Abstract
The production sequence and the processing schedules of multiproduct batch processes can be changed for maximum heat recovery and minimum equipment costs between batch streams. However, the modified production sequence and processing schedule may increase the production cycle time, which causes the bigger equipment sizes required in batch processes. In this study, the required equipment sizes, the production sequence and the processing times of the multiproduct batch processes are mathematically formulated for maximum heat integration and low equipment costs in a mixed integer nonlinear programming. The optimal solution of this formulation was obtained by GAMS/DICOPT programming solver. Examples are presented to show the capabilities of the model.
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Abbreviations
- Ak :
-
empirical coefficient used for equipment cost [$/m3]
- Bk :
-
empirical exponent used for equipment cost [$/m3]
- Bp :
-
batch size of product p [kg]
- BSi :
-
batch size of ith product [kg]
- c:
-
steam and cooling water cost factor [$/kJ]
- Cp :
-
heat capacity of batch stream p [kJ/kg °C]
- CcSjr :
-
heat capacity of cooling batch stream for jth product on unit r[kJ/kg°C]
- ChSik :
-
heat capacity of hot batch stream for ith product on unit k [kJ/kg °C]
- Ccpr :
-
heat capacity of cooling batch stream for product p on unit r [kJ/kg °C]
- Chpk :
-
heat capacity of hot batch stream for product p on unit k [kJ/kg °C]
- (ΔT)min :
-
minimum approach temperature [°C]
- F:
-
flow rate of fluid [kg/hr]
- L:
-
a suitably large number
- Qmax :
-
upper bound amount of heat exchange [kJ]
- Qikjr :
-
heat exchanged between ith product on unit k and jth product on unit r [kJ]
- Rp :
-
production requirement of product p over year [kg]
- RSi :
-
production requirement of ith product over year [kg]
- Ssik :
-
equipment size factor of unit k for ith product [m3/kg]
- SVk :
-
equipment size of unit k for sequence [m3]
- T:
-
total production time over year [kg]
- T sh :
-
starting temperature of hot stream [°C]
- T dh :
-
desired temperature of hot stream [°C]
- T sc :
-
starting temperature of cold stream [°C]
- T cd :
-
desired temperature of cold stream [°C]
- TEik :
-
finishing time of ith product on unit k [hr]
- TIik :
-
starting time of ith product on unit k [hr]
- Tct :
-
total production cycle time [hr]
- tpk :
-
batch processing time of batch p unit k [hr]
- TcsSjr :
-
starting temperature of cold stream of jth product on unit r[°C]
- TcdSjr :
-
desired temperature of cold stream of jth product on unit r[°C]
- ThsSik :
-
starting temperature of hot stream of ith product on unit k[°C]
- ThdSik :
-
desired temperature of cold stream of ith product on unit k[°C]
- TC spr :
-
starting temperature of cold stream of product p unit r °C]
- Tc dpr :
-
desired temperature of cold stream of product p unit r °C]
- Th spk :
-
starting temperature of hot stream of product p unit k °C]
- Th dpk :
-
desired temperature of hot stream of product p unit k °C]
- T +ikjr :
-
artificial positive variable for match between TIik^ and TIjr
- T -ijkr :
-
artificial positive variable for match between TIik and TTjr
- Vk :
-
equipment size of unit k [m3]
- Xpi :
-
0-1 binary variable for sequence
- Yijkr :
-
0-1 binary variable for heat exchange between two batch streams with transfer time TIik and TIjr, respectively
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Kim, J., Lee, B. & Lee, E.S. Optimal production sequence and processing schedules of multiproduct batch processes for heat integration and minimum equipment costs. Korean J. Chem. Eng. 18, 599–605 (2001). https://doi.org/10.1007/BF02706374
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DOI: https://doi.org/10.1007/BF02706374