Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 947-952
Published Online October 2012 (http://www.SciRP.org/journal/jmmce)
Model for Assessment Evaluation of Methane Gas Yield
Based on Hydraulic Retention Time during Fruit Wastes
Biodigestion
Chukwuka Nwoye1*, Asuke Ferdinand2, Ijomah Agatha1, Obiorah Samuelmary1
1Department of Metallurgical and Materials Engineering, Nnamdi Azikiwe University, Awka, Nigeria
2Department of Metallurgical and Materials Engineering, Ahmadu Bello University, Zaria, Nigeria
Received July 13, 2012; revised August 15, 2012; accepted August 25, 2012
ABSTRACT
This paper presents an assessment evaluation of methane gas yield using a derived model based on the hydraulic reten-
tion time (HRT) of the feed stock (waste fruits) undergoing biotreatment in the digester. The derived model;
γ = e(3.5436 α + 2.0259) indicates an exponential relationship between methane yield and the HRT. Statistical analysis of the
model-predicted and experimental gas methane yield for each value of HRT considered shows a standard error of
0.0081 and 0.0114% respectively. Furthermore, the correlation between methane yield and HRT as obtained from de-
rived model and experimental results were evaluated as 0.9716 and 0.9709 respectively. Methane gas yield per unit
HRT as obtained from derived model and experiment are 0.0196 and 0.0235 (m3·kg−1 VS) days−1 respectively. Devi-
ational analysis indicates that the maximum deviation of the model-predicted methane yield from the corresponding
experimental value is less than 16%. It was also found that the validity of the model is rooted on the expression 0.2822
ln γ = α + 0.5717 where both sides of the expression are correspondingly approximately equal.
Keywords: Model; Methane Gas Yield; Biodigestion; Fruit Wastes
1. Introduction
Biowastes such bovine bones and fish scales which could
find application in energy generation have also found [1]
application in medicine, being developed to produce suit-
able materials that act as an interface between the im-
plant and tissue in the body. These materials have been
proved to be biocompatible for tissue engineering.
Solid wastes products such as used tires and lubricant
oils which could be processed for heat energy generation
have been found [2] to cause serious environmental pro-
blems when littered around. Therefore the recycling or
burning of these materials for heat generation and trans-
mission to industries is most appropriate for environ-
mental cleanliness and cheap energy supply.
The need to diversify sources of energy for industrial
growth has resulted to the use of various raw materials
like sugarcane juice and molasses [3,4] sugar beet, beet
molasses [4,5], Sweet sorghum [6] and starchy materials
like sweet potato [7], Corn cobs and hulls [8,9], cellu-
losic materials like cocoa, pineapples and sugarcane
waste [10] and milk, cheese, and whey using lactose hy-
drolyzing fermenting strains [11] for ethanol production.
The possibility and potentialities in fruit wastes mi-
crobial treatment, to produce methane gas used as energy
source have been studied [12]. A research work in re-
spect of this has shown [12] that tomato, mango, pineap-
ple, lemon, and orange processing waste, yielded 0.62,
0.56, 0.77, 0.72 and 0.63 m3 of methane gas/kg of VS
respectively. Mango peel supplemented with urea was
found [13] to adjust the C:N ratio to 20 - 30:1 resulting in
the stability of the digester.
Addition of nitrogen in the form of silkworm waste
and oilseed extracts, such as neem and castor, was found
[13] to increase the methane content of the biogas pro-
duced. Successive addition of fruit and vegetable solid
wastes on the performance of biogas digester shows that
the digester was stable at a loading rate of 3.8 kg VS
m−3·d−1 [14]. The researchers further observed that no
noticeable changes in the rates and yields of biogas oc-
curred as a result of minor manipulation in nutritional
and operational parameters which practically helped in
the functioning of the digester fed with different fruits
(mango, pineapple, tomato, jack fruit, banana, and or-
ange) and vegetable wastes for a considerably long time.
Studies [13] carried out on Pilot plant (of volumetric
capacity 1.5 m3 and digester type KVIC) with mango
*Corresponding author.

C. NWOYE ET AL. 948
peel showed that supplementation with essential nutrients
improved the digestibility of feedstock, yielding as high
as 0.6 m3/kg VS with a methane gas content of 52% at a
loading rate of 8% - 10%. Further research was carried
out and in this case, sugarcane filter mud was added at a
rate of 200 g/4kg of mango peel in 1.5 m3 digester. This
increased biogas yield substantially with a methane con-
tent of 60%. Also addition of extract of nirmali seeds,
hybrid beans, black gram, and guar gum seeds (as addi-
tives) at 2% - 3% level increased the biogas production
significantly. This increment was attributed to the galac-
tomannan constituent of the leguminous seeds which in-
creased the floc formation, thereby retaining the organ-
isms in the digester.
Gases such as methane, hydrogen and carbon mono-
xide can be combusted or oxidized with oxygen or air
containing 21% oxygen and energy release as a result of
the combustion process presents biogas as a very potent
fuel.
Biogas can be used as a low-cost fuel in any country
for any heating purpose, such as cooking and in modern
waste management facilities where it can be used to run
any type of heat engine, to generate either mechanical or
electrical power. Biogas can be compressed, much like
natural gas, and used to power motor vehicles. Biogas is
a renewable fuel, so it qualifies for renewable energy
subsidies in some parts of the world.
Studies [15] were carried out on the microbiology of
digesters fed with tomato-processing waste, and the re-
sults of the investigation revealed that in batch digestion,
the population of methanogens was less due to the drop
in pH of slurry. However in semi-continuous digestion,
biogas yield of 0.42 m3·kg−1 VS was reported following
increase in the population of cellulolysers, xylanolysers,
pectinolysers, proteolysers, lipolysers, and methanogens
with increase in hydraulic retention time (HRT). Results
of previous studies [16] on the feasibility of mango pro-
cessing waste for biogas production indicates a biogas
output of 0.21 m3·kg−1 TS.
The aim of this work is to develop a model for as-
sessment evaluation of methane gas yield based on hy-
draulic retention time (HRT) during biodigestion of fruit
wastes. The model is expected to evaluate the volume of
methane produced based on variation in the HRT while
other input process parameters and conditions are kept
constant during the degradation process.
2. Biomethane Production Process Analysis
The solid phase (wastes) is assumed to be stationary,
contains some un-reacted fruit seeds remaining in the
prepared waste. Conversion of organic matter to methane
was by microbes. This process is anaerobic and is carried
out by action of various groups of anaerobic bacteria.
Complex polymers are broken down to soluble pro-
ducts by enzymes produced by fermentative bacteria
which ferment the substrate to short-chain fatty acids,
hydrogen and carbon dioxide. Obligate hydrogen-pro-
ducing acetogenic bacteria metabolized fatty acids. Hy-
drogen, carbon dioxide, and acetate are the major pro-
ducts after digestion of the substrate by the two groups
are. Hydrogen-oxidizing acetogens converts hydrogen
and carbon dioxide to acetate or to methane by carbon-
dioxide-reducing hydrogen-oxidizing methanogens. Ace-
ticlastic methanogens also converts acetate to methane.
3. Materials and Methods
A weighed quantity of prepared fruit wastes was put in
the digested containing the appropriate microbes. Details
of the experimental procedure and associated process
conditions are as stated in the past report [14].
3.1. Model Formulation
Experimental data obtained from research work [14]
were used for this work. Computational analysis of the
experimental data [14] shown in Table 1, gave rise to
Table 2 which indicate that;
Kln N



 (1)
Introducing the values of N and K into Equation (1)
reduces it to;
0.2822 ln 0.5717



 (2)
0.5717
ln 0.2822








(3)
ln 3.5436 2.0259



 (4)

3.5436 2.0259
e





(5)
where
(γ) = Methane gas yield (m3·kg−1 VS)
(α) = Hydraulic retention time (days)
N = 0.5717; Overall microbe-substrate interaction fac-
tor (determined using C-NIKBRAN [17])
K = 0.2822; Gas—microbe interaction factor (deter-
mined using C-NIKBRAN [17])
3.2. Boundary and Initial Conditions
Consider prepared fruit wastes (in a digester) interacting
with microbes. The digester atmosphere is not contami-
nated i.e (free of unwanted gases and dusts). Range of
HRT used: 10 - 20 days. Mass of wastes used, treatment
temperature, growth rate of microbes and other process
conditions are as stated in the experimental technique
[14].
The boundary conditions are: anaerobic atmosphere to
enhance bacterial action on the wastes (since the digester

C. NWOYE ET AL. 949
Table 1.Variation of methane yield with hydraulic retention
time (HRT) [14].
(α) (γ)
10 0.085
12 0.142
16 0.250
18 0.285
20 0.320
Table 2. Variation of 0.2822 lnγ with α + 0.5717.
0.2822 lnγ α + 0.5717
0.6498 0.6567
0.7012 0.7137
0.7824 0.8217
0.8157 0.8567
0.8454 0.8917
was air-tight closed). At the bottom of the particles, a
zero gradient for the gas scalar are assumed and also for
the gas phase at the top of the waste particles. The bio-
degraded fruit waste is stationary. The sides of the waste
particles are taken to be symmetries.
4. Results and Discussions
The derived model is Equation (5). The computational
analysis of Table 1 gave rise to Table 2.
4.1. Model Validation
The validity of the model is strongly rooted on Equation
(2) where both sides of the equation are correspondingly
approximately equal. Table 2 also agrees with Equation
(2) following the values of 0.2822 lnγ and α + 0.5717
evaluated from the experimental results in Table 1. Fur-
thermore, the derived model was validated by comparing
the methane gas yield predicted by the model and that
obtained from the experiment [14]. This was done using
various analytical techniques.
4.2. Computational Analysis
A comparative computational analysis of the experimen-
tal and model-predicted methane gas yield was carried to
ascertain the degree of validity of the derived model.
This was done by comparing methane gas yield per unit
HRT obtained by calculations involving experimental
results, and model-predicted results obtained directly
from the model.
Methane gas yield per unit HRT MY (m3·kg−1 VS)
days−1 was calculated from the equation;
R
G

  (6)
R
2
= 0.9427
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
510 15 20 25
Hydrualic retention time (days)
Methane yield (m
3
·kg
–1
VS)
Figure 1. Coefficient of determination between methane
yield and HRT as obtained from experiment [14]
.
R
2
= 0.944
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
510 15 20 25
Hydraulic retention time (days)
Methane yield (m
3
·kg
–1
VS)
Figure 2. Coefficient of determination between methane
yield and HRT as predicted by model.
Therefore, a plot of methane gas yield against HRT as
in Figure 1 using experimental results in Table 1, gives
a slope, S at points (10, 0.085) and (20, 0.32) following
their substitution into the mathematical expression;
S=



 (7)
Equation (7) is detailed as
212
S1



 (8)
where
Δγ = Change in the methane yield γ2, γ1 at two HRT
values α2, α1.
Considering the points (10, 0.085) and (20, 0.32) for
(α1, γ1) and (α2, γ2) respectively, and substituting them
into Equation (8), gives the slope as 0.0235 (m3·kg−1 VS)
days−1 which is the methane gas yield per unit HRT dur-
ing the actual experimental process. Also similar plot (as
in Figure 2) using model-predicted results gives a slope.
Considering points (10, 0.0781) and (20, 0.2737) for (α1,
γ1) and (α2, γ2) respectively and substituting them into
Equation (8) gives the value of slope, S as 0.0196
(m3·kg−1 VS) days−1. This is the model-predicted meth-
ane gas yield per unit HRT. A comparison of these two

C. NWOYE ET AL. 950
values of the methane gas yield per unit HRT shows
proximate agreement and a high degree of validity of the
derived model.
4.3. Statistical Analysis
The standard error (STEYX) in predicting and obtaining
methane gas yield from model and experiment for each
value of HRT considered is 0.0081% and 0.0114% re-
spectively. The standard error was evaluated using [18].
Also the correlations between methane gas yield and
HRT as obtained from derived model and experiment,
considering the coefficient of determination R2 from
Figures 1 and 2 was calculated using the equation;
2
R= R (9)
and confirmed using Microsoft Excel [18]. The evalua-
tions show a better correlation (0.9716) for model-predi-
cted values between methane yield and HRT than that
determined from experimental (0.9709) [14]. This sug-
gests that the model predicts accurate and reliable meth-
ane gas yield which are in proximate agreement with
values from actual experiment.
4.4. Graphical Analysis
Critical graphical analysis of Figure 3 shows very close
alignment of the curves from model-predicted methane
gas yield per unit HRT and that of the experiment (ExD).
The degree of alignment of these curves is indicative of
the proximate agreement between both experimental and
model-predicted methane gas yield per unit HRT.
4.5. Deviational Analysis
Comparative analysis of methane yield from experiment
[14] and derived model revealed deviations on the part of
the model-predicted values relative to values obtained
from the experiment. This is attributed to the fact that the
surface properties of the waste material and the physio-
chemical interactions between the waste material and the
microbes (under the influence of the treatment tempera-
ture) which were found to have played vital roles during
the process [14] were not considered during the model
formulation. This necessitated the introduction of correc-
tion factor, to bring the model-predicted methane yield to
those of the corresponding experimental values.
Deviation (Dn) of model-predicted methane gas yield
from that of the experiment [14] is given by
Pe Ee
Dn 100
Ee





(14)
Correction factor (Cr) is the negative of the deviation
i.e
Cr Dn (15)
Therefore
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
510 15 20 25
Hydraulic retention time (days)
Methane yield (m
3
·kg
–1
VS)
ExD
MoD
Figure 3. Comparison of the methane gas yield per unit
HRT as obtained from experiment [14] and derived model.
Pe Ee
Cr 100
Ee





(16)
where
Pe = Model-predicted methane gas yield (m3·kg−1 VS)
Ee = methane gas yield from experiment (m3·kg−1 VS)
Cr = Correction factor (%)
Dn = Deviation (%)
Introduction of the corresponding values of Cr from
Equation (16) into the model gives exactly the corre-
sponding experimental methane gas yield.
Figures 4 and 5 show that the maximum deviation of
the mode-predicted methane gas yield from the corre-
sponding experimental values is less than 16% and quite
within the acceptable deviation limit of experimental
results.
These figures show that least and highest magnitudes
of deviation of the model-predicted methane gas yield
(from the corresponding experimental values) are −8.8%
and −15.72% which corresponds to methane gas yield:
0.1295 and 0.2107 m3·kg−1 VS and HRT; 12 and 16 days
respectively.
Comparative analysis of Figures 4-6 indicates that the
orientation of the curve in Figure 6 is opposite that of the
deviation of model-predicted methane gas yield. This is
because correction factor is the negative of the deviation
as shown in Equations (15) and (16). It is believed that
the correction factor takes care of the effects of the sur-
face properties of the waste material and the physio-
chemical interaction between the waste material and the
microbes which (affected experimental results) were not
considered during the model formulation. Figure 6 indi-
cate that the least and highest magnitudes of correction
factor to the model-predicted methane gas yield are
+8.8% and +15.72% which corresponds to methane gas
yield: 0.1295 and 0.2107 m3·kg−1 VS and HRT; 12 and
16 days respectively.
It is important to state that the deviation of model pre-
dicted results from that of the experiment is just the

C. NWOYE ET AL. 951
-17
-15
-13
-11
-9
-7
-5
00.1 0.20.3
Deviation (%)
Methane yield (m3·kg−1 VS)
Figure 4. Variation of model-predicted methane yield with
its associated deviation from experimental values.
-17
-15
-13
-11
-9
-7
-5
5101520
Hydraulic retention time (days)
Deviation (%)
25
Figure 5. Variation of deviation (of model-predicted me-
thane yield) with HRT.
5
7
9
11
13
15
17
00.10.2 0.3
Correction factor (%)
Methane yield (m3·kg−1 VS)
Figure 6. Variation of model-predicted methane yield with
its associated correction factor.
magnitude of the value. The associated sign preceding
the value signifies if the deviation is deficit (negative
sign) or surplus (positive sign).
5. Conclusion
The derived model gave an assessment evaluation of
methane gas yield based on the HRT of the waste fruits
undergoing biotreatment in a digester while other input
process parameters and conditions are kept constant. Sta-
tistical analysis of the model-predicted and experimental
methane gas yield for each value of (HRT) considered
shows a standard error of 0.0081% and 0.0114% respec-
tively. Furthermore, the correlation between methane
yield and HRT as obtained from derived model and ex-
perimental results were evaluated as 0.9716 and 0.9709
respectively. Methane yield per unit HRT as obtained
from derived model and experiment are 0.0196 and
0.0235 (m3·kg−1 VS) days−1 respectively. Deviational
analysis indicates that the maximum deviation of the
model-predicted methane yield from the corresponding
experimental value is less than 16%. It was also found
that the validity of the model is rooted on the expression
0.2822 lnγ = α + 0.5717 where both sides of the expres-
sion are correspondingly approximately equal.
REFERENCES
[1] M. Sudip, M. Biswanath, D. Apurba and S. M. Sudit,
“Studies on Processing and Characterization of Hydroxya
Patite Biomaterials fron Different Biowastes,” Journal of
Minerals & Materials Characterization & Engineering,
Vol. 11, No. 1, 2012, pp. 52-67.
[2] H. Esher and K. Chen-Ming, “Household Solid Wastes
Recycling Induced Production Values and Employment
Opportunities in Taiwan,” Journal of Minerals & Materi
als Characterization & Engineering, Vol. 1, No. 2, 2002,
pp. 121-129.
[3] S. Morimura, Z. Y. Ling and K. Kida, “Ethanol Produc-
tion by Repeated Batch Fermentation at High Tempera-
ture in a Molasses Medium Containing a High Concentra-
tion of Total Sugar by Thermotolerant Flocculating Yeast
with Improved Salt Tolerance,” Journal of Fermentation
and Bioengineering, Vol. 83, No. 3, 1997, pp. 271-274.
doi:10.1016/S0922-338X(97)80991-9
[4] P. K. Agrawal, S. Kumar and S. Kumar, “Studies on Al-
cohol Production from Sugarcane Juice, Sugarcane Mo-
lasses, Sugarbeet Juice and Sugarbeet Molasses, Sac-
charomyces Cerevisiae,” Proceedings of the 60th Annual
Convention of the Sugar Technologists Association of In-
dia, Shimla, 19-21 September 1998, pp. 34-45.
[5] A. I. El-Diwany, M. S. El-Abyad, R. A. H. EL, L. A.
Sallam and R. P. Allam, “Effect of Some Fermentation
Parameters on Ethanol Production from Beet Molasses by
Saccahromyces Cerevisiae Y-7,” Bioresearch Technology,
Vol. 42, No. 3, 1992, pp. 191-198.
doi:10.1016/0960-8524(92)90022-P
[6] B. Bulawayo, J. M. Brochora, M. I. Munzondo and R.
Zvauya, “Ethanol Production by Fermentation of Sweet
Sorghum Juice Using Various Yeast Strains,” World
Journal of Microbiology and Biotechnology, Vol. 12, No.
4, 1996, pp. 357-360. doi:10.1007/BF00340211
[7] N. K. Sree, M. Sridhar, K. Suresh, I. M. Bharat and L. V.
Rao, “High Alcohol Production by Repeated Batch Fer-
mentation Using Immobilized Osmotolerant Saccharomy-
ces Cerevisiae,” Journal of Industrial Microbiology and
Biotechnology, Vol. 24, No. 3, 2000, pp. 222-226.

C. NWOYE ET AL. 952
doi:10.1038/sj.jim.2900807
[8] D. S. L. O. Beall, A. B. Bassat, J. B. Doran, D. E. Fowler,
R. G. Hall and B. E. Wood, “Conversion of Hydrolysate
of Corn Cobs and Hulls into Ethanol by Recombinant
E.coli B Containing Integrated Genes for Ethanol Produc-
tion,” Biotechnology Letters, Vol. 14, No. 9, 1992, pp.
857. doi:10.1007/BF01029153
[9] S. Arni, M. Molinari, M. D. Borghi and A. Converti,
“Improvement of Alcohol Fermentation of a Corn Starch
Hydrolysate by Viscosity Raising Additives,” Starch
Stärke, Vol. 51, No. 6, 1999, pp. 218-24.
doi:10.1002/(SICI)1521-379X(199906)51:6<218::AID-S
TAR218>3.0.CO;2-7
[10] A. S. Othman, M. N. Othaman, A. R. Abdulrahim and S.
A. Bapar, “Cocoa, Pineapples, Sugarcane Waste for Etha-
nol Production,” Planter, Vol. 68, No. 792, 1992, pp.
125-132.
[11] C. Silva, G. R. J. H. Castro, C. Abercio-da-Silva and R. J.
H. C. Gomez, “Study of the Fermentation Process Using
Milk Whey and the Yeast Kluyveromyces Fragilis,”
Semina Londrina, Vol. 16, 1995, pp. 17-21.
[12] Anonymous, “Final Report Submitted to Department of
Non-Conventional Energy Sources,” Government of In-
dia, New Delhi, 1989.
[13] B. Nagamani and K. Ramasamy, ‘‘Biogas Production
Technology: An Indian Perspective,’’ Fermentation
Laboratory, Coimbatore, Vol. 13, 1994, pp. 33-35.
[14] P. Viswanath, S. Devi and K. Krishnanand, “Anaerobic
Digestion of Fruit and Vegetable Processing Wastes for
Biogas Production,” Bioresearch Technology, Vol. 40,
No. 1, 1992, pp. 43-48.
doi:10.1016/0960-8524(92)90117-G
[15] R. Sarada and R. Joseph, “Characterization and Enumera-
tion of Microorganisms Associated with Anaerobic Di-
gestion of Tomato-Processing Waste,” Bioresearch Tech-
nology, Vol. 49, No. 3, 1994, pp. 261-265.
doi:10.1016/0960-8524(94)90050-7
[16] M. Mahadevaswamy and L. V. Venkataraman, “Integrated
Utilization of Fruit-Processing Wastes for Biogas and
Fish Production,” Biology Wastes, Vol. 32, No. 4, 1990,
pp. 243-251. doi:10.1016/0269-7483(90)90056-X
[17] C. I. Nwoye, “Data Analytical Memory,” C-NIKBRAN,
2008.
[18] Microsoft Excel 2003 Version.