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## Brazilian Journal of Chemical Engineering

##
*Print version* ISSN 0104-6632*On-line version* ISSN 1678-4383

### Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000

#### http://dx.doi.org/10.1590/S0104-66322000000400018

**GENERALIZED DRYING CURVES IN CONDUCTIVE/CONVECTIVE PAPER DRYING**

**O.C.Motta Lima, N.C.Pereira and M.A.L.S.Machado**

Chemical Engineering Department (DEQ),(UEM),

Av. Colombo 5790 , Bloco D90 , CEP 87020-900 , Maringá - PR , Brasil

Phone: (44)261-4323, Fax: (44)263-3440,

E-mail: Oswaldo@deq.uem.br

*(Received: October 10, 1999 ; Accepted: April 06, 2000)*

Abstract- This work presents a study related to conductive/convective drying of paper (cellulose) sheets over heated surfaces, under natural and forced air conditions. The experimental apparatus consists in a metallic box heated by a thermostatic bath containing an upper surface on which the paper samples (about 1 mm thick) are placed. The system is submitted to ambient air under two different conditions: natural convection and forced convection provide by an adjustable blower. The influence of initial paper moisture content, drying (heated surface) temperature and air velocity on drying curves behavior is observed under different drying conditions. Hence, these influence is studied through the proposal of generalized drying curves. Those curves are analyzed individually for each air condition exposed above and for both together. A set of equations to fit them is proposed and discussed.

Keywords: drying, paper drying, generalized drying curves.

**INTRODUCTION**

This work presents a study related to some aspects in conductive/convective drying of paper (cellulose) sheets over heated surfaces under natural and forced air conditions, developed at the Separation Processes Laboratory (DEQ/UEM). The objective is to study contact paper drying and bring out the influence of some variables upon the drying process.

Hence, the influence of initial paper moisture content, drying (heated surface) temperature and air velocity in the behavior of the drying curves is observed under different operational conditions. Also, it is verified if the proposal of generalized (universal) drying curves discussed by Motta Lima (1999) can be also applied to those drying results. These universal curves are analyzed individually for each air condition exposed above and for both together. Furthermore, a set of equations is proposed and discussed to fit them.

**REVIEW**

Brunello (1992) presents a compilation of papers where the drying of grains is analyzed under a generalized point of view. In these works a reduced moisture, define as the ratio of the moisture content (X) to the initial one (X_{0}) or to the initial unbounded moisture content (X_{0} – X_{e}), was correlated to a reduced time, defined as the ratio of the product of drying rate (dX/dt) at t = 0 and time, to the initial moisture content (X_{0}) or unbounded moisture content (X_{0} – X_{e}).

Günther et al. (1984) and Brunello et al. (1992) have studied the behavior of fixed bed drying of cellulose pulp at different operational conditions of temperature, humidity and velocity of the drying air, and for different bed thickness and initial moisture content (but with the same dry basis mass of pulp). They verified that there were no influence of the initial moisture content of the samples and proposed a modification of the dimensionless time, now defined as a ratio to the solid initial mass of water, to eliminate the bed thickness influence. Brunello et al. (1992) also analyzed and proposed a set of equations to correlate air temperature and velocity effects in the initial rate of drying.

Krasnikov (1980) and Ciesielczyk (1996) brought a discussion on the methods of drying curves generalization based upon the regularity of moisture transfer during drying processes. Based on it, Ciesielczyk (1996) proposed a universal drying curve relating the same dimensionless moisture (X / X_{0}) to the dimensionless time, defined from the first period constant drying rate, the time, and X_{0} . It was tested on the experimental results of ammonium sulfate, silica-gel and sand drying in a batch fluidized drier.

Motta Lima (1999) applied successfully the Ciesielczyk (1996) proposal to paper (cellulose) drying inside an oven, studying the influence of initial moisture content, drying (heated surface) temperature and sheet thickness on the behavior of drying curves kinetics.

This paper extends Motta Lima (1999) work to conductive/convective paper drying.

**METHODS**

**Material**

Individual handsheets (15 x 10 cm) of short-fiber cellulose (eucalyptus) approximately 1 mm thick, with no filler, and ambient moisture content ranging from 7 to 10 % (d.b.). The sheets moisture content (d.b.) was determinate by getting constant weight in a oven at 105 °C.

**Drying Schematic Model and Experimental Apparatus**

The schematic model used in this study is based in the simplification of the industrial cylindrical geometry in a flat (rectangular) one, since the cylinder radius is in a great measure than the thickness of the sheets. The model is presented in Figure 1.

The experimental apparatus consists in a metallic box heated by a thermostatic bath containing an upper surface on which the paper samples are placed. The system is submitted to ambient air under two different conditions: natural convection, Figure 2, and forced convection provide by a adjustable blower, Figure 3. Heating surface temperatures were adjusted and periodically verified with a contact thermocouple, air velocities over samples surfaces with a portable anemometer (forced convection) and samples were periodically weighted in a analytical scale to measure their water content.

**Drying Curves**

Drying process was carried out for the two ambient air conditions and the drying curves were built according to the variable (effect) being studied, as follow.

**(a) Natural Convection**

Initial paper sheets moisture content ranging from 130 to 170 % (d.b.) and drying (heated surface) temperature from 60 to 90 °C .

**(b) Forced Convection**

Initial moisture content of about 150 % (d.b.), drying temperature (heated surface) ranging from 60 to 90 ºC and drying air velocity from 2 to 6 m/s.

Details about experimental apparatus and drying curves construction can be found elsewhere in the works of Motta Lima et al. (1998) and Motta Lima et al. (1999).

**RESULTS AND DISCUSSION**

**Drying Curves**

**(a) Natural Convection**

Under the proposed conditions above mentioned, drying curves are presented in Figures 4 to 7 (Motta Lima et al., 1998), for the effects of initial moisture content and drying temperature.

** (b) Forced Convection**

Drying curves for the above conditions are presented in Figures 8 to 11 (Motta Lima et al., 1999), for the effects of drying temperature and air velocity.

From the analysis of these results, Motta Lima et al. (1998) and (1999) show:

(1) the weak influence of initial moisture content on the kinetics (drying rates) of the process ;

(2) the strong dependence of drying process times and kinetics upon drying temperature ;

(3) and that drying air velocity effects were important only for the constant drying rate period, with practically no influences on the falling rate one.

**Generalized Drying Curves**

The proposed methodology of generalized drying curves discussed by Motta Lima (1999) is applied to the drying results. Once again, a dimensionless moisture content (Y = X / X_{0}) is correlated to a dimensionless time variable (t_{Ad }= N_{C }.t / X_{0}).

**(a) Natural Convection**

Table 1 and Figure 12 present, respectively, the values for X_{0} and N_{C} (R^{2} ³ 0.999) obtained from the experimental drying curves and the generalized drying curve for natural convection, built as described above.

**(b) Forced Convection**

For his turn, Table 2 and Figure 13 present the values for X_{0} and N_{C} (R^{2} ³ 0.999) obtained from the experimental drying curves for the three studied air velocities and the respective generalized drying curve.

**(c) General**

Due to the good individuals results for each ambient air condition, the possibility of mixing the effects of both regimes in a unique generalized drying curve was tried. The result can be seen in Figure 14.

As one can see, the results for each air condition, and for all combined (general case), were in good agreement, showing that the proposal of generalized drying curves discussed by Motta Lima (1999) can also be successfully applied in the analysis of conductive/convective paper drying kinetics.

**Generalized Drying Curves Modeling**

Equation 1, proposed by Page (1949), was used to model the generalized drying curves, initially for each air condition, and secondly, for the general case. The results are shown below.

Y = exp (- k where: Y = X / X and t | (1) |

**(a) Natural Convection**

Y = exp [- (1.840).t (R | (2) |

**(b) Forced Convection**

Y = exp [- (1.554).t (R | (3) |

**(c) General**

Y = exp [- (1.707).t (R | (4) |

As can be seen, fitting results show a good performance for the three studied situations and Page (1949) model could be successfully used to simulate these generalized drying curves.

**Constant Rate Drying ( N _{C }) Dependence upon Temperature and Air Velocity**

The dependence of first period constant rate drying (N_{C }[min^{-1}]) upon surface temperature (T_{sf} [^{o}C]), for natural convection, and temperature and air velocity (v_{air }[m/s]), for forced convection, was analyzed, resulting into the following expressions (Eqns. 5 and 6). Figures 18 and 19 show these results, respectively.

N (R | (5) |

(R | (6) |

**CONCLUSIONS**

The generalized (universal) drying curves results confirm that this proposal is a very interesting tool also in the study of conductive/convective drying processes. More specifically in this case, it was shown that the influence of the three operational variables here studied (initial moisture content, surface temperature and air velocity) on paper (cellulose) drying could be analyzed with the generalized drying curve only.

Once again, Pages equation fitting results for the universal curves show a very good performance, that recommends its use for modelling these curves.

**NOTATION**

d.b. | dry basis | [-] |

F | statistics, º ratio between the mean of the square of the predicted values and the mean of the square of the estimation residuals | [-] |

K | "drying constant", equation 1 | [-] |

n | parameter of equation 1 | [-] |

N_{C } | constant rate of drying | [1/T] |

t | drying time | [T] |

t_{Ad } | dimensionless drying time (= N_{C}.t / X_{0}) | [-] |

T_{air} | drying air temperature | [q] |

T_{sf} | heating surface temperature (drying temperature) | [q] |

X | moisture content (d.b.) | [-] |

X_{0 } | initial moisture content (d.b.) | [-] |

X_{e} | equilibrium moisture content (d.b.) | [-] |

Y | dimensionless moisture content (= X / X_{0}) | [-] |

z | spatial variable | [L] |

**REFERENCES**

Brunello, G. ; Secagem no DEQ-EPUSP, RBE, Caderno de Engenharia Química, N__o__ especial 4 (outubro), pp. 25, 39, 81 and 115 (1992). [ Links ]

Brunello G. , Paiva, J.L. , Günther, P.A.S. and Bianchini, E.C. ; Estudo da Cinética de Secagem de Pasta Celulósica em Leito Fixo: Modelo de Capilaridade, in Secagem no DEQ-EPUSP, RBE, Caderno de Engenharia Química, N__o__ especial 4 (outubro), 147-152 (1992). [ Links ]

Ciesielczyk, W. ; Universal Drying Curve, Drying96 (IDS96), A , 103-110 (1996). [ Links ]

Günther, P.A.S. , Brunello, G. , Bianchini, E.C. and Paiva, J.L. ; Secagem de Pasta Celulósica em Leito Fixo, Proceedings of the VI COBEQ, Campinas, BR, 318-329 (1984). [ Links ]

Krasnikov, V.V. ; The Methods of Analysis and Calculation of Drying Kinetics, Drying80, 1, ed. A.S. Mujundar, Hemisphere Publishing Corporation, 57-62 (1980). [ Links ]

Motta Lima, O. C. , Machado, M.A.L.S. and Oliveira, V.M. ; Estudo sobre a Secagem de Papel V: Secagem Condutiva/Convectiva com Ar Ambiente, Proceedings of the XXV COBRASP, 2, ed. CCET/DEQ-UFSCar, São Carlos, BR, 647-653 (1998). [ Links ]

Motta Lima, O. C. ; Generalized Drying Curves in Paper Drying, Abstracts Proceedings and presented at the II ENPROMER, ago/set, Florianópolis, BR, (1999). [ Links ]

Motta Lima, O. C. , Massarani, G. , Pereira, N.C. and Machado, M.A.L.S. ; Estudo sobre a Secagem de Papel VI: Secagem Condutiva/Convectiva com Ar Ambiente em Convecção Forçada, Proceedings of the XXVI COBRASP, ed. , 2, Teresópolis, BR, - (1999). [ Links ]

Page G. E. (1949), cited in Motta Lima, O. C. , Machado, M.A.L.S. and Oliveira, V.M. ; Estudo sobre a Secagem de Papel V: Secagem Condutiva/Convectiva com Ar Ambiente, Proceedings of the XXV COBRASP, 2, ed. CCET/DEQ-UFSCar, São Carlos, BR, 647-653 (1998). [ Links ]