Model for Assessment Evaluation of Methane Gas Yield Based on Hydraulic Retention Time during Fruit Wastes Biodigestion

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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

Email: [email protected]

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











(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;





 (6)

= 0.9427

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

510 15

Hydrualic retention time (days)

Methane yield (m

·kg

–1

VS)

Figure 1. Coefficient of determination between methane

yield and HRT as obtained from experiment [14]

= 0.944

0.05

0.1

0.15

0.2

0.25

0.3

0.35

510 15

Hydraulic retention time (days)

Methane yield (m

·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;







 (7)

Equation (7) is detailed as

212







 (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;

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











(14)

Correction factor (Cr) is the negative of the deviation

i.e

Cr Dn (15)

Therefore

0.05

0.1

0.15

0.2

0.25

0.3

0.35

510 15

Hydraulic retention time (days)

Methane yield (m

·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











(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 (%)

Figure 5. Variation of deviation (of model-predicted me-

thane yield) with HRT.

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.

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