Abstract
Kraft pulping kinetic models are an important component of any fundamental continuity based continuous digester model. These models can be used to further develop our understanding, or as a framework to support the development of real-world control, estimation and optimization strategies. Effective models are tailored to a specific species of wood and must be applicable for a wide range of expected cooking conditions. In this work a series of experiments were conducted on hardwood Aspen chips for 5 different cooking conditions. Each series of cooks were interrupted at different time intervals to capture the dynamic response of the cook. The key chips and liquor components were measured and reconciled at each interval.
A dynamic model was then developed based on a simplification of a continuous digester model under batch conditions. This ensures continuity between the key assumptions governing both the batch kinetics model and the expanded continuous form. A kinetic model structure was adapted from the literature that quantifies all three accepted phases of lignin and cellulose degradation, i. e. the initial, bulk and residual phases as well as the effect of modern cooking practices such as intra-cook white liquor addition on the transition between the bulk and residual phases. Additionally, modifications were made to the kinetic model structure to reduce the overall number of states and to impose a floor limit on degradation, thereby reducing the overall complexity and computational burden. The model was then fit to the data using weighted least squares and simulation optimization techniques.
Funding source: FPInnovations
Funding statement: This research was funded by FPInnovations’ Member Companies.
-
Conflict of interest: The authors declare no conflicts of interest.
References
Alen, R., Hartus, T. (1988) UV Spectrophotometric Determination of Lignin from Alkaline Pulping Liquors. Cellul. Chem., 22:613–618.Search in Google Scholar
Andersson, N., Wilson, D. I., Germgard, U. (2003) An Improved Kinetic Model Structure for Softwood Kraft Cooking. Nord. Pulp Pap. Res. J., 18(2):200–209.10.3183/npprj-2003-18-02-p200-209Search in Google Scholar
Andersson, N., Wilson, D. I., Germgard, U., Lindstrom, T. (2001) Organic Matter Content in Black Liquor Inside and Outside Chips During Kraft Cooking. Pap. Puu, 83(7):538–541.Search in Google Scholar
Andrews, J. D., Alexander, E. G., Hart, P. W. (2015) Reconciling Material Balances with Laboratory Test Results: The Case of the Inorganic-to-Organic ratio in Black Liquor. Tappi J., 14(9):593–597.10.32964/TJ14.9.593Search in Google Scholar
Bhartiya, S., Dufour, P., Doyle III, F. J. (2003) Fundamental Thermal-Hydraulic Pulp Digester Model with Grade Transition. AIChE 49(2):411–425.10.1002/aic.690490212Search in Google Scholar
Chai, X. S., Luo, Q., Yoon, S. H., Zhu, J. Y. (2001) The Fate of Hexenuronic Acid Groups During Kraft Pulping of Hardwoods. J. Pulp Pap. Sci., 27(12):403–406.Search in Google Scholar
Crowe, C. M. (1986) Reconciliation of Process Flow Rates by Matrix Projection. AIChE 32(4):616–623.10.1002/aic.690320410Search in Google Scholar
Crowe, C. M., Garcia Campos, Y. A., Hrymak, A. (1983) Reconsiliation of Process Flow Rates by Matrix Projection. AIChE 29(6):881–888.10.1002/aic.690290602Search in Google Scholar
Gullichsen, J., Fogelholm, C. Chemical Pulping 6A. Fapet Oy, Helsinki, Finland, 1999.Search in Google Scholar
Gustafson, R. R., Sleicher, C. A., McKean, W. T., Finlayson, B. (1983) Theoretical Model of the Kraft Pulping Process. Ind. Eng. Chem. Process Des. Dev. 22(1):87–96.10.1021/i200020a016Search in Google Scholar
Harkonen, E. J. (1987) A mathematical model for two-phase flow in a continuous digester. Tappi J. 70:122–126.Search in Google Scholar
Jiang, Z.-H., Audet, A., Van Lierop, B., Berry, R. (2004) Kappa number testing with better repeatability and at lower cost. In: Pulp and Pater Technical Association of Canada (PAPTAC) 90th Annual Meeting, Montreal, QB, Canada.Search in Google Scholar
Lindgren, C. T., Lindstrom, M. E. (1996) The Kinetics of Residual Delignifications and Factors Affecting the Amount of Residual Lignin During Kraft Pulping. J. Pulp Pap. Sci., 22(8):290–294.Search in Google Scholar
Mansfield, S. D., Weineisen, H. (2007) Wood Fiber Quality and Kraft Pulping Efficiencies of Trembling Aspen (Populus tremuloides Michx) Clones. J. Wood Chem. Technol., 27:135–151.10.1080/02773810701700786Search in Google Scholar
Mathworks Inc., Optimizaing a Simlulation or Ordinary Differential Equation, [Online]. Available: https://www.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html. [Accessed 12 04 2019].Search in Google Scholar
Michelsen, F. A. (1995) A Dynamic Mechanistic Model and Model-Based Analysis of a Continuous Kamyr Digester. PhD Thesis, University of Trodheim, Norway.Search in Google Scholar
Papp, J. (1971) Potentiometric Determination of Sulphur Compounds in White, Green and Black Liquors with Sulphide Ion-Selective Electrode. Cellul. Chem. Technol., 5:147–159.Search in Google Scholar
Radiotis, T., Sullivan, J., MacLeod, M., Syed, S., O’Hagan, T. (2007) Improved methods for measuring residual effective alkali in Kraft black liquors. Part 2: Comparison of titration methods. In: Tappi 2007 Engineering, Pulping and Environmental Conference. Jacksonville, FL.Search in Google Scholar
Sixta, H., Rutkowska, E. W. (2006) Modeling of Eucalyptus Globulus Kraft Pulping. Lenzing AG Process Innovation.Search in Google Scholar
Smith, C. C., Williams, T. J. (1974) Mathematical Modeling, Simulation and Control of the Operation of Kamyr Continuous Digester for Kraft Process. Tech. Re. 64, PLAIC, Purdue Univerisy, West Lafayette, IN.Search in Google Scholar
Sullivan, J., Douek, M. (1994) Determination of carbohydrates in wood, pulp and process liquor samples by high-performance anion-exchange chromatography with pulsed amperometric detection. J. Chromatogr. 671(1-2):339–350.10.1016/0021-9673(94)80259-9Search in Google Scholar
Wetter, M., Wright, J. (2004) A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization. Build. Environ. 39:989–999.10.1016/j.buildenv.2004.01.022Search in Google Scholar
Wisnewski, P. A., Doyle III, F. J., Kayihan, F. (1997) Fundamental Continuous-Pulp-Digester Model for Simulation and Control. AIChE 43(12):3175–3192.10.1002/aic.690431206Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Chemical pulping
- Mapping variation of handsheet properties within loblolly pine trees
- A simplified kinetic model for modern cooking of aspen chips
- Bleaching
- Bleaching of bagasse-pulp using short TCF and ECF sequence
- Mechanical pulping
- Energy efficiency in mechanical pulping – definitions and considerations
- Paper technology
- Development of ash condensation performance of paper materials via saccharides and Nano HAP application
- Effects of calcium silicate synthesized in situ on Fiber loading and paper properties
- Production of fines from refined kraft pulp by fractionation with micro-perforated screens
- Dynamic-head space GC-MS analysis of volatile odorous compounds generated from unbleached and bleached pulps and effects on strength properties during ageing
- Composite paper from an agricultural waste of bagasse sugarcane and pineapple leaf fibre: a novel random and multilayer hybrid fibre reinforced composite paper
- Paper physics
- Phenomenological analysis of constrained in-plane compression of paperboard using micro-computed tomography Imaging
- Paper chemistry
- Preparation and characterization of tung oil-rosin-based polyester internal sizing agent
- Coating
- Research on brightening modification of molecular sieves coated fly ash based on alkaline melting hydrothermal method
- Application of modified cellulose nanofibrils as coating suspension on recycled paper using size press
- Chemical technology/modifications
- Novel calcium carbonate filler for cellulose industry
Articles in the same Issue
- Frontmatter
- Chemical pulping
- Mapping variation of handsheet properties within loblolly pine trees
- A simplified kinetic model for modern cooking of aspen chips
- Bleaching
- Bleaching of bagasse-pulp using short TCF and ECF sequence
- Mechanical pulping
- Energy efficiency in mechanical pulping – definitions and considerations
- Paper technology
- Development of ash condensation performance of paper materials via saccharides and Nano HAP application
- Effects of calcium silicate synthesized in situ on Fiber loading and paper properties
- Production of fines from refined kraft pulp by fractionation with micro-perforated screens
- Dynamic-head space GC-MS analysis of volatile odorous compounds generated from unbleached and bleached pulps and effects on strength properties during ageing
- Composite paper from an agricultural waste of bagasse sugarcane and pineapple leaf fibre: a novel random and multilayer hybrid fibre reinforced composite paper
- Paper physics
- Phenomenological analysis of constrained in-plane compression of paperboard using micro-computed tomography Imaging
- Paper chemistry
- Preparation and characterization of tung oil-rosin-based polyester internal sizing agent
- Coating
- Research on brightening modification of molecular sieves coated fly ash based on alkaline melting hydrothermal method
- Application of modified cellulose nanofibrils as coating suspension on recycled paper using size press
- Chemical technology/modifications
- Novel calcium carbonate filler for cellulose industry