Modelling the Transport and Reactions within a Biofilm

In spite of the heterogeneity of the biofilm, it is assumed in most of the models that the substrate is transported by molecular diffusion and, therefore, that an effective diffusivity is a characteristic constant of the system. (Atkinson and Fowler 1974; Harremoes and Riemer 1975; Harremoes, 1975, 1976, 1978,; Arvin and Harremoes 1990; La Motta 1976 ; Williamson and McCarty 1976 ; Grasmick et al., 1979, 1981; Rittman and McCarty 1981).

The rate of reaction in a biofilm is based on the concept of the limiting substrate. If the waste water is aerobic, the limiting substrate will consist of oxygen, organic carbon and/or ammonia.

The intrinsic reaction rate of a limiting substrate can be described, depending on the authors, as a Monod-type, first, or zero order equation.

In waste water treatment, it has been shown that the best approximation is the zero order (La Motta 1976; Riemer and Harremoes 1978; Grasmick 1982). Depending on the penetration into the biofilm, the apparent reaction rate will be zero order kinetics for full penetration, and half-order kinetics for partial penetration (Harremoes 1978). Table 5.1 presents values for the biofilm kinetics.

Arvin and Harremoes (1990) proposed that the basic feature in the biofilm model is the kinetics of the processes performed by the active bacteria in the film. This approach can be used for describing processes other than the nitrification and denitrification such as aerobic mineralization, sulphate reduction, fermentation, or methanogenesis.

Bacterial activity:

If ^max and Y can be considered universal, then the bacterial activity can be described by transforming the monod equation (3.11) to:

where:

kx = the maximum soluble substrate (zero order) utilization rate. The kinetic characteristic of the biofilm reactor is:

1. The diffusion resistance to the movement of the substrate into the biofilm.

2. The products developed in the biofilm.

There is a difference in the performance of a reactor depending upon whether a substrate can penetrate the biofilm fully or partly (Harremoes 1978).

The diffusion resistance:

The diffusion resistance affects both the removal rate and the order of reaction. Arvin and Harremoes (1990) explain that:

- A first order reaction in the interior of the biofilm is converted into a first order bulk reaction at a reduced rate.

- A zero order reaction in the interior of the biofilm remains a zero order bulk reaction, if the biofilm is fully penetrated, but is converted into a half-order reaction, if the film is only partly penetrated.

Assuming that the reaction rate for the nitrification and denitrification is zero order, the following kinetic equations can be used:

The biofilm where the substrate penetrates fully:

(zero order)

The biofilm where the substrate penetrates partly:

(half order)

(half order)

where:

dS/dt = the reaction rate per unit surface of the biofilm.

kB = the intrinsic reaction rate per unit volume of the biofilm.

L = the thickness of the biofilm. D = the diffusion coefficient.

S = the substrate concentration, which can be forms of nitrogen carbon or oxygen.

The transition from zero order to half order kinetic is governed by the relative penetration of the substrate and the rate order can be determined using the following equation.

kb-l2

Where (3 > 1 than the biofilm is fully penetrated by the substrate, and where fB < 1 it is partly penetrated.

The biofilm in a trickling filter treating domestic waste water will usually follow a half order kinetic.

The appearance of non-diffusible matter in the biofilm reactor.

The theories for substrate removal in the biofilm suffer from the fact that only very little is known about how the biofilm affects non-diffusible matter (Levine 1985; and Odegaard 1987).

The two main questions concerning non-diffusible matter are:

- How can particulate matter be attached to the biofim surface?

- What is the mechanism for the extracellular degradation of the attached particulate matter?

The removal of the particulate matter depends on the following aspects (Arvin and Harremoes 1990):

1. The size and the chemical charge of the particulate.

2. The size, shape and chemical composition of the support media.

3. The surface of the biofilm.

4. The waste water flow through the biofilter.

Table 5.1 Values for the biofilm kinetic using zero order or an apparent half-order kinetic coefficient.

Pollution

Limiting substrate

Conditions

Temp. °C

Intrinsic zero order rate per unit biofilm

(kg/m3 S 1CT3)

Apparent halforder coefficient per unit biofilm volume

(kgKnfHs'1 1CT5

Apparent halforder coefficient per unit reactor volume

(kg^m^s1 1CT3)

Reference

Milk

02

fixed bed

20

0,12

Grasmick et al. (1980)

Beef extract

02

fixed bed

20

0,32

Grasmick et al. (1980)

Methanol

methanol

rotating reactor

22

0,16-0,19

0,38- 1,58

Jansen and Kristensen (1980)

Milk

TOC

rotating

20

0,27 - 0,59

0,083-0,18

Grasmick (1982)

From: Grasmick (1985)

From: Grasmick (1985)

The transport of non-diffusible matter into the biofilm is very slow, compared to the transport of diffusible matter.

Degradation of particulate matter outside the biofilm is conducted by extracellular enzymes, released into the waste water by the biofilm, or enzymes working on the membrane of the biofilm. This conversion of particulate matter into a soluble product, that is able to diffuse into the biofilm, may be by a special mechanism, which facilitates the penetration of the biofilm.

The liquid film diffusion.

Before any reaction takes place inside the biofilm, the substrate needs to be transferred from the bulk liquid to the solid phase. The existence of a mass transfer resistance in liquid-biofilm har been demonstrated. (La Motta 1976; Grasmick 1982)

The flux, J, of substrate into the biofilm follows Fick's first law.

where: S and Ss are the bulk and interfacial concentrations; LB is the thickness of the boundary diffusion layer. LB can be determined using a method described by Bouwer and McCarty (1985).

In practice, oxygen is always the rate limiting factor rather than the ammonia concentration, because the critical ratio between the two concentrations for performing nitrification is of the order of 0.3-0.4 mg NH3 per mg 02 (Gônec 1982). If the concentration of 02 is, for example, 4 mg/l, then the concentration of NH3 has to be smaller than 1.3 mg/l to be limiting. Table 5.2 presents values for the effective diffusivity in pure water and in biofilms.

Bacterial population dynamics in the biofilm.

If a biofilm has to oxidize carbon matter and nitrify simultaneously, the two electron donors will compete for the same electron acceptor, oxygen. Both processes will take place in the aerobic zone of the biofilm. The relative use of the limited electron acceptor resource is determined by the population dynamic of the heterotroph and nitrifiers in the biofilm. In the aerobic zone, both types of bacteria will grow, but at different rates, determined by the available substrate and the growth rate of the different species of bacteria.

At a particular ratio of organic matter to ammonia, the nitrifiers will be outgrown by the heterotroph, and no nitrification will occur. This effect is similar to the wash-out of the nitrifiers in an activated sludge plant at too low a sludge age. If the biofilm is not fully penetrated by oxygen (Fig. 5.4), it will be divided into an aerobic part adjacent to the bulk liquid and an underlying anaerobic part. Applying clinoptilolite as a support medium in an upflow fixed bed reactor (UFBR) (See section 5.8.1) it was possible to obtain simultaneous nitrification and denitrification (Halling-Sorensen and Hjuler 1992).

The biofilm composition is always a "mirror" of the composition of the waste water applied to the treatment system. Different zones may be developed as a function of the loading of substrate to the biofilm. According to Kinner (1983) (see Table 5.3) the most varied biofilm induced by a heavily loaded waste water can have four different layers, as follows:

1. An outer layer with heterotrophic oxidation of organic carbons, nitrification and denitrification and sulfide oxidation.

2. A microaerophilic layer with denitrification and fermentation.

3. An anaerobic layer with sulphate respiration and fermentation activity.

4. An anaerobic layer adjacent to the support material with methanogenesis and fermentation.

If the waste water becomes less heavily loaded, or possibly acquires a different composition, the biofilm will be built up of layers 1 and 2 only, or consists of layer 1 only.

At steady-state the fraction of organisms fj, in one of the layers is given, indicating a balance between growth and decay, as:

ra = the removal rate per unit surface area of substrate utilized by organism group i.

Y| = the yield constant for organism group i. b| = the decay constant for the organism group i. Xa = biomass of the whole biofilm.

el f| = the fraction of organism group i. I = the length of the zone with organism group i.

The product Xa*fj*l = ra * Y/b is derived from equation (5.7) and reflects the steady-state active biomass of organism group i per unit area of biofilm.

The pH effect in the biofilm.

Nitrification is an acidity-producing process, while denitrification is an alkalinity producing process as outlined in sections (3.4) and (4.4). In bulk waters of low alkalinity the result can, therefore, be a significant drop in pH in the biofilm conducting nitrification. This can lead to an inhibition of the nitrification because of too low a pH.

In the denitrifying biofilm, the pH can be increased in the rear of the film to an extent where precipitation of phosphate can occur (Arvin and Christensen 1979). There is no mention in the literature of the pH in a biofilm conducting simultaneous nitrification and denitrification.

5.5 A Massbalance Equation for a Biofilm Plant

A mass-balance equation for a biofilm plant without recirculation can be outlined as follows:

Table 5.2. Values for the effective diffusivity in pure water and in biofilms.

Pollution

Substrate

Conditions

Temp. (°C)

Effective diffusivity 10~10 (nrr/s )

Reference

Pure water

02

20

15

Milk

o2

fixed bed

20

3-9

Grasmick et al. (1980)

Beef extract

02

fixed bed

20

8 - 10

Grasmick et al. (1980)

Wastewater

o2

rotating cylinder

20

12 - 17

Tomlinson and Snaddon (1966)

Glucose

02

20

4 - 20

Matson and Charaklis (1976)

Nitrogen compounds

02

pure culture Nitrobacter Nitrobacter + Nitrosomonas

25

Williamson and McCarty (1976)

Methanol

Glucose

TOC

rotating reactor rotating reactor rotating reactor

22 22 25

20 - 50 1 - 5 6 - 50

Jansen and Kristensen (1980) La Motta (1976) Grasmick (1982)

From: Grasmick (1985).

From: Grasmick (1985).

Table 5.3 The different chemical processes in the four different layers (Source Kinner 1983).

Predominant Bacteria

Metabolic process

Reactions

Limiting substrate

Reactants + products

Aerobic + nitrifying heterotrophs

Beggiatios like filaments

Sulphate reducers Facultative anaerobs

Metanogens Facultative anaerobs

Aerobic respiration

Heterotrophic nitrification Sulphur storage

Nitrate reducers Denltritiers Facultative anaerobe

Sulphate reduction Fermentation

Methanogenesis Fermentation

Nitrate reduction 5 CH20 + 4 N03" t4H*,

Denltrltication 2 N2 + 5 C02 + 7 H20

Fermentation (CH2°)n + H2° - (CH2°)n-i + C02 + H2 + 2 H*

2 CHjO + SO/' _ S2' + 2 C02 + 2 H20 (OHjO)n + H20 - (CH20)n., + C02 + H2 + 2 H*

CH,O

CHjO

CHjO

RBC Plastic media k

Aerobic + nitrifying heterotrophs

Nitrate reducers Denitrifiers Facultative anaerobe

Aerobic respiration

Heterotrophic nitrification

Nitrate reduction

Denitrlfication

Fermentation

RBC Plastic media

Aerobic + nitrifying heterotrophs

Aerobic respiration

Heterotrophic nitrification

CH20N,NH4'

ch2o

Autotrophic nitrifiers Nitrification

Qinf = the influent flow in l/s.

Cinf = the influent substrate concentration in mg/l.

rx s = the process reaction rate in kg substrate per kg biomass /m3

V = the volume of the reactor in m3.

Qeff = the effluent flow in l/s.

Ceff = the effluent substrate concentration in mg/l.

Because it is difficult to quantify or estimate the biomass concentration XB in a biofilm plant, it has been suggested in the literature that the term rxs • V * XB be changed to a term taking into account the volume or the area of growing bacteria.

In the literature the following removal terms have often been used.

where rvs = the amount of substrate removal per m3 per day, expressed as a volumetric reaction rate. ra,s = the am0Lint of substrate removal per m2 per day (a term often used for RBC plants), expressed as a surface reaction rate. Using one of the above terms avoids the necessity of knowing the concentration of the biomass XB, but can simply relate the reaction rate to the present biomass XB, under steady-state conditions, of a specific area or volume. Table 5.4 show the different units which indicate the substrate (nitrogen) removal rate.

Depending upon whether the substrate can fully penetrate the biofilm or not, the kinetic will follow zero order or Vz order kinetics. Equation (5.2) or (5.3) must then be introduced as the kinetic rate.

Applying zero order kinetics the mass-balance for the biofilm plant will be:

Qinf ' Cinf - (2 ' D ' kB * S)* ' A = Qeff * Ceff (5.11)

where:

The use of this equation requires also the knowledge of the biomass concentration XB, therefore kB is usually an experimentally found constant observed in a special set of conditions , which also makes possible the estimation of biomass.

Table 5.4 The different units which indicate the substrate (nitrogen) removal rate.

nitrification rate term as biomass rx s as volumetric rate rv s as surface rate ra c unit kg N/kg biomass per m3*d kg N/ m3 * d. g N/m2'd.

If recirculation of the waste water is used in a biofilm plant, the following equation of biomass-balance can be used:

Qinf * Xinf + rx,x " V * XB = Qeff * Xeff + Qsedimentation * Xsedimentation (5.13)

where:

rx x = the rate of biomass activity per unit of biomass. The recirculation of water is used to ensure a constant water passage through the support material.

5.6 The Nitrifying Trickling Filters (NTF)

The trickling filter was introduced at the end of the last century, and is one of the first methods used for the removal of nitrogen from waste water. At first the trickling filters were only a primitive form of land treatment, where sewage was spread at intervals over sandy ground, allowing the sand to dry between each spreading.

Later, the sand was replaced by stones, but the operational procedures remained the same, with down flow application of the waste water. Trickling filters were first introduced in Great Britain. They were circular and supplied with a rotating distributor at the top of the filter, and measures were taken to secure accurate aeration.

An underdrain system is designed to carry away the treated waste water and the sloughed biomass. Several operational modes are available for trickling filters. Standard-rate filters have low hydraulic loading and do not include provision for recycling. High-rate filters maintain high hydraulic loading by recirculating portions of the effluent. Filters placed in series increase the effective depth, thus increasing the efficiency. A great number of possibilities exists for different flow regimes.

Figure 5.1 shows the basic design of a trickling filter. Modern trickling filters (sometimes called bio-towers) are packed with different types of plastic media , which allow the filters to be more efficient and also able to treat highly polluted industrial waste water. Plastic media consists of either vertical-flow or cross-flow substances.

The advantages of using plastic media are a high specific surface in addition to high void fraction and low weight, reducing the construction costs and high stability to shock-loads; this again, allows the construction and application of smaller trickling filters.

Process improvements of trickling filters, using bioflocculation components as a post-treatment following biological treatments, have produced higher quality effluents than previously. This improvement makes the trickling filter compatible with the activated sludge systems, and can produce a high quality effluent, comparable with that produced using the activated sludge process.

Trickling filters used for nitrification, are employed either to nitrify secondary effluent, or to combine organic removal with nitrification of the primary effluent. Depending upon the composition of the influent waste water, a different bacterial population will be developed.

Reduced removal efficiency of nitrogen can occur in a trickling filter for a variety of reasons. Most important among these is the removal of biofilm by predators (worms and fly larvae), and incomplete wetting of the media. Depressed nitrification rates can, however, also result from competition between nitrifiers and heterotrophs for dissolved oxygen.

Parker and Richards (1986) determined that a soluble BOD5 concentration above 20 mg/l was sufficient to prevent nitrification in a Nitrifiying Trickling Filter (NTF).

A typical removal rate for a conservatively loaded NTF is between 0.20 and 0.39 g N / m2 * d. With the development of the Biofilm-Controlled-Nitrifying-Trickling-Filter (BCNTF) in the late 1980's the reaction rate in these filters has been increased significantly.

As a comparison, the normal removal of organics with a trickling filter is in the order of 2-3 kg BOD /m3 * d. But extreme removal rates of up to 10-20 kg BOD/m3 " d have been reported (Audoin et al. 1971).

5.6.1 The Performance of Trickling Filters

The performance of trickling filters is affected by many factors, such as the hydraulic, organic and nitrogen loadings, characteristics of the influent waste water, its temperature, distribution, distribution frequency, and composition. Other factors are concentration of bacteria and macroorganisms, oxygen supply, the volume and geometric shape of the filter medium, and depth of filter.

The trickling filter medium.

The requirements for the trickling filter medium are to present a large surface for the bacterial population to grow on, and provide a large enough empty space to secure aeration.

Only by applying plastic-medium is it possible to satisfy these two requirements simultaneously, because of its low weight. The geometric shape of the packing is also of importance, not only in relation to the maximum available surface for biological growth, but for its influence on the hydrodynamics of the filter; this again, influences the retention time in the filter. Table 5.5 show propoerties of the trickling filter media.

The influence of variation of nitrogen and organic load on a trickling filter.

Significant load variations of ammonium-nitrogen are normal during the course of the day. The nitrifying trickling filter must, therefore, be designed to be able to treat peak loads, otherwise an ammonium breakthrough must be expected in the effluent. Trickling filters are specially sensitive to ammonium-nitrogen in the effluent, because of the very short hydraulic residence time coupled with the down flow system.

As the lower parts of the trickling filter obtain ammonium for only a few hours each day, it may require a long time to establish a fully developed biofilm at the bottom of the reactor. During periods of warm weather only the upper part of the trickling filter may be active, due to the higher reaction rate per unit area. Sudden temperature drops may, therefore, cause an ammonium breakthrough since the biofilm may not be developed at the bottom of the reactor. To avoid this, Boiler and Gujer (1986) suggested that two trickling filters should operate in series. Their sequence should be reversed once every week to obtain a homogeneous distribution of biomass throughout the reactors.

Easily degradable organics will always be preferred by the bacteria, and the capacity of the trickling filter, treating waste water with such a composition will, therefore, be high.

Several investigators have shown that the removal per volume filter at moderate loads can be described as a linear function of the load per volume.

Thus, the performance of the trickling filter evaluated for removal of organics and nitrogen would depend on the amount of total organic load applied to the filter, rather than its concentration or the flow rate.

The oxygen transfer in a nitrifying biofilm in an NTR plant.

By calculating the total oxygen transfer to a nitrifying biofilm, the maximum removal of nitrogen can be determined for different types of plastic media as shown in Fig. 5.5.

Cross-flow media are predicted to produce a higher nitrification rate than vertical flow media of identical surface area, because of fluid disruption at mixing points in the cross-flow media (Parker et at. 1989).

Table 5.5 Properties of trickling filter media.

Medium

Nominal size mm

Mass/unit volume kg/m3

Specific surface area nf/m3

Void space per cent

River rock Small Large

25-65 100-120

1250-1450 800-1000

55-70 40-50

40-50 50-60

Blast-furnace slag Small Large

50-80 75-125

900-1200 800-1000

55-70 45-60

40-50 50-60

Plastic Conventional High-specific surface

600x600x 1200 30-100 600 x 600x 1200 30-100

80-100 100-200

94-97 94-97

Redwood

1200x 1200x500 150-175

40-50

70-80

From: Metcalf and Eddy (1991)

A. Vertical Media B. Cross Flow Media

Figure 5.5 Downward flow pattern in vertical and cross-flow media. After Parker and Merrill (1984).

The hydraulic load.

The hydraulic load is a factor affecting the retention time, which is considered one of the most important factors influencing the performance of the trickling filter.

A high loading rate results in rapid growth of the biomass, and excessive growth may result in the plugging of pores and subsequent flooding of portions of the medium. Increasing the hydraulic loading rate, increases sloughing and helps to keep the bed open.

One of the limitations is the incomplete wetting of the packing at low loads and percolation at high loads. But other factors can also enhance or slow down the performance of the trickling. If diffusion in the liquid film somewhere in the filter controls the reaction rate, an increased flow rate will increase the reaction.

For plastic-packed trickling filters with a high specific surface, this effect will most likely influence the reaction rate at even normal loadings (for NTF 0.20-0.40 g N /m2 * day). In the literature the influence of the hydraulic load on the wetted area of the filter has been suggested to be an important factor in this performance. The wetted area might vary with depth, because of an uneven distribution of biomass in the filter.

The relation of the depth and retention time for the trickling filter.

The retention time is considered to be directly proportional to depth, and therefore using the retention time automatically includes depth. Depth is normally used as a measure of total available biomass, while retention time is a measure of time of contact between organisms and substrate. The following equation is generally accepted in calculating the retention time in a trickling filter:

Q"

where:

Q = the flow in l/hour H = Hydraulic retention time n = no of recyclings t = time

As the removal of organic pollutants from liquids takes place mainly through adsorption and absorption, the time of contact between organisms and substrate is considerably longer than the retention time of the liquid.

The removal per unit of biofilm surface sometimes increases at higher flow, which is contrary to the theory, used in most models, that only the flow influences the retention time. The same is observed when applying the SND mechanism, as shown in Section 5.8.1.

The influence of temperature on the performance of the trickling filter.

Very little information is available on the relationship between nitrification rate and temperature (see Fig. 5.6), because most studies of combined carbon oxidation and nitrification trickling filters have been carried out above 16 °C.

Data for lower temperatures can hardly be obtained because of lack of investigation, and nitrification data obtained at higher temperatures cannot be easily converted to represent performance at ten degrees lower for example, because changes in the nitrification rate will reflect changes in the relative growth rates of two different types of organisms in the treatment plant. No information is available on the influence of temperature on the competition between nitrifiers and heterotrophs.

The interfaces of biomass, water and air also makes the trickling filters extremely sensitive to variations in temperature. Effluent quality is thus likely to show drastic seasonal changes, due primarily to changes in ambient air temperatures. The temperature of the waste water and air also determine the direction of air flow through the medium. Cool water absorbs heat from the air, and the cooled air sinks towards the bottom of the filter in a co-current fashion with the water.

Conversely, warm water heats the air, causing it to rise through the underdrain and up through the medium. Extreme cold may result in icing and destruction of the biofilm.

The effect of recirculation in a trickling filter.

Recirculation is done to ensure that a constant volume of waste water enters the plant, to dilute a strong or toxic waste, to increase the surface load, or to prolong the retention time, so that each "substrate particle" passes through the filter more than once.

In several investigations, recirculation has been proved to enhance the efficiency of the plant. The most important factor in determining the extent of recirculation is to identify which factor controls the reaction rate, because the effect of recirculation might change the control of the reaction rate from one factor to the other, for example a process controlled by liquid diffusion might become controlled by biofilm diffusion or metabolic activity.

The influence of substrate composition on performance of the trickling filter.

With a complex substrate such as domestic sewage, there will most likely exist different organic and nitrogen compounds which can be difficult to break down. Such differences in composition of the waste water are very important to take into account in the calculation of possible efficiency.

+ y Central Valley

@ Lima ^"Midland

10 15

Figure 5.6 The effect of temperature on nitrification in a trickling filter. After Gujer and Boiler (1986).

5.6.2 Equations for Modelling the Nitrifying Trickling Filter (NTF)

The most commonly used formula for designing a trickling filters was proposed by Erkenfelder (1961), and is as follows:

SNH4e = effluent substrate concentration, mg/l

SNH4i = influent substrate concentration, mg/l

Q = hydraulic loading rate m3/m2 * min.

k = treatability constant relating to the waste water and the medium characteristics, min"1.

n = Coefficient relating to the medium characteristics.

The values of the treatability constant k range from 0.01 to 0.1. The average value for municipal waste on plastic media is of the order of 0.06 at 20 °C (Germain 1966)

Correction for other temperatures can be made by adjusting the treatability factor kT as follows:

The treatability factors kT should be determined for each situation from a pilotplant analysis of the waste water, and for the selected medium. The coefficient n for plastic media is 0.5 following Benefield and Randall (1980).

Including recirculation of the waste water into the equation, equation 5.15 can be modified to:

Table 5.6 Typical design criteria for the Trickling filter.

Item

Low-rate filter

Intermediate rate filter

High rate filter

Hydraulic loading m3/m2 • d

1-4

4-10

10-40

Depth m

1.5-3.0

1.25-2.5

1.0-2.0

Recirculation ratio

0

0-1

1.3

Filter media

Rock, slag etc

Rock, slag etc

Rock, slag Synthetic materials

Power requirements kW/103 m3

2-4

2-8

1-10

Filter flies

Many

Intermediate

Few, larvae are washed away

Dosing intervals

Less than 5 min

15-60 sec

Less than 15 sec

Effluent

Usually fully nitrified

Partially nitri-nitrified

Nitrified at low loadings

FROM: Metcalf and Eddy (1991)

FROM: Metcalf and Eddy (1991)

SNH4,a = the content in the mixture of raw and recycled mixture applied to a medium.

R = the ratio of the recycled flow to the influent flow.

Gujer and Boiler (1986) proposed the following line-fit equation for the decline in the nitrification rate with depth in a trickling filter:

where:

z = depth in tower in metres.

rn,z=o,t = nitrification rate at the top of the tower, gN/m2' d.

k = empirical parameter describing the decrease of the rate with depth (k varies between 0.075 and 0.16).

t = temperature in degrees Celsius.

Gujer and Boiler (1986) developed a biofilm model for predicting the surface nitrification rate as a function of the ammonia concentration in the bulk fluid, that considered mass balance for oxygen and ammonia within the biofilm.

By combining equation 5.18 with the normal monod kinetic equation, Gujer and Boiler developed the following two solutions for the design of NTF's.

Introducing k (the empirical parameter) different from 0:

where:

Sn = bulk liquid ammonia nitrogen concentration in mg/l.

Sn j = influent ammonia-nitrogen concentration in mg/l.

jn,max = maximum nitrification rate at high ammonia levels, g N/m2 • d.

jn(s,t) = nitrification rate at ammonia concentration g N/m2 * d. N = saturation parameter mg/l.

a = specific surface area of the trickling filter media in m2/m3. Vn= hydraulic load on the trickling filter in l/m2 * s. 181

Because the oxygen transfer efficiency of different plastic media differs, the following equation can be used to correct the nitrification rate for this difference:

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