Mathematical modeling of multiple-effect evaporators and energy economy

doi:10.1016/j.energy.2006.09.002

Energy

Volume 32, Issue 8, August 2007, Pages 1536-1542

https://doi.org/10.1016/j.energy.2006.09.002 Get rights and content

Abstract

In this study, a mathematical model was developed for multiple-effect evaporators. These evaporators have cocurrent, countercurrent and parallel flow operation options. Each operation was investigated with and without pre-heaters. The effect of pre-heating on evaporation process was investigated from the point of energy economy. A sugar factory's data was used with the applied models as a case study. The results obtained for pre-heated and non-pre-heated situations were compared with each other. The maximum COP is found as 3.33 for countercurrent operation with pre-heating. The minimum COP is 2.57 for parallel flow operation without pre-heating.

Introduction

The sectoral distribution of energy consumption in Turkey is approximately 35% for residential, 34% for industrial, 23% for transportation sectors and 8% for others [1]. The thermal energy in industry accounts for 2/3 of the total energy consumption. Industrial heat energy demand below 200 °C is 20–25% of the energy consumption.

Multiple-effect evaporation is, in general, applied in large-scale companies to reduce steam consumption [2], [3]. For example, in a sugar factory, sucrose juice is extracted by diffusion. This juice is concentrated in a multiple-stage evaporator to produce syrup. The liquor goes through a series of four stages, and each passage its brix (sucrose concentration) increases. The juice steam recovered from the first stage is used as a heat source for the second stage, and so on until the last stage. The cost of sugar manufacturing depends highly on the multiple-stage evaporator's steam consumption [4]. More precisely, the sugar evaporation processes should be designed in such a way that the energy used is optimized, and the required quality of the final product is achieved [5], [6].

There are several recent studies about mathematical modeling of thermal systems such as those by Mithraratne and Wijeysundera [7], Lissane Elhaq et al. [5], and Lopez and Lacarra [8]. The aim of this study is to develop mathematical models for multiple-effect evaporators and to investigate the effect of pre-heating in the evaporation process from the point of energy economy.

Section snippets

General modeling of a quadruple-effect evaporators system

In modeling of multiple-effect evaporators, a pressure and temperature value is set for each evaporator. The necessary enthalpies for these pressure values are found from thermodynamic tables and diagrams. The mass, component and energy balances are provided for each evaporator and also for the system. These balances are transformed to linearly independent equations after necessary assumption. In an evaporator system, which has N evaporator number, N+1 linear equations are obtained. These

The definition of sample problem

The sample problem is from a sugar industry. The solution obtained from sugar beet or cane is sent to sugar tank. The temperature of solution is 35 °C. The solution mass flow is 100,000 kg/h and its concentration is 15%. The solution is concentrated in a multiple-effect evaporator. The final product is syrup in 65% concentrations. The pressure, temperature and sensible heat of initial steam are 1.5 bar, 111.4 °C, 2226.5 kJ/kg, respectively.

The specific heat for the solution is 3.81 kJ/kgK [9], [10],

Conclusions

In multiple-effect evaporations, the mathematical models for cocurrent, countercurrent and parallel flow operation types under with/without pre-heating cases were developed. A sample study has been done using a sugar factory's data. The maximum COP is found as 3.33 for countercurrent operation with pre-heating while the minimum COP is 2.57 for parallel flow operation without pre-heating. For all the other cases COP is between 2.57 and 3.33. The best operation for economic steam consumption is

References (12)

S. Lissane Elhaq et al.
Modelling, identification and control of sugar evaporation—theoretical design and experimental evaluation
Control Eng Practice
(1999)
P. Mithraratne et al.
An experimental and numerical study of the dynamic behavior of a counter-flow evaporator
Int J Refrig
(2001)
A. Lopez et al.
Mathematical modelling of thermal storage systems for the food industry
Int J Refrig
(1999)
I. Kilicaslan et al.
Sugar cane as an alternative energy source for Turkey
Energy Convers Manage
(1999)
Energy Management in Industry, Prepared by EIE/NECC, vol. I: EIEI/UETM. Ankara, Turkey;...
W.L. Badger et al.
Introduction to chemical engineering
(1995)

There are more references available in the full text version of this article.

Cited by (70)

Design and optimal tuning of fraction order controller for multiple stage evaporator system
2023, Digital Chemical Engineering
The tight control of the process parameters through appropriate tuning of controllers is an art that imperatively employed to various process industries. Most of these industries are influenced by the nonlinearity that occurred due to the input parameter variation and presence of disturbances. The aim of this work is to investigate the nonlinear dynamics of a paper industry based energy intensive unit named Multiple Stage Evaporator (MSE) in presence of different Energy Reduction Schemes. MSE is used to concentrate the weak Black Liquor (BL), a biomass based byproduct. Hence, to extract the bioenergy from the BL, the quality of the product liquor needs to be appropriately controlled. The quality of BL is measured by two process parameters, product concentration and temperature. Hence, in this work, an intelligent controller Fraction Order Proportional-Integral-Derivative controller has been studied and employed to resolve the servo and the regulatory problem occurred during the process. A state-of-art metaheuristic approach, Black Widow Optimization Algorithm has been proposed here to tune the controller parameters and compared with another optimization approaches named Water Cycle Algorithm. The simulated result demonstrates the usefulness of the proposed strategy and confirm the performance improvement for the process parameters. To enlighten the advantages of the proposed control scheme, a comparative analysis have also been performed with conventional PID, 2-DOF-PID and FOPID controllers.
Renewable integration and energy reduction in multiple stage evaporator
2023, Materials Today: Proceedings
Multiple Effect Evaporator (MEE) is an imperative part of the paper industry. It is used to process the waste byproduct named Black Liquor to enhance its solid concentration that may be further utilized to produce biomass-based energy. This process accounts very high energy consumption which leads to the energy intensiveness of this unit. A substantial amount of energy-saving may be accumulated by integrating various Energy Reduction Schemes (ERSs) with the MEE. Steam splitting, feed splitting, feed liquor preheating, thermo-vapor compressor, etc. are the well-known ERSs that may be incorporated with the MEE to reduce energy utilization. Hence, this study investigates the hybrid ERSs incorporated with MEE to observe their energy efficiency in an optimal manner. The prime focus of this investigation is to achieve enhanced energy efficiency in teams of maximum steam efficiency which is computed by formulating the nonlinear mathematical models of the MEE. To achieve the maximized energy efficiency, an optimization function has been developed under a constraint environment and solved by using metaheuristic-based approach named Flow Direction Algorithm. Another ERSs named flash tanks can also be integrated with this system to encourage waste heat re-utilization and ensures an increase in energy efficiency with constant steam consumption. This work also deals with the incorporation of the Linear Fresnel Reflector with ERSs integrated MEE which is capable of reducing the conventional energy load. The overall integrated MEE model achieves an energy-efficient and renewably operated MEE unit that may enhance the self-sustainability of the industry.
Enhanced fractional-order PI<sup>λ</sup>D<sup>μ</sup> control for a forced circulation evaporator system via advanced disturbance observer
2022, ISA Transactions
Strong disturbances, time delays, and coupling effects complicate the control of evaporator systems. In this paper, to overcome these difficulties a three-stage controller design is given and as a first step a disturbance observer (DOB) is designed. Then, fractional order PI $^{λ}$ D $^{μ}$ controllers (PI $^{λ}$ D $^{μ}$ FOC) with inverted decoupling structure are realized. Finally, PI $^{λ}$ D $^{μ}$ FOC is enhanced via DOB and applied to control of a considered forced circulation evaporator system. Controlling the evaporator system with the DOB-enhanced PI $^{λ}$ D $^{μ}$ FOC is showed more accurate and precise control results when compared with the optimally tuned PID and fuzzy logic controller (FLC). The DOB-enhanced PI $^{λ}$ D $^{μ}$ FOC method has remarkable superiority in disturbance rejection and the proposed control method is improved the tracking ability of the system for reference changes.
Controller design for optimal operation of Multiple Effect Evaporator of paper mills
2022, Results in Control and Optimization
The Kraft recovery process in the paper mills is highly complex and nonlinear. The evaporation of black liquor using Multiple Effect Evaporators (MEE) in the recovery unit of the Kraft process is an energy-consuming procedure. The challenge lies in designing a proficient control strategy to conserve energy and guarantee good product quality. In this article, the 2-DOF-PI controller is designed to enable efficient control of MEE and eliminate process uncertainties. The Heptads’ Effect Falling Film Evaporator in the backward feed flow configuration is used as a working platform. The steady-state and transient behavior of MEE is modeled and analyzed to assist in controller design. The steady-state process parameters, that guarantee optimum energy efficiency, are estimated using Moth–Flame Optimization (MFO). MFO is also employed to estimate the optimal 2-DOF-PI controller parameters to attain improved product quality and energy-efficient performance of MEE. The competence of MFO towards controller tuning is shown by a fair comparison with some well-known optimization techniques. The quantitative investigation of the statistical results demonstrates that MFO outperforms the other algorithms. To validate the proficiency of the designed control scheme, its performance is compared with basic PI/PID control strategy for set-point tracking, noise suppression, and process uncertainties. The simulation results indicate that the designed MFO-tuned 2-DOF-PI controller offers efficient control action and, therefore, proves to be an appropriate control algorithm to ensure sustainable production.
Dynamic simulation of multiple-effect evaporation
2022, Case Studies in Thermal Engineering
Citation Excerpt :
The steam used in this process is bled from the multiple-effect evaporation and this is the reason why MEE operates in a non-steady state. MEE allows many configurations to be designed; for example, Kaya [7] has modelled many systems, such as counter-current, co-current, and parallel-current; Ahmetović [8,9] used vapor recompression to recycle steam. In the sugarcane industry, the co-current configuration is preferred to avoid sucrose degradation [10].
The main purpose of this work is to simulate multiple-effect evaporation and its variation as a result of the interconnection between batch and continuous unit operations. Therefore, the challenges posed by the hybrid continuous-discrete character of the model are addressed. The computer code is based on detailed fundamental material and energy balance equations, physical and thermodynamic properties, and well-proven correlations for the heat transfer coefficients. A sugarcane industry was used to demonstrate the effectiveness of the model; in this industry, there is an interconnection between a batch and a continuous process. The steam consumed in the batch process changes in each batch step. The results showed that changing the steam flow rate changes the pressure of the steam produced in a multiple-effect evaporation. Additionally, when a bypass valve and a relief valve are used to maintain constant steam pressure, it increases the overall steam consumption.
Integration of solar field with multiple stage evaporator to sustain eco-energy in pulp and paper plant
2022, Journal of Cleaner Production
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.

View all citing articles on Scopus

View full text

Mathematical modeling of multiple-effect evaporators and energy economy

Abstract

Introduction

Section snippets

General modeling of a quadruple-effect evaporators system

The definition of sample problem

Conclusions

Control Eng Practice

Int J Refrig

Int J Refrig

Energy Convers Manage

Introduction to chemical engineering