INTRODUCTION
Excellent design and operation of biological systems have the potential of
being the most cost effective ways to treat toxic and hazardous chemicals because
almost complete oxidation may be accomplished (Amer et
al., 2008). The toxicity of phenol and the need to find ways of removing
it from the environment have made the compound a prime candidate for study.
Many microbes are capable of utilizing phenol as a source of carbon and energy
provided it is not present in too high concentrations (Pawlowsky
et al., 1973; Solomon et al., 1994;
RuizOrdaz et al., 2001; Paller
et al., 1995; Hill and Robinson, 1975; Nikakhtari
and Hill, 2006; Afzal et al., 2007; Udayasoorian
et al., 2007; Agarry et al., 2008;
Agarry et al., 2010). Several studies have been
carried out on the kinetics of phenol degradation by various microorganisms
and on its inhibitory effects (Hill and Robinson, 1975;
Yang and Humphrey, 1975; Schroeder
et al., 1997; Folsom et al., 1990;
Oboirien et al., 2005; Agarry
and Solomon, 2008; Li et al., 2010). The
concept of material and energy balance in biotechnology has been identified
and widely used in the analysis of experimental data concerning product formation,
biomass formation and substrate consumption (Erickson, 1980;
Layokun et al., 1985; Solomon
et al., 1985, 1994). Also, the role of statistical
techniques in data analysis and parameter estimation in biological system is
widely gaining recognition (Yang et al., 1984;
Solomon et al., 1984, 1985;
Layokun et al., 1985; Beniwal
and Chhokar, 2010). This is because measurement errors make accurate estimation
of yield and maintenance parameters a difficult task (Layokun
et al., 1985). Erickson and other researchers (Erickson,
1980; Solomon et al., 1984; Yang
et al., 1984) have identified some multivariate statistical procedures
which can be used to improve the quality of estimated parameters by making use
of all the measured variables.
Most data in the literature on phenol biodegradation by mixed culture do not
lend themselves to energetic analysis using the concept of carbon and available
electron balances which have been widely used for data analysis (Erickson,
1980; Ferrer and Erickson, 1979; Oner
et al., 1986; Solomon et al., 1984,
1985, 1994, 1995).
The reason for this is that the data are incomplete as many variables required
are either not measured or reported. Biomass concentration, substrate consumption
rates, carbon dioxide production and oxygen uptake rates are considered as measured
variables. For a complete data, all these variables ought to be measured to
allow for a comprehensive energetic analysis. In spite of the extensive use
of phenol biodegradation processes, surprisingly, no work has been published
on the estimation of energetic parameters of phenol microbial degradation using
a mixed culture and an influent phenol concentration of 100 mg L^{1},
a level that is lower than what has been investigated by previous studies.
The main objective of this study was to estimate and evaluate or analyze the
growth parameters, true growth yields and maintenance coefficients (i.e., energetic
parameters) from a complete biodegradation data obtained on the aerobic degradation
of phenol by binary mixed culture of Pseudomonas aeruginosa and Pseudomonas
fluorescence in chemostat culture. The data used for the estimation include
parameters that were measured at various dilution rates: biomass concentration,
substrate consumption rates and carbon dioxide production and oxygen uptake
rates. In this work, the multivariate statistical technique which has been referred
to as the covariate adjustment technique (Solomon et
al., 1983, 1994, 1995)
was employed in the estimation of true biomass energetic yield (η_{max})
and maintenance coefficient (m_{e}) associated with the growth of mixed
culture of P. aeruginosa and P. fluorescence on phenol. The consistency
of the data obtained was examined using the concept of material and energy balance.
The analysis should provide accurate estimates of the significant design and
model growth parameters, true growth yields and maintenance coefficients. The
parameters were estimated using two similar growth models that belong to two
different classes. One is Pirt’s model (Pirt, 1965),
which assumes that substrate uptake is a consequence of growth. The second model
is a modified form of Pirt’s model (Solomon et al.,
1994) which assumes that growth is a consequence of substrate uptake.
MATERIALS AND METHODS
Materials: The microorganisms, Pseudomonas aeruginosa and Pseudomonas fluorescence being indigenous bacteria strains isolated from an oilpolluted area in NigerDelta region of Nigeria were procured from the Department of Microbiology, Obafemi Awolowo University, IleIfe, Nigeria. The microorganisms were maintained on nutrient agar slant and stored at 4±1°C for further use. The study was conducted in the Biochemical Engineering Research Laboratory, Department of Chemical Engineering, Obafemi Awolowo University, IleIfe, in 2008.
Methods
Preparation of culture medium and inoculum: The mineral salt medium used
was a modified form of the one used by Bettmann and Rehm
(1984). The mineral salt medium was composed of the following per litre:
700 mL deionized water, 100 mL buffer solution A, 100 mL solution B, 50 mL solution
C and 50 mL solution D. Composition of each solution was as follows: Buffer
solution A composition: K_{2}HPO_{4} 1.0 g; KH_{2}PO_{4}
0.5 g; (NH4)_{2}SO_{4} 0.5 g; Solution B composition: NaCl 0.5
g; CaCl_{2} 0.02 g; MnSO_{4} 0.02 g; CuSO_{4}.5H_{2}O
0.02 g; H_{3}BO_{3} 0.01 g; Solution C composition: Mg SO_{4}.7H_{2}O
0.5 g; Solution D composition: FeSO_{4 }0.02 g; Molybdenum powder 0.02
g. To prevent the precipitation of CaSO_{4} and MgSO_{4} in
storage, the medium was prepared by autoclaving water, buffer solution A, solution
B, Solution C and Solution D. After cooling the four solutions was mixed together
and kept as stock solution from which known quantities was taken for the cultivation
of microorganisms.
A primary culture of P. aeruginosa and P. fluorescence was each prepared by transferring two loop full of microorganisms from an agar slant culture (using an inoculating loop which has been sterilized by heating to redness in a spirit flame and allowed to cool by oscillating briefly in air) into 100 mL of feed medium (Nutrient medium) containing 20 mL of mineral salt medium and 80 mL of phenol solution (50 mg L^{1}) in a two different 250 mL Erlenmeyer conical flask. Each flask was then placed in a New Brunswick gyratory incubator shaker (G25R model, N.J.S.A) and incubated for 48 h at a temperature of 30°C and agitated with a speed of 120 rpm.
A secondary culture was prepared by transferring 10 mL of each primary culture into 100 mL of feed medium (made up of 20 mL mineral salt medium and 80 mL of phenol solutions) in a two different 250 mL Erlenmeyer conical flask. Each flask was placed in the gyratory incubator shaker and the incubation process was repeated. The secondary culture was used as the inoculum for the cultivation or fermentation experiments as this ensures that the microorganism had fully adapted to growth on the phenol as sole source of carbon and energy. Each of the secondary culture (P. aeruginosa and P. fluorescence) was then mixed in the ratio 1:1 (v:v) which was used as the binary mixed culture for the studies.
Continuous cultivation in bioreactor: The continuous culture was cultivated in a 7½ L capacity bioreactor (New Brunswick Microferm Twin Fermentor, N.J., USA) with a working volume of 4 L. The feed medium was fed into the bioreactor by 101U/R peristaltic pump (WatsonMarlow, England). And the effluent (culture broth) was collected through the side arm into a reservoir or harvest vessel. The culture volume in the bioreactor was constantly maintained by means of a constant level overflow which is located at the side of the fermentor growth vessel. The mass flow of the feed medium was controlled by a balance.
To start the continuous runs, a batch culture was initiated by addition of
200 mL of the inoculum into the fermentor growth vessel containing 800 mL of
mineral salt medium and 3 L of phenol solutions (50 mg L^{1}). Just
after the exponential growth has ended, continuous pumping of feed medium containing
100 mg L^{1} of phenol was started and smoothly increased for several
hours until the required dilution rate was reached. All cultivations were carried
out at a temperature of 30°C while the pH was maintained at 7.0 being adjusted
by the addition of 1.0 M sodium hydroxide solution and 0.5 M sulphuric acid
solution when necessary. Aeration was done with compressed air at a flow rate
of 3.0 vvm and the stirrer speed (agitation) was set at 300 rpm. Fifty milliliter
samples were withdrawn from the harvest vessel for phenol and biomass determination
only when steady state has been established and this occurred after the system
has operated for several hydrodynamic residence times (τ = D^{1}).
In order to establish a steady state, the fermentor was left to equilibrate
over three to five hydrodynamic residence times and steady state was assumed
when the absolute difference in consecutive measurements of biomass and phenol
concentrations differed by less than 3%. The exhaust gas from the reactor was
analyzed for carbon dioxide and oxygen content using the Infra Red (IR) absorption
for CO_{2} and the paramagnetic properties of oxygen for O_{2}
measurement. The dilution rate was varied between 0.01 h^{1} and the
washout point and the corresponding steady state data was recorded. The undegraded
phenol was estimated quantitatively by measuring its absorbance at a wavelength
of 510 nm using UVvisible Spectrophotometer (Lambda 35, PerkinElmer, USA)
and 4aminoantipyrene as colour indicator (Yang and Humphrey,
1975). The biomass concentration was estimated using the dry weight method
(Agarry et al., 2008).
Methods of data analysis
Consistency tests of experimental data: When phenol is oxidatively
converted to biomass with concomitant carbon dioxide and water production as
the only other end products, the growth process can be represented stoichiometrically
as:
where, Ch_{m}O_{l} and Ch_{p}O_{n}N_{q}
represent the elemental compositions of the organic substrate (phenol in this
case) and biomass, respectively. The carbon and available electron balances
on Eq. 1 yield Eq. 2 and 3,
respectively (Solomon et al., 1994):
where, y_{c} and d are fractions of substrate carbon incorporated into
biomass and that which is evolved as carbon dioxide, respectively; η and
ε are fractions of substrate energy utilized in biomass formation and heat
evolution, respectively. Equation 2 and 3
may be used to check the consistency of data as earlier reported (Solomon
et al., 1984, 1985, 1994;
Layokun et al., 1985).
For chemostat operation, where D = μ:
where, MCO_{2} is molecular weight of CO_{2} (gg mol^{1}); MO_{2} is molecular weight of O_{2} (gg mol^{1}); OCO_{2} is rate of OCO_{2} production (mg L^{1} h^{1}); QO_{2} is rate of O_{2} uptake (mg L^{1} h^{1}). S is s ubstrate concentration, subscripts 0 and 1 stand for inlet and outlet respectively (mg L^{1}); X is biomass concentration (mg L^{1}); γ is reductance degree (equivalents of available electrons per gram atom carbon)(subscripts ‘b’ and ‘s’ stand for biomass and substrate); μ is specific growth rate (hσ^{1}); σ, mass fraction carbon (subscripts ‘b’ and ‘s’ stand for biomass and substrate) and D is dilution rate (h^{1}).
Estimation of true yield (η_{max} and Y^{max}) and
maintenance coefficient (m_{e}): Pirt’s model (Pirt,
1965, 1982) for growth processes has been written
in the following forms: based on specific rates of substrate consumption (r_{s}),
oxygen uptake (RO_{2}) and carbon dioxide production (rCO_{2}),
respectively:
where, m_{s} is maintenance coefficient due to substrate; mO_{2}, maintenance coefficient due to oxygen; mCO_{2}, maintenance coefficient due to carbon dioxide and Y^{max} with subscripts x/s, x/o_{2 }and x/co_{2 }is true yield due to substrate, oxygen and carbon dioxide, respectively.
These equations have been reparameterized in energetic terms and shown to be
correspondingly equivalent (Solomon et al., 1994)
to:
where, η_{max} is true biomass energetic yield; m_{e}, maintenance coefficient due to available electrons; e_{k1} (k = 1, 2, 3) are correlated error terms with mean 0 and variancecovariance matrix φ and n is the number of observations.
The estimates of η_{max} and m_{e} are the averages of
individual estimates from Eq. 8b10b.
However, combined estimates of the true biomass energetic yield, η_{max}
and maintenance coefficient, m_{e} can be obtained using Eq.
11 as given below:
Nonetheless, the information contained in X_{1i}, X_{2i} and
X_{3i} may not be efficiently utilized (Yang et
al., 1984; Layokun et al., 1985). Thus,
by application of the covariate adjustment technique (Solomon
et al., 1985, 1994, 1995)
in which appropriate chosen set of covariates Z_{1i} and Z_{2i}
which have expected values of zero and are linear function of X_{1i},
X_{2i} and X_{3i} are included in the above Eq.
11, thereby, a better estimate may be obtained. Hence, the model (Yang
et al., 1984; Layokun et al., 1985),
Eq. 12 is preferred:
In this study, we assume the full set of linearly independent covariates that have zero means as:
Although, due to measurement errors (which lead to data inconsistencies), the
values of Z_{1i} and Z_{2i} are not usually zero. By using this
full set of covariates, the least square estimates of η_{max} and
m_{e} based on model Eq. 12, then becomes the maximum
likelihood estimates (that is estimate with minimum variance), based on the
combined models, Eq. 8b, 9b and 10b.
However, maximum likelihood estimates may not the best estimates as in cases
where covariates which are uncorrelated with
are excluded. In such cases, the residual variance of model (Eq.
12) is not decreased but that of the degree of freedom for fitting the model,
because the covariates included contain no information about X_{1} (Layokun
et al., 1985). Therefore, a measure of goodness of a set of covariates
that should be included in Eq. 12 is J = σ^{2}'(nrc1)
where σ^{2} is the mean square error for fitting the model, r is
the number of parameters of interest, c is the number of covariates included
in the model and n is the number of observations. For this study, r = 2 and
0≤c≤2 and selection of the best estimate is based on the value of σ^{2}/(n3c)
which is a measure of the goodness of the set of covariates that are included
in Eq. 12. The lowest value of J was considered the best
for fitting the model for the range when no covariate is included to when both
covariates are included. Further details of this statistical method are found
in Solomon et al. (1984) and Yang
et al. (1984). Nonetheless, the above equations are based on Monod
kinetics, which is:
where, μ_{max} is the maximum specific growth rate (h^{1})
and K_{s}, the halfsaturation constant (mg L^{1}). Equation
13 requires a well defined substrate consumption rate. However, in many
cases, growth of microbes is a consequence of substrate consumption and not
vice versa (Sonnleitner and Kappeli, 1986; Solomon
et al., 1994). It has been shown that in this approach as S tends
to 0, μ = 0 and yet a finite quantity of substrate consumption, m_{e}
is required (that is due to maintenance) (Solomon et
al., 1994). Hence, there is a substrate consumption even for S = 0 which
is physiologically impossible. Also the substrate consumption is the limiting
step and the microorganism’s growth actually follows substrate availability;
therefore, instead of Eq. 13, a model of the form:
where, r_{s}^{max} is the maximum specific substrate consumption
rate (mg/mg/h). Equation 14 makes more biological as well
as mathematical sense. Therefore, in place of Eq. 8a to 10a,
the following would become valid:
The Eq. 15a to 17a have been reparameterized
in energetic terms and are shown to be correspondingly equivalent (Solomon
et al., 1994) to:
where, m' = m_{e} η_{max}. The values of m' have the
same dimension as μ mathematically and hence cannot be referred to as the
maintenance. They may be described as specific death rates and physiologically
as energy not available for growth (Solomon et al.,
1994). Equations 15b to 17b were
also used to estimate η_{max }and m'_{e}.
RESULTS AND DISCUSSION
Data consistency test: The calculated values of phenol consumption rates
(Q_{s}), oxygen uptake rate (QO_{2}) and carbon dioxide production
rate (QCO_{2}) (Table 1) were used for the estimation
of the biomass energetic yield (η) and carbon yield (y_{e}) for
the binary mixed culture of P. aeruginosa and P. fluorescence
using the carbon and available electron balances as given in Eq.
47. For the estimation, the average values of σ_{b}
= 0.490 and γ_{b }= 4.793 which have been calculated from the measured
composition of Pseudomonas species obtained by Layokun
(1982) were used. The instantaneous available electron and carbon balances
results obtained are presented in Table 2. From Table
2, it could be seen that the biomass energetic yield (η) and carbon
yield (y_{c}) are low (i.e., less than 1) which thus agree with the
available electron and carbon balance equation.
Table 1: 
Calculated oxygen and carbon dioxide transfer rates for the
continuous degradation of phenol by binary mixed culture of P. aeruginosa
and P. fluorescence 

Table 2: 
Examination of data consistency using instantaneous available
electron and carbon balances for the growth of binary mixed culture of P.
aeruginosa and P.fluorescence in phenollimited continuous culture
(chemo stat operation) 

It could also be seen from Table 2 that both the biomass
energetic yield (η) and carbon yield (y_{c}) decreased as the dilution
rate increased. This observation may be due to decrease in steady state biomass
concentration and decrease in phenol removal at high dilution rate (Agarry
et al., 2008). Consistency tests (checks) were made using Eq.
23. It has been established (Solomon
et al., 1981) that in consistency analysis allowance has to be made
for deviation from the ideal. The parameters by which consistency is defined
should satisfy 0.94≤ (y_{c}+d) ≤1.06 and 0.93≤(η+ε)≤
1.07. The results of the data consistency tests are as shown in Table
2. Thus, it could be seen from Table 2 that the consistency
equations are generally satisfied. Also, it could be seen from Table
2 that the (y_{c}d) and (η+ε) values generally decreased
as the dilution rate increased. This is in agreement with the report of Solomon
et al. (1995). Generally, therefore, the consistency tests suggest
that in phenollimited chemostat culture, the binary mixed culture of P.
aeruginosa and P. fluorescence were able to oxidatively metabolized
phenol to carbon dioxide and water with concomitant biomass production.
Table 3: 
Estimates of true biomass growth yields and maintenance coefficient
for the growth of mono and mixed culture of Pseudomonas species in
phenollimited continuous culture using Pirt’s model (Eq.
8a10a) 

Table 4: 
Estimates of true biomass energetic yields and maintenance
coefficient for the growth of binary mixed culture of P. aeruginosa
and P. fluorescence in phenollimited continuous culture using Pirt’s
model (Eq. 8b10b) 

Estimation of true yield and maintenance coefficient: Pirt”s model
for growth as given in Eq. 8a to 10a
was used to estimate the true yields and maintenance coefficients in terms of
substrate, oxygen and carbon dioxide. The calculated specific rates of phenol
consumption (r_{s}), oxygen uptake (rO_{2}) and carbon dioxide
production (rCO_{2}) obtained for the binary mixed culture were plotted
as a function of dilution rate (D) to obtain the true growth yield and maintenance
coefficients, respectively. The estimated values are given in Table
3.
The Pirt’s model was reparameterized to produce multiresponse models with
common parameters as given in Eq. 8b to 10b
and application of covariate adjustment technique (Solomon
et al., 1994) to these equations resulted in a unit variate linear
model with covariates. These allow combined point and interval estimates of
biomass energetic yield and maintenance coefficient to be obtained using standard
multiple regression programs. Therefore, using Eq. 8b to
10b, various estimates of the true biomass energetic yield
and maintenance coefficients based on the data in Table 1
were obtained for the binary mixed culture and are presented in Table
4. The first three estimates in Table 4 are the individual
least square estimates using substrate and biomass data and Eq.
8b and oxygen and biomass data and Eq. 9b and carbon
dioxide and biomass data and Eq. 10b, respectively. These
estimates are quite comparable but differ because of measurement errors. At
low dilution rates, measurement errors are usually significant because of low
gas consumption and production rates which cannot be measured accurately (Solomon
et al., 1995).
When all the measured data were used (i.e. Q_{s}, Qo_{2}, Qco_{2}, μ) the best estimate was the Maximum Likelihood Estimate (MLE) which corresponded to when one covariate (Z_{2}) was included. This was based on the lowest value of J = 3.030x10^{5}. The respective combined point estimates for η_{max} and m_{e} were 0.396 and 0.020 h^{1} with the corresponding 95% confidence intervals (0.380, 0.413) and (0.033, 0.007) h^{1}. When the carbon dioxide data were excluded (i.e.,Q_{s}, Qo_{2}, μ were used), then the respective best point and interval estimates for η_{max} were 0.393 and (0.378, 0.410) and the m_{e} are 0.019 h^{1} and (0.032, 0.006) h^{1}. With the oxygen data excluded (i.e., Q_{s}, Qco_{2} were used), η_{max} = 0.396 with interval (0.382, 0.412) and m_{e} = 0.018 h^{1} with interval (0.029,0.006) h^{1}. Lastly, when substrate measurements were excluded (i.e. Qo_{2}, Qco_{2} were used), η_{max} = 0.392 with interval (0.376, 0.404) and m_{e} = 0.018 h^{1} with interval (0.029, 0.007) h^{1}.
For the mixed culture of organisms studied, even though the respective values
of these combined point estimates were different from one another, all the 95%
confidence intervals were overlapping and included all the point estimates.
Generally, based on the least measure of goodness of fit value, the best estimate
was obtained when J = 3.030x10^{5} which was for the case when all
the measured data were used and corresponded to the Maximum Likelihood Estimate
(MLE) value of η_{max} = 0.396 with 95% confidence intervals (0.380,
0.413) and m_{e} = 0.020 h^{1} with interval (0.033, 0.007)
h^{1}. In earlier applications of this procedure (Solomon
et al., 1981,1983) the best combined estimates
was always assumed to be obtained when all the measured data were used. The
results obtained for binary mixed culture (P. aeruginosa and P. fluorescence)
have shown that a combined estimate from all the measured data might in fact
lead to a better estimate. This is in agreement with the observations of Layokun
et al. (1985) and Solomon et al. (1994,
1995) when all the measured data was used.
The estimates of η_{max} and m_{e} using the modified
Pirt model (Eq. 15b17b) and the data
in Table 1 are presented in Table 5. For
these cases, only the individual estimates have been made because the covariate
adjustment technique was not suitable. However, there was good agreement between
the corresponding individual estimates for the two cases (Pirt’s model
and the modified Pirt’s model) as shown in Table 4 and
5, respectively. The most reliable estimate in Table
5 was the average which gave η_{max }= 0.392 and m_{e }=0.019
h^{1} with the respective 95% confidence interval (0.377, 0.407) and
(0.030, 0.008) h^{1}. The individual estimates (η_{max}
and m_{e}) obtained for the binary mixed culture of P. aeruginosa
and P. fluorescence using modified model equation (Eq.
15b17b) were found to be lower than the individual
estimates obtained using the reparameterized Pirt’s model. A similar observation
has been reported by Solomon et al. (1994, 1995).
The estimates of m_{e} in Tables 4 and 5
are statistically significantly lower than zero and therefore negligible. Hill
and Robinson (1975) reported that the maintenance coefficient for phenol
degradation is negligible.
The true yields and maintenance coefficients in terms of substrate, oxygen
and carbon dioxide were obtained using the modified model. The true yield (Y^{max})
and maintenance coefficient in terms of substrate, oxygen and carbon dioxide
obtained using the modified model were found to be slightly lower than the individual
estimates obtained when Pirt’s model was used (Table 6).
Table 5: 
Estimates of true biomass energetic yields and maintenance
coefficient for the growth of binary mixed culture of P. aeruginosa
and P. fluorescence in phenollimited continuous culture using modified
Pirt’s model (Equations 15b17b) 

Table 6: 
Summary of true biomass growth yields and maintenance coefficient
for the growth of binary mixed culture of P. aeruginosa and P.
fluorescence in phenollimited continuous culture 

The true biomass energetic and growth yield obtained for the binary mixed culture
of P. aeruginosa and P. fluorescence was found to be higher than
that obtained for the monoculture of P. fluorescence (η_{max}
= 0.262 and Y^{max}_{x/s} = 0.463) and P. aeruginosa
(η_{max}= 0.359 and Y^{max}_{x/s} = 0.540) (Agarry,
2009). However, it is lower than that obtained for monoculture of P.
cepacia G4 (η_{max} = 0.432 and Y^{max}_{x/s}
= 0.785) by Solomon et al. (1994).
CONCLUSIONS
The advantage of combined estimates using covariate adjustment technique has been demonstrated. This analysis showed that with a combined use of material and energy balances and statistical procedure, discrimination may be made between various variables to identify those with more errors. The results demonstrated that the Pirt’s model approach (based on Monod kinetics) which require welldefined substrate consumption as well as the modified approach which assumed that substrate consumption was rate limiting were similar and led to similar estimates However, the latter approach did not allowed the application of a multivariate statistical method for parameter estimation.
From this analysis, about 3841% of the energy in phenol may be incorporated
into binary mixed culture of P. aeruginosa and P. fluorescence
biomass, while the balance, 58.762% is mostly evolved as heat with little energy
use for maintenance of the cells. When compared with the degradation of phenol
by P. cepacia G4 (Solomon et al., 1994),
the energetics were similar. However, less substrate energy was incorporated
into biomass and hence more evolved as heat in the case of binary mixed culture
of P. aeruginosa and P. fluorescence. This might probably be due
to differences in ATP production and utilization in the processes (Solomon
et al., 1995). The combined estimates, which seems to be an improvements
on the estimates made from individual measurements are the values most likely
to be used when true biomass energetic yield and maintenance coefficients are
applied to the design of fermentors.