MATHEMATICAL MODELLING AND ANALYSIS OF PULP WASHING PROBLEM FOR OPTIMUM OPERATION

Abstract

Mathematical modeling is an indispensable tool now a day to analyze, correlate, simulate, optimiz and finally control of any chemical process plant. Pulp and paper industry —a core sector industr is not the exception. In fact, this industry is very capital intensive industry. Huge amount of ral materials, chemicals, energy, and water are consumed in the process of paper manufacture wit requirement of large labor force generating an enormous quantum of pollution loads. Mathematics approach to quantify the optimal parameters will be of immense potential to alleviate this today' burning problem of paper industry's survival. For sustainability in production of paper, it is imperative necessity to look in to all subsystems fc their optimization and to explore the possibilities of eliminating the operational bottlenecks t fetch maximum economy. In the present investigation both steady state mathematical and statistical modeling to the variou interactive subsystems are attempted for optimizing a multi-stage brown stock washing (BSW plant. Accordingly an objective function has been formulated based on minimum annual cost. Thi objective function involves terms related to other important operations such as multiple effet evaporator, multi-stage bleaching, effluent treatment plant along with usage of heating value c black liquor in recovery furnace operation. The minimum cost function comprises of costs due t washing equipments (PO, maintenance and repair (PM), power consumption for drum rotatiot back shower pump, vacuum pump, (P0*C13), for repulper-shredder (P0*C5), liquor spray (P0*Co for screw conveyer at the last BSW (Po*C4), due to evaporation (PE*CE), steam for hot wash watt (PA*CA), steam generated due to heat value of BLS (PE*C1,), condensate saving (Ps*Cs), bleac chemical consumption due to carry over solids (PNB*CNB), and labor cost (Cm),cost of effluet iii treatment(PEff*CE0 , cost due to soda loss(Psi*Csi), cost due to solid loss(PteCtsi) . The objective function is modeled as follows: Min (CT)—(13„+Prn)*N+PE*(CE+CA+CL)+Ps*Cs+PNB*CNa+(C13*N+Cs*(N-1)+C6*N+C4)*Po+CLW+ PEtT*CEff PSI*Csi Ptsl*Cts1 • Where C13= power consumption due to drum rotation (C1)+ back shower pump (C2)+vacuum pump (C3). For solution of the above objective function, the decision variables are dilution factor (DF) and number of stages (N). For optimization and simulation purpose each terms require model development as a function of DF and N in various subsystem of a paper mill. The interactive subsystems as envisaged in the objective function are BSW, MEE, multi-stage bleach plant. effluent treatment plant (ETP) and recovery furnace operation for steam generation. Each in turn demands development of mathematical models. In order to develop models in all the subsystems, a typical Indian mill configuration using hardwood / bamboo with normal operational conditions has to be known. For BSW operation static models for fluid flow through porous medium (mat in this case) has been employed to estimate different operational and design parameters. Equations are also developed for power consumption calculations. Where equations are not available, data has been collected from a running Kraft mill using hardwood and bamboo. For simulation purpose, worst conditions are considered. Various algorithms have been constructed for solid reduction ratio of Perkins (77) and material balance for multistage washers. These are subjected to computer program C++ and data are generated. The parametric influence is found in close agreement with those obtained from the previous investigators (64,96). For the estimation of steam consumption in black liquor evaporator system for paper mill as a function of DF and number of stages, the first attempt is made to design a set of multiple effect iv evaporator (MEE) consisting of six number of bodies (sextuple effect). This is pursued through designing a cost model with minimum total annual cost as an objective function. This is a single valued non-linear function with N as a decision variable. The profile displayed a unimodal function exhibiting an inflexing point as minima. The sextuple effect evaporator thus developed, now needed for steady state mathematical modeling. For the present case a typical backward feed sequence is considered. For modeling an analysis is made using degrees of freedom and other standard procedures. Finally a system of 12 nonlinear simultaneous equations are generated based on steady state mass and energy balances, and heat transfer rate equations. The model of overall heat transfer coefficients is taken from. Gudmundson (33) whereas the models for physico-chemical/physico-thermal properties of liquor and equilibrium relationships for boiling point rise are so selected from many rival models tha they can fit for bamboo and hardwood liquors. Numerical techniques using Newton-Raphson Jacobian matrix and method of Gauss elimination are employed to solve the problem. A generalized algorithm is developed for the simulation of this backward feed multiple effec evaporator system. Algorithm is also developed to estimate overall heat transfer coefficient base on Gudmundson model. To process a large body of data within limited time and to generate a dal bank a computer program has been developed based on Fortran 77. Subroutine-subprograms fc the physico-thermal properties of liquor including boiling point rise and overall heat transfl coefficients are also developed to inter-link with main program. Normal parameters practiced Industry are employed to simulate the system. The influences of various input parameters e.g. t] temperatures of saturated steam, feed and last body vapor, feed concentration and flow rate ( steam consumption, steam economy and area requirements are examined. Further, the data bank thus generated for steam consumption and condensate flow rates statistically analyzed. Non-linear statistical regression models are developed to interlink w brown stock washing operation as a function of DF and N for further optimization of the later system. For bleach plant optimization a pragmatic strategy for optimizing a multi-stage bleach plant has been developed. To fulfil the objective a detailed optimization scheme has been designed which is then simulated for a typical bleach plant sequence CEDED as an example. The non-linear models needed linearization, specifying the operating constraints and are solved through linear programming techniques with the help of MATHCAD AND UNDO SOFTWARE PACKAGE. The control set points based on the models are optimized using annual operating cost as decision variable. The total annual cost as objective function has been formulated and simulated with various values of operating conditions such as consistency, temperature, time of reaction, chemicals consumed and final pH within their respective ranges normally followed by industry. The cost related to ETP required for optimization of BSW operation are usually determined by the quantum of pollution parameters constrained by the pollution control authorities. To examine the effects of carry over solids and kappa number of brown stock, which consumes extra bleaching chemical and generates equivalent COD, BOD5 and AOX/TOC1 in bleach plant effluents, models are developed to predict effluent parameters for various bleaching sequences. The statistical models for various cases are found to be linear, nonlinear (parabolic and polynomial type) for single variable and multiple regressions for multivariable problem. In order to validate the models the experimental data and correlations determined by earlier investigators are compared. The accuracies of the statistical models are further tested through the absolute error, percentage of error. R2 values and residual plot. For estimating heating value of BLS, heat utilized to produce steam and parametric effects on these values a modified version of Green and Grace model and that due to Frederick(22) is proposed after incorporating DF and N terms. Two algorithms and their computer programs using vi C++ language are developed to calculate heat value of black liquor solids, steam production from recovery furnace and other parameters. From the proposed model the effect of BLS on HV, whicl in turn a function of DF and N are evaluated. The effect of sulphidity, active alkali, percentage o BLS on HV and heat utilized for steam generation are examined. These closely agree with those o previous investigators(74,1). Based on the data a regression model of nonlinear type is developer for further optimization. All the relevant streams from BSW operation, MEE, multi-stage bleach plant, ETP and recovery operation are now converted in cost terms. Total annual cost per tonne of pulp comprising of man: cost terms including capital fixed charges together with, power cost of BSW operation, statistical multivariate regression model for steam and condensate flow, carry over of solids and neutralization cost in bleaching operations and heat value of lignin and its impact on overall gain in the recovery furnace are incorporated in the objective function. This is then subjected to nonlinear constraint optimization by Fletcher-Reeves method. Optimum number of stages for BSW and economic dilution factor are thus found out for a variety of conditions. Relative contribution of all cost terms towards total annual cost are evaluated.