis-
Introduction
eases’, such as asthma, allergies, diabetes, and repro-
Certain man-made materials that were not available ductive dysfunction problems have been linked to
50 years ago, such as composite wood, polymeric ‘modern exposure’ (Birnbaum, 2012; Colborn et al.,
flooring, plastics, and cleaning agents, are now used 1997; Sundell, 2010). In China, the transition from
extensively. These materials may emit an array of traditional to modern exposure has been especially
harmful organic compounds including very volatile great due to the rapid industrial and economic devel-
organic compounds (VVOCs) such as formaldehyde; opment over the past two decades (Zhang et al.,
volatile organic compounds (VOCs) such as benzene, 2013).
toluene, and xylene; and semivolatile organic com- Toeffectivelycontrolhazardousorganiccompounds
pounds (SVOCs) such as phthalate esters and bromi- in indoor air, it is necessary to quantitatively under-
nated flame retardants (Weschler, 2009; Weschler standthepathwaysorthe‘flow’ofthepollutantsfrom
and Nazaroff, 2008). Exposure to such chemicals has their sources to health risks, and where control strate-
39
Zhanget al.
Outdoor
environment 5. Control
–Engineering -Personal -Policies -Others
Ventilation, filtration
1. Indoor source 2. Indoor
3. Exposure 4. Health risk
characteristics concentrations
-Process description -Monitoring -Pathway -Assessment
-Key parameters -Interaction -Intake dose -Others
-Influencing factors -Ventilation -Others
-Emission correlations -Others
-Others
Fig. 1 Schematicshowingcomponentsofunderstandingandcontrollingindoorairborneorganiccompounds
gies can be applied to affect the ‘flow’ (Figure 1). A cules from a region of higher concentration to one of
fundamental understanding of mass transfer is there- lower concentration (or rather from a region of
fore essential. Mass transfer studies addressing energy higher chemical potential to one of lower chemical
problems have a long history, have been plentiful, and potential). In a closed system, diffusion makes the
have received substantial financial support, whereas concentration difference smaller and smaller and
mass transfer studies addressing ‘modern exposure’ eventually reaches a state known as ‘dynamic equilib-
problems in various indoor environments have been rium’. Usually, the diffusion flux can be expressed as
scarce. Fortunately, in our opinion, mass transfer follows (Incropera, 2011):
research directed at controlling airborne organic com-
pounds in indoor environments has increased over the J¼(cid:2)D(cid:3)rCðforthree(cid:2)dimensionalproblem;
past two decades. The objective of this study was generalfromÞ
threefold: (i) to briefly introduce mass transfer
@C ð1Þ
knowledge and review some representative works in ¼(cid:2)D ðforone(cid:2)dimensionalproblem;
whichmasstransfertheorywasappliedornewlydevel- @x
oped, (ii) to present some important problems that mostcommonlyusedfromÞ
warrant further study, and (iii) to attract more multi-
disciplinary researchers, including mass transfer field whereJisthe‘diffusionflux’ofthetargetspecies,mol/
researchers,toaddresstheso-called‘modernexposure’ m2/sorkg/m2/s;Cistheconcentrationofthespeciesin
issues. thematerialphase,mol/m3orkg/m3;Disthediffusion
coefficientor diffusivity,m2/s;andx is theposition,m.
Therearethreetypesofmoleculardiffusion:Fick’sdif-
Fundamentalsofmasstransfer fusion, Knudsen diffusion, and diffusion involving
bothFickandKundsendiffusion.
Basicmasstransferconceptsandlaws
Mass transfer and mass transfer of molecular spe- Fick’s diffusion—This is the diffusion of molecules that
cies. Masstransferisthemovementofspeciesormass move in a system whose scale length is much larger
in a medium or between media. Mass transfer of than the mean free path of the molecules involved.
molecularspeciesisonecategoryofmass transfer.Itis Therefore, the diffusivity for Fick’s diffusion is not a
aconsequenceofamolecularspeciesconcentrationdif- functionofsystemscalelength.
ference (or rather chemical potential difference) in a
mixture. Mass transfer of molecular species occurs in Fick’s law—Fick’s law quantitatively reveals the rela-
many processes, for example, solution of salt in water, tionship between the molecular diffusion flux and the
dehumidificationofairbycondensation,absorptionor concentration gradient for a given species in the form
adsorption, humidification of indoor air by evaporat- ofequation (1),inwhichDisnotafunctionofthesys-
ing water, and dilution of indoor air pollutants by an tem.
inflow of clean outdoor air. There are two types of
mass transfer of molecular species: molecular diffusion Knudsen diffusion—This is the diffusion occurring in a
andconvectivemasstransfer. system whose scale length (designated as L) is not lar-
ger than the mean free path of the molecules involved
Molecular diffusion. Molecular diffusion, also simply (designated as k). In Knudsen diffusion, the molecules
called diffusion, is the thermal motion of all (liquid collide with the system wall more frequently than with
or gas) molecules. It describes the net flux of mole- each other. The Knudsen number, Kn (=k/L), is an
40
Airborneorganiccompounds:masstransfer
indicator of the relative significance of Knudsen diffu-
sion. When Kn>>1, Knudsen diffusion dominates in m ¼m kCa ð3Þ
the whole diffusion effect. In practice, Knudsen diffu- max1þkC
a
sion applies only to gas-phase diffusion because the
mean free path for molecules in liquid phase tends to where m is the mass of adsorbate adsorbed per unit
be close to the molecular diameter so that it can be mass of adsorbent, mg adsorbate/g adsorbent; k the
ignored. Knudsen diffusion may be important within Langmuir equilibrium constant, m3/mg or m3/mol; C
a
porous media where the pore sizes are smaller or com- adsorbate concentration, mg/m3 or mol/m3; and m
max
parabletomeanfreepathofthemolecules. is the maximum mass of adsorbate adsorbed per unit
massasC increases,mgadsorbate/gadsorbent.When
a
Knudsendiffusioncoefficient—SeeDataS1. kC(cid:4)1, equation (3) can be rewritten as:
m = m kC = KC .
max a a
Convective mass transfer. This includes both molecular
diffusion and the bulk movement of fluid (gas or Freundlich equation—Another commonly used adsorp-
liquid)inwhichthelatteroftendominates. tion isotherm is Freundlich equation (Freundlich and
Hatfield,1926)asfollows:
Convective mass transfer equation—The convective mass
transfer rate m_ or Ja (mol/s or kg/s) can be expressed m ¼ KfCa1=n ð4Þ
as:
where K and n, determined by experiments, are con-
f
m_ ¼ h AðC (cid:2)C Þ ð2aÞ stantsforagivenadsorbateandadsorbentataparticu-
m s a
lar temperature; m and C are parameters used in
a
equation (3).
J ¼ UC ð2bÞ
a a
Brunauer–Emmett–Teller (BET) equation—This equa-
where m_ describes net transport rate from a surface
tiondescribesthemultilayerphysicaladsorptionofgas
while J is the mass transfer flux of purely convective
a molecules on a solid surface as follows (Brunauer
transport, mol/m2/s or kg/m2/s; A is the convective
et al.,1938):
masstransferarea,m2;h istheconvectivemasstrans-
m (cid:4) (cid:5)
fer coefficient, m/s; Cs is the concentration of the spe- 1 c(cid:2)1 p 1
cies in the fluid adjacent to the fluid/material interface, (cid:1) (cid:3) ¼ þ ð5Þ
mol/m3orkg/m3;C istheconcentrationofthespecies v½ p0 (cid:2)1(cid:5) vmc p0 vmc
a p
in the main fluid flow, mol/m3 or kg/m3; and U is the
localfluidvelocity,m.
wherepandp aretheequilibriumandsaturationpres-
0
sure of adsorbates at the temperature T; v is the
Sorption. This is a physical and/or chemical process adsorbed gas volume; v is the monolayer adsorbed
m
by which gas-phase molecules are attached to a liquid- gasvolume;andcistheBETconstant.
or solid-phase medium. There are two types of sorp- Note that Langmuir, Freundlich, and BET equa-
tion: (i) absorption, in which the gas-phase molecules tions are only limited to a single sorbate and that the
of one substance are dissolved into another substance Freundlich equation only applies when the sorbent is
in the liquid or solid phase and (ii) adsorption, in notsaturated.
which gas-phase molecules physically or chemically
bond onto the solid surface of another substance. The Competitive adsorption—The phenomenon in which
gas-phase substances being absorbed or adsorbed are individual species of a mixture of compounds are
called absorbate and adsorbate, respectively, while the adsorbed by adsorbent is called competitive adsorp-
liquid or solid substances that sorb the absorbate or tion.Competitiveadsorptionofsomecompoundsonto
adsorbate are called absorbent and adsorbent, respec- the surface of adsorbent can be calculated using the
tively. Generally speaking, an adsorbent is a porous Polanyi adsorption model or L-H rate model (Rosene
material. andManes,1976;Zhanget al.,2007).
Langmuir equation—Also known as the Langmuir iso- Porous material—Porous material is material that con-
therm or Langmuir adsorption equation, this equation tains many pores (voids). The pores contain liquid or
relates the extent of coverage or adsorption of mole- gas. A porous material is most often characterized by
cules on a solid surface to gas pressure or concentra- its porosity and specific surface area. Generally speak-
tion of a medium above the solid surface at a fixed ing, the greater the specific surface area of an adsor-
temperature. The equation rewritten from the original bent, the more adsorbate the adsorbent can adsorb.
formdevelopedbyLangmuir(1916)is: Many indoor materials such as wood, PVC flooring,
41
Zhanget al.
carpets, cement, and ceramics can be regarded as por- indoors (Salthammer and Uhde, 2009; Weschler, 2011;
ousmaterials. Weschler et al., 1992, 2007) impact the boundary con-
ditionsofmasstransportprocesses.
Catalysis. Catalysis reduces the activation energy bar- In many cases, the emission or sorption scenario
riersothatitcanspeedupachemicalreactionwithout occurs in two-layer or multilayer building materials.
changing the thermodynamic outcome of the reaction. For multilayer emissions, the controlling equation in
In the process, the catalyst is not consumed and can each layer is the same as that of single-layer emissions,
thereforeberecycledsothatonlyatinyamountofcat- and the difference lies in partitioning in the solid/solid
alystisrequired. interface (Hu et al., 2007; Kumar and Little, 2003a).
Therelationattheinterfaceisdescribedby:
Masstransferanalysis Ci ¼ Ciþ1 ð9Þ
The process of mass transfer analysis is composed of Ki Kiþ1
thefollowingsteps:(i)describetheproblembybuilding
a series of equations with the boundary and/or initial where,C andC aretheconcentrationsofspeciesin
i i+1
conditions;(ii)simplifytheproblemmathematicallyby the ith and (i+1)th layers of the building material,
making some (possibly) reasonable assumptions; (iii) respectively;K andK arethepartitioncoefficientof
i i+1
solvetheproblem;(iv)validatethesolutionbycompar- species in the ith and (i+1)th layers of the building
ingitwithavailableresultsormakecorrections/modifi- material,respectively.
cationstothepreviousstepsandvalidateagain;and(v)
applythesolutiontoaddressthesimilarproblems. Simplifytheprobleminmathematics. Thesecond step is
to simplify the problem by making (possibly) reason-
Describe the problem by mean of a series of closed mathe- able assumptions. The assumptions do not have to be
matical equations. The first step in a mass transfer valid at this beginning stage as they can be verified or
analysisistoobtain anequationorequationsthat link corrected after the solution is compared with experi-
the unknown parameter(s) and the known parameter mentaldataorresultsfromtheliterature.
(s) and/or the condition(s). The general form of such
equationsis: Findthemathematicalsolutionoftheproblem. There are
twokindsofmethodsforsolvingtheseequations:ana-
F ðy ;y ;...y ; x ;x ;...x Þ¼0;ðj¼1;2;...mÞ ð6Þ lyticalmethodsandnumericalmethods.
j 1 2 m 1 2 n
whereF isthejthfunctionwhichlinkstheindependent Analytical methods—Analytical solutions, also known
j
variables, x , x ,...x , and the unknown parameters y as exact solutions, can be used to get results at any
1 2 n j
(j = 1,2,...m). pointand/ortimeofinterestandtoverifytheresultsof
For example, the general diffusion equation for a numerical methods. In addition, they may clearly
species diffusing in a medium is written as (Incropera, express the relationship between variables in function
2011): form.Themostcommonlyusedanalyticalmethodsfor
solving a partial differential equation are the variable
r(cid:3)ðDrCÞþN_ ¼ @C ð7Þ separation method and the Laplace transformation
@t method, the details of which can be found in (Ozisik,
1993).
where D and C are the parameters used in equa-
_
tion (1); N is the rate at which the species in the med- Variable separation method—The variable separation
iumisgenerated,mol/m3/sorkg/m3/s;tisthetime,s. method is the oldest method for solving linear partial
The general convective mass transfer equation can differential equations. It transforms partial differential
bewrittenas: equationsintoseveralordinarydifferentialequations.
r(cid:3)ðDrCÞþN_ ¼ @Cþr(cid:3)ðC(cid:3)mÞ ð8Þ Laplace transformation method—The Laplace transfor-
@t mation methodhasbeen widely used tosolve transient
heat/mass transfer problems (particularly one-dimen-
wherevisthevelocityofthefluid,m/s. sional problems), because it can eliminate the partial
The mass transfer phenomena or processes directly derivative of the time variable from differential equa-
relatedtoorganicchemicalcontaminantsintheindoor tions.
environment usually take the form of partial differen-
tial equations. Therefore, the initial and/or boundary Other methods—There are other analytical methods,
conditions are necessary to close the equations. In such as the integral transformation method and
addition, gas-phase and surface chemical reactions Green’s function method. As they are seldom used to
42
Airborneorganiccompounds:masstransfer
address mass transfer problems, they are not described movement and/or interaction of molecules on a scale
inthispaper. below the molecular free path, in contrast to macro-
scale models, which amalgamate details into
Numerical methods. For many complicated problems, observed phenomena on a scale greater than the
suchasthosewithirregulargeometry,complexbound- molecular free path. Mesoscale is between the micro-
aryconditions,and/orvariablephysicalproperties,itis and macroscales. Micro-, meso-, and macroscale
very difficult or even impossible to obtain exact solu- models can be used together to understand different
tionsusinganalyticalmethods.Inthesecases,theprac- aspects of the same problem (revised from Wikipe-
tical alternative is to employ numerical methods to dia, the free encyclopedia). In this study, macroscale
solve problems. In contrast to an analytical solution analysis (dimensionless) means analysis by summariz-
that allows for determination of an unknown at any ing the common features of a group of similar mac-
point and/or time of interest, a numerical solution roscale processes.
enables determination of an unknown value only at Physical properties, such as the diffusion coefficient
discrete space/time points. The most commonly used and partition coefficient, are necessary to understand
numerical methods to address mass transfer problems anddescribethecharacteristicsofaspecificmasstrans-
are finite-difference, state-space and finite element fer-related process. Mesoscale or even microscale mass
methods,andsimulation. transfer analysis is very useful in understanding rela-
tionships between these physical properties and their
Finite-differencemethod—Thefinite-differencemethodis influencing factors. Once these characteristics are
the easiest to use and as such has been widely applied known, the mechanisms behind various phenomena
to heat/mass transfer problems. The essence of this can be understood and the associated physical proper-
methodistouseapproximatedfinite-differentialvalues ties can be predicted or controlled to some extent.
toreplace thepartialderivatives.Accuracydependson Usually macroscale mass transfer analysis is used to
the number of designated nodal points (not only for understand the characteristics of a specific mass trans-
space but also for time). If this number is large (a fine fer related process. However, it is difficult to get the
mesh and short enough interval), solution accuracy general characteristics of a group of processes that
canbesatisfactory(Incropera,2011;Ozisik,1993). share common features. Dimensionless analysis is a
powerful approach to address this problem and has
State-space method—In contrast to the discrete treat- beenwidelyusedinheattransfer(Incropera,2011).
ment of both space and time in the finite-difference
method that may cause calculation errors, the state-
Approachtoinverseproblems
spacemethodonlytreatsspacediscretely, while timeis
keptcontinuous.Thisnumericalmethodhasprovedto Forward problems are those in which model results
be very powerful for addressing Indoor Air Quality (that tend to be observed), y (j = 1, 2,...m), can be
j
problems(Guo,2013;Yanet al.,2009). obtained by inputting the model parameters, x (i = 1,
i
2,...n).Forwardproblemscanbebrieflyexpressedas:
Finite element methods and simulation—Finite element
methodsandsimulationarepowerfulpracticaltoolsfor y ðj ¼ 1; 2;...mÞ ¼ f½xði ¼ 1; 2;...nÞ(cid:5) ð10Þ
j i
solving the partial differential equations governing the
multiphysics of mass transport in buildings (Deng and wherefdesignatesafunction,amodel,oranoperator.
Kim,2007;Yanget al.,2001a;ZhangandNiu,2004). Inverse problems are the ‘inverse’ of the above pro-
cessandcanconceptuallybeformulatedasfollows:
Test the solution and make corrections and modifica-
tions. Thethirdstepistotestthesolutionusingexperi- x ði ¼ 1; 2;...nÞ ¼ f(cid:2)1½yðj ¼ 1; 2;...mÞ(cid:5): ð11Þ
i j
mental results or verified data found in the literature.
Suchtesting cannotcompletely verify the solution. If at
The objective of an inverse problem is to find the
thispointthereareconflictswithexperimentalresultsor most suitable model parameters, x (i = 1, 2,...n), to
i
with commonly accepted results, some corrections or make the model results, y (j = 1, 2,...m), be maximal
j
modificationsshouldbemadetotheassumptionsinthe
orminimal(Zhangetal.,2015).
previousstepsandthentryvalidatingagain.
Examplesofmasstransferanalysisaimedatunderstandingand
Apply the solution to address similar problems. If the
controllingairborneorganicchemicalcontaminantsinindoor
solution is validated, it can be used to analyze similar
air
problemsinvariousapplications.
We introduce some representative studies to illustrate
Macroscale (dimensionless), mesoscale, and microscale the application of mass transfer to address problems
masstransferanalysis. Microscale models describe the outlined in Figure 1: (i) predicting or controlling the
43
Zhanget al.
emissions of indoor VVOC/VOC/SVOC sources, (ii)
determining the average concentration of target indoor
airborne pollutants for a given period, (iii) estimating
dermal exposures to some SVOCs, and (iv) optimizing
theperformanceof variousaircleaningtechniques.The
mass transfer analyses presented in those studies span
the micro-, meso-, and macroscale and include normal
mass transfer modeling, methods in statistical physics,
inverseproblemsolution,anddimensionlessanalysis.
Wearemainlyinterestedinchemicalsthathavebeen
introduced into the indoor environment in the last 50
(or so) years. The mass transfer of interest is how they
get from the building materials (walls, floors), and fur-
niture into the indoor environment and how they can
be removed. This process is essentially transfer of
molecular species. Therefore, this study focuses on the
studies of molecular mass transfer. However, the stud-
Fig. 2 Schematic of mechanisms governing emissions from a
ies on mass transfer associated with liquid sources
materialslabinachamberorroom
(water, aqueous solutions, emulsions, and organic sol-
vents)areexcludedinthispaper.
@2C @C
VVOC/VOC/SVOCsource/sinkcharacteristics ¼ ð12Þ
@x2 @t
ToclearlyunderstandandcontrolindoorVVOC/VOC/
SVOC source/sink characteristics, it is necessary to (a) subjecttothefollowinginitialcondition,
describe or estimate the emission process characteris-
tics, (b) find the generalized emission correlations, (c) Cðx;t ¼ 0Þ ¼ C for0(cid:6)x(cid:6)LðthicknessoftheslabÞ
0
rapidly and accurately determine the emission charac- ð13Þ
teristic parameters to be used in addressing the above
problems, (d) evaluate the accuracy of test results, (e)
andthefollowingboundaryconditions,
obtain therelationship between the emission character-
istic parameters and influencing factors, and (f) reduce @C
¼0fort[0;x ¼ 0ðtheslabisrestingona
theVOCemissionratesofindoormaterials. @x
VOC-impermeablesurfaceÞ ð14Þ
Describe or estimate the emission process characteris-
tics. VVOCs/VOCs—For problem (a) (see Figure 2), Cðx;tÞ ¼ KC fort [ 0; x ¼ L ð15Þ
a
Little et al. (1994) carried out pioneering work. The
model they developed forms the basis of later develop- Inaddition,theVOCconcentrationofthechamberair
mentsinVOCandSVOCemissionmodeling. C (t)canbewrittenasfollows:
a
To simplify the problem, Little et al. assumed the (cid:6)
fcoolmlopwoiunng:d(ini)athbeuilidniintigalmcaotnercieanltsrlaatbio,nC0o,fistuhneifotarrmgleyt VdCdatðtÞ ¼ (cid:2)DA@C@ðxx; tÞ(cid:6)(cid:6)(cid:6)x¼L(cid:2)CaðtÞQ; t[0
distributed;(ii)theconvectivemasstransfercoefficient,
ð16Þ
h ,isinfinitesothattheconvectivemasstransferresis-
m
tance can be ignored compared with the internal diffu-
where V is the chamber volume, m3; A is the emission
sion mass transfer resistance; (iii) the inlet and initial
areaofthecarpet,m2.
VOC concentrations of the chamber or room are zero;
Employing the variable separation method, C (t)
(iv) mass transfer is one-dimensional; (v) the diffusion a
and the VOC emission rate m_ðtÞ from the slab are
coefficient D and the partition coefficient K are con-
obtained,whichcanalsobesimplifiedasfollows:
stant; (vi) the chamber or room air is well mixed; and
(vii) equilibrium always exists between the contami-
nant concentration in the surface layer of the material C ðtÞ ¼ f ðD; K; C ; V; A; L; Q; tÞ ð17Þ
a 1 0
andthechamberair.
Based upon these assumptions, Little et al. obtained m_ðtÞ ¼ f ðD; K; C ; V; A; L; Q; tÞ ð18Þ
2 0
the governing equation describing the transient
diffusion through a material slab (a simplified type of Equations (12-18) together with the assumptions are
equation (7))asfollows: calledtheLittle model.Analysisrevealsthatthephysi-
44
Airborneorganiccompounds:masstransfer
cal properties D and K and the initial concentration of
targetVOCinmaterialC arethethreekeyparameters 8000
0
ofindoormaterial,whichdeterminetheemissionchar-
Experiment
acteristics. Therefore, they are referred to by Little Little's model
6000
et al.as‘emissioncharacteristicparameters’(Liuet al., Xu and Zhang's model
2013b). 3m)
Assumptions (i) through (iii) of the Little model are g/
µ 4000
not always valid in real situations. How significant are (a
C
the errors caused by the assumptions and under what
conditionscansucherrorsbeignored?Inaddition,what 2000
about multilayer materials? How about the sink behav-
ior of single-layer materials? How about an integrated
0
predictionformultiplesourceandsinkmaterials?
Continuing research has addressed these questions. 0 20 40 60 80 100
Yang et al. (2001b) combined a three-dimensional Time (h)
(3D) numerical mass transfer analysis to calculate the
Fig. 3 Comparisonofexperimentalresultswiththesolutionsof
external convective mass transfer in chamber air, with
the Little model and Xu and Zhang’s model (Xu and Zhang,
a one-dimensional (1D) approach as used in the Little 2003)
model for the internal diffusion of material and parti-
or dC /dt is approximately equal to zero, which is rea-
tioning at the material/air interface. Their model con- a
sonable for many emission scenarios due to the rela-
sidered the case of composite materials with two or
tively low and stable VOC concentrations in typical
more layers of homogeneous materials. Although the
indoor air compared to C. This minor limitation has
Yanget al.modelcanbeappliedtosolvemorecompli-
been overcome by Qian (2007) in their derivation of a
cated problems than the Little model, numerical solu-
series of dimensionless correlations to predict VOC
tions of the 3D convective mass transfer equations are
emissions. The definitions of dimensionless concentra-
quitecomplicated(Liuet al.,2013b).
tionsinthematerialandairphaseareasfollows:
HuangandHaghighat(2002)studiedthesameprob-
lem of Little et al. (1994) without assuming hm to be C(cid:7) ¼ C ; C(cid:7) ¼ KCa ð19Þ
infinite and using convective mass transfer correla- C a C
0 0
tions. They obtained a numerical solution for C(x, t),
m_ðtÞ, and C (t) based on the finite-difference method.
a Deng and Kim (2004) obtained a fully analytical
UndertheconditionthatCa(t)(cid:4)C(x = L,t)/K,which solution of C (t) and m_ðtÞ without using assumption
a
is reasonable for many scenarios, they derived a fully
(ii) of the Little model. Compared with Xu and
analyticalsolutionforC(x,t),m_ðtÞ,andC (t).
a Zhang’s semi-explicit solution, Deng and Kim’s solu-
Figure 3 shows that the relative errors of the Little
tion is fully explicit and can be conveniently applied.
modelforearlystageconcentrationoftargetVOCinthe
However,itsapplicationis relatively narrowbecauseit
indoor environment cannot be ignored. Xu and Zhang
usesassumption(iii)oftheLittlemodel.Theanalytical
(2003) did not use assumptions (ii) and (iii) of the Little
solution of C (t) derived by Deng and Kim (2004) is
a
modelandinsteadusedh asestimatedbyavailablecor-
m representedasfollows:
relations.Theyobtainedasolutionbythevariablesepa-
X1
rraeltaiotinonmshetiphobde.twXeuenanedrroZrhsaanngd(2in0fl03u)enaclsinogdfeascctroibresdsuthche CaðtÞ ¼ 2C0b qnsGinqne(cid:2)Dd(cid:2)2q2nt ð20Þ
n¼1 n
ash ,whichcanbeusedtoidentifytheconditionsunder
m
whichassumption(ii)oftheLittlemodelcanbeignored
where G ¼ ½Kbþða(cid:2)q2ÞKBi(cid:2)1þ2(cid:5)q2cosq þ½Kbþ
(see section Dimensionless analysis of emission charac- n n m n n
ða(cid:2)3q2ÞKBi(cid:2)1þa(cid:2)q2(cid:5)q sinq , a = Qd2/D V,
teristicsanditsapplicationsfordetail). n m n n n m
b =Ad/V,Bi = h d/D ,andq arethepositiverootsof
For the scaling of VOC emission characteristics, m m m n
Zhang and Xu (2003) firstly performed dimensionless
analysis on the aforementioned controlling equation q tanq ¼ a(cid:2)q2n ðn ¼ 1;2;...Þ ð21Þ
together with the initial and boundary conditions of n n Kbþða(cid:2)q2ÞKBi(cid:2)1
n m
VOC emissions and found that the dimensionless con-
centrations or emission rates are functions of two Furtheranalysisbasedonthethismodelrevealsthat
dimensionlessparameters,theratiooftheBiotnumber another two dimensionless parameters are also impor-
to partition coefficient (Bi /K), and the Fourier num- tant for characterizing the VOC emissions, that is, the
m
ber for mass transfer (Fo = Dt/d2). In the dimension- dimensionless air exchange rate (a) and the ratio of
m
lessanalysis,thereisanimplicitassumptionindefining material volume to chamber volume (b) (Qian, 2007;
the dimensionless concentration that C is a constant Qianetal.,2007).
a
45
Zhanget al.
In addition to that, Kumar and Little (2003a) followingtwoequations:
established a fully explicit analytical solution for dou-
dM
ble-layer material emissions. Further, the analytical ¼ k C (cid:2)k M(cid:2)k ðM(cid:2)EÞ ð24Þ
a a d diff
solution for multilayer materials (Hu et al., 2007) and dt
the solution that considers chemical reactions (Wang
dE
andZhang,2011)insidethematerialswereproposed. ¼ k ðM(cid:2)EÞ ð25Þ
diff
Yan et al. (2009) ‘first introduced the state-space dt
method to indoor environmental quality modeling. The
In this model, it should be noted that the parameter
advantageofthemethodisthatitreducesthecomputa-
k is not a true diffusion coefficient but a coefficient
tional complexity by transforming a partial differential diff
that indicates the mass transfer rate between surface
equation problem into a series of discrete, ordinary dif-
and embedded sink. As the adsorption, desorption,
ferential equations that are more suitable for comput-
anddiffusionprocessesoccursimultaneously,itisdiffi-
ing’ (Guo, 2013). After that, Guo (2013) developed a
cult to propose a method to measure the parameters
framework for modelingthe dynamic concentrations of
k , k and k directly. These parameters are usually
SVOCs indoors by a modified state-space method. This a d, diff
determined by nonlinearly fitting the model to experi-
method is very powerful in developing high-perfor-
mentaldataratherthanbyindependentexperiments.
manceIndoorAirQualitysoftware.
Based on fundamental mass transfer theory for VOC
Generally, sorption is the reverse process of emis-
sorption into buildingmaterials, Denget al.(2010)per-
sion. Almost all existing sorption models assume that
formeddimensionlessanalysisanddevelopedaseriesof
sorption is fully reversible, and thus, several source
dimensionless correlations between the sorption satura-
models can be used as sorption models. Other models,
tion degree (SSD) and three dimensionless parameters:
focused at sorption phenomena, have been proposed
the dimensionless air change rate, the dimensionless
by researchers. Tichenor et al. (1991) developed a
mass capacity, and the Fourier number. The SSD pro-
widely used sorption model, the linear Langmuir
vides a new evaluation index for sorption capacity and
model, to characterize the adsorption/desorption
canbeusedtoclarifythedifferencebetweentheairsatu-
behaviorsoccuratthematerial/airinterface:
rationstateandmaterialsaturationstate.
dC Additionalrepresentativeworksarebrieflyintroduced
V a ¼ k AM(cid:2)k AC (cid:2)QC ð22Þ
dt d a a a inTableS1,SupportingInformation.Itshouldbenoted
that three recent review papers (Guo, 2013; Liu et al.,
dM 2013b; Yu and Kim, 2013) are particularly informative
¼ kaA(cid:2)kdM ð23Þ onmasstransfer-relatedresearchinthepastdecades.
dt
where C is the concentration in the chamber or room SVOCs—The emissions of semivolatile organic com-
a
air, lg/m3; M is the mass in the sink surface, lg/m; k pounds (SVOCs) from materials are similar to those of
a
is the adsorption rate constant, 1/s; and k is the VOCs. However, there is an important difference
d
desorptionrateconstant,m/s. between SVOC and VOC emissions, namely that the
The linear Langmuir model only considers the fast emitted SVOCs in the air phase will be strongly
adsorption/desorption process at the interface and adsorbedontoorabsorbedbytheinteriorsurfacemate-
neglects the relatively slow diffusion process inside the rials and suspended particles due to their low volatility
building material, so it cannot predict long-term emis- andstrongsorptionpotential.Therefore,thecontrolling
sionscenarios.Toovercomethisdeficiency,somesorp- equation and boundary conditions for internal diffu-
tion-constrained diffusion models have been proposed sion, interface partitioning, and external convection are
which not only consider adsorption and desorption the same for both SVOC and VOC emissions, as equa-
rate at the interface, but also account for the diffusion tions (8) and (12) indicate. However, the SVOC mass
process inside the material. Little and Hodgson (1996) conservationequationinachambershould bemodified
proposed a diffusion-controlled sink model to charac- to account for sorption onto interior surfaces and air-
terize VOC diffusion processes inside materials and borneparticles(Liuet al.,2012;XuandLittle,2006):
derived an analytical model that ignored convective
dC ðtÞ @C dq ðtÞ dq ðtÞ
monastshitsrwanosrfke,rKpuromcaesrsaesndouLtistitdlee(m20a0t3ebri)adlse.riEvxepdaandgeinng- V dat ¼(cid:2)AD@xjx¼L(cid:2)Ai;s dst (cid:2)V dpt
eralized sink model that allows for a non-uniform ini- (cid:2)QCaðtÞ(cid:2)QqpðtÞ ð26Þ
tial material-phase concentration and a transient
influent gas-phase concentration. Jørgensen et al. where A is the emission area of indoor SVOC source,
(2000)proposedamodelthatintroducedanembedded m2; A is the interior surface area of a chamber or
i,s
sink (E) to represent the diffusion effect inside the room, m2; q is the adsorbed or absorbed SVOC sur-
s
materials, so that equation (23) is replaced by the face concentration, lg/m2; and q is the adsorbed or
p
46
Airborneorganiccompounds:masstransfer
absorbed SVOC particle-phase concentration, lg/m3, tions. For the simplified SVOC emission model, only
which can be calculated by equation (27) with the equations (27-29)arerequiredtoobtaintheSVOCcon-
assumptionthatthereisalinearinstantaneousequilib- centration in the chamber. It should be noted that the
rium relationship between the particles and SVOC in simplified model assumes that y remains constant,
0
thechamberair: which is reasonable for some SVOC emission scenarios
inwhichthechemicalofinteresttakesasignificantfrac-
q ¼ K C TSP ð27Þ tion of the mass of the source, as for example, the con-
p p a
tent of di(2-ethylhexyl)phthalate (DEHP) in vinyl
where K is the particle/air partition coefficient, flooring can be as high as 30–40% of the mass. Con-
p
m3 air/lg particles; TSP is the total suspended particle trary to common belief, whether y will change during
0
concentration,lgparticles/m3air. the emission process has nothing to do with the SVOC
A convective boundary layer also exists between the concentration in the source. What really matters is the
chamber surface and the bulk air and can be repre- partition coefficient (K). In order for y to remain con-
0
sentedbythefollowingequation(Liuet al.,2013a;Xu stant, K must be sufficiently large. If y decreases with
0
et al.,2012): time,amodificationofthesimplifiedmodelisneeded.
(cid:7) (cid:8) It should be noted that chemical potential or fugac-
dq ðtÞ q ðtÞ ity is the real driving force of mass transfer, that is,
s ¼ h C ðtÞ(cid:2) s ð28Þ
dt m a K mass always transfers from a high fugacity to a low
s
fugacity even across different materials. We often take
where h is the convective mass transfer coefficient concentration as the driving force in practical applica-
m
near the sorption surface, m/s and K is the surface/air tions. However, it is possible for a species to transfer
s
partition coefficient, m. It is noted that h can become from low to high concentration across an interface
m
between two media. Although the concentrations at
several fold greater because of the adsorption or
theinterfacearedifferent,thefugacityvaluesareequal
absorption of gas-phase SVOCs by the particles in the
at the interface (Data S2). This can be understood
airboundarylayeradjacenttoindoorSVOC sourceor
usingtheanalogyofheattransfer.‘Chemicalpotential’
sink material (Liu et al., 2012). The penetration depth
is rather small for common indoor SVOCs. For other or‘fugacity’(notconcentration)inmasstransfercorre-
adsorption models, the readers can go to a review arti- spondsto‘temperature’inheattransfer.Thus,inaddi-
tion to the concentration-based models of diffusion
cle (Guo, 2014) for detail. It should be noted that the
partition coefficient (K ) in equation (28) may not be a and convection mass transfer, a fugacity approach is
s
alsousedtoaddresstheemissionandfateofSVOCsin
constantfornon-Langmuiradsorption.
the indoor environment (Bennett and Furtaw, 2004;
VOC emissions from building material are mainly
Yuan et al., 2007; Zhang et al., 2009). It should be
controlled by the internal diffusion, and external con-
notedthatafugacitymodelcanalwaysbetransformed
vectiontakeseffectonlyduringtheinitialperiodofthe
emission process (Xu and Zhang, 2003). In contrast to intoaconventionalmodelandviceversa.
that, SVOC emissions are mainly controlled by exter-
nalconvectionwhenthepartitioncoefficient(K)issuf- Dimensionless analysis of emission characteristics and its
ficiently large. A more detailed explanation is given in applications. The Little model is sufficiently accurate
for engineering applications except for the early stages
section Dimensionless analysis of emission characteris-
of emission. However, it is important in some applica-
tics and its applications. Therefore, equation (26) can
tionstounderstandtheconditionsunderwhichtherel-
besimplifiedasfollows:
ative error caused by assuming h to be infinite can be
m
ignored. In addition, scaling of the experimental data
dC ðtÞ dq ðtÞ dq ðtÞ
V a ¼ hmA½y0(cid:2)CaðtÞ(cid:5)(cid:2)Ai;s s (cid:2)V p fromchamberconditionstopracticalconditionsisalso
dt dt dt
veryusefulforengineeringapplications.
(cid:2)QC ðtÞ(cid:2)Qq ðtÞ
a p Dimensionless analysis is a powerful approach to
ð29Þ solving the two aforementioned problems. Xu and
Zhang (2003) normalized the Little equations using
wherey isthegas-phaseSVOCconcentrationadjacent dimensionless analysis without the assumption that h
0 m
to the material surface, lg/m3, which is often taken as is infinitely large. They found that the dimensionless
a constant for a given temperature (Clausen et al., emission rate of VOCs is afunction of Bi /K and Fo ,
m m
2012; Liang and Xu, 2014a,b). It should be noted that where Bi is the Biot number for mass transfer, K is
m
equations (26) and (29) ignore the particle loss due to thepartitioncoefficient,andFo istheFouriernumber
m
deposition on chamber walls and, thus, mayunderesti- for mass transfer. The finding reveals general emission
matetheemissions. characteristicsofVOCsfrombuildingmaterials.Based
Applying h [y (cid:2)C (t)] for the material emission rate upon their dimensionless analysis, the applicable con-
m 0 a
significantlyreducesthecomplexityofsolvingtheequa- dition of the Little model is as follows: If Fo > 10(cid:2)4
m
47
Zhanget al.
and Bi /K > 35, the relative error of the calculated
m
emission rate or overall mass is <5%. To simplify the
expression, we suggest naming Bi /K, the dimension-
m
less parameter, as the Little number, Lt. The physical
meaning of Lt is the ratio of diffusion mass transfer
resistance in material to convective mass transfer resis-
tance in air with mass transfer expressed as chemical
potentialorfugacity.
XuandZhang’s(2003)workalsoprovidesabasisfor
fittingexperimentaldatatoformulateempiricalcorrela-
tionsofVOCemissions.Theirworkwasfoundtobethe
first approach using dimensionless analysis to obtain
generalized VOC emission correlations for building
material (Yu and Kim, 2013). Qian et al. (2007) pre-
sented a detailed dimensionless analysis of VOC emis-
sions. They obtained dimensionless correlations
between VOC emission rate and total VOC emission Fig. 4 Comparison between the correlation predictions and
quantity and validated these with experimental results experimentaldataforconcentrationsinventilatedchambers.[In
the experiments, C was directly measured. Using the corre-
fromtheliterature(Figure 4).Thecorrelationscancon- a
sponding condition parameters, C can be calculated using the
veniently estimate the influence of air velocity, loading a
correlation.BaseduponaseriesofthetwoC values(measured
a
factor (the ratio of emission area to chamber volume), and correlation prediction), all the points in Figure 4 can be
andairexchangerateontheVOCemissionfromindoor obtained.]
materials measured by chamber tests. They can also be
used to scale up the emission results in chamber condi-
Rapid and accurate determination of the emission charac-
tiontopractical conditions orto compare theresults of
teristic parameters. As the Little model cannot accu-
differentchamberconditions.
rately predict emission characteristics for the initial
ItshouldbenotedthatthecorrelationsofQianet al.
period(severalhoursormore),itisnotsuitableforuse
(2007) are applicable only to ventilated conditions.
in rapid and accurate determination of VOC emission
Correlations for airtight conditions are also needed.
parameters.Xu and Zhang(2003,2004)and Dengand
Xiong et al. (2011c) derived a group of correlations
Kim (2004) provided a theoretical foundation for fast
between the dimensionless emission rate and three
and accurate determination of VOC emission parame-
dimensionless parameters that can conveniently scale
ters for materials containing VOCs. Based on their
upthetestresultsinanairtightchamberwithoutventi-
work, a series of rapid and accurate methods to mea-
lation. The agreement between the predicted correla-
sure the initial VOC concentration (C ), the diffusion
tionsandexperimentalresultsisquitegood. 0
coefficient (D) and the material/air partition coefficient
For VOC emissions from building materials, the
(K) have been developed. Some representative works
material/airpartitioncoefficientisgenerallyintherange
of102–105, whichresults inLt >10. Thismeansthatthe areintroducedbelow.
emission characteristics are mainly controlled by inter-
C-history method—The C-history method focuses on
nal diffusion and that external convection only occurs
the emission process of VOCs from some building
duringtheinitialperiodoftheemissionprocess(Xuand
materials in a closed chamber (Xiong et al., 2011a). It
Zhang, 2003).ForSVOC emissions, onthe other hand,
the partition coefficient is usually in the range of 107– can be used to simultaneously determine the three
1011 (Liu et al., 2014; Xu and Little, 2006), making Lt characteristic parameters, C0, D, and K. As the emis-
far <0.1. That is for SVOC emissions, external convec- sion process approaches equilibrium, the material/air
partition process is assumed to conform to equa-
tion becomes dominant so that diffusion in indoor
tion (3), so that C can be derived based on VOC
SVOCsourcematerialcanbeignored. equ
massconservationbetweenthematerialandairphases:
A dimensionless mass transfer analysiswas presented
by Liu et al. (2013a) to describe the SVOC emission
C b
process in a test chamber. The specific conditions are C ¼ 0 ð30Þ
presented for three cases: (i) with SVOC sorption to equ Kbþ1
chamber surfaces neglected, (ii) with convective mass
transfer resistance at sorption surfaces neglected if the wherebistheratioofmaterialvolumetochambervol-
sorption effect cannot be ignored, and (iii) with the ume.
material-phase concentration in the source as assumed Using mass transfer analysis for the emissions in a
to be constant. Several practical and quantifiable ways closedchamber,astraightlinecanbeobtainedbyplot-
toimprovechamberdesignwerealsoproposed. tingln[(Cequ–Ca(t))/Cequ]vs.time:
48