Evaporation processes are used within the process industries in order to produce concentrated products by evaporating part of water from different feeds-diluted water solutions. Concentrated products can represent final products (fruit and vegetable juices) or intermediate products in cases that crystalized (salt, sugar) or dried (milk powder) final products should be produced. Large amounts of steam and cooling water are consumed in these processes. In order to reduce energy and water consumption within evaporation processes different systems can be applied, namely, multiple-effect evaporation, vapor recompression (thermal and mechanical) or their combinations. Additionally, these processes can be integrated with other process subsystems in order to achieve improved energy and water integration. To address these issues different computer-aided tools have been proposed. However, most studies have focused on analysis and simulation of evaporation processes. Some of the initial studies [1, 2] considered the synthesis of evaporation processes in order to develop tools for computing the minimum utility use for a multiple-effect evaporation system, which was heat-integrated with process hot and cold streams. These studies were based on a modified grand composite curve and heat-path diagram. Also, the focus of the recent works have been on multiple-effect evaporation systems [3] and their energy integration with the background processes in order to minimize the energy consumption within the overall system [4]. These studies have motivated us to further expand research in this direction, by applying mathematical programming approach for the analysis of existing and the design of new evaporation systems as well as their heat integration with other process subsystems or process streams. The main goal of this paper is to develop models based on mathematical programming that can be applied for the analysis, synthesis and optimization of multiple-effect evaporation systems. The proposed models will be developed in General Algebraic Modeling System (GAMS). The developed models will enable examination of different scenarios of multiple-effect evaporation in order to address the analysis of existing, retrofit and/or design new evaporation process. Within the proposed framework, a network consisting of a multiple-effect evaporation system and heat exchanger network will be investigated in order to achieve the improved heat integration within the overall system. Two strategies will be considered to achieve this task, namely, sequential and simultaneous. The developed models will be tested on several examples, and also applied to different feed streams. New results are expected to be obtained within this field. Keywords: multiple-effect evaporation, analysis, synthesis, optimization, mathematical programming. Acknowledgment The authors are grateful to the Swiss National Science Foundation (SNSF) and the Swiss Agency for Development and Cooperation (SDC) for providing financial support within the SCOPES 2013â??2016 (Scientific Co-operation between Eastern Europe and Switzerland) joint research project (CAPEâ??EWWR: IZ73Z0_152622/1). References: [1] Hillenbrand JJB, Westerberg AW. The synthesis of multiple-effect evaporator systems using minimum utility insightsâ??I. A cascaded heat representation. Computers & Chemical Engineering. 1988;12:611. [2] Westerberg AW, Hillenbrand JJB. The synthesis of multiple-effect evaporator systems using minimum utility insightsâ??II. liquid flowpattern selection. Computers & Chemical Engineering. 1988;12:625. [3] Khanam S, Mohanty B. Energy reduction schemes for multiple effect evaporator systems. Applied Energy. 2010;87:1102. [4] Sharan P, Bandyopadhyay S. Energy Integration of Multiple Effect Evaporators with Background Process and Appropriate Temperature Selection. Industrial & Engineering Chemistry Research. 2016;55:1630.
In recent work, a general superstructure and a Non-Linear Programming (NLP) model were presented for Multiple-Effect Evaporation Systems (MEESs). This NLP model was combined with a Heat Exchanger Network (HEN) model in order to simultaneously perform optimisation and heat integration of the overall system. The results of a forward-feed evaporation system integrated with hot and cold streams of the evaporation system as well as with the background process were presented. In this paper, the superstructure is extended by including multi-stage flash vessels for improving energy efficiency within the overall system. Additionally, various flow-patterns of heat-integrated MEES are studied. Also, trade-offs between energy and investment costs of heat-integrated MEES are explored for different numbers of evaporation effects in order to determine the optimum number of effects. The proposed Mixed-Integer Non-Linear Programming (MINLP) model of the combined MEES-HEN networks is implemented in a General Algebraic Modelling System (GAMS) and solved simultaneously using a two-step solution strategy. In the first step of the strategy, the NLP model of MEES is solved, providing an initialisation point for solving the MINLP model of the combined MEES-HEN network within the second step. A case study of a milk concentration process is used to illustrate the method. The results show that the forward feed flow-pattern with three evaporation effects is totally integrated with hot and cold process streams from the background process, and the system exhibits the minimum Total Annualised Cost (TAC).
This work presents a formalized methodology for salt's separation from three component electrolytic systems. The methodology is based on the multi-variant modelling block of a generalized crystallization process, with options for simulating the boundary conditions of feasible equilibrium processes and the elements of crystallization techniques. The following techniques are considered: cooling crystallization, adiabatic evaporative-cooling crystallization, salt-out crystallization, isothermal crystallization, and a combination of the mentioned techniques. The multi-variant options of the crystallization module are based on different variable sets with assigned values for solving mathematical models of generalized crystallization processes. The first level of the methodology begins with the determination of salt crystallization paths from a hypothetical electrolytic AX-BX-H2O system, following by an examination of salt-cooling crystallization possibilities. The second level determines feasible processes by the communication of a feed-system with the environment through a stream of evaporated water, or introduced water with introduced crystallized BX salt. The third level determines the value intervals of the variables for feasible processes. The methodological logic and possibilities for the created process simulator are demonstrated on examples of sodium sulphate separation from the NaCl-Na2SO4-H2O system, using different salt concentrations within the feed system.
In this paper, a computer aided analysis and synthesis of the crystallization processes from multicomponent electrolyte systems were studied. In addition, the vacuum crystallization processes with adiabatic cooling of the system are presented. The cooling process of a multicomponent electrolyte system can be considered as a process with the concentration of the system and/or the crystallization of the solid phase from the system. Requirements for multivariant options of the process simulator are the result of practical needs in the design of new processes or the improvement of exploitation processes. According to this, there are needs for a simulation of a simple flashing of the system as well as for the vacuum cooling crystallization processes with the cyclic structure. The possibilities of the created process simulator are illustrated on three component electrolyte systems. Application of the process simulator for any other electrolyte systems requires only an update of the thermodynamic model, and physico-chemical properties related to electrolyte system.
Determination of process structure of thermal utilization of mineral mat?ters from waste streams, is a multi-variant problem. These processes are energy-intensive and it is very important to determine the process structures for realization of the required processes in the starting phases of process development. The structure of the process system, beside the system equilibrium, depends on vector parameters of the feed stream. In this work a newly developed methodology for determination of process variants of thermal utilization of mineral salts from a hypothetical three-component AX-BX-H2O system is presented. The methodology is created on starting synthesis problem for which a set of types of process units for realization process and type of desired crystal product is determined. The methodology includes process decomposition in two subsystems: concentration (saturation) subsystem and crystallization subsystem. Concentration of feed stream is realized in isothermal conditions of water evaporation and crystallization process using various techniques: isothermal water evaporation, cooling of solution in vacuum and cooling of solution through contact surface. Determination of physical feasible processes is performed by simulation of the process superstructure in which each particular process structure is a special case of the created process superstructure. Realization of mentioned activity is provided by creating algorithms and programming software (process simulator) in which the equation system of the superstructure mathematical model is solved for various variants of set of specified variables. The created methodology and possibilities of the created process simulator are presented in the illustrative case study of waste stream utilization of the NaCl-KCl-H2O system. In addition to this, for conditions of total heat integration of subsystems is demonstrated that a small change of salt concentration of feed stream can require transfer non-cyclic in cyclic process structure.
In this paper we address the synthesis problem of distributed wastewater networks using mathematical programming approach based on the superstructure optimization. We present a generalized superstructure and optimization model for the design of the distributed wastewater treatment networks. The superstructure includes splitters, treatment units, mixers, with all feasible interconnections including water recirculation. Based on the superstructure the optimization model is presented. The optimization model is given as a nonlinear programming (NLP) problem where the objective function can be defined to minimize the total amount of wastewater treated in treatment operations or to minimize the total treatment costs. The NLP model is extended to a mixed integer nonlinear programming (MINLP) problem where binary variables are used for the selection of the wastewater treatment technologies. The bounds for all flowrates and concentrations in the wastewater network are specified as general equations. The proposed models are solved using the global optimization solvers (BARON and LINDOGlobal). The application of the proposed models is illustrated on the two wastewater network problems of different complexity. First one is formulated as the NLP and the second one as the MINLP. For the second one the parametric and structural optimization is performed at the same time where optimal flowrates, concentrations as well as optimal technologies for the wastewater treatment are selected. Using the proposed model both problems are solved to global optimality.
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