10937 Schaanfeld Paper

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On the Drying Dynamics in Biofilters

Friedhelm Schnfeld*11Hochschule RheinMain - University of Applied Sciences,

FB Ingenieurwissenschaften

Am Brckweg 26, 65428 Rsselsheim, [email protected]

Abstract:To a large extent the performance ofbiofilters relies on the presence of suitableamounts of water in order to provideconditions needed for microbiologicaldegradation of pollutants to take place. Inmany cases breakdown of filtrationperformance occurs due to inappropriate watercontents in the filter material. The presentstudy focuses on the drying dynamics withinsuch filters, which are modeled as wetted

porous media. Analyzing the governingequation of gas flow and water content revealsthat such systems are prone to exhibit instablebehavior. Small variations in the initialconditions e.g. slight inhomogeneities inmoisture or porosity are likely to be amplifiedduring operation until breakdown occurs. Thetime constants for such coupled dryingprocesses are analyzed within a 1-D modelingapproach. Furthermore, details of flowheterogeneity and drying are investigated bymeans of two and three dimensional models,which are solved by means of COMSOL

Multiphysics.

Keywords:biofilter, porous media, drying

1. Introduction

Biofilters provide cost efficient means forremoval of odors and other pollutants from airstreams. The humidified air stream passesthrough the biofilter substrate, wherepollutants are degraded by microbiologicalprocesses. Among others the filtrationperformance relies on the presence of the right

amount of water in the biofilter material. Oneof the most frequent reasons for breakdown ofbiofilters lies in unfavorable water contents inthe filter material. On the one hand too muchofwater causes agglomeration and clogging ofthe filter material, while on the other hand toolittle water leads to complete drying andbreakdown (cf. Figure 1).

Figure 1.Partly dried out biofilter.Courtesy of REINLUFT Umwelttechnik, Germany.

In spite of the importance of the water balancein the filter, details of the drying process havenot been analyzed in depth so far, to the best ofthe authors knowledge. In the present studywe formulate a minimum model taking flowdistribution, evaporation and the waterdependent permeability into account. We findthat due to the strong interdependenciesthereof, the operation of biofilters can sufferfrom inherent instabilities. A small variation inthe initial moisture can lead to a completebreakdown of the filter as schematically shownin Figure 2.

reduced flow

resistance

increased mass transfer

(evaporation)

locally reduced

water content

higher flow rate

reduced flow

resistance

increased mass transfer

(evaporation)

locally reduced

water content

higher flow rate

Figure 2. Processes involved in drying withinbiofilters, leading to a possible instable behavior,and breakdown.

2. Modeling approach

The present study focuses on the mathematicalmodeling of drying and gas flow. First, thetime constants for such coupled dryingprocesses are analyzed within a 1-D modelingapproach. Second, details of flowheterogeneity and drying are investigated bymeans of two dimensional (2-D) and threedimensional (3-D) FEM models. For theformulation of a minimum model, we restrictourselves to the most important aspects, viz.

fluid dynamics of the gas stream in free anporous regions, evolution of the liquid watercontent in the filter medium and mass transfer
mailto:[email protected]:[email protected]:[email protected]


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from the liquid into the air stream. On the onehand the restriction to these phenomena helpskeeping the model tractable, while on the otherhand it allows identifying the basic mechanismfor the formation of dry zones. Surely, themodel is way too simple to allow predictivesimulations of the complete biofilterperformance, since metabolism and heatgeneration of micro organisms, the formationof biofilms, condensation, external influencesand several further aspects are notincorporated. However, as will be shown themodel is valuable to gain insight into the basicmutual dependence between gas flow andreduction in water content and allowsanalyzing the basic drying dynamics.

2.1 Governing equations 1-D Model

A generic model geometry is shown inFig. 3. For writing down the basic equations inthe one dimensional case we define y(t) as thetime dependent average volume fraction ofliquid water within the filter material. Thefilter material is modeled as a porous medium,for the porosity of which we assume

( ) ( )0

y 1 y . (1)

y=1 denotes complete wetting with the filtermedium being blocked for the gas stream(1, while y=0denotes the dry state withthe maximum porosity 0.The pressure drop of the gas flow within theporous medium obeys a Forchheimer type ofequation which according to Ergun [1] reads

( ) .2

g g

3 2 3p p

p 1 10 0L d d

150 u 1 74 u

2 . (2)

Here, u0, g and g denote the superficial

velocity, dynamic viscosity and density of thegas stream, respectively. dp, denotes theequivalent particle diameter of the porousmedium andLdenotes the length of the packedbed in flow direction. For a given pressuredrop the gas flow velocity depends on theporosity yvia Eq. (2).In order to account for mass transfer from thewetted material into the gas stream we applythe correlation for the Sherwood number givenby Ranz [2] (see also Levenspiel [3])

/ /

( )

( )( ) .g p 0

ggH O2

1 3 1 2d u y

yDSh y 2 1 8

,

(3)

whereg

H O2

D denotes the diffusion coefficient of

vapor in the gas phase and gthe kinematic gasviscosity. The overall reduction in the massdensity of liquid water in the porous medium isgoverned by

( )g

H O2

2p

D g

H Odm Sh y A c , (4)

with A being the specific total wetted

area (p

60d

A 1 ) and2

g

H Oc being the

difference between the equilibrium vapor

concentration at the water interface and thevapor concentration in the gas stream. CastingEq. (4) into the respective equation governingthe reduction of the water volume fraction andinserting Eq. (3) we find

( )( ). 0u yyy 2 1 8 , (5)

where all material parameter have beenlumped into the constants and , given in

Appendix II. denotes the superficial

velocity given by Eqs. (1) and (2) for specificmaterial parameters and a prescribed, constantpressure drop. Within the present study werestrict ourselves to low and moderatevelocities in the filter medium and regard onlythe linear term in the Ergun equation (2). Byinserting Eq. (1) and the linear term of (2)equation (5) translates to

( )0u y

( ). 0 11 1 yy 2 1 8 1 , (6)

with and given in Appendix II. Thesolution of the differential equation (6), whichinvolves the product logarithm, is numericallycomputed by means of Mathematica [4].

2.2 Use of COMSOL Multiphysics

2-D and 3-D models have been set up usingthe modules Free & Porous Media Flow ofCOMSOL [5] for simulating the air/vaporflow in the whole filter and the PDE modulehas been applied for the simulation of the

water content in the filter material. The model


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specifications together with a generic 2-Dgeometry are sketched in Fig. 3.

As a first step, simulation data have beencompared to the 1-D model (Eq. (6)), solvedby means of Mathematica, in order to validatethe FEM approach. To this end a homogeneousporosity and water volume fraction wasspecified as initial guess and a slip boundarycondition has been applied to the walls of theporous matrix. It was found that thedifferences between the results of bothapproaches are below 1%.

Figure 3. Generic geometry of a 2-D biofiltersimulation and COMSOL model tree showing theapplied modules.

4. Results

4.1 1-D Model

Results for the homogeneous averagevolume fraction of water within the pores ofthe filter material y(t) are shown in Fig. 4, forinitial water contents 0.8 y0 < 1. Thecomplete set of parameters used in thesimulations is given in Appendix III. Largevolume fractions close to one imply slow flowvelocities due to the high pressure drop leadingto relatively low drying rates. Whereas a lower

water content causes an accelerated flow andhigher drying rates. Note, that a strongdependence of the drying time on the initialwater content is observed, e.g. reducing theinitial water content from almost one by 5%leads to a reduction in the drying time of about30%.With respect to real biofilters these simulationsshow that the drying dynamics, in particularthe time for completed drying, stronglydepends on the initial amount of water in thefilter medium.

( )y t

[ ]/ st54 10

58 10 . 61 2 10

Figure 4. Homogeneous model: time dependentwater volume fraction for various initial values0.8 y0< 1.

The sensitivity of the drying rate on the initialcondition is also highlighted in Fig. 5 showing

the absolute initial drying rate, i.e. absolute ofthe right hand side in Eq. 6., as function of theinitial water content.

0y

Figure 5. Absolute drying rate vs. watercontent (cf. Eq. 6).

Moreover, the 1-D model approach, Eq. (6),can be used to investigate the dependence ofdrying on the porosity of the dry filtermaterial, 0. Corresponding results for y0=0.8and four different porosities are shown in Fig.6.

( )y t

[ ]/ st5

4 105

8 10 . 61 2 10

Figure 6. Homogeneous model: water volumefraction results for various porosities, 0 = 0.2, 0.4,0.6 and0.8(from left to right).


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Again a strong sensitivity of the drying time,here on the dry material porosity, is observed.

4.2 2-D Model

In order to investigate the consequences of theanalyzed drying dynamics with respect to

biofilters a 2-D FEM model has been set up.This time, the initial volume fraction of waterwas randomly distributed (0.95 y0


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[3] O. Levenspiel, Chemical ReactionEngineering, 3rded, p. 401, Wiley, NY (1999). II. Model constants[4] www.wolfram.com[5] www.comsol.com g g

H O H O0 2 2

20 l

p

D c1

d6

Acknowledgements

/ / /

2

1 3g 1 2 1 6

H O p gD d

The work has been funded by the German

Ministry of Research and Education (BmBF)in the framework of the 4th IngenieurNach-wuchs program.

/

g

1 2p

p 150 Ld

III. Values

Simulations have been exemplarily performedwith following values:

Appendix

I. Notation

.

/ .

32

2

2

3

3

gg

H O m

g 9 mH O s

p

g

kg

g m

kg3

l m

Pam

mm

Pas

c 17

D 10

d 1

18

1 2

10

p L 208

A specific wetted surface area

difference between equilibriumvapor concentration and va

concentration in the gas stream

2

g

H Oc por

diffusion coefficient of vapor ingH O2

D

the gas phase

pd equivalent particle diameter

0 porosity of dry filter medium

, ( )y porosity of wet filter mediumThe values are only partly motivated by real

biofilters used in industrial applications,furthermore by pre-tests by means of modellab-systems. The investigation of realisticmaterial parameters is the subjected toongoing work.

L filter length | thickness

m reduction rate of mass densityof liquid water

g dynamic gas viscosity

g kinematic gas viscosity

p pressure drop across packed bed

g gas density

l liquid density

Sh Sherwood number

0u superficial gas velocity

y(t) average volume fraction ofliquid water within the filtermaterial
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10937 Schaanfeld Paper