Kinetic model description

KINETIC MODEL OF THE OZONE CONTACTOR

5.3 Kinetic model description

The current section describes the inputs to the kinetic model based on the calculated flow results based on the hydrodynamic model from Chapter 3. The details of the geometry and the mesh have been described in Section 3.3.1. The assumptions of the kinetic model, the reactions represented, the implementation and the related boundary conditions are discussed from Section 5.3.1 to Section 5.3.4.

5.3.1 Assumptions

The transfer efficiency of static mixers has been reported to be very high, approximately 85 to 98% (Bin and Roustan. 2000). It was based on this that static mixers were installed at Wiggins Waterworks to pre-mix ozone and water. Therefore a negligible ofT-gas loss was assumed for the present model. It was also assumed that the ozone mass transfer was completed in the static mixer. This assumption modifies Figure 4-1 to the distribution of dissolved ozone shown in Figure ,5-1 .

5·2

Chapter 5 Kinet!c model

{ ^{?;~~~::~ ved}

organics; inorganic

~ ____ , ,_______ . compounds

I / / '\ •

ConsumptIOn

.' Disinfection

e.g. C. parvum ."

..

^,

Disso

...

lved 0)

.... , ^/

I "-., __ :.--<---.

^Self-decomposition

Figure 5-1: Distribution of dissolved ozone (adapted from Huang el al •• 2004b)

The ozone-consuming substances (DeS) in raw water consist of oxidisable species such as dissolved organic compounds, or reduced inorganic species such as Fe (Il) and Mn (11). The overall decrease in dissolved ozone concentration was modelled as:

_ a[o,j =-k,[O,j-k,[O,][ocsj

at

^(5-1)

The first term on the right hand side of the equation describes the ozone self-decomposition reaction, the second the reaction with

oes.

Values for the kinetic constants k~ and k. were obtained from the literature.

A lthough pathogens form part of the DeS, they consume a very small mass of ozone due 10 their extremely low concentrations (Huang et al., 2004). The disinfection reaction was therefore modelled separately. A pathogenic organism typically resistant to water treatment chemicals was chosen as an indicator compound to assess the performance of the Wiggins Waterworks' ozone contactor.

The boundary conditions in the kinetic model were based on the operating values at the time when the experimental measurements were taken.

5.3.2 Simulated reactions

The details of ozone kinetics chemistry were discussed at length in Section 2.3.2 from the viewpoint of the categorised compound groups. In natural waters where a significant number of different compounds are present, it becomes impractical to analyse for each individual compound present and to model for each reaction. From the viewpoint of process operation, it is more important to examine the reaction categories from the aspect of dissolved ozone using Eqn. (5-1). The rate constants for each reaction category implemented in the kinetic model are discussed in the following sub-sections.

5.3.2.1 Selj-decomposilion

The self-decomposition of ozone in water has been studied by several authors as a first-order reaction wilh respect to ozone (park et al.. 2000; Muroyama et al.. 1999; Beltran. 1995; Hoigne and Bader. 1994;

Staehelin and Hoigne, 1985). It was also shown in Section 2.3.3 that the self-decomposition of ozone cannot be ignored. The reaction rate was observed to increase with increasing pH and dissolved ozone concentration. The self-decomposition rate constant. k, (S·I), was examined by Beltran (1995) at a wide range of pH values.

At pH = 7 (5-2)

5-3

Chapter 5 Kinetic model

Since the pH of the raw water received at the Wiggins Waterworks varies only slightly around an average of 7. the decomposition rate constant al pH 7 (refer to Eqn. (5-2» detennined by Seltrin (1995) was used for the present model. The applicable temperature is not known; however, the rate constant is particularly sensitive to pH. This was discussed in Section 2.3.2.1 that pH of water has a significant effect on the self-decomposition of ozone.

5.3.2.2 Consumption by ozone-consuming substances

Muroyama (1999) assumed the reaction between ozon~_and the oes is first order with respect to ozone as well as to the OCS. The ozone consumption reaction rate constant, k .. was referenced by Muroyama (1999) from experimental results. Muroyama reported 40 kL.kg·l.min·¹ as an average reaction rate.

Calculation details were included in the spreadshect anached. This value was then inferred to be:

le, "" 21.33 kL.kmorl.s·¹ _(5-3) The amount of OCS present in the water was estimated from the total organic carbon (TOC) content in water. High TOC generally indicates high level of NOM and hence OCS. The conversion from TOC to OCS is based on the assumption that all of the TOC is glucose. Glucose was a representative organic molecule which has the right atomic ratios (C:H:O) to approximate naturally occurring organic matter found in water. The amount of the carbohydrates present in river or groundwater is generally more abundant (100 to 500 mg CL·^I) than other organic substances (Sablon et al., 1991a), This representative molecule was introduced into the model to address the following:

• The Fluent reaction model fonnulation which needed a molecular species to be specified;

• The kinetic constant value from literature was converted into molar units as required by Fluent by assuming I: I stoichiometry;

• The measurement of TOe is a routine analysis at Umgeni Water. The amount of OCS mass fraction present in the water was re-calculated from the TOC measurements as though the NOM were glucose.

A typical value of TOC in the Wiggins Waterworks' raw water is 3.3 mgL'^I, which yields 8.26 mg.L·¹ OCS.

5.3.2.3 Disinfection

The probability ofprimo-infection by ingestion of a potentially pathogenic organism, possibly through the drinking water route is quite well established (Masschelein. 2000). The prima-infection probabilities of some selected organisms which are potentially infectious are listed in Table 5-1.

Because the existence of these organisms at extremely low concentrations can pose serious health risks. it is reasonable to model a pathogenic organism as a perfonnance indicator oflhe ozonation. For the purpose of the study. Cryplosporidium parvum oocyst is the chosen perfonnance indicator.

'·4

Chapter 5 Kinetic model

Table 5-1: Infection probability of potential pathogens (Masscbelein, 2000) Potential infectious organism

Salmonella typhi Giardia (lamblia) Cryplosporidium parvum (estimate)

Shingella

Primo-infection probability 0.0004

0.02

0.02 (preliminary)

0.007

Cryprosporidium parvum oocyst (c. parvum) is found to be extremely resistant to most commonly used disinfectants (Korich et al., 1990). C. parvum can survive at low temperature for a long period of time (Oriedger et al., 2000). Ozone remains an effective disinfectam for C. parvum, even at low temperatures where the efficacy of ozone is decreased to 1/3 of the value produced at room temperature (Finch et al., 1999; Li et al., 2001). In comparison with Giardia, it has been reported that C. parvum is 30 times more resistant to ozone, and 14 times more resistant to chlorine (Korich et al., 1990). The waterbome disease cryptosporidiosis has been recognized as a cause of diarrhoea-type illness. Traditional chlorination was shown to be not effective against C. parvum (Li et al., 2001).

The reaction kinetics between C. parvum and ozone is based on the classical Chick-Watson inactivation model presented in Eqns. (2-14) and (2-15), for n = I:

(2-14)

(2-15)

where N/N(J is the survival ratio ofthe micro-organism, C is the residual ozone concentration,

r

is the contact time, and

k.J

is the inactivation rale constant.

The value of

k.J

appears 10 be influenced by the quality of water, such as pH and temperature (Joret et al.

1997, GyUrek et al. 1999; Rennecker et al. 2000, Oriedger et al. 2000, Li et al. 2001). This is reflected by the wide range of k" reported in the literature. The disinfection rate constant,

*" .

^is calculated from the experimental results reported by Li et al. (2001) using an average residual ozone concentration 0.85 mg.L"1 and a contact time of 4 min, with the observed kill of 1.5 log-units. From Eqn. (2-15),

5.3.3 Reaction model

k,j = 0.441 L.mg"l.min·l

= 352.9 kL.kmorl.s"l ^(5-4)

The mass balance equation for chemical species in FLUENT takes the following general fonn (Fluent, 2003):

(5-5)

where Y, is the local mass fraction of each species, Ri is the net rate of production by chemical reaction; SI is the rate of creation by addition from the dispersed phase plus any user-defined sources (Fluent, 2003).

5-5

Chapter 5 K"Ie\IC model

Since the mass fraction of the species must add up to unity, the Nth mass fraction is detennined as one minus the sum of the N-) solved mass fractions. For this reason, the ^Nth species should be the one which has the largest overall mass fraction in order to minimise numerical error.

The source tenn in Eqn. (5-5) represents the reaction rates. The laminar finite-rate model in FLUENT was chosen for the purpose of the kinetic modelling study. Since the flow field has been solved in the hydrodynamic model in Chapter 3, the laminar finite-rate model reduces computational effort by avoiding the re-calculation of the hydrodynamics-related variables. The net production rate is defined by Eqn.

(5-6), neglecting the turbulent fluctuations (Fluent, 20ii3):

N.

"oM " ' -

n j ... L.J ni.r (5-6)

.. ^,

where M,.~ is the molecular weight of species ; and Rv is the Arrhenius molar rate of creation/destruction of species j in reaction r.

For the rill reaction which is non-reversible, the general fonn is given in Eqn. (!i-7):

·u ",.

N M

• ~Vj.r i

I-I I_I

(5-7)

where N is the number of chemical species in the system;

v ;. ,

is the stoichiometric coefficient for reaclanl

j in reaction r; v,~, is the stoichiometric coefficient for producl i in reaction r; M/ stands for the species i;

Ie,.r is the forward rate constant for reaction r (Fluent, 2003).

5.3.4 Boundary condition

The reaction modelling in FLUENT requires the reactant concentrations to be specified as mass fractions at the inlet. A typical ozone dose of2.5 mg.L·¹ ozone is translated into a mass fraction of 2.5)(10-6. The OCS concentration is represented using glucose as a representative compound as discussed in Section 5.3.2.2. For an average TOe concentration on.3 mgL'^I, the corresponding mass fraction is calculated to be 8.26)(10-6. In the case of pathogens. the mass fraction is not known or relevant. The parameter of interest is the survival ratio, NlNo. representing the probability that a viable organism will survive the process. To represent this in the model, the inlet mass fraction was set to an arbitrary value of 10", and survival ratios were calculated by ratioing simulated mass fractions to this value. The value 10" was simply chosen to be sufficiently low that its effect on the ozone consumption would be negligible.