State-task network

Another important aspect of batch plants relates to the representation of the recipe which is invariably the underlying feature of the resultant mathematical formulation. The most common representation of recipe in the published literature is the state task network (STN) that was proposed by Kondili et al. (1993), which comprises of 2 types of nodes, viz. state nodes and task nodes. The state nodes represent all the materials that are processed within the plant. These are broadly categorized into feeds, intermediates and final products. On the other hand, task nodes represent unit operations or tasks that are conducted in various equipment units within the process. 

Fig. 1.10 (a) State task network vs (b) state sequence network for the illustrative example... 

In this chapter, state sequence network (SSN) representation has been presented. Based on this representation, a continuous-time formulation for scheduling of multipurpose batch processes is developed. This representation involves states only, which are characteristic of the units and tasks present in the process. Due to the elimination of tasks and units which are encountered in formulations based on the state task network (STN), the SSN based formulation leads to a much smaller number of binary variables and fewer constraints. This eventually leads to much shorter CPU times as substantiated by both the examples presented in this chapter. This advantage becomes more apparent as the problem size increases. In the second literature example, which involved a multipurpose plant producing two products, this formulation required 40 binary variables and gave a performance index of 1513.35, whilst other continuous-time formulations required between 48 (Ierapetritou and Floudas, 1998) and 147 binary variables (Zhang, 1995). 

The same problems occur using state task network (STN) formulations that use binary variables. There, possible events may occur for each instant expressed by a binary variable and the models become very large. No calculation was carried out for this formulation. 

The plant is used to produce two chemically different EPS -types A and B in five grain size fractions each from raw materials FI, F2, F3. The polymerization reactions exhibit a selectivity of less than 100% with respect to the grain size fractions Besides one main fraction, they yield significant amounts of the other four fractions as by-products. The production processes are defined by recipes which specify the EPS-type (A or B) and the grain size distribution. For each EPS-type, five recipes are available with the grain size distributions shown in Figure 7.2 (bottom). The recipes exhibit the same structure as shown in Figure 7.2 (top) in state-task-network-representation (states in circles, tasks in squares). They differ in the parameters, e.g., the amounts of raw materials, and in the temperature profiles of the polymerization reactions. 

The most relevant contribution for global discrete time models is the State Task Network representation proposed by Kondili et al. [7] and Shah et al. [8] (see also [9]). The model involves 0-1 variables for allocating tasks to processing units at the beginning of the postulated time intervals. Most important equations comprise mass balances over the states, constraints on batch sizes and resource constraints. The STN model covers all the features that are included at the column on discrete time in Table 8.1. 

Minimization of makespan with discrete-time state-task network formulation.. Ind. Eng. Chem. Res., 42, 6252-6257. 

At a more disaggregated level a deconstruction of the core value chain can be considered (for example to focus certain plants on specific process steps). In a first step all technically separable elements of the value chain should be identified and their respective processing characteristics established. To illustrate the concept behind this analysis, the State-Task-Network of the pilot application value chain depicted in Figure 36 is revisited in Figure 41. For example, after completion of t7 the product is dried... 

Representation of Operational Alternatives Using State Task Network... 

The batch distillation operation can be schematically represented as a State Task Network (STN). A state (denoted by a circle) represents a specified material, and a task (rectangular box) represents the operational task (distillation) which transforms the input state(s) into the output state(s) (Kondili et al., 1988 Mujtaba and Macchietto, 1993). For example, Figure 3.1 shows a single distillation task producing a main-cut 1 (Di) and a bottom residue product (Bj) from an initial charge (B0). States are characterized by the amount and composition of the mixture residing in them. Tasks are characterized by operational attributes such as then-duration, the reflux ratio profile used during the task, etc. 

Figure 5.1. State Task Network for Batch Distillation...

Figure 7.1. State Task Network for Binary Batch Distillation with One Main-Cut and One Off-cut. [Mujtaba and Macchietto, 1993]a...

State Task Network (STN) representation of operating sequence for binary and multicomponent batch distillation... 

Symbolic-network representations of these separation systems, called state-task networks (STNs), are shown in Fig. 13-64. In this representation, the states (feeds, intermediate mixtures, and products) are represented by the nodes (ABC, AB, BC, A, B, C) in the network, and the tasks (separations) are depicted as lines (1, 2,. .., 6) connecting the nodes, where arrows denote the net flow of material. This STN representation was used by Sargent to represent distillation systems [Comp, ir Chem. Eng., 22, 31 (1998)] and has been widely used ever since. Originally STNs were introduced by Kondili, Pan-... 

FIG. 13-64 State-task networks, [a] Direct split, (h) Prefractionator system. 

Sargent (1994) presents a related approach to the synthesis of distillation processes. His goal is to generate a superstructure of interconnected columns from a state/task network. The superstructure contains all the process alter-... 

Keywords sequence synthesis, multicomponent, rectification body method, state task network... 

The same separation steps (same feed and product compositions) can occur in different sequences. This can be seen in Fig. 1, where the first and the second sequence have the first separation in common. This property is used in a superstructure to reduce the complexity of the multicomponent systems. The state task network [3] is applied. In this superstructure, every possible composition, which can be attained, is called a state. The states represent the feed, possible intermediate products and products of the separation sequence. 

The application of the state task network requires the specification of linearly independent products. If products are linearly dependent, which in this case means that they could be attained by mixing other products, the state task network formulation is not applicable. This is due to the fact that the tasks would not be independent from the sequence. The main advantage of superstructure is that the number of tasks only grows with the third power of the number of products, compared to the exponential growth of the number of sequences (Fig.l) [2]. 

In MultiVBD column, the products will be produced simultaneously while in the conventional column these will be produced sequentially as shown by State Task Network (STN) in Figure 3. Note, there is an extra middle vessel to produce an off-cut between D and Dj. 

Maravelias and Grossmann (2004) have recently developed a hybrid MILP/CP method for the continuous time state-task-network (STN) model in which different objectives such as profit maximization, cost minimization, and makespan minimization can be handled. The proposed method relies on an MILP model that represents an aggregate of the original MILP model. This method has been shown to produce order of magnitude reductions in CPU times compared to standalone MILP or CP models. 

Maravelias C.T. and Grossmann LE. 2003. A new general continuous-time state task network formulation for short term, scheduling of multipurpose batch plants, I EC Res., 42, 3056-3074. 

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