Multi-objective optimization of the scheduling of a heat exchanger network under milk fouling
Introduction
Fouling of heat exchangers by dairy liquids is a major problem in milk pasteurization industries. Milk pasteurization is done by heat to destroy the micro-organisms dissolved in milk, so that it can be consumed safely [42]. Upon heating, complex biological constituents of milk get destructed and form heavy layers of deposition known as fouling. Milk fouling is caused due to the formation and deposition of serum protein molecules and precipitation of calcium ions that are dissolved in milk [33].
Fouling is an undesirable phenomenon, major effects of which include decrease in heat transfer coefficient leading to reducing heat transfer rate, increase in pressure drop leading to decreasing pumping efficiency, loss in product as a portion of the processing fluid gets precipitated on the walls of the heat exchangers, and contamination in the product by the loosened deposits [33].
Fouling can be reduced either by improving the design of the heat exchangers or through process control. The design improvement includes proper selection of heat exchanger type, appropriate heat exchanger design, and heat exchanger surface modification or coating [18], [29], [39], [40], [45]; while the process control encourages to adjust physical parameters like air content, temperature, pressure, flow rate, type of flow (laminar or turbulent), preheating, etc. [2], [4], [7], [8], [22], [34], [67]. Although the design improvement and process control are two effective ways to reduce fouling to a certain extent, cleaning of the heat exchangers in a periodic manner is also necessary to maintain fouling at a lower level and to restore the process performance.
There are basically three cleaning techniques that are employed in industries, namely cleaning-in-place (CIP), cleaning-out-of place (COP) and manual cleaning [49]. Out of these, the CIP technique is found to be the most effective one for dairy industries, as this cleaning is done in the plant itself without disassembling the heat exchanger network (HEN) and other accessories [65]. Only the production process has to be stopped during CIP of a heat exchanger. In order to avoid complete halt of the production process, the HEN needs to be scheduled in such a way that at any time instant, while some heat exchangers remain shutting down for CIP, the rest of the heat exchangers continue to be in operation.
Because of the high extent of fouling, milk pasteurization industries require rapid and effective cleaning on daily basis in a duration of 5–6 hours, which involves high cost unlike in other industries where cleaning is usually performed on annual basis [27]. It is found in milk pasteurization industries that around 80% of the total production cost goes on cleaning [2] only, which calls optimization tools to minimize the cleaning cost subject to fulfillment of various process conditions.
Motivated by the above requirement of minimizing the cleaning cost of heat exchangers, three mixed-binary evolutionary algorithms (EAs); namely genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO); are investigated here for effective scheduling of a HEN engaged to a practical application of a milk pasteurization process under milk fouling. It is observed in the numerical experimentation that although the EAs could minimize the cleaning cost to certain levels, the optimum solutions of all the EAs are also associated with overheating of milk and a higher temperature of the heating medium (steam) at the outlet of the HEN. The overheating of milk from a predefined temperature consumes extra energy not only on excess heating, but may also be required in cooling down milk to the required temperature. On the other hand, the heating steam leaving the HEN at a higher difference in temperature means that the heat of steam is not fully utilized in heating milk, thus causing a higher flow rate of steam than the minimum requirement. It is obvious that the minimization only of the cleaning cost could not take these two major requirements into account. Therefore, finally the milk heat treatment process is formulated as a multi-objective optimization problem for simultaneously minimizing the total cleaning cost, overheating of milk and flow rate of steam. In the numerical experimentation of this case, the EAs are found to be able to maintain a better balance among the three non-commensurable objectives.
The main contribution of the present work is the detail study of the milk pasteurization process in a HEN considering the periodic cleaning of the HEN along with two new but significant process related issues, namely the overheating of milk and higher steam flow rate. Accordingly, the process is formulated as a multi-objective optimization problem for simultaneously minimizing the cleaning cost, overheating of milk (energy consumption) and steam flow rate. Further, owing the difficulties in handling the process related constraints of combinatorial nature, three repairing mechanisms are also proposed for steering infeasible solutions to the feasible region during the optimization process. Finally, three mixed-binary evolutionary algorithms are investigated to a case-study of effective scheduling of a HEN under milk fouling.
The rest of the article is structured as follows: the related specialized literature is reviewed in Section 2. The description and mathematical formulation of the problem are presented in Section 3, followed by Section 4 proposing some problem-specific mechanisms for forcibly repairing an infeasible solution so as to ease and speed up the search process of an optimizer. The EAs for solving the problem are presented in Section 5. The numerical experimentation and findings therein are discussed in Section 6. Finally, some concluding remarks are drawn in Section 7.
Section snippets
Literature review
The literature review is categorized into three parts: research done on milk fouling, present industrial status of CIP technique, and research performed on cost and process optimization under milk fouling.
The process of milk fouling, its causes and effects were studied in depth in many works [21], [33], [34], [67]. Burton [7] classified the deposits formed by milk fouling into two types: type A deposit and type B deposit. Beiny and Fryer [3] illustrated that type A deposit occurs when milk is
Problem description and formulation
In the considered problem of milk pasteurization, milk is to be heated in a series-type heat exchanger network (HEN) going through periodic cleaning of each heat exchanger in order to restore its performance by removing milk fouling. The task is to schedule the HEN in a way to optimize some economic and thermal performance criteria subject to given processing constraints as stated below:
- •
Determine
- 1.
Operational status (heating or cleaning) of each heat exchanger at every time instant.
- 2.
Final outlet
- 1.
The repairing mechanisms
Constraint handling is still a challenge to any optimizer, particularly in the case of combinatorial optimization problem like the scheduling of heat exchangers in the milk pasteurization process. Since the size of the discrete search space of the present problem increases exponentially with increasing number of heat exchangers to be scheduled, it would be difficult for any algorithm to steer an infeasible solution to the feasible region of the problem. Therefore, in order to speed up the
Evolutionary algorithms (EAs) for solving the problem
The basic component of an EA is an individual that represents a complete solution of a problem. It is usually an array of some elements, where a sub-array of elements or a single element describes a variable of a problem. A set of individuals (solutions) forms a population, which is gradually improved toward the optima by applying some algorithm-specific operators until certain termination criteria are met, usually until a predefined maximum number of generations (iterations) are performed or
Numerical experimentation
The EAs (NSGA-II, ridDE and ridPSO) for optimizing the heat treatment process of milk in a network of serial heat exchangers are coded in the C programming language and executed in the Ubuntu 12.04 Linux environment. The details of the considered case study, results, comparison, and discussion are presented in this section.
Conclusion and future scope
A severe complication with the heat treatment process in milk pasteurization is the decaying performance of heat exchangers due to the deposition of solid particles, known as the milk fouling, on the surfaces of the heat exchangers. Therefore, in order to restore their original performances, the heat exchangers are to be cleaned periodically, which necessitates scheduling of the involved heat exchanger network (HEN) at minimum cleaning cost subject to the fulfillment of various process
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