재진입 흐름을 고려한 다목적 회분식 공정의 일정계획

강진수, 문성득, 이태용

한국과학기술원

Scheduling of Multipurpose Batch Processes with Reentrant Flows

Jin-su Kang, Sungduk Moon,& Tai-yong Lee

KAIST

Introduction

Pipeless plants have recently been discussed in the literature as potential alternatives to traditional batch plants (e.g. Niwa, 1993; Takahai and Fujii, 1990). Their main distinguishing characteristics is that material is transported from one stage of processing to another in transferable vessels. Processing takes place at a number of processing stations, and normally the same vessels used for transferring material also hold the material while it is being processed at each station. The elimination of fixed piping networks for material transfer enables pipeless plants to be considerably more flexible than their conventional counterparts.

In the formulation of scheduling by Pantelides et al. (1995), it characterizes vessel utilization only in an aggregate sense since the balances are formulated for numbers of vessels rather than individual ones. Post-processing the results of the optimization should be done to obtain the utilization of individual vessels. Moreover, its discrete time representation makes a lot of computational loads as models become large.

This paper proposes a novel scheduling model of multipurpose batch plants by restructuring the problem of pipeless batch plants with the definition of reentrant flows and continuous time representation.

Problem Description

To provide a context for the discussion of the simulation results we will use the example of pipeless plants that is the same as that used in the earlier scheduling formulation by Pantelides et al. (1996).

The manufacture of three related products through a sequence of blending and reaction operation carried out in a pipeless plant is considered. The process STN is shown in Figure 1.

The Plant comprises the following processing stations:

□A charging station for adding A to a transferable vessel from a dedicated storage tank;

□A charging station for adding B to a transferable vessel from a dedicated storage tank

Figure 1. Plant topology

□Two blending stations, each of which can be used for any of the four blending task: each is connected to supplies of each of the three additives A1, A2, and A3.

□Two reaction stations, each of which can be used to carry out the reaction task; they are connected to a dedicated storage vessel holding the third raw material C.

□A discharging station which can be used to discharge an of the three products into appropriated dedicated storage tanks.

Mathematical Models

In general, the reentrant flows may not be characterized by traditional scheduling algorithms for multiproduct or multipurpose batch plants.

Figure 2. six different routes generated by the original path

Assuming that a complete path to produce a product consists of several productions routes to be the same direction, effect of the reentrant flows can be modeled as a multipurpose batch plant.

Then, Figure 2 shows that six different routes are generated by decomposing the original path in Figure 1.

The production path of the problem can be decomposed into six routes. First, product is produced through one of route 1, route 2, route 3, and route 4. Then it moves towards route 5 or route 6 to complete remaining parts of the process. Both the selection of path and the selection of units will be considered in the proposed formulation.

Its objective function is to maximize the profit.

[eqn: Max~ sum_i ~ n_i beta_i]                                            (1)

where ni is the number of product produced during executing this process and □i is the cost factor for each product.

There are two kinds of binary variables introduced in this model.

Xvkc = □ 1, if vessel v with production route c is assigned to time slot k

□ 0, otherwise

Yiv = □ 1, if product i is produced in vessel v

□ 0, otherwise

Xvkc enables to identify each vessel. By assigning a vessel to a time slot, it determines optimal production sequence based on the continuous time representation. Yiv is the binary variable for identifying the number of each product produced. In this model, two vessels are operated to produce one product. One is for the operation before the reentrant flow and the other is for the reentrant flow.

Results and Discussion

The modeling system GAMS version 2.25(Brooke et al., 1992) was used to implement the model and the solution method. The model was solved with CPLEX on a SUN/SPARC station. The problem is described above and it consists of 7 stations and 8 unit. And three kinds of products are produced. There are eight vessels to operate. This process will produce 12 products. Processing time in each unit is given in Table 1 and the result is listed in Table 2.

For the scheduling problem considered here, the problem was solved based on the continuous time representation. The objective function value is 17.5 units. Since the problem was formulated for an individual vessel, there was no need for post processing the optimization results. Figure 3 shows the utilization of vessels in this process. The use of continuous time representation and restructuring by reentrant flow can make more larger size of problem in chemical plant solved with reduced computational load.

Table 1. Processing time

Units	Duration (hr)	Units	Duration (hr)
Charger 1	0.5	Charger 2	0.5
Blender 1	0.5	Blender 2	0.75
Reactor 1	0.75	Reactor 2	0.5
Discharger	0.5	Cleaner	0.5

Table 2. The result of the example

the result	Value
no. of binary variables	306
no. of continuous variables	389
makespan (hr)	10.25
objective value (profit)	17.5
CPU time (s)	475.28

no. of real vessels : 8,  no. of imaginary vessels : 24

Figure 3. Optimization result

References

[1] Niwa, T., "Pipeless plants boost batch processing," Chem. Engng., 102-107           (1993).

[2] Takahasi, K. and Fujii, H., "New concept for batchwise specialty chemical           production plant," Intl. Chem. Engng. (September/October, 1990).

[3] Pantelides, C.C., Realff, M.J., and Shah, N., "SHORT-TERM SCHEDULING OF      PIPELESS BATCH PLANTS," IChemE, Vol 73, Part A (1995).