Techno-Economic Evaluation of Geothermal Energy Utilization of Co-Produced Water from Natural Gas Production

Abstract

The utilization of thermal energy from co-produced water during natural gas production offers a promising pathway to enhance energy efficiency and reduce carbon emissions. This study proposes a techno-economic evaluation model to assess the feasibility and profitability of geothermal energy recovery from co-produced water in marginal gas wells. A wellbore fluid flow and heat transfer model is developed and validated against field data, with deviations in calculated wellhead temperature and pressure within 10%, demonstrating the model’s reliability. Sensitivity analyses are conducted to investigate the influence of key technical and economic parameters on project performance. The results show that electricity price, heat price, and especially government one-off subsidies have a significant impact on the net present value (NPV), whereas the effects of insulation length and annular fluid thermal conductivity are comparatively limited. Under optimal conditions—including 2048 m of insulated tubing, annular protection fluid with a thermal conductivity of 0.4 W/(m·°C), a 30% increase in heat and electricity prices, and a 30% government capital subsidy—the project breaks even in the 14th year, with the 50-year NPV reaching 0.896 M$. This study provides a practical framework for evaluating and optimizing geothermal energy recovery from co-produced water, offering guidance for future sustainable energy development.

1. Introduction

The global energy demand has surged due to continued population growth, accelerated urbanization, and deepening industrialization. It is projected that global energy consumption will increase by 49% over the next two decades, with approximately 75% of the world’s energy supply still dependent on fossil fuels [1]. This energy structure not only lacks sustainability but also contributes to the intensification of the greenhouse effect, posing a significant barrier to sustainable global economic development and environmental governance. Geothermal energy, characterized by its abundant reserves, wide availability, high utilization efficiency, and immunity to weather and seasonal fluctuations, has emerged as a prominent focus in the renewable energy sector [2,3]. However, according to the International Energy Agency (IEA) report [4], geothermal energy accounted for only 2% of global renewable energy consumption in 2021, in contrast to hydropower (58%), wind energy (20%), solar energy (12%), and bioenergy (8%). A major factor contributing to the limited market share of geothermal energy is its high development cost, particularly drilling and completion expenses, which typically account for 30–40% of the total project cost [5]. Therefore, repurposing abandoned or active petroleum wells can significantly reduce these costs, offering a promising and cost-effective pathway for geothermal energy development and utilization. To this end, this study integrates a wellbore flow and heat transfer model with a net present value (NPV)-based economic evaluation model into a unified assessment framework. The thermal model is used to simulate wellhead temperature and heat extraction power, and its outputs serve as inputs to the economic model for calculating the NPV. This integrated approach enables a simultaneous evaluation of both technical performance and economic potential.

The primary focus of the petroleum industry is the extraction and refining of oil and natural gas. During oil and gas production from underground reservoirs, water is often brought to the surface as well, referred to as “co-produced water” [6]. In the early stages of natural gas production, high reservoir pressure results in gas-dominated flow, and bound water remains immobile, leading to low water production. As extraction proceeds, reservoir pressure gradually declines, allowing edge or bottom water to invade pore spaces due to the pressure differential, leading to increased water production. Simultaneously, changes in the relative permeability between gas and water cause water to occupy flow channels, resulting in the “water-lock effect” [7], which significantly increases water production and reduces gas output in the later stages [8]. When gas production revenue falls below operational and maintenance costs, the economic viability of the gas well declines, leading to its eventual abandonment [9]. Notably, co-produced water from natural gas wells possesses substantial geothermal energy potential. Implementing heat recovery in the petroleum industry offers an opportunity to save costs, reduce fuel consumption, and lower greenhouse gas emissions [5]. Therefore, the comprehensive utilization of geothermal energy from co-produced water throughout the operational lifecycle of a well can generate additional economic benefits, potentially influencing decisions regarding well abandonment.

In recent years, several field tests and preliminary studies have been successfully conducted to extract geothermal energy from oilfields.

Table 1. Typical research on the use of co-produced water in the petroleum industry for geothermal energy utilization.

Investigators	Utilization Method	Highlights
El Leil et al. [10]	Electricity generation	Investigation of geothermal energy production for electricity generation in petroleum fields using Organic Rankine Cycle (ORC) technology, revealing that temperature and water flow rate are crucial factors affecting power output.
Céspedes et al. [11]	Co-generation	Assessment of technical and environmental feasibility of geothermal energy from co-produced fluids in oil fields, emphasizing significant carbon footprint reduction potential.
Alimonti et al. [12]	Electricity generation	Case study on extending the life of a northern Italian oilfield through integration of an ORC-based geothermal plant scheme for co-production of oil and thermal energy.
Yuan et al. [13]	Direct-use heating	Feasibility analysis of converting multi-stage hydraulically fractured shale gas wells into a hybrid geothermal-gas production system by integrating vertical injection wells with existing horizontal well infrastructure.
Liu et al. [14]	Electricity generation	Proposed roadmap with geological, reservoir, production, and economic criteria for assessing feasibility of low-temperature waste heat recovery.
Oh et al. [15]	Direct-use heating and cooling	Evaluation of geothermal resources, heating/cooling demand, and techno-economic potential of four oil and gas wells repurposed for geothermal energy production.
Singh [16]	Direct-use heating	Detailed design and discussion of heat recovery using a double-pipe heat exchanger from high-temperature co-produced water in deep oil/gas wells or shallow geothermal formations.
Hirst et al. [17]	Direct-use heating	Cost-effective modification of existing oilfield infrastructure to extend economic life by utilizing naturally warm connate and injection waters for clean, continuous heating.
Augustine et al. [18]	Electricity generation	Geographic information system (GIS)-based estimation of near-term market potential for electricity generation from water produced as a byproduct of active oil and gas operations.
Yang et al. [19]	Electricity generation	Design of a low-temperature geothermal Organic Rankine Cycle (ORC) system for electricity generation from abandoned oil wells in China’s Huabei oilfield.

summarizes the most representative research on the use of co-produced water in the petroleum industry for geothermal energy utilization.

Table 1 shows numerous established cases of geothermal utilization from co-produced water, including applications in direct heating and cooling, electricity generation, and co-generation. Current research on geothermal utilization from co-produced water primarily emphasizes technical aspects, while comprehensive and mature economic evaluations remain limited or neglected. To address this gap, this study develops a techno-economic evaluation model specifically designed for geothermal energy recovery from co-produced water in natural gas wells. By integrating a detailed wellbore–reservoir heat transfer model with a long-term net present value (NPV) assessment, the proposed framework allows for simultaneous evaluation of thermal performance and economic feasibility. This integrated approach provides a more holistic and realistic assessment of project potential and holds significant theoretical and practical value for oilfield operators aiming to achieve combined heat, electricity, and gas recovery while advancing energy efficiency and emissions reduction goals.

2. Model for Technical Evaluation

2.1. Description of Co-Produced Water for Geothermal Energy Utilization

As illustrated in Figure 1, the process of geothermal energy utilization from co-produced water during natural gas production can be described as follows.

(1)

Driven by the pressure gradient, the subsurface fluid mixture (i.e., natural gas and co-produced water) ascends through the wellbore and enters the Christmas tree at the wellhead.

(2)

The mixed fluid is then directed into a gas–liquid separator, where phase separation occurs. The separated natural gas is transported via pipeline to the gas gathering station, while the co-produced water is routed directly to an ORC unit for electricity generation.

(3)

After partial heat extraction in the ORC system, the geothermal water is conveyed to the district heating system, thereby achieving cascading utilization of geothermal energy. Finally, the water is reinjected into the target reservoir through dedicated injection wells.

2.2. Mathematical Model of Wellbore Fluid Flow and Heat Transfer

2.2.1. Basic Assumptions

(1)

The heat transfer from the formation to the fluid is assumed to occur in a one-dimensional, radially unsteady state, while the fluid flow within the tubing is considered to be one-dimensional and axially steady.

(2)

Natural convection of the annular protection fluid between the tubing and casing is neglected, and its radial heat transfer is treated purely as thermal conduction.

(3)

The formation temperature at a sufficiently large radial distance from the wellbore center is assumed to remain unaffected by wellbore heat transfer, with the original geothermal gradient considered constant [20].

(4)

The shapes of the subsurface pipe strings (including tubing, casing, and cement) are assumed to be geometrically regular.

(5)

As methane accounts for more than 90% of the natural gas composition, the reservoir gas (excluding C₂⁺ hydrocarbons and non-hydrocarbon gases) is approximated as pure methane for analytical purposes.

(6)

The Joule–Thomson effect during wellhead throttling is not considered due to the lack of detailed throttling process data, and its influence on fluid temperature is therefore omitted in the current model.

(7)

The thermodynamic behavior of the surface gas–liquid separator is not modeled in this study, as its primary function is to separate the produced gas and water streams. Since it does not significantly affect the wellbore temperature or heat extraction calculations, it is excluded from the detailed simulation.

2.2.2. Governing Equations

Figure 2 illustrates the fluid flow and heat transfer processes along the wellbore. The natural gas and co-produced water flow axially while exchanging heat with the surrounding media. These processes are governed by the continuity, momentum, and energy equations, which form the theoretical foundation of the mathematical model developed in this study.

(1)

Continuity Equation

As per basic assumption (1) and considering that there is no mass exchange between the working fluid and the surrounding media—since the gas well forms a closed system—the continuity equation can be simplified as shown in Equation (1):

$${\displaystyle \frac{\partial \left({\rho }_m{v}_m\right)}{\partial l}}=0$$

(1)

where ρ_m is the density of the mixture fluid, kg/m³; v_m is the average velocity of the mixture fluid, m/s; and l is the axial coordinate along the well depth, m.

(2)

Momentum Equation

Similarly to the justification for simplifying the continuity equation, the momentum equation can also be simplified, as shown in Equation (2):

$${\displaystyle \frac{\partial p_m}{\partial l}}={\rho }_{m}g\mathit{cos}\theta +{\displaystyle \frac{f{\rho }_m{v}_m^2}{2d_{pi}}}+{\rho }_m{v}_m{\displaystyle \frac{\partial v_m}{\partial l}}$$

(2)

where p_m is the pressure of the mixture fluid, Pa; g is the gravitational acceleration, 9.81 m²/s; θ is the inclination angle of the well, °; d_pi is the inner diameter of the tubing, m; and f is Darcy friction coefficient, dimensionless, which can be calculated using Equation (3) [21], applicable to all flow regimes:

$$f=8\left\{{\left({\displaystyle \frac{8}{{Re}_m}}\right)}^{12}+{\left[{\displaystyle \frac{1}{{\left(A+B\right)}^{\frac{3}{2}}}}\right]}^{{\displaystyle \frac{1}{12}}}\right\}$$

(3)

with

$$A={\left\{2.45\ln \left[{\displaystyle \frac{1}{{\left(\frac{7}{{Re}_m}\right)}^{0.9}+0.27\left(\frac{\mathsf{\Delta }}{d_{pi}}\right)}}\right]\right\}}^{16}$$

(4)

$$B={\left({\displaystyle \frac{37530}{{Re}_m}}\right)}^{16}$$

(5)

where Δ is the mean roughness, m; and Re_m is the Reynolds number, dimensionless, defined as

$${Re}_m={\displaystyle \frac{{\rho }_m{v}_m{d}_{pi}}{{\mu }_m}}$$

(6)

where μ_m is the viscosity of the mixture fluid, Pa·s.

(3)

Energy Equation

During the production process of a natural gas well, the upward-flowing mixture fluid continuously absorbs or releases heat to/from the surrounding formation. According to the First Law of Thermodynamics, the energy balance can be expressed by Equation (7):

$${\displaystyle \frac{T_g-T_f}{R_L}}+q_m{\displaystyle \frac{\partial \left(c_m{T}_f\right)}{\partial l}}+S_L={\displaystyle \frac{1}{4}}\pi d_{pi}^2{\displaystyle \frac{\partial \left(c_m{{\rho }_{m}T}_f\right)}{\partial t}}$$

(7)

where T_g and T_f are the temperatures of the formation and the mixture fluid, respectively, °C; R_L is the total thermal resistance between the mixture fluid and the formation per unit length, °C·m/W, where the influence of the cement on wellbore heat transfer has been highlighted [22]; q_m is the mass flow rate of the mixture fluid, kg/s; c_m is the specific heat capacity of the mixture fluid, J/(kg·°C); S_L is the heat source in the wellbore per unit length, W/m; and t is the time coordinate, s.

Based on the thermoelectric analogy, R_L in Equation (7) is a series connection of multiple thermal resistances, which can be expressed as Equation (8):

$$R_L=R_{hL}+{\sum }_{i=1}^n{\left(R_{\lambda L}\right)}_i+R_{gL}$$

(8)

where R_hL is the thermal convection resistance between the tubing and the mixture fluid per unit length, °C·m/W; ΣR_λL is the total thermal conduction resistance per unit length, including contributions from tubing, annular protection fluid, casing, cement, and the insulation (if any), °C·m/W; and R_Lg is the thermal conduction resistance of the rock formation per unit length, °C·m/W.

• Thermal convection resistance (R_hL)

$$R_{hL}={\displaystyle \frac{1}{\pi d_{pi}h}}$$

(9)

where h is the convective heat transfer coefficient, W/(m²·°C), which can be calculated using Equation (10):

$$h=8.69{\left({\displaystyle \frac{1}{X_{tt}}}\right)}^{0.37}{h}_1$$

(10)

where h₁ is the convective heat transfer coefficient of liquid phase, W/(m²·°C), which can be calculated by the Dittus–Boelter equation [23]; and X_tt is the Martinelli number, dimensionless, which can be determined using Equations (11)–(14) [23]:

$$X_{tt}={\left({\displaystyle \frac{1-x}{x}}\right)}^{0.9}{\left({\displaystyle \frac{{\rho }_{gas}}{{\rho }_l}}\right)}^{0.5}{\left({\displaystyle \frac{{\mu }_l}{{\mu }_{gas}}}\right)}^{0.1}$$

(11)

$$x={\displaystyle \frac{v_{sg}{\rho }_{g}as}{{v_{sg}\rho }_{gas}+{v_{sl}\rho }_l}}$$

(12)

$$v_{sg}={\displaystyle \frac{q_{Vg}}{A}}$$

(13)

$$v_{sl}={\displaystyle \frac{q_{Vl}}{A}}$$

(14)

where x is the mass fraction of natural gas, dimensionless; ρ_gas and ρ_l are the densities of natural gas and co-produced water, respectively, kg/m³; v_sg and v_sl are the superficial velocities of natural gas and co-produced water, respectively, m/s; q_vg and q_vl are the volumetric flow rates of natural gas and co-produced water, respectively, m³/s; and A is the cross-sectional flow area, m².

• Thermal conduction resistance (R_λL)

$$R_{\lambda L}={\displaystyle \frac{1}{2\pi {\lambda }_i}}\ln \left({\displaystyle \frac{d_{outer}}{d_{inner}}}\right)$$

(15)

where λ_i is the thermal conductivity of the i-th layer materials, W/(m·°C); and d_inner and d_outer are the inner and outer diameters, respectively, of the i-th material layer, m.

• Thermal conduction resistance of the rock formation (R_λgL)

$$R_{\lambda gL}={\displaystyle \frac{T_D}{2\pi {\lambda }_g}}$$

(16)

where T_D denotes the dimensionless temperature, which can be determined based on the previous study [24]; and λ_g is the thermal conductivity of the rock formation, W/(m·°C).

Moreover, S_L in Equation (7) is the heat source per unit length within the wellbore, which primarily arises from the viscous dissipation of the mixture fluid during its flow and can be calculated using Equation (17):

$$S_L={\displaystyle \frac{8f{q}_m^3}{{\pi }^2{d}_{pi}^5{\rho }_m^2}}$$

(17)

2.2.3. Uniqueness Conditions

To ensure that the solution of the mathematical model for the geothermal well system is both unique and physically meaningful, a set of uniqueness conditions is established. These conditions encompass geometric configurations, physical property definitions, initial conditions, and boundary conditions.

(1)

Geometric Conditions

The geometric conditions primarily refer to the dimensions of the tubing string and the wellbore in the natural gas well.

(2)

Physical Properties Conditions

As per basic assumption (5), the physical properties of methane are adopted to represent those of natural gas in the model. Additionally, the model includes the physical property calculations for co-produced water and the mixture fluid.

• Physical properties of methane

The density of methane can be calculated using Equation (18):

$${\rho }_{gas}={\displaystyle \frac{pM}{ZRT}}$$

(18)

where p is the pressure, Pa; T is the temperature, K; M is the molar mass of methane, i.e., 0.016 kg/mol; R is the universal gas constant, equal to 8.314 J/(mol·K); and Z is the compressibility factor of the gas, dimensionless, which can be determined using the Peng–Robinson (PR) equation of state [25].

The viscosity of methane can be calculated using the Dean–Stiel model [26], as given by Equation (19):

$${\mu }_{gas}={\mu }_0+{\displaystyle \frac{10.8\times {10}^{-5}\left(e^{1.439{\rho }_{g,r}}-e^{-1.439{\rho }_{g,r}^{1.858}}\right)}{\zeta }}$$

(19)

where μ_gas is the viscosity of methane, Pa·s; μ₀ is the viscosity of methane under standard conditions, Pa·s; ρ_g,r is the relative density of methane, dimensionless; and ζ is the viscosity contrast coefficient of methane, dimensionless, which can be calculated using Equation (20):

$$\zeta =\left\{\begin{array}{ll}{\displaystyle \frac{34\times {10}^{-5}{\left(\frac{T}{T_c}\right)}^{\frac{8}{9}}}{{\mu }_0}}& {\displaystyle \frac{T}{T_c}}\le 1.5\\ {\displaystyle \frac{166.8\times {10}^{-5}{\left(0.1338\frac{T}{T_c}-0.0932\right)}^{\frac{5}{9}}}{{\mu }_0}}& {\displaystyle \frac{T}{T_c}}>1.5\end{array}\right.$$

(20)

where T_c is the critical temperature of methane, K.

The thermal conductivity and specific heat capacity of methane are calculated using Equations (21) and (22), respectively:

$${\lambda }_{gas}=-0.0086+0.0001T$$

(21)

$$c_{gas}=388.7508p^{0.0625}{T}^{0.3087}$$

(22)

where λ_gas is the thermal conductivity of methane, W/(m·°C); and c_gas is the specific heat capacity of methane, J/(kg·°C).

• Physical properties of co-produced water

The density, viscosity, thermal conductivity, and specific heat capacity of co-produced water can be calculated using Equations (23)–(26) [27], respectively:

$$\begin{gathered} {\rho }_l=999.797+0.068\left(T-273.15\right)-0.011{\left(T-273.15\right)}^2+8.214\times {10}^{-4}{\left(T- \\ 273.15\right)}^{2.5}-2.303\times {10}^{-4}{\left(T-273.15\right)}^3 \end{gathered}$$

(23)

$${\mu }_l={\displaystyle \frac{1}{557.256+19.409\left(T-273.15\right)+0.136{\left(T-273.15\right)}^2-3.116\times {10}^{-4}{\left(T-273.15\right)}^3}}$$

(24)

$$\begin{gathered} {\lambda }_l=0.565+2.64\times {10}^{-3}\left(T-273.15\right)-1.252\times {10}^{-4}{\left(T-273.15\right)}^{1.5}- \\ 1.515\times {10}^{-6}{\left(T-273.15\right)}^2-9.413\times {10}^{-4}{\left(T-273.15\right)}^{0.5} \end{gathered}$$

(25)

$$\begin{gathered} c_l=4217.436+5.618\left(T-273.15\right)+1.299\times {10}^{-4}{\left(T-273.15\right)}^{1.5}- \\ 0.115{\left(T-273.15\right)}^2+4.150\times {10}^{-3}{\left(T-273.15\right)}^{0.5} \end{gathered}$$

(26)

where ρ_l, μ_l, λ_l, c_l are the density, kg/m³, viscosity, Pa·s, thermal conductivity, W/(m·K) and specific heat, J/(kg·K), respectively.

• Physical properties of mixture fluid

As per the weighted average method, the physical properties of the mixture fluid can be calculated using Equations (27)–(30):

$${\rho }_m={\rho }_g{f}_{gas}+{\rho }_l\left(1-f_g\right)$$

(27)

$${\mu }_m={\mu }_{gas}{f}_{gas}+{\mu }_l\left(1-f_g\right)$$

(28)

$${\lambda }_m={\lambda }_{gas}{f}_{gas}+{\lambda }_l\left(1-f_g\right)$$

(29)

$$c_m=c_{gas}{f}_{gas}+c_l\left(1-f_g\right)$$

(30)

where f_gas is the gas volume fraction, dimensionless, which is described using Equation (31):

$$f_{gas}={\displaystyle \frac{q_{Vg}}{{q_{Vl}+q}_{Vg}}}$$

(31)

(3)

Boundary conditions

• Temperature and pressure of mixture fluid at the wellbore bottom

The temperature and pressure of mixture fluid at the wellbore bottom are the same as those of the formation, i.e.,

$$T_f=T_g at {l=l}_{max}$$

(32)

$$p_f=p_g at {l=l}_{max}$$

(33)

where l_max is the maximum well depth, m; and p_g is the pressure of the formation.

• Formation temperature

As per the basic assumption (3), the temperature of the formation can be determined from the geothermal gradient, i.e.,

$$T_g^0=T_g^1=\cdots =T_g^n=T_0+G·h_V$$

(34)

where G is the geothermal gradient, °C/m; h_v is the vertical depth, m; and T₀ is the ground temperature, °C.

2.2.4. Model Solution

(1)

Discretization of the Mathematical Model

The system is meshed and discretized, as shown in Figure 3.

The discretized momentum and energy equations are shown in Equations (35) and (36), respectively:

$${\displaystyle \frac{p_i-p_{i-1}}{\mathsf{\Delta }l}}={\displaystyle \frac{{\rho }_{m,i}+{\rho }_{m,i-1}}{2}}\cos \theta -{\displaystyle \frac{8\left(f_i+f_{i-1}\right)q_m^2}{{\pi }^2{\left({\rho }_{m,i}+{\rho }_{m,i-1}\right)d}_{pi}^5}}+{\displaystyle \frac{4q_m\left({\rho }_{m,i}+{\rho }_{m,i-1}\right)}{{\pi }^2{d}_{pi}^2\mathsf{\Delta }l}}\left({\displaystyle \frac{1}{{\rho }_{m,i}^2}}-{\displaystyle \frac{1}{{\rho }_{m,i-1}^2}}\right)$$

(35)

where Δl is the grid size, m.

$${\displaystyle \frac{T_{g,i}^n-T_{f,i}^n}{R_L}}+q_m{\displaystyle \frac{c_{m,i}^n{T}_{f,i}^n-c_{m,i-1}^n{T}_{f,i-1}^n}{\mathsf{\Delta }l}}+S_L^n={\displaystyle \frac{1}{4}}\pi d_{pi}^2{\displaystyle \frac{{\left(c\rho \right)}_{m,i}^n{T}_{f,i}^n-{\left(c\rho \right)}_{m,i}^{n-1}{T}_{f,i}^{n-1}}{\mathsf{\Delta }t}}$$

(36)

where Δt is the time step, s.

Based on the solution principle of fully implicit finite difference method [28], Equation (36) can be converted as Equation (37):

$$\left[{\displaystyle \frac{\frac{\pi }{4}{d}_{pi}^2{\left(c\rho \right)}_{m,i}^n}{\mathsf{\Delta }t}}+{\displaystyle \frac{1}{R_L}}-{\displaystyle \frac{{q_{m}c}_{m,i}^n}{\mathsf{\Delta }l}}\right]T_{f,i}^n-{\displaystyle \frac{\frac{\pi }{4}{d}_{pi}^2{\left(c\rho \right)}_{m,i}^{n-1}}{\mathsf{\Delta }t}}{T}_{f,i}^{n-1}-{\displaystyle \frac{1}{R_L}}{T}_{g,i}^n+{\displaystyle \frac{{q_{m}c}_{m,i-1}^n}{\mathsf{\Delta }l}}{T}_{f,i-1}^n=S_L^n$$

(37)

Making $a_{f,i}^n={\displaystyle \frac{\frac{\pi }{4}{d}_{pi}^2{\left(c\rho \right)}_{m,i}^n}{\mathsf{\Delta }t}}+{\displaystyle \frac{1}{R_L}}-{\displaystyle \frac{{q_{m}c}_{m,i}^n}{\mathsf{\Delta }l}}$, $a_{f,i}^{n-1}-{\displaystyle \frac{\frac{\pi }{4}{d}_{pi}^2{\left(c\rho \right)}_{m,i}^{n-1}}{\mathsf{\Delta }t}}$, $a_{g,i}^n=-{\displaystyle \frac{1}{R_L}}$, $a_{f,i-1}^n={\displaystyle \frac{{q_{m}c}_{m,i-1}^n}{\mathsf{\Delta }l}}$, and $a_L^n=S_L^n$, the discretization equation can be further simplified as Equation (38):

$$a_{f,i}^n{T}_{f,i}^n+a_{f,i}^{n-1}{T}_{f,i}^{n-1}+a_{g,i}^n{T}_{g,i}^n+a_{f,i-1}^n{T}_{f,i-1}^n=a_L^n$$

(38)

After introducing the Uniqueness conditions, a closed equation is formed, and the temperature and pressure distribution of the whole wellbore can be obtained by solving it. Further, the ORC power generation and geothermal water heating power are obtained.

(2)

Solution Steps

The aforementioned discretized equations can be solved following these steps:

Step 1: Define the geometric parameters by inputting the dimensions of the natural gas well.

Step 2: Specify the grid size (Δl) and time step (Δt).

Step 3: Establish the boundary conditions, including the mass flow rate, formation temperature, and formation pressure.

Step 4: Set the initial conditions by assuming an initial temperature distribution in the wellbore (T_assume).

Step 5: Compute the thermophysical properties of the fluids using Equations (18)–(31), based on the assumed temperature. Determine the thermal resistances using Equations (8)–(16).

Step 6: Calculate the updated wellbore temperature distribution (T_new) using Equation (38).

Step 7: Evaluate convergence using a predefined criterion $\left|T_{new}-T_{assume}\right|\le {\epsilon }_T$ (ε_T = 0.01 °C in this study). If convergence is not achieved, return to Step 4 and iterate until the criterion is satisfied.

Step 8: Calculate the wellbore pressure distribution using Equation (35).

Step 9: Update the initial conditions and repeat the calculations for the next time step until the entire simulation duration is completed.

Step 10: Output the final temperature and pressure distribution profiles along the wellbore.

Figure 4 presents a flowchart that illustrates the solution procedure of the mathematical model governing fluid flow and heat transfer.

After determining the wellhead temperature and pressure, the thermal efficiency of the ORC power generation system is subsequently evaluated using Equation (39) [29]:

$${\eta }_{th}=0.58{\displaystyle \frac{T_{in}-T_c}{T_{in}+T_c}}$$

(39)

where η_th is the thermal efficiency of the ORC system; T_in is the wellhead temperature of the co-produced water, °C; and T_c is the outlet temperature of the co-produced water after heat exchange with the organic working fluid, °C.

Accordingly, the power generation capacity of the ORC system can be estimated using Equation (40):

$$E_{ORC}={\eta }_{th}{q}_{ml}\left(h_{in,l}-h_{out,l}\right)$$

(40)

where E_ORC is the power output of the ORC system, kW; q_ml is the mass flow rate of the co-produced water, kg/s; and h_in,l and h_out,l are the inlet and outlet enthalpies of the co-produced water within the ORC, respectively, kJ/kg.

Even after exiting the ORC unit, the temperature of the co-produced water remains above the ambient level, indicating its continued potential for thermal utilization. The corresponding heating power can be calculated using Equation (41):

$$E_h={\eta }_h{q}_{ml}\left(h_{out,l}-h_{0,l}\right)$$

(41)

where E_h is the heating power, kW; η_th is the thermal efficiency of the heating system, assumed to be 85%; and h_0,l is the enthalpy of the co-produced water under ambient conditions, kJ/kg.

3. Model for Economic Evaluation

3.1. Basic Concepts and Theories

In capital budgeting research, the Net Present Value (NPV) criterion is widely regarded by the academic community as the “gold standard” for evaluating both certainty and risk. Accordingly, NPV is considered appropriate for analyzing risk and conducting preliminary design assessments of geothermal energy projects utilizing co-produced water from natural gas wells.

NPV represents the difference between the present value of cash inflows and outflows over time, and is defined by Equation (42) [30]:

$$NPV={\sum }_{y=0}^{SL}{\displaystyle \frac{I_y-C_y}{{\left({1+i}_c\right)}^y}}$$

(42)

where NPV is the net present value, M$; SL is the service life of the natural gas wells, year; I_y and C_y are the expenses and revenues of the project in y year, respectively, M$; i_c is the discount rate, dimensionless; and y is the production time, year.

3.2. Revenues

The project revenue primarily derives from the economic value of utilizing co-produced water for ORC-based power generation and district heating. It can be calculated using Equation (43):

$$I_s=y\left(E_{ORC}{P}_{e-price}+E_h{P}_{h-price}\right)$$

(43)

where P_e-price and P_h-price are the unit prices of electricity and heat, respectively, M$/kWh.

In addition, compared to conventional energy sources, the reduction in fuel costs and CO₂ emissions achieved by using co-produced water for power generation and heating are regarded as implicit revenues of the project. These benefits are monetized and incorporated into the NPV cash flow analysis. The corresponding revenues can be calculated using Equations (44)–(47):

$$I_c=I_{coal}+I_{{co}_2}$$

(44)

$$I_{coal}=m_{coal}{P}_{c-price}$$

(45)

$$I_{coal}=m_{coal}{P}_{c-price}$$

(46)

$$m_{coal}={\displaystyle \frac{{\int }_0^{t_{0,e}}{E}_{ORC}dt+{\int }_0^{t_{0,h}}{E}_{h}dt}{{\eta }_{fuel}{\eta }_{coal}}}$$

(47)

where I_coal is the revenue from fuel savings, M$; I_CO2 is the revenue from CO₂ emission reductions, M$; m_coal is the mass of standard coal saved, t; P_c-coal is the unit price of standard coal, M$/t. P_CO2-coal is the unit price of carbon emissions, M$/t. t_0,e and t_0,h are annual operational hours of the power generation and heating systems, respectively, h. η_fuel is the combustion efficiency (assumed to be 90%, based on typical values for conventional thermal power plants); and q_coal is the calorific value of standard coal, which is typically 19,000 MJ/t [31].

Therefore, the total revenues can be determined using Equation (48):

$$I_y={I_s+I}_c$$

(48)

3.3. Expenses

The expenses associated with geothermal energy utilization of co-produced water from natural gas production primarily include the cost of installing heating pipelines to end-users, the investment in ORC power generation units, and the costs related to operation and management. Accordingly, the total project expenses can be estimated using Equation (49):

$$C_y=C_{pipe}+C_{ORC}+C_{op}+C_{ad}$$

(49)

where C_pipe, C_ORC, C_op, and C_ad are the costs of heating pipelines, ORC power generation units, operation and additional expenditures, respectively, M$. Among these, C_pipe, C_ORC and C_ad are categorized as initial investments, incurred only in the first year of the project, while C_op is recurring annual operational expenses.

Furthermore, the cost of heating pipelines can be calculated using Equation (50) [32]:

$$C_{pipe}=\left(1+f_x\right){\displaystyle \frac{{\rho }_{pipe}\pi {\delta }_{pipe}^2}{4}}{l}_{pipe}{P}_{pipe}+3.6\times {10}^{-6}{h}_{pipe}\pi \left(T_h-T_e\right)\left(1+\beta \right)t_0{P}_{h-price}$$

(50)

where f_x is the maintenance fee rate, %; ρ_pipe is the density of the heating pipe material, kg/m³; δ_pipe is the wall thickness of the heating pipe, mm; l_pipe is the length of the heating pipe, m; P_pipe is the price of the heating pipe, M$/kg; h_pipe is the average heat transfer coefficient of the heating pipe, W/(m²·°C); T_h and T_e are the temperatures of the co-produced water and the soil surrounding the pipe, respectively, °C; t₀ is the annual operation time, h; and β is the additional coefficient accounting for heat dissipation losses, dimensionless.

The cost of ORC power generation units can be calculated using Equation (51):

$$C_{ORC}=k{E}_{ORC}$$

(51)

where k is the cost per unit power output, which is 10 $/W for electricity generation using an ORC system [33].

The operation costs consist of electricity, labor, maintenance, and insurance expenses. The annual operation cost can be calculated using Equation (52) [34,35]:

$$C_{op}={\displaystyle \frac{E_{ORC}{t}_0}{3.6\times {10}^{11}}}{P}_{e-price}+0.005\left(C_{pipe}+C_{ORC}\right)+0.528f_c{t}_0{q}_V$$

(52)

where f_c is the load factor; and q_V is the volume fluid flow rate, m³/h.

In addition, C_ad is the additional costs incurred to enhance the heating performance of the co-produced water, including the cost of insulated tubing and insulated annular protection fluid.

3.4. NPV Model

By substituting the expressions for various revenues and expenses into Equation (42), a comprehensive formulation for the NPV of a geothermal energy utilization project based on co-produced water from natural gas wells can be derived, as shown in Equation (53):

$$\begin{gathered} NPV={\sum }_{y=0}^{SL}{\displaystyle \frac{\begin{array}{c}\left[y\left(E_{ORC}{P}_{e-price}+E_h{P}_{h-price}\right)+m_{coal}{P}_{c-price}+\frac{44}{12}{m}_{coal}{P}_{{co}_2-price}\right]-\left[\frac{E_{ORC}{t}_0}{3.6\times {10}^{11}}{P}_{e-price}+0.005\left(C_{pipe}+C_{ORC}\right)+0.528f_c{t}_0{q}_V\right]\\ \end{array}}{{\left({1+i}_c\right)}^y}}- \\ \left[\left(1+f_x\right){\displaystyle \frac{{\rho }_{pipe}\pi {\delta }_{pipe}^2}{4}}{l}_{pipe}{P}_{pipe}+3.6\times {10}^{-6}{h}_{pipe}\pi \left(T_h-T_e\right)\left(1+\beta \right)t_0{P}_{h-price}+C_{ORC}+C_{ad}\right] \end{gathered}$$

(53)

4. Results and Discussion

4.1. Technical Analysis and Discussion

4.1.1. Mathematical Model Validation of Wellbore Flow and Heat Transfer

(1)

Basic Parameters

To verify the accuracy of the established mathematical model for wellbore flow and heat transfer, actual field data from a representative natural gas well in western Sichuan was selected for validation. The fundamental parameters of the well are provided in

Table 2. Basic parameters of tubing string assembly and casing program.

Parameters	Inner Diameter	Outer Diameter	Length
Tubing	37.92 mm	50.62 mm	4855 m
Surface casing	482.6 mm	508 mm	202 m
Intermediate casing	247.96 mm	273.1 mm	1922 m
Intermediate casing	152.5 mm	177.8 mm	4636 m
Production casing	108.62 mm	127 mm	4855 m

,

Table 3. Geometric dimensions and ground temperature gradient of the natural gas wells.

Parameters	Value
Well depth	4855 m
Vertical depth	4834 m
Horizontal displacement	166.18 m
Inclination point	4435 m
Well inclination angle	18.18°
Ground temperature gradient	0.0217 °C/m

and

Table 4. Thermal physical parameters of different media.

Physical Parameter	Tubing	Casing	Cement	Formation
Density (kg/m3)	\	\	\	2640
Specific heat (J/[kg·K])	\	\	\	800
Thermal conductivity (W/[m·K])	40	40	3.2	2.25

and Figure 4.

Based on the conceptual model of the oil field [36], Figure 5 illustrates the production performance of the representative natural gas well.

As illustrated in Figure 5, with the increase in production time, the gas output from the natural gas wells gradually declined, whereas the production of co-produced water exhibited an upward trend. Specifically, the daily gas production dropped from an initial 4.445 × 10⁵ m³/d to 6.98 × 10⁴ m³/d, continuing to decline thereafter. In contrast, the daily water production rose from 89 m³/d to 350 m³/d and subsequently stabilized. Simultaneously, the formation pressure decreased consistently—from over 70 MPa at the start of production to approximately 50 MPa.

(2)

Model Validation Results

Based on the basic parameters provided in the previous section, the wellhead temperature and pressure calculated using the proposed model were compared with the measured values, as illustrated in Figure 6 and Figure 7.

As shown in Figure 6 and Figure 7, the model-calculated wellhead temperature and pressure exhibit high consistency with the measured data. All calculated values fall within a ±10% deviation from the measured values, demonstrating the model’s strong capability to accurately predict the trends of wellhead temperature and pressure.

4.1.2. Analysis of Technical Sensitivity Factors

(1)

Water–gas Ratio

Based on the analysis of Figure 5, it is observed that during the production phase of natural gas wells, the output of co-produced water remains relatively stable, whereas gas production continuously declines. To further investigate the influence of the water–gas ratio on the wellhead temperature, this section examines the variation in wellhead temperature under different water–gas ratio scenarios, while keeping the water production rate constant. The results are presented in Figure 8.

Figure 8 illustrates that the wellhead temperature exhibits only a minimal change with increasing water–gas ratio, displaying an overall gentle downward trend. Specifically, when the water–gas ratio increases from 16.67 m³/10⁴ m³ to 31.67 m³/10⁴ m³, the wellhead temperature decreases from 83.94 °C to 82.89 °C—a difference of only 1.05 °C, indicating an insignificant temperature variation. This result suggests that, under the condition of stable water production, variations in the water–gas ratio have a negligible impact on wellhead temperature. In the later production stage of the natural gas well, the co-produced water output remains essentially constant; thus, it can be inferred that the outlet temperature of the co-produced water also remains largely unchanged.

(2)

Insulation Tubing Length

To investigate the effect of insulation tubing length on wellhead temperature, insulation tubing was incrementally extended from the wellhead to depths ranging from 0 to 4855 m. All other parameters remained consistent with those listed in Table 2, Table 3 and Table 4. The corresponding impact on wellhead temperature is illustrated in Figure 9.

As shown in Figure 9, the wellhead temperature increases with insulation tubing length; however, the rate of increase gradually diminishes. Specifically, extending the insulation tubing from 0 m to 2400 m raises the wellhead temperature from 83.94 °C to 99.38 °C—an increase of 15.44 °C. Further extending it from 2400 m to 4855 m results in a smaller increase of 5.50 °C, bringing the final temperature to 104.88 °C. The length of the insulation tubing directly affects wellbore heat loss: longer insulation reduces heat loss, allowing more thermal energy to reach the surface and elevating the wellhead temperature.

Notably, insulation tubing is more effective in the upper sections of the wellbore due to the larger temperature differential between the formation and the fluid. In contrast, the incremental thermal benefit diminishes in deeper sections. Therefore, determining the optimal insulation tubing length necessitates further economic evaluation to balance thermal performance with cost.

(3)

Thermal Conductivity of Annular Protection Fluid

The primary function of annular protection fluid is to form a chemical barrier within the tubing–casing annulus, thereby offering comprehensive protection for downhole tubulars and equipment. Simultaneously, it serves as a heat transfer medium between the formation and wellbore fluids, thus influencing the wellhead temperature. To investigate the effect of varying thermal conductivities of annular protection fluid on wellhead temperature, values ranging from 0.1 to 0.6 W/(m·°C) were sequentially set. All other parameters remained consistent with those listed in Table 2, Table 3 and Table 4. The influence of thermal conductivity on wellhead temperature is illustrated in Figure 10.

Figure 10 reveals a significant inverse relationship between the thermal conductivity of the annular protection fluid and the wellhead temperature. When the thermal conductivity decreases from 0.6 W/(m·°C) to 0.1 W/(m·°C), the wellhead temperature increases from 84.8 °C to 98.9 °C, representing a rise of 14.1 °C. This behavior is attributed to the reduced heat loss along the wellbore due to lower thermal conductivity, allowing more heat to be preserved and transmitted to the wellhead.

Although reducing thermal conductivity can enhance geothermal energy recovery efficiency and improve project economics, the associated material costs also increase significantly. Therefore, practical engineering applications require multi-objective optimization to balance thermal performance and economic feasibility.

4.2. Economic Analysis and Discussion

4.2.1. Basic Economic Parameters

Based on market research and relevant Chinese policy, the economic parameters used in the calculations are summarized in

Table 5. Basic economic parameters used in the calculations.

Parameters	Value
Production time (years)	1–50
Annual heating time (days)	120
Annual electricity generation time (days)	360
Thermal efficiency for heating	85%
Metered heating price for the first year (M$/kWh)	4.833 × 10−8
Electricity price for the first year (M$/kWh)	8.972 × 10−8
Discount rate (%)	5
Maintenance fee rate (%)	3
Density of heating pipe material (kg/m3)	7900
Wall thickness of heating pipe (mm)	13
Length of heating pipe (m)	3000
Average heat transfer coefficient of heating pipe [W/(m2·°C)]	1.5
Soil temperature (°C)	10
Additional coefficient	0.2
Price of heating pipe (M$/kg)	8.333 × 10−7
Price of standard coal (M$/t) [37]	9.722 × 10−5
Price of carbon emissions (M$/t) [38]	4.646 × 10−6
Price of insulation tubing (M$/m)	1.15 × 10−3

and

Table 6. Price of annular protection fluid.

Thermal Conductivity	Price
0.1 W/(m·°C)	0.236 M$/well
0.2 W/(m·°C)	0.167 M$/well
0.3 W/(m·°C)	0.111 M$/well
0.4 W/(m·°C)	0.069 M$/well
0.5 W/(m·°C)	0.042 M$/well
0.6 W/(m·°C)	0.028 M$/well

.

4.2.2. Analysis of Economic Sensitivity Factors

(1)

Production Time

Based on the parameters provided in Table 2, Table 3, Table 4, Table 5 and Table 6, the established economic evaluation model was applied to calculate the temporal variation in the NPV over a 50-year production period. The results are illustrated in Figure 11.

Figure 11 illustrates that, under the specified calculation conditions, the geothermal project utilizing co-produced water from natural gas wells consistently yields a negative NPV throughout the 50-year evaluation period, indicating economic non-viability and an overall loss-making operational profile. The initial NPV of −0.931 M$ in the first year reflects substantial upfront capital investment without immediate financial returns. Although the NPV gradually improves over time, reaching −0.102 M$ by year 50, the continued negative values highlight limited profitability under the current operational parameters. This outcome underscores the need for further investigation into key economic drivers and the development of potential optimization strategies to improve the viability of the co-production system.

(2)

Insulation Tubing Length

As analyzed in Section 4.1.2, although increasing the length of insulated tubing enhances the wellhead temperature—thus improving project revenue—it also leads to higher capital expenditures. To assess this trade-off, the established economic evaluation model was applied to calculate the variations in NPV under different insulated tubing lengths over a 50-year continuous production period. The results are presented in Figure 12.

Figure 12 illustrates that the installation length of insulated tubing has a limited yet non-negligible effect on the project’s NPV. As the length increases, the NPV exhibits a concave trend—initially rising and subsequently declining. Specifically, when the installation length increases from 0 to 2000 m, the 50-year NPV improves from –0.102 M$ to 0.029 M$, with profitability achieved in the 46th year. However, extending the length further to 2500 m results in diminishing returns, with the NPV declining to near-breakeven levels (0.00051 M$). This behavior indicates the presence of an optimal installation length in the range of 2000–2500 m. Based on data fitting and economic analysis, the optimal length is determined to be 2048 m.

(3)

Thermal Conductivity of Annular Protection Fluid

As discussed in Section 4.1.2, lowering the thermal conductivity of the annular protection fluid effectively increases the wellhead temperature, thereby enhancing project revenue. However, the cost of advanced insulating fluids escalates sharply with decreasing thermal conductivity. To quantitatively assess the impact of this trade-off on project economics, the established economic evaluation model was employed to analyze the effect of annular protection fluids with different thermal conductivities. The corresponding results are shown in Figure 13.

Figure 13 demonstrates that the thermal conductivity of the annular protection fluid exerts a relatively modest influence on the overall project economics. Specifically, when the thermal conductivity varies from 0.1 W/(m·°C) to 0.6 W/(m·°C), the NPV remains negative throughout the 50-year operational period. Among the six evaluated values, the annular protection fluid with a thermal conductivity of 0.4 W/(m·°C) delivers the most favorable economic performance. At this value, the NPV at year 50 reaches –0.058 M$, representing an improvement of 0.043 M$ compared to the baseline case (–0.102 M$) without insulation. Therefore, a thermal conductivity of 0.4 W/(m·°C) may be regarded as the optimal value for the annular protection fluid under the given conditions.

(4)

Heat price

The heat price is a critical economic factor, as it directly affects the revenue derived from geothermal heating applications. To assess the sensitivity of the project’s NPV to changes in heat price, the established economic evaluation model was applied under various pricing scenarios. Specifically, the baseline heat price was incrementally increased by 0%, 10%, 20%, and 30%, with all other parameters held constant. The resulting variations in NPV over the 50-year production period are illustrated in Figure 14.

Figure 14 demonstrates that heat price is indeed a critical factor influencing the profitability of the project. As the heat price increases, the project’s NPV improves accordingly. However, even with a 30% increase in heat price, the project still fails to achieve positive profitability over the 50-year evaluation period. Specifically, when the heat price rises from the baseline to 10%, the NPV at year 50 improves from −0.102 M$ to −0.074 M$. Further increases of 20% and 30% result in NPVs of −0.045 M$ and −0.017 M$, respectively. This outcome highlights that while raising the heat price enhances project economics, it alone is insufficient to make the project financially viable under current conditions.

(5)

Electricity price

In addition to the heat price, the electricity price also plays a significant role in determining the economic viability of the project, as it directly affects the revenue generated from ORC-based power generation. To assess the sensitivity of the project’s NPV to electricity price variations, the established techno-economic evaluation model was applied under different electricity price scenarios. Specifically, the electricity price was increased by 0%, 10%, 20%, and 30%, while all other parameters remained un-changed. The resulting variations in NPV over the 50-year production period are illustrated in Figure 15.

Figure 15 shows that the impact of electricity price on NPV follows a similar upward trend as that of heat price; however, the influence of electricity price is more pronounced. When the electricity price is increased by 10%, the NPV over the 50-year period rises from −0.102 M$ to −0.046 M$. A 20% increase in electricity price results in an NPV of 0.011 M$, with the project becoming profitable in the 48th year. Further increasing the electricity price by 30% raises the NPV to 0.067 M$, and profitability is achieved as early as the 40th year. This underscores the critical role of electricity pricing in determining the economic feasibility of geothermal energy utilization from co-produced water.

(6)

Government one-off subsidy rate

To promote the development and utilization of renewable energy, governments often provide financial support for such projects [39,40]. Among these, one-off capital subsidies are a common form of incentive used to alleviate the high initial investment burden. To evaluate the impact of different government one-off subsidy rates on the project’s NPV, the established economic evaluation model was applied under various subsidy scenarios. Specifically, scenarios with subsidy rates of 0%, 10%, 20%, and 30% of the initial investment were considered, while all other parameters remained unchanged. The variations in NPV over the 50-year production period are presented in Figure 16.

As shown in Figure 16, the government one-off subsidy rate has the most significant impact on the NPV among all evaluated factors. The higher the subsidy rate, the greater the NPV. Specifically, with a 10% subsidy, the 50-year NPV rises from −0.102 M$ to −0.005 M$. A 20% subsidy raises the NPV to 0.092 M$, with the project becoming profitable in the 35th year. Further increasing the subsidy to 30% results in an NPV of 0.189 M$ and profitability is achieved as early as the 26th year. This outcome highlights that government financial support—especially in the form of upfront capital subsidies—plays a pivotal role in improving the project’s economic feasibility, making it a key enabler for the commercial deployment of geothermal energy utilization from co-produced water.

4.2.3. Discussion on Enhancing Project Profitability

Based on the above analysis, several strategies can be adopted to enhance the economic performance and profitability of geothermal energy utilization from co-produced water in natural gas wells:

(1)

Extend the Operational Life of Natural gas wells

Although natural gas production inevitably declines over time due to reservoir depletion, the co-produced water still retains significant thermal potential for continued utilization. To prolong the productive life of the wells, reinjection of co-produced water into the reservoir can be employed to help maintain formation pressure and enable sustained geothermal extraction.

(2)

Seek Government Financial Support

Numerous countries have introduced fiscal and tax policies to support the development of geothermal energy. Similar incentives should be further reinforced in the future. Given the substantial social and environmental benefits associated with geothermal utilization, governments are encouraged to provide sustained financial support and preferential policies to enterprises engaged in geothermal energy development. These may include feed-in tariffs or price subsidies for geothermal power generation and heating, as well as one-time capital subsidies to reduce the burden of initial investments.

(3)

Enhance Scientific Research and Material Innovation

As demonstrated in this study, factors such as the length of insulated tubing and the thermal conductivity of annular protection fluids significantly influence project performance. While current materials exhibit certain thermal conductivities, further reduction is technically possible. Enhanced research into advanced insulation materials and cost reduction strategies will undoubtedly have a positive impact on the profitability of geothermal projects.

Under optimal conditions—comprising 2048 m of insulated tubing and annular protection fluid with a thermal conductivity of 0.4 W/(m·°C), a 30% increase in heat price and electricity price, and a 30% government one-off subsidy rate—the variation in NPV over the 50-year production period is illustrated in Figure 17, along with a comparison to the baseline scenario using original parameters.

To summarize these findings,

Table 7. Comparison of original and optimal parameters and their impacts on project NPV performance.

Parameters	Original Value	Optimal Value
Production time (years)	1–50	1–50
Insulated tubing length (m)	0	2048
Thermal conductivity of annular protection fluid [W/(m·°C)]	0.6	0.4
Heat price increase	0%	30%
Electricity price increase	0%	30%
Government one-off subsidy rate	0%	30%
NPV at year 50 (M$)	–0.102	0.896
Break-even year	Not achieved	Year 14

presents the optimal values of the key technical and economic parameters, along with the corresponding NPV outcome. For comparison, the original values are also included.

Table 7 clearly shows that the implementation of optimized technical and economic parameters markedly improves the project’s financial viability. Under these optimal conditions, the NPV turns positive as early as the 14th year, indicating the onset of profitability, and the 50-year NPV reaches as high as 0.896 M$.

5. Conclusions

This study investigates the utilization of co-produced water from natural gas production by establishing a coupled techno-economic evaluation model. Through this model, key factors influencing project economics were systematically analyzed from both technical and economic perspectives, and corresponding optimization strategies were proposed to enhance profitability. The main findings are summarized as follows:

(1)

The developed wellbore flow and heat transfer model exhibits high predictive accuracy, with calculated wellhead temperatures and pressures deviating from measured values by no more than ±10%. This demonstrates its strong applicability for engineering applications.

(2)

Increasing the installation length of insulated tubing and reducing the thermal conductivity of the annular protection fluid effectively enhance the wellhead temperature, with respective increases of 19.56 °C and 14.1 °C, indicating a significant thermal optimization potential.

(3)

The sensitivity analysis reveals that among the evaluated factors, government one-off subsidies exert the most significant influence on the project’s NPV, followed by electricity price and heat price. While technical improvements such as optimizing insulation tubing length and annular fluid conductivity contribute to economic enhancement, targeted policy incentives and favorable energy pricing structures are essential to ensure the financial viability of geothermal utilization in gas field co-production systems.

(4)

An optimized configuration—comprising 2048 m of insulated tubing and annular protection fluid with a thermal conductivity of 0.4 W/(m·°C), a 30% increase in heat price and electricity price, and a 30% government one-off subsidy rate—substantially improves economic performance. Under this scheme, the project’s NPV becomes positive in the 14th year, and increases to 0.896 M$ by the 50th year, effectively shortening the payback period and enhancing overall project viability.

In future work, the proposed techno-economic evaluation model will be applied to a wider range of geological formations and economic scenarios across different regions. Such efforts will facilitate the validation of the model’s robustness and adaptability under diverse subsurface conditions and policy environments, thereby enhancing its applicability to geothermal energy recovery from co-produced water in global contexts. Furthermore, future studies will aim to incorporate more detailed financial mechanisms—such as inflation, tax incentives, asset depreciation, and discount rate—into the economic model. This will improve the accuracy and realism of long-term profitability assessments and broaden the model’s relevance for practical investment decisions in geothermal applications.