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In the present work a number of configurations and difficulties of MEE system such as condensate flashing, vapor bleeding, steam splitting, preheating of liquor using condensate, variable physical properties and boiling point rise are taken into consideration to analyze the evaporation system. For this purpose seven effect evaporator system of a typical Indian pulp and paper industry is considered. The model developed is a set of nonlinear algebraic equations that include total and solute mass balances, energy balances, heat transfer rate equations, and the composition and temperature dependence of thermodynamic properties such as vapor pressures and enthalpies. The model is solved using nonlinear equation solver.
Economic evaluation to optimize the number of flash tanks is carried out for seven effect evaporator system. The two different types of configurations of vapor bleeding are considered and compared. Considering optimum number of flash tanks and best configuration of vapor bleeding, a system is designed. Further, a modified system is found considering optimum number of flash tanks and preheating of liquor using condensate. This modified design enhances the steam economy by 23.77% and reduces the steam consumption by 36.76% in comparison to base case and thus, it is selected as optimum design. Finally, Pinch analysis of the MEE network has also been carried out and it is found that predicted results are compared well with base case.

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... MEE trains concentrate black liquors from a dry solids mass fraction of approximately 15% to about 80-85% [8]. The evaporation step makes up 24-30% of the total energy used by a pulp mill, which justifies its optimization [9]. ...

... The black liquor Boiling Point Rise (BPR) also needs to be considered in evaporator calculations. BPR is accounted for using Equations (3) and (4), where T P is the boiling temperature of water at pressure P. A more realistic 6-effect system was adapted from [9] and is shown in Figure 3. It should be noted that black liquor exiting the first effect is flashed and its vapor is fed to the fourth effect. ...

... All heat transfer areas were assumed to be equal. Figure 2: Realistic 6-effect MEE system, adapted from [9]. The two systems were input to the simulator without supplying any initial estimates for the variables, which means that they were calculated by first solving the simplified models. ...

An equation-oriented process simulator was developed for simulating evaporation plants. The simulator graphical user interface was written in Python 2.7, and its engine, in C++. The simulator orders and partitions the system of equations that describe the evaporator system under study and solves the partitions sequentially using the Newton-Raphson method. If no good initial estimates can be provided by the user, the simulator solves a simplified problem to generate the estimates, which greatly facilitates convergence. Calculations are based on steam table correlations and on black liquor enthalpy correlations described in the literature. Two multiple-effect counter-current evaporator scenarios were extracted from the literature and used to validate the simulator: a simple 3-effect system and a realistic 6-effect system. The simulator converged to the solutions with relative ease, provided that the model equations were written as described, that equations were ordered and partitioned, and the simplified model was used to generate good initial estimates. Good agreement was found between the calculated values and those reported in the literature, indicating that the proposed simulation framework could be extended to accommodate more complex systems. Deviations from the reported values can be explained by the different choices of physical properties correlations.

... MEE trains concentrate black liquors from a dry solids mass fraction of approximately 15% to about 80-85% [8]. The evaporation step makes up 24-30% of the total energy used by a pulp mill, which justifies its optimization [9]. ...

... All heat exchange areas were assumed to be equal. A more realistic 7-effect system was adapted from [9] and is shown in Figure 3. It should be noted that black liquor exiting the first effect is flashed and its vapor is fed to the fourth effect. ...

... Realistic 7-effect MEE system, adapted from[9]. ...

An equation-oriented process simulator was developed for simulating evaporation plants. The simulator graphical user interface was written in Python 2.7, and its engine, in C++. The simulator orders and partitions the system of equations that describe the evaporator system under study and solves the partitions sequentially using the Newton-Raphson method. If no good initial estimates can be provided by the user, the simulator solves a simplified problem to generate the estimates, which greatly facilitates convergence. Calculations are based on steam table correlations and on black liquor enthalpy correlations described in the literature. Two multiple-effect counter-current evaporator scenarios were extracted from the literature and used to validate the simulator: a simple 3-effect system and a realistic 7-effect system. The simulator converged to the solutions with relative ease, provided that the model equations were written as described, that equations were ordered and partitioned, and the simplified model was used to generate good initial estimates. Good agreement was found between the calculated values and those reported in the literature, indicating that the proposed simulation framework could be extended to accommodate more complex systems. Deviations from the reported values can be explained by the different choices of physical properties correlations.

... Ref. [3] performs a theoretical evaluation of the process not considering the solute and solvent. Another issue in the literature is the analysis and optimization of heat exchangers or some specific processes [4][5][6][7][8][9][10], and eventually, some specific applications such as a biorefinery industry [11,16] and caustic soda solution in water [12,13]. The main concern of the literature is related to saltwater evaporation to obtain drinking water since this system is the most usual and a competitor with osmotic salt water purification [9,14,15,17,19]. ...

... The set of nonlinear equations that mathematically represent the system consisting of the mass and energy balances plus equations describing liquid-vapor equilibrium has been the focus of papers dedicated to solution techniques for systems with different configurations [10,11]. More recently, studies have been published on the optimization of energy consumption and investment cost [3,[12][13][14], exergy analysis [7,10,[14][15][16][17] and evaluation of vapor recompression as an energy-saving alternative [6,7,9,14,17,19]. However, besides the importance of chlor-alkali industries, there have been relatively few studies published dedicated to the evaporation step of the process, e.g., [6,12]. ...

... The total exergy of the solution is the summation of physical and chemical exergy, as indicated, respectively, by Eqs. (13)(14)(15). Therefore, ...

A study on process alternatives for reducing steam consumption was carried out in a multistage evaporation system of a chlorine–alkali industrial complex. A phenomenological model was developed, based on the mass and energy balances and on gas–liquid equilibrium correlations for the ternary mixture of caustic soda, sodium chloride and water. The design specifications of the plant were adopted as a reference to validate the mathematical model, which comprises 153 nonlinear equations. Different process conditions were simulated by taking into account the most important process variables and their effect on steam consumption. Differently from previously published studies, in which the conservation laws are mainly focused on the heat exchangers and their optimization, the present study considers the whole multistage evaporation unit. The model also enabled to evaluate the effect of changes in the plant configuration, either by considering a side product stream at a specified concentration, designated to another production unit in the industrial complex, or by including mechanical vapor recompression, which has proven to be a better solution to reduce steam consumption from the energy and exergy points of view. Results indicate an expressive decrease in steam consumption to around 1% of the original configuration. Moreover, from the exergy perspective, if the power generation is considered, the MVR is a better choice from the energy and exergy point of view. © 2018, The Brazilian Society of Mechanical Sciences and Engineering.

... Heating within an evaporator is usually performed using a water steam which condenses on the heating side of the evaporator and transfers its latent condensation heat to the evaporation side. Evaporation can be used for concentrating various feed streams (milk [7], salt water [8], tomato juice [9], black liquor [10], fruit juice [11], sugar solution [12]), or for recovering by- ...

... Most studies in this field have focused on analysis, design [22] and steady- state simulation of stand-alone evaporation systems [23], and optimisation of steam economy [24] of various flow patterns [25] with and without pre-heating [26] of feed stream. Also, considering HI of bled vapours and FC [10], optimally integrating TVR with a MEE system was investigated in order to maximise steam economy [19]. In a recent study, MEE-TVC was explored together with a solar system to determine the optimal solar radiation and steam temperatures [27]. ...

This paper proposes a general superstructure and a Mixed-Integer Nonlinear Programming (MINLP) model for the synthesis and simultaneous optimisation and Heat Integration (HI) of Single- and Multiple-Effect Evaporation (SEE/MEE) systems including Mechanical Vapour Recompression (MVR) and the background process. The proposed superstructure also includes different flow patterns (forward feed, backward feed, parallel feed and mixed feed), Flashing of Condensates (FCs), single- and multi-stage MVR systems and various HI opportunities for preheating of feed stream (e.g. with condensates, bled vapours, and hot streams from the background process). The newly proposed SEE/MEE-FC-MVR superstructure is combined with a Heat Exchanger Network (HEN) superstructure for performing simultaneous optimisation and HI. On the basis of this combined superstructure, an MINLP model with tight bounds on the variables is developed and implemented for its solution in the General Algebraic Modeling System (GAMS). The model is solved using a two-step solution strategy. The proposed model enables to explore simultaneously all interconnections within the proposed superstructure in order to find the configuration with the optimal trade-offs between capital and energy costs as demonstrated in this paper for different cases of a milk concentration process.

... The consumption of fuel, primarily coal, required to achieve this energy requirement forms ∼15-20% of the total production cost which is significantly high compared to non-Indian pulp and paper mills [13][14][15]. Additionally, most of the energy is utilized in producing steam for various process units, specially the Kraft process, which is inherently responsible for consuming more than 24-30% of fresh steam needed for total plant [16][17][18]. An estimate reveals that for each ton of pulp produced, about 7 tons of black liquor with 15% solids (∼10% organic and ∼5% inorganic chemicals) is produced [19]. ...

... In pursuit to find such optimum conditions, the linear mathematical model may translate into a more accurate nonlinear model. In many of the previous literature, nonlinear models for MSE have also been developed [16,34]. However, nonlinearity is the thumb rule, rather than an exception in most of the industrial processes. ...

Maximization of the steam efficiency of a multiple stage evaporator employed for concentrating black liquor in pulp and paper mills carries immense significance and relevance in today's scenario. Nonlinear mathematical models of heptads' effects backward feed flow with various energy saving schemes namely, steam-split, feed-split, feed-preheating and their hybrid operations have been developed. The steam economy as a cost function translates the problem into a nonlinear optimal search problem. The mass and heat balance equations act as nonlinear equality constraints while vapor temperatures and liquor flows appear as inequality constraints. The formulated problem has been solved efficiently to attain optimal solution using Genetic Algorithm approach which demonstrates advantages of convergence and relative less sensitivity towards initial values versus conventional algorithms. The simulations indicate that a hybrid of steam-split, feed-split and feed-preheating process arrangements with backward feed flow could provide the highest heat transfer across evaporator effects with an optimum steam economy of 6.47 and consumption of 6541.93. kg/h.

... Consequently, the equipment used for this evaporation process is known as multiple-effect evaporator. In addition to being used in the sugar industry, multiple-effect evaporators have been used for concentrating black liquor (Bhargava et al., 2008;Khanam and Mohanty, 2010;Jyoti and Khanam, 2014), tomato juice (Miranda and Simpson, 2005;Simpson et al., 2008), orange juice (Balkan et al., 2005), and for desalination (El-Dessouky, 1998). ...

... Low-pressure steam can be bled from vessels of the multiple-effect evaporator for this purpose (Rein, 2007). It should be noted using bled vapor to preheat the solution is also found to increase the energy efficiency of the evaporation process in the pulp and paper industry (Khanam and Mohanty, 2010;Jyoti and Khanam, 2014). ...

A multiple-effect evaporator is used to evaporate water from sugar juice in a series of pressure vessels. Steam is used for evaporation in the first vessel, and vapor from all vessels except the last one is used for evaporation in subsequent vessels. In order for evaporator surfaces to be used efficiently, juice entering the evaporator should be at the saturation temperature. Therefore, incoming juice with a low temperature must be heated in a juice heater. The heating medium in the juice heater is vapor bled from the evaporator. It is apparent that the multiple-effect evaporator and the juice heater interact through mass and energy balances. Previous investigations have focused on only the multiple-effect evaporator, and paid little attention to the juice heater. This paper presents the model of the interaction between the multiple-effect evaporator and the juice heater. The model is used to investigate how variations of surfaces in the evaporator and the juice heater affect the two performance parameters of the system, which are the amount of sugar juice processed by the system and the ratio of the amount of water evaporated from sugar juice in the evaporator to the amount of high-pressure steam required by the evaporator.

... A steady-state cascade simulation with linearized equations was performed for the countercurrent multiple effect evaporation (MEE), in order to calculate pressure, temperature, flow rates, and compositions at each stage [16] . A process model was suggested for the seven-effect evaporation applied in the pulp and paper industry [17] to find an optimum configuration of flash tanks [18] . A general mathematical model for the countercurrent MEE system was established to investigate the effect of heat pump, solution and water flashes on energy saving in fruit juice concentration [19] . ...

... where q t,MEE (=1,292 kW) is the theoretical and additional heat duties of the four evaporators, A i the heat transfer area in m 2 , and ∆T lm,i is the logarithmic mean temperature difference between the slurry and steam. The average heat transfer coefficients of black liquor from a pulp factory and milk from a dairy farm were 670 [18] , and 1,800 [15] W/m 2 /K, respectively, using falling-film evaporators. It was reported for a lab-scale fry-drying study that U was 500 W/m 2 /K concerning an industrial wastewater sludge [7] . ...

A commercial fry-drying and torrefaction (FDT) plant for producing bio-solid fuel from 45 t/d organic sludge with 80% water was proposed. The FDT plant was modeled by a process simulator with the aid of plant data. Two double-effect evaporators were used in series to vaporize water, using heat-carrying oil. Torrefied and pelletized bio-solid was produced at 413 kg/h, comprising 4.4 and 4.8% of water and oil, respectively, and 67% of its mass was used as heat source. The total energy consumption was 1,369 kW, including 93 kW electrical and 1,276 kW thermal energies. The total heat duty was 788 kcal/kg-water.

... Em uma indústria de celulose, o processamento para conversão de cavacos de madeira em polpa celulósica gera um líquido denso e viscoso -o licor preto -composto pela dissolução de materiais orgânicos como lignina, hemiceluloses e uma parte secundária das fibras [1][2][3][4][5][6]. A principal função dos evaporadores no processo é concentrar o licor preto proveniente da lavagem da polpa a um teor de 65% a 85% de sólidos para possibilitar sua queima na caldeira de recuperação [1,4]. ...

... Em uma operação evaporativa, o maior custo está associado ao consumo de vapor [1][2][3][4][5][6][7]. O método mais comum para redução deste custo é usar o vapor gerado no primeiro evaporador para alimentar um segundo [1,7]. ...

Em indústrias de celulose, o licor preto, depois de concentrado em evaporadores de múltiplo efeito, é usado como combustível. A queima deste fluido, rico em lignina e sais inorgânicos, gera vapor empregado num primeiro momento na obtenção de energia elétrica e posterior-mente como fonte de energia térmica. Os fenômenos físicos e quími-cos inerentes ao processo de concentração do licor preto podem ser descritos empregando-se, principalmente, os conceitos de balanços de massa, de transferência de calor e de
termodinâmica. Além da descrição do processo em condições normais de operação, a mode-lagem fenomenológica pode simular outras condições operacionais. Por se tratar de um sistema com significativa demanda energética é desejável conhecer quais são as condições que otimizem seu desem-penho. Sendo assim, o objetivo deste trabalho é o uso da modelagem fenomenológica para descrição do comportamento dinâmico dos eva-poradores, uma etapa crítica da operação. Neste trabalho foi propos-to um modelo fenomenológico para descrição de um evaporador do primeiro efeito, analisando prioritariamente a eficiência energética do sistema e empregando dados industriais reais do processo.

... • Díaz-Ovalle et al. [50] and Galván-Ángeles et al. [51] proposed global mass and energy balances through liquid pathways to model whichever MEEs sequence. • Jyoti and Khanam [52] developed generalized mass/ energy balances in a cocurrent flow. • Chantasiriwan [53,54] carried out a nonlinear model of a MEE by including a direct condenser and solved it by an iterative procedure. ...

Evaporators are one of the most important equipment in the food process industries such as sugar, fruit juices, dairy products, edible oils, tomato paste, and coffee. They need a lot of energy in the form of steam from boiler and it is necessary to minimize their energy consumption. One of the best strategies for this purpose is the design and application of multiple-effect evaporators (MEEs), in which the vapor from one stage (effect) is the heating medium for the next stage. There are various configurations and designs for MEEs and they can also be equipped with vapor compression systems and steam ejectors to further reduce the energy consumption and increase their economic efficiency. This article is covering the fundamentals, design, simulation, control, and application of MEEs in various food industries for the first time with discussing recent advances in this field.
Graphical Abstract

... In the cost calculations, literature data and data from similar full-scale facilities were used. Jyoti and Khanam (2014) reported that annual operating cost of a multi-effect evaporator process was 2,371,000 USD with a capacity of 56,200 kg/h. As stated in the ECM Reference Document, real values (for the year 2021) were calculated using the current price index values (for nominal price) (OECD 2022a) and seasonally adjusted GDP deflator values (OECD 2022b), the unit operating cost for this facility was calculated as 5.28 USD/m 3 . ...

Caustic can be recovered from textile mercerization wastewaters by evaporation or membrane filtration. The main objective of this study was to evaluate and compare these two processes in environmental and economic terms, employing the methodology presented in the Integrated Pollution Prevention and Control (IPPC) Reference Document on Economics and Cross-Media Effects (ECM). Cross-media effects for caustic recovery alternatives were calculated on environmental themes including potentials of human toxicity (HTP), aquatic toxicity (ATP), global warming (GWP), acidification (AP), eutrophication (EP), ozone depletion (ODP), and photochemical ozone creation (POCP). For all the environmental themes, membrane filtration exhibited better environmental performance (lower environmental impact) than evaporation. Due to relatively dilute caustic solution to be obtained by membrane processes, ‘membrane filtration + evaporation’ option was also investigated. Findings showed that combination of membrane filtration and evaporation reduces the environmental benefits of membrane filtration alone. The cost-effectiveness values of evaporation and membrane filtration were calculated as 375–625 and 457–685 USD/ton caustic, respectively. Considering the mass of caustic recovered, unit total cost, net present value, internal rate of return, and payback period parameters, it was concluded that evaporation process is more cost-effective than membrane filtration with lower annual unit total cost and payback period. Evaporation may be preferred over membrane filtration in cases where concentrated caustic solution must be obtained for mercerization, although evaporation exhibits lower environmental performance. In cases where dilute caustic solution is adequate or the recovered dilute caustic is to be mixed with new concentrated caustic solution for further use in production processes, membrane filtration can be preferred over evaporation.
Graphical abstract

... The energy used in the black liquor evaporation process takes up about 25% to 30% of the total energy needed in the kraft pulping process, and this causes a big problem in the cost of operation. 8,9 To save energy, a multiple-effect evaporator (MEE) is mostly used to increase the concentration of WBL. 10 MEE reduces steam consumption of the evaporation process by reusing the heat of secondary steam emitted from the evaporators which are arranged in series under different conditions as a heat source. [11][12][13][14] Recently, there has been active research undertaken to reduce the steam that is consumed during the black liquor evaporation process by controlling the condition of MEE. ...

In the pulp and paper industry, black liquor, which is a biomass resource, is burned to produce electricity. Black liquor is concentrated to 21 wt% water through an evaporator before being burned in a boiler. For the evaporator, a multiple-effect evaporator (MEE) is mainly used, but it requires a large amount of energy and cost. Therefore, it is crucial to reduce energy and cost of evaporation process. Hence, this study suggested a novel process model that integrated mechanical vapor recompression (MVR) with MEE to increase the energy efficiency. The suggested MVR-assisted evaporation process was composed of preheating and evaporation processes to effectively concentrate black liquor. In addition, it reduced the steam consumption of MEE by using MVR, which uses relatively inexpensive electric energy in the pre-evaporation process. In the simulation results, the steam, electricity consumption, and the latent heat recovered from the secondary vapor of the suggested process were quantitatively analyzed to verify the energy efficiency. The results indicate that the proposed process increases substantial energy efficiency compared to the conventional process. Then, the appropriateness of the suggested process was evaluated by the techno-economic analysis. The total annualized cost (TAC) is determined for both current and potential future economic benefits. TAC of the MVR-assisted MEE configuration can be reduced by up to 77.54%.

... Those evaporators are an essential part of the kraft pulp and paper process to concentrate the black liquor for chemical recycling. 21 However, thermal evaporation technologies are known to be highly energy-intensive. 22,23 In India, the energy requirement for black liquor evaporators is ∼24−30% of the total boiler steam, making it the sixth largest energy consuming industrial sector in the country. ...

... To obtain the heat transfer in the first effect of the MEE, the Nusselt number [10] ...

The effects of heat transfer performance of systems can be studied in combination with thermodynamic performance. The design solution of maximizing heat transfer always leads to increased entropy generation else if minimizing entropy was aimed then heat transfer got minimized. Hence there is need for holistic optimization. This paper attempts to merge the two competing criteria’s - (i) heat transfer and (ii) the thermodynamic performance of a solar assisted multiple effect evaporator system and optimize study parameters for its energy efficient operation. Solar assisted multiple effect evaporators use steam as source of energy to evaporate wastewater.
The idea of amalgamating these two factors is to observe how much reduction in the performance of one factor will improve the performance of the other. This study couples the two criteria, which has been dealt with separately, to arrive at the parameters of interest which must be fine-tuned for ensuring system performance.
Mass flow rate of steam and wastewater appeared to chiefly influence heat transfer and entropy generation of the system, negligible influence was observed on changing the concentration of the waste water or optical efficiency of the solar concentrator in single legged analysis. However through this holistic optimization study, it was found that variations in Prandtl number, i.e., the concentration of the waste water and optical efficiency of solar concentrator drastically shift the optimization balance of entropy generation and heat transfer rate.

... Many efforts have been made to build process models to represent industrial MEE units. Evaporation steady-state models were developed to represent the process in simulation and optimization contexts, but with lack of validation with actual industrial data [1][2][3]. On the other hand, some authors developed steady-state models that could provide good fits of industrial data [4][5][6][7], but these tools have been used so far for off-line applications. ...

Digital twins are rigorous mathematical models that can be used to represent the operation of real systems. This connection allows for deeper understanding of the actual states of the analyzed system through estimation of variables that are difficult to measure otherwise. In this context, the present manuscript describes the successful implementation of a digital twin to represent a four-stage multi-effect evaporation train from an industrial sugar-cane processing unit. Particularly, the complex phenomenological effects, including the coupling between thermodynamic and fluid dynamic effects, and the low level of instrumentation in the plant constitute major challenges for adequate process operation. For this reason, dynamic mass and energy balances were developed, implemented and validated with actual industrial data, in order to provide process information for decision-making in real time. For example, the digital twin was able to indicate failure of process sensors and to provide estimates for the affected variables in real time, improving the robustness of the operation and constituting an important tool for process monitoring.

... Como se ha explicado, la integración de procesos se basa en que de la obtención de productos principales se generan corrientes residuales que se pueden utilizar en el propio proceso o en otros procesos haciendo de dos o varios procesos que una vez fueron independientes un complejo industrial [4][5][6]. También la integración de procesos se basa en que todos los procesos consumen energía térmica para sus producciones, la cual en ocasiones se pierde en corrientes residuales y que puede ser recuperada y aprovechada por el propio proceso o por otros disminuyendo de esta manera el consumo de una utilidad, ya sea caliente o fría [7][8][9]. ...

The possibility of process integration in the production of sugar and alcohol was evaluated through the exchange of raw matter such molasses, diluted juice, and bagasse from the sugar process for their use in the ethanol production. The energy integration was also carried out in these processes with the use of the pinch method, for that the cold and heat streams were analyzed with possibilities for it. The steam consumption was estimated in turbogenerators, exergetic efficiency and other were calculated too for a better knowledge of the operational state of the same ones, being these below the technical norms, for what intended a change in the cogeneration system for a better use of the system obtaining higher values for the efficiencies when comparing them with the installed technology. The economic balances were carried out in the cogeneration scheme and as result were obtained that support the possibility of the technology change, what would benefit to the processes of sugar and alcohol in the improvement of their productions, given the possibility to have a bigger availability for raw matter for both processes.

... Evaporation process requires a large amount of energy to evaporate water, so evaporation can be seen as an energy-intensive operation [10]. Do [11] discovered that evaporation consume 75% of energy, which meant there was a promising prospect for energy conservation. ...

... Evaporation is an important unit operation in many industrial processes. These processes use multiple-effect evaporators to evaporate water from diluted solutions, such as black liquor (Khanam and Mohanty, 2010;Jyoti and Khanam, 2014), milk (Ribeiro and Andrade, 2003), tomato juice (Sogut et al. 2010), orange juice (Balkan et al., 2005), sugar juice (Srivastava et al., 2013), and sea water (Sagharichiha et al., 2014). Multiple-effect evaporator in the sugar industry operates in the co-current mode with steam or vapor and sugar juice flowing in the same direction. ...

The evaporation process in raw sugar manufacturing consists of juice heater, multiple-effect evaporator, and crystallizer. Two performance parameters of the evaporation process are the rate of processed sugar juice and the steam economy, defined as the ratio between water content of sugar juice entering the process to the amount of steam required to run the process. If the total surface area of the multiple-effect evaporator is fixed, the performance parameters are affected by the distribution of the surface area among the effects of the evaporator. Although the optimization of evaporator surface area distribution has been investigated in previous studies, they have considered only the multiple-effect evaporator, and overlooked interactions between the three components of the evaporation process. The current investigation proposes a model of the evaporation process that takes into account interactions between the three components of the process through mass and energy balances. The model is used to find the optimum surface area distribution that maximizes the rate of sugar juice processed by the system and the optimum surface area distribution that maximizes the steam economy are different.

... Some of the noteworthy efforts in the steady-state analysis are made by Kern (1950); Nishitani and Kunugita (1979); Ayangbile et al. (1984); Jyoti and Khanam (2014); Ruan et al. (2015); Verma et al. (2016b). Mathematical modeling of MSE starts from application of first principles of thermodynamics. ...

This research article attempts to investigate the dynamic behavior of the heptads’ effect evaporator (HEE) used to concentrate the weak black liquor during the Kraft recovery process in a paper industry. In order to fully characterize the HEE unit, a complete understanding of its performance for steady state and transient conditions is required. For this purpose, a set of first order nonlinear differential equations have been developed for the backward feed flow configuration (BFFC) for an unsteady state. Further, the developed non-linear model is linearized and linear state space equations obtained. The dynamic response of the system in terms of vapor temperature and liquor concentration changes for different changes in input liquor flow rate has been investigated. The rise, delay and settling times for the temperature deviation from steady state have been found to be significantly less as compared with that for the concentration deviation. The results also indicate that each effect of HEE acts as an individual first order system. The placement of such first order systems in series makes both the liquor concentration and vapor temperatures response more sluggish progressively with each subsequent effect. Finally, a Cascade-PID control strategy has been implemented and shown to exhibit differentiated and improved dynamic performance of the HEE system versus open-loop dynamic response.

... A large amount of energy or heating source in the form of steam is consumed in P&P mills to concentrate the weakly concentrated liquor during the evaporation process. As per reported data for worldwide energy/steam consumption in P&P mills, weak black liquor concentration con-sumes~12% of total recovery boiler steam in Switzerland [3] and 24e30% of total energy consumption in India [4]. The P&P industry in India is the sixth largest energy consumer in industrial sector [5]. ...

The maximization of the energy (steam) efficiency of a multi-stage evaporator system used for concentrating the black liquor in pulp and paper mills carries immense significance in today’s scenario. The nonlinear mathematical models of heptads’ effect backward feed flow with various energy saving schemes namely, steam-split, feed-split, feed-preheating and their hybrid operations have been developed. The steam economy as a cost function translates the problem into a nonlinear optimal search problem. The mass and heat balance equations act as nonlinear equality constraints while vapor temperatures and liquor flows appear as inequality constraints. The formulated optimal problem has been solved efficiently using Interior-Point Method which demonstrates advantages of convergence and less sensitivity towards initial values versus conventional algorithms. The simulation results indicate that a hybrid of steam-split, feed-split and feed-preheating process arrangements with backward feed flow could provide the highest heat transfer across evaporator effects with optimum of steam economy of ∼6.49 and consumption of ∼1.97 kg/s.

... O In order to improve the energy efficiency with enhancement of quality of final product in MSE, it is essential to formulate and simulate the nonlinear steady and transient models of nonlinear Heptads' Effect Evaporator (HEE) steady state process with Backward Feed Flow (BFF). Though the steady state analysis for MSE has been well explored in literature [8][9][10][11], proper optimization of its efficiency would require development of suitable advanced control strategies based on their dynamic simulation. Unfortunately, the area of dynamic modeling and simulation of MSE has not been extensively investigated. ...

The dynamic model of heptads’ stage evaporative unit employed in concentrating black liquor in paper industry show tremendous complexity. In this work, linearization of such a complex nonlinear model consisting of 14 first order nonlinear differential equations and determination of the system transfer functions has been explored through an exhaustive state space representation technique. The transfer functions that relate the product concentration change to liquor flow rate deviation have been evaluated and presented through this work for the first time. These serve as an input to design a PID controller and study its response for a set point change in product concentration. The response analysis indicated a noticeable overshoot, undershoot and Integral Square Error (ISE), that may collectively influence the product quality. To overcome this issue and to make controlling of product concentration more robust, an intelligent Mamdani type Fuzzy Logic-Proportional-Integral-Derivative (FLC-PID) controller has been additionally designed and its response simulated. A comparison of response of FLC-PID and PID indicated that the rise time of former is larger than the latter. However, FLC-PID response settles faster with ∼49% smaller settling time than PID, possesses zero undershoot, a ∼93% reduced overshoot and 21% reduced ISE. The results demonstrate improved tracking capability, and hence, better control performance of FLC-PID for transient changes in product concentration.

... Measures well known to improve the steam economy of a MEE include condensate flashing and liquor preheating (Jyoti, Khanam 2014). Pinch analysis was originally developed by as a tool for minimizing the needs for external heating and cooling through designing optimal internal heat exchanger networks. ...

The primary objective of this study was to quantify the amount of excess energy that is present in the evaporation system of an integrated pulp and paper-board mill and to analyze a number of energy recovery cases. These focus on improving the energy efficiency in the evaporation plant and are mainly based on the process data of performance tests from the full-scale production site. A computer script was developed in order to analyze the process streams and can be used to construct the Grand Composite Curve (GCC) of the evaporation system. In addition, the study identified seasonal variations in the potential excess of energy (higher in warmer weather and lower, or even non-existent, in colder) and suggestions are made as to how this energy may be used in a thermodynamically optimal way.In the case studies, the thermodynamically optimal method of recovering heat involved a combination of sensible heat and flash evaporation, indicating the maximum reduction in steam consumption. For the case of only utilizing sensible heat outside the evaporator system to pre-heat one of the liquor flows, the results indicated a lower reduction in steam but also a lower capital cost.

... Different simulation methods have 52 been developed, such as an equation-solving method and a simultaneous modular method. Each of 54 modeling, programming, and solving the model equations) [12][13][14][15][16][17][18]. 55 ...

... More realistic models, however, incorporate actual steam and solution properties, which make models nonlinear. Further complications arise from possibilities of flashing of condensate and product, and splitting of steam (Gautami and Khanam, 2012;Jyoti and Khanam, 2014). The model of multiple-effect evaporator illustrated in Fig. 1 is more simplified than previous models. ...

Multiple-effect evaporator is used to increase the concentration of a solution in a series of pressure vessels. If the total surface area of the evaporator is fixed, the performance of the evaporator is affected by the distribution of surface area among vessels. Previous studies have been concerned with optimization of surface area distribution with the assumption that no fouling occurs. The present study considers a more realistic case when the last-effect vessel is subjected to fouling. The model of multiple-effect evaporator yields a system of nonlinear equations. Specified parameters are pressures and juice concentrations at inlet and outlet of the evaporator. The solution obtained from an iterative procedure is used to compute two objective functions, which are maximized at different optimum surface area distributions. Given a known rate of fouling, it is shown quantitatively how much the area of the last-effect vessel must be increased relative to the areas of the other vessels in order to achieve the maximum overall steam economy or the maximum amount of input to the evaporator.

... Other works considering optimization in MED process have been published. Jyoti and Khanam [15] developed the model of a MED system for different operating configurations such as steam splitting, condensate flashing, vapor bleeding, etc. Likewise, they carried out the optimization of the number of flash tanks in the system based on an economic analysis. ...

This paper proposes a novel concept for the optimal design of multi-stage vacuum membrane distillation (VMD). Generally, a multi-stage VMD is designed with an equal temperature difference between each stage. However, such a design is energy inefficient and increases VMD area requirements. An analytical methodology for calculating the optimal stage temperature is proposed. By selecting the optimal stage temperature, the energy efficiency and required membrane area can be potentially improved by 16% and 30%, respectively. The proposed concept applies to all heat sources, including latent, sensible, and waste heat. To illustrate the method, multi-stage VMD is integrated with the waste heat from a supercritical water desalination (SCWD) system to achieve zero liquid discharge. SCWD is an energy-intensive process, requires high-quality thermal heat (>450 °C), and exhibits high waste heat rejection. The integrated VMD-SCWD approach is approximately 50% more energy-efficient and 35% more cost-efficient than the standalone SCWD system. Compared to the commercially used brine concentrator and crystallizer, the multi-stage VMD-SCWD system is more energy efficient for feed concentrations >5%. It is around 30% less expensive for all feed concentrations due to less expensive membrane distillation modules compared to a brine concentrator. The proposed design concept can replace the brine concentrator and crystallizer as an improved alternative for a zero-liquid discharge desalination system.

Deploying renewable energy to unit design energy-efficient technologies may fulfill the additional demand of various energy-intensive industries for their sustainability and resiliency. Multiple Stage Evaporator (MSE) is one of the most energy-intensive units used to extract the water content of the weak liquor in various industries, including the paper industry. This energy intensiveness may be reduced by integrating various Energy Reduction Schemes (ERSs). Hence, this work proposes a ERSs integrated MSE model to analyze its energy efficiency. These ERSs includes Thermo-Vapor Compressor, Steam-, Feed- Split, Feed Preheater, and Flash Tanks. Further, the performance of the proposed model is investigated under two important real-time plant complexities: Boiling Point Elevation and Fouling to achieve more realistic results. The performance analysis is initiated with the formulation of a nonlinear constrained optimization problem to increase the steam economy (SE). Also, the simulation is extended to validate at two different product concentrations (52% and 65%) by employing state-of-art optimization algorithms: CONOPT, and SCA in GAMS and MATLAB respectively. The simulated results shows an increment 1.64% and 1.37% of SE for both 52% and 65% concentration of weak liquor respectively in case of CONOPT than SCA. Also, the waste heat of the condensate, feed, and product may be further utilized for the heat recovery by incorporating the flash tanks which leads to a countable energy saving. Eventually, integrating the solar fields: PTC and LFR ensures a notable reduction in conventional heat utilization by 85.96% and 92.85%, respectively and hence, enhance the energy efficiency.

La evaporación como operación unitaria ha cobrado gran importancia en la industria debido a que puede disminuir los costos del transporte de fluidos sin alterar las propiedades fisicoquímicas de la sustancia. Este artículo hace una revisión bibliográfica acerca de los diferentes tipos de evaporadores de uso común en la industria, así como de los principales factores que han sido estudiados para mejorar su eficiencia. Igualmente, aquí se trata sobre el modelamiento y simulación de estos equipos para realizar procesos de optimización y sobre el uso de nuevas tecnologías para ampliar el campo de aplicación de dicho procedimiento.

The black liquor is concentrated in a multiple evaporation system to achieve steam economy. The focus of this paper is to solve complex mass and energy balance non-linear equations and to reduce them to a simple matrix form using MATLAB. A detailed analysis is done to observe parameters effects on the entire process and on steam consumption according to the increase in the number of effects of evaporation. Complexity of the process is solved using mathematical modelling and simulation with MATLAB and MINITAB using ANOVA Analysis. The process is repeated for three-effect, five-effect and seven-effect evaporator. The comparison is analysed to show the effectiveness of steam economy and to conclude if it is beneficial to increase the number of evaporators to have effective energy conservation. According to the mathematical analysis, the number of effects is important to achieve steam economy, whereas the number of effects has no impact on parameters.

In this paper, a novel methodology based on process superstructures is described that enables structure and heat-transfer areas to be simultaneously considered in optimization without having to resort to any previously selected arrangements. This methodology is applied to an industrial evaporator case study of simultaneously sizing and determining the best way to arrange additional evaporator bodies in an existing system to increase maximum load. An equation-oriented simulator for chemical pulp mill evaporator plants, based on a Trust Region method, was developed and used in conjunction with a differential evolution optimizer. Two multiple-effect evaporator plants were used as case studies: a small three-effect system, to highlight the workings of the new method, and a more realistic six-effect system, both of which were assumed to undergo a 15% increase in black liquor mass flow rate. The methodology was capable of determining the optimal arrangement and heat-transfer areas for both systems.

The sugar juice evaporation process consists of juice heater, evaporator, and crystallizer. The juice heater increases the temperature of diluted sugar juice from the ambient temperature to the boiling point. The evaporator removes most water content of diluted sugar juice. The crystallizer removes the remaining water content, yielding raw sugar as the final product. Since both the juice heater and the crystallizer require vapor bled from the evaporator, there are interactions between the three components. A model of interactions between the three components of the sugar juice evaporation process is presented in this paper. The model yields a system of nonlinear equations that, under some specified assumptions and conditions, consists of only two free parameters. This implies that there is a unique distribution of a given total juice heater surface when vapor is bled from the first two effects of the evaporator. In contrast, if vapor is bled from the first three or four effects, there are many possible surface distributions. It is shown that there is an optimum surface distribution when vapor is bled from either the first three or four effects of the evaporator that minimizes the steam economy. The optimum four‐effect vapor bleeding arrangement results in the largest steam economy. However, the two‐effect vapor bleeding arrangement produces a larger mass flow rate of processed sugar juice than either three‐effect vapor bleeding arrangement or four‐effect vapor bleeding arrangement.
Practical applications
This paper presents a mathematical model of a sugar juice evaporation process. Although one specific process design is under consideration, the model can easily be adjusted for a different process design. This model will be useful for analysis and optimization of the process. One optimization problem mentioned in the paper is the optimum allocation of a fixed total surface among the four heat exchangers of the juice heater, which is used to increase juice temperature to the boiling point before entering the quintuple‐effect evaporator. It is found that there are two different optimum surface allocations corresponding to the maximum rate of processed juice and the minimum amount of steam required by the process. Results of this paper should provide a guideline to a process designer in selecting the juice heater that will both satisfy the required heating duty and yield the optimum performance.

Increasing energy demand, high cost of energy and global warming issues across the globe require energyintensive industries, such as paper mills to improve energy efficiency. Multi-stage evaporators used to concentrate the black liquor in such mills form its most energy consuming unit and require a strong understanding of steady and unsteady state behavior to ensure energy savings. The modeling of nonlinear heptads’ effect system yielded a set of complex nonlinear algebraic and differential equations that are analyzed using Interior-point method and state space representation. Dynamic response of product concentration and system vapor temperatures along with system stability and controllability have been explored by disturbing the flow rate, concentration and temperature of feed, and fresh steam flow rate. Simulations predict that steam flow rate, feed flow rate and its concentration invariably are major controlling factors (in decreasing order) of vapor temperature and product concentration. The interactive behavior between different effects translates into slower responses of the effects with increasing separation from disturbance source. This steady state and transient study opens many new explanations to this relatively less explored area and helps to propose and implement industrial PID controllers to reduce steam consumption and control product quality.

This chapter describes the development of a mathematical model of a vertically stacked, forward feed (FF), low-temperature multi-effect distillation (LT-MED) plant. The model was developed by taking into consideration the same design and operational characteristics as the pilot multi-effect distillation (MED) plant at Plataforma Solar de Almería, in the southeast of Spain. The model has been validated, comparing the results of the model with the experimental data from the pilot plant.

This paper presents the genetic algorithm approach to solve the highly complex set of fourteen simultaneous nonlinear algebraic benchmark problem for the backward feed seven effect evaporator. Generally, Newton’s method may be considered a better numerical technique to solve such nonlinear problems. However, a higher number of effects (seven in this case) complicates the evaluation of a 14 × 14 Jacobian matrix that involves determining the analytical derivative of all system variables. Also, such a simultaneous nonlinear algebraic equations model exhibits the problem of divergence and instability when initial values have not been chosen appropriately. In this work, genetic algorithm approach has been demonstrated to be very efficient to solve such complex nonlinear models for a large number of effects in evaporative system without any complications. To make the model more realistic and representative of physico-thermal properties of liquor, boiling point elevation of the liquor during evaporation has been incorporated. Finally, the developed models are solved using genetic algorithm to determine the process variables, namely liquor and steam flow rates, which yield process performance parameters of energy efficiency (steam economy and consumption). The results indicate that a maximum steam efficiency may be achieved for a 50 % steam split in the first two effects.

The performance of the multi-stage evaporator (MSE) system used in the pulp and paper industry for the Kraft recovery process may vary significantly during the transient time of start-up, shutdown, load changes and rejections, troubleshooting, etc. This makes it quite imperative for a process engineer to know the transient behavior of the system under operation. Although, the steady-state models for the MSE system have been analyzed quite exhaustively by the researchers in the past but the dynamic model has not been extensively investigated. The purpose of the paper is to develop and present a detailed dynamic model for the study of transient behavior of the evaporator unit with varying process designs. A heptads’ effect evaporator system with the backward feed flow configuration has been considered for the dynamic modeling in the present work. Some important and pertinent energy saving operating strategies such as live steam split, liquor feed split, feed pre-heating and their hybrids, have been incorporated in the process design. The systematically evaluated material and heat balance equations evolve into different transient models with a set of nonlinear first order differential equations. The finally derived model equations may be conveniently simulated so that the performance of process control strategies could be compared and an optimized operating strategy be screened for use by industry under different operating conditions without disturbing the paper mill production and without imperiling the equipment.

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.

Multiple effect evaporators (MEE) are energy intensive equipments. Often the focus is on minimizing the energy consumption of MEE as a standalone system, rather than that of the entire plant. In this paper, process integration techniques are applied to integrate various stages of a MEE with the background process. To identify various energy conservation opportunities, MEE is represented as a Grand Composite Curve (GCC) and integrated with the GCC of the background process. Change in utility consumption in the first effect, due to energy shift (in the GCC) between various effects, is determined in this paper. It is proved that for the minimum energy requirement all effects should be pinched. Using these mathematical results, a methodology for optimally integrating MEE with background process is developed. Furthermore, additional energy may be conserved by appropriately selecting effect temperatures. A methodology for appropriate selection of effect temperatures is also proposed in this paper. Applicability of the proposed methodologies is demonstrated through a case study. It is observed that 9.8% energy can be conserved by properly integrating MEE with the background and an additional 25.87% of energy can be conserved by selecting optimal effect temperatures.

Food frying is very energy intensive and in industrial potato crisp production lines frying is responsible for more than 90% of the total energy consumption of the process. This paper considers the energy flows in crisp frying using a First Law of Thermodynamics modelling approach which was verified against data from a potato crisp production line. The results indicate that for the frying process considered, most of the energy used is associated with the evaporation of water present in the potato and on the surface of potato slices. The remainder is from evaporation of frying oil and air of the ventilation system and heat losses from the fryer wall surfaces by convection and radiation. The frying oil is heated by an industrial gas furnace and the efficiency of this process was calculated to be 84%. The efficiency of the overall frying process which was found to be of the order of 70% can be improved by employing exhaust heat recovery and optimising other operating and control parameters such as exhaust gas recirculation.

Using equations of material and energy balance, heat transfer rate and boiling point, a mathematical model of multiple effect evaporator systems with various feed arrangements has been developed. It has been solved by the application of Newton-Raphson method to determine flow rate of liquid and vapour streams, temperature and concentration in each effect of the evaporator. The model has been tested for solute concentration, liquor temperature and vapour temperature in each effect against the industrial data of a few typical mills of sugar, caustic soda and pulp and paper.

This guide, for practising engineers, presents simple but highly effective design techniques which have been fully proven in many industrial applications and can be used in the design of new plant and to retrofit projects. There is a comprehensive summary of the principles of process integration followed by chapters on heat exchangers and case studies of their use. A further chapter outlines the general strategy for applying the principles in the guide. Finally, the relative merits of general education, the use of experts, and the use of computer software are briefly discussed. There is a subject index.

Cited By :46, Export Date: 4 January 2015
Published in UK in hardcopy format 2006, US (hardcopy) and electronic format 2007. Kindle and Chinese editions also available. Publication date generally quoted as 2007 (as printed in book).
For further details, see entry with 2007 publication date.
The book is the extensively revised and expanded 2nd edition of the IChemE User Guide on Process Integration for the Efficient Use of Energy, 1st edition published 1983. Scope is confined to energy aspects (not water pinch or mass integration).

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.

In the present work mathematical models based on set of nonlinear equations have been developed for the synthesis of multiple effect evaporator (MEE) systems. A number of configurations and complexities of real MEE system such as condensate, feed and product flashing, vapor bleeding, steam splitting, variable physical properties and boiling point rise are accounted to develop of different models. Along with these a model for predicting fouling resistance is also developed using the experimental data.Developed models for MEE system are compared based on product concentration and steam economy to select the optimum model. The results of the selected model are validated with published model and industrial data. The operability analysis with pressure constraints is carried out for the selected model and for the modified MEE system capital investment, operating cost, profit as well as payback period is computed.

This paper represents the 2nd part of a paper in two parts. In part I a 2nd Principle analysis of a Multiple-Effects-Evaporation (MEE) process has been proposed. In this Part II perspectives for process improvement will be investigated, along two distinct research lines: the thermoeconomics-aided optimization of a new system and the increase of thermal efficiency for existing systems by a pinch-based plant retrofit. As concerns the first research line, a detailed productive structure for the plant stage (i.e. effect) examined in Part I is presented; the cost formation structure is then used to improve a simplified optimization process, revealing capable to properly reflect the interactions among exergy flows. It is shown that the flash at brine inlet and the exergy destruction at the pre-heaters, both apparently playing a secondary role with respect to heat transfer at the evaporators, become main sources of irreversibility when the ΔT between two consecutive effects increases. Then, as a corollary to the low exergetic efficiency calculated in Part I of this paper, the potential for exergy saving through process integration is discussed. Although detailed calculations are not included, a conceptual application of pinch-based techniques is proposed, which reveals scarce margins for integration at process level and a much higher potential for process/hot-utility integration. The use of heat cascades can be optimized looking at the Thermal Desalination Process as a black box; economics of cogeneration systems integrated with the desalination plant and targeted on heat supply, in fact, essentially depends on the cost of feed steam, fuel and electricity.

Quadruple-effect evaporator units are commonly used in food focus area in sector is evaporative unit. It consumes about 60% of total energy input. The present study evaluates the performance of quadruple-effect evaporator unit (QEEU) by using exergy analysis based on actual operational data. A tomato paste factory is chosen for the analysis. The highest exergy destruction/loss occurs in the first effect with 158.2 kW, 52.7% of exergy input in first effect. Steam temperature should be decreased in order to decrease exergy destruction in first effect. Also, third effect achieves the highest exergy efficiency with 93.3%. Exergetic improvement potential of each effect varies between 0.3 kW and 83.6 kW. The highest and lowest exergetic improvement potential occurs in first and third effect of QEEU system, respectively. Exergetic improvement potential is equals to 52.80%, 11.10%, 6.73% and 69.8% of exergy loss/destruction from the first effect to the last effect, respectively. Total exergetic improvement potential is achieved as 128 kW (55% of total exergy loss/destruction) in QEEU system. It is expected that analyses result provide important information for designer and/or resources of multiple effect evaporator unit.

A performance analysis is presented for the vapour compression parallel feed multiple effect evaporation water desalination system. The systems include mechanical (MVC) and thermal (TVC) vapour compression. The system models take into account the dependence of the stream physical properties on temperature and salinity, thermodynamic losses, temperature depression in the vapour stream caused by pressure losses and non-condensable gases, flashing within the effects, and the presence of flashing boxes. The analysis is performed as a function of the brine distribution configuration (parallel or parallel/cross flow), the top brine temperature, the temperature of the brine blowdown, and the temperature difference of the compressed vapour condensate and the brine blowdown. The analysis is focused on variations in the parameters that control the product cost, which includes the specific heat transfer area, the thermal performance ratio, the specific power consumption, the conversion ratio, and the specific flow rate of the cooling water. Results show consistent behaviour with industrial practice, where the thermal performance ratio of the TVC system decreases at higher top brine temperatures, while the specific power consumption of the MVC systems decreases at higher temperatures. Also, the specific heat transfer area for all configurations decreases at higher operating temperatures. The conversion ratio is found to depend on the brine flow configuration and to be independent of the vapour compression mode. For the parallel flow configuration, the conversion ratio decreases with the increase of the operating temperature. On the other hand, the conversion ratio for the parallel/cross flow system decreases with the increase of the brine blowdown temperature. Predictions of both models show good agreement with field data.

The optimization of the flow-pattern for a multiple effect evaporator system is discussed as a vector minimum problem. First a new program to solve the design problem for various flow-patterns with no stream mixing or splitting and an arbitrary number of effects is described. Second the set of noninferior flow-patterns is generated by enumerating one-by-one for all flow-patterns. This method works well in synthesizing multiple effect evaporator configuration.

Besides the largest energy consumption in the process of sugar production, evaporation also presents many opportunities of thermal integration with the remaining of the process. That occurs due to the possibility of making use of the vapor generated during the evaporation operation (vegetal vapor), as a heating source, from extractions to process. Regarding the thermal integration of the multiple effect evaporator (MEE), previous studies showed that, in general, the energy recovery is usually larger when extractions are practiced in the last effects of the operation. Although the results found can be used for development of new projects, as heuristic rules, the application has been limited due to the lack of understanding on the subject. In the present investigation, a study was carried out by defining equations that can be used as a reference for thermal integration projects, including MEEs. The equations are also helpful for elaborating a systematic way to apply pinch analysis in sugar plant with an algorithm.

We present the computational experiences which we encountered during the simulation of a triple effect evaporator used for concentrating the caustic soda solution. Besides, empirical correlations for the enthalpies of steam condensate, and caustic soda solution have been developed. A new arrangement of model equations is also proposed to facilitate their solution

A calculational procedure useful in the design of multiple-effect evaporator systems is presented in this work. This algorithm reduces the series of nonlinear algebraic equations that govern the evaporator system to a linear form and solves them iteratively by a linear technique, e.g., Gaussian elimination. The algorithm is simple, easy to program, inherently stable, and virtually guarantees convergence, thereby eliminating the biggest problems with general nonlinear methods. Boiling point rise and nonlinear enthalpy relationships are included and require only a knowledge of their functions in temperature and composition. These relationships are obtained by curve fitting or interpolation. For a given number of stages, the calculational procedure computes design variables such as area (or area ratios between effects), externally supplied steam rate, stage temperatures and flows, etc. Such results are directly useful in design analysis and economic optimization programs.

In this study, heat recovery from rotary kiln was examined for a cement plant in Turkey. At first, an exergy analysis was carried out on the operational data of the plant. Results indicated the presence of 217.31 GJ of waste heat, which is 51% of the overall heat of the process. Then a mathematical model was developed for a new heat recovery exchanger for the plant. It was determined that 5% of the waste heat can be utilized with the heat recovery exchanger. The useful heat obtained is expected to partially satisfy the thermal loads of 678 dwellings in the vicinity through a new district heating system. This system is expected to decrease domestic-coal and natural gas consumption by 51.55% and 62.62% respectively. CO2 emissions may also be reduced by 5901.94 kg/h and 1816.90 kg/h when waste heat is used instead of coal and natural gas.

Mathematical modeling of the multiple effect evaporation (MEE) desalination process has been carried out to determine the effects of the important design and operating variables on the parameters controlling the cost of producing fresh water. The model assumes the practical case of constant heat transfer areas for both the evaporators and feed preheaters in all ef-fects. In addition, the model considered the impact of the vapor leak in the venting system, the variation in thermodynamic losses from one effect to another, the dependence of the physical properties of water on salinity and temperature, and the influence of noncondensable gases on the heat transfer coefficients in the evaporators and the feed preheaters. The modi-fied fixed-point iterative procedure is used to solve the large number of highly nonlinear equations describing the MEE desalting system. The algorithm consists of 10 calculation blocks and 6 logical blocks. The algorithm is implemented using L-A-S computer aided language. Results show that the heat transfer coefficients increase with the boiling temperature. Also, the heat transfer coefficient in the evaporator is always higher than that in the feed preheater at the same boiling temperature. The plant thermal performance ratio is nearly independent of the top brine temperature and strongly related to the number of effects. The specific heat transfer area increases by raising the number of effects and reducing the top brine temperature. The effect of the top brine temperature on the specific heat transfer area is more pronounced with a larger number of effects. The required specific heat transfer areas at a top brine temperature of 100 °C are 30.3% and 26% of that required at 60 °C when the number of effects are 6 and 12, respectively. The specific flow rate of cooling water is nearly constant at different values of top brine temperature and tapers off at a high rate as the number of effects is increased. Two correlations are developed to relate the heat transfer coefficients in the preheater and the evaporator to the boiling temperature. Design correlations are also developed to describe variations in the plant thermal performance, the specific heat transfer area, and the specific flow rate of cooling water in terms of the top brine temperature and the number of effects.

Chemical process simulation has proven to be an effective tool for performing a systematic and global analysis of energy systems to identify routes for maximizing the process efficiency concerning to the heat recovery. This paper shows an application of computer simulations in a Brazilian pulp mill, using two strategies for minimizing the mill energy consumption. In the first one, the overall heat transfer coefficient has been predicted for each body of the multiple effect evaporators by using continuous on-line data from the industrial plant in the black liquor recover unit. By monitoring oscillations of this heat transfer coefficient, the suitable time for washing the evaporator heat transfer surfaces can be well determined, reducing the energy loss during black liquor evaporation. In the second strategy, the liquor combustion has been simulated as function of the black liquor solids concentration to analyze its effect on the recovery boiler efficiency improvement.

This paper describes a phenomenological, stationary and dynamic model of a multiple effect evaporator for simulation and control purposes. The model includes empirical knowledge about thermophysical properties that must be characterized into a thermodynamic equilibrium. The properties selected evolved from an economical optimisation because of their influence on the temperature and concentration variations parameters. The developed model consists of differential and algebraic equations that are validated using a parameter sensitivities method that uses data collected in the industrial plant. The simulation results show a qualitatively acceptable behaviour. The values of the estimated parameters are physically appropriate for the process. The study of parametric sensitivity and more generally of the model sensitivity, with respect to variables has been judicious for the parameter estimation as for the choice of suitable data for model validation. This study shows also that the most important parameters of the process are the global heat transfer coefficient and the latent heat of vaporization.

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.

Evaporation is a key operation in many industries and its optimization is required for the efficient management of water and energy within the process. During the operation, dissolved solids settle on the heat exchange surfaces with the consequent increase in the heat transfer resistance. Therefore, periodic shutdowns of the trains of evaporators are required for the cleaning of the units in order to restore acceptable performance. In this work the simultaneous re-design and scheduling of multiple effect evaporation systems is addressed. A mixed integer nonlinear programming model based on a discrete time representation is proposed and applied to a typical evaporation system in the sugar industry with several multiple effect parallel lines and time decaying performance.

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.

Contenido: Fundamentos y modelado de procesos de equilibrio; Evaporación; Introducción a los fundamentos de la destilación; Absorbedores y disolventes; Métodos numéricos y gráficos para resolver problemas de extracción; Fundamentos y modelado de procesos de valoración; Formulación de ecuaciones requeridas para describir modelos de procesos; Relaciones de transferencia de masa y su aplicación a los modelos clásicos de torres de absorción; Fundamentos y procedimientos para las torres de destilación; Uso de los resultados de las pruebas de campo en el modelado de torres de destilación; Modelado de una columna de extracción líquido-líquido.

Multiple effect evaporator performance for black liquor-I simulation of steady state operation for different evaporator arrangements

- D J Bremford
- H Muller-Steinhagen

D.J. Bremford, H. Muller-Steinhagen, Multiple effect evaporator performance
for black liquor-I simulation of steady state operation for different evaporator
arrangements, APPITA J. 47 (1994) 320e326.