Study on the Multiphase Flow Behavior in Jet Pump Drainage and Natural Gas Hydrate Production Wells with Combined Depressurization and Thermal Stimulation Method

Abstract

Natural gas hydrate (NGH) trials have been performed successfully with different development methods and gas recovery drainage technologies. Multiphase flow in a wellbore and the drainage of natural gas hydrate are two important parts for its whole extraction process. Additionally, the choice of the drainage method is linked to the development method, making the drainage of NGH more complex. Jet pump drainage is usable for NGH production wells with the combined depressurization and thermal stimulation method. The objective of this study is to shed more light on the multiphase flow behavior in jet pump drainage and NGH production wells and put forward suggestions for adjusting heat injection parameters. The mechanism of jet pump drainage recovery technology for NGH wells was analyzed and its applicability to NGH development by the combined depressurization and thermal stimulation method was demonstrated. In addition, multiphase flow models of tubing and annulus were established, respectively, for the phenomenon of the countercurrent flow of heat exchange in the process of jet pump drainage and gas production, and the corresponding multiphase flow laws were derived. On the basis of these studies, sensitivity analysis and the optimization of thermal stimulation parameters were conducted. It is demonstrated that jet pump drainage gas recovery technology is feasible for the development of onshore NGH with the combined depressurization and thermal stimulation method. The laws of multiphase flow in the tubing and annulus of jet pump drainage and NGH production wells were disclosed in this study. Numerical simulation results show that the temperature and pressure profiles along the wellbore of jet pump drainage and NGH production wells during the drainage recovery process are affected by injection conditions. Increasing injection rate and injection temperature can both improve the effect of heat injection and reduce the hydrate reformation risk in the bottom of the annulus. This study offers a theoretical basis and technical support for production optimization and hydrate prevention and control in the wellbore of jet pump drainage and NGH production wells.

1. Introduction

Known as “combustible ice”, NGH has the potential to provide a new source of clean and abundant energy, but there are still many challenges and technical difficulties in its exploitation and production. Depressurization technology has been proved as an economical and effective method for the production trials of an NGH reservoir, such as two offshore tests in Nankai Trough in Japan [1,2], two production trials in the Shenhu area in China [3,4] and others. Nonetheless, integrating depressurization with thermal stimulation emerges as a more promising strategy compared to solely employing either approach [5].

Up to now, several studies on fluid dynamics in NGH wells have been conducted, mainly focusing on flow assurance in deepwater drilling and electric submersible pump (ESP)-lifted gas drainage recovery, etc. J. Petersen launched a dynamic kick simulator to analyze the flow behavior of a drilling well and the possibility of hydrate formation during well control operations [6]. Fu et al. established mathematical models to analyze multiphase behavior and factors affecting the hydrate generation region in the deep water drilling process [7]. Wang et al. investigated the hydrate generation region and analyzed its influencing factors on annulus fluid flow characteristics during the same process [8]. Bassani et al. introduced the effects of the deposition of a hydrate layer of constant thickness on the pipe wall in a two-phase gas–liquid mechanistic slug flow model [9]. Wei et al. applied numerical calculation methods to acquire the non-equilibrium multiphase flow laws of marine NGH reservoirs by solid fluidization development [10]. ESP drainage gas recovery technology is mostly employed in NGH reservoirs with depressurization [1,2]. Sukru et al. developed a simulator to predict gas hydrate formation risks along a wellbore during the process of gas production from methane hydrates through an ESP production string [11]. Liu et al. established a gas–liquid flow model in an offshore NGH production system, considering the coupling of the wellbore, the formation and the ESP [12]. Ping et al.’s research sought to predict multiphase characteristics and assessed the risk of NGH regeneration in ESP-lifted NGH production wells [13].

However, little research has been reported to investigate the feasibility and flow dynamics of the fluid in jet pump drainage and NGH production wells using the combined depressurization and thermal stimulation method. There are many challenges to the drainage and extraction of a hydrate, such as low BHP, a high GLR, the presence of a hydrate, etc. [14]. Jet pump drainage and gas production technology is more feasible for complex fluids, such as those with a high GLR and high sand content, than an ESP and deserves more consideration than other drainage methods to unload hydrate wells [14,15]. This technology was used in a CO₂-CH₄ displacement experiment in Alaska North Slope [16]. Multiphase behavior in jet pump drainage and NGH production wells is the basis for the design of drainage and the optimization of heat injection parameters. Understanding the multiphase behavior of jet pump drainage and NGH production wells can significantly enhance their thermal stimulation efficiency. Therefore, it is necessary to study multiphase flow in jet pump drainage and NGH production wells.

In this paper, the feasibility and mechanism of jet pump drainage gas recovery technology for NGH development using the combined depressurization and thermal stimulation method were investigated. The multiphase flow dynamics of jet pump drainage and gas production wells were described in detail by mathematical modeling. In addition, the thermal stimulation parameters of jet pump drainage and NGH production wells were optimized. This study can provide valuable guidance for optimizing production and assessing the risk of hydrate regeneration of jet pump drainage and NGH production wells, as well as suggestions for hydrate prevention strategies.

2. Feasibility Analysis and Mechanism Study of Jet-Pump-Lifted NGH Wells

2.1. Feasibility Analysis

The combined depressurization and thermal stimulation technique beautifully blends the strengths of the individual depressurization and thermal stimulation approaches. It is remarkably more effective compared to a solo method like depressurization and can compensate for the energy utilization of the depressurization method [17]. Given the substantial energy consumption associated with heat loss when utilizing thermal stimulation in sea water wells, this combined approach appears ideal for offshore NGH extraction in marine areas [5].

A jet pump, which is a unique hydraulic device, uses the momentum exchange between power and formation fluid for smooth liquid flow without any moving parts. It is feasible for a wide range of displacement operations and applicable to a high GOR, high sand and other complex fluids, meeting the requirements of the drainage gas recovery of flooded gas wells. In addition, chemicals such as glycol can be added to jet pumps as a power fluid, inhibiting hydrate formation [14]. The sand resistance of a jet pump is higher than that of an ESP. At the same time, it can also avoid the problem of underloading stops of the pump caused by an insufficient liquid supply. When the well condition changes, the size of the throat and nozzle can be adjusted, and the operating cost is lower than that of an ESP [15]. Therefore, jet pump drainage gas recovery technology is more feasible than an ESP for the development of offshore NGH using the combined depressurization and thermal stimulation method.

2.2. Mechanism Study

As shown in Figure 1, the ground plunger pump is applied to increase the high pressure of the power fluid and pressurized hot water is injected from the tubing into the well to drive the downhole jet pump to perform drainage gas recovery. As for jet pump drainage and NGH production wells with the combined depressurization and thermal stimulation method, hot water injected from the tubing can be used as the high-pressurized power fluid for energy conversion between natural gas and water extracted from the reservoir. Natural gas and water are discharged to the surface together with the hot power fluid, which increases the temperature of the annulus fluid and greatly reduces the risk of hydrate regeneration in the annulus.

When the jet pump operates, the speed of high-pressurized power fluids is accelerated considerably through the nozzle, inducing a dip in the suction chamber’s pressure, as shown in Figure 2. Simultaneously, natural gas and water extracted from the hydrate reservoir are quickly drawn into the suction chamber inside the pump throat. After the injected high-pressurized power fluid and low-pressurized water and natural gas at the bottom of the well are combined in the throat, the mutual transfer of energy and mass takes place. Within the diffuser, the velocity and pressure of the blended fluid augment, propelling it upwards through the annulus [18].

3. Model Establishment and Solution

3.1. Establishment of Wellbore Flow Model of Jet-Pump-Lifted NGH Wells

Standard circulation is one of the jet pump configurations, which means that power fluid is pumped down through the tubing string and produced fluid is returned through the annulus [19]. For the standard circulating jet pump drainage and NGH production well, hot water is injected from the head of the tubing at the surface and passes through the jet pump nozzle into the annulus during the hydrate development process with the depressurization and thermal stimulation method. It is commingled with natural gas and water extracted from the hydrate reservoir in the annulus and then delivered to the surface. A flow schematic of the gas hydrate production system using the combined depressurization and thermal stimulation method is presented in Figure 3. Multiphase flow models of the tubing and annulus can be established, respectively, for the phenomenon of the countercurrent flow of heat exchange in the process of jet pump drainage and gas production based on the flow process of jet-pump-lifted NGH wells.

3.1.1. Continuity Equation

Based on the principle of mass conservation, the continuity equation for the fluid injected from the tubing can be expressed in Equation (1).

$${\displaystyle \frac{\partial {\rho }_{wi}}{\partial t}}+{\displaystyle \frac{\partial ({\rho }_{wi}{\nu }_{wi})}{\partial z}}=0$$

(1)

The continuity equation of the two-phase flow with the gas phase and the liquid phase in the annulus can be described in Equations (2) and (3).

$${\displaystyle \frac{\partial ({\rho }_g{E}_g)}{\partial t}}+{\displaystyle \frac{\partial ({\rho }_g{E}_g{\nu }_g)}{\partial z}}=q_g$$

(2)

$${\displaystyle \frac{\partial ({\rho }_{wi}{E}_{wi}+{\rho }_{wp}{E}_{wp})}{\partial t}}+{\displaystyle \frac{\partial ({\rho }_{wi}{E}_{wi}{\nu }_{wi}+{\rho }_{wp}{E}_{wp}{\nu }_{wp})}{\partial z}}=q_{wp}$$

(3)

3.1.2. Momentum Conservation Equation

The fluid flow in the jet pump drainage and NGH production well is mainly influenced by gravity, friction and a change in acceleration. According to the principle of the conservation of momentum, the wellbore pressure distribution model for a hot water injection well can be expressed in Equation (4):

$$-{\displaystyle \frac{d{P}_t}{dz}}={\displaystyle \frac{\partial ({\rho }_{wi}{\nu }_{wi})}{\partial t}}+{\displaystyle \frac{\partial ({\rho }_{wi}{\nu }_{wi}^2)}{\partial z}}-\mathrm{g}{\rho }_{wi}\cos \theta +{\displaystyle \frac{2f_r{\rho }_{wi}{\nu }_{wi}^2}{d_t}}$$

(4)

Similarly, the pressure distribution model for the gas–liquid two-phase flowing in the annulus can be obtained:

$$-{\displaystyle \frac{d{P}_a}{dz}}={\displaystyle \frac{\partial ({\rho }_m{\nu }_m)}{\partial t}}+{\displaystyle \frac{\partial ({\rho }_m{\nu }_m^2)}{\partial z}}+\mathrm{g}{\rho }_m\cos \theta +{\displaystyle \frac{2f_r{\rho }_m{\nu }_m^2}{d_{ea}}}$$

(5)

3.1.3. Energy Conservation Equation

It is assumed that the heat transfer is unsteady for the formation and steady for the tubing and annulus. In the process of jet pump drainage gas recovery, there is a phenomenon of the countercurrent flow of heat exchange between the hot water injected through the tubing and the commingled fluid in the annulus. The temperature of fluid in the flow process reaches thermal equilibrium with the temperature of the strings, cement and formation [20]. A heat balance diagram for the strings and formation is shown in Figure 4.

The heat balance relationship between the single-phase flow of hot water in the tubing and the gas–liquid two-phase flow in the annulus can be described as follows:

$$Q_t(z+dz)=Q_t(z)+Q_{ta}$$

(6)

Heat amount transfers from the annulus to tubing can be given by

$$Q_{ta}={\displaystyle \frac{C_{pa}}{A}}(T_a-T_t)dz$$

(7)

$$T_a=T_t+B{\displaystyle \frac{d{T}_t}{dz}}$$

(8)

where

$$A={\displaystyle \frac{w_a{C}_{pa}}{2\pi r_t{U}_{ta}}}$$

(9)

$$B={\displaystyle \frac{w_t{C}_{pt}}{2\pi r_t{U}_{ta}}}$$

(10)

The rate of heat transfer between the formation and the annulus is as follows:

$$Q_a(z+dz)-Q_a(z)=Q_{ta}-Q_{fa}$$

(11)

$$Q_{fa}={\displaystyle \frac{C_{pa}}{C}}(T_{ei}-T_a)dz$$

(12)

where

$$C={\displaystyle \frac{C_{pa}{w}_a}{2\pi }}({\displaystyle \frac{k_e+r_{co}{U}_a{T}_D}{r_{co}{U}_a{k}_e}})$$

(13)

3.2. Model Solution

3.2.1. Boundary Conditions

The fluid parameters at the wellhead of the tubing can be monitored, so the boundary condition for the tubing can be given as follows:

$$\{\begin{array}{c}{T}_{\mathrm{twh}}=T_{inj}\\ P_{\mathrm{twh}}=P_{\mathrm{inj}}\\ Q_{\mathrm{wiwh}}=Q_{\mathrm{inj}}\end{array}$$

(14)

Similarly, the boundary condition for the annulus can be given as follows:

$$T_{\mathrm{awh}}=T_{measure}$$

(15)

At the bottom of the jet pump well, the injected fluid is mixed with the extracted fluid from the hydrate reservoir. The Hasan–Kabir–model was used to calculate the temperature at the bottom of the annulus [15].

$$T_{abh}={\displaystyle \frac{w_a-w_t}{w_a{C}_{pa}}}{C}_{pcom}{T}_{eibh}+{\displaystyle \frac{w_t}{w_a{C}_{pa}}}{C}_{pt}{T}_{thb}$$

(16)

3.2.2. Methodology

The tubing fluid temperature model can be given by

$$CB{\displaystyle \frac{d^2{T}_t}{d{z}^2}}+D{\displaystyle \frac{d{T}_t}{dz}}-T_t+T_{ei}=0$$

(17)

where

$$D=C-{\displaystyle \frac{CB}{A}}-B$$

(18)

The general solution for Equation (17) is as follows:

$$T_t=\alpha e^{{\lambda }_{1}z}+\beta e^{{\lambda }_{2}z}+D{g}_G+g_{G}z+T_{eiwh}$$

(19)

The solution for the annulus fluid temperature model can be expressed by

$$T_a=(1+{\lambda }_{1}B)\alpha e^{{\lambda }_{1}z}+(1+{\lambda }_{2}B)\beta e^{{\lambda }_{2}z}+D{g}_G(B+D)+g_{G}z+T_{eiwh}$$

(20)

The coefficients in Equations (19) and (20) can be expressed in the following:

$$\alpha ={\displaystyle \frac{(T_{twh}-T_{eiwh}-D{g}_G)(1+B{\lambda }_2)e^{{\lambda }_{2}H}+g_G(B+D+H)+T_{eiwh}-T_{thb}}{(1+B{\lambda }_2)e^{{\lambda }_{2}H}-(1+B{\lambda }_1)e^{{\lambda }_{1}H}}}$$

(21)

$$\beta ={\displaystyle \frac{(T_{twh}-T_{eiwh}-D{g}_G)(1+B{\lambda }_2)e^{{\lambda }_{1}H}+g_G(B+D+H)+T_{eiwh}-T_{thb}}{(1+B{\lambda }_1)e^{{\lambda }_{1}H}-(1+B{\lambda }_2)e^{{\lambda }_{2}H}}}$$

(22)

$${\lambda }_1={\displaystyle \frac{-D+\sqrt{D^2+4BC}}{2BC}}$$

(23)

$${\lambda }_2={\displaystyle \frac{-D-\sqrt{D^2+4BC}}{2BC}}$$

(24)

3.2.3. Solution Process

The multiphase flow models of the tubing and annulus were constructed for the phenomenon of the countercurrent flow of heat exchange in jet pump drainage and gas production well with the Hasan–Kabir–model [15] in this study. The flowchart for calculating wellbore countercurrent heat transfer models is shown in Figure 5.

3.2.4. Model Validation

Up to now, no hydrate production test has been conducted with jet pump drainage and gas production technology. Fortunately, the physical process and heat transfer in the case in which heavy oil is produced by adding light oil are similar to this NGH production well extracted with the method of depressurization and hot water injection. Therefore, the proposed models can be validated using the case of a heavy oil well with the injection of light oil diluent in the Tahe oil field in China. The basic parameters for model validation are presented in

Table 1. Basic parameters for model validation.

Parameter	Value
Well depth (m)	5500
Surface temperature (°C)	20
Geothermal gradient (°C/100 m)	1.9
Density of heavy oil (kg/m3)	980
Density of light oil (kg/m3)	830
GOR (m3/m3)	25.3
Injection temperature (°C)	80
Injection rate (m3/d)	60
Production rate (m3/d)	75
Injection pressure (MPa)	3
Temperature at well bottom (°C)	123.4

.

As shown in Figure 6, the calculated temperature profile matches well with the measured data. After model validation, sensitivity analysis and parameter optimization can be conducted based on the proposed models.

4. Results and Discussion

4.1. Basic Parameters for Simulations

The basic parameters of the NGH reservoir and jet pump drainage and gas production well are collected from the Mallik permafrost site in Canada [21], as presented in

Table 2. Basic parameters for simulations.

Parameter	Value
Top depth of reservoir (m)	900
Well depth (m)	1110
Initial pressure of reservoir (MPa)	12.5
Surface temperature (°C)	−29
Gas specific gravity	0.643
Geothermal gradient (°C/m)	0.0379
Pump depth (m)	1000
Injection temperature (°C)	60
Injection rate (m3/d)	100
Gas flow rate (m3/d)	2000
Injection pressure (MPa)	1
Measured temperature at casing wellhead(°C)	55.5
Water flow rate (m3/d)	10

.

4.2. Analysis of Multiphase Flow Behavior in Jet Pump Drainage and NGH Production Wells

The multiphase flow behavior of the fluid in jet pump drainage and NGH production wells can be described by solving the multiphase flow models of the tubing and annulus for the countercurrent heat transfer process.

4.2.1. Temperature Profiles of Tubing and Annulus

The temperature distribution in the annulus is significantly more influenced by the tubing temperature than by the formation temperature since the overall heat transfer resistance between the tubing and the annulus fluid is much lower than that between the annulus fluid and the formation. The temperature distribution trends between the annulus and tubing in the jet pump drainage and NGH production wells with hot water as the power fluid are consistent, and the farther down the well bottom, the smaller the temperature difference, as displayed in Figure 7. The reason for this phenomenon is that the annulus fluid gains more heat from the tubing fluid than it loses to the surrounding area, and this difference in heat increases rapidly as the fluid in the annulus approaches the wellhead. The sudden change in the temperature profile at the bottom of the annulus in Figure 7 is caused by mixing natural gas and water from the gas hydrate reservoir with hot water injected from the tubing, making the derivative of the fluid temperature at the bottom of the annulus not zero [15].

4.2.2. Pressure Profiles in Tubing and Annulus

As shown in Figure 8, the pressure gradient of the annulus is smaller than that of the tubing, which is mainly caused by the decrease in fluid density in the annulus after gas from natural hydrate decomposition enters the annulus. When natural gas and water flow through the jet pump, there is a significant change in pressure at the discharge of the jet pump under its pressurizing influence.

4.2.3. Gas Volume Fraction Profiles in Annulus

With the upward flow of the commingled fluid in the annulus, the gas volume fraction gradually increases, which is caused by the pressure drop along the annulus, as shown in Figure 9.

4.2.4. Effect of Production Parameters on Flow Behavior

Gas production in the annulus is derived from the decomposition of the natural hydrate reservoir. When water production is fixed and gas production increases, the pressure gradient in the annulus decreases and the pressure drop slows down, as shown in Figure 10. The larger the GWR, the higher the pressure when flowing to the wellhead at a fixed BHP. Meanwhile, the increases in gas production can lead to changes in the physical properties of fluid and temperature distribution. An increase in gas production has a much greater effect on the pressure gradient than on the temperature gradient due to the fact that the difference between the density of the gas and the liquid is more sensitive to pressure than the difference in the specific heat capacity of the gas and the liquid is sensitive to temperature.

4.3. Optimization of Thermal Stimulation Parameters

The temperature and pressure distribution in the wellbore of the jet pump drainage and NGH production wells are affected by injection conditions. Based on the sensitivity analysis of the multiphase flow behavior of the fluid in the jet pump drainage and NGH production wells, the thermal stimulation parameters of the jet pump wells can be optimized.

4.3.1. Injection Temperature

As displayed in Figure 11, as the injection temperature ascends, both the temperature within the annulus and tubing correspondingly increase. Increasing the injection temperature can mitigate the threat of hydrate reformation within the annulus.

The temperature of the injected hot water is related to the risk of hydrate regeneration in the annulus during the jet pump drainage process of NGH with the combined depressurization and thermal stimulation method. The simulation results of this case well show that the closer to the wellhead, the greater the difference between the temperature of the fluid in the annulus and the phase equilibrium temperature of NGH, and therefore, the lower risk of hydrate regeneration, as shown in Figure 12. It is recommended that the temperature of injected hot water should be higher than 60 °C, which can effectively reduce the risk of hydrate regeneration for this case well. In addition, adding ethylene glycol to the power fluid of the jet pump is also an effective means to inhibit hydrate reformation in the annulus.

4.3.2. Injection Rate

As the injection rate increases, a significant rise in temperature is observed in both the tubing and annulus. In particular, the temperature distribution patterns across these two areas gradually align with a more linear trend as the injection rate reaches 500 m³/d, as displayed in Figure 13. Moreover, an increase in the injection rate can effectively circumvent possible threats from hydrate reformation in the annulus. When the injection rate increases, the injection pressure in the tubing and annulus also increases, as shown in Figure 14.

The difference between the phase equilibrium temperature of the hydrate at different injection rates and the temperature of fluid in the annulus are compared in Figure 15. The phase equilibrium temperature in the annulus increases with the increase in the injection rate, and there is a risk of hydrate reformation at the bottom of the annulus when the injection rate is very low. The simulation results of this case well with jet pump drainage and NGH production show that when the injection rate is greater than 300 m³/d, the phase equilibrium temperature of NGH is higher than the fluid temperature in the annulus and the risk of hydrate reformation in the wellbore can be eliminated.

4.3.3. Injection Pressure

As presented in Figure 16, it is apparent that an escalating injection pressure has a substantial influence on the pressure profile of both the tubing and the annulus. As can be seen, with increased injection pressure, the annulus pressure decreases, reducing the potential risk of hydrate reformation in the annulus.

From Equation (19), it can be seen that the temperature profile inside the tubing is related to the mass flow rate of hot water in the tubing, injection temperature, and other static factors. Due to the weak compressibility of the water, resulting in little change in density, regarding the mass flow rate, injection pressure has minimal impact on the temperature distribution along the tubing because the difference between the density of the gas and the liquid is more sensitive to pressure than the difference in the specific heat capacity of the gas and the liquid is sensitive to temperature. On the other hand, the annular temperature distribution is related to the temperature profile along the tubing and the surrounding formation temperature. Therefore, injection pressure has a negligible impact on the temperature distribution along the annulus when the temperature change in the tubing is very small and the surrounding temperature is constant.

5. Conclusions

The following conclusions can be reached:

(1) Compared with an ESP, jet pump drainage and gas production technology is more feasible for offshore NGH extraction with the combined depressurization and thermal stimulation method.

(2) The temperature distribution trends between the annulus and tubing of the jet pump drainage and NGH production wells with hot water as the power fluid are consistent, and the farther down the well bottom, the smaller the temperature difference. The pressure gradient in the annulus is smaller than that in the tubing and the gas volume gradually increases with the upward flow of the commingled fluid within the annulus.

(3) Despite the potential improvements in thermal stimulation effects by augmenting the injection rate and temperature of hot water, it was observed that increased injection pressure influences the pressure curve in both the tubing and the annulus without noticeably altering the temperature curve in the wellbore.

(4) There is a risk of hydrate reformation at the bottom of the annulus when the injection rate or injection temperature is low. Increasing either the injection rate or the temperature of hot fluid proves to be a robust strategy for mitigating the risk of hydrate reformation during the operation of jet pump drainage and NGH production wells.