Theoretical Study of a Novel Power Cycle for Enhanced Geothermal Systems

Abstract

As obtained geofluids from enhanced geothermal systems usually have lower temperatures and contain chemicals and impurities, a novel power cycle (NPC) with a unit capacity of several hundred kilowatts has been configured and developed in this study, with particular reference to the geofluid temperature (heat source) ranging from 110 °C to 170 °C. Using a suitable CO₂-based mixture working fluid, a transcritical power cycle was developed. The novelty of the developed power cycle lies in the fact that an increasing-pressure endothermic process was realized in a few-hundred-meters-long downhole heat exchanger (DHE) by making use of gravitational potential energy, which increases the working fluid’s pressure and temperature at the turbine inlet and, hence, increases the cycle’s power output. The increasing-pressure endothermic process in the DHE has a better match with the temperature change of the heat source (geofluid), as does the exothermic process in the condenser with the temperature change of the sink (cooling water), which reduces the heat transfer irreversibility and improves the cycle efficiency. Power cycle performance has been analyzed in terms of the effects of mass fraction of the mixture working fluids, the working fluid’s flowrate and its DHE inlet pressure, geofluid flowrate, and the length of the DHE. Results show that, for a given geofluid’s temperature and mass flowrate, the cycle’s net power output is a strong function of the working-fluid’s flowrate, as well as of its DHE inlet pressure. Too high or too low of a DHE inlet pressure results in a lower power output. When geofluid temperature is 130 °C, the optimum DHE inlet pressure is found to be 11 MPa, corresponding to an optimum working-fluid flowrate of 6.5 kg/s. The longer the DHE, the greater the corresponding working-fluid flowrate and the higher the net power output. For geofluid temperature ranging from 110 °C to 170 °C, the developed NPC has a better thermodynamic performance than the conventional ORC. The advantage of using the developed NPC becomes obvious when geofluid temperature is low. The maximum net power output difference between the NPC and the ORC happens when the geofluid temperature is 130 °C and NPC’s working fluid mass fraction (R32/CO₂) is 0.5/0.5.

1. Introduction

In recent years, utilization of enhanced geothermal system (EGS) geothermal energy has attracted increasing attention. As most obtained geofluids from the EGS geothermal resources usually have lower temperatures and contain chemicals and impurities, binary cycle geothermal power generation technologies associated with ORC (organic Rankine cycle) or TRC (transcritical Rankine cycle) were usually proposed [1,2,3].

Binary ORC is a relatively common technology using medium or low temperature geothermal resource for power generation [4,5]. Compared with the subcritical ORC, TRC has an advantage in reducing the heat transfer irreversibility when the supercritical working fluid is gaining heat from the heat source, because the temperature of the working fluid is not constant during this heating process, which has a better match with the heat source temperature change [6]. Research on TRC with CO₂ as working fluid was carried out by Zhang et al. [7]; they studied a solar thermal power generation cycle using CO₂ as working fluid and obtained the thermal efficiency of power generation cycles and COP (coefficients of performance) [8] during summer and winter in Japan through experiments. Chan et al. [9] compared the performance of a carbon dioxide-based transcritical power cycle and an ORC using R123 as working fluid in industrial waste heat recovery and found that TRC had a higher power output than ORC.

CO₂ has good mobility and excellent heat transfer performance, so it has been considered to be a suitable geothermal exploitation fluid or a working fluid for power cycles. Compared with water, CO₂ has higher density sensitivity to temperature; using CO₂ as geothermal exploitation fluid will provide a buoyancy-driven thermosiphon phenomenon [10] and hence reduce the power consumption of the circulation pump. Sun et al. [11] established a single-well geothermal model that used CO₂ as a working fluid. They asserted that, compared with water, CO₂ had a reduced heat mining capacity; however, it could obtain higher outlet pressure and temperature and could reduce the required pump power. Adams et al. [12] compared four CPG (CO₂ plume geothermal) systems and two brine-based geothermal systems and found that the CPG direct geothermal system obtained the highest net power output. Although the use of CO₂ as a TRC working fluid increases the parasitic losses, CO₂ TRC still gets a higher net power output because CO₂ has a better thermodynamic performance than the organic working fluid R245a. Amaya et al. proposed a different geothermal system [13]. They put a 330 m-long concentric tube as a downhole heat exchanger into the geothermal production well with upward flowing geofluid. CO₂ was used as working fluid to absorb the heat from the geofluid through the concentric tube, and then directly entered a turbine for power generation. In this way, the problem of non-condensable gases (NCGs) in the geofluid was avoided, and a higher outlet temperature of working fluid in the downhole heat exchanger was obtained. Since they only used pure CO₂ as a working fluid without using a pump in their experiment, the CO₂ flowrate driven by the thermosiphon effect was relatively small; hence, the heat obtained from the geofluid was constrained by the CO₂ flowrate. In their system, a supercritical CO₂ Brayton cycle was used for power generation, with the turbine outlet pressure of CO₂ being above its critical pressure.

Because the critical temperature of CO₂ is low (31.2 °C), using pure CO₂ as a working fluid for TRC will have a condensation problem. In most cases, the cooling-water temperature is close to, or even higher than, the critical temperature of CO₂; hence, it is impossible to condense the exhaust vapor from the turbine. In this case, the cooling process cannot undergo a phase change unless under the supercritical condition, as happened in the CO₂ Brayton cycle. Some recent studies showed that mixing another organic fluid that has a higher critical temperature with CO₂ could solve this problem [14]. The CO₂-based mixture working fluid allowed us to still use a conventional “condenser” (with phase change), instead of using “cooler” (with no phase change). Due to the temperature glide of the mixtures in the two-phase region, the temperature profile of the heat dissipation process in the condenser can be better matched with the cooling water and a less irreversible loss can be achieved. Dai et al. [15] used seven kinds of CO₂-based mixtures as working fluids of a trans-critical Rankine cycle and analyzed the thermal efficiency and power output of the cycle; their results showed that power cycles using these mixture working fluids had higher thermal efficiencies and lower working-pressures compared with those when pure CO₂ was used as a working fluid. Wu et al. [16] selected six CO₂-based mixture working fluids as the working fluids of a geothermal power generation cycle and analyzed their thermal efficiency and economic performance. Their calculation result indicated that R161/CO₂ had the highest thermal efficiency and economic performance and that the CPP (cost per net power) of the mixture was lower than that of CO₂.

This study was inspired by the work carried out by Amaya et al. [13]. The aim of this study was to develop a power cycle (with a unit capacity of several hundred kilowatts) for enhanced geothermal systems supplying geofluids, with particular reference to the geofluid temperature (heat source) ranging from 120 °C to 170 °C. Different from the working fluid (pure CO₂) and the power cycle (Brayton cycle) that Amaya et al. adopted, in this study, CO₂-based mixture working fluids were investigated and a different power cycle was configured, which had the following characteristics:

(1)

The critical point of each CO₂-based mixture working fluid investigated in this study is higher than that of the pure CO₂; hence, a condensing process with phase change could be realized. As a result, a conventional condenser could be used, without being restricted to the use of costly large-area coolers, as in a Brayton cycle. Thus, it was thermodynamically possible to realize a transcritical power cycle with a higher thermal efficiency.

(2)

An increasing-pressure endothermic process (instead of an isobarically endothermic process) could be realized in a few-hundred-meters-long downhole heat exchanger (DHE) by making use of gravitational potential energy [17]. This resulted in an increase of the cycle’s heat gain. In addition, the CO₂-based mixture working fluid used in this proposed power cycle had a obvious buoyancy-driven thermosiphon effect; hence, the working-fluid’s DHE outlet pressure (i.e., the working-fluid’s turbine inlet pressure) could be increased. As a result, the cycle’s power output was increased.

(3)

In the downhole heat exchanger (DHE), the working fluid absorbed heat from the geofluid with a higher temperature at depth; thus, a higher working-fluid’s DHE outlet temperature (i.e., a higher working-fluid’s turbine inlet temperature) could be obtained, which would also benefit the cycle’s power generation.

In this theoretical study, the proposed power cycle has been described in detail and its thermodynamic performance has been investigated by analyzing the influences of important parameters on the system. The investigated parameters included: mass fraction of the mixture working fluids, working fluid DHE inlet pressure and flowrate, geofluid flowrate, and length of the DHE. Different CO₂-based mixture working fluids have been analyzed and their performances have been discussed, as well. In addition, thermodynamic performance (in terms of the net power output) has been compared between the proposed power cycle and the conventional organic Rankine cycle (ORC).

2. System Description

The schematic diagram of the geothermal power generation system investigated in this study is shown in Figure 1. Since enhanced geothermal systems can supply artesian geofluid in production wells, as reported by Hogarth and Bour (2015) [18], and Hogarth and Holl (2017) [19], it is assumed that the upward geofluid flow in the production well is artesian. The temperature-entropy (T-s) diagram of the power cycle corresponding to the system in Figure 1 is shown in Figure 2.

As can be seen in Figure 1, a coaxial double-pipe downhole heat exchanger is placed in a geothermal production well and forms a closed loop consisting of the turbine, condenser, and pump on the surface. The condensed working fluid (state 1) enters the pump and is pressurized into a supercritical condition (state 2) and is then injected into the downhole heat exchanger, forming a downward annulus flow that extracts heat from the upward flowing geofluid outside the heat exchanger, corresponding to the heat transfer process 2–3, as shown in the red line in Figure 2. The working fluid then moves into the inner pipe at the bottom of the downhole heat exchanger and flows upwards from the bottom (state 3) to the top (state 4), corresponding to the blue line (3–4) in Figure 2. The heated working fluid enters the turbine to generate shaft work (process 4–5) once it leaves the heat exchanger on the top. The exhaust (working fluid) of the turbine (state 5) is condensed in the condenser until it is in a saturated liquid state (state 1); then, another cycle starts.

When the working fluid flows downwards in the annulus, it forms a counter-flow with the geothermal water in the production well. This enables the working fluid to exchange heat with the deeper geothermal water at a higher temperature, resulting in a higher turbine inlet temperature and, hence, a higher power generation.

One unique feature of this power cycle lies in its increasing-pressure endothermic process, process 2–3 (the red line in Figure 2), which is determined based on the heat transfer model shown in Section 2 of this study. This increasing-pressure endothermic process can only be realized by taking advantage of the gravitational potential energy in a large-scale and closed-loop downhole heat exchanger. The dashed black line just below the red line in Figure 2 is a constant-pressure endothermic process (2–4) that occurs when the heat transfer between the geofluid and working fluid is made on the ground, as is commonly used in conventional ORC geothermal power stations. Simulation shows that the heat obtained by the mixture working fluid from process 2–3 is greater than that from process 2–4.

Since the mixture working fluid absorbs heat through the DHE at a few hundred-meter depth in the well and can get higher temperature, and since the buoyancy-driven thermosiphon effect in the DHE can boost the working-fluid’s DHE outlet pressure, the working-fluid’s temperature and pressure at the turbine inlet can be increased. As a result, the cycle’s power output becomes greater.

It is worth pointing out that the endothermic process under supercritical condition not only has a better match with the temperature change of the heat source (geofluid), but the exothermic process in condenser (5-1), which is a temperature-drop process, also has a better match with the temperature change of the cooling water. Both of them can reduce the heat transfer irreversibility and, hence, can improve the power cycle performance.

As mentioned earlier, CO₂-based mixture working fluids have been investigated in this study. In the selection of working fluids, the following aspects have been considered: thermal properties, stability, toxicity, flammability, environmental friendliness, and price. The physical, safety and environmental data for some relevant refrigerants are shown in

Table 1. Physical, safety and environmental data of the refrigerants investigated.

Substance	Molecular Mass (g/mol)	Tb (°C)	Tc (°C)	Pc (MPa)	OEL (PPMv)	LEL (%)	ASHRAE 34 Safety Group	Atmospheric Life (yr)	ODP	GWP
R32	52.02	51.7	78.1	5.78	1000	14.1	A2	4.9	0	675
R1270	42.08	47.7	92.4	4.66	660	2.0	A3	0.001	0	~20
R161	48.06	37.6	102.2	5.09	-	3.8	-	0.21	0	12
R1234yf	114.04	29.5	94.7	3.38	500	6.2	A2L	0.029	0	<4.4
R134a	102.03	26.1	101.1	4.06	1000	None	A1	14.0	0	1370
R152a	66.05	24.0	113.3	4.52	1000	4.8	A2	1.4	0	124
R1234ze	114.04	19.0	109.4	3.64	1000	7.6	e	0.045	0	6

[20]. The temperature glide characteristic of a mixture is an essential criterion in the selection. However, once the temperature glide exceeds a certain level, a high concentration shift and fractionation of the mixture components can appear [21]. In consideration of these factors, the following combinations were selected: CO₂/R32, CO₂/R1270, CO₂/R161, CO₂/R1234yf, CO₂/R134a, CO₂/R152a, and CO₂/R1234ze. All the thermodynamic and transport properties of the mixtures have been calculated using REFPOP 9.0. The accuracy of each calculated property basically depends on the binary interaction parameter that is fitted by experimental data. According to Bell and Lemmon [22], the error can be less than 5% in the bubble point.

3. Model Development

The power cycle model corresponding to the system described in Section 1 was developed. The mixture working fluid underwent the following major thermodynamic processes: expansion process in the turbine generating shaft work; non-isothermal condensation process in the condenser; pressurization process in the injection pump; and heat gaining process in the coaxial double-pipe downhole heat exchanger. The parameters used in the simulation can be found in

Table 2. Parameters used in the simulation.

Parameters	Value
Turbine isentropic efficiency, ηT	0.75
Pump isentropic efficiency, ηP	0.80
Condenser pinch temperature difference (°C)	4
Cooling water inlet temperature, TCW,in (°C)	18
Inner diameter of the wellbore (m), dwi	0.215
Outer diameter of the wellbore (m), dwo	0.380
Inner diameter of inner pipe of the DHE, dti (m)	0.073
Outer diameter of inner pipe of the DHE, dto (m)	0.089
Inner diameter of annulus of the DHE, dai (m)	0.120
Outer diameter of annulus of the DHE, dao (m)	0.138
Density of formation rock, ce (kg/m3)	2650
Heat capacity of formation rock, ρe [J/(kg·°C)]	837
Thermal conductivity of casing, λca [W/(m·°C)]	30
Thermal conductivity of formation rock, λe [W/(m·°C)]	2.5
Thermal conductivity of insulated tube, λt [W/(m·°C)]	0.02
Thermal conductivity of cement, λce [W/(m·°C)]	0.72

. The condensation pressure is determined by the temperature of the cooling water and the pinch point method [9,23,24]. Because of the temperature glide of the mixtures during the condensation process, the problem of pinch points can be alleviated [25] and the utilization efficiency can be improved [26]. It is worth mentioning that the values of pump and turbine internal efficiencies used in this study are less than those adopted by previous theoretical studies [27,28,29,30], where the range of turbine efficiencies used is from 82% to 93%, and the range of compressor efficiencies used is from 81% to 93%.

As the coaxial double-pipe downhole heat exchanger and the geothermal production well are concentric, the 3-dimensional heat transfer model has been simplified to a radially symmetric model. The heat transfer covers the following aspects: heat transfer between the inner pipe and the outer pipe of the heat exchanger, heat transfer between the outer pipe and the geofluid, heat transfer between the geofluid and formation, and the heat transfer in the formation, which is defined by the formation transient heat conduction time function f(t). The overall heat transfer model was coupled with the flow model and was calculated by the finite difference method. The temperature and pressure distributions of the working fluid, as well as the geofluid, are coupled and solved at the same time.

3.1. Assumptions and Boundary Conditions

The power generation system was modeled and analyzed based on the following assumptions:

(1)

The entire system is analyzed under steady-state conditions.

(2)

Friction losses and heat losses in pipes (except in the downhole heat exchanger) and in the condenser are ignored.

(3)

The working fluid is in a saturated liquid state at the condenser outlet

(4)

The working fluid is pressurized to a pressure higher than the working fluid’s critical pressure before it is injected into the downhole heat exchanger.

(5)

The geofluid temperature is defined to be that at the bottom of the downhole heat exchanger; both the geofluid temperature and the pressure at the wellhead are set as the boundary conditions.

3.2. Power Cycle Model

The power cycle model consists of thermodynamic processes in the turbine, condenser, injection pump, and coaxial double-pipe downhole heat exchanger.

3.2.1. Turbine

Working fluid enters the turbine to expand and generate shaft work (process of 4–5 in Figure 2) for power generation. The exhaust state is determined based on the condensing pressure and turbine efficiency. The relevant parameters used in the simulation can be found in Table 2. The turbine power output and the turbine efficiency are as follows:

$$W_{\mathrm{T}}=m\left(h_4-h_5\right)$$

(1)

$${\eta }_{\mathrm{T}}=\left(h_4-h_5\right)/\left(h_4-h_{5^{\prime }}\right)$$

(2)

where $W_{\mathrm{T}}$ is the power output of turbine, kW; $m$ is the mass flowrate of working fluid, $h_4$ is working-fluid specific enthalpy at the turbine inlet, kJ/kg; $h_5$ is working-fluid’s real specific enthalpy at the turbine outlet, kJ/kg; $h_{5^{\prime }}$ is working-fluid specific enthalpy at the turbine outlet, assuming that the working-fluid undergoes an isentropic expansion to the same pressure as at state 5, kJ/kg; ${\eta }_{\mathrm{T}}$ is the turbine isentropic efficiency.

3.2.2. Condenser

The working fluid from the turbine enters the condenser and condenses to a saturated liquid state, corresponding to the process 5-1 in Figure 2. The condensation process of the mixture working fluid is non-isothermal, showing the existence of a temperature glide, which has a better match with the temperature change of the cooling water, and which results in less heat transfer irreversibility. The condensing pressure is determined by the pinch point and the temperature of the cooling water; the pinch point temperature difference and the temperature of the cooling water are specified in Table 2. The corresponding energy balances are as follows:

$$Q_{\mathrm{C}}=m\left(h_5-h_1\right)$$

(3)

$$m_{\mathrm{CW}}=m\left(h_{\mathrm{C}, \mathrm{pinch} }-h_5\right)/\left(h_{\mathrm{CW}, \mathrm{pinch} }-h_{\mathrm{CW}, \mathrm{in} }\right)$$

(4)

where $Q_{\mathrm{C}}$ is the heat transfer rate of condenser, kW; $h_1$ is the condenser outlet specific enthalpy of working fluid, kJ/kg; $m_{\mathrm{CW}}$ is the mass flowrate of cooling water, kg/s;$h_{\mathrm{C}, \mathrm{pinch} }$ is the pinch-point specific enthalpy of working fluid, kJ/kg; $h_{\mathrm{CW}, \mathrm{pinch} }$ is the pinch-point specific enthalpy of cooling water, kJ/kg; $h_{\mathrm{CW}, \mathrm{in} }$ is the specific enthalpy of the inlet cooling water, kJ/kg.

3.2.3. Injection Pump

The working fluid from the condenser is then pressurized to a supercritical condition (process of 1–2 in Figure 2). The power consumption and efficiency of the injection pump are given by

$$W_p=m\left(h_2-h_1\right)$$

(5)

$${\eta }_p=\left(h_{2^{\prime }}-h_1\right)/\left(h_2-h_1\right)$$

(6)

where $W_p$ is the pump power consumption, kW; $h_2$ is working-fluid’s real specific enthalpy at the pump outlet, kJ/kg; $h_{2^{\prime }}$ is the working-fluid specific enthalpy at the pump outlet, assuming that the working-fluid is compressed isentropically to the same pressure as at state 2, kJ/kg; ${\eta }_p$ is the pump isentropic efficiency.

3.2.4. Coaxial Double-Pipe Downhole Heat Exchanger

The working fluid affected by the gravity field in the downhole heat exchanger was considered in the calculation. The temperature field and the velocity field are related and solved by coupling the mass, momentum, and energy equations. The densities of CO₂ and CO₂-based mixtures vary greatly with the temperature and pressure profiles, resulting in variations of fluid flow velocities. The flow velocity variations affect the temperature via friction losses and the Joule–Thomson cooling effect; thus, they all need to be considered in the simulation.

In order to make the main text concise and readable, the simulation models of pressure, temperature, and heat transfer in the downhole heat exchanger, as well as the model solution procedure, are presented in Appendix A.1, Appendix A.2, Appendix A.3 and Appendix A.4, respectively.

3.2.5. Cycle’s Net and Specific Power Output

The net power output, W_net, is given by

$$W_{\mathrm{net} }=W_T-W_P$$

(7)

The net specific power output is calculated as follows

$$SPO=W_{\mathrm{net}}/3.6m_{\mathrm{geo}}$$

(8)

where, W_net is the net power output of the power cycle, kW; SPO is the power cycle’s net specific power output, in kWh/(ton of geofluid) or Wh/(kg of geofluid); m_geo is the geofluid mass flowrate, kg/s.

4. Results and Discussion

4.1. Comparison of Using Different CO₂-Based Binary Working Fluids

The maximum net power output (kW) is chosen as the objective function and the pattern search algorithm (PSA) is used in the system optimization. The mixture working fluid’s DHE inlet pressure, mixing ratio and flowrate are used as independent variables of PSA. The ranges of these three independent variables investigated in the study are: inlet pressure from 10 MPa to 18 MPa, mixing ratio from 0.01 to 0.99, and flowrate from 1 kg/s to 10 kg. The optimal net power outputs of the power cycle using different mixtures as working fluids for geofluids at 140 °C are shown in

Table 3. Optimal net power outputs of the power cycle using different mixture working fluids (geofluid temperature = 140 °C).

Working Fluids	Optimal Mixing Ratio	Optimal Inlet Pressure (MPa)	Optimal Flowrate (kg/s)	Maximum Net Power Output
R161/CO2	0.094/0.906	13.9	8.0	141.3
R32/CO2	0.7/0.3	12	7.5	151.5
R134a/CO2	0.042/0.958	15.7	8.3	138.4
R1270/CO2	0.084/0.916	15.1	7.9	140.2
R152a/CO2	0.045/0.955	15.5	8.1	139.5
R1234yf/CO2	0.01/0.99	15.2	8.3	137.2
R1234ze/CO2	0.01/0.99	15.1	8.3	137.3

.

It can be seen from Table 3 that the mixture working fluids R32/CO₂ has the best thermodynamic performance among the seven mixtures, with a specific net power output of 151.5 W·h/kg.

In the following parts of this study, R32/CO₂ has been used for the power cycle performance analyses in terms of the effects of the following parameters: mixture mass fractions, working-fluid’s flowrate and its DHE inlet pressure, geofluid flowrates and downhole heat exchanger lengths.

4.2. Effect of Mixture Mass Fractions

The optimal results of the power cycle for geofluid temperatures ranging from 100 °C to 170 °C are shown in

Table 4. Optimal net power outputs of the power cycle using different mixture working fluids.

Geofluid Temperature (°C)	Optimal R32/CO2 Mass Fraction	Optimal DHE Inlet Pressure (MPa)	Optimal Working Fluid Mass Flowrate (kg/s)	Maximum Net Power Output (kW)
100	0.2	11	6	63.8
110	0.3	11	6.5	83.0
115	0.3	11	6.5	91.6
120	0.4	11	6.5	103.8
125	0.4	11	6.5	114.1
130	0.5	11	6.5	126.1
135	0.6	11	6.5	139.6
140	0.7	12	7.5	151.5
145	0.7	12	7.5	165.3
150	0.8	12	7.5	182.1
155	0.8	12	7.5	199.3
160	0.9	12	7.5	221.8
165	0.9	12	7.5	238.4
170	1	12	8	269.4

. Here, R32/CO₂ mass fraction, DHE inlet pressure, and working fluid mass flowrate were optimized simultaneously to obtain the cycle’s maximum net power output.

As can be seen in Table 4, the optimal mass fraction (R32/CO₂) increases as the geofluid temperature rises. This indicates that, the lower the geofluid temperature, the more CO₂ in the mixture is required to obtain a higher net power output, whereas, more R32 is needed for better performance if the geofluid temperature is high, indicating that the optimal mass fraction is a strong function of the heat source (geofluid) temperature. As can be seen in Table 4, the optimal R32/CO₂ mass fraction is only 0.2 when the geofluid temperature is 100 °C; it becomes 0.6 if the geofluid temperature is 135 °C; when the geofluid temperature is 170 °C, the optimal R32/CO₂ mass fraction becomes 1.0. This means using pure R32 as a working fluid has a better power cycle performance than using the R32/CO₂ mixture under the condition that geofluid temperature is equal or greater than 170 °C. Using pure R32 as a working fluid in this proposed power cycle does not change the system’s advantage of using gravitational potential energy to realize the increasing-pressure endothermic process. Our calculation shows that the need for working fluid R32 in the downhole heat exchanger is approximately 0.5 ton, which is not greater than that used in the conventional ORC’s evaporator.

It is worth pointing out that the aim of this study is to use low temperature geofluid (ranging from 110 °C to 160 °C) artesian geofluid in a production well to produce several hundred kilowatts of electricity. Under such temperature conditions, the mixture working fluid R32/CO₂, with an optimal fraction, as shown in Table 4, should be used.

In the following parts of this study, the scenario with the geofluid temperature of 130 °C is analyzed and discussed with a particular reference to a potential application for the EGS project that has been carried out in Gonghe Basin, Qinghai, China.

4.3. Effect of Working-Fluid’s DHE Inlet Pressure

The working fluid R32/CO₂ with an optimal mass fraction (as shown in Table 4) has been investigated for six different DHE inlet pressures (shown in the legend of Figure 3) under the conditions that the geofluid mass flowrate is 5 kg/s and the geofluid temperature is 130 °C. The effects of the working fluid’s flowrate and its DHE inlet pressure on the cycle’s net power output, as well as on the working-fluid’s DHE outlet temperature, are shown in Figure 3a,b respectively. As can be seen from Figure 3a, for each given DHE inlet pressure, there is a maximum net power output with a corresponding optimum working-fluid flowrate. The top curve (12 MPa curves) has the highest net power output with a value of about 120 kW when the working-fluid flowrate is 6.5 kg/s. Too high or too low DHE inlet pressure results in lower power output. In the scenario investigated here, the optimum DHE inlet pressure for obtaining maximum net power output is 11 MPa, as shown in Table 4.

Figure 3b shows the effect of DHE inlet pressure on the DHE outlet temperature with respect to the change of the working-fluid’s mass flowrate. When the working-fluid flowrate is less than 4 kg/s, the DHE outlet temperature is almost same under the six investigated DHE inlet pressure conditions. This means that, when the working-fluid flowrate is small (less than 4 kg/s), the heat supply from the geofluid is big enough to enable the working fluid to approach the geofluid’s temperature.

When the working-fluid flowrate is greater than 4 kg/s, for any given DHE inlet pressure, the DHE outlet temperature starts to decline. As can be seen from Figure 3b, the decline rate of the DHE outlet temperature is different with the increase of the working-fluid flowrate; the greater the DHE inlet pressure, the smaller the decline rate, the higher the DHE outlet temperature.

It is worth pointing out that the higher DHE outlet temperature does not necessarily mean that the power cycle has a higher power output. This can be seen in Figure 3a, where the bottom power output curve corresponds to the highest DHE inlet pressure (20 MPa). Higher DHE inlet pressure means a higher pump work and, hence, a greater deduction in the net power output. Therefore, for a given geofluid temperature and mass flowrate, the working-fluid’s flowrate and its DHE inlet pressure should be optimized simultaneously.

4.4. Effect of Geofluid Mass Flowrate

Figure 4 shows the effect of a geofluid mass flowrate on the cycle’s net power output and working-fluid’s DHE outlet temperature with respect to different working-fluid flowrates. The corresponding specific power output (power, in W, generated by a unit mass flowrate of geofluid, in kg/h) is also plotted in Figure 4a for discussion.

Four different geofluid mass flowrates (2, 3, 5, and 9 kg/s) have been investigated under the conditions that the geofluid temperature is 130 °C, mass fraction of working fluid R32/CO₂ is taken as 0.5/0.5 (optimal value), and working-fluid’s DHE inlet pressure is taken as 11 MPa (optimal value). The optimal values are seen in Table 4.

In Figure 4a, for each given geofluid flowrate, there is a corresponding optimal working-fluid flowrate. The higher the geofluid flow, the greater the optimal working-fluid flow. When the geofluid flowrate is 2 kg/s, the optimal working-fluid flowrate is 3 kg/s, corresponding to a specific power output of about 7.8 Wh/kg. Under the condition that the geofluid’s flowrate is 3 kg/s or 5 kg/s, the peak value of the specific power output in each case is gradually decreased. When the geofluid flowrate is 9 kg/s, there is an obvious decrease in the peak value of the specific power output. The specific power output, in this case, is only about 5.8 Wh/kg, with an optimal working-fluid flowrate of about 10 kg/s. A higher working-fluid flowrate (10 kg/s) means a higher pump work and, hence, a lower specific net power output. However, higher geofluid flowrate scenario shows a better off-design operation characteristic because the curve around its peak value is flatter. The optimal working-fluid flowrates can also be determined from the net power output curves. They are the same as those found using the specific power output curves. Different from the specific power output, the net power output increases as the geofluid flowrate becomes greater.

Figure 4b shows the variation of the working-fluid’s DHE outlet temperatures with respect to the working-fluid mass flowrate. When the geofluid flowrate is 9 kg/s, the working-fluid’s DHE outlet temperature is almost constant. Because the mass flowrate of the geofluid is high, the heat supply from the geofluid is so big that it enables the working fluid to approach the geofluid’s temperature. However, when the geofluid flowrate is not high (e.g., 2 kg/s), the outlet temperature starts to decline after the working-fluid flowrate is greater than 3 kg/s, with an obvious decrease rate, implying that an optimum match between the geofluid flowrate and the working-fluid mass flowrate becomes important when the geofluid flowrate is low.

4.5. Effect of the Downhole Heat Exchanger (DHE) Length

Figure 5a shows the change of net power output for a given DHE length with respect to the working-fluid flowrate. Six DHE lengths (100 m, 200 m, 300 m, 400 m, 500 m, and 600 m) were investigated under the conditions where the geofluid mass flowrate is 5 kg/s, the geofluid temperature is 130 °C, and the working-fluid’s DHE inlet pressure is 11 MPa. The mixture ratio of working fluid R32/CO₂ is 0.5/0.5. It can be seen from Figure 5a that the length of DHE has an obvious influence on the net power output. For each given DHE length, the net power output has a peak value corresponding to an optimum working-fluid flowrate. The longer the DHE, the greater the optimum working-fluid flowrate, the higher the net power output. When the DHE is 100 m long, the optimum working-fluid flowrate is 5 kg/s with a maximum net power output of about 73 kW; whereas, when the DHE is 600 m long, the optimum working-fluid flowrate becomes 7.5 kg/s, corresponding to a maximum net power output of about 143 kW, which is almost two times the output when a 100 m-long DHE is used. Of course, in an engineering application, the optimum length of the DHE should be determined not only based on thermophysical analysis, but also on engineering economic analysis, with consideration of the costs of both DHE and the working fluid.

The influence of the DHE length on the working-fluid’s DHE outlet temperature is shown in Figure 5b. It can be seen that, when the DHE is short (100 m), the working-fluid’s outlet temperature starts to decrease once the working-fluid mass flowrate is greater than 1 kg/s. When the DHE is long (600 m), the outlet temperature can maintain a constant value if the working-fluid’s flowrate is less than 8 kg/s. This is not difficult to understand. Shorter DHE means a less heat transfer area. Once the working-fluid flowrate increases to a certain value, the area of the short DHE is no longer enough to maintain the outlet temperature and, hence, there is a temperature decline, as shown in Figure 5b. Therefore, the longer the DHE, the more stable the outlet temperature. It is also seen from Figure 5b that, the longer the DHE, the lower the outlet temperature (in the stable section). Longer DHE means that more heat loss occurs in the inner pipe upward-flow and, hence, causes a slight decrease of the outlet temperature.

4.6. Performance Comparison between the Developed NPC and Conventional ORC

Thermodynamic performance (in terms of the net power output) has been compared between the developed novel power cycle (NPC) and the conventional organic Rankine cycle (ORC), which is widely used in geothermal power industry.

The ORC model of Lu et al. (2018) [31] has been used in this study. Based on the literature [32,33,34,35], R245fa and R601 were found to have better thermodynamic performance for the temperature range investigated and, hence, have been selected as the ORC’s working fluids for the comparative study here.

The key parameters of the ORC model are listed in

Table 5. Key parameters of the ORC model.

Simulation Parameters	Value
Turbine isentropic efficiency	0.75
Pump isentropic efficiency	0.80
Condenser pinch temperature difference (°C)	4
Evaporator pinch point temperature difference (°C)	7

. The heat source and heat sink parameters are shown in

Table 6. Heat source and heat sink parameters.

Cooling Water Temperature °C	Geofluid Temperature °C	Cooling Water Flowrate kg/s	R245fa Condensing Temperature °C	R601 Condensing Temperature °C
18	110	22.53	30	30
	120	26.45	30	30
	130	22.89	33	33
	140	29.58	32	32
	150	35.03	31	31
	160	36.24	32	32
	170	38.91	33	32
25	110	16.55	38	38
	120	16.18	40	40
	130	17.05	41	41
	140	30.95	38	37
	150	36.54	37	37
	160	37.59	38	38
	170	39.01	39	38

.

The heat source inlet temperature for the ORC’s evaporator is the wellhead geofluid temperature, assuming that there is no 300-m downhole heat exchanger (DHE) in the well and that the geofluid flows upward in the well with heat transfer to the surroundings (formations) of the well through the wall of the wellbore until it reaches the wellhead. In this scenario, the wellhead geofluid temperature is some degree lower than the geofluid temperature at 300 m-depth in the well. Our numerical simulation for this scenario shows that the temperature of the geofluid that reaches the wellhead is at least 5 °C lower than that of the geofluid at the depth of 300 m in the well. Therefore, in this comparative study, the heat source inlet temperature for the ORC’s evaporator is set to be a temperature that is 5 °C lower than the geofluid temperature at the 300 m-depth.

Figure 6 shows the comparison of net power output between the developed NPC and the conventional ORC that uses R245fa or R601 as working-fluid, respectively. Here, two cooling water temperature scenarios, 18 °C and 25 °C, were investigated. In order to analyze the influence of the thermal conductivity (${\lambda }_{\mathrm{t}}$) of the DHE inner pipe on the power output, two values, 0.2 W/(m·°C) and 0.02 W/(m·°C), were considered in this simulation.

The net power outputs of the four scenarios (shown in the legends of Figure 6) were simulated for geofluid temperatures ranging from 110 °C to 170 °C, using the heat source and heat sink parameters in Table 6, under the condition that the geofluid mass flowrate is 5 kg/s, and the DHE length is 300 m long.

As can be seen from Figure 6a,b, under any geofluid temperature conditions (from 110 °C to 170 °C), the net power output of the developed NPC is greater than that generated by the ORC using either R245 fa or R601 as working-fluid, no matter whether the cooling water temperature is low (18 °C) or high (25 °C), or the DHE inner pipe thermal conductivity is low (0.02 W/(m·°C)) or high (0.2 W/(m·°C)). This indicates that, under the heat source and heat sink conditions investigated, the developed NPC has a better thermodynamic performance than the conventional ORC. The advantage of using the developed NPC is more obvious when the geofluid temperature is low. The maximum net power output difference between the NPC and the ORC happens when geofluid temperature is 130 °C and NPC’s working fluid mass fraction (R32/CO₂) is 0.5/0.5.

5. Conclusions

In this theoretical study, a power cycle with a unit capacity of several hundred kilowatts was configured and developed specifically for enhanced geothermal systems supplying geofluids with temperatures less than 170 °C. The thermodynamic performance of the developed novel power cycle (NPC) was analyzed in terms of the effects of the following important parameters: mass fraction of the mixture working fluids, working fluid’s flowrate and its DHE inlet pressure, geofluid flowrate, and length of the DHE. In addition, thermodynamic performance (in terms of the net power output) has been compared between the developed NPC and the conventional organic Rankine cycle (ORC). The following conclusions can be drawn from this study:

(1)

A transcritical power cycle with a higher net power output was developed using a suitable CO₂-based mixture working fluid. Since the critical point of each used CO₂-based mixture working fluid is higher than that of the pure CO₂, a condensing process with a phase change can be realized. As a result, conventional condenser can be used, without being restricted to the use of costly large-area coolers, as in a CO₂ Brayton cycle.

(2)

In the developed novel power cycle, an increasing-pressure endothermic process (instead of an isobarically endothermic process) was realized in a few-hundred-meters-long downhole heat exchanger (DHE) by making use of gravitational potential energy, which increases the cycle’s heat gain, as well as the working fluid’s pressure at the turbine inlet and, hence, increases the cycle’s power output.

(3)

In the downhole heat exchanger, the working fluid absorbs heat from the geofluid with a higher temperature at depth; thus, a higher outlet temperature of working fluid can be obtained, resulting in an increase of the working fluid’s temperature at the turbine inlet, contributing to a higher power output.

(4)

The increasing-pressure endothermic process in the DHE has a better match with the temperature change of the heat source (geofluid), as does the exothermic process in the condenser with the temperature change of the sink (cooling water), which reduces the heat transfer irreversibility and improves the power cycle efficiency.

(5)

For a given geofluid mass flowrate, the working-fluid’s flowrate and its DHE inlet pressure should be optimized simultaneously to get the maximum net power output. Higher geofluid mass flowrate usually corresponds to a higher optimum working-fluid flowrate.

(6)

From the thermophysical point of view, the longer the DHE, the greater the corresponding (optimum) working-fluid flowrate, the higher the net power output. In practice, however, the optimum length of the DHE should be determined based on engineering economics, considering the costs of both the DHE and the mixture working fluid.

(7)

In terms of the net power output, the developed NPC has a better thermodynamic performance than the conventional ORC for the geofluid temperature ranging from 110 °C to 170 °C. The lower the geofluid temperature, the more advantage of using the developed NPC.

(8)

Future research regarding an experimental study on the condensing process of the CO₂-based mixture working fluid has been planned and will be carried out later.