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Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges.

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Dev. Chem. Eng. Mineral Process. 12(5/6). pp. 515-530, 2004.
Kinetic Model for the Water Oxidation
Method for Treating Wastewater Sludges
M.A. Imteaz* and A. Shanableh'
Design Services, Parramatta City Council, PO Box 32, Parramatta,
New South Wales 2124, Australia
'School of Engineering, University of Sharjah, Sharjah. UAE
A generalized kinetic model for the hydrothermal oxidation of organic matter in
biological wastewater treatment sludge was developed using a simplified first-order
reaction scheme. The model was based on a series of experimental results obtained
using a continuous-flow hydrothermal reactor system used to destroy the organic
component of the sludge. Forty-eight hydrothermal treatment experiments using
three sets of inflow conditions were performed. Using excess oxygen, the treatment
involved sludge destruction under subcritical (<3 74OC) and supercritical r>3 74°C)
water oxidation temperatures. The chemical oxygen demand (COD) was used to
measure the organic content and progress of the oxidation reaction. The Arrhenius
equation was used to model the reaction rate constant. In the Arrhenius equation,
the pre-exponential factor was fued and the activation energy was found to v a v
with temperature. The activation energy increased up to approximately 263°C then
stabilised at temperatures above 263°C. The variation of the activation energy with
temperature reflected the complexity of the composition of the organic content of
the sludge, which generally consists of proteins, lipids, carbohydrates and fibres.
In hydrothermal oxidation, the various organic compounds oxidize at different
rates, with the easily oxidized matter being removedfirst. As such, the activation
energy reflected the changing composition of the remaining organic matter with the
progress of the oxidation reaction. Above about 263OC, the activation energy
became virtually independent of temperature. A functional relationship was
established between activation energy and average temperature of the reactor. A
mathematical model for the destruction of COD in the presence of excess oxygen
was set using a kinetic equation having an average pre-exponential constant and
temperature dependent activation energy. With the new equation and known
influent COD, efluent COD was simulated for the entire set of experiments and was
compared with the actual measured effluent COD.
* Author for correspondence (
M.A. Imteaz and A . Shanableh
Sludges from wastewater treatment plants require the development of innovative
treatment and disposal technologies, in addition to the existing conventional
technologies. The growing amounts of wastewater sludges generated by industrial
and domestic sources represent a major concern around the world especially for
local governments. While the use of sludge as a fertiliser is an attractive option, the
accumulation of toxic heavy metals and toxic organic compounds in the soil and
plants, the cost of sludge transport from urban centres to areas suitable for land
application, and the availability of land to absorb generated sludge quantities may
limit the feasibility of this option (Shanableh and Gloyna, 1998). Due to these
limitations treatment options with efficient mass and volume reductions of sludge
are recommended.
Hydrothermal treatment of sludge at sub-critical and supercritical water
temperatures presents an innovative alternative. Hydrothermal treatment is one of
the efficient processes of sludge treatment that can reduce the mass and volume
considerably. Subcritical water oxidation occurs at temperature less than 374.2OC
and supercritical water oxidation occurs at temperature greater than 374.2OC.
Traditionally, the wet air oxidation (WAO) technology was used for sludge
conditioning and some organic destruction utilising a relatively low-temperature
process. The Zimpro process (Zimmerman, 1958; Teletzke, 1964) utilises oxidation
temperatures of 15OoCto 350OC. Wet air oxidation or the Zimpro process is capable
of 50% to 90% COD removal, depending on the reaction temperature and residence
time employed. Only supercritical water oxidation using temperatures above 374°C
is capable of more than 99.9% COD removal (Shanableh and Gloyna, 1998).
From several studies it was found that when the oxidation of organic
compounds and wastewaters is carried out above the critical point of water
(temperature 374.2'C and pressure 22.1 MPa), then the destruction of organic
compounds is rapid and complete (Helling, 1986; Staszak et al., 1987; Gloyna et al.,
1990; Lee et al., 1990). Due to the high solubility of organics, and high diffusivity
and complete miscibility of oxygen, high organic conversion of many harmful
pollutants can be achieved in supercritical water with short residence time.
Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges
Therefore, supercritical water oxidation (SCWO) with proper process engineering
development can be an effective and environmentally attractive treatment process
for managing the growing amount of organic sludge and toxic wastewater.
Biological wastewater treatment plant sludge is complex in composition. The
organic content contains the main components of living cells, protein,
carbohydrates, lipids and fibre in addition to many other compounds. The kinetics
of oxidation of such a complex matter is not easy to define. In t h s study, a
simplified first-order reaction model was used to model the oxidation of sludge.
The model was based on using the chemical oxygen demand (COD), which is a
lump-sum parameter that represents the organic content of sludge. The generalized
kinetic model developed in this study can be a useful tool for the design of water
oxidation processes, and for understanding the general oxidation mechanisms
involved. Li et al. (1991) have developed a relatively complex kinetic model and
validated it for different types of sludges using different reaction coefficients. The
objectives of the present model development are to represent the oxidation reaction
mechanism by simpler kinetics, and to develop a general kinetic model for the
destruction of COD by a continuous flow reactor.
Kinetics of Sludge Destruction
Li et al. (1991) provided a comprehensive review of the mechanisms associated
with hydrothermal oxidation of organic matter. This involves a free radical reaction
mechanism as depicted in reactions 1-6. At the start, free radicals are formed
through the reaction of oxygen and the weakest C-H bond in the complex organic
matter (reaction 1). The free radical R* has the ability to oxidise all organic
compounds containing hydrogen through hydrogen abstraction mechanics that
proceeds according to the simplified model presented in reactions 2-4. In the
process, the free radical R* reacts with oxygen forming an organic proxy radical
ROO*, which hrther abstracts a hydrogen ion from the organic compound. Thus
producing an organic hydroperoxide and a new organic radical.
The organic
hydroperoxides formed are unstable and decompose leading to the formation of
intermediates with lower carbon numbers. These reactions continue until the more
51 7
M.A. lmteaz and A. Shanableh
stable products, such as acetic and formic acids, are formed. Acetic and formic
acids in turn are oxidised to produce carbon dioxide and water, but at a slower rate
and in more aggressive oxidation conditions.
The hydrothermal oxidation of a complex organic waste such as sludge follows
a similar mechanism. Initially, the organic compounds that contain the weakest
C-H links are oxidised followed by the intermediate-strength C-H links, then the
stronger ones. The process leads to the formation of significant quantities of acetic
acid, which remains as the last organic compound. As such, the reaction rate for
sludge slows down as the reaction progresses as the easy-to-oxidise components are
removed first.
Following the formation of free radicals,
H202 + M
+ 2HO*
RH + HO* .) R* +H2O
R* + 0
2 .
) ROO*
ROO* -t RH I) ROOH + R*
Where, R denotes the organic functional group; R* is the organic radical; HO* is
the hydroxyl radical; M can be either a homogeneous or heterogeneous species; and
ROOH is organic hydroperoxide.
Studying the kinetics of sludge oxidation can be achieved by following the
removal of individual compounds, however this is a cumbersome and lengthy
process. The other way is to classify the sludge into general components based on
their oxidation. This paper attempts to demonstrate a convenient way for evaluating
the nature of sludge components based on their oxidation mechanisms. While the
specific organic compounds in sludge can be identified and the kinetics of their
destruction can be followed, the analytical procedures are both lengthy and
complex, and the results may be too specific to be practical. Therefore, researchers
usually describe sludge treatment processes qualitatively (Takamatsu et al., 1970;
Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges
Baillod et al., 1982).
Ploos and Rietema (1973) have divided the organic
components of biological sludge under wet oxidation conditions into three
components: (1) easy to oxidise component; (2) difficult to oxidise component; and
(3) non-oxidisable component. The proportions of these components are dependent
upon the strength of the oxidising environment. The kinetic results indicate that at
subcritical temperatures the initial rate of oxidation of organic contents of sludge is
high, followed by a slower rate of oxidation after heatup time as oxidation
progressed. Acetic acid is produced as oxidation proceeds, and this acetic acid
retards the reaction rate.
The destruction of biosolids may proceed directly or indirectly. In the direct
mechanism, the biosolids in contact with oxygen are oxidised. In the indirect
mechanism, the biosolids first dissolves then oxidise. The biomass from wastewater
treatment plants consists of a solid and a liquid component. A non-specific measure
of the organic content of sludge, such as COD, can be useful in modelling the
process of water oxidation. Here COD of the organic solid component of sludge is
denoted by X, and COD of the soluble component of sludge is denoted by Y , and
the end product resulting from the subcritical and supercritical water oxidation of
these organic sludges is denoted by Z. The transformations of the organic
compounds as X, Y and Z during the course of the thermal oxidation process are
described in Figure la. The pathway X to Y describes the thermal hydrolysis of the
solid organic matter (i.e. transformation of insoluble COD to soluble COD). The
pathways from X to Z and Y to Z describe the overall oxidation (i.e. solid-phase
oxidation plus the liquid-phase oxidation) process as simplified in Figure lb.
Neglecting the reaction pathway from X to Z results in the in-series reaction steps
shown in Figure lc.
Figure la.
Figure 1b.
Figure Ic.
M.A. Imteaz and A. Shanableh
For the wastewater with complex mixture, a global reaction model is proposed
as given below:
d(X +Y )
=-k* EXP(-En/ R T ) * [ X + Y ] " [ O ] "
pre-exponential factor;
activation energy;
gas constant;
concentration of oxidant;
order of the reaction with respect to the organic reactant;
order of the reaction with respect to the oxidant;
temperature (K).
total chemical oxygen demand;
Kinetic data from several experiments presented by Li et al. (1991) conclude
that the order of reaction with respect to the organic reactant is unity (m = 1). If
hydrogen peroxide is used as a source of oxygen or for the case of supercritical
water, it is found that the oxidation rate is independent of the oxygen concentration
0). Considering the first order reaction kinetics for the total organic
components, and independence of oxygen concentration as presented by Shanableh
(1990), the chemical reaction can be presented as:
d ( X + Y ) =-k*EXP(-E,/ R T ) * [ X + Y ]
Experimental Conditions
The continuous-flow reactor consisted of two concentric SS 316 tubes, 5.74 m long,
mounted vertically as shown in Figure 2. For the outer tube, outside diameter was
50.8 mm and inside diameter was 25.4 mm. For the inner tube, outside diameter
Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges
was 12.7 mm and the inside diameter was 10.9 mm. The waste stream was pumped
to the top of the reactor and preheated before the oxygen was injected into the
annular section at the middle of the reactor. The waste flow rate was 50 and
100 g/nin and the pressure was maintained at approximately 27.5 MPa. The
pressure in the reactor was controlled by the back-pressure regulator and was
measured by both a pressure gauge and a pressure transducer interfaced with digital
readout capability. The system was heated using nine electric band heaters
distributed along the lower two-thirds of the reactor.
The biological sludge was obtained from a plant treating refinery,
petrochemical, pulp and paper wastewaters. Details of the experimental conditions
are described by Shanableh (1990). Temperatures at different points at the surface
and at the core were measured. The system was operated for 48 different conditions
of heating temperature. Three different sets of inflow conditions were selected. In
the first set, the flow rate 50 &in,
inflow COD 31850 mg/l and T S of 3% was
used. In the second set, flow rate 100 g/min, inflow COD 31390 mg/l and TS of
3%. In the third set, flow rate 100 g/min, inflow COD 103 10 mg/l and TS of 1.1%.
I Effluent
Sampling Port and
Oxygen Supply
Figure 2. Details of continuousjlow reactor.
s2 I
M.A.Imteaz and A. Shanableh
It is found that sludge containing different components oxidises at different
rates. For the batch system, over 60-80% organic compounds were oxidised during
the initial heat-up time. After the heat-up time, the oxidation rate became slower
and remaining organic matter required a longer time to oxidise. One of the reasons
for this slower rate is that during heat-up time, acetic acid is produced which retards
the later reaction rate. Shanableh and Gloyna (1998) presented a simple first-order
reaction rate for the remaining difficult-to-oxidise organic components. From
several experimental results at various temperatures, they have presented different
reaction rates. The simple reaction used by Shanableh and Gloyna is:
d(X +Y )
= -KT
*[X+ Y ]
where KT is the first order reaction rate constant (per second) at a selected
temperature (2').
Model Setup and Results
To analyse the results and develop the model, the 5.74 m tubular reactor was
divided into a number of segments, each 0.5 m long. From the measured
temperatures, the average temperature between the top and bottom surface of each
segment was calculated. Density of the water under experimental pressure and
corresponding temperature was calculated for each segment. Then from the flow
rate, the residence time for each segment was calculated. The data in Figure 3 show
an example profile of temperature, density and residence time along the reactor for
subcritical temperatures with flow rates of 50 g/min and 100 g/min. The data in
Figure 4 show another profile of temperature, density and residence time for
supercritical temperatures with flow rates of 50 g/min and 100 g/min. Using the
stated first-order kinetic equation, residence time, average temperature, initial COD,
and correct reaction constants, the final COD for each segment was calculated such
that the effluent COD for a section became the initial COD for the subsequent
Kinetic Modd for the Water Oxidation Method f o r Treating Wastewater Sludges
To simulate the experimental results, correct values for the pre-exponential
constant and activation energy for each of the 48 experiments were selected by trial
and iteration. The trial and iterative procedure aimed at determining the correct
values for the pre-exponential factor and activation energy such that the COD from
the final segment was equal to the measured effluent COD from the tubular reactor.
The immediate observation that was made is that the procedure resulted in 48
pre-exponential factors (k) for all the runs that were close to each other, as shown in
Figure 5. The pre-exponential factors were thus averaged for the generalized model.
On the other hand (see Figure 6), the activation energy (EN)values for the 48
experiments, and up to a certain temperature, increased with the average
temperature of the reactor, above that temperature the activation energy became
relatively independent of temperature. The trends in Figures 5 and 6 were well
established reflecting an important issue related to the oxidation of mixed organic
matter in the complex composition of the sludge. The activation energy in this case
reflects the order at which various organic compounds oxidize in the reactor. Some
of the organic matter can be oxidized at lower temperatures while others need
higher temperatures. The data in Figure 6 establishes the experimental range of
activation energies that reflect the removal of COD, a lump sum parameter that
represents the sum of the various organic compounds in the sludge.
Above approximately 263"C, the activation energy became relatively
independent of temperature. This may indicate that the organic matter that is
represented by the activation energy above 263°C is dominated by one compound,
which can be considered the most thermally resistant to oxidation. This conclusion
is supported by two facts that are known about hydrothermal oxidation of sludge.
The first fact is that acetic acid is generated in large quantities as a by-product of
hydrothermal sludge oxidation. Second, that acetic acid is the last significant
organic matter to be oxidized, or is the most thermally resistant material in sludge
oxidation (Shanableh, 1990).
With increase of temperature, energy required for the oxidation of organic
matter increases as oxidation progresses from easy-to-oxidise components to
difticult-to-oxidise components. At a certain stage E,l becomes independent of
M.A.lmteaz and A. Shanableh
temperature, this is the stage with the organic components of the highest level of
difficulty in oxidation.
The data in Figure 6 can be represented by generalized equations representing
the relationship between (EJR) and average temperature of the reactor. As shown in
Figure 6 , a linear relationship between the average temperature and EJR was
established up to 263"C, after which the E,JR is assumed to be constant as follows:
5.9416.5*(T) + 2839; for T < 263 "C
for T 2 263°C
Using the established expressions for EJR and average value for the preexponential factor ( k
21961), the developed generalized model was used to
simulate the results of the 48 experiments using the respective influent COD. The
effluent COD was calculated for each experiment, and simulated COD was
compared with the actual final effluent COD. The data in Figure 7 shows the
comparison between the actual and predicted final effluent COD. Although the
agreement between the actual and predicted effluent COD is not very good, it is
acceptable considering the generalized nature of the model.
7 1.2
: -=.=Density
g 200
: 0.7
Residence Time (min)
Figure 3a. Profile of temperature and density with residence time
f o r 50 g/minflow rate and subcritical temperature).
Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges
Figure 3b. Profile of temperature and density with residence time
f o r I00 g/min flow rate and subcritical temperature).
~ " ". ."
. ( . . . . I . .!
. I n . . . ( .
- 1
Residence Time (min)
Figure 4 a Profile of temperature and density with residence time
Ifor 50 g/min flow rate and supercritical temperature).
M.A. Imteaz and A. Shanableh
Resldence Time (rnin)
Figure 46. Profile of temperature and density with residence time
f o r 100 g/minflow rate and supercritical temperature).
Figure 5. Values of k for different runs.
Kinetic Model for the Water Oxidation Method for Treating Wastewater Sludges
Avg. Temp.
Figure 6. Relation of EJR with average temperature of reactor.
4000 -.
*' 'c
6000 -
o ? ' " : " ' :
Figure 7. Comparison of model results with actual data.
52 7
M.A. Imteaz and A. Shanableh
Figure 8. Comparison of model results for time varying COD destruction.
Using the proposed model, time-varying COD was simulated for some cases
(for which final simulated effluent COD was close to actual effluent COD) and
compared with the actual temporal COD variations. Figure 8 shows the comparison
for such a case. It is found that the model simulations for temporal variation of
destruction of COD are very close to actual temporal variation of COD destruction.
A generalized first-order kinetic model with COD representing the oxidation of the
organic component of sludge was developed using 48 hydrothermal sludge
oxidation experiments in a continuous flow reactor. The Arrhenius model
parameters were an averaged pre-exponential factor of approximately 2 1,96 1 per
second and activation energy that is dependant on the average reaction temperature.
Kinetic Model for the Water Oxidation Methodfor Treating Wastewater Sludges
The activation energy divided by the gas constant (EJR) was represented by a
linear function that increased in the range of 3900 (1K)to 4400 (1/K)
as a function
of temperature in the range of 180°C to 263°C. Above 263"C, EJR was considered
constant at about 4400 (1K).
The variations of activation energy with temperature represent the ease or
difficulty at which the various organic compounds in sludge oxidize. The low
activation energies represent the organic compounds that can be oxidized at lower
reaction temperatures and visa versa. The constant activation energy above 263°C
represents the oxidation of organic matter dominated by acetic acid.
The kinetic model developed in this study revealed important features related
to the reaction of the various organic components of sludge and can be used to
evaluate the technical feasibility of utilising hydrothermal treatment as a sludge
management option.
Baillod, C.R. 1982. Fate of specific pollutants during wet oxidation and ozonation, Environ. frog.,
2. Gloyna, E.F., Li, L., and Bravo, J.L. 1990. Destruction of aqueous hazardous wastes in supercritical
water, Sytnp. on High Pressure Chemical Engineering, Erlangen, Germany.
3. Helling, R.K. 1986. Oxidation kinetics of simple compounds in supercritical water: Carbon
monoxide, ammonia and ethanol, Ph.D. Diss., MIT, Cambridge, Massachusetts, USA.
Lee, D.S., Li, L., and Gloyna, E.F. 1990. Efficiency of hydrogen peroxide and oxygen in
supercritical water oxidation of acetic acid and 2,4-Dichlorophenol. AIChE Meeting, Orlando,
Florida, USA.
Li, L., Chen, P., and Gloyna, E.F. 1991. Generalized kinetic model for wet oxidation of organic
compounds, AlChE Journal, 37( I I), 1687-1697.
6. Ploos, V.A., and Rietema. K. 1973. Wet air oxidation of sewage sludge, Chetn. Ing. Tech., 45(20),
7. Shanableh, A. 1990. Subcritical and supercritical water oxidation of industrial, excess activated
sludge, Ph.D. Diss.. Dept of Civil Engineering, University of Texas, Austin, Texas, USA.
Shanableh, A.. and Gloyna, E.F. 1998. Destruction of wastewater treatment sludge in supercritical
water, Rev. High Pressure Sci. Technol.. I, 1383.
M.A.Imteaz and A. Shanableh
9. Staszak, C.N., Malinowski, K.C., and Killilea, W.R. 1987. The pilot scale demonstration of the
MODAR oxidation process for the destruction of hazardous organic waste materials, Environ. frog.,
6( I ), 39.
10. Takamatsu, M. 1970. Model identification of wet-air oxidation process thermal decomposition.
Wnrcr Rcscnrch. 4 3 3 .
I I . Teletzke, G.H. 1964. Wet air oxidation, Chcm. Eng. f r o g . , 60(1), 3 3 .
12. Zimmerman, E.J.1958, New waste disposal process, Chem. Eng. (New York), 117.
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