Modeling pulp digester

To illustrate how different m(X ) and x may happen to be, let s consider as a specific example (others can be found in Saraiva and Stephanopoulos, 1992c) a Kraft pulp digester. The performance metric y, that one wishes to minimize, is determined by the kappa index of the pulp produced and the cooking yield. Two decision variables are considered H-factor (xj), and alkali charge (X2). Furthermore, we will assume as perfect an available deterministic empirical model (Saraiva and Stephanopoulos, 1992c), /, which expresses y as function of x, i.e., that y =/(xi, X2) is perfectly known. 

In order to verify how close to a known true optimum the final solutions found by our learning methodology happen to be, we will describe here its application to a pulp digester, for which a perfect empirical model /(x) is assumed to be available. Other applications are discussed in Saraiva and Stephanopoulos (1992c). 

Adaptive Control of Continuous Pulp Digesters based on Radial Basis Function Neural Network Models... 

Implementation of a Model Based Controller on a Batch Pulp Digester for Improved Control... 

Kilian, A (1999), Control of an Acid Sulpite Batch Pulp Digester Based on a Fundamental Process Model, Master s Dissertation, University of Pretoria... 

Moczydlower, D., 2002, Modeling and Control of a Continuous Pulp Digester, PhD Thesis, Federal University of Rio de Janeiro, Brazil (in Portuguese). 

In the case of distributed plug flow processes, hybrid model design focuses on reducing the number of sections by overall fuzzy relationships. A pulp digester has been used as an example. The original model is the so-called Purdue Model (Smith and Williams, 1974), which is a detailed and industrially accepted digester model. 

Fig. 30.15. Pulp digester (a), simulation model (b) hybrid model (c).

Fig. 30.16. Hybrid model of one section of a pulp digester, i denotes the different components.

The fuzzy sub-model characteristics for the pulp digester are shown in Table 30.5. 

Table 30.5. Fuzzy sub-model characteristics for pulp digester R, reaction rate p, density T, temperature.

Dayal, B. S., MacGregor, J. F., Taylor, P. A., Kildaw, R., and Marcikio, S., Application of Feedforward Neural Networks and Partial Least Squares Regression for Modelling Kappa Number in a Continuous Kamyr Digester, Pulp Paper Can., 95(1) 26 (1994)... 

Smart Enterprise for Pulp and Paper Digester Modeling and Validation... 

Christensen, T., Albright, L.F. and Williams, T.J. 1982, A Mathematical Model of the Kraft Pulping Process . Tech. Rep. 129, Purdue University, PLAIC, West Lafayette, IN. Gustafson, R.R., Sleicher, W.T., McKean, W.T. and Finlayson, B.A. 1983, Theoretical Model of the Kraft Pulping Process . Ind. Eng. Chem. Process Des. Dev., 22,87-96. Harkonen, E.J., 1987, A Mathematical-Model for 2-Phase Flow in a Continuous Digester . TAPPIJ., 70(12), 122-126. 

Michelsen, F., 1995, A Dynamic Mechanistic Model and Model-Based Analysis of a Continuous Kamyr Digester . PhD Thesis, University of Trondheim, Trondheim. Wisnewski, P.A., Doyle, F.J. and Kayihan, F. 1997, Fundamental continuous-pulp-dlgester model for simulation and control . AIChE J., 43(12), 3175-3192. 

The Kraft process is not only the dominant chemical pulping process, but also the most important overall concerning the various production methods. Several studies have been reported on modeling of continuous digesters at different levels of complexity. Michelsen and Foss (1996) have developed a dynamic model that describes the transfer... 

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