Optimal design of wastewater equalization systems in batch processes
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:In 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.: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.
References (28)
- et al.
Optimization of water use in batch process industries
Computers and Chemical Engineering
(1999) A review of recent design procedures for water networks in refineries and process plants
Computers and Chemical Engineering
(2000)- et al.
The automated design of discontinuous waster systems
Process Safety and Environmental Protection
(2004) - et al.
Effluent treatment system design
Chemical Engineering Science
(1997) - et al.
Designing for the interactions between water-use and effluent treatment
Chemical Engineering Research and Design
(1998) - et al.
A software tool for helping in decision-making about water management in batch process industries
Waste Management
(2000) - et al.
Optimal water allocation in a petroleum refinery
Computers and Chemical Engineering
(1980) - et al.
A design methodology for multiple-contaminant water networks with single internal water main
Computers and Chemical Engineering
(2003) - et al.
Design of distributed effluent treatment systems
Chemical Engineering Science
(1994) - et al.
Synthesis of an optimal wastewater reuse work
Waste Management
(2000)
Rationalizing the water use in batch process industry
Computers and Chemical Engineering
New structure and design methodology for water networks
Industrial & Engineering Chemistry Research
Optimal design of distributed wastewater treatment networks
Industrial & Engineering Chemistry Research
Cited by (23)
A simple strategy to maximize water-reuse in multistage, multiproduct batch processes
2021, Chemical Engineering Research and DesignCitation Excerpt :Along with wastewater minimization with or without storage tanks, the use of regeneration or water treatment unit can also be used to minimize freshwater consumption. For wastewater treatment, the use of buffer tanks for concentration equalization and then sending the wastewater to the treatment units is discussed by Chang and Li (2006). The batch operations were modeled as water generating operations and not water-using operations.
A multi-objective approach for property-based synthesis of batch water networks
2013, Chemical Engineering and Processing: Process IntensificationCitation Excerpt :Similarly to the interception units, the existence or inexistence for the storage tanks is determined through logical relationships using binary variables. The TAC is the unique objective function in most of the problems reported in literature [27–44], but in this paper the TS for the batch water network is also included as an objective function, which is aimed to take into account an innovative definition of process intensification [61], especially in reference to the minimization of storage of hazardous substances, under this concept in this paper has been developed a model from which is possible to determine a relationship between the total annual cost and the total storage to show the results through Pareto curves that tradeoff these objectives. Finally, the optimization formulation consists in minimizing Eqs. (21) and (22) subject to restrictions given by Eqs. (1)–(20), which yields a moMINLP (multi-objective Mixed-Integer Non-Linear Programming Problem).
A review: Energy recovery in batch processes
2012, Renewable and Sustainable Energy ReviewsCitation Excerpt :There are a great number of works that have proposed different methodologies aimed at increasing batch process efficiency. These approaches include: make-span reduction and annual throughput maximization [24–27]; process measurements [28,29]; freshwater and wastewater minimization through the exploitation of inter- and intra-process water reuse, batch schedules optimization and/or wastewater treatment [30–35]; reduction of waste generation [36,37]; decreasing the necessity of resources [38,39]; environmental impact assessment [40]; heat recovery…and/or integration of some of these approaches. For example, Linainger et al. created Batch Design Kit which integrated ecological (health, safety, environmental impact) and economic issues [41].
Wastewater minimization in multipurpose batch plants with a regeneration unit: Multiple contaminants
2011, Computers and Chemical EngineeringCitation Excerpt :Wastewater treatment deals with the purification of water to such an extent that it can be discharged safely to the environment. This concept has been discussed by Chang and Li (2006) whereby buffer tanks were utilized to achieve wastewater flowrate and contaminant concentration equalization. The batch processes were modeled as water generating operations and not water using operations.
Simultaneous optimization of batch process schedules and water-allocation network
2009, Computers and Chemical EngineeringMinimizing water and energy use in the batch and semi-continuous processes in the food and beverage industry
2008, Handbook of Water and Energy Management in Food Processing