Abstract
This work proposes an optimization approach for designing efficient water networks for the shale gas production through the recycle and reuse of wastewater streams reducing the freshwater consumption and effluents considering economic and environmental goals. The economic objective function aims to minimize the total annual cost for the water network including the costs associated with storage, treatment and disposal (capital cost) as well as freshwater cost, treatment cost and transportation costs. The environmental objective is addressed to deal with the minimization of the environmental impact associated with the discharged concentration of total dissolved solids in the wastewater streams and the freshwater consumption through an environmental function that represents the benefit for removing pollutants using the eco-indicator 99 methodology. The methodology requires a given scheduling for the completion phases of the target wells to be properly implemented by the available hydraulic fracturing crews during a time horizon. The model formulation is configured to determine the optimal sizes for the equipment involved by the project, particularly the sizes for storage and treatment units are quantified by the optimization process. A case study is solved to evaluate the effectiveness of the proposed optimization approach.
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Abbreviations
- \(AvailV_{t}^{fresh\_\hbox{max} }\) :
-
Availability of freshwater in the reservoirs (m3/s)
- \(CapCost^{storage}\) :
-
Capital cost for the installation of tanks in the storage system (US$/y)
- \(CapCost^{tank}\) :
-
Capital cost for the installation of tanks of the flowback recovery system ($US/y)
- \(CapCost^{treat}\) :
-
Capital cost for the installation of treatment system ($US/y)
- \(CapCost^{waste}\) :
-
Capital cost for the piping and pumping system to send the final disposal ($US/y)
- \(Cost^{fresh}\) :
-
Cost of the freshwater considering the price for industrial use ($US/y)
- \(Cost^{op\_treat}\) :
-
Cost associated with the operation of the treatment units that involves the acquisition of chemical, use of external energy services, etc. ($US/y)
- \(Cost^{trans\_fb}\) :
-
Cost for transporting the flowback fluid to the interception water network, mainly defined for piping and pumping costs ($US/y)
- \(Cost^{trans\_fresh}\) :
-
Transportation cost to send freshwater from the reservoirs to the water network feed ($US/y)
- \(Cost^{trans\_storage\_treat}\) :
-
Transportation cost to send the flowback fluid from the recovery storage system to the treatments units ($US/y)
- \(Cost^{trans\_tank\_dis}\) :
-
Transportation cost to send the treated flowrate from the treatment units to the final disposals ($US/y)
- \(Cost^{trans\_tank\_well}\) :
-
Transportation cost to recycle the treated flowrate from the storage tanks through the feed of the water network ($US/y)
- \(C_{c,t}^{bypass}\) :
-
Concentration of total dissolved solids in the bypass flowrate (ppm)
- \(C_{c}^{fresh}\) :
-
Concentration of total dissolved solids in the feeding of the freshwater in the water network (ppm)
- \(C_{c,j}^{storage}\) :
-
Concentration of total dissolved solids at the storage tanks before the treatment system (ppm)
- \(C_{c,i,t}^{treat\_in}\) :
-
Concentration of total dissolved solids that enters to the treatment system (ppm)
- \(C_{c,i}^{treat\_\hbox{max} }\) :
-
Maximum concentration of total dissolved solids to be processed by each treatment technology (ppm)
- \(C_{c,i}^{treat\_out}\) :
-
Concentration of total dissolved solids from the treatment units to be disposed (ppm)
- \(C_{c,d,t}^{waste}\) :
-
Concentration of total dissolved solids in the wastewater effluents to be disposed (ppm)
- \(C_{c}^{waste\_\hbox{max} }\) :
-
Maximum concentration limit of total dissolved solids in the effluents to be discharged to the disposals (ppm)
- \(C_{c,n,t}^{well\_in}\) :
-
Concentration of total dissolved solids that enter to the wells as fracturing fluid (ppm)
- \(C_{c}^{well\_\hbox{max} }\) :
-
Maximum concentration limit of total dissolved solid that is permitted as feed to the shale gas wells (ppm)
- \(IMPIN_{p,t}\) :
-
Environmental damage that can be produce if the effluents can be discharge without treatment, eco-points
- \(IMPOUT_{p,t}\) :
-
Environmental damage that can be produced by the discharge of effluents with treatment
- \(IMPTOL\) :
-
Total environmental damage for the implementation of the treatment system for the effluents
- \(ff_{n,t}^{bypass\_well}\) :
-
Flowrate that is recycled from the derivation to the system feed (m3/s)
- \(ff_{d,t}^{bypass\_dis}\) :
-
Flowrate in the bypass that is sent to the disposals directly (m3/s)
- \(ff_{n,t}^{fresh}\) :
-
Flowrate of freshwater that enters to the wells (m3/s)
- \(ff_{j,t}^{storage\_bypass}\) :
-
Flowrate from the recovery tanks to the bypass (m3/s)
- \(ff_{j,i,t}^{storage\_treat}\) :
-
Flowrate from the recovery tanks to the treatment units (m3/s)
- \(ff_{n,i,t}^{tank\_well}\) :
-
Flowrate from the storage system to the wells as recycled fluid (m3/s)
- \(ff_{i,d,t}^{tank\_dis}\) :
-
Flowrate from the storage system to the disposal alternatives (m3/s)
- \(ff_{n,j,t}^{well\_storage}\) :
-
Flowrate from the wells to the storage system (m3/s)
- \(FC^{storage}\) :
-
Fixed cost to install the storage system ($US/y)
- \(FC_{i}^{treat}\) :
-
Fixed cost to install the treatment system ($US/y)
- \(F_{d,t}^{waste}\) :
-
Total flowrate that is discharged to the final disposals (m3/s)
- \(F_{n,t}^{well\_in}\) :
-
Total flowrate that enters to the wells as fracturing fluid (m3/s)
- \(F_{i,t}^{treat\_in}\) :
-
Total flowrate that enters to the treatment system (m3/s)
- \(F_{i,t}^{tank\_out}\) :
-
Total flowrate that leaves each tank in the storage system (m3/s)
- \(F_{j,t}^{storage\_in}\) :
-
Total flowrate that enters to each tank in the storage system (m3/s)
- \(F_{j,t}^{storage\_out}\) :
-
Total flowrate that leaves each tank in the storage system (m3/s)
- \(FC^{tank}\) :
-
Fixed cost to install tanks in the recovery system (m3/s)
- \(FC^{waste}\) :
-
Fixed cost for sending the effluents to the final disposals (m3/s)
- \(F_{i}^{treat\_cap}\) :
-
Total flowrate that the treatment technologies can be processed (m3/s)
- \(F_{i,t}^{treat\_in}\) :
-
Flowrate that is fed in the treatment units (m3/s)
- \(F_{i}^{treat\_\hbox{max} }\) :
-
Maximum flowrate limit for the treatment units (m3/s)
- \(F_{i,t}^{treat\_out}\) :
-
Flowrate that leaves the treatment units (m3/s)
- \(F_{j,t}^{storage\_in}\) :
-
Flowrate that enters to the recovery tanks during the shale gas exploitation (m3/s)
- \(F_{j,t}^{storage\_out}\) :
-
Flowrate that leaves the recovery storage system (m3/s)
- \(F_{n,t}^{well\_out}\) :
-
Total flowrate of flowback fluid that leaves each pit (m3/s)
- \(F_{t}^{bypass}\) :
-
Total flowrate in the bypass stream (m3/s)
- \(F_{t}^{fresh}\) :
-
Freshwater fed to the water network (m3/s)
- \(H^{time}\) :
-
Time conversion factor, time of unit operation (s)
- \(k_{F}\) :
-
Annualization factor (y−1)
- \(TAC\) :
-
Total annual cost ($US/y)
- \(TCC\) :
-
Total capital cost ($US/y)
- \(TOC\) :
-
Total operational cost ($US/y)
- \(TWR\) :
-
Total water requirements (m3)
- \(UC^{fresh}\) :
-
Unit cost for freshwater ($US/m3/s)
- \(UOC_{i}^{treat}\) :
-
Unit cost for treatment technology ($US/m3/s)
- \(UTC_{n}^{fresh}\) :
-
Freshwater unit transportation cost ($US/m3/s)
- \(UTC_{n,j}^{well\_storage}\) :
-
Unit transportation cost of flowrate from the wells to the recovery storage system ($US/m3/s)
- \(UTC_{j,i}^{storage\_treat}\) :
-
Unit transportation cost of flowrate from the recovery system to treatment units ($US/m3/s)
- \(UTC_{i,d}^{tank\_dis}\) :
-
Unit transportation cost of flowrate from the recovery storage system ($US/m3/s)
- \(UTC_{n,i}^{tank\_well}\) :
-
Unit transportation cost of flowrate from the treated storage system recycled to the pit ($US/m3/s)
- \(VC^{storage}\) :
-
Variable cost for storage units ($US/m3)
- \(VC^{tank}\) :
-
Variable cost for tanks ($US/m3)
- \(VC^{waste}\) :
-
Variable cost for discharging the effluents to the disposals ($US/m3)
- \(VC_{i}^{treat}\) :
-
Variable cost for installing treatment units ($US/m3)
- \(V_{d}^{waste\_cap}\) :
-
Volume of effluents that can be discharged to the final disposal alternatives (m3)
- \(V_{d}^{waste\_\hbox{max} }\) :
-
Maximum volume that can be discharged to final disposal alternatives (m3)
- \(V_{i}^{tank\_cap}\) :
-
Capacity of tanks in the storage system (m3)
- \(V_{i}^{tank\_\hbox{max} }\) :
-
Maximum capacity of tanks in the storage system (m3)
- \(V_{i,t}^{tank}\) :
-
Volume of the tanks after the treatment unit in certain time period (m3)
- \(V_{j}^{storage\_cap}\) :
-
Capacity of storage units (m3)
- \(V_{j}^{storage\_initial}\) :
-
Capacity of storage units at the initial conditions (m3)
- \(V_{j}^{storage\_\hbox{max} }\) :
-
Maximum capacity of storage units (m3)
- \(V_{j,t}^{storage}\) :
-
Capacity of storage units in certain time period (m3)
- \(V_{j,t - 1}^{storage}\) :
-
Volume of the storage units in a previous time period (m3)
- \(y_{d}^{waste}\) :
-
Binary variable to decide the optimal final disposal
- \(y_{i}^{treat}\) :
-
Binary variable to decide the installation of treatment units
- \(y_{j}^{storage}\) :
-
Binary variable for the installation of tanks in the storage system
- \(\alpha_{i}^{treat}\) :
-
Conversion factor for the flowrate in the treatment units
- \(\beta^{tank}\) :
-
Factor that represents the economies of scale for tanks
- \(\beta^{waste}\) :
-
Factor that represents the economies of scale in cost for discharge of effluents to a specific final disposal
- \(\beta^{storage}\) :
-
Factor that represents the economies of scale in cost for storage units
- \(\beta^{treat}\) :
-
Factor that represents the economies of scale in cost for treatment units
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Authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) for the provided financial support.
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López-Díaz, D.C., Lira-Barragán, L.F., Rubio-Castro, E. et al. Optimal design of water networks for shale gas hydraulic fracturing including economic and environmental criteria. Clean Techn Environ Policy 20, 2311–2332 (2018). https://doi.org/10.1007/s10098-018-1611-6
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DOI: https://doi.org/10.1007/s10098-018-1611-6