C. Sandrock and Philip L. de Vaal

Organisation and address

Department of Chemical Engineering, University of Pretoria, Pretoria 0001, South Africa



process modelling, batch digester, digester control, kinetic parameters.


Effective control of the sulphite pulp digestion process is limited by a number of factors. These include the following:

1. Difficulty of measuring the controlled variable - the degree of polymerisation (DP) of the cellulose in the wood pulp. Measurement of DP inferred from a viscosity measurement of the pulp is normally used.

2. For practical reasons, a single, off-line laboratory analysis to determine DP is performed during a cook. The analysis is time-consuming and leaves very limited scope for control action once the result of the analysis is known.

3. Due to extreme operating conditions, continuous measurement of pH,  that would enable on-line inference of the DP, is not practical and would not lead to a cost-effective solution to the problem. 

4. Adding to this the fact that the process is carried out in a series of batch digesters results in a challenging control problem. 

Use  of a model-based inferential technique to estimate DP offers a feasible methodology to control the process. A simplified fundamental model with adjustable parameters was developed and its accuracy to predict DP based on given operating conditions was developed and tested using available plant data.

Use of this model enables provision of adaptive response to changing conditions on the plant by optimal adjustment of the kinetic parameters in the plant model to fit the measured characteristics of the digester. Using parameters forming part of fundamental relationships, realistic bounds can be placed on the parameters enabling a better understanding of the behaviour of the model when compared with a purely empirical relationship.

By automating this optimisation process, the controller becomes independent, requiring no human intervention for day-to-day operation. The controller was implemented on a working digester and data were collected to compare its performance with that of a legacy controller which is based on a simplified model (S-factor model), which is not performing adequately on the plant.

The fundamental model-based controller outperforms the legacy controller when comparing the control predictions made by the new controller to the control actions of the current controller.


In the production of high-quality pulp, it is important to ensure tight control of the viscosity of the pulp. Effective control of the digestion process is limited by a number of factors.  The main factor is the difficulty of measuring the controlled variable the degree of polymerisation (DP) of the cellulose in the pulp.  This property is not readily measured,  the viscosity of the pulp is measured and used to infer the DP.  Models also exist that relate the pH of the cooking liquor to the viscosity, but due to extreme operating conditions, continuous measurement of pH is not practical and would not lead to a cost-effective solution to the problem. The process that is being investigated utilises batch digesters, which makes it difficult to use classical controllers due to the lack of continuous process data. 

Use  of a model-based inferential technique to estimate DP offers a feasible methodology to control the process. A simplified fundamental model with adjustable parameters was developed and its accuracy to predict DP based on given operating conditions was developed by Killian (1999). The focus of this study is the implementation of this controller, and verification of the predictions the controller makes for the manipulated variable (MV) the maximum temperature of the cook process.


2.1. Wood composition
Wood is composed of many organic substances, many of which can be used for commercial purposes.  Being a living entity, a tree consists of living cells, an organic framework for these cells and various substances which are used to transport nutrients and waste (Kollman and Ct, 1968). The structural integrity of a tree is supplied by cells with rigid cell walls consisting of the polymers cellulose and hemicellulose bound together by lignin, an organic resin (Watson, 1992).

The most useful of these components is cellulose, which is the main structural component of the cell wall (Rydholm, 1965). Cellulose is an organic polymer which is linear and possesses a certain stiffness that is desirable in living plants and in pulp-based products.

Being a polymer, many of the properties of cellulose is determined by its chain length.  A convenient way of referring to the chain length is by using a degree of polymerisation (DP) value instead of the actual chain length.  The DP is formally defined as the number of repeating units of anhydroglucose in the polymer and is an average value for a specific sample (Rydholm, 1965).

2.2. Pulp
Pulp is a collective name for fibres liberated from wood or similar organic material.  In industrial terms, pulp refers almost exclusively to high-cellulose content pulps suitable for producing paper, textiles and other products.  The process whereby pulp is obtained from the raw material is known as pulping.

There are several methods for extracting fibres from organic material, but the most commercially important process used is chemical pulping. Chemical pulping produces what is known as a dissolving pulp.  This is pulp with a very high cellulose content (more than 90%) and a narrow range of DP value (typically between 40 and 90).

2.3. Chemical Pulping
During the production of dissolving pulps, using the sulphite pulping method, high pressure and an acidic environment is used to dissolve the lignin binding cellulose fibres together in wood.  This process is known as 'cooking' the wood.  The reactor used for this process is known as the digester, as the wood is 'digested' to form pulp.

During the digestion process, the wood is packed into the digester, cooking liquor (an acidic solution of SO2 in water) is added and the digester is pressurised.  Next, the temperature and pressure inside the reactor are taken through pre-determined profiles. The main MV in the process is steam flow to an external heat exchanger that is responsible for raising the temperature inside the digester by heating a circulation stream that is pumped through it. Additionally, pressure release at a certain maximum pressure is included for safety.

Inside the digester, the liquor impregnates the chips and dissolves the lignin.  At the same time, the chain length of the cellulose fibres in the wood is reduced.

2.4. Measurements
The variables that are important in the production of pulp are the DP, which has already been mentioned, the composition of the wood, the strength of the liquor and the temperature and pressure profiles that the digester are taken through. The temperature and pressure profiles are easily measured through traditional methods. The composition of the wood and the strength of the liquor are more difficult to measure, but both of these variables are usually accepted as being relatively constant with time.

The DP, which is most often the controlled variable in a controlled cook system, is hard to measure online.  The laboratory tests used to measure this value mostly infer the value from a viscosity test.  This is difficult to reproduce with sufficient accuracy online.

A further inferential measurement could be made from the pH of the solution in the digester, but the costly measuring equipment would have to be replaced frequently due to the harsh conditions inside the reactor, ruling this option out as a feasible alternative.

2.5. Manipulated variables
The digester is fitted with a heat exchanger that heats liquor which is circulated from the bottom of the digester after passing through a grille to remove any wood chips.  The steam flow to this heat exchanger provides the only control over the temperature of the digester.  The pressure profile is dependent on the generation of gases from the chemical reactions inside the reactor and on temperature.


The controller implemented on a digester must be able to deliver a desired DP for the pulp discharged from the digester at the end of a fixed cook time, while obeying constraints on the temperature and pressure profiles.

The variables that can be measured accurately are the temperature and the pressure inside the reactor. Due to constraints on the cooking process, the total cooking time has to be kept constant. The shape of the temperature profile is shown in Figure 1.

Figure 1

Figure 1: Generic temperature profile used for the digester. T1 and T2 are fixed temperatures and the slopes between temperatures are fixed

As mentioned before, the only useful MV is the steam sent to the heat exchanger that heats the digester contents. Specifically the maximum temperature, Tmax of the curve in   can be specified, as the slopes up to that point are constrained due to the effect of liquor entering the wood chips.  If the liquor enters the chips too slowly, only the outside of the chip will have its lignin reduced, while if it happens to quickly and the temperature increases quickly, the chips may be 'burned', leading to a spoilt batch.


4.1. Pulping reactions
The main reactions during the pulping process are

  • delignification (removal of lignin from the chip mass),
  • strong acid neutralisation,
  • cellulose degradation (shortening chains) and
  • hemicellulose degradation.

The hemicellulose degradation is however not commonly modelled as it is deemed to have little impact on the cellulose chain length.

Much work has been done since the early sixties to obtain satisfactory rate equations for the above reactions. Some work of importance to this project is summarised below.

4.2. S-factor model
Based on the assumption that there is a correlation between the lignin content of the solid phase in the reaction and the pulp viscosity, the delignification rate equation would be sufficient to find the final viscosity of a cook. 

The rate equation used in this approach is given by Hagberg & Schn (1973) as

equations 1

4.3. Other models
The four significant reactions already mentioned can be described by the following rate equations (Hagberg & Schn, 1973):

Equations 2

The temperature dependence of all the k factors above except for kSA can be described by the Arrhenius relationship

equations 3

with E and k0 known for each of these reactions.  The hydrogen and bisulphite ion concentrations are obtained via electroneutrality arguments combined with the assumption that equilibrium is obtained between the SO2 in the space above the digesting liquid and in the liquid itself.

The process model used in the control structure was developed by Kilian (Kilian, 1999).  The model uses the reaction dynamics described above to model the reactions inside the reactor.

4.4. S-factor control
Equation 4 can be rewritten to isolate the S-factor target SF.  Remembering that this equation was the result of an integration, the continuous sum of the factors in equation 2 can be assumed to approximate this factor. Hence, when this continuous sum reaches the target value, the viscosity should be equal to the desired viscosity.

This control strategy, with some minor modifications, is currently in place at the SAICCOR plant. The results obtained using this strategy have been unsatisfactory, even though several modifications have been implemented in an attempt to improve control.


5.1. Feed-forward control
The control objective of any controller can be seen as keeping the effect of disturbances low while allowing the controlled system to produce the desired output values, as well as allowing the system to move between sets of desired outputs without incident.

This leads to a conceptual picture of the control process required for the digester. A controller will have a DP setpoint, and read as many of the process variables, p, as it can.  Using these data, the controller will attempt to specify a maximum temperature for the digester, which will in turn produce pulp with a certain DP based on the maximum temperature, the measured process variables and unmeasured disturbances, d.  This concept is shown in Figure 2.

Figure 2

Figure 2. Conceptual working of pulp viscosity controller

This strategy can be expressed in a formal block diagram as shown in Figure 3.

Figure 3

Figure 3. Modified feedforward control structure

As can be seen, the classic feedforward structure has been used, with p and d both vectors. The separation of the different transfer functions is for utility only.  During the implementation of the controller, a single model is used that takes the process variables p into account as a matter of course.  The working of the controller is therefore very similar to the concept shown in Figure 2.

It should be clear that some form of inverse model is required as with all feedforward control.  This inverse is obtained iteratively by obtaining the value of Tmax that gives DP=DPset.  This is due to the fact that a highly non-linear time domain model has already been developed, and finding this inverse is computationally intensive.

5.2. Adaptive model
Upon examination of , it is clear that the controller does not have any specific measurement of control error.  When the conditions on the plant change causing plant-model mismatch, control can be expected to degrade.  In order to provide model adaptability to changing conditions on the plant, it is therefore necessary to react to controller errors by modifying the controller parameters.

In the implementation of the controller, this was done by optimising parameters periodically so that the DP predicted by the model approached the value measured for those cooks using laboratory testing.  This ensures that the model is constantly in close accord with the conditions on the plant.

5.3. Plant interaction
Interaction with the plant was done using direct queries to the plant database to obtain all the data required for operation. Both continuous and historical data can be obtained in this manner, so that operation is entirely automated. Due to concerns regarding this experimental controller the Tmax setpoint is not written directly to the plant, but is processed by an operator to ensure that the values seem reasonable.


The model used in the controller has been shown to be accurate using existing plant data (Killian, 1999). Recent experiments have also shown that the controller predictions for Tmax outperforms the current S-factor controller. Table 1  shows the actual and predicted temperatures, along with the resulting viscosities for six cooks done in June 2002. 

Table 1. Temperatures obtained and predicted by the program during June.

Cook number

% Difference between Tmax reached using S-factor control and Tmax predicted by the new model

Normalised Viscosity (%)



















It is important to note that higher temperatures will typically result in lower viscosities. With this in mind, the DP error (DPtarget-DPactual) can be plotted along with the temperature adjustment (Actual Tmax- Predicted Tmax) suggested by the program.  These results can be seen in Figure 4.

Figure 4

Figure 4. DP errors and suggested adjustments

The results look promising, showing a corrective action in lowering the temperature when the viscosity was low.  It is, however, important to ascertain whether this is due to a low temperature bias or whether the controller will increase the temperature when the viscosity is high.   does not show this effect, but experiments are currently underway to collect more data to confirm these effects.


A model based control algorithm that interacts with an industrial batch digester has been implemented at SAICCOR.  The control predictions made by the controller improve on the control by the current controller which is based on a more simplified model of the pulping reactions.  





Concentration of X




Unmeasured disturbances


Activation energy


Transfer function




Reaction rate constant




Process variables


Strong Acids


S factor constant
















Bierman, C. J. (1996) Handbook of Pulping and Papermaking, 2nd ed., Academic Press, California.

Hagberg, B., Schn, N.-H. (1973) "Kinetical aspects of the acid sulfite cooking process: Part 1:  Rates of dissolution of lignin and hemicellulose", Svensk Papperstidning,(15), 76, 561-568.

Kilian, A (1999), Control of an Acid Sulphite Batch Pulp Digester Based on a Fundamental Process Model, Master's thesis, University of Pretoria

Kilian, A.,  de Vaal, P.L (2000) "Potential for improved control of an acid sulfite batch digester using a fundamental model" TAPPI Journal (83) November.

Kollman, F. F. P., Ct, W. A. (1968) Principles of Wood Science and Technology, 1 ed., Springer-Verlag New York Inc., New York.

Rydholm, S. A. (1965) Pulping processes, 1st ed., Interscience Publications, London.

Watson, E. (1992) "Mathematical modeling and experimental study of the kinetics of the acid sulphite pulping of Eucalyptus wood" In Department of Chemical Engineering University of Natal, Durban.


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