1996-2000 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.

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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 non-trivial 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 co-current 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 co-current 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 counter-current 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 blow-line (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.



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 much-simplified approach due to the following assumptions:

  1. Non-porous solid chips and free liquor constitute the only two phases in the system.
  2. The two phases are in local thermal equilibrium.
  3. There are no mass or thermal diffusion limitations within the phases.
  4. The impregnation vessel is represented by instant mixing (dilution) followed by same transport delay for both phases.
  5. In the digester vessel compaction profile is static and known.
  6. Both phases in the digester move as plug flows with local space velocities based on compaction and volumetric flowrates.
  7. Reaction kinetics follow the suggestions of the "Purdue Model" but the heats of reactions are ignored.
  8. Reactions and mixing during the process affect solid and liquor densities but not volumes, i.e., volumes are conserved.
  9. Wood extractives are ignored and initial moisture is instantly mixed with white liquor at the feed conditions.
  10. Delignification reactions occur only in the digester vessel.
  11. Changes in heaters, trim liquor additions and other process inputs are instantaneous.



The material and enthalpy balances for the cook zone, where both solid and liquor phases are moving in the same direction, are




The corresponding equations for countercurrent flow zones are

Reaction rates for solids are specified as

with reaction rate constants kAi = kAoi exp (-EAi/RT) and kBi = kBoi exp (-EBi/RT).

Liquor component rates are related through stoichiometric relationships as

Where RLG = RS1 + RS2 , RC = RS3 + RS4 + RS5 and RS = RLG + RC


At the mixing zone of the impregnation vessel the liquor balance and the density dilutions, due to moisture in wet chips, are


j = 1, , 4


The model equations are not solved as PDEs but as ODEs with the following interpretation of the plug flow sections:


cocurrent2.jpg (12684 bytes)

countercurrent2.jpg (12792 bytes)

CSTR approximations for co-current 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


For the cook zone, solid and liquor material and the thermal balances for any CSTR are


For the countercurrent zones the corresponding equations are:






symbol description nominal rate values slow rate fast rate
  (if different) (if different)
A Digester cross section area (same for all zones) [m2] 1    
b EAC Stoichiometric coefficient for mass of effective alkali (EA) consumed/mass of reacting carbohydrate 0.45    
b EAL Stoichiometric coefficient for mass of effective alkali consumed/mass of reacting lignin 0.20    
b HSL Stoichiometric coefficient for mass of hydrosulfide (SH-) consumed/mass of reacting lignin 0.05    
EAi Activation energies, i = 1,,5 [kJ/gmol] [29.3 115 34.7 25.1 73.3]    
EBi Activation energies, i = 1,,5 [kJ/gmol] [31.4 37.7 41.9 37.7 167]    
h Volume fraction of liquor, compaction [0.85 0.80], 0.81, 0.82    
K# Kappa number = 654*lignin mass/total solid mass 92.3, 45.1, 29.7 92.3, 45.2, 29.7 92.6, 45.3, 29.7
kAoi Pre-exponential factors [m3 liq/min/kgEA] 0.356 1.31x1011 25.3 6.37 5240]    
KBoi Pre-exponential factors [m3 liq/min/(kgEA kgEA)1/2] 11.2 1.68 112 43.1 2.9x1016    
q Reaction rate effectiveness factor 0.65    
r Lj Liquor component densities, j = 1,,4 [kg/m3 of liquor], indices are respectively: effective alkali (EA), hydrosulfide (HS), dissolved solids and dissolved lignin      
r Loj White liquor component densities [kg/m3 of liquor] [100 30 0 0]    
r Si Solid component densities, i = 1,,5 [kg/m3 of solid], indices are respectively: high reactivity lignin, low reactivity lignin, carbohydrate, galactoglucomman and araboxylan      
r Soi Solid component densities in wood chips [kg/m3 of solid] [150 225 675 75 375]    
r Si Unreactive portion of solid component densities in wood chips [kg/m3 of solid] [0 0 420 18 0]    
r w Water density [kg/m3] 1000    
R Gas constant [kJ/gmol oK] 0.0083144    
RLj Reaction rate of liquor component j [(kg/min)/(m3 of liquor)]      
RSi Reaction rate of solid component i [(kg/min)/(m3 of solid)]      
TC Cook zone heater temperature [oK] 425 414 435
Te Emcc zone heater temperature [oK] 415 412 431
Tm Mcc zone heater temperature [oK] 420 409 425
t L CSTR liquor residence time [min]      
t S CSTR solid residence time [min]      
n L Volumetric liquor flowrate [m3/min] [0.090 0.090 0.080] [0.0459 0.04483 0.04073] [0.18 0.1895 0.163]
n S Volumetric solid (chips) flowrate [m3/min] 0.0267 0.0133 0.0533
u L Liquor space velocity [m/min]      
u S Chips space velocity [m/min]      
wo Chip moisture fraction (based on total mass) 0.50 0.50 0.50
  IV time delay [minutes] 30 60 15
  cook zone height [meters] 13.71429    
  mcc zone height [meters] 16.84    
  emcc zone height [meters] 17.78    
  upper extract flowrate [m3/min] 0.09 0.0459 0.18



Y & D: possible measurements
(performance and disturbance)
All volumetric (or mass) flowrates
White liquor densities (EA and HS) (dissolved solids and lignin measurement technologies are available but not commercial yet)
Chip moisture
Upper and lower extract densities (see white liquor)
Blow line (product) Kappa number
U: possible manipulated variables Upper extract flowrate
Trim white liquor flowrates (mcc and emcc)
Tcook, Tmcc and Temcc
D: possible disturbances Chip flowrate and properties
White liquor (including trims) densities
Dilution flowrate




(nominal operating rate conditions)

digester1.jpg (76153 bytes)

IETek 1996-2002, all rights reserved.


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