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The shell of melon seed obtained from New Market Ogui Enugu, Nigeria was washed to remove dirt. It was subsequently dehydrated beneath the sun. The dehydrated substrate was powdered with an electric grinder, filled in polyethylene bags and kept at room temperature prior to analysis. The chemicals used were purchased from Gerald Chemicals Ltd. Ogbete Main Market, Enugu, Enugu State, Nigeria and they were of analytical grade.

The Microkjeldahl Method was employed for the crude protein determination in addition to the Sohxlet method being applied for oil measurement (Horwitz and Latima, 2005; Ighodaro, 2012). The lignocellulosic characterisation of melon (Egusi) seed shell was done by the procedure given by Augustine (2015):
The lignin content was determined by treating 205.51 g of the defated sample with 500 mL of 7.5% (w/V) aqueous hydrogen peroxide at 90^{℃} for 2 h.
Meanwhile, the concentration of hemicelluloses in the melon seed shell was analysed by treating 204.74 g of the bleached sample with 500 mL of 18% NaOH solution at room temperature for 30 min and subsequently washed with 500 mL of 20% acetic acid in hot water. The solution was washed again with hot distilled water to neutralise the residue and tested with pH meter to confirm the neutrality of the residue. The residue was allowed to dry. The percentages of cellulose and other extractives were given as:
Composition of the CVSSS is shown in Table.

Alkaline peroxide pretreatment of sample was done according to the method of Ana et al. (2013). The 200 g of powdered melon seed shell was weighed into a 1000 mL flat bottom flask. The 500 mL of 7.5% (V/V) hydrogen peroxide solution was introduced into the sample. A solution of 5 mol/L sodium hydroxide was used to adjust the pH of the media to 9 using a table top pH meter (Metler Toledo, Seven Compact Series). The flask containing the media was fixed to a reflux condenser with water circulating at the outer column. The whole set up was heated at 90 ℃ for 2 h. It was left to cool and filtered using Buckner funnel connected to a pressure pump. The residue was washed numerous times by using distilled water to neutralize the alkaline solution. The residue, which was the pretreated sample, was dried in a hot air oven at 50 ℃.

The Aspergillus niger was isolated and screened for cellulase actions using the procedure described by Ezeonu et al. (2011). The isolated A. niger was afterwards reproduced by aseptically conveying a pinch of the fungus into various test tubes comprising (Potato Dextrose Ager (PDA)) fixed in slant positions.

The 0.5% inoculum of the multiplied A. niger from a PDA slant was prepared by aseptically transferring 0.25 g of the pure and screened A. niger from the slant to a 50 mL volumetric flask. Distilled water autoclaved at 121 ℃ for 15 min was added to make the mark of the flask. The autoclaved water was left to cool before use. This inoculum was used for the whole hydrolysis experiment.

The 5% (w/V) commercially available dry form of saccharomyces cerevisiae yeast, was dispersed in 100 mL of sterile distilled water heated to 39 ℃. The shake flask containing the mixture was left on a shaker at 150 r/min for 10 min (Ocloo and Ayernor, 2008). The cell concentration of the inoculum was monitored with the aid of a haemocytometer and adjusted by adding sterile distilled water and the final concentration set at 5.3 × 10^{7} cells per mL. Hence, the mass of the yeast required per litre of inoculum was 2.12 g/L.

The enzymatic hydrolysis was carried out in 100 mL conical flask containing 2.0 g of pretreated melon seed shell in 50 cm^{3} of distilled water and incubated at 30 ℃ for 1 d and at a pH of 3. Enzyme dosage was 0.5 mL of 2.5 g per 50 mL concentration. The mixture was filtered and the soluble sugar yield in the filtrate was obtained using the refractometer (Model RF M960 accessible at PRODA, Enugu), whereas the reducible sugar yield was obtained using the Dinitrosalicylic acid (DNS) method. The effect of time, temperature, enzyme dosage and pH were investigated following the GrecoLatin square design of experiment shown in Table 2. The variation levels for time were 1, 3, 5, 7 and 9 d; 30, 40, 50, 60 and 70 ℃ for temperature; 0.5, 1.0, 1.5, 2.0 and 2.5 mL per 50 mL of hydrolysis solution for dosage; and 3, 5, 7, 9 and 11 for pH, respectively. The pH was adjusted using NaOH and H_{2}SO_{4.}
Component Composition (% w/w) Lignin 0.37 Hemicellulose 21.18 Ash 3.00 Fats and oil 1.92 Cellulose 73.54 Table 1. Composition of Colocynthis vulgaris Shrad seeds shell (CVSSS).
M1 M2 M3 M4 M5 T1 1A 3B 5C 2D 4E T2 2B 4C 1D 3E 5A T3 3C 5D 2E 4A 1B T4 4D 1E 3A 5B 2C T5 5E 2A 4B 1C 3D Table 2. GrecoLatin square design for screening of factors in enzymatic hydrolysis and fermentation of melon seeds shell.

The temperature of the hydrolysis or fermentation, pH of the process, duration of the hydrolysis or the fermentation process and the dosage of the enzyme or yeast were screened for their statistical significance on the yield of simple sugar and ethanol from melon seeds shell by enzymatic hydrolysis and fermentation.

GrecoLatin Square is a fractional factorial design of experiment that is used to distinguish the effect of three inequalities in a factor or to screen the effect of four factors that affect the response parameter (Zivorad, 2004).
There are four possible factors that could affect the yield of simple sugars and ethanol; the screening was done using the GrecoLatin square design of experiment at five levels of each of the factors. The model for a GrecoLatin Square with one observation in the cell is:
where $\Sigma \alpha_{i}=\Sigma \beta_{j}=\Sigma \tau_{k}=\Sigma \lambda_{l}=0$
Variables α_{i}, β_{j}, λ_{l}, τ_{k} are the actual effect of i rows, j columns, k factor and l factor levels. The GrecoLatin square design is given in Table 2 while the analysis of variance (ANOVA) table of the GrecoLatin Square is as presented in Table 3. The significance of the factors was determined by comparing the Fstatistic which is the ration of the factor mean square to the error mean square with the critical Fstatistic at the given degree of freedom (Murray and Larry, 2011). The operational matrix of the GrecoLatin square design is given in Table 4.
Source of variation DF SS MS Variance ratio(Fvalue) Row n–1 $ {SS}_{R}=\frac{\sum _{i}{\mathrm{Y}}_{\mathrm{i}°°°}^{2}}{m}\frac{{Y}_{°°°°}^{2}}{{m}^{2}} $ $ {MS}_{R}=\frac{{SS}_{R}}{m1} $ $ {F}_{1}=\frac{{MS}_{R}}{{MS}_{E}} $ Column n–1 $ {SS}_{C}=\frac{\sum _{j}{\mathrm{Y}}_{{°\mathrm{j}°}。}^{2}}{m}\frac{{Y}_{°°°°}^{2}}{{m}^{2}} $ $ {MS}_{C}=\frac{{SS}_{C}}{m1} $ $ {F}_{2}=\frac{{MS}_{C}}{{MS}_{E}} $ Factor N n–1 $ {SS}_{N}=\frac{\sum _{k}{\mathrm{Y}}_{°。\mathrm{k}°}^{2}}{m}\frac{{Y}_{°°°°}^{2}}{{m}^{2}} $ $ {MS}_{N}=\frac{{SS}_{N}}{m1} $ $ {F}_{3}=\frac{{MS}_{N}}{{MS}_{E}} $ Factor P n–1 $ {SS}_{P}=\frac{\sum _{l}{\mathrm{Y}}_{°。。\mathrm{l}}^{2}}{m}\frac{{Y}_{°°°°}^{2}}{{m}^{2}} $ $ {MS}_{P}=\frac{{SS}_{P}}{m1} $ $ {F}_{4}=\frac{{MS}_{P}}{{MS}_{E}} $ Residual (m–1)(m–2) $ {SS}_{E}=\sum \sum \sum \sum {Y}_{ijkl}^{2}\frac{{Y}_{°°°°}^{2}}{{m}^{2}}{SS}_{R}{SS}_{C}{SS}_{N}{SS}_{P} $ $ {MS}_{E}=\frac{{SS}_{E}}{\left(m1\right)(m2)} $  Total m^{2} $ \sum \sum \sum \sum {Y}_{ijkl}^{2}\frac{{Y}_{°°°°}^{2}}{{m}^{2}} $   Table 3. ANOVA table of GrecoLatin square design.
Run Time (d)(M1–M5) temperature (℃)(T1–T5) Enzyme/Yeast dosage (mL per 50 mL)(A–E) pH(1–5) 1 1 30 0.5 3 2 3 30 1.0 7 3 5 30 1.5 11 4 7 30 2.0 5 5 9 30 2.5 9 6 1 40 1.0 5 7 3 40 1.5 9 8 5 40 2.0 3 9 7 40 2.5 7 10 9 40 0.5 11 11 1 50 1.5 7 12 3 50 2.0 11 13 5 50 2.5 5 14 7 50 0.5 9 15 9 50 1.0 3 16 1 60 2.0 9 17 3 60 2.5 3 18 5 60 0.5 7 19 7 60 1.0 11 20 9 60 1.5 5 21 1 70 2.5 11 22 3 70 0.5 5 23 5 70 1.0 9 24 7 70 1.5 3 25 9 70 2.0 7 Table 4. Design matrix (GrecoLatin square) for factors screening in enzymatic hydrolysis and fermentation.
In Table 2, T1–T5 stand for temperature at five levels (30, 40, 50, 60 and 70 ℃), M1–M5 represent time at 5 levels (1, 3, 5, 7 and 9 d), A–E stand for enzyme dosage at five levels (0.5, 1.0, 1.5, 2.0 and 2.5 mL per 50 mL), 1–5 represent pH at five levels (3, 5, 7, 9 and 11), respectively.

The fermentation was carried out in a 100mL conical flask containing 50 cm^{3} of the medium obtained from enzymatic hydrolysis (Farah et al., 2011). The medium was inoculated with 5% (V/V) growth medium containing the activated Saccharomyces cerevisiae and incubated at 30 ℃ for 1 d at pH of 3. The effect of time, temperature, yeast dosage and pH were investigated following the GrecoLatin square design of experiment shown in section 2.3.1. However, the optimization of the fermentation procedure was done using a response surface methodology at temperature levels of 30, 50 and 70 ℃; pH levels of 3, 6 and 9 and time levels of 1, 5 and 9 d, respectively. At the end of each run, the fermented liquor was decanted, distilled and the yield of ethanol was measured.

The 40 mL of the fermented filtrate was introduced into flat bottom distillation flask. A condenser was connected to the flask. A 100 mL measuring cylinder was set at the receiving end. Water was left to go through the outer jacket of the condenser. The sample distilled to 35 mL mark of the measuring cylinder. After this, distilled water was used to make up the volume of the distillate to the original 40 mL. The distillate was collected at 100 ℃.

The specific gravity of each of the distillate (aqueous ethanol) was determined. This was done by weighing pycometer (w_{1}), whose volume is 25 mL. The distillate was used to fill the pycometer to the mark and weighed (w_{2}).
The specific gravity of the sample was traced against percentage alcohol (V/V) using alcohol graph. Specific gravity of aqueous ethanol solutions is a function of alcohol (%, V/V) (Amerine and Ough, 1974).

The domain of the optimization experimental design was chosen based on the result of the screening of factors. The results of the screening experiment showed that enzyme dosage was not statistically significant and could be fixed at a constant value. Only three numeric factors were considered for optimization. The screening experiment also showed that the impact of time variations could be felt within 5 d of incubation and the pH that gave the highest glucose yield was between 3 and 9, while the domain for temperature was selected between 30 ℃ and 60 ℃. The BoxBehnken Design is given in Table 5.
Name Symbol Low Center High Time (d) X1 1 3 5 pH X2 3 6 9 Temperature (℃) X3 30 45 60 Table 5. The BoxBehnken Design.

An optimization research was done to obtain the optimum parameters, for the fermentation of the hydrolysed CVSSS. The BoxBehnken Design was as well applied for this study.

In chemical and biochemical processes, kinetic models are necessary because, process performance is explained. However, the interactions between enzyme and substrate could be understood by the kinetic models for enzymatic hydrolysis. To the authors' best of knowledge, there is little or no literature information on the use of MichaelisMenten kinetic model or any other kinetic model to study the syntheses of glucose and ethanol from the CVSSS.
The kinetics model stands dependent on the following theorems.
The rate of the reaction is offered by the equation:
where C_{A} is the concentration of the limiting reactant (g/dm^{3}), in this case the limiting reactant is the cellulose and hemicellulose content of the Egusi melon seed shell. The deferential, dC_{A}/dt can be calculated by numerical method (Fogler, 2006).
The numerical differential formula was used when the data points in the independent variable were equally spaced, such as: t_{1} – t_{0} = t_{2} – t_{1} = Δt. The threepoint differential formula is applied in this work. Considering the following Table 6:
Time (h) t_{0} t_{1} t_{2} t_{3} t_{4} t_{5} C_{A} (g/dm^{3}) C_{A0} C_{A1} C_{A2} C_{A3} C_{A4} C_{A5} Table 6. Model kinetics table (Concentration variation with time).
The threepoint differential formulae are:
Equations (7)–(10) can be applied in calculating the change in the reactant concentration with time$ \frac{\mathrm{d}{C}_{\mathrm{A}}}{\mathrm{d}t} $.

The formula of the MichaelisMenten kinetic equation referred Fogler (2006):
where r_{A} is the rate of the enzymatic reaction, V_{max} is the maximum rate of the reaction for a given total enzyme concentration, K_{m} is the MichaelisMenten constant, and S is the substrate concentration.
The linearization of the model is given as:
A plot of $ \frac{1}{{r}_{\mathrm{A}}} $ against $ \left(\frac{1}{S}\right) $ gives a straight line where V_{max} and K_{m} can be calculated from the intercept and the slope, respectively.
2.1. Preparation of raw material
2.1.1. CVSSS preparation
2.1.2. Lignocellulosic characterisation of CVSSS
2.1.3. Alkaline peroxide pretreatment of CVSSS
2.1.4. Isolation and screening of Aspergillus niger
2.1.5. Inoculums for hydrolysis
2.1.6. Inoculums for fermentation
2.2. Enzymatic hydrolysis with A. niger
2.3. Design of experiment for factor screening
2.3.1. Design type: GrecoLatin Square
2.4. Fermentation of hydrolysed melon seed shell
2.5. Ethanol distillation
2.6. Ethanol determination
2.7. Optimization of enzymatic hydrolysis using BoxBehnken Design of experiment
2.8. Optimization of fermentation procedure
2.9. Kinetics of hydrolysis and fermentation
2.9.1. Kinetic modelling of enzymatic hydrolysis and fermentation of CVSSS
2.9.2. MichaelisMenten model

Table 1 displays the result of the proximate analysis of melon seed shell. The result confirmed that the shell of melon seed is rich in carbohydrate which can be converted to glucose. Meanwhile, Ogbe and George, carried out studies on the proximate analysis of melon husks and reported that the husk contained an appreciable amount of carbohydrates (61.01% ± 0.35%) among others (Ogbe and George, 2012). Since glucose is gotten from cellulose on hydrolysis, the high cellulose content (73.54%, w/w) of the CVSSS as shown in Table 1, is a good indication that the said substrate, can easily be hydrolysed and thereafter, be fermented. The low percentage lignin content of this shell is also a good indication that the substrate can easily be hydrolysed because, lignin inhibits hydrolysis. Therefore, the CVSSS also known as 'Egusi' melon seeds shell, is one of the biomasses (substrate) that has high percentage of cellulose content, good enough for hydrolysis and fermentation.

Various factors were screened for their significance in enzymatic hydrolysis using the GrecoLatin square design of experiment as described in section 2.3. The results of the screening of factors for enzymatic hydrolysis of melon seed shell are shown in Table 7 and Table 8. The ANOVA table shows that the Fstatistics of time, pH and temperature were more than 1.0 and could be considered as significant factors for further studies according to Zivorad (2004). The Fstatistics for enzyme dosage was less than 1.0. The high glucose yield was obtained within 3 d of incubation compared to other days. The fact that glucose inhibits the enzymatic hydrolysis could be responsible for the drop in glucose yield as time exceeds 3 d. The concentration of enzyme is always required in small quantity for many enzymatic actions. The dosage of enzyme was not a significant factor and could be held constant.
Run Enzyme dosage (g per 50 m) (A–E) Temperature (℃)(T1–T5) pH(1–5) Time (d)(M1–M5) Glucose yield (%) 1 0.5 30 3 1 30.42 2 1.0 30 7 3 29.16 3 1.5 30 11 5 7.56 4 2.0 30 5 7 31.86 5 2.5 30 9 9 31.50 6 1.0 40 5 1 59.22 7 1.5 40 9 3 41.58 8 2.0 40 3 5 41.40 9 2.5 40 7 7 60.30 10 0.5 40 11 9 32.58 11 1.5 50 7 1 40.86 12 2.0 50 11 3 32.76 13 2.5 50 5 5 30.78 14 0.5 50 9 7 30.78 15 1.0 50 3 9 31.50 16 2.0 60 9 1 32.76 17 2.5 60 3 3 31.32 18 0.5 60 7 5 32.40 19 1.0 60 11 7 33.30 20 1.5 60 5 9 54.00 21 2.5 70 11 1 19.08 22 0.5 70 5 3 18.00 23 1.0 70 9 5 19.80 24 1.5 70 3 7 19.44 25 2.0 70 7 9 30.24 Table 7. The GrecoLatin square design matrix with response for enzymatic hydrolysis.
Source of variation Variation Degree of freedom Mean square Fstatistics Time 374.91 3 124.97 1.87 pH 676.81 3 225.60 3.37 Dosage 115.66 3 38.55 0.58 Temperature 1 974.21 3 658.07 9.84 Residual 401.24 6 66.87 – Total 3 551.82 18 – – Table 8. The ANOVA table for enzymatic hydrolysis (factor screening).

The ANOVA was used to evaluate the statistical significance of the model equation and the terms (Agu et al., 2020). A significant level of 95% was utilized. Hence, all terms whose Pvalue are < 0.05 are viewed as significant terms (Asadu et al., 2019). The Design Expert software suggested quadratic model based on the responses of the BoxBehnken Design. The ANOVA table of the quadratic model shows the Fstatistics and the Pvalues of the sources of variation (Table 9).
Source of variation Sum of square DF Mean square Fvalue Prob > F Remark Model 2139.02 9 237.67 305.26 < 0.0001 Significant Atime 15.13 1 15.13 19.43 0.0031 BpH 105.13 1 105.13 135.02 < 0.0001 Ctemperature 60.50 1 60.50 77.71 < 0.0001 A^{2} 74.27 1 74.27 95.40 < 0.0001 B^{2} 1174.27 1 1 174.27 1 508.24 < 0.0001 C^{2} 552.01 1 552.01 709.00 < 0.0001 AB 1.00 1 1.00 1.28 0.2944 AC 0.25 1 0.25 0.32 0.5886 BC 0.25 1 0.25 0.32 0.5886 Residual 5.45 7 0.78 Lack of fit 0.25 3 0.083 0.064 0.9761 Not significant Pure error 5.20 4 1.30 Cor total 2144.47 16 Notes: SD = 0.88, Mean = 44.18, CV = 2.00%, Predicted residual error sum of squares (PRESS) = 12.12, R^{2} = 0.9975, AdjR^{2} = 0.9942, Predicted R^{2} = 0.9943, Adequate precision= 50.647. Table 9. The ANOVA table for the hydrolysis.
When the calculated Pvalue is < 0.05, based on 95% confidence level, the evidence against null hypothesis H_{o} is stronger. However, the Pvalue provides details as to whether a statistical hypothesis is significant or not and how significant it is (Talib et al., 2016). Therefore, the model for the CVSSS hydrolysis was found to be significant as its Pvalue was < 0.0001 and < 0.05, based on 95% confidence level. The lower the Pvalue, the more important or significant the result is.
The Pvalue of the quadratic model is lower than the significance level of 0.05. The Fvalue of the model is 305.26 and the low Pvalue indicates that there is only 0.01% chance that the Fvalue this big might take place because of noise. The Fvalue of lack of fit is 0.064 and there is 97.61% chance that this could happen because of noise. This means that the lack of fit was mainly contributed by noise and not the response signals. The lack of fit was not significant because the Pvalue is higher than 0.05. Nonsignificant lack of fit is good—We want the model to fit. Furthermore, the plot of predicted and actual values presented in figure indicates that the actual values exist along the diagonal showing high correlation of actual and predicted values.
The Pvalues of the main factors (time, pH and temperature) were lower than 0.01 showing that the variations due to the parameters are significant even at 99% confidence. The Fvalue is 19.43 and there is 0.31% chance that this Fvalue could happen because of noise. The Pvalue of time is higher than that of the temperature and pH. Within the domain of 1 and 5 days, time was significant compared with the domain of 1 and 9 days applied during the preliminary study where it was observed when time was not significant. This result therefore implies that the impact of time on hydrolysis could be observed within the first five days of incubation. Temperature variation within the domain of 30 ℃ and 60 ℃ was significant as was observed during the factor screening experiment. The impact of pH within the domain of 3 and 9 was more than that of the domain of 3 and 11. The Fvalues of temperature and pH variations are 135.02 and 77.71, respectively and there is less than 0.01% chance that these Fvalues could occur because of noise.
The goodness of fit of the model was checked by the determination coefficient (R^{2}) and adjusted R^{2} (AdjR^{2}) (Igbokwe et al., 2016; Mazaheri et al., 2017; Agu et al., 2020). For this analysis, only 0.25% of the total variations were not explained by the model, because of the value of R^{2} = 0.9975. A high value of the R^{2} with a significant closeness to 1 is a sign that the model fits the experimental data. The value of the AdjR^{2} = 0.9942 is also high to advocate for a high significance of the model (Tengborg et al., 2001). The AdjR^{2} and Predicted R^{2} should be within 0.2 of each other, as can be seen from this research. A better precision and reliability of the experiments carried out, was proved by a low value of the coefficient of variation (CV = 2.00%). However, the CV is therefore, defined as the ratio of the standard deviation of estimate to mean value of the observed response (Chen et al., 2012). Presented in equations (13) and (14), respectively, are the model equations for the enzymatic hydrolysis of CVSSS in terms of the actual factor with all the terms and without the insignificant terms.

Without the nonsignificant terms, the model equation becomes:
As shown in Table 9, the R^{2} is in close agreement with the predicted R^{2}. The difference between the values is less than 0.1 and the values can be approximated to 1.0. Adequate precision measures the signal to noise ratio. Values higher than 4 are desirable. Adequate precision value of 50.647 shows that the signal is higher compared to noise.

Optimization is concerned with selecting the best among the entire set by efficient quantitative methods. The goal of optimization however, is to find the values of the variables in the process to yield the best value of the performance criterion.
It is not possible to define a single optimum for enzymatic processes since it can change depending on the level of other factors (Tengborg et al., 2001; Pilkington et al., 2014). One of the optimum solutions was however, selected at the desirability of number 1. Therefore, their predicted values for the enzymatic hydrolysis of the CVSSS were time of 3.32 days, pH of 5.68 and temperature of 46.8 ℃ (Table 10). At these optimal conditions, the maximum predicted value of glucose yield from the model was 59.87%. However, to confirm the predicted results of the model, an experiment was carried out at the optimal conditions and was found that a maximum glucose yield of 59% was obtained. The experimental response (59% glucose yield) was approximately 1.5% lower than the predicted maximum response. Hence, the percentage variation shows the model to be fit.
Time (d) pH Temperature (℃) Glucose yield (%) Actual (%) Percentage variation (%) 3.32 5.68 46.8 59.87 59 1.5 Table 10. Numerical optimum values for hydrolysis.
The nearness of the predicted values as well as the actual values was also established, by the graph of the predicted versus the actual values as shown in Fig. 1. The diagonal positions of the optimization data on the squared graph displayed the nearness of the predicted and the actual points. Hence, the quadratic model was fit for the analysis.

(1) Intearctive effects
The 3D and contour plots of the 2factor interactions are shown in Figs. 2–4. The 2factor intractions were not significant at 0.05 significance level, however, there were some levels of interactions. The nonsignificance interactions of pHtime, timetemperature and temperaturepH can be seen from the contour lines. The distances bentween two contours along the doamins were the same. In other words, the contours were somewhat parallel. This also affirms the report of Igbokwe et al. (2016), that the interactive effects of the pH with other factors from the contour graphs, for enzymatic hydrolysis of platian peels were not significant.
The 3D plot of pH and time (Fig. 2) is concave sloping from back to front with the pick at the middle. This shows that variation in pH was more significant than that of time. It also shows that pH within the neutral region or slightly acidic gave rise to a high glucose yield. Also the shape of the 3D plot of time and temperature (Fig. 3) is concave sloping from back to front with the pick at the center. The 3D plot was not cementric at the center showing that the glucose yield at 60 ℃ was higher than that at 30 ℃ but that around 40–50 ℃ was the highest. The 3D plot of temperature and pH (Fig. 4) is concanve sloping both from back to front and left to right with the pick at the middle and concentric contour lines. This indicates that both variations in temperature and pH have almost equal impact on glucose yield.
(2) Effect of temperature
The relationship between temperature and glucose yield was observed to be inverse. The glucose yield decreased with the temperature and the optimum was observed at 46.8 ℃. This is in line with Galbe and Zacchi (2002), who reported that, the optimum temperature aimed at hydrolysis of cellulosic materials, applying pure enzyme lay between 45 ℃ and 50 ℃. This result was also supported from the finding of previous studies whereby temperature at 50 ℃ was mentioned to be the best condition for enzymatic hydrolysis (Chen et al., 2008; Efri et al., 2017).
However, from the ambient to 46 ℃, the glucose yield increased significantly and decreased at a higher temperature. This also affirmed the report of Zakpaa et al. (2009), that the optimum temperature for hydrolysis using Aspergillus niger as a crude enzyme on corncobs was 40 ℃ and stated that there was a sharp decrease in the rate of hydrolysis from 50 ℃ to 60 ℃ due to the fact that enzyme denaturation was faster. It indicated that the hydrolysis raised with temperature up to the peak after which it declined and that the rise in temperature was because of the conforming increase in kinetic energy and the fall after the optimum was because of enzyme denaturation.
The effect of temperature on the yield of glucose was nevertheless, significant as established in Table 9. Temperature therefore, has effective interaction with other factors (time and pH); however none of the interactions was significant (Table 9). This insignificant collaboration can be understood in Figs. 3 and 4 where the contour plots of temperature against pH and time are somewhat straight lines presenting nonsignificant interactions. This is also in agreement with the work of Igbokwe et al. (2016), that the effect of temperature on the glucose yield from plantain peels was significant and showed nonsignificant interaction with pH and time.
(3) Effect of pH
The contour and 3D plot of Figs. 2 and 4 showed that the pH of the solution significantly affected the glucose yield during hydrolysis. This can be understood from Table 9, and the effect of pH is significant.
The collaborative effects of the pH with other factors were not significant. It was presented in Table 9 that the Pvalues were higher than 0.05. This can as well be understood on the contour graphs (Figs. 2 and 4) where the contour plots of pH with temperature and time are somewhat straight lines at certain points. Figures 2 and 4 show that as the pH increases, both temperature and time of incubation should be kept high to have a higher glucose yield. The optimum pH of the hydrolysis recorded 5.68. Similar result has been reported whereby pH 5.5 was found to be the best condition for enzymatic hydrolysis of lignocellulosic biomass from pineapple leaves by using endo1, 4Xylanase (Rosdee et al., 2020). Akponah and Akpomie (2011) reported that the A. niger hydrolysis activities increased from a pH of 4.5 to 5.5 and decreased at a pH of 6.5. The pH of the solution has effects on the structure as well as activity of the enzyme. Enzymes are amphoteric molecules with a huge quantity of acid and basic groups mostly located on their surface. The charges on this group differ, based on their acid dissociation constant, with the pH of the solution (Zakpaa et al., 2009).
(4) Effect of time
From the selected optimum solution, the optimum time of the hydrolysis reaction was 3.32 days (Table 10). This can as well be understood by the result of the kinetics study. At this point, the rate of the degradation of cellulose on day 0 to day 4 declined steadily and later it became almost constant. Time however, had a significant effect on the yield of glucose in hydrolysis.
In the work of Luo et al. (2019), a hydrolysis time of 72 h (3 d) were reported from promoting enzymatic hydrolysis of lignocellulosic biomass by inexpensive soy protein. Zakpaa et al. (2009) reported that there was an increase in enzyme activities from 24 h to 144 h (1–6 d) after incubation and stated that cellulose was an induced enzyme hence its production increased with the increase in fungal biomass.

The same GrecoLatin square of Section 2.3 was used for the fermentation experiment. The design matrix of the Greco Latin square with the response of the ethanol yield is presented in Table 11.
Run Dosage (g per50 mL) (A–E) Temperature (℃)(T1–T5) pH(1–5) Time (d)(M1–M5) Ethanol yield (%, V/V) 1 0.5 30 3 1 6.8 2 1.0 30 7 3 6.94 3 1.5 30 11 5 6.96 4 2.0 30 5 7 7.05 5 2.5 30 9 9 7.13 6 1.0 40 5 1 7.09 7 1.5 40 9 3 7.17 8 2.0 40 3 5 7.15 9 2.5 40 7 7 7.18 10 0.5 40 11 9 6.89 11 1.5 50 7 1 6.98 12 2.0 50 11 3 6.98 13 2.5 50 5 5 7.05 14 0.5 50 9 7 6.86 15 1.0 50 3 9 6.93 16 2.0 60 9 1 6.96 17 2.5 60 3 3 6.98 18 0.5 60 7 5 6.83 19 1.0 60 11 7 6.84 20 1.5 60 5 9 6.86 21 2.5 70 11 1 6.81 22 0.5 70 5 3 6.65 23 1.0 70 9 5 6.67 24 1.5 70 3 7 6.75 25 2.0 70 7 9 6.79 Table 11. GrecoLatin square design Matrix with response for fermentation.
From the fischer troph Table, the critical Fvalue at 95th percentile is 4.76 considering the degree of freedom for the factors and the residual (F_{0.05, 3, 6}). Comparing the Fvalue calculated with the critical Fvalue, it can be deduced that time and pH is statistically not significant at (P < 0.05) showing that time and pH can be considered at any measure or kept constant during fermentation of melon seed shell. In addition, the Fvalue for temperature and dosage is higher than the critical Fvalue as revealed in Table 12, indicating that variation in dosage and temperature affects the fermentation of melon seed shell and as such the four factors are considered and optimized using response surface methodology.
Source of variation Variation Degree of freedom Mean square Fstatistics Time 0.0016 3 0.0005 0.1724 pH 0.0114 3 0.0038 1.3103 Dosage 0.1499 3 0.0499 17.207 Temperature 0.3513 3 0.1171 40.379 Residual 0.0171 6 0.0029 Total 0.5314 18 Table 12. The ANOVA table for fermentation screening of factors.

The ANOVA was used to evaluate the statistical significance of the model equation and the terms (Agu et al., 2020). A significant level of 95% was utilized. Hence, all terms whose Pvalue are < 0.05 are viewed as significant terms (Asadu et al., 2019). The Design Expert software suggested quadratic model based on the responses of the BoxBehnken Design. The ANOVA table contains the sources of variations, the sum of squares, the degree of freedom, the mean square, the Fvalues and the Pvalues. The statistical significance of the model parameters were determined based on the value of Fstatistic or Pvalue. If the Fvalue of any term is more than the critical Fvalue, then, the term is significant at the given significance level. If the Pvalue is less than the significance level, then the term is significant otherwise, the term is not significant at that level.
When the calculated Pvalue is < 0.05, based on 95% confidence level, the evidence against null hypothesis H_{o} is stronger. However, the Pvalue provide details as to whether a statistical hypothesis is significant or not and how significant it is (Talib et al., 2016). Therefore, the model for the CVSSS fermentation was found to be significant as its Pvalue was < 0.0001 and < 0.05, based on 95% confidence level. The model Pvalue is lower than the significance level showing that the quadratic model is adequate even at 0.01 significance level.
The goodness of fit of the model was checked by the R^{2} and AdjR^{2} (Igbokwe et al., 2016; Mazaheri et al., 2017; Chinedu et al., 2020). For this analysis, only 3.22% of the total variations were not explained by the model, because of the value of the R^{2}= 0.9678. A high value of the R^{2} with a significant closeness to 1 is a sign that the model fits the experimental data. The value of the AdjR^{2} (0.9356) is also high to advocate for a high significance of the model (Tengborg et al., 2001). A better precision and reliability of the experiments carried out, was proved by a low value of the CV (3.13%). However, the CV is therefore, defined as the ratio of the standard deviation of estimate to mean value of the observed response (Chen et al., 2012).
The goodness of fit of the model was butressed by the R^{2} values. The R^{2} values stand presented in Table 13, and it can be observed that the values are close to 1. The predicted R^{2} and the AdjR^{2} are in close agreement with the model R^{2} value. Adequate precision measures the signal to noise ratio. A ratio higher than 4 is desirable. The ratio of 18.701 shows an suitable signal. This model can be applied to navigating the design space. Moreover, the plot of predicted against actual values presented in Fig. 5 showed close agreement of the actual values with the predicted values.
Parameter Value Model parameter Result SD 0.23 R^{2} 0.9678 Mean 7.30 AdjR^{2} 0.9356 CV 3.13 Predicted R^{2} 0.8241 PRESS 3.99 Adequate precision 18.701 Notes: SD, standard deviation; PRESS, predicted residual error sum of squares. Table 13. Quadratic model parameter.
The quadratic model terms include the main factors and the interactive terms. The main factors were significant at 0.05 significance level. However, dosage (A) and temperature (B) were not significant at 0.01 significance level. Among the 2F interactions, only temperature/pH (BC) interaction was significant at 0.05 significance level. There were some levels of interactions among others but, the interactions were not significant. The model equations in terms of the actual factors with all the terms and without the terms are provided in equations (15) and (16), respectively.
Standard deviation (SD), mean, CV and predicted residual error sum of squares (PRESS) are all calculations that were done to generate R^{2}, Adj R^{2} and predicted R^{2}. However, AdjR^{2} and predicted R^{2} should be within 0.2 of each other. Mean is the overall average of all the response data. The CV is the SD expressed as a percentage of the mean calculated, by dividing the SD by the mean and multiplying by 100. The PRESS gives a measure that how the model fits each point in the design.

Removing the terms without significant values, the model equation becomes:

The process parameters that gave the maximum ethanol yield were obtained from the model. The numerical optimum solution as predicted by the model for the fermentation of the CVSSS were time of 3.55 days, pH of 7.0, dosage of 1.65 g per 50 mL and temperature of 33.58 ℃ (Table 15). The maximum ethanol yield of the CVSSS predicted by the model was 25.55%.
Source Sum of square DF Mean square Fvalue P > F Remark Model 21.97 14 1.57 30.06 < 0.0001 Significant Adosage 0.31 1 0.31 6.01 0.0280 Btemperature 0.34 1 0.34 6.45 0.0236 CpH 8.72 1 8.72 167.02 0.0001 Dtime 1.40 1 1.40 26.83 0.0001 A2 2.10 1 2.10 40.24 0.0001 B2 2.36 1 2.36 45.16 0.0001 C2 2.488E003 1 2.488E003 0.048 0.8304 D2 8.05 1 8.05 154.20 0.0001 AB 4.225E003 1 4.225E003 0.081 0.7802 AC 0.070 1 0.070 1.34 0.2656 AD 0.040 1 0.040 0.77 0.3962 BC 0.49 1 0.49 9.38 0.0084 BD 0.000 1 0.000 0.000 1.0000 CD 0.12 1 0.12 2.35 0.1479 Residual 0.73 14 0.052 Lack of fit 0.68 10 0.068 5.22 0.0626 Not significant Pure error 0.052 4 0.013 Cor total 22.70 28 Notes: SD = 0.23, Mean = 7.30, CV = 3.13%, PRESS = 3.99, R^{2} = 0.9678, Adj.R^{2} = 0.9356, Predicted R^{2} = 0.8241, Adequate precision = 18.701. Table 14. The ANOVA table for quadratic model of fermentation optimization.
Optimum solution Value Dosage (g per 50 mL) 1.65 Temperature (℃) 33.58 pH 7.0 Time (d) 3.55 Predicted ethanol yield (%) 25.55 Experimented yield (%) 24.9 Percentage variation (%) 2.6 Table 15. Optimum numerical solution for fermentation.
The numerical values were validated by carrying the experiment at the optimum values and the percentage ethanol yield was 24.9% which was in close agreement with the theoretical value (25.55%). The percentage variation of 2.6 shows the model to be fit. Table 15 confirms that the predicted value was close to the actual experimental value at the optimum condition. The graph of the predicted versus the actual shown in Fig. 5 (The actual points lay along the diagonal) also confirmed that the prediction was accurate with an adequate model.

(1) Effect of pH on fermentation
The pH of the solution is a significant factor of fermentation (Pvalue < 0.0001, Table 14). The optimum pH is 7 (Table 15). The optimum pH for most microorganisms is near the neutral point pH 7.0 (Mike and Sue, 1998). The pH had an interactive effect with time, dosage and temperature as can be observed from the contour plots of Figs. 6, 7 and 8. The interaction of pH with time was however not significant (P = 0.1479, Table 14). The interaction of pH with dosage was not significant (P = 0.2656). The interaction of pH with temperature was significant (P < 0.05). The contour plots of pH against temperature shown in Fig 8 are all curves showing the significant effect of the interaction.
(2) Effect time on fermentation
The optimum duration for the fermentation of the melon seed shell was 3.55 days (Table 15). The duration of the fermentation had a significant effect on fermentation as presented in Table 6 (P < 0.0001). Time had an interactive effect with dosage, temperature, and pH as can be observed from the contour plots of Figs. 6, 9 and 10. The significant effect of time can as well be observed from the ANOVA table of Table 14. The interactive effect of time with pH is obvious from the contour plot of Fig. 6, but the ANOVA table shows that the interaction is not significant. The interaction of time with dosage was not significant likewise with temperature. Akponah and Akpomie (2011) documented an ethanol yield of 17.52% (V/w) over 72 h of incubation of cassava peels hydrolysed using A. niger. Streamer et al. (1975) reported that biter kola fermented with baker's yeast could yield up to 2.16% (V/V) ethanol.
3) Effect of temperature on fermentation
The optimum temperature aimed at the fermentation of the hydrolysed melon seed shell was 33.58 ℃ (Table 15). Temperature was not a significant factor of fermentation as can be observed from the ANOVA table of Table 14 (P = 0.0236). The significant interactive effect of temperature with pH can be noticed from the contour plot of Fig. 8; likewise, from the ANOVA table of Table 14 the significant interactive effect can be observed. The optimum fermentation temperature of 30 ℃ had been extensively described by other researchers (Highina et al., 2011; Lebaka et al., 2011; Oyeleke et al., 2012; Itelima et al., 2013). Highina et al (2011) reported a too much enzyme degradation as well as a loss of cell viability at temperature beyond 30 ℃.
4) Effect of dosage on fermentation
The optimum dosage for the fermentation of melon seed shell was 1.65 g per 50 mL (Table 15). Dosage was not a significant factor of fermentation as can be noticed from the ANOVA Table 12 (P = 0.0280). Dosage had an interactive effect with temperature, pH, and time. Though, the interactions were not significant.

Some fuel properties of the produced bioethanol were conducted and the obtained results are shown in Table 16. The table shows some of the properties of ethanol produced against the market available ethanol. The viscosity of the produced bioethanol, which measured the friction that opposed the motion of fuel, was investigated and the result obtained as presented indicated that the viscosity of the produced bioethanol was 1.34 mm^{2}/s which was a little higher than the set limit of 1.20 mm^{2}/s. High viscosity meanwhile, showed a low flow rate in an engine.
Ethanol property Bioethanol produced Bioethanol ASTM Standard Moisture (%) 16.76 20 Specific gravity 0.9922 0.87 Refractive index 1.3582 1.36 Viscosity (mm^{2}/s) 1.34 1.20 Source: Abdulkareem et al., 2015. Table 16. The ASTM Standards properties of bioethanol.
Viscosity however, is a very important characteristic of fuel. It influences the flow of fuel via the nozzles, injection pipe and orifice (Abdulkareem et al., 2015). Also tested for, is the refractive index of the produced bioethanol from the CVSSS. Ethanol with high refractive index value presents higher concentration (Pornpuunyapat et al., 2014). The result as presented indicates that the refractive index of the produced bioethanol was 1.3582 which is approximately the same with the literature value (1.36). The purity of fuel is verified by refractive index. The result obtained on the moisture content of the bioethanol produced was found to be 16.76%, which deviated from the literature value of 20%. Abdulkareem et al (2015) reported a 0.52% of moisture content for bioethanol produced from Sugarcane bagasse. The result as presented indicated that the specific gravity of the produced bioethanol from was 0.9922 which was a bit higher than the set limit of 0.87 by the ASTM. The 0.92 of specific gravity was reported by Abdulkareem et al. (2015) for ethanol from Sugarcane Bagasse. The little difference or variation in some of the properties can be attributed to the nature of the feedstock (CVSSS) used in this study.

The goal of kinetic modelling of enzymatic hydrolysis is to understand better, and the mechanism by which enzyme acts on their substrates. This kinetic study shows a decline in concentration of cellulose contained in the melon seeds shell with time at a known concentration of the enzyme. The differential change of the cellulose concentration was calculated by applying the numerical method (Lazic, 2004).

The linear form of the MichaelisMenten kinetic model is given by Fogler (2006), in Equation (17):
The values of the kinetics parameters are presented in Table 17, while the linear plot is given in Fig. 11. The value of the correlation coefficient R², being close to 1 showed that MichealisMenten model described the kinetics of the enzymatic hydrolysis. Hence, the concentrations of the enzyme (A. niger) and the substrate (CVSSS) were exchanged in the MichaelisMenten equation, and the enzyme released into the medium at the end of the reaction. It can be observed that the rate of the reaction decreases with time and remains almost constant after the fifth day. Igbokwe et al (2016) reported a decreased rate of reaction with time until the fifth day during Plantain peels enzymatic hydrolysis with A. niger.
Parameter Value K_{m} (g/L) 35.5 V_{max} ((g·L^{–1})/d) 29.1 R^{2} 0.9708 Table 17. MichaelisMenten kinetic parameters for hydrolysis.
The parameters of hydrolysis were determined by fitting to experimental data and theoretical values calculated using model equations with the determined parameters (Sakimoto et al., 2017). In this study, a model equation for enzymatic hydrolysis of CVSSS was established.
Using the MichaelisMenten parameters calculated, the kinetics equation for the hydrolysis is given by Equation (19).
Two constants (V_{max} and K_{m}) play an important role in a mathematical elucidation of enzyme action as developed in 1913, by Leonor Michaelis and Maud Menten (https://www2.chem.wisc.edu/deptfiles/genchem/netorial/modules/biomolecules/modules/enzymes/enzyme4.htm).According to University College London, the K_{m} of an enzyme, relative to the concentration of its substrate under normal conditions permits prediction of whether or not the rate of formation of product will be affected by the availability of substrate (https://www.ucl.ac.uk/~ucbcdab/enzass/substrate.htm). A low K_{m} indicates that, only a small percentage of substrate is required to saturate the enzyme, hence, a high affinity for substrate. Meanwhile, V_{max} reflects how quick the enzyme can catalyse the reaction.
Carrillo et al. (2005) studied the kinetics of the hydrolysis of pretreated wheat straw using different concentrations of commercial cellulose (Novozymas A/S), and measured the initial velocities of a rate equation derived from a MichaelisMenten mechanism. Similarly, Igbokwe et al. (2016) reported the MichaelisMenten kinetic model for enzymatic hydrolysis of Plantain peels as $ {r}_{\mathrm{A}}=\frac{20.4{C}_{\mathrm{A}}}{16.2+{C}_{\mathrm{A}}} $. A research on MichaelisMenten kinetic parameters of coconut coir enzymatic hydrolysis, showed values of V_{m} and K_{m} as 4.9 × 10^{–4} 1/h and 4 195 mg/L, respectively (Rudy and Akbariningrum, 2015). The variations in the results of V_{max} and K_{m} can be attributed to the use of different biomass and enzyme.
Plots of $ \frac{1}{{r}_{\mathrm{A}}} $ versus $ \frac{1}{{C}_{\mathrm{A}}} $ which gave the slope as $ \frac{K\mathrm{m}}{V\mathrm{m}} $ and intercept as $ \frac{1}{V\mathrm{m}} $ were used to express the Menten model, and calculated and experimented values of the reaction rates for enzymatic hydrolysis were plotted against $ \frac{1}{{C}_{\mathrm{A}}} $ as shown in Figs. 12 and 13. The correlation coefficients R^{2} for both calculated and experimented values were > 0.9, which indicates that the process may have followed the Menten model.

The kinetics of the fermentation was modelled using the MichaelisMenten equation model. The concentration of the glucose in the fermentation is determined with time applying the Dinitrosalicylic (DNS) acid method. The numerical method is employed to estimate the differential change in glucose concentration with time.

Using the linear form of the MichaelisMenten equation shown in Equation (17), the kinetics parameters were gotten as presented in Table 18. The kinetics equation is shown in Equation (18). The closeness of R² to 1 (Fig. 14) confirms that the kinetics of the fermentation is described by the MichaelisMenten equation. Based on the value of the MichaelisMenten parameters obtained, the kinetics equation for fermentation is given as presented in Equation (20).
Parameter Value K_{m} (g/L) 42.52 V_{max} ((g·L^{–1})/d) 25 R^{2} 0.8773 Table 18. MichaelisMenten parameters for fermentation.
Igbokwe et al. (2016) reported the MichaelisMenten kinetic model for ethanol fermentation of Plantain peels as$ {r}_{\mathrm{A}}=\frac{28.6{C}_{\mathrm{A}}}{39+{C}_{\mathrm{A}}} $.
Plots of $ \frac{1}{{r}_{\mathrm{A}}} $ versus $ \frac{1}{{C}_{\mathrm{A}}} $ which gave the slope as $ \frac{K\mathrm{m}}{V\mathrm{m}} $ and intercept as $ \frac{1}{V\mathrm{m}} $ were used to express the Menten model, and experimented and calculated values of the reaction rates for fermentation were plotted against $ \frac{1}{{C}_{\mathrm{A}}} $ as shown in Figs. 15 and 16. The closeness of correlation coefficients R^{2} for both predicted and observed values to 1 indicated that the fermentation process followed the MichaelisMenten model.

MichaelisMenten kinetic model for enzymatic hydrolysis and fermentation was subjected to error analysis, using three statistical tools, mean square error (RMSE), variance and absolute average percentage deviation (AAD), to evaluate the efficiency of the model with the experimental data. The result of the evaluation was presented as shown in Tables 19 and 20. Statistical analysis using RMSE, variance and AAD was investigated. Normally, the higher the value of the R^{2} and lower the values of the RMSE, the better would be the goodness of the model to fit the experimental data (Kitanovic et al., 2008; Igbokwe et al., 2016; Menkiti et al., 2017).
Model K (g/L) R^{2}exp R^{2} model RMSE AAD (%) σ^{2} V_{max} (g·L^{–1})/d MichaelisMenten
$ {r}_{A}=\frac{Vm{C}_{\mathrm{A}}}{Km+{C}_{A}} $35 0.9708 0.9999 0.0130 0.599 0.000169362 29 Table 19. Kinetic parameters of MichaelisMenten model and values of calculated constants for enzymatic hydroysis.
Model K (g/L) R^{2}exp R^{2} model RMSE AAD (%) σ^{2} V_{max} (g·L^{–1})/d MichaelisMenten
$ {r}_{A}=\frac{Vm{C}_{A}}{Km+{C}_{A}} $42.5 0.8773 0.9927 0.256 2.614 0.002631218 25 Table 20. Kinetic parameters of MichaelisMenten model and values of calculated constants for fermentation.
The RMSE is a frequently used statistics in comparing two data; predicted and observed values by a model. The RMSE therefore, could be applied to verify experimental results, obtained in the study of enzymatic hydrolysis and fermentation kinetic models. This can be achieved by showing the differences between the values predicted by a model and the values observed. Hence, the RMSE remains a worthy measure of accuracy. It is also the square root of variance (σ^{2}). However, lesser values of σ^{2}, RMSE and AAD are generally, better than higher values. From Figs. 13 and 16, a quantitative measure of performance was evaluated as shown in Tables 19 and 20.