26

might be used to inform the choice of sample locations, enabling engineers to

avoid regions of backflow or other regions where the concentration might not be

representative of reactor performance.

Second, CFD could be used as a component of the design process, supplementing

and guiding the more intelligent conduct of expensive and time-consuming

experimentation. If, through tracer analysis or other means, engineers determine a

reactor has an unusually short T10, they may opt to alter the reactor design to improve

hydraulics and achieve a higher Ct. A validated CFD could be used to predict

performance of reactors with modifications such as baffle additions, inlet or discharge

reconfigurations or modified sparger placement.

Finally, as is demonstrated in the dissertation, CFD can be used for modeling

multiphase reacting flows. This ability will enable design engineers to progress beyond

models in which the ozone transfer efficiency is assumed. Improved modeling and

understanding will yield reactor designs that improve bubble-liquid contact and mixing

and promote more uniform ozone concentration in the process water.

I.4 CFD in Water and Wastewater Treatment Operations Analysis

Computational fluid dynamics (CFD) is being used more frequently in the water

treatment and wastewater treatment engineering due to improvement in commercially-

available CFD codes (especially improved physics and chemistry submodels) and

because personal computers now have sufficient speed and memory to permit modeling

of realistic water treatment processes.

In water treatment, CFD has been used to

 assess design modifications for improved clarifier performance (Adams and

Rodi 1990; Lyn et al., 1992; Zhou et al., 1994; Brouckaert and Buckley 1999; Craig

et al., 2002),

 simulate and troubleshoot flocculation processes (Ducoste and Clark 1999; Lainé et

al., 1999; Liu et al., 2004),

 model the performance of a static mixer (Jones et al., 2002),

 simulate hydrodynamics and microbial inactivation in pilot and full scale chlorine

contact chambers (Falconer and Ismail 1997; Wang and Falconer 1998; Greene et al.,

2001),

 simulate multiphase flow in flotation processes (Sarrot et al., 2005);

 assess ozone contactor hydraulics, mass transfer and microbial inactivation (Henry

and Freeman 1995; Murrer et al., 1995; Cockx et al., 1999; Do-Quang et al., 1999;

Cockx et al., 2001; Huang et al., 2002; Ta and Hague 2004) and

 assess mixing in water storage tanks and reservoirs (Ta and Brignal 1998).

This list of applications will certainly grow as researchers develop and validate CFD

models for water treatment applications and the environmental engineering community

realizes benefits from CFD studies.

CFD has allowed engineers to perform relatively inexpensive testing and can be

used to assist in reactor scale-up and design (e.g., in design of a UV disinfection reactor

(Valade et al., 2003)). As noted in a previous study (Brouckaert and Buckley 1999),

treatment processes in water and wastewater treatment plants are often carried out in
 28

large vessels prone to non-uniform flow or other non-ideal flow characteristics.

Examples of non-ideal processes that may take place in typical unit operations are:

 Short circuiting or dead zones in reactors;

 Poor mixing of reagents (e.g., coagulants) in flow streams;

 Inefficient settling in clarifiers operated at loadings different from design values;

 Stratification in membrane reactors;

 Stratification or short-circuiting in reservoirs and storage tanks.

Experimental determination of flow conditions in water and wastewater reactors and

appurtenances is costly given the size of reactors and the likelihood that units would have

to be taken off-line to facilitate measurements. Thus, CFD appears to meet a need

currently not addressed in the water treatment industry.

I.5 Need for the Current Study

As illustrated in the literature review below, current design methodology for

ozone contactors relies on simplified, calibrated models that are applicable over a

relatively narrow range of reactor designs and operating conditions. So the current study

was formulated to assess the ability of CFD to model operation of ozone bubble

contactors accurately, inclusive of all significant hydrodynamics, chemistry and biology,

using only submodels for turbulence (mixing), mass transfer, chemistry and microbial

inactivation that are independent of reactor geometry or operating conditions. Such a

capability would be a great benefit to engineers assessing the performance of pilot scale
 29

reactors and designing full-scale reactors in which hydrodynamics may differ

significantly from those encountered at the pilot scale.

Despite an extensive literature related to bubble columns, relatively few studies

have been conducted on the behavior and modeling of countercurrent bubble flows and

the performance of countercurrent bubble columns and even fewer have considered mass

transfer; to date the majority of published studies on bubble contactor operation have

focused on hydrodynamics and have analyzed columns of bubbles injected into a non-

flowing liquid column or cocurrent flow. The work performed in this study was

developed to advance the state of CFD analysis of bubble columns by adding the

complexities of countercurrent flow, mass transfer, reaction and microbial inactivation.

These additions are significant since the objective of a bubble column is to produce

efficient mass transfer between phases and contact between disinfectant and pathogenic

organisms and because many industrial bubble columns are run in countercurrent mode.

Just as a systematic study has been made of CFD submodels for momentum

exchange between phases, so should there be a systematic study of mass transfer models.

The CFD studies identified in the literature survey of this proposal present no strong

justification for their selection of mass transfer submodel and the scientific community

will benefit from a thorough review of the sensitivity of CFD simulations to choice of

mass transfer relation and guidance in selecting a relation for a given design and

operating condition.
 30

I.6 Significance of the Proposed Work

I.6.1 Advancement of Knowledge

The current work is intended to yield three important contributions to the

technical literature:

 Rigorous verification and validation of CFD countercurrent hydrodynamics and mass

transfer submodels for ozone bubble contactor simulations;

 Detailed experimental and modeling investigation of interphase ozone mass transfer

and mass transfer models; and

 Demonstration of simultaneous prediction of microbial inactivation and bromate

formation with a CFD model that does not need to be “calibrated” with experimental

data.

The majority of bubble contactor CFD studies published to date have entailed modeling

hydrodynamics of bubble columns with either stagnant water or cocurrent flow. In the

few studies published that included interphase mass transfer, countercurrent flow and

microbial inactivation, researchers have not provided justification for their selection of

bubble drag, interphase mass transfer or microbial inactivation models. Validation of

submodels is an important step in demonstrating the utility of CFD in design of water

treatment unit operations and will boost the confidence of the water utility community in

CFD analyses.

Since bubble column hydrodynamics has been addressed in other studies, the

mass transfer studies proposed herein will likely yield the greatest immediate benefit to
 31

the scientific community. As described in detail below, mass transfer in bubble

columns is complex and varies with water depth within a given reactor operating at

known water and gas flow rates. The experimental work described below was designed

to allow visualization of the mass transfer process and yield quantitative and qualitative

data on the influence of phase distribution and mixing on the mass transfer rate. The

experiments were novel and, arguably, were a significant improvement over pilot reactor

mass transfer studies that have been performed in the past.

The CFD simulations of interphase mass transfer provide further details on

interphase mass transfer physics and, most important, demonstrate that CFD is a better

design tool than currently-used models and scale-up laws. CFD offers two benefits to the

other approaches:

 Use of first principles in development of the model and

 characterization of the problem in sufficient detail to account for the influence of

reactor geometry on reactor performance.

These benefits allow CFD to be used in more phases of the design process, even

including the design of pilot facilities. Whereas lower-fidelity models such as the one-

dimensional advection-dispersion-reaction model and completely stirred tank reactor

(CSTR) model require calibration and cannot be used for reactors whose geometry differs

from those to which the models were calibrated, CFD may be applied to any geometry.

Prediction of microbial inactivation and bromate formation in a full scale reactor

with a CFD model is significant both because it will be the first such study in a published
 32

work and because it will demonstrate a methodology for achieving an illusive

public health goal – balancing acute microbial risk with long term risk from DBP

consumption.

A final, incremental advancement in scientific knowledge is provided in

simulation of microbial inactivation in continuous flow reactors. The microbial

inactivation modeling performed builds upon the work performed by Greene (2003).

However, this work further develops a procedure for including microbial inactivation in

CFD simulations of continuous flow reactors and may expose alternatives or

modifications to the Ct approach to reactor design leading to reduced deleterious

byproduct formation.

I.6.2 Value to Industry

Compared with engineers from other disciplines, environmental engineers have

been slow to adopt CFD as a design and analysis tool, though in the past 3-4 years the

number of publications of CFD studies related to water and wastewater unit operations

has increased dramatically. Validation and experience with CFD such as demonstrated in

this dissertation should increase the confidence of the engineering community in CFD

analyses and demonstrate the utility of CFD to water utilities choosing between

experimental programs and CFD studies. CFD cannot replace careful experimentation in

water treatment. It can, however, be used in concert with experimentation to shorten

design cycle time, improve design of extant reactors, troubleshoot underperforming

reactors and explore novel reactor designs. This study can act as another stone in the
 33

foundation of studies that will make CFD a more attractive tool to

environmental engineers.

An additional value to industry of the current work is improved understanding of

ozone transfer in bubble contactors. According to calculations and experiments made in

this study and the observations made in past studies (Mariñas et al., 1993), the most

intense ozone transfer in bubble column reactors often takes place over a relatively small

vertical portion of the reactor. Most ozone contactors are designed for nearly 100%

ozone mass transfer efficiency (i.e., 100% of the applied dose transfer to the water). This

design philosophy is necessitated by the expense of generating ozone and a lack of design

relations capable of accurately predicting mass transfer rates in arbitrary geometries. The

insights into mass transfer drawn from the work reported in this thesis may suggest

reactor designs that are consistent with the processes occurring in countercurrent flow

mass transfer and achieve acceptable ozone transfer efficiencies with reduced bromate

formation.

The proposed work can contribute to the development and evaluation of the

models the U.S. EPA current allows for utilities wishing to claim inactivation credit for

ozone bubble contactors. Current guidelines do not allow inactivation credit for the first

chamber in which ozone is introduced into a bubble contactor. The assumption is that

ozone demand and decay in the first dissolution chamber are so high that no significant

accumulation of dissolved ozone occurs. CFD analyses, as performed in this study, could

allow detailed knowledge of ozone distribution in the first dissolution chamber and

assessment of this guideline. In addition, CFD calculations can be compared with results
 34

from CSTR, extended CSTR and segmented flow models of ozone bubble

contactors. These comparisons will provide information that will help utilities make

appropriate choices for modeling to claim inactivation credit and will provide

information to U.S. EPA on whether the segmented flow model is appropriate for ozone

bubble contactors and how best to apply it.

II LITERATURE SURVEY

This chapter surveys studies of bubble column reactor hydrodynamics and

performance, ozone disinfection and byproduct formation, modeling studies apropos to

ozone bubble contactors and ozone bubble column reactor design and scale up.

First, a description of phenomena occurring in bubble column reactors in general

and ozone bubble contactors in specific is presented. Next, models for the physical and

chemical phenomena occurring in ozone bubble contactors are reviewed. This review is

merited since these models are employed in CFD simulations and because CFD

simulations may provide a means to estimate some of the parameters commonly used in

reactor design.

Significant processes that occur in diffused ozone bubble column reactors are:

 Gas injection and bubble dynamics

o Introduction of gas into liquid stream

o Evolution of bubble shape and acceleration to terminal velocity

o Bubble breakup, collision and agglomeration

 Mixing

o Large length scale liquid phase turbulence related to the reactor intake, discharge

and geometry and exchange of momentum between the bubble plume and liquid

outside the bubble plume

o Small length scale liquid phase turbulence related to dissipation of turbulence and

hydrodynamics of bubble wakes

 Mass transfer

o Dissolution of gaseous ozone molecules through chemical and physical barriers at

the bubble surface and into the liquid phase

o Diffusion (penetration) of dissolved ozone into liquid adjacent to the bubble

surface

o Exchange of liquid at the bubble surface with liquid from the bulk liquid phase

o Exchange of ozone-rich liquid in the bubble plume with ozone-poor liquid outside

the bubble plume.

 Chemical reaction and microbial inactivation

o Ozone demand

o Ozone decay

o Bromate and disinfection byproduct (DBP) formation

o Microbial inactivation.

Studies that provide insight into or quantification of these processes are

summarized below. The data and relations presented are drawn from a rich literature on

bubble column reactors. The vast majority of published studies describe performance of

pilot scale cylindrical bubble column reactors operated in either co-current mode (with

the liquid and gas phases flowing in the same direction) or with non-flowing liquid phase.

Because bubble column reactor performance is strongly dependent on column geometry

(especially diameter to height ratio) and operating conditions (especially gas to liquid
 37

volumetric flow ratio), the studies summarized below should be applied to

countercurrent bubble column flow only after consideration of mode of operation and

scale.

After description of phenomena occurring in diffused bubble ozone contactors,

models that have been developed for bubble column reactors and ozonation processes are

summarized. Models differ in spatial dimensionality (0, 1 2 and 3 dimensional models),

type (empirical, stochastic and deterministic) and in the physics, chemistry and biology

included. Particular attention is paid to the application of computational fluid dynamics

(CFD) to bubble column reactors and to ozone bubble contactors.

II.1 Bubble Column Reactor Phenomena

Figure 5 is an illustration of the interrelated processes that occur in bubble

columns (Heijnen and Van't Riet 1984). As indicated in the diagram, flow and mass

transfer in bubble columns are related to the choice of sparger, liquid properties, gas

properties, bubble column operating conditions and bubble column geometry. Bubble

columns may be operated in co-current mode (with bulk gas and liquid flows in the same

direction), countercurrent mode (with liquid and gas phase bulk flows in opposite

directions) and without net liquid flow. Note that, even in the absence of net liquid flow,

bubbles produce large- and small-scale liquid motions in bubble columns. Dispersion,

hold-up and mass transfer differ significantly for bubble columns undergoing these three

modes of operation.

For all three modes of operation, changing the ratio of gas flow rate to liquid flow

rate changes the interactions between bubbles and between the phases. For relatively low
 38

gas flow rates and liquid flow rates less than the bubble terminal rise velocity,

bubbles tend to be small, non-interacting and dispersed and flow is in the “ideal bubbly

flow” or “dispersed flow” regime. In this regime, bubbles tend to be monodisperse and

there is not significant breakup or coalescence of bubbles.

Figure 5: Interrelated Processes in a Bubble Column (adapted from Heijnen and

II.1.1 Countercurrent Two-phase Flow Modeling

Depending upon the relative velocity of the phases in a countercurrent bubble

column, three flow regimes are possible: bubble flow (also called ideal bubbly flow);
 39

churn turbulent flow; and bubble down flow (Uchida et al., 1989). Bubbly flow

is characterized by a narrow, monomodal distribution of bubble diameter and negligible

break-up or coalescence (Olmos et al., 2003). Churn turbulent flow and the transition

region between bubbly flow and churn turbulent flow are also termed heterogeneous

flow. Homogeneous and heterogeneous bubble flows are illustrated in Figure 6. Other

regimes (churn turbulent and slug flow) may be encountered at very high gas flow rates,

but are not depicted in Figure 6 because it is unlikely they would be encountered in

typical ozone contactor bubble column operation.

Figure 6: Illustration of Homogeneous and Heterogeneous Bubbly Flow (Camarasa

Bubble column flow regimes are shown schematically in Figure 7 (adapted from

Uchida, Tsuyutani et al. (1989)). The trends depicted in Figure 7 are based on
 40

experimental data collected for a single bubble column (4.6 cm inner diameter)

operated in countercurrent mode over a range of gas to liquid flow ratios. Data were

collected for air bubbled into water and glycerol solutions of 5%, 10% and 15%.

The transition from bubble flow (ideal bubbly flow) to churn turbulent flow

occurred in a well-defined band (depicted with dashed lines) of gas-liquid flow ratios for

the liquids studied. The transition from bubble flow to bubble downflow was, not

surprisingly, strongly dependent on liquid composition (and surface tension, which

influences bubble shape and surface mobility) and temperature. The family of solid

curves drawn on Figure 7 indicates the transition associated with the liquids tested.

Transition occurred earliest (at the lowest gas flow rate) for the 15% glycerol solution

and latest (at the highest gas flow rate) for the lowest-temperature water tested.

Based on their results, Uchida, Tsuyutani et al. determined that the boundary

between churn turbulent flow and other flow regimes was insensitive to the composition

and properties of the liquid phase and dependent mainly on reactor design and choice of

sparger. The boundary between ideal bubbly flow and bubble down flow was strongly

dependent on the composition of the liquid phase. This may be due to differences in

properties in the liquid phase and/or differences in bubble properties and tendency to

coalesce. Lockett and Kirkpatrick (1975) suggest that the transition from ideal bubbly

flow to churn turbulent may be related to liquid circulation due to spatial variations in gas

phase holdup at a given axial location or the presence of large bubbles. Flooding (not

shown on Figure 7) is unlikely for the flow conditions typically encountered in bubble
 41

columns and likely plays no role in the transition from ideal bubbly flow to

churn turbulent flow.

Figure 7: Countercurrent Bubble Column Flow Regimes Schematic Diagram

Ruzicka, Drahoš et al. (2001) quantified the effect of liquid depth and bubble

column diameter (for cylindrical columns) on the critical gas hold-up (column volume

occupied by gas divided by column volume) at which transition from homogeneous

bubbly flow to heterogeneous regime occurs. Although their work was done in bubble

columns with stagnant liquids, it can be assumed that transition from ideal to churn

turbulent flow in countercurrent bubble columns is also dependent on column diameter

and liquid depth. In general, the authors found that increasing the column

diameter caused transition to heterogeneous bubble flow at lower void ratios and

increasing liquid depth in the column caused transition to heterogeneous bubble flow at

lower void ratios. In reviewing bubble column transition literature, Ruzicka et al. found

the effect of column diameter on transition was due to turbulence scale, intensity of

circulations, back-mixing, dispersion, wall friction and turbulent viscosity. The

dependence of liquid depth on critical void ratio was attributed to the relative importance

of the flow regions at the top and bottom of the column (compared with the region in the

middle of the column).

As described by Camarasa, Vial et al. (1999), the behavior and modeling of

liquid-solid two phase systems is significantly different from that of gas-liquid two-phase

systems. In gas-liquid two-phase systems, the properties of the dispersed phase (bubble

shape and size, distribution of bubbles in the column, influence of bubbles on each other)

depend on reactor geometry and operating conditions and the physico-chemical

properties of the continuous phase. According to Camarasa, this coupling of dispersed

phase properties with continuous phase behavior precludes a priori bubble column

reactor design given current knowledge of processes in bubble columns. Based on these

considerations, hydrodynamics and mass transfer are likely fundamentally different in

cocurrent bubble columns, countercurrent bubble columns and bubble columns in which

gas is introduced into non-flowing liquids. Specifically, liquid-phase dispersion,

circulation in the bubble column and bubble breakup and coalescence differ significantly

between the column configurations.

Cocurrent bubble column flow has been studied in greater depth than

counter current bubble column flow. For example, Deckwer, Burckhart et al. (1974)

performed cocurrent flow experiments in bubble columns of 15 cm and 20 cm and

employing different spargers. The experiments were conducted with air bubbled into tap

water and various salt and molasses solutions. The primary objective of these studies

was development of relations to predict oxygen mass transfer. Based on measured gas

phase holdup and analysis of samples taken at an unspecified number of axial locations in

the reactor, the authors concluded that, for the cocurrent configuration employed,

 there was little or no axial variation in oxygen mass transfer rate in the columns;

 the mass transfer rate was influenced more by sparger type than column dimensions;

 for the liquids studied, the mass transfer rate, kLa, varied roughly linearly with gas

velocity

 addition of electrolytes to the solution appeared to reduce bubble size (increasing

specific surface area, a) but decrease mass transfer coefficient, kL, resulting in a

slightly lower overall mass transfer rate.

II.1.1.1 Bubble Size and Interfacial Area

The shape of bubbles and the drag they impart on the water depends upon the

water surface tension (which may, in turn, depend on the concentration of impurities in

the feed water), the manner in which they are injected into the water (gas flow rate and

diffuser type), the flow rate of the water column, and the temperature. Moore (1959)
 44

suggests that bubble shape is the dominant feature in determining bubble drag

and rise velocity in the flow regimes normally encountered in bubble column flows.

Bubble size is largely a function of sparger type, aqueous phase properties and gas

velocity. Though it is convenient to work with a characteristic bubble diameter in

performing calculations, it should be remembered that there is variation in bubble

diameter at a given axial station in a contactor and that bubbles change size in the

contactor, often having significantly different average diameter near the sparger

compared with mean diameter in the rest of the bubble column.

The two processes integral to determining bubble size are injection and

coalescence. Injection of gas into a liquid column may be via nozzles, porous discs or

two-phase injectors (Heijnen and Van't Riet 1984). The type of sparger largely

determines the size of bubble introduced to the liquid while the behavior and possible

coalescence of bubbles in the liquid column is mainly a function of aqueous phase

properties. Pure liquids tend to cause bubbles with more mobile surfaces that have a

greater tendency to coalesce. Less pure waters tend to produce smaller, more rigid

bubbles.

For relatively large-diameter bubble columns, interfacial area is usually

approximated by (Roustan et al., 1996):

6 g
a (12)
db 1   g

where a is specific surface area (net surface area per reactor volume), db is effective

bubble diameter (diameter of a spherical bubble whose volume is the same as that of the
 45

bubble) and g is gas phase holdup (i.e., the gas phase volume divided by the

total reactor volume). For very small gas holdup, interfacial area can be approximated

by

6 g
a (13)
db

For smaller-diameter columns, the column geometry may influence gas holdup and Akita

and Yoshida (Akita and Yoshida 1974) propose the relation

0.5 0.1
1 g d 2    g d c3  1.13 1 0.5 0.1 1.13
ad c   c L   2   g  Bo Ga  g (14)
3    L  3

where dc is column diameter, g is gravitational acceleration, L is liquid phase density, 

is surface tension, L is liquid phase kinematic viscosity, Bo is Bond number and Ga is

Galileo number. The Akita-Yoshida relation was developed based on analysis of data

from a 2.5 m high rectangular cross section bubble column outfitted with a porous plate

sparger.

Many relations have been proposed for bubble diameter, some of which are

presented in Table 5. These relations must be used with care. First, the relations predict

a single diameter bubble though in reality spargers discharge bubbles with a range of

diameters. Second, small differences in sparger manufacture, fouling of sparger or

corrosion may significantly alter discharge bubble diameter. Finally, relations are

generally derived for bubbles either at the sparger discharge or far enough into the liquid

column that coalescence and other changes are complete and a uniform, steady diameter

is established. Choosing just one of these locations as representative is a simplification.