Abstract
This paper presents a multi-objective mixed integer linear programming problem for the optimization of seawater air-conditioning systems using deep seawater as a cooling utility. The optimization formulation was developed including the technical, economic and environmental aspects of the problem. The model is used to define the optimal scheduling of deep seawater use and electricity needed to satisfy the air-conditioning requirements in a group of hotels. It also addresses the optimal planning for biocide, neutralization chemical dosing and mechanical maintenance required to maintain optimal operation conditions in the system. The proposed model is applied to a case study in Mexico. Results show the trade-offs between economic and environmental aspects. Optimal solutions compensating economic and environmental objectives are identified through a Pareto front.
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Abbreviations
- i :
-
Hotels
- t :
-
Period of time in days
- \(F_{t}^{\text{water}}\) :
-
Flowrate taken from the ocean (m3/day)
- \(F_{t}^{\text{trat}}\) :
-
Flowrate leaving the treatment plant (m3/day)
- \(f_{i,t}^{i}\) :
-
Flowrate sent to hotel i in time t (m3/day)
- \(f_{i,t}^{o}\) :
-
Flowrate leaving hotel i in time t (m3/day)
- \(F_{t}^{\text{out}}\) :
-
Flowrate treated in the neutralization system (m3/day)
- \(F_{t}^{\text{bio}}\) :
-
Flowrate of biocide (m3/day)
- \(F_{t}^{\text{chem}}\) :
-
Flowrate of chemical (m3/day)
- \(Q_{i,t}^{\text{water}}\) :
-
Heat load can be removed by using the seawater (kWh/day)
- \(Q_{i,t}^{\text{e}}\) :
-
Heat load can be removed by using conventional AC (kWh/day)
- \({\text{Cost}}_{i,t}^{\text{e}}\) :
-
Cost paid to the local electricity company ($/day)
- \({\text{Elect}}_{i,t}^{\text{e}}\) :
-
Energy consumption (kWh/day)
- \(Q_{i}^{\text{qwm}}\) :
-
Maximum heat load in any time t (m3/day)
- \(A_{i}\) :
-
Heat exchangers area (m2)
- \({\text{Cost}}_{i}^{\text{unit}}\) :
-
Unit cost for heat exchangers ($)
- \({\text{heateCost}}\) :
-
Total cost of heat exchangers ($)
- \({\text{MaintCost}}\) :
-
Cost of maintenance ($)
- \({\text{BiocideCost}}\) :
-
Biocide cost ($)
- \({\text{chemicalCost}}\) :
-
Chemical cost ($)
- \({\text{ElectricityCost}}\) :
-
Total cost for electricity ($)
- \({\text{Pcf}}^{\text{trat}}\) :
-
Unit cost of pipeline from the deep ocean to treatment plant ($)
- \({\text{Pcf}}_{i}\) :
-
Unit cost of pipeline from treatment plant to hotel i ($)
- \({\text{Pcf}}_{{^{i} }}^{\text{out}}\) :
-
Unit cost of pipeline from hotel i to neutralization plant ($)
- \({\text{PipingCost}}\) :
-
Piping costs ($)
- \({\text{Pcost1}}\) :
-
Unit cost of pump from deep ocean to treatment plant ($)
- \({\text{Pcost2}}_{i}\) :
-
Unit cost of pump from treatment plant to hotel i ($)
- \({\text{Pcost3}}_{i}\) :
-
Unit cost of pump from hotel i to neutralization plant ($)
- \({\text{PumpingCost}}\) :
-
Total pumping cost ($)
- \({\text{fwm}}_{i}\) :
-
Maximum flowrate in each segment of pipeline from treatment plant to hotel i (m3/day)
- \(F^{\text{trat}}\) :
-
Maximum flowrate from the deep ocean to treatment plant (m3/day)
- \({\text{Pumpequip}}\) :
-
Total cost for the pumps ($)
- \({\text{TAC}}\) :
-
Total annual cost ($/year)
- \({\text{Emelec}}_{i,t}\) :
-
Emissions for the use of electricity from the hotel i (Ton CO2 eq./day)
- \({\text{Emisionselect}}\) :
-
Total emissions for the use of electricity (Ton CO2 eq./year)
- \({\text{Power}}_{t}\) :
-
Power of the pump from deep ocean to treatment plant (kW)
- \({\text{Power2}}_{i,t}\) :
-
Power of the pump from the treatment plant to hotel i (kW)
- \({\text{Power3}}_{i,t}\) :
-
Power of the pump from the hotel i to neutralization plant (kW)
- \({\text{TotalPower}}\) :
-
Power consumed in the pumps (kW)
- \({\text{EnergyPump}}\) :
-
Total energy consumed in the pumps (kWh)
- \({\text{Emisionprocess}}\) :
-
Total emissions for the pumps (Ton CO2 eq./year)
- \({\text{GHGE}}\) :
-
Total greenhouse gas emissions (Ton CO2 eq./year)
- \(\rho\) :
-
Density of seawater (kg/m3)
- \({\text{Cp}}_{\text{sw}}\) :
-
Heat capacity of seawater (kJ/kg °C)
- U :
-
Global heat transfer coefficient (W/m2 °C)
- COP:
-
Coefficient of performance
- \(Q_{i,t}^{\text{H}}\) :
-
The required heat load to be removed from the air in hotel i in time t (kWh)
- \({\text{consp}}_{i,t}\) :
-
Total electric input spent with conventional AC (kWh)
- \(\Delta T\) :
-
Temperature differential (°C)
- \({\text{UCE}}\) :
-
Unitary cost for electricity ($/kWh)
- \(\Delta T_{\text{ml}}\) :
-
Logarithmic mean temperature difference (°C)
- EFE:
-
Emissions factor (kg CO2/kWh)
- \(C^{\text{bio}}\) :
-
Concentration to have a biocidal effect (kg/m3)
- \(C_{t}^{\text{in}}\) :
-
Commercial biocide concentration (kg/m3)
- \(\xi\) :
-
Unit cost for biocide ($/m3 of treated seawater)
- \(\gamma\) :
-
Unit cost for chemical ($/m3 of treated seawater)
- \(\beta\) :
-
Unitary cost per maintenance ($)
- \(\tau\) :
-
Number of programmed maintenances per year
- \(H_{Y}\) :
-
Hours of operation per year (h/year)
- \(\eta\) :
-
Pump efficiency
- \(f\) :
-
Friction factor
- \(D\) :
-
Pipeline diameter (m)
- L :
-
Length of pipeline (m)
- \(k_{\text{F}}\) :
-
Factor used to annualize the capital costs (year−1)
- \(k_{\text{m}} ,m\) :
-
Pipe cost parameters that depend on the pipe material
- \(\delta\) :
-
Exponent for heat exchangers area cost
- \({\text{VCost}}_{i}^{\text{unit}}\) :
-
Unit variable cost for the heat exchangers ($)
- \({\text{FCost}}_{i}^{\text{unit}}\) :
-
Unit fixed cost for the heat exchangers ($)
- \({\text{PPC1}}_{t}\) :
-
Pumping cost from deep ocean to treatment plant ($/m3)
- \({\text{PPC2}}_{i,t}\) :
-
Pumping cost from treatment plant to hotel i ($/m3)
- \({\text{PPC3}}_{i,t}\) :
-
Pumping cost from hotel i to neutralization plant ($/m3)
- \({\text{CVP}}^{\text{pump}}\) :
-
Unit variable cost for pumps ($/m3)
- \({\text{CFB}}^{\text{pump}}\) :
-
Unit fixed cost for pumps ($)
- \(\varOmega\) :
-
Slope in the linear regression obtain for each pump
- \(\varPsi\) :
-
Intercept in the linear regression obtain for each pump
- \(F^{\text{trat,max}}\) :
-
Maximum flowrate in treatment plant (m3/day)
- \(f^{\text{hotel,max}}\) :
-
Maximum flowrate in hotel i (m3/day)
- \(y_{i}^{\text{he}}\) :
-
Binary variable for the existence of heat exchangers
- \(y^{\text{trat}}\) :
-
Binary variable for the existence of pipeline segment from the ocean to the treatment plant
- \(y_{i}^{\text{hotel}}\) :
-
Binary variable for the existence of pipeline segment from the treatment plant to each hotel
- \(y_{i}^{\text{out}}\) :
-
Binary variable for the existence of pipeline segment from the hotel to the neutralization plant
- \(y^{\text{main}}\) :
-
Binary variable for the existence of maintenance
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Acknowledgements
The authors acknowledge the financial support from the Mexican Council of Science and Technology (CONACYT) (Grant No. 413489) to the Scientific Research Council of the Universidad Michoacana de San Nicolás de Hidalgo and also to the Texas A&M University.
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Hernández-Romero, I.M., Nápoles-Rivera, F., Mukherjee, R. et al. Optimal design of air-conditioning systems using deep seawater. Clean Techn Environ Policy 20, 639–654 (2018). https://doi.org/10.1007/s10098-018-1493-7
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DOI: https://doi.org/10.1007/s10098-018-1493-7