Abstract
A superstructure-based mathematical model is established for single-contaminant heat-integrated water networks (HIWN), and the water loss of both wastewater regeneration recycling and regeneration reuse is considered. Furthermore, a sequential optimization procedure is established to achieve multi-objective optimization. The loss rate of water is taken into the mathematical model as there must have water loss in regeneration process, so that the optimization would be more realistic. Two cases are optimized using proposed model with regeneration recycling and regeneration reuse considered, respectively; the results show the differences between these two modes. Compared with the optimization method in the literature, the proposed method is more realistic.
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Abbreviations
- a :
-
The partition coefficient of contaminant mass load between two subunits
- B :
-
The cost coefficient of regenerated water
- c :
-
The contaminant concentration of streams
- Cp :
-
Specific heat at constant pressure (kJ (kg °C)−1)
- F :
-
Flow rate of stream
- Lr :
-
Loss rate of water in regeneration process
- M :
-
The contaminant load of water using unit (g h−1)
- N :
-
The annual running time (h)
- P :
-
The set of water units before decomposition
- PR :
-
Proportion of annual running time
- Q :
-
Heat (kW)
- r :
-
The removal rate of the contaminant in the regeneration unit R (g h−1)
- R :
-
Regeneration unit
- T :
-
Temperature (°C)
- u :
-
The unit cost ($)
- U :
-
Constant related to the number of connections
- X :
-
The set of water units after decomposition
- y :
-
Binary variables for network connection
- Z :
-
The annual total operating cost of system ($ a−1)
- ξ 1 :
-
Constant which related to the freshwater consumption
- ξ 2 :
-
Constant which related to the amount of regenerated water
- com :
-
Parameters related to decomposition process
- D :
-
Discharge of water using unit
- in :
-
Inlet of water using unit
- min :
-
The minimum value of parameters
- max :
-
The maximum value of parameters
- out :
-
Outlet of water using unit
- s :
-
Definite value
- W :
-
Freshwater consumption
- C :
-
Set of cold streams
- CU :
-
Cooling utility
- F :
-
Flow rate of streams
- H :
-
Set of hot streams
- HU :
-
Heating utility
- k :
-
Temperature degrees
- K :
-
Temperature intervals
- n :
-
Temperature degrees
- m :
-
Hot streams in the set H
- q :
-
Cold streams in the set C
- R :
-
Regeneration unit
- uti:
-
Utility consumption
- b :
-
Water using unit after decomposition
- d :
-
Water using unit
- i :
-
Water using unit
- j :
-
Water using unit
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The financial support for this research is provided by the National Natural Science Foundation of China under grant 21736008.
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Shen, R., Zhang, Y. & Ma, J. A Mathematical Programming Method for Optimizing the Single-Contaminant Regeneration Heat-Integrated Water Networks. Process Integr Optim Sustain 3, 167–178 (2019). https://doi.org/10.1007/s41660-018-0041-6
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DOI: https://doi.org/10.1007/s41660-018-0041-6