## Optimization of Ethanol Production Process from Cassava Starch by Surface Response

199

subsequent fermentation of alcohol with Saccharomyces cere- visiae, based on 2^{2 }experimental designs with three central points and using statistical software to define the experimental

Table 1 shows the comparison between the kinetic model (equation 1) and the quadratic regression model (equation 2) on the average error and the adjustment coefficient (R^{2}).

area through a response surface.

# Results and Discussion

## Kinetic model of acid hydrolysis

The standard deviation between the model and experi- mental data of cassava starch degradation was 4.12 % and the experimental data and the quadratic regression was 5.22 % (Figure 2). The most significant variation was founded as t = 0 due to the independent term of the quadratic model with respect to the kinetic model and experimental data.

Figure 1 shows the experimental results of starch degradation with respect to time. It is noted that the starch concentration decreases following the linear behavior, as demonstrated by the linear correlation obtained with adjustment coefficient of 0.9911 (R^{2}).

From the experimental data of starch concentration and using the equation 9, it was found an average value of k being

= 0.542169 h^{-1}, substituting this value and obtained k average c o n s i d e r i n g [ C s i ] = 1 7 0 g / L , t h e r e s u l t i n g k i n e t i c m o d e l w a s :

[Cs] = 170 e^{-0.542169t }

(1)

Performing the analysis at concentrations of 150 and 190 g/L, the average value of k`s were 0.523491 and 0.541425 respectively, whose standard deviation between the three val- ues of k was 0.010575. The proposed model in equation 1 was employed in this study.

From the data obtained and considering an initial concen- tration of starch from 170 g/L was quantified the value of the reaction rate (r) for different intervals of reaction (Table 2) being obtained as r_{avg }= 76.0318 g/h L for this process.

Using the model established in equation 1, a simulation of the process was done, considering the concentrations used in the experimental design 150, 170 and 190 g/L. Figure 3 shows the dynamic behavior of the cassava starch degradation, according to the points in the experimental design.

It can be observed that starch degradation was significant- ly reduced after 4 h, being less than 2 % in the firth hour. This allowed to establish that the processing time used in testing the experimental design is 4.5 h, due to the conversion was sig- nificantly reduced, impacting directly in a reduction of energy consumption.

## Optimization of acid hydrolysis process

A second order regression was carried out using the value of starch concentration with respect to time in order to com- pare with the kinetic model and with the experimental data, obtaining:

The results of experimental design were analyzed using the statistical software NCSS-2004 [19]. For the purpose of defin- ing an experimental space it was determined the optimization trend by adjusting the second order of the results (equation 3), obtaining an adjustment of 99.09 %.

## [Cs] = 169.673 - 67.533 * t + 7.774 * t ^{2 }

(2)

Table 1. Evaluation of average error and adjustment coefficient for different models.

5.5

Model

Average Error

R2

Ln [Cs] = 5.1628 - 0.5566t

Quadratic Regression

5.15 %

0.9955

5

R^{2 }= 0.9911

Kinetic Model

3.28 %

0.9982

4.5

Ln [Cs] (g/L)

4

3.5

3

2.5

0

1

2

3

4

5

Time (h)

Fig. 1. Behavior of starch degradation caused by the effect of acid hydrolysis with H_{2}SO_{4}.

Time (h)

Rate of reaction g/h L

0.0

92.1687

0.5

70.3544

1.0

52.9345

1.5

39.2934

2.0

33.8388

2.5

26.9206

3.0

18.6223

3.5

11.6179

4.0

10.7329

4.5

7.3912

Table 2. Rate of reaction for acid hydrolysis function within a spe- cific timeframe.