ENERGY CONSERVATION IN MULTIPLE EFFECT EVAPORATORS

Abstract

The present investigation pertains to a theoretical study of energy conservation in multiple effect evaporator by simulating the variables of an evaporator for an improvement in steam economy. Basically, it deals with the development of mathematical models for the evaporation of aqueous solutions of sugar, black- liquor, and caustic soda in quadruple-, quintuple-, and triple- effect evaporator, respectively under forward, backward, and mixed feed arrangements and their solutions to determine steam economy. It also includes the parametric effect of operating variables on the steam economy and end-product concentration so as to obtain the condition for improved steam economy of the evaporator. Finally, it describes a procedure to counteract a change in end-product concentration caused by any upset in operating variables in such a way that steam economy of the evaporator does not suffer at all. Using the equations ofsolute material balance, overall material balance, energy balance, heat transfer rate, and boiling point rise in individual effects ofan N-effect evaporator, pertinent models of4N nonlinear simultaneous algebraic equations have been developed for quadruple, quintuple-, and triple- effect evaporators employing aqueous solutions of sugar, black-liquor, and caustic soda, respectively with forward, backward, and mixed feed arrangements. The equations have been linearised by Newton-Raphson method and then solved by L-U decomposition method to determine the values of unknown variables and thereby steam economy and the end-product concentration. A set of initial guess value of unknown variables has been used to initiate theiterative computation. Thevalue ofan unknown variable has been taken to be converged when the deviation between two successive values of the variable is found to be of the order of one tenth of a micro unit. The model has predicted pertinent quantities ofsteam consumption; saturation temperature of vapour of each effect; concentration, flow rate, and temperature of the aqueous solution in each effect for the known values ofoperating variables viz; feed temperature, feed concentration, feed rate, pressure in the last effect, and steam pressure for a given solution and feed arrangement. The validity of the model for its applicability to industrial situations has been examined by comparing the predicted values of solute concentration, saturation temperature of vapour, and the liquid temperature in individual effects ofthe multiple effect evaporator against the plant values for the known values of the operating variables being used in Indian mills. The maximum deviation between the predictions and the plant values has been found to be of the order of ±10%. Parametric effect of operating variables on steam economy has been studied for the multiple effect evaporators using various solutions and feed arrangements. As a result of it,the range of operating variables for the highest steam economy of the evaporator has been determined. These values, undoubtedly, are likely to revamp the performance of existing evaporators and also help in the design of energy-efficient multiple effect evaporators. Application of multiple linear regression analysis to the values of steam economy and operating variables has resulted in the development of various correlations for aqueous solutions of sugar, black-liquor, and caustic soda with forward, backward, and mixed feed arrangements. The maximum deviation for each of the correlation has been of the order of .+5.5%. The correlations are of the following general form: E = Crf"XfbFcT1dTe Where values of the constant, C and the exponents, a, b, c, d, and e depend upon the aqueous solution to be concentrated and the feed arrangement used in evaporator. Present analysis has also been extended to investigate the parametric effect of operating variables on the end-product concentration of evaporators so that the results may be of direct relevance to maintain end-productconcentration at a specified level as might be necessary due to process constraints. Based on it, end-product concentration has been found to vary directly with feed temperature and steam pressure and inversely with feed rate and pressure in last effect of the evaporator. Effect of feed concentration on the end-product concentration has differed from solution to solution. Using multiple linear regression analysis the end-product concentration of the evaporator has been correlated with operating variables for aqueous solutions of sugar, black-liquor, and caustic-soda with various feed arrangements. The general form of the correlation is as follows: X = Kr/X^FT.T' p If Is Where the valuesof constant, Kand the exponentsp, q, r, s, and t vary with feed arrangement and the aqueous solution used in evaporator. The maximum deviation of a correlation from its mean value has been of the order of ±5.26%. This investigation has also attempted toevolve a procedure to meet the situation of thechange in end-product concentration that might arise due to unforeseen variation in one or more operating variables and thereby the steam economy of theevaporator undergoes a change. Based on the generalized correlation of end-product concentration, the following equation has been obtained to determine the corresponding change in the operating variables so that end-product concentration does not alter. [p(Ar/rr) +q(AX/Xr)+ r(AF/F) +s(AT/T)) +t(ATi/T)l - pq(Ar/r()(AX/Xf)-rs(AI7iO(A'l/i;)-st(Aiyri)(A'r/r>)-rt(Al<71')(A'iyi;) ii This, obviously, leads to many options for the readjustment ofoperating variable. Each is likely to provide adifferent value of steam economy. Therefore, each option must be evaluated for its impact on steam economy and thereby the most appropriate one which yields the highest steam economy must be selected. Following relationship has been developed for the calculation ofdeviation in steam economy of the evaporator with readjusted changes in values of operating variables: [AE/E] = a(Ar/rf) + b(AX/Xf) + c(AF/F) + dCAT/T^ + e(AT/T) + a(Ar/Tf) {b(AX/Xf) + c(AF/F) + d(AT/T,) + e(AT/T)} + b(AX/Xf) (c(AF/F) + dCAT/T,) + e(AT/T)} + c(AF/F) {dCAT/T,) + e(AT/T)} + de(AT/T,)(AT /T) Above equations provide a useful procedure to determine the necessary changes the operating variables needed to nullify the variation in end-product concentration caused by any upset in other variables of the evaporator. Besides, the resultant variation in the steam economy can also be determined, and then the operating variables can be readjusted to provide the highest steam economy. This will reduce the steam consumption to the evaporator under consideration. in