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Optimal reconfiguration of water networks based on properties

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Abstract

This paper presents a mathematical programming model for the reconfiguration of existing water networks based on the stream properties that impact the performance of the process units and the environment. To develop an improved configuration, the model simultaneously evaluates the repiping of the existing network through the placement/reassignment of the existing treatment units, and the addition of new treatment units while addressing environmental constraints. The model also accounts for the options of process modification and increased capacity of the plant. The objective function of the optimization model seeks to minimize the total annualized cost of the system which incorporates the capital investment associated with process retrofitting and the operating cost which includes the cost of fresh resources. The applicability of the proposed model is illustrated through several case studies.

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Abbreviations

i :

Process sources

in:

Inlet

j :

Sinks

max:

Maximum

min:

Minimum

n :

Sections for the capital cost for the treatment units

out:

Outlet conditions

p:

Properties

pla :

Stages

r :

Fresh sources

u :

Treatment units

u′u :

Treatment units existing prior to the retrofit process

u″u :

New treatment units required after the retrofit process

NPROP :

Set for the properties (p|p = 1,…, NPROP)

NFRESH :

Set for the fresh sources (r|r = 1,…, NFRESH)

NPLATES :

Number of stages for the treatment units (pla|pla = 1,…,NPLATES)

NSECTION :

Set for the disjunctions for the capital costs (n|n = 1,…, NSECTION)

NSINKS :

Set for the sinks (j|j = 1,…, NSINKS)

NSOURCES :

Set for the process sources (i|i = 1,…, NSOURCES)

NTREAT :

Set for the treatment units (u|u = 1,…, NTREAT)

δ :

Lower limit for the flowrate in the pipes

τ ij :

Binary parameter to indicate the existence for the pipe before the retrofit process

τ iu :

Binary parameter for the existence of pipe between source i and unit u prior to the retrofit

τ rj :

Binary parameter for the segment of pipe between the fresh source r to the sink j before the retrofit process

\(\tau_{{uu^{\prime } }}\) :

Binary parameter for the existence of the pipe between units u and u′ before to the retrofit

τ uj :

Binary parameter for the existence of pipes between unit u and sink j prior to the retrofit

\(CF_{ij}^{D}\) :

Unit cost for the pipe from source i to sink j

\(CF_{ij}^{ \hbox{max} }\) :

Upper limit for the cost of pipe between source i to sink j

\(CF_{iu}^{D}\) :

Unit cost for the pipe between source i with unit u

\(CF_{iu}^{ \hbox{max} }\) :

Upper limit for pipe between source i and unit u

\(CF_{rj}^{D}\) :

Unit cost for the pipe between the fresh source r to the sink j

\(CF_{rj}^{ \hbox{max} }\) :

Upper limit for the cost of pipe between fresh source r to sink j

\(CF_{uj}^{D}\) :

Unit cost for the pipe between the unit u and sink j

\(CF_{uj}^{ \hbox{max} }\) :

Upper limit for the cost of pipe between unit u and sink j

\(CF_{{uu^{\prime } }}^{D}\) :

Unit cost for the pipe between unit u and unit u′

\(CF_{{uu^{\prime } }}^{ \hbox{max} }\) :

Upper limit for the pipe cost for the segment between units u and u′

\(CF_{{u^{\prime \prime } n}}\) :

Fixed cost to install the new unit u″ in section n

\(CFA_{{yu^{\prime } }}\) :

Fixed cost to increase the capacity of unit u′

\(CFP_{{yu^{\prime } }}\) :

Fixed cost to improve the efficiency of unit u′

\(CO_{u}\) :

Operational cost for unit u per kg treated

\(Costo_{r}\) :

Fresh source cost

\(Costop_{{u^{\prime } }}^{ \hbox{max} }\) :

Maximum cost to increase the capacity of the unit u′

\(Costop_{{u^{\prime \prime } n}}^{ \hbox{max} }\) :

Upper limit for the cost for new unit u″ in section n

\(Costopla_{{u^{\prime } p}}^{ \hbox{max} }\) :

Upper limit for cost for unit u′

\(CV_{{u^{\prime \prime } n}}\) :

Variable cost to install the new unit u″ in section n

\(CVA_{{yu^{\prime } }}\) :

Variable cost to increase the capacity of unit u′

\(CVP_{{yu^{\prime } }}\) :

Variable cost to improve the efficiency of unit u′

\(EF_{{p,u^{\prime } }}\) :

Efficiency for unit u′ for property p before retrofit

\(fac_{{u^{\prime } ,p,pla}}\) :

Factor to improve the efficiency for unit u′ for property p

\(G_{j}^{ \hbox{min} }\) :

Minimum flowrate for the sink j

\(G_{j}^{ \hbox{max} }\) :

Maximum flowrate for the sink j

\(H_{Y}\) :

Hours per year that the plant operates

\(H_{{yu^{\prime } }}^{e}\) :

Flowrate existing prior to the retrofit inlet to unit u′

\(H_{{yu^{\prime } }}^{ \hbox{max} }\) :

Maximum flowrate inlet to unit u′

\(H_{{yu^{\prime \prime } n}}^{ \hbox{min} }\) :

Lower limit for the flowrate in unit u″ in section n

\(H_{{yu^{\prime \prime } n}}^{ \hbox{max} }\) :

Upper limit for unit u″ in section n

\(K_{F}\) :

Factor used to annualize the capital costs

pip ij :

Pumping cost for segment i to j

pip iu :

Pumping cost for segment i to u

pip rj :

Pumping cost for segment r to j

pip uj :

Pumping cost for segment u to j

\(pip_{{uu^{\prime } }}\) :

Pumping cost for segment u to u′

W i :

Flowrate for process source i

Ψ pi :

Operator for property p in the stream i

Ψ max pj :

Maximum operator for property p in sink j

Ψ min pj :

Minimum operator for property p in sink j

CF ij :

Pipe cost for segment between i to j

CF iu :

Pipe cost for segment between i to u

CF rj :

Pipe cost for segment between r to j

CF uj :

Pipe cost for segment between u to j

\(CF_{{uu^{\prime } }}\) :

Pipe cost for segment between u to u′

\(Costp_{{u^{\prime } }}\) :

Capital cost for unit u′ for installation and modification

\(Costp_{{u^{\prime \prime } }}\) :

Capital cost for new unit u″

\(Costpla_{{u^{\prime } }}\) :

Capital cost to improve the performance of unit u′

\(Costpla_{{u^{\prime } }}^{\text{disp}}\) :

Disaggregated variables for Costpla u′

\(d\psi_{{pu^{\prime } pla}}^{\text{out}}\) :

Disaggregated variables for \(\psi_{{pu^{\prime } }}^{\text{out}}\)

F r :

Flowrate used for fresh source r

f rj :

Segregated flowrate from fresh source r to sink j

G j :

Total flowrate inlet to sink j

h 1uj :

Segregated flowrate from unit u to the sink j

\(h_{{2uu^{\prime } }}\) :

Segregated flowrate from unit u to unit u′

H u :

Total flowrate inlet to unit u

\(H_{{u^{\prime \prime } n}}^{\text{dis}}\) :

Disaggregated variables for \(H_{{u^{\prime \prime } }}\)

\(H_{{u^{\prime } }}^{{{\text{dis}}1}} ,H_{{u^{\prime } }}^{{{\text{dis}}2}}\) :

Disaggregated variables for H u′

w 1ij :

Segregated flowrate from source i to sink j

w 2iu :

Segregated flowrate from source i to unit u

\(y_{ij}^{pip}\) :

Binary variable for the use of pipe between i to j

\(Y_{ij}^{pip}\) :

Boolean variable for the use of pipe between i and j

\(y_{iu}^{pip}\) :

Binary variable for the use of pipe between i to u

\(Y_{iu}^{pip}\) :

Boolean variable for the use of pipe between i and u

\(y_{rj}^{pip}\) :

Binary variable for the use of pipe between r to j

\(Y_{rj}^{pip}\) :

Boolean variable for the use of pipe between r to j

\(y_{{u^{\prime } }}\) :

Binary variable to indicate the use of the unit u′

\(Y_{{u^{\prime } }}\) :

Boolean variable to indicate the use of the unit u′

\(y_{{u^{\prime } 1}} , \, y_{{u^{\prime } 2}}\) :

Binary variables to indicate that an existing unit u′ increases its capacity or not

\(Y_{{u^{\prime } 1}} , \, Y_{{u^{\prime } 2}}\) :

Boolean variables to indicate that an existing unit u′ increases its capacity or not

\(y_{{u^{\prime } p}}\) :

Binary variable to indicate that it is required to increase the efficiency for unit u′

\(Y_{{u^{\prime } p}}\) :

Boolean variable to indicate that it is required to increase the efficiency for unit u′

\(Y_{{u^{\prime \prime } }}\) :

Boolean variable to install the new unit u″

\(y_{{u^{\prime \prime } }}\) :

Binary variable to install the new unit u″

\(Y_{{u^{\prime \prime } n}}\) :

Boolean variable to install the new unit u″ and that is in section n

\(y_{{u^{\prime \prime } n}}\) :

Binary variable to install the new unit u″ and that is in section n

\(y_{uj}^{pip}\) :

Binary variable for the use of pipe between u to j

\(Y_{uj}^{pip}\) :

Boolean variable for the use of pipe between u to j

\(y_{{uu^{\prime } }}^{pip}\) :

Binary variable for the use of pipe between u to u′

\(Y_{{uu^{\prime } }}^{pip}\) :

Boolean variable for the use of pipe between u to u′

\(\psi_{pu}^{\rm in}\) :

Value for the property operator at the inlet of unit u for property p

\(\psi_{pu}^{\rm out}\) :

Value for the property operator at the exit of unit u for property p

ψ pj :

Value for the property operator at the inlet of sink j for property p

References

  • Alfadala HE, Sunol AK, El-Halwagi MM (2001) An integrated approach to the retrofitting of mass exchange networks. Clean Technol Environ Policy 2(4):236–247

    Google Scholar 

  • Bai J, Feng X, Deng C (2010) Optimal design of single-contaminant regeneration reuse water networks with process decomposition. AIChE J 56(4):915–929

    CAS  Google Scholar 

  • Brooke A, Kendrick D, Meeruas A, Raman R (2013) GAMS-Language guide. GAMS Development Corporation, Washington, DC

    Google Scholar 

  • Chen CL, Hung PS (2005) Retrofit of mass-exchange networks with superstructure-based MINLP formulation. Ind Eng Chem Res 44(18):7189–7199

    Article  CAS  Google Scholar 

  • Deng C, Feng X (2011) Targeting for conventional and property-based water networks with multiple resources. Ind Eng Chem Res 50(7):3722–3737

    Article  CAS  Google Scholar 

  • Dhole VR, Ramchandani N, Tainsh RA, Wasilewski M (1996) Make your process water pay for itself. Chem Eng 103(1):100–103

    CAS  Google Scholar 

  • Doyle SJ, Smith R (1997) Targeting water reuse with multiple contaminants. Chem Eng Res Des 75(3):181–189

    CAS  Google Scholar 

  • El-Halwagi MM, Gabriel F, Harell D (2003) Rigorous graphical targeting for resource conservation via material recycle/reuse networks. Ind Eng Chem Res 42(19):4319–4328

    Article  CAS  Google Scholar 

  • El-Halwagi MM, Glasgow IM, Qin XY, Eden MR (2004) Property integration: componentless design techniques and visualization tools. AIChE J 50(8):1854–1869

    Article  CAS  Google Scholar 

  • Faria DC, Bagajewicz MJ (2009) Profit-based grassroots design and retrofit of water network in process plants. Comput Chem Eng 33(2):436–453

    Article  CAS  Google Scholar 

  • Feng X, Bai J, Zheng XS (2007) On the use of method to determine the targets of single-contaminant regeneration recycling water systems. Chem Eng Sci 62(8):2127–2138

    Article  CAS  Google Scholar 

  • Foo DCY (2013) A generalized guideline for process changes for resource conservation networks. Clean Technol Environ Policy 15(1):45–53

    Article  Google Scholar 

  • Foo DCY, Kazantzi V, El-Halwagi MM, Manan ZA (2006) Surplus diagram and cascade analysis techniques for targeting property-based material reuse network. Chem Eng Sci 61(8):2626–2642

    Article  CAS  Google Scholar 

  • Fraser DM, Hallale N (2000) Retrofit of mass exchange networks using pinch technology. AIChE J 46(10):2112–2117

    Article  CAS  Google Scholar 

  • Gabriel F, El-Halwagi MM (2005) Simultaneous synthesis of waste interception and material reuse networks: problem reformulation for global optimization. Environ Prog 24(2):171–180

    Article  CAS  Google Scholar 

  • Galan B, Grossmann IE (1998) Optimal design of distributed wastewater treatment networks. Ind Eng Chem Res 37(10):4036–4048

    Article  CAS  Google Scholar 

  • Grossmann IE, Lee S (2003) Generalized convex disjunctive programming nonlinear convex hull relaxation. Comput Optim Appl 26(1):83–100

    Article  Google Scholar 

  • Hallale N (2002) A new graphical targeting method for water minimization. Adv Environ Res 6(3):377–390

    Article  CAS  Google Scholar 

  • Hu N, Feng X, Deng C (2011) Optimal design of multiple-contaminant regeneration reuse water networks with process decomposition. Chem Eng J 173(1):80–91

    Article  CAS  Google Scholar 

  • Kazantzi V, El-Halwagi MM (2005) Targeting material reuse via property integration. Chem Eng Prog 101(8):28–37

    CAS  Google Scholar 

  • Kheireddine H, Dadmohammadi Y, Deng C, Feng X, El-Halwagi MM (2011) Optimization of direct recycle networks with the simultaneous consideration of property, mass, and thermal effects. Ind Eng Chem Res 50(7):3754–3762

    Article  CAS  Google Scholar 

  • Kheireddine HA, El-Halwagi MM, Elbashir NO (2013) A property-integration approach to solve screening and conceptual design of solvent-extraction systems for recycling used lubricating oils. Clean Technol Environ Policy 15(1):35–44

    Article  CAS  Google Scholar 

  • Khor CS, Shah N, Mahadzir S, Elkamel A (2012) Optimization of petroleum refinery water network systems retrofit incorporating reuse, regeneration and recycle strategies. Can J Chem Eng 90(1):137–143

    Article  CAS  Google Scholar 

  • Lancu P, Plesu V, Lavric V (2009) Regeneration of internal streams as an effective tool for wastewater network optimization. Comput Chem Eng 33(3):731–742

    Article  Google Scholar 

  • Lee S, Grossmann IE (2000) New algorithms for nonlinear generalized disjunctive programming. Comput Chem Eng 24(9–10):2125–2141

    Article  CAS  Google Scholar 

  • Lee S, Grossmann IE (2003) Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints: applications to process networks. Comput Chem Eng 27(11):1557–1575

    Article  CAS  Google Scholar 

  • Lee S, Grossmann IE (2005) Logic-based modeling and solution of nonlinear discrete/continuous optimization problems. Ann Oper Res 139(1):267–288

    Article  Google Scholar 

  • Li BH, Chang CT (2011a) A model-based search strategy for exhaustive identification of alternative water networks design. Ind Eng Chem Res 50(7):3653–3659

    Article  CAS  Google Scholar 

  • Li BH, Chang CT (2011b) Multiobjective optimization of water-using networks with multiple contaminants. Ind Eng Chem Res 50(9):5651–5660

    Article  CAS  Google Scholar 

  • Lira-Barragan LF, Ponce-Ortega JM, Serna-González M, El-Halwagi MM (2011a) Synthesis of water networks considering the sustainability of the surrounding watershed. Comput Chem Eng 35(12):2837–2852

    Article  CAS  Google Scholar 

  • Lira-Barragan LF, Ponce-Ortega JM, Serna-González M, El-Halwagi MM (2011b) An MINLP model for the optimal location of a new industrial plant with simultaneous consideration of economic and environmental criteria. Ind Eng Chem Res 52(2):953–964

    Article  Google Scholar 

  • Lira-Barragan LF, Ponce-Ortega JM, Nápoles-Rivera F, Serna-González M, El-Halwagi MM (2013) Incorporating the property-based water networks and surrounding watersheds in site selection of industrial facilities. Ind Eng Chem Res 52(1):91–107

    CAS  Google Scholar 

  • Manan ZA, Tan YL, Foo DCY (2004) Targeting the minimum water flow rate using water cascade analysis technique. AIChE J 50(12):3169–3183

    Article  CAS  Google Scholar 

  • Nápoles-Rivera F, Ponce-Ortega JM, El-Halwagi MM, Jiménez-Gutiérrez A (2010) Global optimization of mass and property integration networks with in-plant property interceptors. Chem Eng Sci 65(15):4363–4377

    Article  Google Scholar 

  • Ng DKS, Foo DCY, Tan RR, Pau CH, Tan YL (2009) Automated targeting for conventional and bilateral property-based resource conservation network. Chem Eng J 149(1–3):87–101

    Article  CAS  Google Scholar 

  • Ng DKS, Foo DCY, Tan RR, El-Halwagi MM (2010) Automated targeting technique for concentration- and property-based total resource conservation networks. Comput Chem Eng 34(5):825–845

    Article  CAS  Google Scholar 

  • Ponce-Ortega JM, Jiménez-Gutierrez A, Grossmann IE (2008) Simultaneous retrofit and heat integration of chemical processes. Ind Eng Chem Res 47(15):5512–5528

    Article  CAS  Google Scholar 

  • Ponce-Ortega JM, Hortua AC, El-Halwagi MM, Jiménez-Gutiérrez A (2009) A property-based optimization of direct-recycle networks and wastewater treatment processes. AIChE J 55(9):2329–2344

    Article  CAS  Google Scholar 

  • Ponce-Ortega JM, El-Halwagi MM, Jimenez-Gutierrez A (2010) Global optimization for the synthesis of property-based recycle and reuse networks including environmental constraints. Comput Chem Eng 34(3):318–330

    Article  CAS  Google Scholar 

  • Ponce-Ortega JM, Mosqueda-Jimenez FW, Serna-Gonzalez M, Jimenez-Gutierrez A, El-Halwagi MM (2011) A property-based approach to the synthesis of material conservation networks with economic and environmental objectives. AIChE J 57(9):2369–2387

    Article  CAS  Google Scholar 

  • Ponce-Ortega JM, Nápoles-Rivera F, El-Halwagi MM, Jiménez-Gutiérrez A (2012) An optimization approach for the synthesis of recycle and reuse water integration networks. Clean Technol Environ Policy 14(1):133–151

    Article  Google Scholar 

  • Quesada I, Grossmann IE (1995) Global optimization of bilinear process networks with multicomponent flows. Comput Chem Eng 19(12):1219–1242

    Article  CAS  Google Scholar 

  • Raman R, Grossmann IE (1994) Modeling and computational techniques for logic based integer programming. Comput Chem Eng 18(7):563–578

    Article  CAS  Google Scholar 

  • Rubio-Castro E, Ponce-Ortega JM, Serna-González M, El-Halwagi MM (2012) Optimal reconfiguration of multi-plant water networks into an eco-industrial park. Comput Chem Eng 44:58–83

    Article  CAS  Google Scholar 

  • Saw SY, Lee L, Lim MH, Foo DCY, Chew IML, Tan RR, Klemez JJ (2011) An extended graphical targeting technique for direct reuse/recycle in concentration and property-based resource conservation networks. Clean Technol Environ Policy 13(2):347–357

    Article  Google Scholar 

  • Sawaya NW, Grossmann IE (2005) A cutting plane method for solving linear generalized disjunctive programming problems. Comput Chem Eng 29(9):1891–1913

    Article  CAS  Google Scholar 

  • Sawaya NW, Grossmann IE (2007) Computational implementation of non-linear convex hull reformulations. Comput Chem Eng 31(7):856–866

    Article  CAS  Google Scholar 

  • Shelley MD, El-Halwagi MM (2000) Componentless design of recovery and allocation systems: a functionality-based clustering approach. Comput Chem Eng 24(9–10):2081–2091

    Article  CAS  Google Scholar 

  • Smith R (2005) Chemical process: design and integration. Wiley-Blackwell, Oxford

  • Sotelo-Pichardo C, Ponce-Ortega JM, El-Halwagi MM, Frausto-Hernandez S (2011) Optimal retrofit of water conservation networks. J Clean Prod 19(14):1560–1581

    Article  Google Scholar 

  • Sujo-Nava D, Scodari LA, Slater CS, Dahm K, Savelski MJ (2009) Retrofit of sour water networks in oil refineries: a case study. Chem Eng Process 48(6):892–901

    Article  CAS  Google Scholar 

  • Takama N, Kuriyama T, Shiroko K, Umeda T (1980) Optimal water allocation in a petroleum refinery. Comput Chem Eng 4(4):251–258

    Article  Google Scholar 

  • Tan RR, Cruz DE (2004) Synthesis of robust water reuse networks for single-component retrofit problems using symmetric fuzzy linear programming. Comput Chem Eng 28(12):2547–2551

    Article  CAS  Google Scholar 

  • Tan YL, Manan ZA (2006) Retrofit of water networks with optimization of existing regeneration units. Ind Eng Chem Res 45(22):7592–7602

    Article  CAS  Google Scholar 

  • Tan YL, Manan ZA, Foo DCY (2007) Retrofit of water network with regeneration using water pinch analysis. Process Saf Environ Prot 85(4):305–317

    Article  CAS  Google Scholar 

  • Vecchietti A, Lee S, Grossmann IE (2003) Modeling of discrete/continuous optimization problems: characterization and formulations of disjunctions and their relaxations. Comput Chem Eng 27(3):433–448

    Article  CAS  Google Scholar 

  • Wagialla KM (2012) Pinch-based and disjunctive optimization for process integration of wastewater interception with mass and property constraints. Clean Technol Environ Policy 14(4):597–608

    Article  CAS  Google Scholar 

  • Wang YP, Smith R (1994) Wastewater minimization. Chem Eng Sci 49(7):981–1006

    Article  CAS  Google Scholar 

  • Yin LT, Manan ZA (2008) A new systematic technique for retrofit of water network. Int J Environ Pollut 32(4):519–526

    Article  Google Scholar 

Download references

Acknowledgments

Financial support from CONACyT is gratefully acknowledged.

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Authors and Affiliations

  1. Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, 58060, Morelia, Michoacán, Mexico

    César Sotelo-Pichardo, José María Ponce-Ortega, Fabricio Nápoles-Rivera & Medardo Serna-González

  2. Chemical Engineering Department, Texas A&M University, College Station, TX, 77843, USA

    Mahmoud M. El-Halwagi

  3. Adjunct Faculty at the Chemical and Materials Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia

    Mahmoud M. El-Halwagi

  4. Biochemical and Chemical Engineering Department, Instituto Tecnológico de Aguascalientes, 20256, Aguascalientes, Aguascalientes, Mexico

    Sergio Frausto-Hernández

Authors
  1. César Sotelo-Pichardo
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  2. José María Ponce-Ortega
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  3. Fabricio Nápoles-Rivera
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  4. Medardo Serna-González
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  5. Mahmoud M. El-Halwagi
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  6. Sergio Frausto-Hernández
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Corresponding author

Correspondence to José María Ponce-Ortega.

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Sotelo-Pichardo, C., Ponce-Ortega, J.M., Nápoles-Rivera, F. et al. Optimal reconfiguration of water networks based on properties. Clean Techn Environ Policy 16, 303–328 (2014). https://doi.org/10.1007/s10098-013-0631-5

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