MATHEMATICAL MODELLING AND SIMULATION IN PULP MILL OPERATIONS

Abstract

Pulp and paper industry is an energy intensive industry. Huge amount of raw material, chemical, energy and water are consumed in the process of paper manufacturing. Some energy intensive subsystems of the integrated pulp mill that are the focus of present study are brown stock washing, multi-effect evaporation, and multi-stage bleaching which significantly .affect the economy as well as environment. In the present study the dynamic model has been developed by using material & energy balance and various other parametric equations reported in the literature in last five decades. Dynamic model helps us in better understanding of the process and behavior of its variables, thereby helps in determining a better control system. The work presented on the washing subsystem is based on dynamic simulation of single and multi stage brown stock washing (BSW) sys tern. Mathematical model for pulp washing was described by using basic material balance equation (Transport Equation) and including the relevant mathematical equations for adsorption-desorption isotherms (linear as well as non-linear). To validate the solution technique the transport equation is solved by using `pdepe' solver in MATLAB source code and compared with the results of analytical given by Brenner (1962) as well as results of Grabs (1974) obtained through numerical methods. The results show the good agreement. After the validation of the solution technique (`pdepe' solver) the solution of single stage washing is obtained by using different adsorption-desorption isotherms to show the suitability of the isotherm coupled with the washing model. Rate of mass accumulation in the solid phase due to adsorption-desorption is taken into consideration for evaluation of the solute concentration in the fiber by the linear isotherms given by [Lapidus and Amundson (1952), Perron and Lebeau (1977) and Sherman (1964)] and non linear Langmuir isotherm. Linear isotherm based model gives satisfactory profile, although the model with isotherm given by Sherman (1964) gives the erratic values of the solute concentration. However, non linear Langmuir isotherm is the best suitable for the satisfactory model performance. Further for the simulation of washing model for multistage washing non linear Langmuir isotherm is used with various boundary conditions. The system of simultaneous differential equations (i.e. transport equation and adsorption isotherm) is solved by using lidepe' solver in MATLAB source code with various boundary conditions for the sodium ion specie. Data obtained by Grabs (1974) for the species sodium (Na`) by using softwood (pine) sulphate pulp is used for simulation. On the basis of the solution, three dimensional (3-1`.1) graphs of the behavior of solute concentration with respect to time as well as cake thickness are obtained for single stage and for each washer of multistage washing system. For the optimal control of the multistage washing system the parametric effect of various parameters namely (i) Peclet number, (ii) kappa number and (iii) porosity also studied for the individual washer. The breakthrough curves are also plotted for exit solute concentration versus time and cake thickness for each washer of the four stage washing system. The transport equation is given by f 02C \ ale OC Ifrz) (Ft P( E) The `pdepe' solver used in the present investigation is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters and show a comparable performance with average numerical errors. The use of MATLAB for the simulation of such type of complex system is a good alternative to the available techniques. The work presented on the evaporation subsystem is based on the dynamic simulation of multi-effect evaporation system. The dynamic behavior of multi-effect evaporator system of a paper industry is obtained by disturbing the feed flow rate, feed concentration, live steam temperature and feed temperature. For this purpose an unsteady-state model for the multi-effect evaporator system is developed for backward, mixed and split feed sequence respectively. Each effect in the .process is represented by a number of variables which are related by-the energy and material balance equationsfor the feed, product and vapor flow. In this study a generalized mathematical model is proposed which could be applied to any number of effects and all kinds of feeding arrangements like forward feed, backward feed, mixed feed and spilt feed in the MEE system with simple modifications. The model developed is based on the work proposed by Aly and Marwan (1997). To study the dynamic response of any chemical process initial values of the process variables are needed. For this purpose steady state solution of the system is obtained first. Data for simulation purpose is taken from literature given by Gupta (2001). The range of operating parameters is also taken from the literature and duly modified values are considered according to Indian Paper mill evaporation conditions. The steady state solution of the dynamic model is obtained by taking the accumulation terms equal to zero and- using Isolve' solver in MATLAB source code for the solution of simultaneous nonlinear algebraic equations. To predict the system time-dependent parameters under various transient conditions the solution of the system of simultaneous ordinary differential equations is obtained by using `ode45' solver in MATLAB source code. To study the dynamic response of outgoing liquor ii and steam characteristics (Concentration of outgoing liquor and steam temperature) disturbances is applied on various input variables such as feed flow rate, feed concentration, steam temperature and feed temperature. The parametric influences of various input parameters on output parameters steam consumption (SC), steam economy (SE) and area requirement (A) for backward, mixed and split feed sequences is studied by obtaining the steady state solution by varying the range of input parameters and find that in all cases the mixed feed sequence is optimal. As no dynamic data are available for further validation, further comparisons could not be made at this time. However, the steady-state validation together with the fact that the observed responses follow the same nature of the dynamic responses of the fundamental distributed parameter model, based on first-principles knowledge about the fluid dynamics and heat transfer processes. The dynamic behavior of each effect's temperature and product concentration was studied by disturbing the liquor flow rate, feed concentration, steam and feed temperatures by 110% step input for backward, mixed and split feed sequences. The disturbance in feed temperature does not bring noticeable change in the temperature and product concentration of each effect. Temperature of each effect is changed significantly while no significant change in the product concentration is observed with disturbance in feed temperature and steam temperature. The dynamic behaVior of effect's temperature With respect to disturbances in feed concentration shows slight change in temperature, but ehange.in product concentration is significant. The transient study shows that the steady state is reached more quickly for temperature in comparison of the solid concentration and all of the responses converge in a smooth fashion for all the feed sequences. The work presented on the bleaching subsystem is based on the modelling and simulation of multi-stage bleach plant. Steady state model is described for DED bleach plant based on the work presented by Dogan and Guruz (2004). In the steady state modelling, model equations related to mixer are simple mass balance equations and are easy to solve. Study of the pulp washing operation is already done in the present study. So the main focus is on the modelling of retention tower. The most important parameter in the modelling of retention tower is the bleaching reaction kinetics. In the literature different kinetic models are proposed. Most of the delignification models are based on the kinetic study conducted by Ackert et al. (1975). Ackert (1973) presented chlorination kinetics model comprising by two parallel reactions, identified as fast substitution and slow oxidation. Based on this slow fast combination of the reaction Tessier iii and Savoie (1997) presented a kinetic model for 100% chlorine dioxide delignification based on experimental data. Bleaching reaction kinetics for chlorine dioxide substitution were also studied by Chandranupap and Nguyen (2000), Barroca et al. (2001), Barroca and Castro (2003), Gu and Edwards (2003) and Jain et al. (2007, 2009). An attempt has been made to study the kinetic models for chlorine dioxide and extraction stages reported in literature and evaluate their suitability for indigenous raw material. For the purpose laboratory experiment is done for the chlorine dioxide and extraction stages and studied the kappa number reduction with respect to different times as well as temperatures. For suitability of kinetic models given by some earlier researchers, the solutions of the kinetic models are fitted with the experimental results. It is found by comparison that the kinetic models given by Jain et al. (2009) fitted well and can be used for the modelling purpose. However, the experiment should be carried out to get the exact. value of the kinetic parameters i.e. activation energy and frequency factor.