Reusable water storage

Figures 4.1 and 4.2 depict the superstructures on which the mathematical model is based. Figure 4.1 represents a situation where reusable water storage does not exist. In this situation, water used in each water using operation j can be supplied from the fresh water header, the recycle/reuse water header or a combination of both headers. Water from each operation j can be recycled to the same operation, reused in downstream processes and/or dispensed with as effluent. On the other...

Fig. 4.1 Superstructure for the mathematical formulation with no reusable water storage (Majozi, 2005)...

Scenario 1 Formulation for fixed outlet concentration without reusable water storage... 

Scenario 2 Formulation for fixed water quantity without reusable water storage The following formulation, which is also based on the superstructure given in Fig. 4.1, is applicable in a situation where the quantity of water is fixed and the outlet concentration is allowed to vary. In this situation, constraints (4.1), (4.2), (4.3) and (4.4) still hold, but constraints (4.5) and (4.6) have to be modified as follows. 

Constraints (4.18) states that the inlet stream into any operation j is made up of recycle/reuse stream, fresh water stream and a stream from reusable water storage. On the other hand, the outlet stream from operation j can be dispensed with as effluent, reused in other processes, recycled to the same operation and/or sent to reusable water storage as shown in constraints (4.19). The inlet concentration into operation j is the ratio of the contaminant amount in the inlet stream and the quantity of the inlet stream as stated in constraints (4.20). The amount of contaminant in the inlet stream to operation j consists of the contaminant in the recycle/reuse stream and the contaminant in the reusable water storage stream. The following storage specific constraints are also imperative for the completeness of the model for scenario 3. 

Scenario 4 Formulation for fixed water quantity with reusable water storage Constraints (4.18), (4.19), (4.3), (4.20), (4.16), (4.17), (4.21), (4.22), (4.23), (4.24), (4.25) and (4.26) together constitute a complete water reuse/recycle model for a situation in which the quantity of water in each water using operation is fixed. This is also a nonconvex MINLP for which exact linearization is not possible. 

The following constraints address the time dimension for water reuse/recycle in batch processes in the absence of central reusable water storage. 

Constraints (4.35) and (4.36) stipulate that when the water stream is transferred from operation j to reusable water storage, then the time of transfer should coincide with the completion of operation j. however, operation j will only be completed and able to transfer water to storage at time point p if it started at time point p- 1. Also, the fact that operation j commenced at time point p- 1 does not necessarily mean that it will transfer water to storage at time point p, since this water could be immediately reused/recycled and/or dispensed with as effluent. This is captured by constraints (4.37). The following constraints (4.38), (4.39) and (4.40) are similar to (4.35), (4.36) and (4.37), but apply to the outlet stream of reusable water storage. 

Constraints (4.41) ensures that if reusable water is transferred from reusable water storage to operation / at time point p and later transferred to the same or another operation j at time point p, then the later time point must correspond to a later time. If the transfer of water from reusable water storage to different operations j and/ takes place at the same time point p, then this time point must correspond to exactly the same time as enforced by both constraints (4.42) and (4.43). 

For this particular example, scenarios 3 and 4 yielded the same networks as scenarios 1 and 2, respectively. This is due to the fact that processes 1 and 3 commence as soon as process 2 is complete, i.e. at 0.5 h. As a result there exists no opportunity for reusable water storage. 

In scenarios 2 and 4, i.e. fixed water quantity and existence of reusable water storage, the following constraints is necessary to ensure that the capacity of reusable... 

It is evident from Fig. 4.11 that the existence of central reusable water storage allows the time constraints to be overridden, thereby providing an opportunity for reuse from operation A to operations C and E. This is the main reason for the significant reduction in freshwater requirement. Scenario 1, which is similar to scenario 3 without the presence of reusable water storage, resulted in 25% instead of 45.53% freshwater reduction. It is worth noting that the solution suggests a smaller... 

The overall model for this scenario involves 5614 constraints, 1132 continuous 280 binary variables. Three major iterations with an average of 1200 nodes in the branch and bound search tree were required in the solution. The objective value of 1560 kg, which corresponds to 33.89% reduction in freshwater requirement, was obtained in 60.24 CPU seconds. An equivalent of this scenario, without reusable water storage, i.e. scenario 2, resulted in 13% reduction in fresh water. Figure 4.12 shows the water recycle/reuse network corresponding to this solution. 

The operating costs entail raw material costs and effluent treatment costs. Only scenarios 1 and 3, i.e. fixed outlet concentration with and without reusable water storage, are considered. The additional information provided for the case study pertains to the mass ratios between raw material streams and freshwater. In process 1, 1 kg of water (aqueous phase) is required to wash 3 kg of raw material stream (organic phase) to the desired specification. In process 2, 1 kg of water is required for every 2 kg of raw material stream. These requirements are dictated by mass transfer. 

Table 4.4 is the summary of the mathematical model and the results obtained for the case study. The model for scenario 1 involves 637 constraints, 245 continuous and 42 binary variables. Seventy nodes were explored in the branch and bound algorithm. The model was solved in 1.61 CPU seconds, yielding an objective value (profit) of 1.61 million over the time horizon of interest, i.e. 6 h. This objective is concomitant with the production of 850 t of product and utilization of 210 t of freshwater. Ignoring any possibility for water reuse/recycle, whilst targeting the same product quantity would result in 390 t of freshwater utilization. Therefore, exploitation of water reuse/recycle opportunities results in more than 46% savings in freshwater utilization, in the absence of central reusable water storage. The water network to achieve the target is shown in Fig. 4.14. 

Majozi, T., 2005. Wastewater minimization using central reusable water storage in batch processes. Comput. Chem. Eng., 29(7) 1631-1646. 

Fig. 5.1 Impact of reusable water storage on freshwater demand (Majozi, 2006)... 

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