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An attempt has been made in this present investigation to design a sextuple effect black liquor evaporator system for paper industry. This required to develop a system of 12 nonlinear simultaneous equations based on steady state mass and energy balances, heat transfer rate, equilibrium relationships and same physico-chemical/physico-thermal properties of liquor. Numerical techniques using Newton-Raphson-Jacobian matrix method and method of Gauss elimination are employed to solve the problem. A generalised algorithm is developed for the simulation of this multiple effect evaporator systems with backward feed. To process a large body of data within limited time and to generate a data bank a computer program has been developed based on Fortran 77. Normal parameters practiced in Industry are employed to simulate the system. Anticipated saving of steam consumption is indicated. The design procedure developed can bring accuracy in assessing the performance of an existing evaporator system or can help in designing a new system for a green field pulp and paper mill.

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... For the analysis of MEE system mathematical models have been reported in the literature since last five decades. A few of these were developed by [1], [5], [7]- [14], [17], [20], [24] and [26]- [27]. These models are generally based on a set of linear or nonlinear equations and can accommodate effects of varying physical properties of vapor/steam and liquor with change in temperature and concentration [22]. ...

... Reference [1]- [4] attempted to simulate a sextuple effect black liquor evaporator system for paper industry. This required developing a system of nonlinear simultaneous equations based on steady state mass and energy balances, heat transfer rate, equilibrium relationships and same physicochemical/physico-thermal properties of liquor. ...

... This process consumes more time and mathematical skills. In the present study we describe the steady state Mathematical model for six effect evaporator in the similar manner as used by [1] with some necessary modifications and used different physicochemical/physico-thermal properties of black liquor given by [15]. The simulated results are obtained for the backward (→6→5→4→3→2→1), mixed (feed into 5 th effect as, →5→6→4→3→2→1) and split feed (equal feed in 5 th and 6 th effects as, shown in Fig. 3) for a sextuple effect evaporator and compare with the results of previous workers [1], [3]- [4] respectively. ...

This paper describes a steady state model of a multiple effect evaporator system for simulation and control purposes. The model includes overall as well as component mass balance equations, energy balance equations and heat transfer rate equations for area calculations for all the effects. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow for backward, mixed and split feed. For simulation 'fsolve' solver in MATLAB source code is used. The optimality of three sequences i.e. backward, mixed and splitting feed is studied by varying the various input parameters.

... Generally, the ERSs used in the MEE systems are condensate-, feed-and product-flashing and vapor bleeding. Since last seven decades many investigators analyzed the MEE system using mathematical models with the induction of condensate flashing [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. Many researchers [3, 5, 12, 13, 14, 15] also incorporated vapor bleeding to pre-heat the feed in the MEE system. ...

... The MTPs for different flow sequences for models, proposed by Kern [10] and Nishitani & Kunugita [12], are shown in Table A.1 and A.2, respectively.Table 5 Comparison of results of present approach with that of other models ...

In the present work different energy reduction schemes (ERSs), used to reduce the consumption of steam for a multiple effect evaporator (MEE) system, are developed. These ERSs are condensate-, feed- and product-flashing and vapor bleeding. Further, a new scheme is proposed where condensate of vapor chest of an effect is used to preheat the liquor, which is entering into that effect using a counter current heat exchanger. This work also presents a comparative study between existing ERSs and selects the best ERS amongst these based on steam consumption as well as number of units involved. Further, in the present paper a simple graphical approach named "modified temperature path (MTP)" is developed for the analysis of different feed flow sequences of a MEE system to screen best possible feed flow sequence. To study the effect of different ERSs on steam consumption and MTP analysis an example of septuple effect flat falling film evaporator (SEFFFE) system, employed for concentrating weak black liquor in an Indian Kraft Paper Mill, is considered. The results show that ERSs reduce the steam consumption up to 24.6%.

... In all these F steam is splitted equally and fed in first two effects. These F are selected based on the flow sequences of MEE systems reported in the literature (Ray et al., 2000) as well as that have been employed in industry. However, the present model can be used to simulate any flow sequence. ...

A nonlinear model is developed for a SEFFFE system employed for concentrating weak black liquor in an Indian Kraft Paper Mill. The system incorporates different operating strategies such as condensate-, feed- and product-flashing, and steam- and feed-splitting. This model is capable of simulating a MEE system by accounting variations in τ, U, Qloss, physico-thermal properties of the liquor, F and operating strategies.The developed model is used to analyze six different F including backward as well as mixed flow sequences. For these F, the effects of variations of input parameters, T0 and F, on output parameters such as SC and SE have been studied to select the optimal F for the complete range of operating parameters. Thus, this model is used as a screening tool for the selection of an optimal F amongst the different F.An advantage of the present model is that a F is represented using an input Boolean matrix and to change the F this input matrix needs to be changed rather than modifying the complete set of model equations for each F. It is found that for the SEFFFE system, backward feed flow sequence is the best as far as SE is concerned.

The black liquor is valuable biomass that can be recycled in the form of CO2-neutral fuels and is burned in recovery boiler furnaces to produce steam for power generation. However, the combustion of biomass results in a large amount of ash deposits, which reduce the heat transfer efficiency. Therefore, all recovery boilers have an ash deposit removal system (ADRS). However, its operation is inefficient, significant amounts of steam energy are wasted, and CO2 emissions are increased. To solve these problems, this study addressed optimizing ADRS to maximize biomass recycling as renewable energy for CO2 reduction. This study mainly consists of two parts. First, to predict power generation, a process model of the recovery boiler with an ADRS was developed, and the model was used to define mathematical equations. Second, a mathematical model was proposed to maximize biomass recycling. The increase in biomass recycling is calculated by multiplying net power generation and the amount of saved biomass. As a result, 16.135 ton/d of black liquor was saved, and the CO2 emissions were decreased by 541–996 ton/y following an increase in the power generation by 2,987 MWh/y and in the net present value by $ 16,797,303.

A general and rigorous mathematical model is developed for a multiple effect evaporator system which includes various energy reduction schemes (ERSs). These ERSs are thermal vapor compression, vapor bleeding, condensate flashing and solution flashing. The model can achieve the function of pumping steam at any effect and can work as an effective screening tool for the selection of optimal feed flow sequence (OFFS). In order to solve the model, the iteration method combining with matrix methods is proposed. To study effect of different ERSs on steam consumption (SC), an example of the co-current quadruple effect evaporator system is considered. These schemes can reduce the SC up to 46.56% if the feed is heated up to 88 °C and ejection coefficient at 3rd effect is set to 0.3. The OFFS is forward sequence as long as preheating temperature is high enough when constraints of heat transfer driving force can be satisfied.

A wide range of mathematical models for multiple effect evaporators in process industry including paper industry are well reported in the literature but not so extensive work on the dynamic behavior of MEE system is available in the literature. In the present study 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. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow. A generalized mathematical model 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 was finally obtained. Finally model for mixed feed sextuple effect falling film evaporators system was solved using MATLAB. For the steady state and dynamic simulation the ‘fsolve’ and ‘ode45’ solvers in MATLAB source code is used respectively.

A scalable new model is developed for the analysis of multiple effect evaporator (MEE) systems with the induction of condensate flashing. It uses the concepts of stream analysis and temperature path for the formulation of model equations. In addition to above the model also takes into account boiling point rise and variable physico-thermal properties of steam/vapor condensate and liquor while simulating the MEE system.The present model consists of linear equations, which are automatically generated through temperature path. To establish the reliability of the present model it was run for four different case studies and the results are compared well with the published models. This paper shows the trade-off between annual capital and operating costs, which decides optimum number of flash tanks as well as their positions in the MEE system.

A new simplified scalable mathematical model, based on concepts of stream analysis, temperature paths and internal heat exchange, has been developed for synthesis of a multiple effect evaporator systems. In this model, fresh feed is assumed to be composed of product and number of condensate streams, which come out from different effects and these are treated as separate streams. For the present work a septuple effect flat falling film evaporator system, used for concentrating black liquor in an Indian Kraft Pulp and Paper mill, has been considered. This system is being operated under backward sequence with condensate-, feed- and product-flashing as well as steam splitting in first two effects. The set of linear algebraic equations for this model are self-generated through programming and is solved simultaneously using Gaussian Elimination Method with partial pivoting. Results of the present approach are validated with published model and industrial data.

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