The PIS Operational Philosophy

The models developed to take the PIS operational philosophy into account are detailed in this chapter. The models are based on the SSN and continuous time model developed by Majozi and Zhu (2001), as such their model is presented in full. Following this the additional constraints required to take the PIS operational philosophy into account are presented, after which, the necessary changes to constraints developed by Majozi and Zhu (2001) are presented. In order to test the scheduling implications of the developed model, two solution algorithms are developed and applied to an illustrative example. The final subsection of the chapter details the use of the PIS operational philosophy as the basis of operation to design batch facilities. This model is then applied to an illustrative example. All models were solved on an Intel Core 2 CPU, T7200 2 GHz processor with 1 GB of RAM, unless specifically stated. 

The PIS operational philosophy is novel and thus requires further explanation. When a batch operation is scheduled a Gantt chart is usually generated, such as 

When the PIS operational philosophy is not used, as in Fig. 3.3, 50 t of dedicated intermediate storage unit, ds,s, was required. The reason for this is that the 

In order to illustrate the uses of this novel operational philosophy, i.e. PIS operational philosophy, this chapter has been divided into two parts. Firstly, the applicability of the operational philosophy will be proven and used to determine the minimum amount of intermediate storage required while maintaining the throughput achievable with infinite intermediate storage. Secondly, the PIS operational philosophy will be used to design storageless batch plants. 

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In order to ensure the completeness of the model that takes the PIS operational philosophy into account, the basic scheduling model developed by Majozi and Zhu (2001) has to be modified as follows. 

The balance over a dedicated intermediate storage unit has to be modified because of the possibility of latent storage. Constraint (3.34), provides the link for the inlet and outlet mass balance between units, as shown in constraints (3.17) and (3.18). Constraints (3.35), (3.36) and (3.37), are similar to constraints (3.4), (3.5) and (3.6), however they apply to the case where the PIS operational philosophy is taken into account. 

Fig. 3.7 Literature example without using the PIS operational philosophy...

The model was solved using GAMS and the CPLEX solver version 9.1.2. The computational results for case 1 are shown in are shown in Table 3.3. From these results it is clear to see the potential benefits for using the PIS operational philosophy, with a 50% increase in throughput. 

MILP and MINLP models have been developed to take into account the PIS operational philosophy for assessing the efficacy of this philosophy and design, respectively. The MILP model is used to determine the effectiveness of the PIS operational philosophy by, firstly, solving the model with zero intermediate storage with and without the use of latent storage. In the illustrative example a 50% increase in the throughput was achieved. 

Secondly, the minimum amount of intermediate storage is determined with and without the PIS operational philosophy. In both cases the production goal was set to that which was achieved when the model was solved with infinite intermediate storage. In the illustrative example a 20% reduction in the amount of intermediate storage is achieved. The design model is an MINLP model due to the non-linear capital cost objective function. This model is applied to an illustrative problem and results in the flowsheet as well as determining the capacities of the required units. 

The industrial case study presented in this section is taken from the petrochemicals industry. The project is in the design phase and as such the design model will be used to determine the design which leads to the minimum capital cost, while using the PIS operational philosophy. For secrecy reasons the example has been modified and the names of the raw materials and products have been changed to the generic form. 

Two distinctive models were developed in order to investigate the effectiveness of PIS operational philosophy. The first model is separated into two parts. The first part is used to determine the optimal throughput when there is zero intermediate storage available. Two situations were studied. Firstly the model was solved without the use of the PIS operational philosophy. Secondly, the model was solved with the PIS operational philosophy. In the simple example shown in this section a 50% increase in the throughput was achieved when the PIS operational philosophy was used. In both cases the models developed were a MILP, thus guaranteeing global optimality. 

The second mathematical formulation presented, is a design model based on the PIS operational philosophy. This formulation is an MINLP model due to the capital cost objective function. The model is applied to a literature example and an improved design is achieved when compared to the flowsheet. The design model is then applied to an industrial case study from the phenols production facility to determine its effectiveness. The data for the case study are subject to a secrecy agreement and as such the names and details of the case study are altered. 

The model in the above form does not take into account the possibility of using latent storage, i.e. PIS operational philosophy. There are a number of additional constraints needed to fully capture this operational philosophy. 

Figure 3.3 PI provides radically innovative principles in process and equipment design that can benefit process and chain efficiency, capital and operating expenses, quality, wastes, process safety and more, and align perfectly with the Triple-P philosophy of sustainable industrial chemistry. Source adapted from EU Roadmap for Process Intensification (www.creative-energy.org).

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