Biomethanization of Cattle Manure, Pig Manure and Poultry Manure Mixture in Co-digestion with Waste of Pineapple Fruit and Content of Chicken-Gizzard- Part I: Kinetic and Thermodynamic Modelling Studies

2.1. Feedstock Collection and Preparation

Animal wastes made up of cattle dung, pig dung and poultry droppings were collected from LAUTECH agricultural farm, Ogbomoso, Oyo State, Nigeria. The pineapple fruit wastes were collected from Bodija market, Ibadan, Oyo state, Nigeria. While the content of chicken-gizzard (used as inoculum) was collected from Mokola market, Ibadan, Oyo State, Nigeria. The samples collected were maintained in a refrigerator at 4°C to avoid microbial action until further use. The substrates (mixed animal wastes) and co-substrates (pineapple fruit waste and chicken inoculum) were prepared according to the method of Iyagba et al. [46]. The substrates and co-substrate were washed, sundried for twenty days; oven dried at 105°C for 24 h and then mechanically crushed using a mortar and pestle to ensure homogeneity. Table 1 shows the physical and chemical characterization of the animal wastes, pineapple fruit wastes and inoculum. The characterization was carried out according to standard methods [47, 48]. The parameter that can be used to describe the suitability of a substrate for anaerobic fermentation or digestion is the carbon-nitrogen (C/N) ratio. It has been reported that very high C/N ratio in an anaerobic digester can result in a too low nitrogen concentration for microbial growth [49] as well as result in the consumption of nitrogen by the methanogens for protein production while some leftover carbon will remain unreacted, thereby leading to low biogas generation [50]. In contrast, a low C/N ratio can lead to ammonia nitrogen accumulation which can result in the digestion process inhibition [49]. Thus, it has been reported that the optimal C/N ratio for anaerobic digestion ranges from 20 to 30:1 [49]. Table 1 shows that the C/N ratios of cattle manure, pig manure and chicken manure are lower than the required optimum while the C/N ratio of the pineapple fruit waste is higher and thus can serve as a co-substrate to improve the overall C/N ratio of the anaerobic biodigester feed ingredient. The microbial species present in the feedstock were also characterized and identified according to standard methods. The results of the characterization and micro-organisms identified in each of the feedstock waste; pineapple fruit waste, cattle manure, pig manure, and poultry manure were predominantly bacteria and they are Escherichia coli, Staphylococcus species, Salmonella species, Bacillus species, Lactobacillus species, Flavobacterium species, Methanobacterium species and Pseudomonas species. The presence of these organisms in the waste may be as a result of the type of nutrient in the waste and the physical-chemical properties of the wastes [7, 11]. The chicken-gizzard content, as inoculum and source of microorganisms’ surplus was used to improve the performance of the biodigester. The microorganisms identified in the chicken-gizzard content include, Escherichia coli, Bacillus species, Lactobacillus species, and Flavobacterium species.

2.2. Apparatus Set-Up and Experimental Procedure

The biodigester experimental set-up for the biogas/biomethane production is as shown in Fig. (1).

Three holes were drilled on the lid to serve as inlet valve for loading the feed, outlet valve for the collection of biogas produced and a central hole which accommodate the shaft of a stirring system (Model: RW 16 Basic I KA) with a speed range of 10 to100 rpm. Two rubber hoses was each connected to the inlet valve for injection of feed substrates and the other connected to the outlet valve through which the biogas produced will be collected into a gas bag connected to it. The rubber hose connected to the gas bag is airtight, and has a three-way valve that can be opened to collect gas samples. A digital pH meter was used to measure pH of the digested slurry and a thermocouple was used as a heating element for the digester. The digester was equipped with a control panel which permits the regulation of temperature and agitation. Efficient agitation was achieved by propeller with flat stirring paddles and four vertical baffles.

Fifteen anaerobic biodigesters labeled D1 to D15 with a working capacity of 12 kg were used. Each biodigester was operated at a given operating variable while keeping other variables constant (i.e. one variable or factor at a time). The fermentation slurry was prepared according to the composition and given amount or quantity as presented in Table (2), and then charged into the respective biodigester. The biodigesters were incubated for 70 days (i.e. 10 weeks) retention time.

Anaerobic fermentation of the slurry (made up of mixed animal wastes with pineapple fruit wastes and content of chicken-gizzard) was carried out at feed/inoculum ratio of (1:1, 1:2, 1:3, 2:1, and 3:1), temperature of (25, 30, 40, 50 and 60 °C), and agitation speed of (30, 40, 50, 60 and 70 rpm), respectively. Control experiment without agitation was also carried out. Biogas produced from the digester was collected directly into a gas bag and the biogas bag was then weighed by means of weighing scale. The mass of biogas produced was obtained from the difference between the initial mass of the biogas bag and the final mass of biogas bag plus biogas. The volume of biogas was obtained using Eq. (1):

(1)

Biogas yield (Y) was determined using Eq. (2) [51]:

(2)

2.3. Qualitative Gas Analysis

The biogas was analyzed by means of gas chromatography using the thermal conductivity detector (TCD). The equipment model is Hp6890 with HP Chem Station and Rev. A09.01 (1206) software. The carrier gas was helium at 20 ml/min flow rate with the inlet temperature of 145°C while the inflow of the carrier gas was 26 ml/min in the column with dimensions and type 30m x1/8mm x 0.85µm of and Heysep DB 100/120; Deerfield, Illinois respectively. The oven temperature was programmed at 140°C in 6 min and ramped at 50°C/min to and maintained at 175°C.

2.4. Kinetic Modelling of Biogas Generation

The biogas production kinetics for the description and evaluation of methanogenesis was carried out by fitting the experimental data of biogas production to various kinetic equations. Cumulative biogas production rates of mixed animal wastes co-digested with pineapple fruit wastes) was simulated using logistic kinetic model, exponential rise to maximum and modified Gompertz kinetic models. Logistic kinetic equation is shown in Eq. (3) [52]:

(3)

Where, C, cumulative biogas production (dm³/gm); k, kinetic rate constant (day^-1); t = hydraulic retention time, which is the time (i.e. days) the biodigester is incubated in the course of biogas production; a , b are the constants. Exponential rise to maximum is presented in Eq. (4) [53-55]:

(4)

Modified Gompertz kinetic model equation (Eq. (5)) is a modified form of the Gompertz equation which is commonly used to simulate the cumulative biogas production [48]. This model assumes that cumulative biogas production is a function of hydraulic retention time. The modified Gompertz equation can be presented as follows [52, 56, 57]:

(5)

Where, P is the cumulative of the specific biogas production (dm³/gm), A is the biogas production potential (dm³/gm), r_m is the maximum biogas production rate (dm³/gm/day), λ is the lag phase period or the minimum time required to produce biogas (day).

2.5. Thermodynamic Consideration of Biogas Generation

The thermodynamic parameters (mass fractions, specific gas constant, specific heats, ratio of the specific heats, internal energy, and enthalpy) of the biomethanization process were calculated using Eqs. (6) to (16) [58-60]. The mass fraction (m_a) is estimated as given in Eq. (6):

(6)

The specific biogas constant (R) was estimated as given in Eq. (7):

(7)

Specific heat at constant pressure (C_p); specific heat at constant volume (C_v); and the ratio of the specific heats (γ), of biogas can be estimated using Eqs. (8) to (10), respectively.

(8)

(9)

(10)

Where for diatomic gases, C_viand C_pican be estimated using Eqs. (11) to (12), respectively.

(11)

and

(12)

While for poly atomic gases, C_vi and C_pican be estimated using Eqs. (13) to (14), respectively.

(13)

and

(14)

The specific internal energy (u) and specific enthalpy (h) of the biogas can be calculated using Eq. (15) and Eq. (16), respectively.

(15)

(16)

Where, R₀ is the universal gas constant; R_i is the specific gas constant of a component gas in the biogas mixture; M_i is the mass of a component gas in the mixture; C_vi and C_pi are respectively the specific heat at constant volume and at constant pressure for component gas of the biogas mixture.

3.1. Effect of Operating Variables on Cumulative Biogas Yield and Biomethane Content

Fig. (2) shows the effect of operating variables on the biomethanization of mixed animal wastes, co-digested with pineapple fruit waste and chicken rumen (inoculums).

The cumulative biogas yield and its biomethane content generally increased with increase in the feed/inoculum ratio (Fig. 2A) where the inoculum fraction of the ratio was increased from 1:1 to 1:2 and 1:3, respectively and as well as where the feed (substrate) fraction of the ratio was increased from 1:1 to 2:1 and 3:1, respectively for biomethanization of mixed animal wastes co-digested with pineapple fruit wastes and inoculum (content of chicken-gizzard). That is, minimum cumulative biogas yield was obtained with the feed/inoculum ratio of 1:1 and the maximum with ratio 1:3 and 3:1, respectively.

Fig. (2B) shows the effect of temperature on the cumulative biogas yield and its biomethane content. It was observed that the rate of biomethanization increased with increase in temperature. Similar observations have been reported. Manik et al. [61] obtained a maximum gas production with enriched biomethane content of 62% at 40 ^oC while Usman et al. reported that temperature between 30 and 60 ^oC influence biogas generation from lignocellulosic material [11-61]. In this study, it was observed that the digester that was subjected to a temperature of 60^oC had the highest biomethane yield of 66.8% with a cumulative biogas yield of 6.8149 dm³/gm of slurry. This was relatively followed by that obtained at 50 ^oC (63.1%; 6.5678 dm³/gm of slurry), 40 ^oC (60.4%; 6.2853 dm³/gm of slurry), 30 ^oC (59.2%; 5.2754 dm³/gm of slurry), and 25 ^oC (50.1%; 3.5311dm³/gm of slurry), respectively. The increase in biogas yield and biomethane content in the biogas is due to higher digestion rate and improved solids settling [62, 63]. According to Parker, there are two temperature ranges required 25- 40°C for mesophilic and 45-60°C for thermophilic methane production; thus, the observation of higher biogas yield and biomethane content at 50 and 60 ^oC in this present study suggests that there are consortium of both mesophilic and thermophilic micro-organisms present in the substrates [64]. Methanogens are the bacteria that help decompose the substrate in the mesophilic temperature range, however, they become inactive at extremely high and low temperatures. Usman et al. have reported that stable reactor performance can be obtained at 55 ^oC and 65 ^oC, respectively [11]. Adeniran et al. [51] obtained a biogas yield of 26.86 ml/kg of slurry (equivalent to 0.00003 dm³/gm) in the anaerobic digestion of poultry wastes and cow dung at 37^oC [51]. While Okuo et al. obtained a cumulative biogas yield of 487.5 cm³/kg (equivalent to 4.875 ×10^-4 dm³/gm), 467.5 cm³/kg (equivalent to 4.675 ×10^-4 dm³/gm) and 457.5 cm³/kg (equivalent to 4.575 ×10^-4 dm³/gm) in the anaerobic digestion of the mixture of cattle manure, swine manure and poultry manure in the ratio 4:1:3, 2:1:1 and 4:3:1, respectively, at temperature range of

The effect of agitation speed on the cumulative biogas yield and its biomethane content is shown in Fig. (2C). It was observed that the rate of biomethanization of mixed animal wastes co-digested with pineapple fruit waste and inoculums decreased with increase in agitation speed from 30 to 70 rpm. The digester subjected to 30 rpm agitation speed had the highest biogas yield (6.2853 dm³/gm) with biomethane content (58%) and relatively followed by that of 40, 50, 60, and 70 rpm with corresponding biogas yield of 6.0028, 5.7203, 5.4379 and 5.0443 dm³/gm of slurry and biomethane content of 57.1%, 55%, 50% and 48%, respectively. The power supplied by agitation was estimated using Eqs. (17) and (18) and the result is as shown in Fig. (2D).

(17)

Where N_p is power number and is a function of the Reynolds number (N_Re) [i.e. N_p= f (N_Re)]

(18)

ρ is density of fermentation slurry, N is rotational speed of impeller, μ is viscosity of fermentation slurry, D is impeller diameter and V_s is volume of fermentation slurry, respectively.

Fig. (2D) shows that as the agitation speed increases so does the power supplied or consumed per volume of slurry/waste also increases and the cumulative biogas yield relatively decreased. Nevertheless, the cumulative biogas yield with its biomethane content obtained from the biomethanization process with agitation (30 – 70 rpm) was found to be relatively higher than the cumulative biogas yield of 4.7882 dm³/gm of slurry with biomethane content of 46% that was respectively obtained without agitation. Thus, with agitation speed of 30 – 70 rpm, increase in the cumulative biogas yield ranged from 5.3 to 31.3% and its biomethane content from 4.3 to 26.1% above the cumulative biogas yield and biomethane content obtained without agitation. According to Muthanna et al., biogas production will increase by 15% for mixed digester compared to an unmixed one [65]. Karima et al. in their study have observed an increase of 10 to 30% in biogas production with agitation [24]. Kaparaju et al. have also reported that an increase of 7% in biogas yield was attained with intermittent mixing as compared to continuous mixing [22]. Thus, a moderately agitated digester is required for optimal gas production.

3.2. Effect of Operating Variables on Start-Up Time of Biogas/Biomethane Generation

Fig. (3) shows the effect of operating variables on the start-up time of the biomethanization process of cattle manure, pig manure and chicken manure mixture co-digested with pineapple fruit waste and content of chicken-gizzard (inoculums).

The biomethanization process started with the generation of biogas/biomethane on day 5 without the use of inoculum while it started on day 1 with the production of biogas/biomethane for the use of feed/inoculum ratio of 1:1, 1:2, 1:3, 2:1 and 3:1 and the biogas production increased until it reached its peak on day 42 (6^th week) and remained constant till day 70 (10^th week) (Fig. 3A).

The effect of temperature on start-up time is shown in Fig. (3B). The biomethanization process started with biogas/biomethane production on day 5 for temperature of 25^oC (ambient temperature) while biogas/biomethane generation started on day 1 for temperature of 30 ^oC, 40 ^oC, 50 ^oC, and 60 ^oC, respectively. The set up at 25 ^oC displayed the least production rate with peak biogas accumulation yield obtained on day 49 (7^th week) and remained constant till day 70. It is observed that the biodigester set up at 60 ^oC has the fastest production rate as it attains peak performance on day 28 (4^th week) and remained constant till day 70 (10^th week). This is relatively followed by biodigester set up at 50 ^oC, 40 ^oC and 30 ^oC, each with peak biogas accumulation yield obtained on day 35 (5^th week) and remained constant till day 70 (10^th week). A similar observation has been reported by Manjula et al. stating that maximum biogas production rate occurred at about 25 days for all the three cases of temperature (55 ^oC, 45 ^oC and 35 ^oC) that was investigated [12]. From this study, it is obvious that maximum biogas production was enhanced by the thermophilic methanogenic bacteria at 60 ^oC, 50 ^oC and 40 ^oC while at 25 ^oC; the action of the methanogenic bacteria was less effective.

Fig. (3C) shows the effect of agitation speed on start-up time. The biomethanization process without agitation started biogas/biomethane generation on day 5 while it started biogas/biomethane production on day 1 for agitation speed of 30 rpm, 40 rpm, 50 rpm, 60 rpm, and 70 rpm, respectively. It is observed that the biodigester set up at 30 rpm has the fastest production rate as it attained peak performance on day 35 (5^th week) and this remained constant till day 70 (10^th week). While the digester set up at 40 rpm has the second fastest production rate with peak accumulation yield on day 35 (5^th week) and remained constant till day 70. This is relatively followed by the biodigester set up at 50 rpm, 60 rpm and 70 rpm which had their biogas peak accumulation yield on day 49 (7^th week,), 56 (8^th week) and 49 (7^th week), respectively, and remained constant till day 70.

3.3. Kinetics of Mixed Animal Wastes Biomethanization Process

The kinetics of biogas production from biomethanization of mixed animal wastes co-digested with pineapple fruit wastes and inoculum (chicken rumen) was carried out by fitting the biogas production experimental data obtained at different operating parameters of feed/inoculums ratio, temperature and agitation speed to three forms of kinetic model equations which are logistic kinetic model, exponential rise to maximum and modified Gompertz kinetic model using the non-linear regression tool of MATLAB 7.0 software package and the estimated kinetic parameters and coefficient of determinations (R²) obtained are presented in Tables 3 to 5 respectively.

As presented in Tables (3 to 5), the R² is relatively higher for modified Gompertz kinetic model (0.9568-0.9937); (0.9713-0.9837) and (0.9524-0.9937) as well as for exponential rise to maximum (0.959-0.9767); (0.9598-0.9676) and (0.9519-0.9767) as compared to that of the logistic kinetic model (0.3884-0.4665); (0.4101-0.4458) and (0.3842-0.4665) at different feed/inoculums ratio, temperature and agitation speed, respectively. The higher value of R² above 0.90 for both modified Gompertz and exponential rise to maximum kinetic models indicates that both models fitted very well to the experimental biomethanization data and thus can be used to simulate biogas production from biomethanization of mixed animal wastes co-digested with pineapple fruit wastes at different condition of feed/inoculums ratio, temperature and agitation, respectively. As it could be seen in Tables (3 to 5), the kinetic constants of exponential rise to maximum, i.e. the first order kinetic constant (k) and the cumulative biogas production (A) increased with increase in the feed/inoculum ratio where the inoculum fraction of the ratio was increased (1:1, 1:2, 1:3) and where the feed (substrate) fraction of the ratio was increased (1:1, 2:1, 3:1), respectively (Table 3).

In addition, these constants i.e. the first order kinetic constant (k) and the cumulative biogas production (A) generally increased with increase in temperature and decreased with increase in agitation speed Tables (4 and 5). Similarly, for modified Gompertz equation, biogas production potential (A) and biogas production rate (r_m) generally increased with increase in the feed/inoculum ratio where the inoculum fraction of the ratio was increased (1:1, 1:2, 1:3) and where the feed (substrate) fraction of the ratio was increased (1:1, 2:1, 3:1) respectively, while the lag phase (λ) decreased with increase in the feed/inoculum ratio where the inoculum fraction of the ratio was increased (1:1, 1:2, 1:3) and where the feed (substrate) fraction of the ratio was increased (1:1, 2:1, 3:1), respectively (Table 3).

Furthermore, the biogas production potential (A) and biogas production rate (r_m) also generally increased with increase in temperature and decreased with increase in agitation speed, respectively while the lag phase (λ generally decreased with increase in temperature and increased with increase in agitation speed, respectively (Tables 4 and 5). In logistic kinetic model, the kinetic rate constant was found to increase with increase in feed/inoculums ratio up to 2:1 and decreased at feed/inoculums ratio 3:1 (Table 3). Also, the logistic kinetic rate constant decreased with increase in temperature as well as increased with increase in agitation speed (Tables 4 and 5).

3.4. Estimation of Thermodynamic Parameters and Activation Energy

The chromatographic analysis of biogas obtained from the biomethanization of cattle manure, pig manure and chicken manure mixture co-digested with pineapple fruit waste and content of chicken-gizzard at different temperature of 25, 30, 40, 50 and 60 ^oC indicated that the gas constituents are CH₄, CO₂, H₂S, CO and NH₃. Using Eq. (6) to Eq. (16), the estimated mass fractions of the biogas constituents, gas constant, specific heat capacities and ratio of the specific heats of the biogas produced at different temperature of 25, 30, 40, 50 and 60 ^oC, from the biomethanization of cattle manure, pig manure and chicken manure mixture co-digested with pineapple fruit waste and content of chicken-gizzard are presented in Table 6.

As presented in Table (6), it could be seen that the CH₄ has the highest molar composition at various temperatures which is an indication of the high quality of the biogas produced. It also has the highest specific heat at constant volume and pressure at various temperatures. These specific heats increased with increasing temperature which is a confirmation of their temperature dependency. A similar observation has been reported for biogas generation from cattle dung by Yaru et al. [59]. The other components of biogas produced in their decreasing order of molar composition are CO₂, H₂S, CO and NH_3. The heat capacities of these components followed the same trend as CH₄. An important constant in the estimation of heat capacities of gases is the ratio of specific heat at constant pressure to constant volume (γ). All the components of the biogas produced except for CO are polyatomic gases with the value of γ being 1.33 (for polyatomic gas) while CO has 1.44 (for diatomic gas). The value of γ for the biogas is also 1.33 which is a reflection that the biogas is predominantly composed of polyatomic gases and this is in agreement with the observation and report of Yaru et al. and Eastop and McConkey [59, 66].

The specific internal energy (u) and enthalpy (h) of biogas and biomethane content obtained from biomethanization of cattle manure, pig manure and chicken manure mixture co-digested with pineapple fruit waste and content of chicken-gizzard at different temperature was calculated based on Eq. (15) and Eq. (16), respectively, and the results are presented in Fig. (4A). Fig. (4A) shows the plot of specific internal energy of biogas and specific internal energy of biomethane content against temperature (K).

As seen in Fig. (4A), the value of specific internal energy of biogas and specific internal energy content of biomethane respectively increased as temperature increased. A similar observation has been reported [59]. The maximum specific internal energy of biomethane (CH₄) content obtained is 223.8712 kJ/kg and the lowest, 127.4457 kJ/kg while the maximum specific internal energy of biogas is 335.0503 kJ/kg and the lowest being 252.9978 kJ/kg. Yaru et al. obtained 279.48923 kJ/kg and 273.95479kJ/kg as the maximum specific internal energy and the lowest specific internal energy of biogas from cattle dung, respectively [59].

Fig. (4B) shows the plot of specific enthalpy of biogas and biomethane content against temperature (K). As shown in Fig. (4B), the values of specific enthalpy of biogas and specific enthalpy of biomethane content respectively increased with increased temperature. The maximum specific enthalpy of biomethane (CH₄) content is 298.4948 kJ/kg and the minimum is 169.9274 kJ/kg while the highest specific enthalpy of biogas is 446.7335kJ/kg and the lowest being 337.4935 kJ/kg. Yaru et al. obtained 375 kJ/kg as the maximum specific enthalpy of biogas obtained from cattle dung anaerobic digestion [59]. In comparison with the values obtained by Yaru et al., this study revealed that the biogas produced from the biomethanization of cattle manure, pig manure and chicken manure mixture in co-digestion with waste of pineapple fruit and content of chicken-gizzard possess higher values of specific internal energy and specific enthalpy than biogas generated from mono-anaerobic digestion of cattle manure (or substrate) [59].

In order to study the feasibility of the biomethanization process, thermodynamic parameters such as changes in standard Gibb’s free energy (ΔG⁰ ), standard enthalpy (ΔH⁰ ), and standard entropy (ΔS⁰ ). can be estimated. The standard Gibb’s free energy (ΔG⁰ ) was calculated according to Eyring-Polanyi equation (Eq. (19)) [67]:

(19)

(20)

Taking natural logarithm of Eq. (19) and substituting Eq. (20) into Eq. (19) gives:

(21)

Where k is the rate constant (s^-1), T is the absolute temperature (K), R, k_b and h are the universal gas (8.314 J mol^-1 K^-1), Boltzmann (1.38 x 10^-23 J/K) and Planck’s (6.63x 10^-34 J s) constants, respectively. The transmission coefficient κ is often taken as unity. From the plot of ln (k/T) vs. 1/T (Fig. 5),

ΔH⁰ and Δ S⁰ were obtained from values of the slope and intercept, respectively, and thus Δ G⁰ was obtained using Eq. (20). The results are presented in (Table 7).

As presented in Table 7, the positive value of Δ H⁰ indicates that the biomethanization process is endothermic in nature. The positive value of Δ S⁰ revealed that the biomethanization process is entropy driven. The negative value of H⁰ Δ G⁰ depicts that the biomethanization reaction is feasible and spontaneous. The positive value of Δ H⁰ in this present study implies that the biomethanization process made use of heat energy from the surrounding environment and also suggests that acetoclastic methanogens may not be the predominant microorganisms in the biodigester as these methanogens function optimally at mesophilic temperature. Krakat et al. in their studies observed that methane generation from energy crops at a higher temperature of 60°C resulted in dominance of hydrogenotrophic Methanobacteriales as compared to acetoclastic methanogens among the microbial communities with a corresponding increase in methane production in thermophilic biogas fermentor [68]. These workers reported that their observation contradicts the common anaerobic digestion model 1 (ADM1) which states that two-thirds of methane is obtained from the acetoclastic methanogens and one-third from hydrogenotrophic methanogens [69]. The negative value of (ΔG⁰ and the positive value of (ΔH⁰ ) obtained for the biomethanization process in this study would suggest in accordance with the observation of Krakat et al. that at higher temperature or thermophilic temperature (50 - 60°C) the forward reaction was highly favoured (i.e. increased product formation, in this case, biomethane) as well as the predominance of hydrogenotrophs in the biodigester which perhaps could mostly be responsible for the biomethane generation through the hydrogenotrophic methanogenesis pathway than through the acetoclastic methanogenesis pathway [68].

The activation energy of biogas production from the biomethanization of mixed animal wastes co-digested with pineapple fruit waste and inoculum at different temperature was obtained from the application of Arrhenius form of equation (Eq. (22)).

(22)

Where, A and E_a are the Arrhenius parameters which stand for frequency factor or pre-exponential coefficient (min^-1) and activation energy (J/mol), respectively. k, is the rate constant (min^-1), R is the molar universal gas constant (8.314 J mol^-1 K^-1) and T is the absolute temperature (K). By taking the natural logarithm, Eq. (22) can be expressed as:

(23)

The activation energy (E_a) was obtained from the plot of ln k against 1/T as shown in Fig. (6).

The activation energy was estimated to be 3.324 kJ/mol. The positive value of E_a that the biomethanization process is endothermic in nature and thus favoured by moderate to high temperature.