factorial design as an effective tool for optimization of ... · factorial design as an effective...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 44

151303-5858-IJMME-IJENS © June 2015 IJENS I J E N S

Factorial Design as an Effective Tool for Optimization of

Alcoholic Wine Production from Paw Paw Fruits

1Ume, J.I.,

2Ejikeme, P.C.N.,

2Ejikeme, Ebere .M.

1Department of Mechanical Engineering, University of Nigeria, Nsukka, Nigeria

2Department of Chemical Engineering, Enugu State University of Science and Technology, Enugu, Nigeria

Abstract-- Optimization of process conditions for alcoholic wine production from

pawpaw fruit was achieved using 2 level full factorial designs with centre points. The

factors that were considered were pH, initial sugar concentration, yeast concentration,

and fermentation time with specific gravity of the wine as the response.

ANOVA confirmed curvature to be significant which showed that higher order model

can predict the process well when augmented to Response Surface Method that

estimates quadratic terms. Linear model generated can be used to predict response at

the factorial points only because of the significant curvature. Minimization

optimization predicted specific gravity of the wine to be 0.9767 at pH of 5, initial sugar

concentration of 20g/l, fermentation time of 13 days and yeast concentration of 9g/l at

desirability of 0.945.

The optimum conditions were validated with little error of 0.14% confirming the

adequacy of the model in predicting the process.

Index Term-- ANOVA, Factorial design, Paw-paw, Saccharomyces Cerevesia,

I. INTRODUCTION

Wine is a popular drink being enjoyed all over the World [1]. Wines are alcoholic

beverages made from fruits juice by the fermentative action of selected yeast

adapted to a particular type of wine followed by the ageing process [2].

Traditionally, wines are produced from apples, pear, grape, berry and prime fruits

[2]. Wines have also been produced from tropics fruits such as cashew by

Akanwale [3] and Joseph [2], banana by Isitua and Ibeh [4], pineapple by Ume J.I

et al [5], mango by Reddy and Reddy [6], cocoa by Disney et al [7]. Any fruit with

good proportion of sugar may be used in producing wine and the resultant wine is

normally named after the fruit [8]. The fermentation of fruit juice into wine is a

complex biochemical process, during which yeasts utilize sugars and other

constituents of grape juice as substrate for their growth, converting them to

ethanol, carbon dioxide and other metabolic end products that contribute to the

chemical composition and sensory quality of the wine [9]. Saccharomyces

Cerevesia, also known as brewers‟ yeast, is the most widely used fermentation

microbe because of the baking and beer brewing Industries [10]. During alcoholic

fermentation, Saccharomyces cerevesia yeast do not only convert sugars to ethanol

and carbohydrate [11], they also produce a wide range of metabolites, for example,

glycerol, acetic acid, acetaldehyde, pyruvate and lactic acid [12]. The Keto acids

principally pyruvate and α-ketoglutarate, have Implications for wine stability and

quality due to their abilities to bind sulphur dioxide and to react with phenols [13],

[14], [15], [16], [17]. Acetic acid is of particular importance, as it imparts vinegar

like character and becomes objectionable at concentrations of 0.7 – 1.1 g/l.

Depending on the style of wine and yeast strain, the acceptable concentration is

0.2 – 0.7g/l [18]. Glycerol is a major product of alcoholic fermentation, which

imparts tastes of slightly sweet, as well as having an oily and heavy mouth – feel

[11]. Pawpaw (Carica papaya) belongs to the family of caricaceae, a native of

tropical Africa, but now spread all over the tropical regions of the world. It is

known by different names in different countries. Pawpaw is grown mostly for

fresh consumption or for production of latex [19]. Pawpaw fruit is a good source

of carbohydrate, vitamins (VC and VA) and minerals (copper and magnesium)

[11]. The flesh varies from 2.5 to 5.0cm in thickness, it is a very wholesome fruit

and relished for the attractive colour, flavor, succulence and characteristics aroma.

Fresh pawpaw fruits are very perishable, thereby making their export problematic.

Large quantities of these fruits are produced yearly in Nigeria in amounts that are

in excess of their consumption and disposed off due to non-availability of or poor

storage facilities [19]. The nutrients that are lost can be harnessed and made

available all year round, if the fruits are put to other use such as wine production.

Several factors affect alcoholic fermentation of wine, including clarification of

juice, yeast concentration, temperature of fermentation, pH, initial sugar

concentration and so on.

In this work, some vital process factors that affect alcoholic fermentation were

optimized using 2 level full factorial designs with center points to check for

curvature.



II. MATERIALS AND METHODS

A. pawpaw fruit

Pawpaw fruits were obtained from local Abakpa market in Enugu, Enugu State of

Nigeria. The yeast, saccharomyces cerevesia was purchased from De cliff

integrated, main market Enugu.

B. Production of alcoholic wine

The paw paw fruits were pulped in a blender to a slurry consistency. Sodium

metabisulphite solution 5.6 % was added to the slurry and blended for 10 minutes.

Fruit juice was stirred and sieved from the pulp using screens of 120 μm and 100

μm aperture. The juice was reconstituted; 1.5 litres of fruit juice with 4 litres of

distilled water and ameliorated to 25% sugar content with sucrose and 0.01755%

w/v ascorbic acid. This formed what is known as „must‟. The „must‟ was then

sieved through a standard sieve mesh no. 35 or cheese cloth and transferred into a

5 L fermentation tank inoculated with a known quantity of baker‟s yeast and

allowed to ferment at room temperature for specified time intervals. The

experimental work was strictly carried out based on the 2 levels full factorial

design matrix as depicted in Table II.

C. Optimization Using 2 Level Full Factorial Design With Centre Points

Two level factorial experiments are factorial experiments in which each factor is

investigated at only 2 levels. The early stages of experimentation usually involve

the investigation of a large number of potential factors to discover the vital few

factors. Two level factorial designs are used during these stages to quickly filter

out unwanted effects so that attention can then be focused on the important ones.

The factorial experiments, where all combinations of the levels of the factors are

run, are usually referred to as full factorial experiments. Full factorial two level

experiments are also referred to as 2k designs where K denotes the number of

factors being investigated in the experiment. In DOE, these designs are referred to

as 2 level factorial design. A full factorial two level design with k factors requires

2K runs for a single replicate. In this work, two level experiments with four factors

were used giving 2 x 2 x 2 x 2 = 24 = 16 runs with four centre points giving total of

20 runs.

If a factorial experiment is run only for a single replicate, then, it is not possible to

test hypotheses about the main effects and interactions as the error sum of squares

cannot be obtained [20]. This is because the number of observations in a single

replicate equals the number of terms in the ANOVA model. Hence the model fits

the data perfectly and no degree of freedom is available to obtain the error sum of

squares. In the absence of error sum of squares, hypothesis tests to identify

significant factors cannot be conducted. A number of methods of analyzing

information obtained from unreplicated 2K design is to pool higher order

interactions, using normal probability plot of effect or including centre point

replicates in the design [20].

The centre point is the response corresponding to the treatment exactly midway

between the two levels of all factors. Running multiple replicates at the midpoint

provides an estimate of pure error. Another advantage of running centre point

replicates in the 2K design is checking for the presence of curvature. The test of

curvature investigates whether the model between the response and the factors is

linear. The centre point replicates are treated as an additional factor in the model.

The factor is labeled as curvature in the result. If curvature turns out to be a

significant factor in the results, then, this indicates the presence of curvature in the

model. The presence of curvature means that 2K factorial design is not capable to

be used in modeling the process, because it can only give a linear model. In this

case, the experiment will be augmented to Response Surface Methodology (RSM)

for higher order model prediction. Augmenting to RSM involves adding only the

axial points on the experimental run. In the order way, if curvature is not

significant in 2K design, it means that linear model can predict the process well.

Using 2K design with centre points for modeling saves resources and time in case

where linear model is capable of explaining the process.

In this work, four factors were considered in the optimization process, pH, yeast

concentration, fermentation time and initial sugar concentration with specific

gravity as the response. The factors and levels used for the 2K design with centre

points are shown in table I while the design matrix with the response data are

shown in table II.

Table I

FACTORS AND LEVELS FOR 2K DESIGN

S/N Factors Units Levels

-1 0 +1

1 Yeast Conc. g/L 5.0 7.0 9.0

2 pH - 5.0 5.75 6.5

3 Initial sugar conc. %bix 14.0 17.0 20.0

4 Fermentation time Days 7.0 10.0 13.0



Table II

DESIGN MATRIX FOR 2K WITH CENTRE POINT

Std Run yeast pH Sugar conc. Ferment. S.G

Order order conc(g/l) (-) (%brix) time (-)

(days)

12 1 9.00 6.50 14.00 13.00 1

20 2 7.00 5.75 17.00 10.00 0.995

18 3 7.00 5.75 17.00 10.00 0.99

6 4 9.00 5.00 20.00 7.00 0.98

7 5 5.00 6.50 20.00 7.00 1

15 6 5.00 6.50 20.00 13.00 0.98

19 7 7.00 5.75 17.00 10.00 1

13 8 5.00 5.00 20.00 13.00 0.98

4 9 9.00 6.50 14.00 7.00 0.98

9 10 5.00 5.00 14.00 13.00 1

10 11 9.00 5.00 14.00 13.00 0.98

1 12 5.00 5.00 14.00 7.00 1

17 13 7.00 5.75 17.00 10.00 1

11 14 5.00 6.50 14.00 13.00 1

8 15 9.00 6.50 20.00 7.00 1

2 16 9.00 5.00 14.00 7.00 0.98

5 17 5.00 5.00 20.00 7.00 0.985

16 18 9.00 6.50 20.00 13.00 0.98

3 19 5.00 6.50 14.00 7.00 0.985

14 20 9.00 5.00 20.00 13.00 0.975

III. RESULT AND DISCUSSIONS

A. ANOVA with Centre Points Detected

The ANOVA is presented in two ways – with the centre point information

(curvature) separated from the regression model (adjusted) and with the centre

point included in the regression model (unadjusted). If curvature is significant, the

design will be augmented to add runs that estimate the quadratic terms. On the

other hand, if curvature is not significant, the adjusted and unadjusted models will

be similar and (assuming model is significant and lack of fit is insignificant) either

may be used for prediction[21].

B. Adjusted Model

The factorial model was augmented with coefficients to adjust the mean for

curvature, which is to remove curvature sum of squares from lack of fit sum of

squares. Thus, provides the factorial model coefficients you would get if there

were no centre points. Thus model separates problems due to curvature from those

due to the model not fitting the factorial points. This model is appropriate for

calculating diagnostics. If curvature is significant, it will be used for predicting

only the factorial points, but not any other points. Table III shows ANOVA for

adjusted model. Table III

ANOVA FOR MODEL THAT ADJUSTED FOR CURVATURE

Source

Sum of

Square

df

Mean

Square

F

Value

P-

Value

Comment

Model 1.438E-

003

1

1.797E-

004

13.86

0.0002

Significant

A-Yeast

Conc.

1.891E-

004

1

1.891E-

004

14.58

0.0034

B –pH 1.266E-

004

1

1.266E-

004

9.76

0.0108

C-Sugar

Conc.

1.266E-

004

1

1.266E-

004

9.76

0.0108

AB 1.266E-

004

1

1.266E-

004

9.26

0.0108

AC 7.656E-

006

1

7.656E-

005

5.90

0.0355

CD 4.516E-

004

1

4.516E-

004

34.82

0.0002

BC 7.656E-

005

1

7.656E-

005

5.90

0.0355

BCD 2.641E-

004

1

2.641E-

004

20.36

0.0011

Curvature 2.278E-

004

1

2.278E-

004

17.57

0.0019

Significant

Residual 1.297E-

004

10

1.279E-

005

Lack of fit 6.094E-

005

7

8.705E-

006

0.38

0.8684

Not

Significant

Pure Error 6.815E-

005

3

2.292E-

005

Cor. Total 1.795E-

003 19



Since curvature is significant, this model can only be used for predicting only the

factorial points unless is augmented to RSM to estimate quadratic terms.

Table IV

ANOVA for Model that does not Adjust for Curvature

Source

Sum of

Square

df

Mean

of Sq.

F

Value

P-Value

Prob > F

Comment

Model 1.438E-

003

8

1.797E

-004

5.53

0.0056

Significant

A-

Yeast

Conc

1.891E-

004

1

1.891E

-004

5.82

0.0345

B –pH 1.266E-

004

1

1.266E

-004

3.89

0.0741

C-

Sugar

Conc.

1.266E-

004

1

1.266E

-004

3.89

0.0741

AB 1.266E-

004

1

1.266E

-004

3.89

0.0741

AC 7.656E-

006

1

7.656E

-005

2.36

0.153

CD 4.516E-

004

1

4.516E

-004

13.89

0.0033

BC 7.656E-

005

1

7.656E

-005

2.36

0.1531

BCD 2.641E-

004

1

2.641E

-004

8.13

0.0158

Residu

al

5.106E-

004

11

3.250E

-005

Lack of

of fit

4.419E-

004

8

3.609E

-006

1.58

0.3869

Not

Significant

Pure

Error

6.875E-

005

3

2.292E

-005

Cor.

Total

1.795E-

003

19

A. Unadjusted Model

In this model, the factorial model coefficients were fitted using all the data

(including the center points), this is the usual regression model since there was

significant curvature, the factorial points predictions will be biased higher or

lower by the center point Information. Since the quadratic coefficients needed to

model curvature were aliased with one another, curvature cannot be modeled and

curvature sum of square was included in lack of fit sum of square[21]. Since

curvature was significant, this model is not appropriate for prediction. The

ANOVA table for the unadjusted model is shown on table 4

B. 2 Level Factorial Model Selection Effects to include in model can be selected in one of two ways for factorial design.

For 2 levels factorial, half normal plot and Pareto chart are mainly used. Half

normal plot was used to select effects that were included in the model. Large

effects (absolute values) appear in the upper-right section of the plot. The lower –

left portion of the plot contains effects caused by noise rather than a true effect.

The half normal plot for 2k factorial design with center point is shown in fig.1.

Pareto

Fig. 1. Half normal plot 2k design with center points.

It can be seen from the plot that single effect of yeast concentration, PH and Initial

sugar concentration, interaction effects of Initial sugar concentration and

fermentation time, interaction effect of yeast concentration and PH, sugar

concentration and fermentation time were selected. From the plot, distinct

inflection point in the noise effect was noticed, which indicated a transaction

between significant (model) and Insignificant (noise) effects. The Pareto chart was

an additional graphic used to display the values of the effects. Thus Pareto chart

was equally used to check for one more significant effect that was not obvious on

the half normal plot. It displays the effects on their order of magnitude. The

Pareto chart is shown on fig. 2.

Design-Expert® SoftwareS.G

Error estimates

Shapiro-Wilk testW-value = 0.856p-value = 0.139A: Yeast ConcB: pHC: Sugar ConcD: Fermentation time

Positive Effects Negative Effects

Half-Normal Plot

Ha

lf-N

orm

al

% P

rob

ab

ilit

y

|Standardized Effect|

0.000 0.003 0.005 0.008 0.011

0

10

20

30

50

70

80

90

95

99

A

BCAB

ACBC

CD

BCD



Fig. 2. chart for 2k factorial design.

Any effect above the t-value was included in the model but those below the t-

value were considered to be caused by noise.

Since curvature is significant, the ANOVA for the model that adjusts for curvature

was selected from ANOVA table 3, it can be seen that F-value of 13.86 showed

that the model was significant. There is only 90.02% chance that a model F-value

this large could occur due to noise. Values of “Prob > F” less than 0.05 indicated

that model terms were significant. In this case, the single effect of yeast

concentration, pH, initial sugar concentration, interaction effects of yeast

concentration and pH, yeast concentration and initial sugar concentration, initial

sugar concentration and fermentation time, interaction effect of pH, sugar

concentration and fermentation time were significant. Lack of fit f-value of 0.38

showed it was not significant relative to pure error. There is 88.84% chance that a

“lack of fit F – value” this large could occur due to noise.

Adjusted R-squared value of 0.6560 was in reasonable agreement with predicted

R-squared of 0.5524. 80.08% of the total variations on the response values were

explained by the model. Adequate Precision of 7.518 that measures the signal to

noise ratio was high indicating adequate signal.

C. Model Equation

The model equation was presented only on coded form because it was not

hierarchical.

Specific gravity = +0.99 – 3.438E-003A + 2.812E-003AC + 2.813E -003BC –

5.312E – 003CD – 4.063E – 003BCD (1)

This model equation can be used to predict the factorial points only. The

coefficients of the terms show their relative contributions to the response. Table 5

shows the predicted values with the actual values according to their standard order.

Predicted values of center points include center point coefficient.

Table V

PREDICTED VALUES WITH THE ACTUAL VALUES ACCORDING TO STANDARD ORDER.

Standard Actual Predicted

Order Value Value 1 1.00 1.00

2 0.98 0.98

3 0.98 0.98

4 0.98 0.98

5 0.98 0.99

6 0.98 0.98

7 1.00 1.00

8 1.00 1.00

9 1.00 1.00

10 0.98 0.98

11 1.00 1.00

12 1.00 1.00

13 0.98 0.98

14 0.97 0.97

15 0.98 0.98

16 0.98 0.98

17 1.00 1.00

18 0.99 1.00

19 1.00 1.00

20 1.00 1.00

D. Interaction Effects

The interaction effects considered significant by ANOVA were studied. Fig. 3(a –

d) shows all the interaction effects. From fig 3a, it was seen that at higher pH

value, change in yeast concentration had no effect on the specific gravity of the

wine. At higher pH, increasing yeast concentration decreased the specific gravity

Design-Expert® SoftwareS.G

A: Yeast ConcB: pHC: Sugar ConcD: Fermentation time

Positive Effects Negative Effects

Pareto Chart

t-V

alu

e o

f |E

ffe

ct|

Rank

0.00

1.48

2.95

4.43

5.90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bonf erroni Limit 3.82734

t-Value Limit 2.22814

CD

BCD

A

B C AB

AC BC



of the wine. Fig. 3b shows that increase in yeast concentration had no effect at

higher initial sugar concentration but at lower initial sugar concentration, its

reduction decreased the specific gravity of the wine.

(a)

(b)

(c)

(d)

Fig. 3. Interaction effects of the process factors (a) pH with yeast concentration (b) yeast concentration

with initial sugar concentration (c) initial sugar concentration with pH (d) fermentation time with initial

sugar concentration.

From fig. 3c, it can be seen that pH had no effect on specific gravity of wine at

lower initial sugar concentration but at higher initial sugar concentration, increase

in pH increased the specific gravity of the wine. Fig. 3d shows that change in

initial sugar concentration had effect on the specific gravity of the wine at both

high and low fermentation time. Increase in initial sugar concentration increased

the specific gravity of the wine at low fermentation time, while increase in initial

Design-Expert® SoftwareFactor Coding: ActualSpecific gravity

Design Points

X1 = A: Yeast Concentration (g/l)X2 = B: pH

Actual FactorsC: Sugar Concentration (%brix) = 17.00D: Fermentation time (days) = 10.00

B- 5.00B+ 6.50

B: pH

5.00 6.00 7.00 8.00 9.00

A: Yeast Concentration (g/l)

Sp

ec

ific

gra

vit

y

0.975

0.98

0.985

0.99

0.995

1

1.005

2

Interaction


Design Points

X1 = A: Yeast Concentration (g/l)X2 = C: Sugar Concentration (%brix)

Actual FactorsB: pH = 5.75D: Fermentation time (days) = 10.00

C- 14.00C+ 20.00

C: Sugar Concentration (%brix)

5.00 6.00 7.00 8.00 9.00

A: Yeast Concentration (g/l)

Sp

ec

ific

gra

vit

y

0.975

0.98

0.985

0.99

0.995

1

1.005

2

Interaction


Design Points

X1 = B: pHX2 = C: Sugar Concentration (%brix)

Actual FactorsA: Yeast Concentration (g/l) = 7.00D: Fermentation time (days) = 10.00

C- 14.00C+ 20.00


5.00 5.30 5.60 5.90 6.20 6.50

B: pH

Sp

ec

ific

gra

vit

y

0.975

0.98

0.985

0.99

0.995

1

1.005Warning! Term involved in BCD interaction.

2

Interaction


Design Points

X1 = C: Sugar Concentration (%brix)X2 = D: Fermentation time (days)

Actual FactorsA: Yeast Concentration (g/l) = 7.00B: pH = 5.75

D- 7.00D+ 13.00

D: Fermentation time (days)

14.00 15.00 16.00 17.00 18.00 19.00 20.00


Sp

ec

ific

gra

vit

y

0.975

0.98

0.985

0.99

0.995

1

1.005Warning! Term involved in BCD interaction.

2

Interaction



sugar concentration decreased the specific gravity of the wine at high fermentation

time.

E. Surface Plots

3D surface plots with the contour plots shown in fig. 4(a – d) for all the significant

interaction effects confirmed by ANOVA. From fig 4a, it can be seen that as the

yeast concentration and pH decreased, specific gravity of the wine decreased. As

yeast concentration and initial sugar concentration were increased, the specific

gravity of wine decreased as shown in fig 4b. Fig. 4c shows the specific gravity of

the wine to decrease with decrease in pH and increase in initial sugar

concentration.

(a)

(b)

(c)


Design points above predicted value1

0.975

X1 = A: Yeast Concentration (g/l)X2 = B: pH

Actual FactorsC: Sugar Concentration (%brix) = 17.00D: Fermentation time (days) = 10.00

5.00

5.30

5.60

5.90

6.20

6.50

5.00

6.00

7.00

8.00

9.00

0.975

0.98

0.985

0.99

0.995

1

1.005

S

pe

cif

ic g

rav

ity

A: Yeast Concentration (g/l) B: pH



0.975

X1 = A: Yeast Concentration (g/l)X2 = C: Sugar Concentration (%brix)

Actual FactorsB: pH = 5.75D: Fermentation time (days) = 10.00

14.00

15.00

16.00

17.00

18.00

19.00

20.00

5.00

6.00

7.00

8.00

9.00

0.975

0.98

0.985

0.99

0.995

1

1.005

S

pe

cif

ic g

rav

ity

A: Yeast Concentration (g/l) C: Sugar Concentration (%brix)



0.975

X1 = B: pHX2 = C: Sugar Concentration (%brix)

Actual FactorsA: Yeast Concentration (g/l) = 7.00D: Fermentation time (days) = 10.00

14.00

15.00

16.00

17.00

18.00

19.00

20.00

5.00

5.30

5.60

5.90

6.20

6.50

0.975

0.98

0.985

0.99

0.995

1

1.005

S

pe

cif

ic g

rav

ity

B: pH C: Sugar Concentration (%brix)



(d)

Fig. 4. 3D surface with contour plot for (a) interaction of pH and yeast concentration, (b) interaction of

initial sugar concentration and yeast concentration, (c) initial sugar concentration and pH, (d)

fermentation time and initial sugar concentration

Fig 4d showed curvature at the centre which showed that decrease in fermentation

time and increase in initial sugar concentration decreased the specific gravity of

the wine to a point that further increase in initial sugar concentration and decrease

in fermentation time increased the specific gravity. Here, there was an optimum

operating conditions that favors decrease in specific gravity of the wine.

F. Cubic Plot

Cubic plot was necessary since interaction effect of three factors were significant.

Interaction effect of pH, initial sugar concentration and fermentation time is shown

in fig. 5.

Fig. 5. cubic plot of the interaction effect of pH, initial sugar concentration and fermentation time

From the plot, it can be seen that the lowest specific gravity of the wine which was

desired was 0.980438 at the uppermost right side at high initial sugar

concentration (C+), high fermentation time (D+) and low pH (B-). The highest

specific gravity of the wine was 1.00231 and occurred at the inner uppermost left

side of the cube at high fermentation time (D+), high pH (B+), and low initial

sugar concentration (C-).

G. Process Optimization

Minimization optimization was desired because specific gravity is inversely

proportional to ethanol content. Decreasing the specific gravity means increasing

the alcohol content of the wine which was desired. The optimum conditions were;

9g/l yeast concentration, pH of 5.0, initial sugar concentration of 20%brix and

fermentation time of 13 days with predicted specific gravity of 0.9767 at 0.945

desirability.

H. Validation of Optimal Condition

To validate optimum conditions, the alcoholic wine was produced at the specified

optimum conditions and the experimental value was compared with the predicted

value. The difference was calculated as percentage error. Table 6 shows the result

of the validation.



0.975

X1 = C: Sugar Concentration (%brix)X2 = D: Fermentation time (days)

Actual FactorsA: Yeast Concentration (g/l) = 7.00B: pH = 5.75

7.00

8.00

9.00

10.00

11.00

12.00

13.00

14.00

15.00

16.00

17.00

18.00

19.00

20.00

0.975

0.98

0.985

0.99

0.995

1

1.005

S

pe

cif

ic g

rav

ity

C: Sugar Concentration (%brix) D: Fermentation time (days)

Design-Expert® SoftwareFactor Coding: ActualSpecific gravityX1 = B: pHX2 = C: Sugar Concentration (%brix)X3 = D: Fermentation time (days)

Actual FactorA: Yeast Concentration (g/l) = 7.00

CubeSpecific gravity

B: pH

C:

Su

ga

r C

on

ce

ntr

ati

on

(%

bri

x)

D: Fermentation time (days)

B-: 5.00 B+: 6.50

C-: 14.00

C+: 20.00

D-: 7.00

D+: 13.00

0.990438

0.992938

0.982937

0.980438

0.983563

1.00231

1.00106

0.982313

4



Table VI

Validation of optimum conditions

Initial

Sugar

Concent.

(%brix)

Yeast

Conc.

(g/l)

pH Ferment.

Time

(days)

Specific

gravity

Error

(%)

Predicted

value

Experimental

value

20.0 9.0 5.0 13.0 0.9767 0.9781 0.14

From the table, it can be seen that the experimental value was in close range with

the predicted value. This was equally confirmed with the low error obtained. This

showed that the model can predict the process well.

Conclusion

The following conclusion can be drawn from this study:

That alcoholic wine can be produced from pawpaw juice using saccharomyces

cerevisae yeast.

That 2 level full factorial design with centre points can be used to test the

adequacy of linear model in predicting the response.

That pH, initial sugar concentration, and yeast concentration affect the quality

of wine produced.

Minimization optimization predicted specific gravity of the wine to be 0.9767

at pH of 5, initial sugar concentration of 20g/l, fermentation time of 13 days

and yeast concentration of 9g/l at desirability of 0.945.

The optimum conditions were validated with little error of 0.14% explaining

the adequacy of the model in predicting the process.

Linear model was established that can predict only the factorial points because

of significant curvature.

ACKNOWLEDGEMENT

The authors wish to thank PYMOTECH RESEARCH CENTRE AND

LABORATORIES ENUGU, ENUGU STATE NIGERIA for all their facilities

used throughout the research work.

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[21] Design expert software, version 8.0.7.1 guide.

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