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Optimal Synthesis of Batch Water Networks Using Dynamic Programming

  • Zhiwei Li
  • Thokozani MajoziEmail author
Original Research Paper
  • 174 Downloads

Abstract

Water minimization in the process industry is becoming increasingly important due to increasingly stringent environmental legislation, especially for batch plants. This work proposes a dynamic programming (DP) method for the optimal design of water-using networks in batch plants. DP is a powerful framework for dealing with a large spectrum of multistage decision-making problems and has been applied in numerous chemical engineering problems. The proposed methodology is explained as follows. Firstly, based on the start time and end time of each operation, the whole process is divided into N stages. Secondly, the water requirement of water-using units in each stage is satisfied and the state of stored water and wastewater generation is determined. The backward procedure of DP is used to solve the DP problems. The target of freshwater consumption of the process and the optimal design of the water network are obtained simultaneously. In order to display the versatility of the proposed approach, four examples from literature are considered. Example 1 is a completely batch process with a fixed flowrate problem. Example 2 is a hybrid batch water system comprising various modes of operations and operating patterns. Example 3 is a fixed-mass load problem with a regeneration unit, while example 4 considers the batch water network design with multiple contaminants. The results obtained in this work were comparable with the results from literature, implying that it can be applicable to both mass transfer-based and non-mass transfer-based batch water networks.

Keywords

Dynamic programming Water integration Network design Batch processes 

Notes

Nomenclature

k the kth stage

Ik a set of available water sources in stage k

Jk a set of available water sources in stage k

m the number of operations

L a set of contaminants l

tsm the start time of operation m

tem the end time of operation m

\( {F}_{j,k}^{Fw} \) the quantity of freshwater consumed by water sink j in stage k

\( {F}_{Tanki}^{St} \) the quantity of water stored in tank i

\( {F}_{i,j,k}^d \) the quantity of directly reused water from water source i to water sink j in stage k

\( {F}_{i,j,k}^{ind} \) the quantity of indirectly reused water from water source i to water sink j in stage k

\( {F}_{i,k}^{Ww} \) the quantity of wastewater from water source i in stage k

\( {F}_{j,k}^{\mathrm{Reg}} \) the quantity of regenerated water for water sink j in stage k

\( {F}_{i,k}^{st} \) the quantity of stored water from water source i in stage k

Fj, k the quantity of water for sink j in stage k

Fi, k the quantity of water for source i in stage k

\( {c}_{i,j,k}^{d,l} \) the concentration of contaminant l direct reuse water from water source i to water sink j in stage k

ci, j, kind, l the concentration of contaminant l of indirect reuse water from water source i to water sink j in stage k

\( {c}_{j,\mathrm{k}}^{\max, in,l} \) the maximum inlet concentration of contaminant l of water sink j in stage k

\( {c}_{j,\mathrm{k}}^{\max, \mathrm{out},l} \) the maximum inlet concentration of contaminant l of water sink j in stage k

\( {c}_{j,\mathrm{k}}^{in,l} \) inlet concentration of contaminant l of water sink j in stage k

\( {c}_{Fw}^l \) the concentration of contaminant l of freshwater

\( {c}_{\operatorname{Re}g}^l \) the concentration of contaminant l of regenerated water

\( {M}_{j,k}^l \) the mass load of contaminant l of water sink in stage k

Funding Information

The authors thank the National Research Foundation (NRF) of South Africa for funding this work under the NRF/DST Chair in Sustainable Process Engineering at the University of the Witwatersrand, Johannesburg.

References

  1. Adekola O, Majozi T (2011) Wastewater minimization in multipurpose batch plants with a regeneration unit: multiple contaminants. Comput Chem Eng 35:2824–2836CrossRefGoogle Scholar
  2. Almató M, Sanmartí E, Espuña A, Puigjaner L (1997) Rationalizing the water use in the batch process industry. Comput Chem Eng 21:S971–S976CrossRefGoogle Scholar
  3. Bagatin R, Klemeš JJ, Reverberi AP, Huisingh D (2014) Conservation and improvements in water resource management: a global challenge. J Clean Prod 77:1–9CrossRefGoogle Scholar
  4. Bellman R (1957) Dynamic programming. Princeton University Press, Princeton, New JerseyzbMATHGoogle Scholar
  5. Chaturvedi ND, Bandyopadhyay S (2014) Simultaneously targeting for the minimum water requirement and the maximum production in a batch process. J Clean Prod 77:105–115CrossRefGoogle Scholar
  6. Chaturvedi ND, Manan ZA, Wan Alwi SR, Bandyopadhyay S (2016) Effect of multiple water resources in a flexible-schedule batch water network. J Clean Prod 125:245–252CrossRefGoogle Scholar
  7. Chen C-L, Lee J-Y (2008) A graphical technique for the design of water-using networks in batch processes. Chem Eng Sci 63:3740–3754CrossRefGoogle Scholar
  8. Chen C-L, Chang C-Y, Lee J-Y (2008) Continuous-time formulation for the synthesis of water-using networks in batch plants. Ind Eng Chem Res 47:7818–7832CrossRefGoogle Scholar
  9. Chen C-L, Chang C-Y, Lee J-Y (2011) Resource-task network approach to simultaneous scheduling and water minimization of batch plants. Ind Eng Chem Res 50(7):3660–3674CrossRefGoogle Scholar
  10. Cheng K-F, Chang C-T (2007) Integrated water network designs for batch processes. Ind Eng Chem Res 46:1241–1253CrossRefGoogle Scholar
  11. Diban P, Abdul Aziz MK, Foo DCY, Jia X, Li Z, Tan RR (2016) Optimal biomass plantation replanting policy using dynamic programming. J Clean Prod 126:409–418CrossRefGoogle Scholar
  12. El-Halwagi MM, Gabriel F, Harell D (2003) Rigorous graphical targeting for resource conservation via material recycle/reuse networks. Ind Eng Chem Res 42:4319–4328CrossRefGoogle Scholar
  13. Foo DCY (2010) Automated targeting technique for batch process integration. Ind Eng Chem Res 49(20):9899–9916CrossRefGoogle Scholar
  14. Foo DCY (2012) Process integration for resource conservation. CRC Press, Boca Raton, FloridaGoogle Scholar
  15. Foo DCY, Lee J-Y, Ng DKS, Chen C-L (2012) Targeting and design for batch regeneration and total networks. Clean Techn Environ Policy 15:579–590CrossRefGoogle Scholar
  16. Foo DCY, Manan ZA, Tan YL (2005) Synthesis of maximum water recovery network for batch process systems. J Clean Prod 13:1381–1394CrossRefGoogle Scholar
  17. Gouws JF, Majozi T, Foo DCY, Chen C-L, Lee J-Y (2010) Water minimization techniques for batch processes. Ind Eng Chem Res 49:8877–8893CrossRefGoogle Scholar
  18. Kim J-K (2011) Design of discontinuous water-using systems with a graphical method. Chem Eng J 172:799–810CrossRefGoogle Scholar
  19. Kim JK, Smith R (2004) Automated design of discontinuous water systems process. Saf Environ 82:238–248Google Scholar
  20. Lee J-Y, Chen C-L, Lin C-Y (2013) A mathematical model for water network synthesis involving mixed batch and continuous units. Ind Eng Chem Res 52:7047–7055CrossRefGoogle Scholar
  21. Lee J-Y, Chen C-L, Lin C-Y, DCY F (2014) A two-stage approach for the synthesis of inter-plant water networks involving continuous and batch units. Chem Eng Res Des 92:941–953CrossRefGoogle Scholar
  22. Lee J-Y, Foo DCY (2017) Simultaneous targeting and scheduling for batch water networks. Ind Eng Chem Res 56:1559–1569CrossRefGoogle Scholar
  23. Li B-H, Liang Y-K, Chang C-T (2013) Manual design strategies for multicontaminant water-using networks in batch processes. Ind Eng Chem Res 52:1970–1981CrossRefGoogle Scholar
  24. Liu Y, Li G, Wang L, Zhang J, Shams K (2009) Optimal design of an integrated discontinuous water-using network coordinating with a central continuous regeneration unit. Ind Eng Chem Res 48:10924–10940CrossRefGoogle Scholar
  25. Liu Y, Yuan X, Luo Y (2007) Synthesis of water utilization system using concentration interval analysis method (II) discontinuous process. Chinese J Chem Eng 15:369–375CrossRefGoogle Scholar
  26. Majozi T (2005) Wastewater minimisation using central reusable water storage in batch plants. Comput Chem Eng 29:1631–1646CrossRefGoogle Scholar
  27. Majozi T (2006) Storage design for maximum wastewater reuse in multipurpose batch plants. Ind Eng Chem Res 45:5936–5943CrossRefGoogle Scholar
  28. Majozi T (2010) Batch chemical process integration: analysis, synthesis and optimization. Springer, HeidelbergCrossRefGoogle Scholar
  29. Majozi T, Brouckaert CJ, Buckley CA (2006) A graphical technique for wastewater minimisation in batch processes. J Environ Manag 78:317–329CrossRefGoogle Scholar
  30. Oliver P, Rodríguez R, Udaquiola S (2008) Water use optimization in batch process industries. Part 1: design of the water network. J Clean Prod 16:1275–1286CrossRefGoogle Scholar
  31. Roberts SM (1964) Dynamic programming in chemical engineering and process control. Academic Press, LondonGoogle Scholar
  32. Wang Y, Smith R (1995) Time pinch analysis. Chem Eng Res Des 73:905–914Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Chemical and Metallurgical EngineeringUniversity of the WitwatersrandJohannesburgSouth Africa

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