Optimal design of wastewater equalization systems in batch processes

https://doi.org/10.1016/j.compchemeng.2005.12.003Get rights and content

Abstract

The demands for fresh process waters and heating/cooling utilities arise intermittently in batch plants. Due to equipment constraints, the quality and flow-rate of each resulting wastewater stream are required to be controlled within specified limits before treatment/regeneration. In this paper, a general mathematical programming model is developed to design the optimal buffer system for equalizing the flow-rates and contaminant concentrations of its outputs. Three examples are provided to illustrate the effectiveness of proposed approach.

Introduction

Sufficient water supply is a prerequisite for running any chemical process. This is because water may be used in almost every aspect of plant operation. In the process system, it may be considered not only as a reactant in reactors but also as a mass-separating agent (MSA) in various separation processes such as absorption, extraction, leaching and stripping. In the utility system, water is constantly consumed in boilers and cooling towers to generate steam and cooling water. Furthermore, it can be utilized for equipment cleaning, fire fighting and various other miscellaneous operations. After these usages, wastewaters are inevitably created. They should be treated/regenerated and then either reused/recycled within the plant boundary or discharged to the environment.

Although water is one of many abundant natural resources on earth, its demand has been increased dramatically in modern age due to rapid economic expansion in many regions worldwide. Consequently, there are real incentives to develop proper water management methodologies with special emphasis on industrial water conservation. In the literature, the related publications in this area are almost all concerned with the continuous processes. Takama, Kuriyama, Shiroko, and Umeda (1980) first studied the optimal water allocation problem in a refinery. A superstructure including all possible reuse options and network connections were built and an iterative decomposition procedure was used to solve the model. In later studies, the water networks in continuous processes were classified into two subsystems, that is, the water-using and wastewater-treatment systems. Most researchers Bagajewicz, 2000, Feng and Seider, 2001, Galan and Grossmann, 1998, Hernandez-Suarez et al., 2004, Kuo and Smith, 1997, Kuo and Smith, 1998, Li et al., 2002a, Li et al., 2002b, Wang and Smith, 1994a, Wang and Smith, 1994b, Wang et al., 2003, Yang et al., 2000 focused on the design issues concerning either one of these two subsystems in order to avoid analyzing the complex interactions between them. An integrated approach for the overall system design remained a challenge until a general non-linear programming (NLP) model was developed by Huang, Chang, Ling, and Chang (1999). In a subsequent work, Tsai and Chang (2001) adopted genetic algorithm to identify the optimum solution of the same problem.

It should be noted that, in practice, batch processing has received increasing attention in recent years. It is the predominant means of manufacturing low-volume high-value commercial products, e.g. specialty chemicals, biochemicals and pharmaceuticals, polymers, electronic materials, ceramics and coatings, etc. It has been well recognized that the batch production schemes are especially suitable for accommodating frequent changes in market demands owing to their inherent operation flexibilities (Rippin, 1991). When compared with the continuous counterparts, the benefits of reduced inventories and/or shortened response time can often be achieved with batch processes. However, very few published studies addressed the important issues of water management in batch plants. In fact only the wastewater-reuse problem has been discussed in depth. For example, Wang and Smith (1995) proposed a modified version of the Pinch method to minimize the total amount of discharged wastewater. Almato et al., 1997, Almato et al., 1999 and Puigjaner, Espuna, and Almato (2000) developed a NLP model to optimize water reuse in batch processes. Recently, Kim and Smith (2004) constructed a MINLP model to automate the design procedure for discontinuous water systems.

An additional point should be brought up here that, in the water-reuse strategy mentioned above, the practical constraints of the wastewater treatment units are not considered in sufficient detail. For example, since the demands for heating/cooling utilities in a batch plant arise intermittently and their quantities vary drastically with time, the generation rates of the resulting spent waters must also be time dependent (Winkel, Zullo, Verheijen, & Pantelides, 1995). A buffer tank can thus be used at the entrance of each utility system to maintain a steady throughput. On the other hand, McLaughlin, McLaugh, and Groff (1992) indicated that the capital cost of a wastewater treatment operation is usually proportional to its capacity. Thus, for economic reasons, flow equalization is needed to reduce the maximum flow-rate of wastewater entering the treatment system. In addition, since the biological-treatment unit is included in most cases, the “shock loads” (mainly in concentration) must be avoided at all times so that the embedded bacteria can always be kept in an active state (Nemerow, 1971). In this situation, a buffer system may also be installed to equalize the wastewater flow-rates and pollutant concentrations simultaneously. The inputs of this equalization system can be the spent utility waters or wastewaters generated from various batch operations, and the outputs can be considered to be the feeds to different utility-producing equipments, wastewater-treatment units and/or discharge points.

From the above discussions, it is clear that wastewater equalization is a common practice required in almost every industrial batch process. A typical example can be found in Tumsen, Velioglu, and Hortacsu (1996), in which the authors tried to equalize wastewater generated in a yeast plant by rescheduling and adding new production equipments. Despite this apparent need in practical applications, the development of systematic design strategies for wastewater equalization systems has not been attempted until recently. In a preliminary study, Li et al., 2002a, Li et al., 2002b adopted both a conceptual design approach and also a mathematical programming model to eliminate the possibility of producing an unnecessarily large combined water flow at any instance by using a buffer tank and by rescheduling the batch recipe. Later, Hui, Li, and Smith (2003) used a two-tanks configuration to remove peaks in the profile of total wastewater flow-rate and also in that of one pollutant concentration.

There are several obvious drawbacks in the present approach to solve the equalization problem. First of all, it may not be enough simply to eliminate the peaks in the time profiles of total flow-rate and pollutant concentration. As mentioned before, it is necessary to ensure that the equalized water flows satisfy the operation constraints imposed upon the downstream facilities. In many cases, each water flow is required to be continuous and its flow-rate and pollutant concentrations must be maintained within specific upper and/or lower limits. Secondly, the implied assumption of a single combined wastewater stream may not be appropriate for the design of optimal water treatment system. The distributed treatment strategy has long been advocated by various researchers Galan and Grossmann, 1998, Hernandez-Suarez et al., 2004, Kuo and Smith, 1997, Li et al., 2002a, Li et al., 2002b, Wang and Smith, 1994b on the ground that pollutants at higher concentrations can be removed more efficiently than those at the average concentrations in most cases. Finally, the system designs obtained under the constraint of a single pollutant are clearly not useful in many industrial problems. The development of a systematic procedure is therefore needed to equalize multiple pollutant concentrations and feed rates to separate downstream units.

The rest of this paper is organized as follows. A formal definition of the equalization system design problem is first presented in the next section. To facilitate the formulation of the mathematical programming model, a superstructure of the buffer network is then given in Section 3. The mixed-integer non-linear program is outlined accordingly in the following section. With this model, a minimum-cost design can be obtained under the constraints imposed upon the network structure, and also upon the flow-rates and concentrations at the inlet(s) and outlet(s) of every buffer tank, mixing node and splitting node in the equalization system. Finally, three illustration examples are provided at the end of this paper to demonstrate the effectiveness of the proposed approach.

Section snippets

Problem statement

To facilitate a precise description of our design problem, let us first introduce the definitions of two unit sets:E=e|eis the label of a batch unit from which the wastewateror spent water is generated;e=1,2,,NEO=o|ois the label of a discharge point,a wastewater-treatment unit or an utility-producingdevice;o=1,2,,NOIn this paper, the units in E are regarded as the sources of spent waters or wastewaters entering the equalization system and the elements in O are referred to as the sinks of

Superstructure

Similar to other optimization study in process synthesis, it is necessary to first build a superstructure in which all possible flow configurations can be embedded. A simple construction procedure of the superstructure is presented below:

  • (1)

    Place a mixing node at the inlet of every buffer tank and every sink.

  • (2)

    Place a splitting node at outlet of every source and every buffer tank.

  • (3)

    Connect the split branches from each source to all mixing nodes.

  • (4)

    Connect the split branches from each buffer tank to all

Mathematical programming model

For formulation convenience, a species set is used for characterizing multiple water contaminants in the equalization system, i.e.:K={k|kis the label of a pollution index,e.g. the concentration of a contaminant,which affects water quality;k=1,2,,NK}In addition, due to the intermittent nature of wastewater flow, it is also necessary to divide the entire period of production cycle into distinct time intervals. Specifically, let us label the time instances when wastewater generation begins or

Illustration examples

To illustrate the implementation procedure of the proposed approach, a series of three examples are presented here. All problems were run on a personal computer with Pentium(R) 4 and CPU frequency of 2.80 GHz. Solver CPLEX is selected for Example 1 and DICOPT for Examples 2 and 3 under the GAMS environment (Brooke, Kendrik, Meeraus, & Ramam, 1998).

Conclusion

A general mixed-integer non-linear programming model is developed in this work for optimal wastewater equalization in batch plants. The inherent fluctuations in the flow-rates and multi-pollutant concentrations of the wastewater streams can be moderated with a network of buffer tanks in the resulting design. The proposed model is simple but practical. To avoid using ordinary differential equations to describe the time-variant water volumes and pollutant concentrations in the buffer tanks, the

Acknowledgement

This work is supported by the National Science Council of the ROC government under Grant NSC92-2214-E006-014.

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