MATHEMATICAL MODELLING OF A BIOFILTER FOR BTEX COMPOU+iDS

A Thesis

Presented to

The Faculty of Graduate Studies

of

The University of Guelph

by

LARS STERNE

In partial fulfilrnent of requirements

for the degree of

Master of Science

September, 1998

O Lars Sterne, 1998

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ABSTRACT

MATHEMAïiCAL MODELLING OF A BIOFILTER FOR BTEX COMPOUNDS

Lars Sterne University of Guelph

Advisor: Professor R. G. Zytner

A biofilter model was developed to predict the performance a biofilter treating

benzene. Model parameter vaIues were obtained from literature sources and both

steady state and dynamic conditions were exarnined. The results indicate that the

biofilter is most sensitive to interstitial velocity, biofilter height, specific surface area

and first order biodegradation rate constant. Using the developed default set of model

parameter values. dynamic biofilter performance was evaluated using a pulse input

to the biofilter. If a benzene regulatory limit of 0.08 g/m3 was irnposed on the biofilter

system, the biofiker modelled in this study would be able to successfully predid input

pulse heights and the corresponding pulse duration. Recommendations for further

study include, incorporating into the model Monod kinetics and inhibition to account

for biofilters treating multiple contaminant input streams.

I would like to thank my advisor Dr. Richard G. Zytner for his patience and

advise in preparing this thesis. I would also like to thank Dr. Gordon Hayward for his

insightç and Dr. Richard Corsi for his advise and encouragement when I began my

thesis. A special thank you is required for my family; my wife Rita and my children

Kara and Erik who have endured my early mornings for more than a few years while

I completed my thesis part-tirne.

As a final thank you, I would like to thank ail of the people 1 have met at the

University of Guelph, their names too numerous to mention, for providing a truly

mernorable experience.

Table of Corrtents

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 INTRODUCTlON 1 . . . . . . . . . . . . . . . . 1.1 Problem Statement and Research Objectives 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Scope of Work 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.0 BACKGROUND 4 . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 General Principles of Biofikration 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Types of Biofilters 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Biofilter Description 6

. . . . . . . . . 2.2 Air Stream Characten'zation from Soil Vapour Extracüon 9 . . . . . . . . . . . . . . . 2.3 Operating Conditions of Experirnental Biofilters 10

. . . . . . . . . . . . . . . . . . . . . . . 2.4 Theoretical Principles of Biofiltration 13 . . . . . . . . . . . . . . . . . . . . . 2.4.1 Biofitter Modelling Approaches 15

. . . . . . . . . . . . . 2.4.1.1 Lumped Model Approach (Yang) 15 . . . . . . . . . . 2.4.1.2 Uniform Biofilm Approach (Devinny) 17

2.4.1.3 Two Phase Model Approach - Interface . . . . . . . . . . . . . . . . . . . . . . . Equilibrium (Ergs) 20

2.4.1.4 Two Phase Model Approach - Biological . . . . . . . . . . . . . . . . . . . . . Kinetics (Shareefdeen) 23

. . . . . . . . . . . . . . . . . . . . . . 2.4.2 Model Parameter Estimation 26 . . . . . . . . . . . . . . . 2.4.2.1 Media Dependent Parameters 27

2.4.2.1.1 Specific surface area of biofilter media (AJ . . 27 2.4.2.1 -2 Effective and actual media biofilm

. . . . . . . . . . . . . . . . . . . . . thickness (6. 6 ) 28 . . . . . . . . . . . 2.4.2.1 -3 Biofilter media void fraction (0) 29

2.4.2.2 Contaminant Dependent Parameters - . . . . . . . . . . . . . . . . . . . . . . . . PhysicaljChemical 30

2.4.2.2.1 Gas/Biofilm equilibrium partition coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . (Hf, HJ 30

. . . . . . . . . . . . . . . . . . 2.4.2.2.2 Biofilm diffusivity (DJ 31 . . . . . . . . . . . . . . . . . . . . 2.4.2.2.3 Gas diffusivity (DJ 32

2.4.2.3 Contaminant Dependent Parameters - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biologid 32

. . . . . . . . . . . . 2.4.2.3.1 Biological yield coefficient (Y) 33 . . . . . . . . . . 2.4.2.3.2 Microbial population density (pb) 34

. . . . . . . 2.4.2.3.3 Biomass growth rate (p, < and p-) 34 . . . . . . . . . . . . . 2.4.2.3.4 Half saturation constant (Q 35

2.4.2.3.5 Andrews kinetic expression constants (Y, KJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4.2.3.6 Zero Order Biodegradation Rate Constant (k") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4.2.3.7 First order biodegradation rate constant (k3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

MODEL DEVELOPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1 Goveming Equationç and Assurnptions . . . . . . . . . . . . . . . . . . . . . 42 3.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

. . . . . . 3.3 Goveming Equations Finite Difference Solution Techniques 47 . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Dynamic State Solution 49

. . . . . . . . . . . . . . . . . . . . 3.3.1.1 Gauss-Seidel Solution 53 . . . . 3.3.1.2 Spatial and Temporal interval Determination 54

3.3.2 Boundary Conditions Finite Difference Solution Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.2.1 Concentration Gradient at BiofilmIMedia

Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 . . . . . . . . . . . 3.3.2.2 Equilibrium at Gas/Biofilm Interface 56

3.3-2.3 Constant Gas Phase Contaminant . . . . . . . . . . . . . Concentration at Biofilter Effluent 57

3.4 Computer Mode1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Model Features 57

3.4.2 Cornputer Code Structure . . . . . . . . . . . . . . . . . . . . . . . . 58

4.0 MODEL INPUT PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 . . . . . . . . . . . . . 4.1 Contaminant Diffusivity in Biofilter Void Space (DJ 61

4.2 Interstitial Velocity (v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.3 Specific Surface Area (AJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Contaminant Diffusivity in Biofilm (DJ . . . . . . . . . . . . . . . . . . . . . . 65 4.5 Void Fraction (8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

. . . . . . . . . . . . . . . . 4.6 Zero Order Biodegradation Rate Constant (0 67

. . . . . . . . . . . . . . . . 4.7 First Order Biodegradation Rate Constant (k) 68 . . . . . . . . . . . . . . . 4.8 Gas/Liquid Equilibrium Partition Coefficient (HJ 69

4.9 Biofilm Thickness (x. 6") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.10 Biofilter Height (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

. . . . . . . . . . . . . . . . . . . 4.1 1 Influent Contaminant Concentration (Cd 70 4.12 Surnmary of Mode1 Parameter Values . . . . . . . . . . . . . . . . . . . . . 71

5.0 MODEL VERIFCATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.1 Compound Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Order of Biodegradation Rate Constant . . . . . . . . . . . . . . . . . . . . . 73 5.3 Steady State Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.4 Dynamic Mode1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.0 STEADY STATE SENSITIVITY ANALYSE . . . . . . . . . . . . . . . . . . . . . . . 80 6.1 Gas Phase Diffusivity (DJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Interstitial Velocity (v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.3 Specific Surface Area (A$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.4 Biofilm Phase Diffusivity (D,) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.5 First Order Biodegradation Rate Constant (k') . . . . . . . . . . . . . . . . 89 6.6 GasILiquid Equilibriurn Partition Coefficient (HJ . . . . . . . . . . . . . . . 91 6.7 Biofilm Thickness (x. 6") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

iii

6.8 Biofilter HeigM (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.9 Influent Contaminant Concentration (Cd . . . . . . . . . . . . . . . . . . . . 97 6.10 Summary of Steady State Removai . . . . . . . . . . . . . . . . . . . . . . . 98

7.0 BIOFILTER RESPONSETO DYNAMIC LOADING . . . . . . . . . . . . . . . . . 101 7.1 Influent Contaminant Concentration Profile . . . . . . . . . . . . . . . . . 101 7.2 Evaluating Biofilter Dynamic Performance . . . . . . . . . . . . . . . . . . 102 7.3 Biofilter Response Family of Curves . . . . . . . . . . . . . . . . . . . . . . 103 7.4 Application of Allowable Biofilter Operational Conditions . . . . . . . . 108

8.0 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9.0 RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

10.0 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

APPENDIX A: Model Source Code (funcüon solving finite difference equations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

APPENDIX 8: Example Model Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

List of Tables

. . . . . . . . . . . Table 2.1 : Soil Vapour Extraco.on VOC ûff-Gas Concentrations 10 Table 2.2: Soil Vapour Extracüon . Bentene. Toluene. Xylene

Off-Gas Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . Table 2.3. Historical Parameters for Compost Biofilters 12

Table 2.4. 4 Values Reported in literature . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Table 2.5: Effective and Actual Biofilm Thickness (6. 6') Values Reported

in Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 . . . . . . . . . . . . . . . . . . . . Table 2.6. Media Porosity (8) Reporteci in Literature 29

Table 2.7: GWBiofilm Equilibrium Partition Coefficient (HJ Values Reported in Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

. . . . . . . . . . . . Table 2.8. Biofilrn Diffusivity (DJ Values Reported in Literature 32 . . . . . Table 2.9. Biological YÏeld Coefficient (Y) Values Reported in Literature 33

Table 2.1 0: Biomass Growth Rate (p . p and p - ) Values Reported in Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

. . . . . Table 2.1 1 : HaIf Saturation Constant (Y) Values Reported in Literature 36 Table 2.12: Andrews Kinetic Expression Constant Vaiues (Y. KJ Reported

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . in Literature 37 Table 2.13: Zero Order Biodegradation Rate Constants (fl Reported

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . in Literature 39 Table 2.1 4: First Order Biodegradation Rate Constants (k') Reported

Table 4.1 : Table 4.2: Table 4.3: Table 4.4: Table 4.5: Table 4.6: Table 4.7:

Table 4.8: Table 5.1 : Table 6.1 : Table 6.2: Table 6.3: Table 6.4: Table 6.5: Table 6.6: Table 6.7: Table 6.8: Table 6.9:

in Lierature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Gas Diffusivity for B T M Compounds . . . . . . . . . . . . . . . . . . . . . . 62

. . . . . . . . Estimation of 4 Based on Compost Media Particle Sire 65 . . . . . . . . . . . . . Biofilrn Diffusivity as a Function of Biofilm Density 66

Biofilm Diffusivity for BTEX Compounds . . . . . . . . . . . . . . . . . . . . 67 . . . . . . . . . . . . . . . . . . Zero Order Biodegradation Rate Constants 68

. . . . . . . . . . . . Default First Order Biodegradation Rate Constants 69 Default Gas/Liquid Equilibrium Partition Coefficient

for BTEX Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 . . . . . . . . . . . . . . . . Summary of Mode1 Default Parameter Values 72

. . . . . . . . . . . . . . Order of Biodegradation Rate Constant Benzene 74 . . . Steady State Conditions at a Biofilter Height of O.8m Varying Dg 82

. . . . Steady State Conditions at a Biofilter Height of O.8m Varying v 84 . . . Steady State Conditions at a Biofilter Height of 0.8m Varying 4 86 . . . Steady State Conditions at a Biofilter Height of 0.8m Varying Df 88 . . . Steady State Conditions at a Biofilter Height of 0.8m Varying k' 90 . . . Steady State Conditions at a Biofilter Height of 0.8m Varying H, 92

. . . . Steady State Conditions at a Biofilter Height of 0.8m Varying x 94 . . . . . . . . . . . . . . Steady State Conditions Varying Biofifter Height 96

. . . Steady State Conditions at a Biofilter Height of 0.8m Varying C, 98 Table 6.10: Summary of Steady State Emissions Varying Input parameters . . 99

List of Figures

Figure 2.1 : Simplified Schematic of a Biofilter . . . . . . . . . . . . . . . . . . . . . . . . 7 Figure 2.2: Conceptual Schematic of Contaminant Transport in Biofiiter

Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Figure 3.1 : Pictorial Representation of Gas and Biofilm Mass Balance

Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Figure 3.2. Generic Grid Structure For Finite Difference Method . . . . . . . . . . . 48 Figure 3.3: Aigorithm Used in the Development of GaussSeidel Solution

Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Figure 5.1 : Biofilter Dynamic Response Using Defauit Model

ConditionslParameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Figure 6.1 : Gas Phase DiffusMty (Dg) and its Effect on Steady State . . . . . . . 82 Figure 6.2. Interstitial Velocity (v) and its Effect on Steady State . . . . . . . . . . . 84 Figure 6.3. Specific Surface Area (As) and its Effect on Steady State . . . . . . . 86 Figure 6.4. Biofilm Phase Diffusivity (DJ and its Effect on Steady State . . . . . . 88 Figure 6.5: First Order Biodegradation Rate Constant (k') and its Effect on

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steady State 90 Figure 6.6. Henry's Law (Hc) and its Effect on Steady State . . . . . . . . . . . . . . 92 Figure 6.7. Biofilm Depth (x) and its Effect on Steady State . . . . . . . . . . . . . . 94 Figure 6.8. Biofitter Height (2) and its Emct on Steady State . . . . . . . . . . . . . 96 Figure 6.9: Biofiiter Influent Contaminant Concentration (Cin) and its Effect

on Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 7.1 : Generic Input Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Figure 7.2: Example Model Generated Response Curve to a Pulse Loading . 103 Figure 7.3. Example Mode1 Response Curve for Varying Pulse Width . . . . . . 104 Figure 7.4: Peak Biofilter Effiuent Concentration for a Pulse Height of 0.34

dm3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Figure 7.5: Peak Biofilter EfRuent Concentration for a Pulse Height of 0.17

and 0.34 g/m3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Figure 7.6: Peak Biofilter Effiuent Concentration for Various Pulse Widths

andHeights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 7.7. Dynamic Response and Air Quality Standards . . . . . . . . . . . . . . 110

NOMENCLATURE

Ab breviations

BTEX

EBRT

EC

SV€ VOC

refers to the volatile organic mmpounds Benzene, Toluene, Ethylbenzene and the Xylenes Empty Bed Retention Tïme [(volume of biofilter bed)/(volume of infiuent airfime) ] Elimination Capacity ((mass of contaminant biodegraded)/(volume of bed ti me) ] Soif Vapour Extraction Volatile Organic Compound

Mathematical Nomenclature

specific surface area of a biofilter media [(m2,,, -)/(m3dJ] cross sectional area of biofilter [m? biofilrn phase contaminant concentration [ h - / m 3 m J biofilm phase contaminant concentration under gas/biofilm equilibrium b d m 3 w i J 3 gas phase contaminant concentration [gwM/m biofilter influent gas phase contaminant concentration [gmm,,Jm3d] contaminant diffusivity in biofilm [m2/s] contaminant diffusivity in void space [m2/s] contaminant diffusivity in water [m2/s] ga iqu id equilibrium partition coefficient for a clean water system (Henry's partition coefficient) [m3w~m3,J gas/biofilm equilibrium partition coefficient in biofitter (modified Henry's partition coefficient) [m3@drn3,J transfer rate constant into biofilm [s"] constant in specific growth rate on Andrews kinetic expression) ~(gmnminanJ/(m3~nJ1 gasibiofilm equilibrium partition coefficient as proposed by Devinny [m3gJm3w J inhibition constant in specific growth rate (Ïn Andrews kinetic expression) [(g~-~J~(m3wiinJ1 haff saturation constant (Ïn Monod biological kinetic expression) [(g~"mnMJ/(m?l partition correction parameter as proposed by Devinny [-] zero order biodegradation rate constant in biofitter biofilm

3 K9mm,J/(m d&I first order biodegradation rate constant in biofilter biofilrn [s"] flux of contaminant from gas phase into the biofilm [(gm-)/(m2,J/s] air flowrate [m3$s] contaminant mass removal due to biodegradation [ (b - ) / (m3dJs ] Retardation factor as proposed by Devinny 1-1

vii

t time [s] V approach velocity (air Row rate d ~ d e d by biofilter cross sectional area)

[mm v interstitiai velocity (appraach veiociiy aivided by void frâc6m) [mis] X, microbial population density [ (gd/ (m3MJ ] x distance in biofilrn from gas/biofilm interface [ml Y contaminant yield cuefkient [(g- produced)/(~,, consumeci)] z distance in biofilter from influent to biofilter [ml

Greek Letters

void fraction ((m3&)/(m3- -a] specific biomass growth rate [s-'1 maximum specific biomass growth rate [s-'1 constant in specific growth rate expression (in Andrews kineüc expression) [s-'9 microbial population density [ ( g 4 / ( m 3 & ] effective biofilm thickness (contaminant penetration depth) [ml biofilrn thickness [ml Thiele number [-]

viii

1 .O INTRODUCTION

The treatment of petroleum contaminated soils using the Soi1 Vapour Extraction

(SVE) technique produces a contaminated air stream. These air emissions may be

treated by a number of developed technologies including liquidvapour condensers,

incinerators, catalytic converters and Granular Activated Carbon (GAC) (Hutzier,

1989). Recent research has indicated the potential use of biafiltration in the treatment

of these contarninated waste air streams.

Biofiltration utilizes microorganisms to biodegrade the gaseous contarninants.

Biofilters have been demonstrated to be effective in treating odorous compounds

(Amirhor. 1995; Lutz, 1994) and volatile organic hydrocarbons (both aiiphatic and

aromatic) (Ergas, 1993; Leson, 1991 ; Ottengraf. 1983: Rho 1 993). Bacteriai

properties and kinetic parameters have been used in attempts to mode1 and therefore

predict the performance of biofitters (Devinny, 1991 ; Ergas, 1993; Ottengraf, 1986a;

Yang, 1994). Model solutions have focused on steady state solutions and

calibrations. The modelling of biofitter responses under dynamic loading conditions

has, however, not been well documenteci.

1.1 Problem Statement and Research Objectives

As indicated previously, biofiltration models have been developed. with

solutions focusing primarily on steady state conditions. The application of these

solutions is therefore limited to conditions where the biofilter is exposed to constant

contaminant mass loadings and air flow rates. These conditions may exist in some

controlled situations, however, in many potential biofïlter applications there will be

fluctuations in the influent air stream characteristics. These fluctuations can be

reduced by placing acüvated carbon upstream of the biofilter (as proposed by

Yavorsky, 1993). This technique may be applied where the variation in influent waste

air Stream characteristics is somewhat predictable and the required amount of

activated carbon can be estimated. However, if the dynamic response of the bioNter

can be predicted, then the amount of activated carbon (and therefore cost) can be

minimized. In addition to potential cost savings, the ability to predict biofilter

performance under varying load conditions will aid in ensuring that regulatory emission

limits placed on a facility can be met This thesis deals with the developrnent and

solution to a non-steady state model for predicting the performance of biofilters. This

non-steady state model rnay be used for both dynamic and steady state influent

conditions. The specific research objectives were:

1) to develop a dynamic compost biofiltration modal,

2) to estimate model input parameter values from those reported in literature,

3) to determine which model parameters have the greatest impact on the steady

state performance of a biofilter,

4) to detemine biofilter performance under varying influent air stream

characteristic..

1.2 Scope of Work

The biofilter model developed was solved by the finite difference method. The

model considered biodegradation of the compounds within the bacterial film, however,

inhibition of this process by other contaminants in the influent air strearn or within the

biofilter media itself was not considered. The values for the parameters used in the

model were oMained from literature sources. The model developed did not account

for the varïability in biofitter performance as a resuit of changes in its media

characteristics (e.g. moisture content and nutrient level).

The contaminants considered in this work were aromatic Volatile Organic

Compounds (VOCs), specifically benzene, toluene. ethyl benzene and xylene. These

compounds were chosen due to their well known h e m risks, especially benzene,

their biodegradability in the presence of bacteria and their suitability for treatment in

a biofilter. The model developed in this work is generic in nature and it may be

possible to apply it to other compounds. However. only low organic loading rates

were considered (c (40 g of contaminant)/(m3 of biofilter hour)). Influent air

flowrates corresponded to empty bed residence times ranging from 1 to 3 minutes.

This thesis is divided into a number of chapters. each focusing on a specific

area of interest. The generd principles of biofikration and modelling approaches that

have been used by other researchen are presented in Chapter 2. Chapter 3 presents

the model used to represent the biofilter in this work and how the coupled difFerentia1

equations used to represent the biofilter were solved using a finite difference

technique. Chapter 4 presents the values used for the model parameters. Chapter

5. model verification, compares some of the model results under steady state and

dynamic operating conditions to those of other researchers. Chapter 6 presents the

results of parameter sensitivity analyses and identifies the parameters which have the

greatest impact on biofilter steady state performance. Chapter 7 presents the results

of biofilter response to pulse dynamic influent loading conditions. Chapter 8 presents

the conclusions of this thesis.

2.0 BACKGROUND

The first section of this chapter examines general principles of biofittration. The

second section characterizes SVE uff-gas that may serve as the influent airstream to

a biofilter. The third section describes operating conditions of experimental biofikters.

The fourth section presents theoretical principles of biofiltration.

2.1 General Principles of Biofiltration

This section examines general principles of biofiltration and includes a

discussion on types of biofilters and describes the packed bed biofilter which is later

rnodelled in this thesis.

2.1.1 Types of Biofilters

Biofiltration is a gas cleaning technique that utilizes microorganisms to

biodegrade contaminants in an air stream. Within the general classification of

biofiltration, a number of technologies exist These technologies include (van

Groenestijn, 1 993):

i> bioscrubbers

ii) trickling bed biofilter

iii) packed bed biofilter.

The fundamentai process, for al1 of the technologies, is the transfer of the

contaminants from the airstream to a liquid, usually water. Bacterial action in the

water then biodegrades the contaminant compounds.

The bioscubber consists of a scrubber and a bioreactor. Water is sprayed

through an inert packing material (scrubber) counter-current to the contaminated gas

fiow resulting in the absorption of contaminants into the liquid phase. This water is

then directed to an activated sludge system where appropriate bacterial populations

are maintained and the contaminants are biodegraded.

The trickling bed biofilter also incorporates counter-current fiows of water and

the contaminated air Stream. lnstead of using an achivated sludge system to maintain

a bacterial population as in the bioscmbber, the trickling bed biofilter relies on the inert

packing media in the tower to support bacterial growth. This principle is similar to that

used by a conventional trickling filter used in treating wastewater.

Unlike the bioscrubber and trickling bed biofilter, the packed bed biofilter does

not use a large continuous flow of water. The media used in the packed bed biofilter

acts as a water resewoir as well as a support structure for the bacteria Water is only

added to replenish water lost from the system (e.g. due to evaporation). The media

is generally an organic material (e.g. compost) which may be augmented with inert

materials (e.g. perlite) .

As indicated previously. the bioscrubber. trickling bed biufdter and the packed

bed biofilter al1 have similar operating principles. The application of each technology,

however. has varied as indicated by van Groenestijn (van Groensüjn, 1993).

Bioscrubbers are generally not applied for compounds where Me dimensionless

Henry's coefficients are greater than 0.01. Trickling bed biofilters are generally not

applied for compounds where the dirnensionless Henry's coefficients are greater than

1. Packed bed biofilters can be applied to contaminants whose dimensionless Henry's

coefficients are as great as 10. The suitability of each technology, as a function of

contaminant gasiair partition coefficient, is largely due to difierence in their specific

gasbiquid surface afea. The greater the specific surface area (packed bed biofilters

have the greatest) the greater the potential for contaminant transfer from the gas

phase to the Iiquid phase and hence the greatest potentiai for removal. As a result,

the packed bed biofilter is a highly suited technology for treating VOC contarninated

air strearns (Le. BTEX). This suitability for treating VOCs has recently direcîed

considerable effort into the treatment of VOC laden air streams by packed bed

biofiltration systerns including work by Hodge (1991), Leson (1991), Medina (1992),

ûttengraf (1 986a). and Seed (1 995).

The remainder of this work will focus specifically on the packed bed biofiltration

technology. In Mure references, the term packed bed biofiltration will be referred to

simply as biofiltration.

2.1.2 Biofilter Description

A simplified schematic of a biofilter (packed bed) is presented in Figure 2.1.

The main components of the systern include:

i) humidification column

ii) supplemental water addition

iii) biofilter media containment vessel.

Each of these cornponents is described in the following paragraphs.

To maintain media moisture and prevent excessive biofilter media drying, the

influent air stream is generally humidified to near saturation levels in a humidification

column. The influent air is passed upward counter-current to a water Row. To

facilitate water transfer to the air, a packing material may be placed in the column.

Leson, Winer and Hodge (1991), Leson and Winer (1991) and Sabo (1993) reported

that the humidified air stream was adequate to maintain the desired media rnoisture

content while othen have reported the need to supply additionai water to the top of

the media (Rho, 1993; van Lm, 1990; Yavorsky, 1993; Zurlinden, 1993).

The supplemental watering system applies water to the top of the media. The

desired media moisture content @y mas) for optimal biofilter performance is generaily

considered to be 40 to 60% (Leson and Winer, 1991 ; Mueller, 1988; Ottengraf, 1983;

van L i i , 1990). Only limited data is available indicating the required supplemental

water requirements. Van Lith (1990) indicated that to prevent structural damage of

the media (theoretical calculation), supplemental water droplet diameten should be

less than 1 mm. In addition, tests as reported by van Lith (1990), indicated that to

prevent media structure darnage, the rate of water addition should be less than 20 to

30 L of water/(d m2 of media). Yavorksy (1 993) did not report the rate of water

addition but only reported a total addition time of 1 to 2 hours per week. Leson and

Wmer (1 991) reported water addition rate requirements of 6.7 to 13.4 mL of water per

1 O00 L of air treated (soi1 bed).

The biofilter media containment vessel houses the media. The airstream fmm

the humidification column may enter the media containment vesse1 from the bottom

(upfiow) or top (downflow). It is in this vessel that contaminant biodegradation occurs.

A large variety of media have been used to support microbial growth including

activated carbon (Hodge, 1 991 ; Medina, 1 992; Severin, 1 993), peat (Rho, 1 993).

compost (Seed, 1995; Zurlinden, 1993) and soi1 (Leson, Winer and Hodge, 1991).

Compost media are often supplemented with inert materials such as perlite and bark

to provide structural strength for the bed and/or to reduce the operational pressure

drop across the bed (Seed, 1995; Zurlinden, 1993; Peters, 1993).

2.2 Air Stream Characterization from Soil Vapour Extraction

As indicated previously. benzene, toluene, ethylbenzene and xylene (BTEX)

al1 have wideiy recognized health dsks associated with them and they are also

considered to be biodegradable. Sources of BTD< contaminated air streams include

volatilization during commercial processes and remediation of contarninated soils. Soil

Vapour Extraction (SVE) is a widely accepted technique for the remediation of volatile

contaminants from unsaturated ground formations (Frank, 1 994). On-gas

concentrations in SVE are characterked by a rapid decline fdlowing initially high

values and then having a prolonged period of relatively low values. Concentrations

and rate of decline are dependent on the nature of the compounds and the age of the

site.

The large variability of contaminant concentrations from SVE sites is indicated

in Tables 2.1 and 2.2 as presented by Seed (1995). In Table 2.4, VOC

concentrations ranged from 20 ppm to 38,000 pprn for the 30 systems tested. In

Table 2.2, benzene, tduene and xylene concentrations ranged from greater than

1,800 ug/L during the first week to l e s than 100 ugR after 56 weeks of soi1 vapour

extraction at a contarninated gasoline station site.

Table 2.1: Soil Vapour Extraction - VOC Off-Gas Concentrations

Number of Flowrate (m3/min, (cfm)) VOC Concentration (ppmv) Systems Surveyed Range Average Range Average

(per weii) well)

Source: Eklund et al. (1992)

Table 2.2: Soil Vapour Extraction - Benzene, Toluene, Xylene off-Gas Concentrations

Air Stream Concentration (pg/L) Week Air Flow Rate

(m'ni) Benzene Toluene Xylene

O 19.2 2,370 4,710 1,840

1 24.8 440 1,640 1,230

7 29.8 90 370 520

38 47.7 42 169 296

56 39.8 7 8 75

Source: van Eyk (1 992) - Data from a contaminated retail gasoline station

2.3 Operating Conditions of Experimental Biofiiters

A complete description of the influent air stream to the biofilter c m be

described in terms of its contaminant mass flow (mass of ContarninanVtime] and its

air flow rate [volume of air / time]. These parameters have historically been modified

and combined to indude the biofilter bed volume and surface area. Common

parameters used in literature to describe biofilter loading and operating conditions

include:

1) Empty Bad Retention Tïme (EBRT) [(voiume of bed)/(vdlume of Muent airbitne)]

2) Elimination Capacity (EC) [(mass of contaminant biodegraded)/(volum of bed

time)]

3) superficial V ~ ~ O C W [(volume of infiuent air)/(cross-sedonai surface area

. tirne)]

4) Removal Efficiency [(fraction of influent contaminant mass fbw removed)].

Table 2.3 (taken in part from Seed (1995)) presents these parameters for many

diierent systems that have used compost as biofilter media. Residence times in the

biofilter range from 0.4 minutes to 6 minutes with 1 to 3 minutes k i n g most common.

Elimination capacities for B T M compounds range from 0.8 to 75 g/(m3h) with 20 to

30 being most common. The removai efficiencies range from 30% to greater than

97%. Biofilter bed depths were less than 1 m with the exception of Sabo (1 993) where

it was 2.5m.

It has been common for authors to report elimination capacities and neglect to

indicate the removal efficiencies that were achieved. However, in order to determine

applications where biofiltration rnay be useful 1 is important to indicate both the

capacity and efficiency of the biofilter. From Table 2.3, removal efficiencies of greater

than 80% generally had elimination capacities of between 7 and 30 g/(m3-h).

Therefore, this range of organic loading was targeted during this work.

Table 2.3: Historical Parameters for Compost Blofilters

Compound(s) Media Type and Ëed Coadlng Rate andlor Superficlal Velocity Removal Efficiency Reference Volume Influent Concentration andlor Residence Time andlor Ellmination Rate

- .- .- -- ---

Mixture: Compost and inert particles Toluene: ~ e l o c i t f ' ~ Toluene: Ottengmf (1 Q83) Et hylacetate 506 - ,308 ghn3 30 - 500 m/h 21 gl(msnh) Toluene V = 5 3 L Buîylacetate EBRP: Mlxture: Butanol 0.41 - 6,O min 75 g Carbon/(ms h)

SV€ offgas bark t peat t perlite t CSS* 470 8r 870 pprn TH?" not indicated TPH": 32 gl(rns-h) Zurilnden (1 993) bentene: 0.8 gl(rnJh)

V= lM)OL toluene: 6.0 gl(rn3+)

85% Kerosene CL"' t cSS' t perllte t 25 - 1000 EBR'I": > 95% @ 152 Peters (1 993) 15% gasoline gypsurn t activatecl sludge Ippm ns/(mz min) J 1 - 3 min [ppm m'/(ma-min)]

BTEX compost

V = 8 L

300 ppm total BTEX EBRP: 1.2 min

compost t perlite 2 - 1 10 g/(ms~h) EBRT": 97% for s 40 gl(m3h) Seed (1 896) 1.7 - 2 min

V = 16.3 L

mixture: bark t Clay t coco fibre t 2 - 60 gCarbonl(m9*h) Velocity? 30 - 85% rernovai Sabo (1 993) sty rene chopped wood 90 - 240 rn/h methanol 16 - 7 gCarbon/(mJ-h)

V=400L EBRT": 3û - 100 seconds

Hexane compost t petilte t crushed 21 ,O g/(mJ*h) veloclty? 24 - 48 mlh 40 - >90% oyster shelis 350 - 700 p g h EBRP; 1 - 2 mln

Morgenroth (1 99û)

Source: Seed (1 995) with the exception of Sabo (1 993) and Morgenroth (1 996) reference. notes: 0: Superficial Velocity = [(alrfiow rate)/(aoss sectional area of blofllter)]

a: EBRT = Empty Bed Retention Time [(airfiow rate)l(bed volume)] *: CSS = Composted Sewage Sludge *: TPH = Total Pertroleum Hydrocarbon m. . CL = Cornposted Leaf and Yard Waste

2.4 Theoretical Principles of Biofilhaoon

The biofilter can be considered a two or three phase system. The two phase

system would include the gas and liquid (biofilm) phases. The three phase system

would include the gas and biofilm phases and a solid phase (media). As indicated

previously in the scope of work, the media is not considered in this work. Therefore,

for the remainder of this study, only the two phase system will be considered. A

conceptual schematic of the two phase system is presented in Figure 2.2.

In Figure 2.2, the contaminated air Stream flows past a liquid phase biofilm.

The biafilm contains microorganisms and is considered to be fixed to the media

Contaminants transfer frorn the gas to the biofilm, where biodegradation occurs. The

gas contaminant concentration is considered to be constant for a given height in the

biofilter. but. the biofilm contaminant concentration can depend on both on the height

position in the biofilter and the position in the biofilm. The biofilm concentration profile

may be horizontal (uniform concentration in biofilm) or Vary throughout the biofilm

depth. Figure 2.2 presents an exponential decay in contaminant concentration

through the biofilm where the actuai depth of contaminant penetration, 6. is equd to

the actual thickness of the biofilm 6'.

A number of researchers have attempted to model biofitters, with the majority

of models developed only considering steady state conditions. Four basic model

approaches presented in literature will be examined in this work. me model

approaches and recent authors utilizing them include:

i) Lumped Model Approach (Yang, 1994)

ii) Uniform Biofilm Model Approach (Devinny. 1991)

13

Contaminated Air Stream (cg)

Media

Figure 2.2: Conceptual Schematic of Contaminant Transport in Biofilter Media

iii) Two Phase Model Approach - Interfacial Equilibriurn (Ergas. 1993)

iv) Two Phase Model Approach - Biologicai Kinetics (Shareefdeen,

1 992).

Model cornplexity increases dramatically from the lumped model approach presented

by Yang to the model incorporating biological kinetics presented by Shareefâeen. In

addition, the number of biofilter parameten required increases from 1 to 8 for the

simplest version of the Shareefdeen presentation. Despite increased complexity, dl

of the models have some common assumptions. These assumptions include:

i) no contaminant sorption to and desorption from the media

ii) biofilm is homogeneous throughout the bed (e.g. constant

microorganism density and uniform thickness)

iii) support media is Rat (i.e. no curvature).

Each of the model approaches will be summarized in section 2.4.1. Following

al1 of the model descriptions, reported literature values for the required model

parameters will be presented (section 2.4.2).

2.4.1 Biofiiter Modelling Approaches

2.4.1.1 Lumped Model Approach (Yang)

Yang (1994) presented a simplified mass balance around the entire biofilter

and made the assumption that the only mechanism for contaminant removal was

biodegradation. The analytically solved equations were assumed to be zero or first

order with respect to biodegradation. The biodegradation rate constants were

estimated from experimental data using linear regression. The biofilter media used

was compost

The general mass balance equation for Me biofilter used by Yang is presented

in Equation 2.1.

where:

cg = gas phase contaminant concentration [g/mi

t = time [SI

R b = contaminant mass removai due to biodegradation [glm3/s]

The biodegradation removal term, Rb, was expressed as a zero and first order term.

The zero order term is presented in Equation 2.2 and the first order term is presented

in Equation 2.3.

zero order: Rb = k O

first ordec Rb = k' Cg

where:

kO = zero order biodegradation rate constant [g/m3/s]

k' = first order biodegradation rate constant [s-'1

cg = biofilm phase contaminant concentration [dm7

The biodegradation rate constants were çubçMuted into Equation 2.1 and anaiyücally

solved. The results for zero order are presented in Equation 2.4 and for first order are

presented in Equation 2.5.

zero order. Cg = C, - kat (2-4)

where:

Ce = biofitter infiuent gas phase contaminant concentration [glm3]

The equations developed by Yang contain only one parameter, k" or k'. Therefore,

curve fitting experimentad data to determine 'k' values can be quickly obtained. The

'k' parameter represents the lurnped effect of ail the conditions under which the

biofilter is operating (e.g. airflow rate, organic loading). Any variation in biofilter

operating conditions will likely change the value of 'k'. Therefore, this mode1 is

appropriate if operating condioons are expected not to Vary or if 'k' values for new

operating conditions have been previously experimentally determined.

2.4.1.2 Uniform Biofilm Approach (Devinny)

Devinny (1 991) presented general partial differential equations for the gas and

liquid (biofilrn) phases in a biofilter. The equations were solved for the steady state

condition with the parameters fitted to experimental data. Biofilter media exarnined

included activated carbon, soi1 and sintered diatomite.

The gas phase equation included expressions for dispersion, advection and

transfer of contaminants into aie film. The film phase equation included expressions

for the transfer of contaminants to the film and first order biodegradation. These

generic gas and film equations are presented in Equations 2.6 and 2.7.

ac' film: - - - K (CL- - Cf) - k'C, at

wtiere:

Dg = diffusivity in void space [m2/s]

z = distance in biofilter from influent to biofilter [ml

v = interstitial velocity [m/s]

8 = void fraction [m3/mi

K = transfer rate constant into biofilm [s"]

cf-q = biofilm contamination under gasfbiofilm equilibrium [g/m3]

The final term in the gas phase equation represents the transfer of

contaminants into the biofilrn. Devinny made the assumption that the biofilm

contaminants are at the gasfilm interface is at equilibrium with the contarninants in

the gas. This assumption allowed the following simplification to be made to the film

equilibrium concentration (Equation 2.8).

CLeq = K"-d cg

vvh ere:

, , = Devinny gas/biofilm parotion coefficient [m3/mi

Equation 2.8 was substituted into Equation 2.6. The result is presented in Equation

2.9. In addition, Equation 2.8 was substituted into Equation 2.7 and then rearranged.

The result is presented in Equation 2.10.

Equation 2.10 was then substhted into Equation 2.9. The result is presented in

Equation 2.1 1.

Although the systern has been reduced to a single partial differential equation, both

gas and liquid phase concentrations are used. The equations presented by Devinny

implicitly make the assumption that the concentration in Me biofilm is uniform

throughout itç depth. As previously indicated, the gmiquid interface is assumed to

be at equilibrium. Thecefore, the gas and liquid phsse concentrations can be

correlated by Equation 2.1 1. In addition, the time defivatives of Equation 2.12 can be

represented by Equation 2.1 3.

Substituting Equations 2.12 and 2.1 3 into Equation 2.1 1 results in equation 2.1 4.

Equation 2.14 was rearranged and simplified to Equation 2.1 5

19

where:

k - d = k - d *((l -0)fe) Devinny partition coefficient correction [-]

%=l +&-CI Devinny retardation factor [-]

Equation 2.15 was solved by Devinny assuming steady state conditions. The steady

state solution is presented in Equation 2.16.

v - (v2 + 4Dgk'Km d)0-5 Cg = C,eim where m = -

20

Equation 2.1 6 is identicai in format to that presented by Yang, in section 2.4.1,

for a first order biodegradation rate. This is expected since Devinny aiso assumed

first order biodegradation kinetics. Devinny, however, removed the 'black box'

scenario as presented by Yang, but in the process increased the number of

parameters to be fitted or determined from one (k') to four (Dg, k', Y, , and 0) with the - assumption that 8 is an easily determined parameter.

2.4.1 -3 Two Phase Mode1 Approach - Interface Equilibrium (Ergas) Ergas (Ergas. 1993) presented equations for the gas and film phases and

assumed, similar to Devinny (Devinny, 1991), equilibrium at the gas/film interface.

However, unlike Devinny, the film was assumed to have a concentration profile

throughout its depth. The biodegradation rate constant for dichloromethane was

estimated by a best fit of the experimental data. The biofilter media used during the

experiment was a 5050 mixture @y volume) of compost and perlite.

20

The difTerential equation used to describe the gas phase contaminant

concentration is presented in Equation 2.1 7. AIthough Ergas only considers the

steady state condition. the time dependence terni is included here. Ergas assumed

that dispersion was negligible and that acivection and mass transfer into the biofÏlm

adequately describe contaminant fate in the gas phase.

aC gas: 0 = v- + NA,

at dz

where:

z = distance in biofilter fom influent to biofilter [ml

N = contaminant R u from gas phase to biofilm [g/rn3/s]

4 = specific surface area of biofilter media [m2/m3]

The flux of the contaminant into the biofilm, N. was assumed to be proportional

to the film contaminant concentration gradient at the gas/film interface. The

contaminant flux expression is presented in Equation 2.1 8.

where:

4 = contaminant diffusivity in biofilm [m2/s]

The differential equation used to describe the biofilm contaminant concentration

is presented in Equation 2.19. The equation includes expressions for diffusion and

contaminant rernoval due to biodegradation.

The biodegradation expression was represented by the Monod subçtrate

utilization expression and is presented in Equation 2.20.

21

acf a2cf film: - - O , - - & - d t dx2

wtiere:

= maximum specific growth rate [s-'1

Pb = rnicrobial population density [grni

Y = contaminant yield coefficient [dg]

= half saturation constant [glm?

Ergas assurneci that the film contaminant concentration was significantly less

than the half-saturation term, Y, and, Equation 2.20 could be simplified to a Rrst order

expression as presented in Equation 2.21.

Ergas equated the term in brackets in Equation 2.21 to the first order biodegradation

rate constant. k'. The resulting expression was substituted into Equation 2.19 and is

presented in equation 2.22. This expression represents the film phase equation for

the mode1 developed by Ergas.

acf - of a* cf film: - - - - k' C, a t ax2

The boundary conditions imposed on the film phase equation include

equilibrium at the gas/film interface (2-film theory) and a no flux boundary condition

at the biofilmjsubstrate interface. These conditions are indicated in Equations 2.23

22

and 2.24.

wttere:

4 = gas/biofÏlm equiiibrium partition coefficient in biofilm [m3/m3]

6 = effecüve biofilm thickness [ml

Since the steady state condition was only considered by Ergas. the time

derivatives in Equations 2.1 7 (gas phase) and 2.22 (biofilm phase) were set to zero.

giving the resulting equations which analytically solved with the assumed boundary

conditions. The resulting equation is presented in Equation 2.25 with the Thiele

parameter expression presenteâ in Equation 2.26.

cP = miele number [-]

The number of media dependent parameters that must be fitted or estimated

for the rnodel developed by Ergas is 5 (kt, b, Df, 4 and Hf).

2.4.1.4 Two Phase Model Approach - Biological Kinetics (Shareefdeen) Shareefdeen (1 993) presented general equations for both the gas and liquid

phases. The biodegradation terni used did not distinguish between zero and first

order. but rather used Monod and Andrews type dependence. Mass transfer to the

film was assumed to be dependent on the film phase concentration profile at the

gasbilrn interface with equilibrium assumed at the gasfilm interface. Steady state

conditions were modeled with aie biofilm thickness used as the fitting parameter for

the experimental data.

Equations were developed for two compounds, methanol and oxygen.

Therefore, two gas phase equations (Le. one each for methanol and oxygen) and two

biofilm equations were used. The experimental work was conducted utilizing a

peat/perlite mixture media.

The dierential equation used to describe each contaminant gas phase

concentration is presented in Equation 2.27. The equation does not account for

dispersion. The contaminant transport mechanisms include advection and m a s

transfer into the biofilm. Although Shareefdeen only considered the steady state

condition, the tirne dependence terni is included here.

ac, - 8% gas: .- - v- + NA, at a t

The flux of the contaminant into the biofilm, N, was assumed to be proportional

to the film contaminant concentration gradient at the gasfilm interface. The

contaminant flux expression is presented in Equation 2.28.

The differential equation used to describe the biofilm contaminant concentration

24

is presented in Equaon 2.29. The equation includes expressions for diffusion and

contaminant removal due to biodegradation .

The boundary conditions imposed on the film phase include equilibnum at the

gasfilm interface and a no Rux boundary condition at the biofilm/substrate interface.

These conditions are indicated in Equations 2.30 and 2.31.

acf film: - a* Cf = D , - Rb at ax2

The biodegradation expression includes kinetic parameters such as

contaminant yield coefficient (Y), rnicrobiai population density (pJ and the compound

specific growth rate (p). The biodegradation tem is presented in Equation 2.32.

where:

CL = specific biomass growth rate [s-'1

The microorganisrn specific growth rate (p) was considered to be dependent

on both methanol and oxygen kinetic parameters. The expression for the methanol

dependence was based on a Andrews kinetics format and the oxygen was dependent

on Monod kinetics format. The expression for the microorganism specific growth rate

is presented in Equation 2.33.

where:

P. = maximum specific growth rate [dl

= constant [s/rnî

l$ = growth inhibition constant [dm7

Shareefdeen considered only steady state conditions when solving equations

2.27 and 2.29. As indicated previously, the coupled equations were solved

numerically. The solution becomes simpler if only one cornpound is used in the

specific growth rate expression. p. If only one compound is considered and the

simpler Monod kinetics format is used, the number of parameters that must be

estimated or fit&ed for the model developed by Shareefdeen is 8 (6. Df, 4, Y, Y, f,

~b and

2.4.2 Model Parameter Estimation

The number of parameters required to solve the mode$ described previously

in section 2.4.1 range from 1 to 8. This section will examine litecature values that

have k e n assigned to these parameters by various researchers. Some of

parameters are presented again in Chapter 4 (Model Input Parameters) when

parameter values are selected for input into the developed biofilter model. The

parameten have been separated into three groups depending on the factor most likely

to influence the parameter value. The three groups include:

i) media dependent parameters

ii) contaminant dependent parameters - physical/chemical

26

iii) contaminant dependent parameters - biological. All types of media and a varïety of cornpounds have been reported in order to provide

a large base on which values can be chosen.

2.4.2.1 Media Dependent Parameters

The media dependent parameters examined include:

i) specific surface area of biofilter media (q)

ii) effective and actuai media biofilm thickness (6, 61

iii) biofilter media porosity or void fraction (0)

2.4.2.1.1 Speciîic surface area of biofilter media (q)

The specific surface area of the biofilter media (A3 was rneasured directly by

Ergas (1993) using a BET analysis and determined by a best fit to data by

Shareefdeen (1 993) and Tang (1 996). Ottengraf (d 983) did not indicate 4 values or

how they were determined, however, their values were calculated using relationships

in the presented model. The % values. biofilter media composition and the parameter

determination method used by each of the authors is presented in Table 2.4.

Shareefdeen and Ottengraf reported values for 4 ranging from 80 to 363

m2/m3. l l e value reported by Ergas was four orders of magnitude greater at 1.6 x

10'. The BET analysis. as used by Ergas, determines the total specific surface area

available in the media. This area, however, may not be representative of the total

exposed area of the biofilrn since the biofilm will likely smooth the media surface when

biofilm covers it. As a result, the 4 value reported by Ergas likely represents the

upper limit of 4 that is possible.

Table 2.4: 4 Values Reported in Literature -- - - - -- -- -

Researcher 4- Biofilter Media Detemination Method (m2&rn3& Type

Tang, 1996 180 compost fitüng parameter for data

1.6 x 10' compost/perlite BET analysis (50:50 by V)

Shareefdeen, 1 993 80 peavperlite fïtüng parameter for data

Ottengraf, 1983 266 to 363 peat compost not indicated in work

2.4.2.1.2 Effective and actual media biofilm thickness (ô, 6')

The biofilm thickness was observed by Shareefdeen (1 993) to be considerably

less than 1 mm. Modelling conducted by Shareefdeen indicated that the effective

biofilm thickness (6) to range from 27 to 110 pm. Ergas (1 993) used the specific

surface area (AJ, determined by a BET analysis, and the water content of the media

to estimate a biofilm thickness of 0.2 pm. Ottengraf (1 983) estimated biofilm

thicknesses considerably greater than those reported by Ergas and Shareefdeen,

thicknesses varying from 1.2 to 2.5 mm. The thickness was caiculated based on the

observed media pressure drop (Ergun function: Ottengraf, 1986b) and a model

assuming zero order kinetics. Fan (1990) indicated a biofilm thickness of acüvated

carbon to be from 1 1 to 27 Pm.

A summary of biofilm thickness values reported in literature are presented in

Table 2.5.

Table 2.5: Effective and Achial BioRlm Thickness (6, b) Values Reported

in Literature

Researcher 6, 6' Biofilter Media Detemination (m) T Y P ~ Method

Ottengraf, 1983 1.2e-3 to 2.5e-3 peat compost calculated using presented mode1

Ergas, 1993 0.2e-6 compostfperl ite based on media water content and 4 (BET analysis)

Shareefdeen, f993 27e-6 to 1 1 Oe-6 peat/perlite caiculated using presented model

Fan, 1990 1 1 e-6 to 27e-6 activated carbon not indicated

2.4.2.1.3 Biofilter media void fraction (0)

Biofilter media porosity was reported by Ottengraf (1 981) to range from 0.40

to 0.60. Both Enviromega (1995) and Ergas (1995) reported values of 0.50.

Ottengraf (1 983) estimated a void fraction of 0.29 based on the pressure drop across

the media bed and using the Ergun relation (Ottengraf, 1986b).

A summary of media void fractions reported in literature is presented in Table

2.6.

Table 2.6: Media Porosity (0) Reported in Literature

ppppp - -

Research er 0 (-1 Biofilter Media Type Ottengraf, 1 981 0.40 - 0.60 peat compost Ottengraf, 1983

Enviromega, 1995 Ergas, 1995

0.29 peat corn p o d O. 50 compost 0.50 compost

** estirnated from pressure drop across media bed using Ergun relation

2.4.2.2 Contaminant Dependent Parameters - PhysicaVChemical The contaminant dependent parameten @hysicai/chernical) examined include:

i) Gas/Biofilm equilibnum paftition coefficient (H,, HJ

ii) Biofilm diffusivity (DJ

iii) Gasdiffusivity(DJ.

2.4.2.2.1 Gas/Biofilrn equilibrium partition coefficient (H, HJ

Aithough not reported explicitly, most researchen assume the gas/biofilm

equilibrium partition coefficient (f-&) qua i to the clean water Henry's Law value (HJ.

The H, value for a contaminant is independent of what is in the water (e.g. particulate

matter), however, the concentration in the liquid phase can be altered by including

material that can sorb the contaminant (e.g. bacteria). If sorption is n a considered

then the assumption that Hf equals H, is valid. This is often assumed since not

considering sorption simplifies the modelling process. In addition to not considering

sorption, operating conditions (Le. temperature) that the values correspond to have

generally not been indicated. Table 2.7 presents partition coefficients reported in

biofilter research. In addition, Table 2.7 presents clean water parütion coefficients (at

25'C) used in the WATER8 database (VVATER8. 1994).

Table 2.7: Gas/Biofilm Equilibrium Partition Coefficient (Hd Values Reporteci

Researcher Hf. H, (m3&m3g,J Ottengraf, 1983 toluene = 0.27

butylacetate = 0.0085 ethylacetate = 0.0051

WATER8, 1994 benzene = 0.225 toluene = 0.262 ethyl benzene = 0.322 m-xylene = 0.304 O-xylene = 0.1 95 p-xylene = 0.304 (al1 values reported at 25°C)

2.4.2.2.2 Biofilm diffusivity (03

Table 2.8 presents biofilm difhsivity values reported in Merature. Ottengraf

(1983) and Ergas (1993) used clean water diffusivity values. Shareefdeen used a

method proposed by Fan (1990) to adjust the clean water diffusivity values when

estirnating the diffusivity in Me biofilm. The equation presented by Fan requires an

estimate of the biofilm biomass concentration. Clean water diffusivity values for the

BTEX compounds used in the WATER8 database (VVATER8.1994) are also included

in Table 2.8.

Tabk 2.8: Blofilm DiffusMty (DJ Values Reporteû in Literature

Researcher Df (m2/s) Detemination Method Ottengraf, 1 983 toluene = 8.5~1 O-'' not indicated

butylacetate = 8x10"~ ethylacetate = 10x1 O-''

Shareefdeen, 1 993 methanol = 0.193 x (diffusivrty in Fan methods, ckan water) biofilm density of 100

kg/m3 was assumed

WATER8, 1994 benzene = 9.8~1 O-'' toluene = 8.6~1 O-'' ethylbenzene = 7.8~10"~ O-xyiene = I ~ X ~ O - ' ~ rn-xylene = 7.8~1 O-'* pxylene = 8.44~10'"

a: Wilke-Change method is presented by Reid (1977) B: empiricaf relation developed by Fan (1 990)

not indicated

2.4.2.2.3 Gas diff usivity @J

Biofilter models have generally assumed that the airflow through the biofilter

is plug-fiow in nature and tharefore, gas dispersion has k e n ignored and Dg set to

zero.

2.4.2.3 Contaminant Dependent Parameters - Biological The contaminant dependent parameters (biological) examined include:

i) biological yield coeffiaent (Y)

ii) microbial population density (pJ

iii) biomass growth rate (p, and p-J

iv) half saturation constant (Y)

v) Andrews kinetic expression constants (Y, Y)

vi) zero order biodegradation rate constant (0

vii) first order biodegradation rate constant (k3

2.4.2.3.1 Biological yield coefficient (Y)

Table 2.9 presents yield coefficients observed by a number of researchers.

Values are bacterial species specific and dependent on operating conditions imposed

on the bacteria during the testing (e.g. oxygen availabil-ity). Generally, a shake fiask

method was used to determine yield coefficients.

Table 2.9: Biological Yield Coefficient (Y) Values Reported in Lierature

Researcher y ~~~~ 1 ~ ~ ~ n d Determination Method Arcangeli, 1992 toluene = 0.88 - 1.1 5

Chang, 1993 benzene = 1.04. toluene = 1.22- xylene = 0.25-

head space sampling method, bacteria isolated from activated carbon fluidized bed reactor

S hareefdeen, 1 993 methanol = 0.28 shake flask

Tang, 1997 toluene = 0.62 batch culture experiment

Zarook, 1997 benzene = 0.708 not indicated toluene = 0.708

+. isolated bacterial strain tested identified as B I *: isolated bacteriai strain tested identified as X I

2w4w2.3-2 Microbial population density (pJ

Shareefdeen (1993) reported that studies conducted on three phase systems

indicated microbial population densities ranging from 23 x lo3 to 220 x lo3 g/m3.

When modelling a steady state system, Shareefdeen chose a mid-point value of 100

x Io3 g/m3.

2.4.2-3-3 Biomass growth rate (CI, p* and p-)

Table 2.10 presents biomass growth rate coefficients observed by a number

of researchers. Values are bacterial species specific and dependent on operating

conditions imposed on the bacteria during the tesüng (e.g. oxygen availability).

Generally, a shake flash method was used to determine biomass growth rates.

Table 2.10: Biomass Growth Rate (p, pw and p,,,J Values Reported

Researcher PB P* and Pm (s-9 Determin ation Mettiod Ottengraf, 1983 Clmex: shake flask

toluene = 0.69 x 1 od butanol = 1 -9 x 1 ethylacetate = 2.0 x 1 O" butylacetate = 2.7 x IO=

Ottengraf, 1 986a m-xylene 9.1 x 1 0" p-xylene 1 0.3 x 1 O&

Shareefdeen, 1993 methanol : ( = 6.1 x lob II,ax = 4.5 x 1obW

shake flask

shake flask

Chang, 1993 benzene: H, = 9.3 x IoS- head space sarnpling toluene: p, = 1 S. 1 XI O&-, method, bacteria

12.5 x 1 os- isolated from activated xylene: p,,,, = 14.9 x 1 O&- carbon fluidized bed

reactor

Tang, 1997 toluene: ~ 2 , = 1.1 3 x 1 o4 not specified

Zarook, 1997 benzene: H, = 1.89 x I O 4 batch culture toluene: p, = 4.1 7 x 1 o4 experiment

a: Nocardia bacteria isolaied tom activated sludge in shake flask test : Shareefdeen reported others have found range from H, = 2.1 x 1 o4 - 13.9 x 10-

5 S-l

-. isolated bacteriai strain tested identified as 81 -- : isolated bacteriai strah tested ideniified as XI

2m4m2.3.4 Half saturation constant (Y)

The haif saturation consiant is utilized when Monod-type kinetics are used.

Table 2.1 1 presents half saturation constants reporteâ in biofilter research.

Table 2.11: Half Saturaion Constant (KJ Values Reparted in Uteranire

Researcher KS (m"> Determination Method Chang, 1993 benzene = 3.17' head space sampling

toluene = 1.96*, 1.88- method, bacteria xylene = 4.5g isolated frorn activated

carbon fluidized bed reactor

WATER8, 1994 Benzene = 13.6 ethylbenzene = 3.3 Toluene = 30.6 m-Xylene = 14.0 O-xylene = 22.7 p-xylene = 14.7

Tang, 1997 toluene = 2.6

f. isolated bacterial strain tested identified as B I *: isolated bacteriai strain tested identified as X1

not indicated

batch culture experiment

2.4.2.3.5 Andrews kinetic expression constants (Y, KJ

The Andrews kinetic constants and K, for methanol were identified in the

model presented by Shareefdeen and described earlier in sedeon 2.4.1. The kinetic

constants used by Shareefdeen were determined by a shake flask method. Zarook

reported values for benzene and toluene. The Shareefdeen and Zarook values are

presented in Table 2.1 2.

Table 2.12: Andrews Kinetic Expression Constant Values (K. KJ Reported in Literature

Researcher YI & ( s / d Determination Method S hareefdeen, 1 993 methanol: shake flask

& = o . ~ ~ x I @ y=20x103

Zarook, 1997 benzene y = 12.22

toluene & = 11.03 K, = 78.94

not indicated

2.4.2.3.6 Zero Order Biodegradation Rate Constant (k?

Table 2.13 presents zero order rate constants reported in literature. The

compounds indicated are generally considered to be biodegradable with

experimentally observed lumped zero order rate constants (e.g method used by Yang,

1994) presented by Yang (1 994) and Enviromega (1 995) ranging from 0.1 x 10" to

40 x 1 o5 g/(m3s). Biologically derived values (e.g. by shaker flask tests) are reported

by WATER8 (1 994), Tang (1 997) and Zarook (1 997). These values were determined

using Monod substrate kinetics as presented in the mode1 proposeci by Ergas (1 993)

and presented previously in section 2.4.1.3. The Monod expression presented in

section 2.4.1.3 is reproduced below.

At large biofilm contaminant concentrations the value of the half-saturation constant

is much srnaller than the contaminant concentration and the biodegradation term is

considered constant or zero order. The zero order biodegradation term is presented

in Equation 2.35.

In Table 2.13, the specific uptake rate does not consider the rnicrobial population @J.

Tang and Zarook used microbial populations of 120.000 g/m3 and 100,000 g/m3,

respecti-vely, to obtain zero order rate constants indicated in Table 2.1 3. The

WATERB and TOXCHEM+ databases presented rate constants independent of

microbial population.

Table 2.13: Zero Order Btodegradation Rate Constants (kq Reported

Researcher (Mm3+) Media Type Yang, 1994% H,S* = 40 x 10" Compost

Enviromega, 1 995" benzene = 1.5 x I O 3 toluene = 1.6 x 1 O3

ethylbenzene = 2.0 x 1 o3 m/p-xylene = 0.8 x 10" O-xylene = 0.1 x 1

Compost

WATER8, 1994' benzene toiuene ethyl benzene m-xylene O-xy l ene p-xy l ene

Tang, 1997' toluene Zarook, 1997' benzene

toluene

*: biofilter influent concentration greater than 400 ppmv a: mode1 assumed microbial population of 120,000 g/m3 B: model assumed microbial population of 100,000 g/m3 n: model derived values for kO P: biologically derived values for kO

- - - - - -

21.8" not indicated 26.7' GAC, compost, 58.8' diatornaceous earth

2.4.2.3.7 First order biodegradation rate constant (k')

Table 2.14 presents first order rate constants reported in literature. Using

lumped parameter methods similar to that used by Yang (Yang, 1994; see section

2.4.1 . l) , Ergas (1 993). Martin (1 994), Yang (1 994) and Enviromega (1 995) reported

values ranging from 0.02 to 0.54 s-'. These values would be examined and an

appropriate value selected if the model to represent a biofilter used the lumped

parameter approach.

Biologicaliy derived values are reported by TOXCHEM+ (1996). WATER8

(1 994), Tang (1 997) and Zarook (1 997) with their findings presented in Table 2.1 4.

If the model used to represent the biofilter was kineücaily based, a representative

value for the specific uptake rate would be selected. These values were determined

using Monod substrate utiiization kinetics as presented in the model proposed by

Ergas (Ergas, 1993) and documented previousiy in section 2.4.1.3. The first order

biodegradation rate expression presented by Ergas (Equation 2.21) iç reproduced

bel ow.

The specific substrate uptake rate presented in Table 2.14 does not consider the

microbial population (pJ and the biofilm contaminant concentration (Cf). Separate

consideration would be given to each of these parameters if a kinetically based model

were used to represent a biofilter. Tang and Zarook used microbial populations of

120,000 g/m3 and 100,000 g/m3, respectively. to obtain the first order rate constants

indicated in Table 2.1 4. The WATER8 database presents rate constants independent

of the microbial population and the TOXCHEM+ database presents first order rate

constants directly (i.e. does not indicate p-, Y or values separately).

Table 2.14: First Order Biodegmdation Rate Constants (k3 Reported

- . - -

Researcher k' (s") Media Type Ergas, 1993" dichloromethane = 0.043 Compost Martin, 1994" toluene = 0.017 to 0.067 Compost Yang, 1994" H,S' = 0.54 Compost

Enviromega, 1995" benzene = 0.0372 Compost toluene = 0.0404

ethylbenzene = 0.û469 m/p-xylene = 0.0253 O-xylene = 0.021 3

Compound

TOXCHEM+, 1996' benzene toluene ethyl benzene m-xy lene O-xylene p-xylene

WATER8, 1994' benzene toluene ethyl benzene m-xylene O-xylene p-xylene

Tang. 1997' toluene Zarook, 1 997' benzene

toluene

specific uptake rate

(m3/grS)"

1.94~1 0" 0.98~1 0" 2.00~1 0" 4.72~1 0" 0.61 XI O" 3.19~1 0"

0.39~1 O" 0.67~1 0" O. 58x1 0" 0.61 x l O" 0.50~1 0" 0.58~1 O"

70.0~1 0" 21.8~1 0" 534x1 o6

*: biofilter influent concentration less than 200 ppmv a: work assumed microbial population of 120,000 g/m3 B: work assumed microbial population of 100,000 g/m3 x: model derived values for k'

8-39" not indicated 2.18' GAC, compost, 5.33" diatomaceous

eart h

P: biologically derived values for k' O: defined as p,,,J(Y Y); does not consider biomass concentration (pJ

3.0 MODEL DEVELOPMENT

This chapter presents the model that was used to predict the non-steady -te

performance of biofikers. The frst section of the chapter examines the equations

used and their associated assumptions. The second section examines the boundary

conditions assumed by the model. The solution techniques used to solve the

governing equations are presented in the third section. The fourth section presents

the actual computer model used.

3.1 Governing Equations and Assumptions

The model was developed to incorporate the following:

. dynarnic response to organic loading expressions to evaluate concentrations for both the gas and liquid (biafilm)

phases

gas phase expression to include dispersion, advection and mass transfer into

the biofilm

biofilm phase expression to include molecular diffusion and biodegradation

mass transfer of contaminants into the biofilm is dependent on the

concentration profile within the biofilm

A model could have been developed to incorporate the three phases present

in the system (gas, biofilm and media), however, to minimize the system complexity

only the gas and biofilm phases were considered.

The equation used ta describe the gas phase is presented in Equation 3.1.

The ternis following the time dependent terni represent dispersion. advection and

contaminant mass transfer into the biofilm. As indicated previously in Chapter 2, the

biofilm depth is measured from the gas/biofilrn interface to the media and is indicated

as the 'x' direction. Also, as indicated in Chapter 2, the gas position is measured from

the biofilter influent and is indicated as the '2' direction.

= gas phase contaminant concentration [g/m3]

= time [s]

= contaminant diffusivity in void space [m2/s]

= distance in biofïlter from influent to biofilter [ml

= interstitiai velocity [m/s]

= specific surface area of biofilter media [m2/m?

= contaminant diffusivity in biofilrn [m2/s]

= void fraction of media [m3/m3].

The equation used to describe the biofilm phase is presented in Equation 3.2.

The terrns followhg the time dependent term represent molecular diffusion and

contaminant removal in the biofilm through biodegradation. Biodegradation is

expressed as either zero or first order.

acf = D a2cf film: - + Rb (where: Rb = -kO or -K c,) a t ax2 where:

cf = biofilm phase contaminant concentration [g/m3]

x = distance in biofilm from gas/biofilm interface [ml

43

R b = contaminant mass removal due to biodegradation [g/m3/s]

k" = zero order biodegradation rate constant [glm3/s]

k ' = first order biodegradation rate constant 1s-'1

A pictorial representation of the terms in the gas and biofilrn phase m a s

balance equations (Equations 3.1 and 3.2) is presented in Figure 3.1. The biafilter

media is composed of many particles, however, for illustraüve purposes, it is

represented in Figure 3.1 by two large irregular shapes. The gas mass balance terms

(dispersion, advecüon, and transfer into the biofilm) are illustrated by solid lines. The

biofilm mass balance ternis (molecular diffusion and contaminant removal

(biodegradation)) are illustrated by dotted lines.

7gure 3.1 : Pictorial Representation of Gas and Biofi1.m Mass Balance Terms

The following assumpüons were made when deriving the gas and biofilm phase

expressions:

no contaminant sorption to and desoption from the biofiiter media:

The media is considered to be inert and only act as a support media for the

bacteria

biofilm is homogeneous throughout the bed:

The microorganism density in the biofilrn and thickness of the biofilm was

assumed to remain constant throughout the biofilter. In addition. this biofilrn

homogeneity implies that contaminant diffusivity remains constant through the

height of the biofilter.

the system is biologica/ly acclimatized:

During the initial operating periods of a biofilter, times ranges from days to

months are required before contaminant off-gas concentrations reach minimum

values. Changes in biodegradation rate constants during this period were not

considered and only constant biodegradation rate coefficients were used.

support media is flat:

No curvature in the media was considered. This assumption is valid if the

biofitm thickness is small relative to media diameters.

equilibrium is maintained at the gasbiofilm interface:

The ratio of the gas to liquid phase contaminant concentrations at the

gas/biofilm interface was assumed to remain constant. This assumption is

consistent with the two-film theory. Advection within the biofilm was not

considered to occur and therefore the above equilibriurn is the mechanism for

mass transfer between the gas and biofilm phases.

diffusion in the brofilm only OCCUIS perpendicular to the biofilm surface:

After contaminant was in the biofilrn, ditfusion with in the film was assumed to

only be perpendicular to the gas flow.

3.2 Boundary Conditions

The following boundary conditions were useâ to define the system:

No coniaminant flux occurred ai ale biofilm/media interface

This boundary condition States that the concentration gradient at the

biofilm/media interface is zero. It implies there is no m a s transfer to the

media and it, therefore, follows that the media is inert. This boundary condition

is represented by Equation 3.3.

(at biofim/media inteiface)

Equilibrium existed at the gas/biofilm interface.

The equilibrium concentration for each phase was determined by Heniy's law

and their relationship is presented in Equation 3.4. This gadiquid phase

boundary condition is consistent with the two-film theory.

- He - - (a t gas/biofilm interface) (3.4) Cr

Constant gas phase contaminant concentration at biofilter effluent.

The gas phase contaminant concentration immediately downstrearn from Me

biofilter was assumed to remain constant and equal to the biofilter gas phase

effiuent contaminant concentration. This condition assumes fresh air at the

biofilter exit does not influence the performance of the uppemost sections of

the biofilter.

3.3 Governing Equations Finite Difference Solution Techniques

The finite difference rnethod was used to nurnerically solve gas and biofilm

contaminant concentrations of the coupled differentiai equations and boundary

condition equations presented in Sections 3.1 and 3.2. The finite dïfference technique

attempts to represent a continuous differentiai equation with an algebraic expression.

The format of these expressions may be either explicit or implicit The explicit format

directiy evaiuates the variable (Le. contaminant concentration) at some Mure time

while the implicit format iteratively determines the variable. The explicit format

generally requires greater computational effort than the implicit format due to the

reduced time increment required to ensure a stable solution 0.e. errors do not

propagate with each tirne increment).

The finite difference uses a grid pattern to define the region of interest to be

modelled. Figure 3.2 presents the grid pattern, at a generic location, in the biofilter.

The gas phase is presented on the vertical axis (labelled as the z-axis) and the biofilm

phase is presented on the horizontal axis (labelled as the x-axis). The location of

interest in the gas and biofilm phases are identified by a solid filled square and circle,

respectively, and are labelled as points 5' and 'i' respectively. Grid locations

immediately before and after the point of interest are identified as 5-1 ' and 'j+1' in the

gas phase and 'if and 7-1' in the biofilm phase.

More specific details and solution procedures regarding the finite difference

technique and its use are presented in several sources (Von Rosenburg, 1969; Smith,

I X +' Biofilm Phase

Biofilm phase contaminant concentration to be determined

Gas phase contaminant concentration to be determined

9gure 3.2: Generic Grid Structure For Finite Difference Method.

1985).

Section 3.3.1 presents the finite difference expressions used to solve the

coupled diffbrential equations. Section 3.3.2 presents the fi nite difference expressions

used to solve the model boundary conditions.

3.3.1 Dynamic State Solution

The coupled differentiai equations used to model the biofilter system were

presented previously in section 3.1. This section examines the finite difference

expressions used to represent these equations.

The spatial componenis of the model (e.g. dC,/ax) were approximated using

the central difference technique in the implicit format The implicit format followed the

Crank-Nicholson procedure where equal weighting is applied to the iteratively

detenined Mure value and the predetermined present value. This method requires

an iterative determination of values and the Gauss-Seidel method was selected for

this purpose. The GaussSeidel method is described later in Section 3.3.1.1.

The temporal components of the differential equations 0.e. dC,/dt and dCJdt)

were approximated by the foward difference format.

The gas phase implicit differential equation presented in Section 3.1 (Equation

3.1) is presented in the finite difference format in Equation 3.5. The biofilrn phase

implicit differential equation presented Section 3.1 (Equation 3.2) is presented in the

finite difference format in Equation 3.6. The format used to express positions in space

and time are described befow.

For the implicit finite difference expressions, the following format was used:

The subscxipt values 0.e. i, i-1 , i+l) represent positions in space.

'if represents the position being evaluated and 'i-1' and 'i+lf represent

positions immediately pnor and folfowing the present position. The term

representing mass transfer into the biofilrn (last terni in Equation 3.5) only

considers the film positions O and 1. These locations correspond to the first

two positions considered in the film side of the gas/biofilm interface (i.e x-O

and x=l).

The superscript values (Le. t, t+l) represent positions in üme.

Y represents the current time and Y+1' represents the incremental Mure time.

The implicft finite difference gas phase expression (Equation 3.5) is rearranged and

simplified in Equation 3.7. The variables used in Equation 3.7 are defined in

Equations 3.8 to 3.1 1 .

where:

E, = D, [O] A z2

The implicl finite difference biofilm phase expression (Equation 3.6) is rearranged and

simplified in Equation 3.1 2. The variables used in Equation 3.1 2 are defined in

Equations 3.1 3 to 3.1 5. Because biodegradation may be rnodelled as either zero or

first order, one of the biodegradation rate constants (ko:zero order rate constant; k' first

order rate constant) must be set to zero.

where:

k' P, = - [bt ] 2

3.3.1 .l Gauss-Seidel Solution Technique

The implicit finite difference gas and biofilm phase equations were presented

previously in Section 3.3.1 (Equation 3.7 and Equation 3.12). As inherent in implicit

techniques. the terms used to calculate the next time step concentration (Le. c/')

requires values for Mure concentrations of the previous and next spatial position (Le.

Ck,"' and Ck,"'). Since concentrations at these spatial positions can not be

determined directly, rnethods have been developed to determine thern. The solution

methods are generally classified as either direct or iterative solution techniques.

lterative methods are generally used if there are a large number of grid points to be

solved and if only a few points about the location (0.g. CL,, C.,,) are used to determine

the location's value (Smith, 1985).

The Gauss-Seidel technique utilizes the iterative solution method and is often

referred to as employing successive displacement. The generalized Gauss-Seidel

equations used in the program are presented in Equations 3.16 and 3.17. For each

of the terms with a future time (Le. c'"), an iteration value 'n' or 'n+l' has been

assigned. An 'n' iteration refers to a previously detemined or estimated value. The

'n+ll iteration refers to the value obtained based on the 'n' iteration. For example, the

first iteration (Le. n=l for some time t+l) could be based on the previous time (i.e.

time t) concentration values. These newly determined values will then be the basis

for the next iteration (n=2). This process is continued with the difference between

successive iteration values becoming smaller. The iteration process is considered

complete when the difference between iterations is l e s than a preset vaiue or

fram-on .

As presented in Equations 3.1 6 and 3.17. the iteration vaiue for grid locations

previous and at the present gnd location 0.e. i. i-1) utilize the new iteration

concentration 0.e. n+l). It is obvious that the concentration at the 'i' poslion will

require the 'n+l ' iteration since this is the location where the concentration is to be

detenined. The concentration at the 'i-1' position is able to use the most recent

iteration since its value for iteration 'n+ll has just been previously determined. The

Jacobi (or simultaneous displacement) technique assumes that both the 5-1 ' and 'i+ll

grid location concentrations are based on the 'nt iteration, however, this technique

generally requires more computational time and was not considered. An explmation

of the algorithm used in the development of the Gauss-Seidel cornputer program

coding is presented later in Section 3.4.

The GaussSeidel technique is considered unconditionally stable and,

therefore, errors are not considered to propagate between successive tirnes. The time

increment. however, can not be arbitrarily chosen to be large since the error will

increase wiih increase in time increment.

3.3.1.2 Spatial and Temporal lnterval Detemination

Although the Gauss-Seidel technique is considered unconditionally stable and

54

any spatial and temporal increments could have been used, increment seledon

guidelines we