CONTINUOUS DIGESTER BENCHMARK MODEL V1.0 A MATLAB^{®} 5.2/5.3 TOOLBOX © 19962000 IETek The objective of the toolbox is to provide a benchmark continuous digester process model for systems engineering research, including but not limited to controller design, identification, model reduction, diagnostic and monitoring. It is expected that investigators in this area will use the toolbox to generate ideas and solution approaches to old and new problems alike, and will be able to compare results on a common basis. The model presented here captures most of the typical process complexities and dynamic interactions. However, it is not intended for equipment design, process optimization or any other predictive purposes for commercial implementations. Additional background on the process can be found in the reference : "A Kamyr Continuous Digester Model for Identification and Controller Design", F. Kayihan, M.S. Gelormino, E.M. Hanczyc, F.J. Doyle and Y. Arkun, 13th IFAC World Congress, San Francisco, 30 June  5 July, 1996. For questions and suggestions, please contact fkayihan@ietek.net. PROCESS DESCRIPTION Continuous digesters are very complex vertical tubular reactors, used in the pulp and paper industry to remove lignin from wood chips. Aqueous solution of sodium hydroxide and hydrosulfide, called white liquor, is used to react with porous and wet wood chips. Usually, continuous digesters are separated into multiple reaction and extraction zones to carry out the specific process sequence. Depending on the production needs of a pulp mill and on the state of the art of digester design at the time of installation, there may be numerous differences between digesters. However, common to all is the general sequence of transport and reaction processes that govern the overall operation. Due to the complexities of these physical and chemical phenomena and the fact that wood chips are nonuniform and constantly changing, regulating product quality in a digester is a nontrivial task. The particular digester design chosen for this toolbox is the dual vessel EMCC (extended modified continuous cooking) arrangement. A brief description of the process is provided to familiarize the toolbox user with the basics. Detailed analysis and descriptions are available in textbooks and PhD theses on the subject. Wet chips are steamed to remove air in the pores and fed into the impregnation vessel (IV) together with white liquor. In the impregnation vessel, white liquor penetrates into the chips and equilibrates with initial moisture for about 30 minutes depending on the production rate. In the IV, both chips and liquor move in the cocurrent downward direction. From the IV, the chips are carried into the top section of the digester with hot liquor that brings the mixture to the desired reaction temperature. The top section of the digester, referred to as the cook zone, is a cocurrent section where the main reactions take place. Chips react from inside out owing to the significant internal pore volume and associated surface area. Therefore, overall reaction rates depend on the concentration levels of entrapped liquor and the diffusion rates from free liquor that replenish the active ingredient holdup in the pores. Spent liquor saturated with dissolved solids at the end of the cook zone is extracted for chemical recovery elsewhere in the mill. Chips follow into the MCC (modified continuous cooking) and the EMCC zones, now countercurrent to fresh dilute white liquor which simultaneously continue mild delignification reactions and extract valuable inorganic solids from the pores of chips. As packed reactors, digesters are very unique in that the packing (main ingredient of the process) is continuously in motion, nonuniform in size and undergo through variable compaction both with respect to conversion and differential head pressure. Extent of reaction, defined through the blowline (exit) Kappa number, is the major performance measurement. Other important factors are the yield of the process and the fiber properties of the final product. Although various operating conditions may yield the same Kappa number, important fiber properties like strength are reaction path dependent.
ASSUMPTIONS Rigorous fundamental approaches to digester modeling are continuing to advance by quantifying more of the transport phenomena and operational details associated with the process. On the other hand, the benchmark model represents a muchsimplified approach due to the following assumptions:
MODEL EQUATIONS The material and enthalpy balances for the cook zone, where both solid and liquor phases are moving in the same direction, are where
and
The corresponding equations for countercurrent flow zones are Reaction rates for solids are specified as with reaction rate constants k_{Ai} = k_{Aoi} exp (E_{Ai}/RT) and k_{Bi} = k_{Boi} exp (E_{Bi}/RT). Liquor component rates are related through stoichiometric relationships as Where R_{LG }= R_{S1} + R_{S2 }, R_{C }= R_{S3} + R_{S4} + R_{S5} and R_{S }= R_{LG} + R_{C}
At the mixing zone of the impregnation vessel the liquor balance and the density dilutions, due to moisture in wet chips, are and j = 1, …, 4
The model equations are not solved as PDEs but as ODEs with the following interpretation of the plug flow sections:
CSTR approximations for cocurrent and countercurrent zones.
Let the CSTR count for any section be: n = 1, … , N where numbering starts from the top. Then, residence times for chips and liquor are and For the cook zone, solid and liquor material and the thermal balances for any CSTR are and For the countercurrent zones the corresponding equations are: and
PARAMETER DEFINITIONS, UNITS and NUMERICAL VALUES
GUIDELINES FOR DYNAMIC ANALYSIS AND CONTROL RELATED VARIABLES
DIGESTER SCHEMATICS REPRESENTING SIMPLIFIED MODELING APPROACH (nominal operating rate conditions) © IETek 19962002, all rights reserved.

