Kinetic analysis of the psychrophilic anaerobic digestion of wastewater derived from the production of proteins from extracted sunflower flour.
ABSTRACT A kinetic analysis of the anaerobic digestion process of wastewater derived from the production of protein isolates from extracted sunflower flour was carried out. The digestion was conducted in a laboratory-scale fluidized bed reactor with saponite (magnesium silicate) as support for the mediating bacteria at psychrophilic temperature (15-19 degrees C). Soluble chemical oxygen demand (COD(s)) removal efficiencies in the range of 95.9-69.0% were achieved in the reactor at organic loading rates (OLR) of between 0.57 and 2.49 g total COD (COD(t))/L d, hydraulic retention times (HRT) of between 20.0 and 4.5 days, and average feed total COD concentration of 11.3 g/L. The yield coefficient of methane production was 0.32 L of methane (at STP) per gram of COD(t) removed. The total volatile fatty acid (TVFA) levels and the TVFA/alkalinity ratio were lower than the suggested limits for digester failure for OLR and HRT up to 2.26 g COD(t)/L d and 5.0 days, respectively. The specific rate of substrate uptake, r (g COD(s)/g VSS d), correlated with the concentration of biodegradable substrate, S (g COD(s)/L), through an equation of the Michaelis-Menten type. The maximum substrate utilization rate, k, and the Michaelis constant, K(s)(), were found to be 0.125 g COD(s)/g VSS d and 124 mg COD(s)/L, respectively. This proposed model predicted the behavior of the reactor very accurately showing deviations lower than 10% between the experimental and theoretical values of substrate uptake rates. A mass (COD(t)) balance around the reactor allowed the COD equivalent of methane volume (W(CH)4) to be obtained, which gave a value of 2.89 g COD(t)/L CH(4), which was virtually coincident with the theoretical value of 2.86 g COD(t)/L CH(4).
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ABSTRACT: A comprehensive literature review was conducted on psychrophilic anaerobic digestion and design of anaerobic digesters for treating animal manures. Anaerobic digestion of caged layer manure was studied in the laboratory at low temperatures (14–23°C). The digesters were operated to determine combinations of temperature and loading rate that gave acceptable methane yield. Acceptable methane yield was obtained for loading rates ranging between 0·15 kg VS/m day and 0·57 kg VS/m3 day for temperatures of 14°C and 23°C, respectively. The resulting data along with that taken from similar tests documented in the literature was found to approximate the van't Hoff-Arrhenius equation. This equation is then suggested as a technique for determining suitable loading rates for psychrophilic digesters based on data for digesters operated at higher temperatures.Biological Wastes. 01/1990;
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ABSTRACT: Human waste was degraded into biogas at a psychrophilic temperature of 15±1°C. Below 20°C methane production was observed only with the addition of temperature-adapted seed culture. Biogas produced was 0·148 m3 per kg total solids degraded/per day, at 30 day retention time, and methane content was 57%. Pathogenic bacterial count per 100 ml in the human waste was reduced from an initial 1024 to 103 after the anaerobic and chemical treatments. COD and BOD were reduced by up to 97 and 40% respectively. Total solids reduction was 77%. An integrated anaerobic digester/toilet was designed, fabricated, commissioned and tested.Bioresource Technology. 01/1994;
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ABSTRACT: The start-up and operation of an expanded granular sludge bed (EGSB) reactor under psychrophilic (10–12°C) conditions was studied. The reactor was seeded with mesophilic methanogenic granular sludge and fed with a mixture of volatile fatty acids (VFA). Chemical oxygen demand (COD) removal efficiencies exceeded 90% at imposed organic loading rates up to 12 g COD·l−1·d−1 at 10–12°C using influent concentrations ranging from 500 to 800 mg COD·l−1. The applied hydraulic retention time (HRT) was between 2.5 and 1.6 h and a liquid upflow velocity of 10 m·h−1 was applied. The effect of temperature on the specific VFA conversion rates was assessed using batch activity assays for the seed sludge and the sludge cultivated in the reactor. The optima temperatures for substrate conversion of sludge exposed to long term psychrophilic conditions were similar to those of the original mesophilic inoculum. Both sludges exerted an optimum substrate conversion rate at 35–40°C. The temperature dependence of acetate conversion between 10°C and 40°C could be described by an Arrhenius derived model. Propionate, butyrate and VFA mixtures degrading activities for the same temperature range could be described by a aquare root model. The specific activities of the sludge in the reactor increased in time indicating enrichment of methanogens and acetogens even at low temperature.Journal of Fermentation and Bioengineering. 07/1995;
Kinetic Analysis of the Psychrophilic Anaerobic Digestion of
Wastewater Derived fromthe Production of Proteins from
Extracted Sunflower Flour
RAFAEL BORJA,*,†ESTHER GONZA Ä LEZ,†FRANCISCO RAPOSO,†
FRANCISCO MILLA Ä N,†AND ANTONIO MARTI ÄN‡
Instituto de la Grasa (C.S.I.C.), Avda. Padre Garcı ´a Tejero 4, 41012 Sevilla, Spain, and
Seccio ´n de Ingenierı ´a Quı ´mica, Facultad de Ciencias, Edificio C-3, Campus Universitario de
Rabanales, Ctra. Madrid-Ca ´diz, km 396, 14071 Co ´rdoba, Spain
A kinetic analysis of the anaerobic digestion process of wastewater derived from the production of
protein isolates from extracted sunflower flour was carried out. The digestion was conducted in a
laboratory-scale fluidized bed reactor with saponite (magnesium silicate) as support for the mediating
bacteria at psychrophilic temperature (15-19 °C). Soluble chemical oxygen demand (CODs) removal
efficiencies in the range of 95.9-69.0% were achieved in the reactor at organic loading rates (OLR)
of between 0.57 and 2.49 g total COD (CODt)/L d, hydraulic retention times (HRT) of between 20.0
and 4.5 days, and average feed total COD concentration of 11.3 g/L. The yield coefficient of methane
production was 0.32 L of methane (at STP) per gram of CODtremoved. The total volatile fatty acid
(TVFA) levels and the TVFA/alkalinity ratio were lower than the suggested limits for digester failure
for OLR and HRT up to 2.26 g CODt/L d and 5.0 days, respectively. The specific rate of substrate
uptake, r (g CODs/g VSS d), correlated with the concentration of biodegradable substrate, S (g CODs/
L), through an equation of the Michaelis-Menten type. The maximum substrate utilization rate, k,
and the Michaelis constant, Ks, were found to be 0.125 g CODs/g VSS d and 124 mg CODs/L,
respectively. This proposed model predicted the behavior of the reactor very accurately showing
deviations lower than 10% between the experimental and theoretical values of substrate uptake rates.
A mass (CODt) balance around the reactor allowed the COD equivalent of methane volume (WCH4)
to be obtained, which gave a value of 2.89 g CODt/L CH4, which was virtually coincident with the
theoretical value of 2.86 g CODt/L CH4.
isolates; extracted sunflower flour
Kinetic analysis; anaerobic digestion; psychrophilic temperature; wastewater; protein
Anaerobic digestion of organic waste is an established process
for biogas production and organic matter removal, and it has
been employed for many years in mesophilic (20-45 °C) and
thermophilic (45-60 °C) temperature ranges. The conversion
of organic matter into biogas at low temperatures (<20 °C) is
referred to as psychrophilic anaerobic digestion (1, 2). Psy-
chrophilic anaerobic digestion has not been studied extensively
because it is a slow and difficult process (3).
However, under psychrophilic conditions anaerobic treatment
of wastewater may give some advantages in energy economy
in comparison with mesophilic and thermophilic digestion. So,
high-rate anaerobic treatment systems at psychrophilic temper-
atures have been recently developed (4, 5). The details of the
low temperature degradation pathways of diverse substrates and
the composition of the microbial communities in various
methanogenic environments are still not completely known. A
number of investigations of degradation pathways in tundra
wetland soil (6), forest soils and leaf litter (7-9), prairie soil
(10), pond silt (11, 12), lake sediments (13, 14), and pig and
cattle manure (15, 16) have shown that acetate is often formed
as a result of homoacetogenesis upon addition of H2/CO2. Under
these conditions, acetoclastic methanogenesis may be the main
pathway of methane formation (5).
The wastewaters produced in the different steps of the
manufacturing process of protein isolates from extracted sun-
flower flour have organic matter concentrations of between 2
and 45 g CODt/L, giving a polluting load of the final wastewater
of the whole process of between 10 and 15 g CODt/L (17). The
high polluting power and large volumes of wastewaters gener-
ated (30-40 L/kg of processed flour) can pose large-scale
environmental problems, taking into account the 4-5 millions
of metric tons of sunflower flour produced in Spain, 50% of
which is produced in the Andalusia community.
Previous works of anaerobic purification of this wastewater
carried out in a laboratory-scale fluidized bed reactor operating
at mesophilic temperature (35 °C) showed total chemical oxygen
demand (COD) removal efficiencies in the range of 98.3-80.0%
at organic loading rates (OLR) of between 0.6 and 9.3 g CODt/L
d and hydraulic retention times (HRT) of between 20.0 and 1.1
days. A methane yield coefficient of 0.33 L methane (at STP)
per gram of CODtremoved was obtained in this experiment,
and the value was virtually independent of the OLR applied
The aim of this work was to carry out a kinetic evaluation of
the psychrophilic anaerobic digestion process of wastewater
derived from the production of protein isolates from extracted
sunflower flour by using a fluidized bed reactor containing
microorganisms immobilized on saponite (magnesium silicate).
This report discusses a laboratory-scale investigation with
emphasis placed on the evaluation of substrate utilization and
gas production rates under different operating conditions at
psychrophilic temperature (15-19 °C). On the other hand,
purifying procedures involving fluidized beds require sturdy
supports of low apparent density in order to reduce power
consumption, which is the case with the medium assayed here.
MATERIALS AND METHODS
Equipment. The fluidized-bed reactor consisted basically of a cone-
shaped glass vessel with a working volume of 1.0 liter. The reactor
column itself had a height of 40 cm and an average internal diameter
of 6 cm. The reactor had an upper settling zone designed to minimize
loss of the biomass or the solids acting as supports for the microorgan-
isms. Effluent was recycled from the settlement zone to the bottom of
the reactor at a constant rate of 10 L/h, enough to provide complete
fluidization of the biomass. The reactor was fed daily by means of an
external feeder, and liquid effluent was removed daily through a
hydraulic seal, comprising a 25-cm liquid column, designed to prevent
air from entering the reactor and biogas from leaving it. This reactor
has been described in great detail elsewhere (18).
The methane volume produced in the process was measured using
5-L Mariotte reservoirs fitted to the reactor. A tightly closed bubbler
containing a NaOH solution (3 M) to collect the CO2produced in the
process was intercalated between the two elements. The methane
produced displaced a given volume of water from the reservoir, allowing
ready determination of the gas. The operating temperature of the reactor,
15-19 °C, was maintained as constant by means of an external water
jacket through which water from a thermostatic bath circulated.
Support Material. Clay particles of saponite (magnesium silicate)
of 0.4-0.8 mm diameter were used as the growth support material.
The main characteristics of this packing medium were low fragility,
medium porosity (19%), low apparent density (0.55 g/mL), and a high
specific surface area (200 m2/g), which facilitated attachment of
anaerobic microorganisms (19, 20). It was selected because of its
favorable kinetic behavior in previous experiments with other types of
food industry wastewaters (21-23). A detailed description of the
composition and features of this support material is given elsewhere
Wastewater. The wastewater used was previously homogenized in
an equalization tank to minimize any variation that might occur as a
result of the batch nature of the manufacturing process. The main
features of this wastewater are summarized in Table 1, which lists the
average values of five separate analyses; there was virtually no variation
(less than 5%) between analyses.
Inoculum. The reactor was inoculated with methanogenically active
biomass from an industrial anaerobic reactor processing brewery
wastewater. Its content in total suspended solids (TSS) and volatile
suspended solids (VSS) was 58.9 and 40.2 g/L, respectively. A detailed
description of the composition and features of the inoculum used are
given in a previous paper (25).
Experimental Procedure. The reactor was initially charged with
425 mL of distilled water, 375 mL of the inoculum, 200 mL of a
nutrient-trace element solution, and 15 g of the support. Although
larger amounts of support provided attachment sites for increased
amounts of biomass, they also increased the apparent viscosity of the
medium and hence hindered mass transfer and slowed biodegradation.
The composition of the nutrient-trace element solution used at the
start-up of the reactor can be found elsewhere (17).
The start-up of the reactor involved stepped increases in COD loading
and substrate concentration. During this period the organic loading rate
was gradually increased from 0.1 to 0.3 g CODt/L d between days 1
and 15, 0.4 g CODt/L d between days 16 and 30, 0.6 g CODt/L d
between days 31 and 45, and finally 0.7 g CODt/L d between 46 and
60 days. During these four steps of the acclimatization stage, the influent
total COD concentrations were 2.8, 5.6, 8.4, and 11.3 g/L, respectively.
This stepped start-up was followed by a series of continuous
experiments using feed flow rates of 50, 75, 100, 125, 150, 175, 200,
and 220 mL/d of the wastewater described in Table 1, which correspond
to hydraulic retention times (HRTs) of 20.0, 13.3, 10.0, 8.0, 6.7, 5.7,
5.0, and 4.5 d, respectively. The bacterial biomass concentration
remained virtually constant at 15.0 g VSS/L throughout the experiments.
The biomass concentration (g VSS/L) was estimated according to the
recommedation of Chen et al. (26).
Once steady-state conditions were achieved at each feed flow rate,
the daily volume of methane produced, total and soluble COD, pH,
total volatile fatty acids, and alkalinity of the different effluents obtained
were determined. The samples were collected and analyzed for at least
5 consecutive days. The steady-state value of a given parameter was
taken as the average of these consecutive measurements for that
parameter when the deviations between the observed values were less
than 3% in all cases. Each experiment had a duration of 2-3× the
The organic loadings applied in this work were increased in a
stepwise fashion in order to minimize the transient impact on the reactor
that might be induced by a sudden increase in loadings.
Chemical Analyses. The following parameters were analyzed
according to Standard Methods (27): total and soluble COD, pH, total
solids (TS), mineral solids (MS), volatile solids (VS), total suspended
solids (TSS), mineral suspended solids (MSS), volatile suspended solids
(VSS), total volatile fatty acids (TVFA), and alkalinity.
RESULTS AND DISCUSSION
Operational Parameters. Table 2 summarizes the steady-
state operating results including HRT, organic loading rates
(OLR), total and soluble CODs, TVFA, and alkalinity of the
effluents and daily methane productions. As can be seen, for
HRT values higher than or equal to 5.0 days, the pH in the
reactor remained within the optimal range for methanogenic
bacteria with 7.9 and 6.7 as extreme values. For an HRT of 4.5
days, the pH decreased until reaching a value of 6.7. In
consequence, an HRT lower than 4.5 days could cause
acidification of the reactor, when it is operated at the psychro-
philic range of temperature. For HRT values over 5.0 d, TVFA
Table 1. Com positionandFeatures of the Wastewatera
totalchem icaloxygendem and(CODt)
solublechem icaloxygendem and(CODs)
aValues are averages of five determ inations; there was virtually no variation
(less than 5%) between analyses.
concentration increased very slightly with a decreasing HRT.
For HRT values less than 5.0 days, the TVFA concentration
increased sharply, achieving a maximum value of 1240 mg/L
(as acetic acid) at an HRT of 4.5 days; this increase was
concomitant with the decrease in pH. Although a failure was
not observed at this HRT, methane production rate was some-
thing depressed at the short HRT. In contrast, high gas yields
and process stability were always observed in the mesophilic
anaerobic treatment of this wastewater at identical HRTs (17).
On the other hand, between HRTs of 20.0 and 5.7 days the
TVFA/alkalinity ratio was found to be lower than the failure
limit (0.3-0.4) value (28). However, at a HRT of 4.5 days and
OLR of 2.49 g CODt/L d, a considerable increase of this ratio
was observed in the reactor (0.93).
One of the major contributing factors to the failure of the
psychrophilic reactor at a 4.5 day HRT is the build-up of longer
chain volatile fatty acids. This is indicative of carbon flow
through to methane being interrupted by an inhibition of the
hydrogen-producing acetogenic bacteria, which are primarily
responsible for the breakdown of these compounds to acetic
acid. If hydrogen is not being effectively removed from solution
by the activity of the autotrophic methanogens then inhibition
of this reaction takes place. Failure at the 4.5 day HRT in the
reactor might therefore be attributed directly to a failure at some
point in this chain of reactions, either directly or by feedback
inhibition (28, 29).
Biodegradability. As can be observed from the data given
in Table 2, the reactor was efficient in terms of soluble COD
removals. Between HRTs of 20.0 and 5.7 days, soluble COD
removal decreased slightly from 95.9 to 86.4%. At an HRT of
4.5 days a marked difference in efficiency was observed
(69.0%). These COD removal efficiencies were something lower
than those observed at mesophilic temperature (17).
Methane Yield Coefficient. The experimental data listed in
Table 2 and the influent substrate concentration were used to
determine the methane yield coefficient. By fitting the (daily
methane production, g CODtremoved) value pairs to a straight
line, the average yield coefficient under standard temperature
and pressure (STP) conditions was found to be 0.32 L CH4
STP/g CODt removed. This agrees with data reported in the
literature (29). This value of the methane yield coefficient was
only somewhat lower than that obtained at mesophilic temper-
ature (0.33 L CH4/g CODtremoved). Taking into account that,
theoretically, 0.35 L of methane is produced per gram of CODt
removed when the starting compound is glucose (30), the
effectiveness of the anaerobic reactor in converting wastewater
derived from the production of protein isolates from extracted
sunflower flour into methane at psychrophilic temperature is
also clearly demonstrated.
Kinetic Analysis. The following two hypotheses can be
established: the anaerobic reactor operates at steady-state
conditions because the VSS concentration in the reactor and
the effluent soluble CODs were maintained virtually constant
for all the flow rates assayed.
Although the feeding carries suspended solids, the quantity
is very small, and it is supposed that all of them are biodegraded
in the reactor; this is equal to supposing that the suspended solids
content of the effluent corresponds to the biomass generated.
Making a COD balance around the reactor, the following
equation is obtained:
where (CODt)0 is the incoming total COD concentration;
(CODs)eis the outgoing soluble COD; (COD)biogasis the fraction
of COD converted into biogas; and (CODVSS)eis the fraction
of COD converted into biomass.
The above equation can be transformed into the following:
where q is the flow rate (L/day); St 0 is the feed total COD
concentration (g CODt/L); St e is the effluent total COD
concentration (g CODt/L); Ss e is the effluent soluble COD
concentration (g CODs/L); qCH4is the daily methane production
(L methane/day); and WCH4is the methane equivalent of COD
(g CODt/L CH4).
From eq 2 the following can be obtained:
By grouping terms and dividing by the flow rate, q, the
following equation can be obtained:
According to eq 4 a plot of the (St 0- St e) versus the quotient
(qCH4/q) should give a straight line of slope equal to WCH4, whose
theoretical value is 2.86 g CODt/L CH4, and intercept on the
y-axis is equal to zero, as illustrated in Figure 1. From Figure
1, it is estimated that WCH4) 2.89 g CODt/L, which was found
to be very similar to the theoretical one. As can be seen in
Figure 1, the points fit a straight line with intercept zero, which
strongly suggests the validity of the proposed model.
Each term of the second member of the previous COD
balance (eq 1) can be referred to the incoming CODt, and in
this way can be calculated the percentage of the incoming CODt
that is converted into methane and biomass, with the rest being
the fraction that goes out with the effluent. Figure 2 shows the
variation of the percentage of CODt converted into biogas,
biomass, and COD that leaves with the effluent (not removed)
as a function of the hydraulic retention time (HRT). As can be
Table 2. Steady-State Results Obtainedunder Different Experim ental Conditionsa
(m g/L) pH
aValues are averages of 6 determ inations takenover6 days afterthe steady-state conditions hadbeenreached. The differences betweenthe observedvalues were
less than4%inall cases. Abbreviations used: HRT, hydraulic retentiontim e; OLR, organic loading rate; TVFA, total volatile fatty acids; qm ethane, daily m ethane production.
(CODt)0) (CODs)e+ (COD)biogas+ (CODVSS)e
q St 0) q Ss e+ qCH4WCH4+ q [St e- Ss e](2)
q St 0) qCH4WCH4+ q St e
(St 0- St e) ) WCH4(qCH4/q) (4)
seen for HRTs lower than 5.7 d, the percentage of CODtthat
converts into biomass approached 20%, which clearly indicates
the growth of hydrolytic and acidogenic bacteria, because the
reactor is acidifying and destabilizing. In contrast, for HRT
higher than 8 days, the percentage of CODttransformed into
biomass is lower than 10%, which indicates clear methanogenic
conditions. According to Stronach et al. (31), the maximum yield
coefficients of acidogenic and methanogenic bacteria are 0.18
and 0.03 g VSS/g CODt, respectively. As a mixed culture was
used in this study, it is difficult to evaluate the kinetics of these
two distinct populations of microorganisms. However, it is
obvious that proper control of the methanogenic phase is a key
step for successful reactor performance because of the lower
substrate yield coefficient of methanogens than that of acido-
genic bacteria. Values (Y ) 0.15 and 0.16 g VSS/g CODt)
similar to those obtained in this work for HRTs lower than 5.7
days were reported in the literature for anaerobic digestion of
whey permeate and ice-cream wastewater using UASB reactors
In the above-given equations S denotes the concentration of
biodegradable substrate; however, the experimental method used
to determine the substrate concentration (total and soluble COD
analysis) does not distinguish between biodegradable and
nonbiodegradable substrate. The experimental values of soluble
COD given in Table 2 must be corrected by subtracting the
fraction of nonbiodegradable substrate. Figure 3 shows the
graphical estimation of the amount of nonbiodegradable sub-
strate on the basis of the relationship between log [log(COD)s e]
and 1/(hydraulic retention time) (33). By least-squares fitting
of the two variables an intercept of 0.385 g CODs/L (correlation
coefficient ) 0.995) was calculated, which corresponds to an
infinite HRT; thus, this can be assumed to be the concentration
of nonbiodegradable substrate.
On the other hand, according to the Michaelis-Menten
kinetic model, the specific substrate utilization rate, r, is related
with the biodegradable substrate concentration, S, by the
where k is the maximum substrate utilization rate (g CODs/g
VSS day) and Ksis the Michaelis constant (g CODs/L). At the
steady-state, r can be obtained by the following equation (18,
where θ is the hydraulic retention time (HRT) (θ ) V/q, V being
the reactor volume in liters) and X is the biomass concentration
in the reactor (g VSS/L).
Therefore, by combining eqs 5 and 6, it is possible to
determine experimentally whether the Michaelis-Menten ex-
pression is applicable for the description of substrate utilization
in the anaerobic fluidized-bed reactor
The observed substrate utilization rates plotted according to
eq 7 as a function of steady-state biodegradable effluent COD
concentration, S, are illustrated in Figure 4. It can be seen from
this figure that the substrate utilization rates fit the Michaelis-
Menten expression, which is a hyperbolic function, quite well.
Both k and Kscan be determined by plotting S/r as a function
and effluent ((CODt)0− (CODt)e) as a function of the quotient between
the daily m ethane production and influent flow-rate (qCH4/q).
Figure 2. Variationof the percentage of incom ing total COD converted
intom ethane, biom assandCODthatleaveswiththeeffluent(notrem oved)
as a function of the hydraulic retention tim e (HRT).
Figure 3. Estim ationof the fractionof nonbiodegradable organic m atter
(soluble COD) contained in the wastewater.
r ) kS/(Ks+ S)(5)
r ) (S0- S)/θ X
r ) (S0- S)/θ X ) k S/(Ks+ S) (7)
S/r ) (Ks/k) + (1/k) S
From this linearized equation, k can be calculated from the slope
of the straight line and Kscan be calculated from the intercept
on the y-axis, as illustrated in Figure 5. From this figure, it is
estimated that k ) 0.125 g CODs/g VSS day and Ks) 124 mg
CODs/L. Substitution of these values into eq 5 allowed the
theoretical rate of substrate uptake to be determined. Figure 6
shows a plot of the theoretical and experimental values of the
specific substrate removal rates. The small deviations obtained
(lower than 10%) suggest that the proposed model predicts the
behavior of this reactor for this wastewater very accurately and
that the kinetic parameters obtained represent the activity of
the microorganisms effecting the anaerobic digestion of this
wastewater at psychrophilic temperatures.
We thank Carmen Sa ´nchez and Alvaro Villanueva for their kind
help with the experimental work.
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Figure 4. Variationof the specific substrate utilizationrate, r(g CODs/g
VSS d), as a functionofthe concentrationofbiodegradable substrate, S
(m g CODs/L).
Figure 5. The plot of the quotient S/r versus the concentration of
biodegradable substrate, S, fordeterm inationof the m axim umsubstrate
utilization rate (k) and Michaelis constant (Ks).
Figure 6. Com parison between the experim ental specific substrate
utilization rate values and those theoretical predicted by eq 5.