b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6

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Mathematical modeling of thin-layer drying of fermented andnon-fermented sugarcane bagasse

Marcio A. Mazutti a,*, Giovani Zabot a, Gabriela Boni a, Aline Skovronski a,Debora de Oliveira a, Marco Di Luccio a, J. Vladimir Oliveira a, Maria Isabel Rodrigues b,Helen Treichel a,*,*, Francisco Maugeri b

a Department of Food Engineering, URI – Campus de Erechim, P.O. Box 743, CEP 99700-000, Erechim – RS, Brazilb Department of Food Engineering, Faculty of Food Engineering, University of Campinas – UNICAMP, P.O. Box 6121, CEP 13083-862,

Campinas – SP, Brazil

a r t i c l e i n f o

Article history:

Received 29 May 2009

Received in revised form

11 December 2009

Accepted 18 January 2010

Available online 2 February 2010

Keywords:

Solid-state fermentation

Sugarcane bagasse

Thin-layer

Mathematical modeling

Kluyveromyces marxianus NRRL

Y-7571

Effective diffusivities

* Corresponding author.** Corresponding author. Tel.: þ55 54 35209

E-mail addresses: mazutti@uricer.edu.br0961-9534/$ – see front matter ª 2010 Elsevidoi:10.1016/j.biombioe.2010.01.021

a b s t r a c t

This work reports hot-air convective drying of thin-layer fermented and non-fermented

sugarcane bagasse. For this purpose, experiments were carried out in a laboratory-scale

dryer assessing the effects of solid-state fermentation (SSF) on the drying kinetics of the

processing material. The fermented sugarcane bagasse in SSF was obtained with the use of

Kluyveromyces marxianus NRRL Y-7571. Drying experiments were carried out at 30, 35, 40

and 45 �C, at volumetric air flow rates of 2 and 3 m3 h�1. The ability of ten different thin-

layer mathematical models was evaluated towards representing the experimental drying

profiles obtained. Results showed that the fermented sugarcane bagasse presents

a distinct, faster drying, behavior from that verified for the non-fermented material at the

same conditions of temperature and volumetric air flow rate. It is shown that the fer-

mented sugarcane bagasse presented effective diffusion coefficient values of about 1.3

times higher than the non-fermented material. A satisfactory agreement between exper-

imental data and model results of the thin-layer drying of fermented and non-fermented

sugarcane bagasse was achieved at the evaluated experimental conditions.

ª 2010 Elsevier Ltd. All rights reserved.

1. Introduction content and temperature of the bed in large-scale bioreac-

Solid-state fermentation (SSF) involves the growth of

microorganisms on moist solid particles with a minimum of

free water in the inter-particle spaces. Due to the particular

environmental conditions imposed on the microorganism,

this fermentation technique has the potential to produce

selected microbial products better than submerged liquid

fermentation. However, SSF processes studied in the labo-

ratory are rarely scaled-up to commercial purposes. One of

the major barriers is the difficulty in controlling the water

000; fax: þ55 54 35209090(M.A. Mazutti), helen@urer Ltd. All rights reserved

tors [1–3].

In the recent years, mathematical models have been

developed as tools to help developing SSF bioreactor design and

establish proper operating strategies to overcome such diffi-

culties. More sophisticated models for packed-bed bioreactors,

which the bed remains static for long periods without the water

addition through the fermentation, taking into account the

simultaneous heat and mass transfer during the SSF, where the

evaporative cooling is the most efficient method to remove the

metabolic heat on the medium. However, as high is the water

.icer.edu.br (F. Treichel)..

Table 1 – Characterization of the substrates employed inthe fermentation medium formulation.

Sugarcane Bagasse Soybean Bran CSL

Moisture (wt%) 3.0 3.0 55.0

Protein (wt%) nd 42.5 18.8

Lipids (wt%) nd 8.5 1.0

Carbohydrate (wt%) 40.0 30.0 7.5

Fiber (wt%) nd 10.0 13.0

Ash (wt%) 2.4 6.0 4.5

nd: not determined.

b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6 781

evaporation through convection more accentuated is the

decreasing of water activity of the solids [3]. The mathematical

models should also take into account how the growth rate of

the microorganism is affected by the amount of water in the

solids [4]. In this case, the isotherm and/or the drying kinetic of

the solids must be known since the water balance equation

calculates the water content of the solids, while the driving

force for evaporation and the growth rate of the process

microorganism are related to the water activity.

Most of the models available in the literature assume

implicitly that the isotherm of the fermenting solids is equal to

that of the substrate itself. Marques et al. demonstrated that

the effect of the biomass on the isotherm needs also to be

considered in mathematical models of SSF bioreactors [1]. In

order to evaluate the effects of the fermentation process on the

drying characteristics of substrate is necessary to investigate

the influence of temperature and volumetric air flow rate on

the drying profiles of fermented and non-fermented material.

Thin-layer drying equations are used to estimate the time

course of drying process of several products and also to

generalize drying curves. Several researchers have proposed

numerous models for thin-layer drying of many agricultural

products [5,6]. Currently, there are three types of thin-layer

models used to describe the drying phenomenon. Namely,

theoretical model, which considers only the internal resistance

to moisture transfer between product and heating air, semi-

theoretical and empirical which consider only the external

resistance [7]. Theoretical model requires assumptions on the

geometry of a typical food, its mass diffusivity and conduc-

tivity; empirical model neglects the fundamentals of drying

process and presents a direct relationship between average

moisture and drying time by means of regression analysis [6].

In this context, the main objective of the present work is to

investigate the drying kinetics of the fermented and non-fer-

mented sugarcane bagasse, evaluating the effects of hot-air

inlet temperature and volumetric flow rate. In addition,

a mathematical model was applied to represent experimental

results of thin-layer drying kinetics of sugarcane bagasse.

2. Material and methods

2.1. Experimental material

Sugarcane bagasse samples were obtained from a local

distillery, manually crushed, dried at 60 �C for 24 h and

Table 2 – Mathematical models applied to the drying curves.

Model Number Model

1 MR¼ exp(�k� t)

2 MR¼ exp(�k� tn)

3 MR¼ exp(�(k� t)n)

4 MR¼ a� exp(�k� t)

5 MR¼ a� exp(�k� t)þb� exp(�k1

6 MR¼ a� exp(�k� t)þb

7 MR¼ a� exp(�k� t)þ(1�a)� exp

8 MR¼ exp(�k� tn)þb� t

9 MR¼ a� exp(�k� t)þb� exp(�k1

10 MR¼ aþb� tþ c� t2

maintained at �8 �C until the moment of the experimental

runs. Samples were observed to have macroscopic non-

homogeneities due to the fibrous structure of material. The

samples were composed of 30 g of dry bagasse, supplemented

with 15% (w/w) of soybean meal and 30% (w/w) of corn steep

liquor, which the individual composition of the substrates

shown in Table 1. The moisture content of the samples was

corrected to 65% (w/w) and autoclaved at 121 �C for 20 min.

The bulk density was measured to be 660 kg m�3 and 95% of

particles present a mean particle size in the range of

0.5–1.98 mm.

2.2. Microorganism, cell production and fermentations

The strain of Kluyveromyces marxianus NRRL Y-7571 was

maintained on YM agar medium (g L�1): yeast extract 3.0, malt

extract 3.0, peptone 5.0, glucose 10.0, agar 20.0, and sub-

cultured every 3 weeks. Cell production for pre-inoculum was

carried out in 50 mL test tubes with 10 mL of liquid YM

medium. The medium was inoculated with a loopful of stock

culture and incubated at 30 �C for 24 h. Medium for pre-inoc-

ulum contained (g L�1): sucrose 20.0, yeast extract 5.0, K2HPO4

5.0, NH4Cl 1.5, KCl 1.15, and MgSO4.7H2O 0.65. Each test tube

with YM medium was transferred to a 500 mL Erlenmeyer

flask with 100 mL of medium and incubated at 30 �C and

150 rpm for 24 h [8].

Fermented samples were obtained through fermentations

carried out in batch tray reactors. The flasks were inoculated

with 3 mL of cell suspension and incubated by 72 h in

a chamber with temperature and humidity control, the former

kept at 36 �C [8]. After the fermentation, samples were dried at

60 �C for 24 h and maintained at �8 �C prior to the experi-

mental runs.

References

Bruce [11]

Menges and Ertekin [5]

White et al. [12]

Henderson and Pabis [13]

� t) Henderson [14]

Togrul and Pehlivan [15]

(�k� a� t) Yaldiz et al. [16]

Midilli et al. [7]

� t)þc� exp(�k2� t) Togrul and Pehlivan [15]

Wang et al. [6]

0 20 40 60 80 100 120 140 160 1800.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 30°C 35°C 40°C 45°C

Moi

stur

e R

atio

Time (min)

0 20 40 60 80 100 120 140 160 1800.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 30°C 35°C 40°C 45°C

Moi

stur

e R

atio

Time (min)

0 10 20 30 40 50 60 70 80 90 100 110 120 1300.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 30°C 35°C 40°C 45°C

Moi

stur

e R

atio

Time (min)

a

b

c

Fig. 1 – Thin-layer drying curves of sugarcane bagasse:

a) sugarcane bagasse before the fermentation process at

volumetric air flow rate of 2 m3 hL1, b) sugarcane bagasse

after the fermentation process at volumetric air flow rate of

2 m3 hL1, c) sugarcane bagasse after the fermentation

process at volumetric air flow rate of 3 m3 hL1.

b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6782

2.3. Experimental apparatus

Drying experiments were carried out in a laboratory-scale

drier (Intecnial S.A. – Brazil). The drier consists basically of

three basic units, a fan providing the desired air velocity,

a heating and heating control unit and a drying chamber. The

heating control unit has an electrical heater (3 kW) placed

inside a duct. The product was spread in a thin layer on an

aluminum tray just 3 cm below a PT100 (Novus-Brazil)

thermo-resistance, located in the center of the chamber. The

dry bulb temperature was measured directly with the PT100

which was attained by electrical resistance heating and

controlled by the heating control unit. The air coming from

the heater at the desired temperature entered into the

chamber through openings on the right-side wall of the

chamber and flowed out through openings on the left-side

wall of the drying chamber. The required air flow rate for

drying was kept at the desired level at about 3 cm just above

the tray surface using a gas meter (LAO Ltda-Brazil). The

amounts of material were weighed on an analytical balance

(Gilbertini E254 with 0.001 g accuracy).

2.4. Experimental procedure

Drying experiments were performed at 30, 35, 40, and 45 �C

with volumetric inlet air flow rates of 2.0 and 3.0 m3 h�1 for the

samples of bagasse before and after the fermentation process,

respectively. The thickness of the sample layer was about

10 mm weighting 30 g. The weight of a tray with the sample

was measured with the analytic balance and periodically

recorded. For measuring the weight of the sample during the

experimentation, the tray with sample was taken out of the

drying chamber, weighed on the digital top pan balance and

placed back on the chamber; the digital balance was very close

to the drying unit. The drying procedure was proceeded until

no appreciable variation of the moisture content of the sample

was recorded. Triplicate runs were performed for experi-

mental conditions investigated in this work.

2.5. Theoretical considerations

2.5.1. Mathematical modeling of the thin-layer dryingkineticsFor investigation of drying characteristics of the fermented

and non-fermented sugarcane bagasse, it is important to try

to represent as accurate as possible the drying behavior. In

this study, the experimental drying data of fermented and

non-fermented sugarcane bagasse at different temperatures

and volumetric air flow rate were fitted using 10 commonly

used thin-layer drying models, listed in Table 2. In these

models, MR represents the dimensionless moisture ratio,

namely:

MR ¼ ðM�MeÞðM0 �MeÞ

(1)

where M is the moisture content of the product, M0 is the

initial moisture content of the product and Me is the equilib-

rium moisture content.

The values of Me are relatively small compared to M and M0

for long drying times and accordingly one can write:

Table 3 – Values of effective diffusivities obtained from different thin-layer drying conditions.

Description Effective Diffusivities (m2 s�1)

30 �C 35 �C 40 �C 45 �C

Non-fermented sugarcane bagasse at volumetric

air flow rate of 2 m3 h�1

1st Period 5.82� 10�9 7.22� 10�9 8.92� 10�9 9.67� 10�9

2nd Period 6.76� 10�11 1.35� 10�10 1.35� 10�10 3.38� 10�10

Fermented sugarcane bagasse at volumetric

air flow rate of 2 m3 h�1

1st Period 5.47� 10�9 9.38� 10�9 1.07� 10�8 1.32� 10�8

2nd Period 1.22� 10�10 1.35� 10�10 2.03� 10�10 2.70� 10�10

Fermented sugarcane bagasse at volumetric

air flow rate of 3 m3 h�1

1st Period 9.18� 10�9 1.12� 10�8 1.24� 10�8 1.47� 10�8

2nd Period 6.76� 10�11 2.03� 10�10 4.05� 10�10 5.40� 10�10

b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6 783

MR ¼ M

M0(2)

2.5.2. Correlation coefficients and error analysisThe ability of the tested mathematical model to represent the

experimental data was evaluated through the correlation

coefficient (R2) and the reduced chi-square (c2) parameter. The

higher the R2 and lower the c2 values, the better is the fitting

procedure. The chi-square (c2) can be calculated as follows:

c2 ¼PN

i¼1

�MRexp;i �MRpred;i

�2

N� z(3)

where MRexp,i and MRpred,i are the ith experimental and pre-

dicted moisture ratio, respectively, N is the number of obser-

vations and z is the number of parameters. In this study, the

nonlinear or linear regression analysis was performed using the

statistica software Statistica 7.0 (Statsoft Inc., Tulsa, OK, USA).

2.5.3. Calculation of effective diffusivitiesIt has been accepted that the drying characteristics of bio-

logical products in falling rate period can be described by

using Fick’s diffusion equation. The solution to this equation

Table 4 – Statistical results of the 10 models for the non-fermented sugarcane bagasse at volumetric air flow rateof 2 m3 hL1 and at different thin-layer dryingtemperatures.

ModelNumber

Statistical tests

30 �C 35 �C 40 �C 45 �C

1 R2¼ 0.8251 R2¼ 0.9767 R2¼ 0.7570 R2¼ 0.6473

c2¼ 0.0065 c2¼ 0.0021 c2¼ 0.0092 c2¼ 0.0126

2 R2¼ 0.9492 R2¼ 0.9766 R2¼ 0.9515 R2¼ 0.9287

c2¼ 0.0020 c2¼ 0.0011 c2¼ 0.0019 c2¼ 0.0027

3 R2¼ 0.9492 R2¼ 0.9766 R2¼ 0.9515 R2¼ 0.9287

c2¼ 0.0020 c2¼ 0.0011 c2¼ 0.0019 c2¼ 0.0027

4 R2¼ 0.8757 R2¼ 0.9607 R2¼ 0.8433 R2¼ 0.7765

c2¼ 0.0049 c2¼ 0.0019 c2¼ 0.0063 c2¼ 0.0085

5 R2¼ 0.9973 R2¼ 0.9982 R2¼ 0.9989 R2¼ 0.9968

c2¼<0.0001 c2¼<0.0001 c2¼<0.0001 c2¼<0.0001

6 R2¼ 0.9920 R2¼ 0.9918 R2¼ 0.9971 R2¼ 0.9951

c2¼ 0.0003 c2¼ 0.0004 c2¼ 0.0001 c2¼ 0.0002

7 R2¼ 0.9090 R2¼ 0.9787 R2¼ 0.8683 R2¼ 0.7914

c2¼ 0.0036 c2¼ 0.0010 c2¼ 0.0053 c2¼ 0.0079

8 R2¼ 0.9982 R2¼ 0.9981 R2¼ 0.9981 R2¼ 0.9930

c2¼ 0.0001 c2¼<0.0001 c2¼<0.0001 c2¼ 0.0003

9 R2¼ 0.9978 R2¼ 0.9989 R2¼ 0.9992 R2¼ 0.9968

c2¼ 0.0001 c2¼<0.0001 c2¼<0.0001 c2¼ 0.0002

10 R2¼ 0.9871 R2¼ 0.9988 R2¼ 0.9690 R2¼ 0.9400

c2¼ 0.0005 c2¼ 0.0001 c2¼ 0.0013 c2¼ 0.0024

developed by Crank can be used for various regularly shaped

bodies such as rectangular, cylindrical and spherical products,

and the form of Eq. (4) can be applicable for particles with slab

geometry, as is the case of the sugarcane bagasse, by

assuming uniform initial moisture distribution [9]:

MR ¼ 8p2

XNn¼0

1

ð2nþ 1Þ2exp

� ð2nþ 1Þ2p2Deff t

4L20

!(4)

where Deff is the effective diffusivity (m2 s�1), L0 is the half

thickness of slab (m). For long drying periods, Eq. (4) can be

further simplified to retain only the first term of the series

allowing re-writing Eq. (4) in a logarithmic form as follows:

lnMR ¼ ln8

p2� p2Defft

4L20

(5)

Diffusivities are typically determined by plotting experi-

mental drying data in terms of ln MR versus drying time in Eq.

(5), providing a straight line with the slope given by:

slope ¼ p2Deff

4L20

(6)

3. Results and discussion

3.1. Analysis of drying characteristics of fermented andnon-fermented sugarcane bagasse

The fermented and non-fermented sugarcane bagasse were

dried at 30, 35, 40, and 45 �C in the convective hot-air drier

with volumetric air flow rates of 2 and 3 m3 h�1, adopting thin-

layer thickness of about 10 mm. The initial moisture content

of sugarcane bagasse was about 0.65 kg water per kg of dry

matter. These experimental conditions were chosen because

they are commonly employed during the cultivation of K.

marxianus NRRL Y-7571 yeast in solid-state fermentation. The

moisture ratio versus drying time for fermented and non-

fermented sugarcane bagasse at the selected temperatures

and volumetric air flow rates are shown in Fig. 1.

Obviously, within a certain temperature range (30–45 �C),

an increase in drying temperature speeds up the drying

process, thus shortening the drying time for both, fermented

and non-fermented sugarcane bagasse. During the operation

of packed-bed bioreactors for SSF using sugarcane bagasse as

substrate, in which a raise in the moist solid temperature is

unavoidable, there is a drastic reduction in the water content

of the solid in the first operation hours, hence limiting the

process performance, since at low water activity levels the

growth is practically inhibited.

b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6784

Inspection of Fig. 1a and b shows the existence of differ-

ences between fermented and non-fermented sugarcane

bagasse for the volumetric air flow rate of 2 m3 h�1. The

moisture ratio experimentally observed for the non-fer-

mented sugarcane bagasse after 180 min drying was around of

0.37 for all temperatures investigated, while for the fermented

material at the same conditions a value of around 0.31 was

reached. On the other hand, comparison of the moisture ratio

for the fermented sugarcane bagasse obtained at the volu-

metric air flow rates of 2 and 3 m3 h�1 at 130 min, shows that

differences in the final values were not significant. Results

thus indicate that the fermented sugarcane bagasse can be

dried faster than the non-fermented one. This may be due to

the fact that the fermentation process by the K. marxianus

NRRL Y-7571 consumes the sugar present in the bagasse

(glucose, fructose, sucrose, amongst others), which can absorb

some water, hence retarding the drying of the material,

altering the drying isotherm of the material.

According to the results obtained, the effect of biomass

and/or the sugar consumption during the fermentation on the

drying process of sugarcane bagasse should be taken into

account in mathematical modeling step of SFF bioreactors so

as to allow safe predictions. Otherwise, not only will the

model fail to predict the changes in the water activity during

the fermentation, but also it will underestimate the amount of

water addition required. This may lead to unexpectedly poor

growth and problems may be more significant with solids for

which the water activity of the solid varies significantly with

water content, and with microorganisms whose growth rate is

more sensitive to small changes in the water activity [1].

Results obtained in the present study show that fermented

solids may lead to a drying isotherm quite distinct from that of

the substrate itself. Similar results are found in the literature

regarding the effects of the fermentation process on the

isotherm of the solids materials. For example, Marques et al.

Table 5 – Estimated parameters and statistical results obtained

Description

30 �C

Non-fermented sugarcane bagasse at volumetric

air flow rate of 2 m3 h�1

R2¼ 0.9973

c2¼<0.0001

a¼ 0.8826

k¼ 0.0153

b¼ 0.1299

k1¼�0.0054

Fermented sugarcane bagasse at volumetric

air flow rate of 2 m3 h�1

R2¼ 0.9979

c2¼ 0.0001

a¼ 0.9987

k¼ 0.0093

b¼ 0.0108

k1¼�0.0154

Fermented sugarcane bagasse at volumetric

air flow rate of 3 m3 h�1

R2¼ 0.9943

c2¼ 0.0003

a¼ 0.6044

k¼ 0.0523

b¼ 0.3836

k1¼ 0.0013

compared the isotherms for non-fermented and fermented

soybeans with Rhizopus oryzae, showing that in solid-state

fermentation the biomass and/or the products obtained

during the fermentation affects the isotherm of the ferment-

ing solids [1]. Corona et al. determined the isotherms at

various incubation times during the growth of Gibberella fugi-

kuori on a solid substrate consisting of wheat bran and soluble

starch [10].

3.2. Determination of effective diffusivities

In this study, two falling rate periods were observed (Fig. 1), one

corresponding to an approximately constant slope from which

the effective diffusion coefficient is calculated. Separation of

first and second falling periods was taken to be at about the

moisture ratio of 0.40. The values of effective diffusivities (Deff)

of fermented and non-fermented sugarcane bagasse for the

two falling periods are presented in Table 3. As expected, the

values of Deff increased with increasing drying temperature.

The effective diffusivities in the first falling period ranged from

5.82� 10�9 to 1.47� 10�8 m2 s�1, whereas for the second period

the variation was from 6.76� 10�11 to 5.40� 10�10 m2 s�1. The

effective diffusivities in the first period were in average 33

times greater than those found for the second period. This

occurs because the diffusion rate is directly proportional to the

moisture content of the solids, and as the drying takes place the

water content decreases thus diminishing the values of Deff. In

the second falling period the moisture content of sugarcane

bagasse approaches the equilibrium moisture content, leading

to low variations in Deff values.

Table 3 shows that the fermented sugarcane bagasse

affords higher values of Deff, about 1.3 times, than the non-

fermented sugarcane bagasse at the volumetric air flow rate of

2 m3 h�1 for the first falling period. Furthermore, upon

increasing the volumetric air flow rate from 2 to 3 m3 h�1 for

from different thin-layer drying conditions for model 5.

Model Parameters

35 �C 40 �C 45 �C

R2¼ 0.9982 R2¼ 0.9989 R2¼ 0.9968

c2¼<0.0001 c2¼<0.0001 c2¼<0.0001

a¼ 1.0033 a¼ 0.7795 a¼ 0.7377

k¼ 0.0092 k¼ 0.0222 k¼ 0.0280

b¼ 0.0050 b¼ 0.2281 b¼ 0.2820

k1¼�0.0199 k1¼�0.0023 k1¼�0.0015

R2¼ 0.9837 R2¼ 0.9987 R2¼ 0.9995

c2¼ 0.0010 c2¼<0.0001 c2¼<0.0001

a¼ 0.9766 a¼ 0.6965 a¼ 0.7472

k¼ 0.0179 k¼ 0.0374 k¼ 0.0359

b¼ 0.0672 b¼ 0.3083 b¼ 0.2589

k1¼�0.0080 k1¼�8.00� 10�5 k1¼�2.43� 10�4

R2¼ 0.9973 R2¼ 0.9923 R2¼ 0.9987

c2¼ 0.0002 c2¼ 0.0005 c2¼<0.0001

a¼ 1.0035 a¼ 0.8197 a¼ 0.7069

k¼ 0.0149 k¼ 0.0322 k¼ 0.0359

b¼ 0.0115 b¼ 0.1970 b¼ 0.2993

k1¼�0.0219 k1¼�0.0041 k1¼�0.0011

Table 6 – Effect of drying temperature on the parameters of the selected model (Model 5).

Description Equations

Non-fermented sugarcane bagasse at volumetric air flow rate of 2 m3 h�1 a¼ 0.0007 T3� 0.0806 T2þ 3.0343 T� 36.5600

k¼�0.00004 T3þ 0.0041 T2� 0.1540 Tþ 1.9258

b¼�0.0007 T3þ 0.0794 T2� 2.9944 Tþ 37.151

k1¼�0.00007 T3þ 0.0075 T2� 0.2826 Tþ 3.4941

Fermented sugarcane bagasse at volumetric air flow rate of 2 m3 h�1 a¼ 0.0008 T3� 0.0876 T2þ 3.1965 T� 37.2600

k¼�0.00004 T3þ 0.0047 T2� 0.1677 Tþ 1.9730

b¼�0.0006 T3þ 0.0702 T2� 2.5415 Tþ 30.1620

k1¼�0.00001 T3þ 0.0012 T2� 0.0411 Tþ 0.4329

Fermented sugarcane bagasse at volumetric air flow rate of 3 m3 h�1 a¼ 0.0009 T3� 0.1032 T2þ 4.0199 T� 50.6500

k¼�0.00009 T3þ 0.0107 T2� 0.4110 Tþ 5.2502

b¼�0.0009 T3þ 0.0101 T2� 3.9179 Tþ 50.2110

k1¼�0.00007 T3þ 0.0086 T2� 0.3290 Tþ 4.1207

b i o m a s s a n d b i o e n e r g y 3 4 ( 2 0 1 0 ) 7 8 0 – 7 8 6 785

the first falling period resulted in a raise of about 30% in Deff

values.

3.3. Modeling of drying curves

In attempt to represent the experimental data obtained, the

experimental moisture content data were used on dry weight

basis. These moisture content data at any time of drying

process obtained at different drying air temperatures and

volumetric air flow rate for the fermented and non-fermented

sugarcane bagasse were converted to the moisture ratio

values and fitted against drying time. Ten thin-layer drying

models were compared in terms of resulting statistical

parameters such as correlation coefficient (R2) and chi-square

(c2). Table 4 presents the statistical results of the different

models, where one can verify the comparison criteria used to

evaluate the fitting quality, namely R2 and c2 for the non-fer-

mented sugarcane bagasse at volumetric air flow rate of

2 m3 h�1 and at different thin-layer drying temperatures.

Experimental kinetic drying results indicated that the lowest

values of c2 and the highest values of R2 were obtained for

models 5 and 9. As model 9 has a greater number of adjustable

parameters and presented a similar performance compared to

model 5 in terms of fitting quality, it was rejected being model

5 chosen to describe the experimental data.

Table 5 presents the parameters estimated for model 5, as

well as the statistical results of the estimation procedure.

Although the experimental and predicted drying profiles are

not presented, a very good agreement between correlated and

experimental data was achieved, as can be checked by the

regression coefficients for each estimation and the low values

obtained for the chi-square. Thus, model 5 showed to be

capable of adequately describing the thin-layer drying

behavior of fermented and non-fermented sugarcane bagasse

at the experimental conditions investigated.

To take into account the effect of drying temperature on

the model parameters, namely a, k, b and k1, and attempting to

generalize the model, a regression analysis was applied to set

up the relationship between these parameters and the

temperature for the fermented sugarcane bagasse at the

volumetric air flow rates of 2 and m3 h�1 and for the non-

fermented sugarcane bagasse at volumetric air flow rate of

2 m3 h�1. The regression equations of these parameters

against drying temperature (�C) for each experimental condi-

tion are presented in Table 6. After comparing the experi-

mental moisture ratio values with predicted ones at any

particular drying condition for validation of the established

model, these values laid around a straight line (data not

shown), which means that, the generalized model is valid at

drying air temperatures of 30–45 �C for each condition or

volumetric air flow rate and for fermented and non-fermented

sugarcane bagasse.

4. Conclusion

The characteristics of drying kinetics of fermented and non-

fermented sugarcane bagasse with about 10 mm of thickness

in a hot-air dryer were evaluated and experimental data were

then represented by commonly employed models. Results

obtained showed that the fermented sugarcane bagasse has

a distinct behavior from that verified for the non-fermented

material at the same conditions of temperature and volu-

metric air flow rate. The fermented sugarcane bagasse dried

faster that the non-fermented material due to the consump-

tion of sugar during the fermentation. It was experimentally

observed that the fermented sugarcane bagasse showed

higher values of Deff, about 1.3 times, than the non-fermented

sugarcane bagasse. Among all tested models, model 5 was

showed to be the most suitable to describe the thin-layer

drying behavior of fermented and non-fermented sugarcane

bagasse for the experimental conditions studied.

Acknowledgements

The authors are grateful to CAPES (Project PROCAD/CAPES

0337/05-6), FAPERGS, CNPq, FEA/UNICAMP and URI-Campus

Erechim for financial support of this work and scholarships.

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