Generalization of drying curves in conductive/convective drying of cellulose

Generalization of drying curves in conductive/convective drying of cellulose

M.Stenzel^I; O.C.Motta Lima^II; N.C.Pereira^II; E.S.Mendes^II

^IDEQ/UNIOESTE

^IIDEQ/UEM, Av. Colombo 5790, Bl. D-90, CEP 87020-900, Phone: [phone], Fax: [phone], Maringá, PR, Brazil

^{Address to correspondence}

ABSTRACT

The objective of this work is to analyze the possibility of applying the drying curves generalization methodology to the conductive/convective hot plate drying of cellulose. The experiments were carried out at different heated plate temperatures and air velocities over the surface of the samples. This kind of approach is very interesting because it permits comparison of the results of different experiments by reducing them to only one set, which can be divided into two groups: the generalized drying curves and the generalized drying rate curves. The experimental apparatus is an attempt to reproduce the operational conditions of conventional paper dryers (ratio of paper/air movement) and consists of a metallic box heated by a thermostatic bath containing an upper surface on which the cellulose samples are placed. Sample material is short- and long-fiber cellulose sheets, about 1 mm thick, and ambient air was introduced into the system by a adjustable blower under different conditions. Long-fiber cellulose generalized curves were obtained and analyzed first individually and then together with the short-fiber cellulose results from Motta Lima et al. (2000 a,b). Finally, a set of equations to fit the generalized curves obtained was proposed and discussed.

Keywords: drying, cellulose drying, drying curves generalization.

INTRODUCTION

This work is a study of some aspects of the conductive/convective drying of paper (cellulose) sheets over heated surfaces, which was developed at the Separation Processes Laboratory (DEQ/UEM). The experiments were carried out at different heated plate (drying) temperatures and velocities of ambient air over the surface of the samples and had the objective of analyzing the possibility of applying the drying curves generalization methodology to conductive/convective hot plate drying of short- and long-fiber cellulose.

This kind of approach is very interesting because it permits comparison of the results of different experiments by reducing them to only one set, which can be divided into two groups: the generalized drying curves, which relate dimensionless moisture content to dimensionless drying time, and the generalized drying rate curves, which relate normalized (dimensionless) drying rate to sample moisture content.

Motta Lima (2000) and Motta Lima et al. (2000a,b) studied the application of this methodology to natural and forced convection drying of short-fiber cellulose with very good results, especially for the generalized drying curves.

In this work, the generalized drying curves approach was applied to data on long-fiber cellulose from Stenzel et al. (2001) and Stenzel (2001). It was also extended to both long-fiber and the short-fiber cellulose results of Motta Lima et al. (2000a,b), and unique generalized drying and drying rate curves were developed. Finally, a set of equations to fit the generalized curves obtained for the two situations studied in this work was proposed and discussed.

METHODOLOGY

Sample material was individual handsheets (15 x 10 cm) of long- and short-fiber cellulose, approximately 1 mm thick (weight basis: 850-900 g/m²) with no filler and an ambient moisture content ranging from 7 to 10 % (d.b.). The moisture content (d.b.) of the sheets was determined from their constant weight in a oven at 105 ° C.

The experimental apparatus (Figure 1) consists in a metallic box heated by a thermostatic bath containing an upper surface on which the paper samples are placed. Ambient air was flowed through the system is under a forced convection regime provided by an adjustable blower to adjust the air velocity close to the surface of the samples to that usually used in paper dryer machines in order to better reproduce the operational conditions of this type of dryer. Heating surface temperatures were adjusted and periodically verified with a contact thermocouple, air velocities over sample surfaces were measured with a portable anemometer and samples were periodically weighed on an analytical balance to measure their water content.

The drying process conditions were as follows: 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. The drying rate curves were drawn by deriving drying curves (finite differences), according to the procedure described in Motta Lima et al. (1999) and Stenzel et al. (2001). Details on obtaining drying curves and data on short-fiber cellulose drying curves can be found elsewhere in the works of Motta Lima et al. (1999) and Almeida and Motta Lima (2000).

RESULTS

Long-Fiber Cellulose (LFC)

The long-fiber cellulose drying and drying rate curves were drawn for three air velocities (2, 4 and 6 m/s) and seven plate temperatures (60, 65, 70, 75, 80, 85 and 90 ºC) (Stenzel, 2001). Figures 2 to 7 show the results for 60, 75 and 90 ºC.

The generalized drying curve for these data is shown in Figure 8. As in Motta Lima (2000) and Motta Lima et al. (2000a,b), the curve was adjusted according to the Page (1949) model, Eq. (1).

where

Fit results are shown in Eq. (2), Figure 9 and Table 1.

As can be seen, the results obtained for the drying curves generalization are very good.

For the drying rate curves generalization the Hodges (1982) approach was used. The normalized drying rate (NDR) is defined as the ratio between the instantaneous rate and the maximum drying rate (assumed here to be the constant drying rate period, N_C), Eq. (3).

Figure 10 shows the generalized drying rate curve and Eq. (4), Figure 11 and Table 2, the fit results for the Hodges (1982) (or NDR) approach.

The results obtained are as not as good as those for the drying curves, but they are acceptable for drying rate estimation.

Long- and Short-Fiber Cellulose (LFC and SFC)

As the proposal of generalized curves showed good results for the drying of short-fiber cellulose (Motta Lima, 2000 and Motta Lima et al., 2000a,b) and for the long-fiber cellulose, as seen above, it was decided to verify the possibility of fitting both types of data on cellulose to only one curve, for each type of generalization. The results are shown in Figures 12 and 13, respectively.

Equations 5 (Page, 1949 model) and 6 (Hodges, 1982 model), Tables 3 and 4 and Figures 14 and 15 show, respectively, the fit results for generalized drying and drying rate curves. As can be seen, these results are also very good (again better for the drying curves) and indicate that this proposal can be satisfactorily applied, regardless of cellulose type.

CONCLUSIONS

The approach of generalized drying curves can be successfully applied to long-fiber cellulose in the same manner as to short-fiber cellulose, with better results for the drying curves than for the drying rate curves.

The drying curves generalization for both long- and short-fiber cellulose also showed good results that can be applied when there is no need for or a lack of specific information on the kind of cellulose with which we are working.

NOMENCLATURE

Received: March 5, 2002

Accepted: August 30, 2002

• Almeida, A.M. and Motta Lima, O.C. (2000). Alguns Aspectos da Transferência de Calor na Secagem Condutiva/ /Convectiva de Papel. Paper presented and Abstract Proceedings of the XXVI Encontro Anual de Iniciação Científica UEL/UEM/UNIOESTE/UEPG, September 2000, Londrina-PR, Brazil.
• Hodges, C.R. (1982). Laboratory Drying Study and Applications for Paper Machine Drying. Drying’82, 99-105.
• Motta Lima, O.C. (2000). The Methodology of Generalized Drying Curves Applied to Paper Drying. Acta Scientiarum Ciências Exatas e Tecnológicas, 22, No. 5, Dez/2000, 1173-1177.
• Motta Lima, O.C., Massarani, G., Pereira, N.C. and Machado, M.A.L.S. (1999). Estudo sobre a Secagem de Papel VI: Secagem Condutiva/Convectiva com Ar Ambiente em Convecção Forçada. In Proceedings of the XXVI COBRASP, Teresópolis-RJ, Brazil, 2, 429-436.
• Motta Lima, O.C., Pereira, N.C. and Machado, M.A.L.S. (2000a). Generalized Drying Curves in Conductive/ /Convective Paper Drying. Brazilian Journal of Chemical Engineering, 17, No. 04-07, December 2000, 539-548.
• Motta Lima, O.C., Pereira, N.C. and Machado, M.A.L.S. (2000b). Generalized Drying Rate Curves in Conductive/ /Convective Paper Drying. Acta Scientiarum Ciências Exatas e Tecnológicas, 22, No. 5, Dez/2000, 1229-1233.
• Page (1949), cited in Motta Lima, O.C. (2000). The Methodology of Generalized Drying Curves Applied to Paper Drying. Acta Scientiarum Ciências Exatas e Tecnológicas, 22, No. 5, Dez/2000, 1173-1177.
• Stenzel, M., Motta Lima, O.C., Almeida, A.M. and Pereira, N.C. (2001). Secagem Condutiva/ Convectiva de Celulose com Ar Ambiente em Convecção Forçada. In Proceedings of the XXVIII COBRASP (ENEMP 2000), Teresópolis-RJ, Brazil, 453-460.
• Stenzel, M. (2001). Estudo da Secagem de Celulose de Fibra Longa e do Papel KLAPAK para Embalagens. M.Sc. Thesis, PEQ/DEQ-UEM Maringá-PR, Brazil, 109p.

Publication Dates

• Publication in this collection
  19 Mar 2003
• Date of issue
  Mar 2003

History

• Received
  05 Mar 2002
• Accepted
  30 Aug 2002