Economic objective

The economic objective is to minimize the LCOE generated from shale gas, formulated as the total net present cost divided by the total electric power generation. The total net present cost comprises of the CAPEX associated with the shale gas processing devices (C^C_proc^APEX) and gathering pipelines (C_trans^CAPEX), and the OPEX related to water management (C_{water t}^OPEX_,), drilling activities (C_{drill t}^OPEX_, ), shale gas production operations (C^OPEX_{prod t,} ), shale gas

processing and upgrading (C_{proc t}^OPEX_, ), transportation activities (C_{trans t}^OPEX_, ), LNG storage (

OPEX OPEX OPEX OPEX OPEX OPEX OPEX

water t drill t prod t trans t stor t power t

The CAPEX of shale gas processing devices comprises of the CAPEX associated with conventional processing plants (C^CAPE_{proc co_}^X_nv) and the CAPEX corresponding to modular manufacturing devices (C_{proc mo}^CAPE_{_}^X _d).

CCAPE is the total CAPEX associated with construction of conventional processing plants. In this study, we adopt a typical nonlinear function to calculate the CAPEX following the existing literature [4, 121].

_

where pri denotes the reference CAPEX of conventional processing plants. PCp denotes the capacity of conventional processing plant p. prc denotes the reference capacity of conventional processing plants. sfp denotes the size factor of conventional processing plants. pci denotes the chemical engineering plant cost index for conventional processing plants. rpci denotes the chemical engineering plant cost index for conventional processing plant of the reference year.

_ proc mo

X d

CCAPE is the net CAPEX associated with modular LNG plants, given as the total installment cost subtracted by the total salvage value of modular LNG plants. The

CAPEX of modular LNG plant is estimated based on a capital cost curve from the literature, which is obtained by fitting the data on capital costs from existing and hypothetical LNG plants from the literature [72].

( )

where camm,k denotes the CAPEX for installing a modular LNG plant with capacity level k at location m. ZIm,k,t is a binary variable that equals 1 if a modular LNG plant with capacity level k is installed at location m in time period t. dr is the discount rate per time period. csmk,t denotes the discounted salvage value of a modular LNG plant with capacity level k installed at time period t.

CAPEX trans

C indicates the total CAPEX of gathering pipelines, calculated by,

, , , , , ,

where tprir denotes the reference CAPEX of gathering pipelines with capacity level r.

XPi,p,r is a binary variable that equals 1 if the gathering pipeline with capacity level r is installed to transport shale gas from shale site i to conventional processing plant p. lspi,p

is the distance between shale site i and conventional processing plant p. Similarly, XMi,m,r is a binary variable that equals 1 if the gathering pipeline with capacity level r is installed to transport shale gas from shale site i to modular LNG plant at location m.

lsmi,m is the distance between shale site i and modular LNG plant at location m.

The water management cost consists of water acquisition cost (Cacq,t) and wastewater treatment costs corresponding to different technologies, namely Class-II disposal wells (Cdisp,t), CWT facilities (Ccwt,t), and onsite treatment (Consite,t).

, , , , , OPEX

water t acq t disp t cwt t onsite t

C =C +C +C +C (A6)

Cacq,t indicates the acquisition cost of freshwater in time period t, which is proportional to the amount of freshwater,

, ,

where fac denotes the unit acquisition cost of freshwater. FWi,t stands for the amount of freshwater acquired from water source to shale site i in time period t.

Cdisp,t denotes the cost associated with underground injection of disposal wells in time period t, given by,

where vd denotes the unit cost for underground injection of wastewater. WTDi,t denotes the amount of wastewater transported from shale site i to disposal wells at time period t.

Ccwt,t indicates the cost associated with CWT treatment facilities in time period t,

calculated by,

where vc denotes the unit treatment cost of wastewater at CWT facilities. WTCi,t denotes the amount of wastewater transported from shale site i to CWT facilities at time period t.

Consite,t is the total onsite treatment cost in time period t, given by,

, , ,

where voo denotes the unit treatment cost of wastewater by onsite treatment technology o. WTOi,o,t denotes the amount of wastewater treated by onsite treatment technology o at shale site i in time period t.

, OPEX drill t

C indicates the total OPEX associated with drilling activities in time period t,

, , ,

where sdci,t denotes the unit cost for shale well drilling and completion at shale site i in time period t. NNi,t denotes the number of wells drilled at shale site i in time period t.

, OPEX prod t

C stands for the total cost associated with shale gas production activities in time period t, calculated as the difference between the gross cost proportional to the amount of shale gas production and the salvage value of shale wells at the end of planning horizon.

where spci,t denotes the unit cost for shale gas production at shale site i in time period t.

SPi,t denotes the shale gas production rate at shale site i in time period t. psg denotes the estimated average unit profit of shale gas remains to be produced in shale wells. euri

denotes the estimated ultimate recovery of shale gas for a shale well at shale site i.

, proc t

COPEX indicates the total OPEX for both modular LNG plant and conventional processing plant in time period t, calculated by,

, _ , _ , _ , ,

C is the total OPEX of modular LNG plants, calculated by,

, , , ,

where vmom,k denotes the unit OPEX for modular LNG plant at location m with capacity level k. SMPi,m,k,t denotes the amount of shale gas sent from shale site i to modular LNG plant at location m with capacity level k in time period t.

_ ,

mod move t

C stands for the moving cost of modular LNG plants in time period t, which can by calculated by the following equation,

(

)

where cdmk denotes the cost of dissembling a modular LNG plant with capacity level k.

cmmk denotes the cost of moving a modular LNG plant with capacity level k for unit distance. ldmm,m’ denotes the distance between potential modular LNG plant locations m and m’. crmk denotes the cost of reassembling a modular LNG plant with capacity level k. ZRm,m’,k,t is a binary variable that equals 1 if a modular LNG plant with capacity level k is moved from location m to m’ in time period t.

_ ,

conv oper t

C is the total OPEX of conventional processing plants in time period t, given by,

where vrop denotes the unit OPEX for conventional processing plant p. SRPi,p,t denotes the amount of shale gas transported from shale site i to conventional processing plant p in time period t.

INGL,t denotes the income from sales of NGLs in time period t, given as the summation

of incomes from both conventional processing plants and modular LNG plants.

, p t, ,

where plt denotes the average unit price of NGLs in time period t. SRPLp,t denotes the amount of NGLs produced at conventional processing plant p in time period t. SMPLm,t

denotes the amount of NGLs produced at modular LNG plant at location m in time period t.

, OPEX trans t

C stands for the total OPEX associated with all the transportation activities in time period t, given by,

, _ , _ , _ ,

OPEX

trans t trans conv t trans mod t trans power t

C =C +C +C (A18)

_ ,

trans conv t

C indicates the variable transportation cost of shale gas from shale sites to conventional processing plants in time period t, given by,

_ , , , ,

where vrt denotes the unit transportation cost of shale gas.

_ ,

trans mod t

C is the variable transportation cost associated with modular LNG plants, including the variable transportation cost of shale gas from shale sites to modular LNG plants and variable transportation cost of LNG from modular LNG plants to LNG storage facilities.

where vmt denotes the unit transportation cost of shale gas from shale sites to modular LNG plants. vts denotes the unit transportation cost of LNG. lmsm,s denotes the distance between modular LNG plants and LNG storage facility s. SMPSm,s,t denotes the amount

of LNG transported from modular LNG plant at location m to storage facility s in time period t.

_ ,

trans power t

C indicates the variable transportation cost associated with power plants in time period t, given as,

_ , , , , , ,

where lsgs,g denotes the distance from storage facility s to power plant g. SSGs,g,t denotes the amount of LNG transported from storage facility s to power plant g in time period t. lmgm,g denotes the distance from modular LNG plant at location m to power plant g.

SMPGm,g,t denotes the amount of LNG transported from modular LNG plant at location

m to power plant g in time period t. vtp denotes the unit transportation cost of natural gas, lpgp,g denotes the distance from conventional processing plant p to power plant g.

SPGp,g,t denotes the amount of natural gas transported from conventional processing

plant p to power plant g in time period t.

, OPEX stor t

C is the total LNG storage cost in time period t, calculated by,

, , , , , ,

where vsi denotes the operating cost for unit input of LNG at storage facilities, vso denotes the operating cost for unit output of LNG at storage facilities. vs denotes the unit storage cost for LNG. INLs,t denotes the amount of LNG stored at LNG storage facility s in time period t.

, OPEX power t

C indicates the total variable cost associated with electric power generation in time period t, calculated by,

, , , , , , ,

where veg denotes the unit cost for electricity generation from natural gas at power plant g.