Home / Regular Issue / JST Vol. 29 (4) Oct. 2021 / JST-2633-2021


Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Surendra Pratap Singh, Mohammad Jawaid, Bhoomika Yadav and Mohd Supian Abu Bakar

Pertanika Journal of Science & Technology, Volume 29, Issue 4, October 2021

DOI: https://doi.org/10.47836/pjst.29.4.33

Keywords: Biomass, black liquor, evaporation, viscosity, wheat straw

Published on: 29 October 2021

Infrared (IR) evaporation characteristics of Weak Soda Black Liquor (WSBL) were determined at five different temperatures of 80, 90, 100, 110 and 120oC. The effect of constant temperature on evaporation rate and moisture content (on a dry basis) of 1.5 gm approx. WSBL tests were contemplated and required a careful time frame of IR dissipation to vanish the dampness content at a different consistent temperature. The dissipation rate expanded with expanding infrared temperature. Therefore, different numerical models, such as Page and Logarithmic, Henderson, Pabis and Lewis, were utilised to fit the experimental data properly. A Gaussian model equation was developed for evaporation rate and moisture fraction of black liquor. The probable empirical parameters, along with the relating of reduced chi-square (X2), Residual Sum of Square (RSS), and coefficients of determination (adjusted R2) from non-linear regression analysis of all the numerical model equations, were examined. In addition, the effect of evaporation temperature on the water removal rate, the effective diffusion coefficient and activation energy were also estimated. The effective diffusion coefficient ranges from 2.67 × 10–10 m2/s to 10.4 × 10–10 m2/s, and the activation energy was 39.19 kJ/mol. The statistical indicators (chi-square and determination coefficient) showed that the Decay model equation and Gaussian equation are the most suitable models for describing the evaporation process of WSBL.

  • Ahou, K., Emmanuel, A. N., Patrice, K., & Benjamin, Y. (2014). Modelling of rough rice solar drying under natural convection. European Scientific Journal, 10(3), 141-156.

  • Alriols, M. G., Tejado, A., Blanco, M., Mondragon, I., & Labidi, J. (2009). Agricultural palm oil tree residues as raw material for cellulose, lignin and hemicelluloses production by ethylene glycol pulping process. Chemical Engineering Journal, 148(1), 106-114. https://doi.org/10.1016/j.cej.2008.08.008

  • Amin, N., Sabli, N., Izhar, S., & Yoshida, H. (2019). Sago wastes and its applications. Pertanika Journal of Science and Technology, 27(4), 1841-1862.

  • Bajpai, P. (2017). Evaporation of black liquor. In Pulp and Paper Industry (pp. 39-66). Elsevier. https://doi.org/10.1016/b978-0-12-811103-1.00003-6

  • Bhargava, V. K. (1966). Drying of wheat grain in thin layers (Doctoral dissertation). University of British Columbia, Canada.

  • Bruce, D. M. (1985). Exposed-layer barley drying: Three models fitted to new data up to 150°C. Journal of Agricultural Engineering Research, 32(4), 337-348. https://doi.org/10.1016/0021-8634(85)90098-8

  • Chen, X. D. (2009). On a relationship proposed for thin layer drying of porous materials. Chemical Engineering and Processing: Process Intensification, 48(11-12), 1583-1584. https://doi.org/10.1016/j.cep.2009.10.001

  • Crank, J. (1975). The mathematics of diffusion. Oxford University Press. https://doi.org/10.1021/ja01562a072

  • Darvishi, H., Azadbakht, M., Rezaeiasl, A., & Farhang, A. (2013). Drying characteristics of sardine fish dried with microwave heating. Journal of the Saudi Society of Agricultural Sciences, 12(2), 121-127. https://doi.org/10.1016/j.jssas.2012.09.002

  • Datta, A. K., & Anantheswaran, R. C. (2001). Handbook of microwave technology for food applications. In A. K. Datta & R. C. Anantheswaran (Eds.), Marcel Dekker, Inc. All Rights Reserved (1st Ed.). Taylor & Francis. https://doi.org/https://doi.org/10.1201/9781482270778

  • Do, N. H., Pham, H. H., Le, T. M., Lauwaert, J., Diels, L., Verberckmoes, A., Do, N. H. N., Tran, V. T., & Le, P. K. (2020). The novel method to reduce the silica content in lignin recovered from black liquor originating from rice straw. Scientific Reports, 10(1), 1-11. https://doi.org/10.1038/s41598-020-77867-5

  • Gögüs, F., & Maskan, M. (2001). Drying of olive pomace by a combined microwave-fan assisted convection oven. Nahrung - Food, 45(2), 129-132. https://doi.org/10.1002/1521-3803(20010401)45:2<129::AID-FOOD129>3.0.CO;2-T

  • Goodell, E. G., & Point, S. (1933). Black liquor recovery process and apparatus (Patent No. US1931536A). Patented Oct 31, 1933.

  • Guo, H. (2011). A simple algorithm for fitting a Gaussian function [DSP tips and tricks]. IEEE Signal Processing Magazine, 28(5), 134-137.

  • Haghsheno, M., & Kouhikamali, R. (2020). Numerical investigation of effective parameters of falling film evaporation in a vertical-tube evaporator. Heat Transfer, 50(3), 2764-2792. https://doi.org/10.1002/htj.22004

  • Hatibaruah, D., Baruah, D. C., & Sanyal, S. (2013). Microwave drying characteristics of assam ctc tea (Camellia assamica). Journal of Food Processing and Preservation, 37(4), 366-370. https://doi.org/10.1111/j.1745-4549.2011.00656.x

  • Hurter, R. W. (1991). Nonwood plant fiber characteristics. Tappi Press.

  • Karlsson, E. (2020). Evaluation of sodium salt scaling in black liquor evaporators using existing process data. Nordic Pulp and Paper Research Journal, 35(4), 516-532. https://doi.org/10.1515/npprj-2020-0038

  • Liu, X., Qiu, Z., Wang, L., Cheng, Y., Qu, H., & Chen, Y. (2009). Mathematical modeling for thin layer vacuum belt drying of panax notoginseng extract. Energy Conversion and Management, 50(4), 928-932.

  • Low, E. S., & Ong, P. (2020). On the formulation of metaheuristic algorithm-based approximation approach for non-linear ordinary differential equations with application to heat exchanger problem. Pertanika Journal of Science and Technology, 28(4), 1221-1265. https://doi.org/10.47836/pjst.28.4.06

  • Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1996). The thin-layer drying characteristics of garlic slices. Journal of Food Engineering, 29(1), 75-97. https://doi.org/10.1016/0260-8774(95)00062-3

  • Meziane, S., Kadi, H., & Lamrous, O. (2006). Kinetic study of oil extraction from olive foot cake. Grasas y Aceites, 57(2), 175-179. https://doi.org/10.3989/gya.2006.v57.i2.34

  • Mujumdar, A. S. (2007). Book review: Handbook of industrial drying (3rd Ed.). Drying Technology, 25(6), 1133-1134. https://doi.org/10.1080/07373930701399224

  • Naqvi, M., Yan, J., & Dahlquist, E. (2010). Black liquor gasification integrated in pulp and paper mills: A critical review. Bioresource Technology, 101(21), 8001-8015. https://doi.org/10.1016/j.biortech.2010.05.013

  • Nasir, N. A. F. M., Jamaluddin, J., Zainudin, Z., Busheri, M. M., Adrus, N., Azim, F. S. S., & Hasham, R. (2020). The effect of alkaline treatment onto physical, thermal, mechanical and chemical properties of Lemba leaves fibres as new resources of biomass. Pertanika Journal of Science and Technology, 28(4), 1531-1547. https://doi.org/10.47836/pjst.28.4.21

  • Overhults, D. G., White, G. M., Hamilton, H. E., & Ross, I. J. (1973). Drying soybeans with heated air. Transactions of the American Society of Agricultural Engineers, 16(1), 112-113. https://doi.org/10.13031/2013.37459

  • Ranganathan, A. (2004). The levenberg-marquardt algorithm. Tutoral on LM algorithm, 11(1), 101-110.

  • Sandu, C. (1986). Infrared radiative drying in food engineering: A process analysis. Biotechnology Progress, 2(3), 109-119. https://doi.org/10.1002/btpr.5420020305

  • Sanjuán, N., Lozano, M., García-Pascual, P., & Mulet, A. (2003). Dehydration kinetics of red pepper (Capsicum annuum L var Jaranda). Journal of the Science of Food and Agriculture, 83(7), 697-701. https://doi.org/10.1002/jsfa.1334

  • Thakor, N. J., Sokhansanj, S., Sosulski, F. W., & Yannacopoulos, S. (1999). Mass and dimensional changes of single canola kernels during drying. Journal of Food Engineering, 40(3), 153-160. https://doi.org/10.1016/S0260-8774(99)00042-4

  • Tütüncü, M. A., & Labuza, T. P. (1996). Effect of geometry on the effective moisture transfer diffusion coefficient. Journal of Food Engineering, 30(3-4), 433-447. https://doi.org/10.1016/s0260-8774(96)00028-3

  • Yagcioglu, A. K., Degirmencioglu, A., & Cagatay, F. (1999, May 26). Drying characteristics of laurel leaves under different drying conditions. In 7th International Congress on Agricultural Mechanization and Enerdy (pp. 565-569). Adana, Turkey.

  • Zogzas, N. P., Maroulis, Z. B., & Marinos-Kouris, D. (1996). Moisture diffusivity data compilation in foodstuffs. Drying Technology 14(10), 2225-2253. https://doi.org/10.1080/07373939608917205

ISSN 0128-7680

e-ISSN 2231-8526

Article ID


Download Full Article PDF

Share this article

Recent Articles