A Numerical Investigation on Kick Control with the Displacement Kill Method during a Well Test in a Deep-Water Gas Reservoir: A Case Study

Abstract

The efficient exploitation of marine oil and gas resources holds significant potential to mitigate the current severe energy crisis. Regrettably, incidents, such as gas kick and even blowouts, can significantly impact normal development activities. The displacement kill method is one effective strategy for well control in deep-water areas. In this study, the detailed mathematical method for determining kill parameters involved in the kill operation by using the displacement kill method was proposed. Of course, this includes both cases: one where the kill fluid leaks during the kill process and another where no leakage occurs. Meanwhile, its applicability was verified through comparison with experimental results. Then, evolution characteristics of kill parameters, when killing fluid leakage occurs and when it does not occur, were analyzed. Finally, factors, such as pit gain and shut-in casing pressure, affecting the kill parameters of kill operation, were explored. It was found that the experimental and calculated results show great similarity, although there are slight differences between them. The total kill time in the simulation is 44 s shorter than that in the verification experiment. This indicates that the model established in this study is suitable for simulating the process of kill operation using the displacement kill method. In addition, the investigation results show that leakage of kill fluid increases the difficulty of the kill operation and prolongs the operation time. The number of kill cycles in the presence of kill fluid leakage is one more than that when there is no fluid leakage, resulting in an additional 70 min of total duration. Furthermore, the increase in pit gain and the rise in shut-in casing pressure can also pose challenges to the kill operations. The total kill time will be extended by 164 min when the mud pit gain increases from 20 m³ to 50 m³. The number of kill cycles rises by two when the shut-in casing pressure is increased from 5 MPa to 20 MPa. To ensure the safety of the drilling operation in abnormally high-pressure reservoirs, it is crucial to monitor parameters such as casing pressure during the drilling process and timely well control measures.

1. Introduction

It is widely acknowledged that fossil fuels, such as oil and gas, will remain the primary energy sources constraining the development of human society for a long time in the future [1,2,3]. However, numerous mature onshore oil fields in the central and eastern regions of China have experienced a significant decline in oil production in recent years [4,5,6,7]. Taking Daqing Oil Field as an example, its oil production has dropped year by year from 56 million tons in the peak period (in 1996) to 30 million tons in 2022 [8]. It is predicted that its oil production will drop sharply to 8 million tons in 2060 [9,10,11,12]. Meanwhile, the increase in production of the newly discovered oil fields in Western China failed to make up for the widespread production decline of these oil fields [13,14,15]. In recent years, China has had to rely on imports for more than 70% of its crude oil demands and more than 40% of its natural gas demands [16,17]. In 2023, the overseas dependence of crude oil was expected to exceed 80%. It is no exaggeration to say that China’s domestic energy security has clearly been threatened [18]. Fortunately, the efficient exploration and development of unconventional oil and gas resources, such as shale gas and offshore oil and gas resources, has become an effective way to alleviate this situation [19,20,21].

Nevertheless, a series of issues or accidents that endanger the safety of the development operation are extremely likely to occur during oil and gas production in the ocean (especially in deep-water areas) [22,23,24,25]. Among them, gas kick (or blowout), which is likely to occur during the drilling operation in high-pressure gas reservoirs, is a typical one [26,27,28]. This issue is caused by the invasion of high-pressure gas from the reservoir into the wellbore annulus under the negative pressure difference between bottom-hole pressure and reservoir pressure [29,30]. For gas wells in deep-water areas, the circulation pipeline of drilling fluids is extremely long, and high-pressure gas in the annulus continuously expands during its migration to the platform [31,32]. The excessive annular pressure caused by gas expansion not only affects the integrity of the wellbore in weak positions, such as casing shoes, but also leads to blowout. Undoubtedly, the severe gas kick naturally poses a significant threat to the drilling operation. For most ordinary wells, gas kick can be effectively controlled by the conventional well killing methods (such as the driller’s method) as long as it was detected in time [33,34]. However, conventional well killing methods are occasionally inadequate for controlling gas kick and blowout occurs in gas wells in deep-water areas. The common conventional methods, such as the driller method, are suitable for drilling operations in areas with simple geological conditions and a well-defined pressure system. However, the geological conditions and pressure systems of oil and gas reservoirs, especially gas reservoirs in deep-water areas, are complex [35,36]. This is especially true in scenarios where the drill string is absent from the wellbore or the drill bit is positioned near the wellhead. In other words, conventional well killing methods are not suitable for well control of oil and gas wells in deep-water areas [37].

Up till now, numerous investigations on the use of unconventional well killing methods for kill operations in deep-water areas have been conducted, and some progress has been made. To name a few, Noynaert and Schubert (2005) simulated blowout control of gas wells in an ultra-deep-water area with the self-developed simulator when dynamic well killing technology was used [38]. This investigation determined the dynamic kill requirements for controlling blowout based on a series of relief well parameters. Yuan et al. (2023) optimized the operational parameters of the kill operation for well kill in a dee-water area based on the dynamic well killing method [11]. It reveals that this method was effective at controlling blowout in worst-case scenarios. Ren et al. (2015) calculated the displacement amount during the dynamic kill process in a deep-water drilling operation after the gas kick occurred [39]. It was found that the investigation can provide theoretical support for solving the complex issue of deep-water gas kick and blowout. The displacement kill method is one of the unconventional well killing methods commonly used in high-pressure gas wells [40]. Figure 1 presents the schematic diagram of the displacement kill method. As can be seen in Figure 1 left, the kill fluid is first injected into the annular space, and its droplets gradually fall to the bottom. Meanwhile, the liquid level in the annulus gradually rises, and gas discharge in the annulus leads to a decrease in annulus pressure (see Figure 1 right). The above-mentioned process is continuously circulated to gradually reduce the annular pressure. This process needs to continue until the wellbore is filled with killing fluid. Unfortunately, few studies on kill operation of high-pressure gas wells in deep-water area based on the displacement killing method have been intensively conducted. Even if there are, most of the relevant investigations are analyses of kill engineering cases that have occurred. It is impossible to provide effective and substantive support for subsequent kill operations at all. Moreover, there are no investigations on a kill strategy for a well test of a high-pressure gas well in a deep-water area.

There are many challenges (such as the narrow safe mud weight window) in the test process of offshore high-pressure gas wells. These challenges can easily lead to gas kick or even blowout, threatening the smooth implementation of the well test operation. At present, there is a scarcity in the number of kill techniques that can be used for reference. Therefore, it is urgent to propose a calculation method for kill parameters during the well test of gas wells in deep-water areas. In the present work, the method for determining kill parameters, such as injection volume, injection pressure, and replacement period during the kill operation with the displacement well kill method, was proposed. Then, the variation patterns of kill parameters mentioned above under different working conditions (such as presence or absence of kill fluid leakage) were simulated. At the same time, its mechanism is analyzed. In fact, the method for determining the well killing parameters used in the well testing process is also applicable to the normal gas reservoir development process, with the only difference being the research objects. Therefore, this study also intends to provide references for well control and the kill operation in normal deep-water oil and gas development.

To highlight the innovation of this study, the highlights are summarized as follows:

(1)

The determination method of the parameters related to the kill operation using the displacement method with and without considering leakage has been proposed.

(2)

A sensitivity analysis was conducted on the kill case during the well test process of the deep-water gas reservoir.

2. Determination of Kill Parameters in Kill Operation

Three kill parameters need to be determined for the kill operation with the displacement kill method: (1) injection volume and injection pressure, (2) single gas release, and (3) displacement period. In this section, the determination method of kill parameters for two situations, kill fluid leakage and no fluid leakage, were discussed or illustrated separately. In this study, the dissolution of gas in liquids needs to be ignored. In addition, the compressibility of liquids in the annulus is not taken into account.

It is necessary to make some assumptions before numerical modeling. In this study, the following assumptions were made

(1)

Throughout the kill operation, both the gas and liquid phases in the wellbore remain macroscopically stationary, and do not flow.

(2)

The compressibility of the gas and liquid phases in the wellbore should be ignored. Furthermore, their properties (such as the rheology) are not affected by changes in temperature and pressure.

(3)

The rate is constant for both the fluid injection and the gas discharge operations.

2.1. Kill Parameters with Kill Fluid Leakage

(1)

Calculation of kill parameters in the first round

If the reservoir is unconsolidated, kill fluid leakage accidents are easy to occur in the kill operation [39,41]. In this case, the injection volume should be properly controlled, and the maximum annulus pressure should be lower than the leakage/fracture pressure [42,43]. The first injection volume of the kill fluid can be determined by Equation (1).

$$\left\{\begin{array}{l}{V}_{\mathrm{Inj}1}=V_1-{\displaystyle \frac{-B_1+\sqrt{B_1^2+4A_1{C}_1}}{2A_1}}\\ V_1={\displaystyle \frac{Z_{1}nR{T}_1}{P_1}}\\ A_1={\displaystyle \frac{0.001{\rho }_{\mathrm{m}}g}{q}}\\ B_1=P_L-{\displaystyle \frac{0.001{\rho }_{\mathrm{m}}g{V}_1}{q}}\\ C_1={\displaystyle \frac{Z_2{P}_1{V}_1}{Z_1}}\end{array}\right.$$

(1)

The height of liquid column formed in the annulus by the kill fluid injected for the first time can be calculated.

$$H_1={\displaystyle \frac{V_{\mathrm{Inj}1}}{q}}$$

(2)

The hydrostatic pressure generated by the injected kill fluid can be represented as follows:

$$\Delta P_1=0.001{\rho }_{\mathrm{m}}g{H}_1$$

(3)

During the first round of fluid injection, gas in annulus is discharged from wellhead when kill fluid reaches the bottom of wellbore. The volume of gas (standard state) discharged from annulus in the first round of fluid injection can be determined.

$$V_{\mathrm{dis}1}={\displaystyle \frac{Z_0{T}_0{V}_{\mathrm{total}}}{P_0{T}_1}}\left({\displaystyle \frac{P_2}{Z_2}}-{\displaystyle \frac{\left(P_{\mathrm{p}}-\Delta P_1\right)}{Z_{21}}}\right)$$

(4)

(2)

Calculation of kill parameters in the second round

When the bottom-hole pressure is equal to the pore pressure, the first round of gas discharge should be stopped. Then, the second round of kill fluid injection can be started. The amount of kill fluid required to be injected into the annulus in the second round is calculated as follows:

$$\left\{\begin{array}{l}{V}_{\mathrm{Inj}2}=-{\displaystyle \frac{-B_2+\sqrt{B_2^2+4A_2{C}_2}}{2A_2}}\\ A_2={\displaystyle \frac{0.001{\rho }_{\mathrm{m}}g}{q}}\\ B_2=P_{\mathrm{L}}-\Delta P_1-{\displaystyle \frac{0.001{\rho }_{\mathrm{m}}g{V}_2}{q}}\\ C_1={\displaystyle \frac{Z_3{P}_{21}{V}_2}{Z_2}}\end{array}\right.$$

(5)

Correspondingly, the height of the liquid column and the hydrostatic pressure generated by injected the kill fluid in the annulus in the second round are expressed as Equations (6) and (7), respectively.

$$H_2={\displaystyle \frac{V_{\mathrm{Inj}2}}{q}}$$

(6)

$$\Delta P_2=0.001{\rho }_{\mathrm{m}}g{H}_2$$

(7)

The volume of gas (standard state) discharged from the annulus in the second round of fluid injection can be determined by Equation (8).

$$V_{\mathrm{dis}2}={\displaystyle \frac{Z_0{T}_0{V}_3}{P_0{T}_1}}\left({\displaystyle \frac{P_3}{Z_3}}-{\displaystyle \frac{\left(P_p-\Delta P_1-\Delta P_2\right)}{Z_{31}}}\right)$$

(8)

Herein, only the determination method of kill parameters in two displacement cycle is given. Notably, the kill operation needs to continue until all the gases in the annulus are discharged.

(3)

Determination of kill times and the kill cycle

The minimum number of well killing operations (c) and the longest kill cycle (t) can be estimated with Equations (9) and (10).

$$c={\displaystyle \frac{H}{H_1}}$$

(9)

$$t=c\left(t_1+t_2\right)$$

(10)

2.2. Kill Parameters without Kill Fluid Leakage

If the reservoir sediments are well cemented, leakage accidents of the kill fluid are less likely to occur during the kill operation [44,45]. In this case, there is no need to consider the risk of kill fluid leakage. However, the situation where maximum annulus pressure (P_amax, in MPa) exceeds the pressure-bearing capacity of the wellhead equipment should be avoided. For calculation of the kill parameters in both cases of kill fluid leakage and no leakage, the only difference lies in the calculation method of the fluid injection volume.

(1)

Calculation of kill parameters in the first round

The injection volume of kill fluid in the first injection round can be determined by the following:

$$V_{\mathrm{Inj}1}=V_{\mathrm{a}\max }\left(1-{\displaystyle \frac{Z_2{P}_1}{Z_1{P}_{\mathrm{a}\max }}}\right)$$

(11)

Calculation of liquid column height in the annulus (H₁) generated by the injected kill fluid and the hydrostatic pressure can be implemented by Equations (2) and (3), respectively. When the first round of injection of the kill fluid reaches the wellbore bottom, some gas in the annulus needs to be discharged. Similarly, gas volume required to be discharged after the first round of fluid injection can also be determined by Equation (4).

(2)

Calculation of kill parameters in the second round

The volume of kill fluid that needs to be injected into annulus in the second round can be expressed as follows:

$$V_{Inj2}=V_{a\max }-{\displaystyle \frac{Z_3{P}_{21}{V}_2}{Z_2{P}_{a\max }}}$$

(12)

where, all parameters involved in Equation (12) have already been illustrated in Section 2.1.

Then, both height of the liquid column and the hydrostatic pressure generated by the second round of kill fluid injection can be calculated using Equations (6) and (7), respectively. Similarly, the volume of gas discharged from the annulus after the completion of the second round of kill fluid injection can also be obtained through Equation (8).

(3)

Determination of kill times and the kill cycle

The minimum number of well killing operations (c) and the longest kill cycle (t) can be estimated with the equations (Equations (9) and (10)) presented in Section 2.1.

Based on the above model, kill parameters can be determined, and the workflow for it is displayed in Figure 2.

3. Applicability Verification of Investigation Methodology

3.1. Basic Data for Kill Simulation

The investigation well involved in this study is located in the northern slope of Baiyun Sag, Pearl River Mouth Basin of the Northern South China Sea. In this area, abnormal high-pressure gas reservoirs are widely spread, and well control during drilling operation is an important issue [46,47,48]. For the investigation well, the wellbore structure is shown in Figure 3, and the basic information of both the wellbore and reservoir are displayed in

Table 1. Basic data for simulating the kill operation.

Parameters		Value
Well depth, m		3550
Water depth, m		186.5
30″ conductor	Size, mm	762
	Setting depth, m	253.4
13-5/8″ casing	Size, mm	340
	Setting depth, m	805
9-7/8″ casing	Size, mm	248.48
	Setting depth, m	3495.5
Reservoir depth, m		3143
Internal pressure strength, MPa		32.98
Casing collapse resistance, MPa		47.38
Permissible casing pressure, MPa		21.0
Surface temperature of seawater, °C		26.6
Geothermal gradient, °C/100 m		3.0
Pore pressure, MPa		32.98
Leakage/fracture pressure, MPa		45.0
Mud weight, g/cm3		1.18
Initial drilling fluid height, m		2050

. During the well test process of this gas well, the TCP (Tubing Conveyed Perforating) + APR (Annulus Pressure Responsive) combined test technology was used. Therefore, the basic data of the test string in the investigation well is shown in

Table 2. The string parameters for well test of a gas well in the South China Sea.

No.	Test String	Outer Diameter, mm	Inner Diameter, mm	Length, m	Depth, m
1	Flowhead	-	-	-	−1.11
2	Lubricator valve	311.15	76.20	1.78	10.08
3	5″ drill pipe	127.00	108.60	191.85	201.93
4	Centraliser	311.15	76.20	1.82	203.75
5	Shear joint	127.00	76.20	0.71	204.46
6	Subsea tree	311.15	76.20	1.26	205.72
7	Expansion joint	127.00	57.15	18.08	3227.10
8	RD circulation valve	127.00	56.00	1.73	3286.82
9	OMNI valve	127.00	56.00	7.46	3294.28
10	LPR-N valve	127.00	56.00	4.83	3310.14
11	Safety joint	154.00	60.00	1.23	3318.89
12	RTTS packer	200.00	60.00	2.18	3321.07
13	Perforating gun	177.80	-	18.00	3373.00

.

In this study, a preliminary program for design and calculation of kill parameters was compiled with VB.NET when the displacement kill method was used, and the kill operation was simulated. With this program, the variation pattern of kill parameters (such as annulus pressure and total injection volume) in the kill operation when the displacement kill method was used were explored. The program interface is shown in Figure 4. From Figure 4, it can be identified that although the interface of this program is simple, it is fully functional. Based on this program, the influence of various factors affecting kick control with the displacement kill method can be explored. Moreover, the simulation results obtained using this program can provide reference for the design of the well killing operation.

3.2. Applicability of the Investigation Methodology

It is necessary to verify the applicability of both the self-designed computer program and the investigation methodology before using it for a case study. In this section, this purpose is achieved by comparing the results obtained using the program with the experimental results obtained using the self-made well control system. The self-made well control system was illustrated as Figure 5. It can be clearly seen from Figure 5 that the experimental system actually occupies an extremely large area, and it is placed in a laboratory covering an area of 200 m². Furthermore, the composition of this experimental system is also extremely complex. As was observed in Figure 5, the well control experimental system mainly includes six subsystems. They are the fluid (gas, liquid) storage system, power system, fluid metering and control system, high-pressure annulus experiment module, gas–liquid separation system and back pressure control system. Among them, the fluid storage system includes a water tank (effective volume: 2 m³) and a gas tank (pressure: 10 MPa, volume: 100 L). The main component of the power system is a high-pressure air compressor with an outlet pressure of up to 10 MPa. In addition, the flow rate of gas and liquid in the system is realized by an electromagnetic flowmeter whose measurement accuracy is 0.5 L/min. The high-pressure annulus experimental module is a transparent plexiglass tube with a length of 15.0 m placed vertically. The inner diameter of the outer tube within the annular space is 120.0 mm, and the outer diameter of the inner tube is 63.0 mm. Based on this experimental system, the applicability of the investigation methodology in this work was verified.

For ensuring experimental safety, nitrogen (N₂) was injected into the wellbore annulus to approximate the gas kick experienced during the drilling operations. In the experiment, the injection rate of the kill fluid and the discharge rate of gas were 10 L/s and 0.32 m³/min, respectively. Additionally, the height of the gas phase in the annulus is 12.5 m. In the experiment, the position of the gas–liquid interface in the annulus was measured every 2.5 min. The comparative results between the simulation and experimental data are illustrated in Figure 6. As can be observed in Figure 6, almost all the experimental results are close to the variation curve of the gas–liquid interface obtained by simulation. This demonstrates that the model and investigation methodology proposed in this study are capable of simulating well kill operations using the displacement method. However, the end time of the well kill operation in the experiment was slightly later than that in the simulation. In the simulation, it takes approximately 856 s for the invading gas within the annulus to be completely discharged. However, in the experiment, this time is extended to at least 900 s. This phenomenon can be attributed to the assumption that the injection rate, gas discharge rate, and other parameters were assumed to remain constant throughout the simulation. However, these parameters fluctuated within a certain range in experiment.

4. Evolution Characteristics of Kill Parameters with and without Kill Fluid Leakage

Only through an in-depth analysis of the variation patterns/characteristics of kill parameters during kill operations can the related design of kill operations be executed more effectively. The evolution of casing pressure, injection volume, and liquid column height during kill operations was investigated for the case of considering kill fluid leakage, and the results was presented in Figure 7. As observed in Figure 7, three stages are involved in any kill cycle: the injection of kill fluid, fluid fall, and the discharge of invading gas in the annulus. The function of the first two stages is to allow the kill fluid to be injected into the annulus and occupy part of its space. However, it should be noted that the sum of the hydrostatic pressure and the casing pressure must not exceed the leakage pressure. The final stage of each cycle is to release the compressed gas in the annular space. Notably, when the gas is released in each cycle, the sum of the casing pressure and the hydrostatic pressure cannot be lower than the formation pressure. The duration of the three stages involved in one cycle varies. In the first cycle in Figure 7, the duration of the injection stage is 94.9 min, and the duration of the discharge is only 32.5 min. The latter is obviously faster than the former. The fall of the kill fluid from the wellhead to the gas–liquid interface in the annulus occurs along with the first stage, the duration of this stage is 19.5 min in the first cycle. For the default investigation case, almost all the gas invading the annulus can be completely displaced through four rounds of the above-mentioned kill cycle using the displacement kill method. The entire kill operation takes about 420 min.

In Figure 7, we can also see that the casing pressure increases continuously during the injection of kill fluid into the annulus in each cycle. This occurs because, as the kill fluid is injected, the space occupied by the gas in the annulus is continuously compressed. Although during this process, a portion of the mixture of the kill fluid and drilling fluid leaks into the reservoir. Taking the first cycle as an example, 13.4 m³ of kill fluid was injected into the annulus, filling a length of 663 m in it. The gas above the liquid level in the annulus is compressed, and the casing pressure increases from 10 MPa to 17.3 MPa during this process. After the throttle valve at the wellhead is opened, the compressed gas inside the annulus is released, causing the casing pressure to decrease accordingly. At the end of the first cycle, the casing pressure decreased to 5.1 MPa, and the distance between the liquid level and the down-hole increased to 2713 m. With the continuous injection of kill fluid during the subsequent kill operation, the position of the gas–liquid interface in the annulus gradually rises. Following four cycles of kill operations, the gas–liquid interface advanced to a position 12 m from the wellhead. Finally, the 12 m long gas column near the wellhead was discharged by injecting the kill fluid while keeping the valve open. The highest and lowest values of casing pressure gradually decrease during each injection exhaust cycle of the entire kill operation.

Figure 8 presents the evolution of casing pressure, injection volume and liquid column height during kill operation when no kill fluid leakage occurs. By comparing Figure 7 and Figure 8, it can be clearly observed that the duration of the kill operation is significantly shortened in the absence of kill fluid leakage. Without kill fluid leakage, the gas in the annulus can be completely discharged in just 350 min, which is 70 min shorter than the result displayed in Figure 7. This should be attributed to the lower amount of injected kill fluid when there is no leakage. Consequently, the number of required kill cycles will be reduced. The number of required kill cycles in the absence of kill fluid leakage is four, one fewer than in the presence of leakage. Moreover, another difference between the results in Figure 7 and Figure 8 is the casing pressure after fluid injection in each kill cycle. Without kill fluid leakage, this casing pressure is a constant value (i.e., permissible casing pressure, 21.0 MPa). This is because, in formations where kill fluid leakage is less likely to occur, the limiting factor for the injection volume of kill fluid is the permissible casing pressure. On the premise of ensuring that the bottom-hole pressure is lower than the leakage pressure, the maximum casing pressure should reach its permissible value at the end of each injection of the kill fluid. However, in formations prone to kill fluid leakage, the limiting factor for the injection volume of kill fluid is the leakage pressure. Under the premise that the maximum bottom-hole pressure does not exceed the leakage pressure, the casing pressure gradually decreases with the increase in hydrostatic pressure during the kill operation (see Figure 7).

5. Sensitivity Analysis and Discussion

5.1. Effect of Pit Gain

Factors such as gas invaded volume and initial casing pressure will seriously affect the construction parameters of kill operations [49,50]. Conducting a comprehensive analysis of these factors and elucidating their mechanisms of influence can offer valuable insights for the engineering design of kill operations. Pit gain refers to the volume of drilling fluid in the annulus that is replaced by the gas kick before shut-in. Generally speaking, this parameter (i.e., pit gain) can indirectly reflect the volume of gas kick in the annulus. A higher pit gain means more gas invaded into the annulus during the drilling operation. Figure 9 illustrates the schematic diagram that reveals the mechanism underlying the discrepancy in pit gain when the amount of invading gas is varied. From what we can see in Figure 9, the amount of drilling fluid in the mud pit is constant, and the pit gain is almost zero throughout the normal drilling operation. However, if a lot of reservoir gas invades the annulus during the drilling operation, there will be a long gas column in the annulus. In this way, the space previously occupied by the drilling mud in the annulus will be occupied by these gas columns. As a result, the drilling mud will be displaced into the mud pit, which will lead to a notable increase in the mud pit gain. Accordingly, more kill fluid is needed to displace and discharge these gases.

The kill parameters, when the quantity of gas invading into the annulus (i.e., pit gain) is different, were determined, and the results are shown in Figure 10. As illustrated in Figure 10, when the pit gain is only 20 m³, the length of the gas column in the annulus is relatively short. Only two kill cycles are needed to completely discharge the reservoir gases that have invaded the annulus, and the total kill time is 296 min. In this instance, the injection of 10.5 m³ of kill fluid raised the liquid level in the annulus to 3080 m from the bottom of the well in the first kill cycle. In the second cycle, only about 9.5 m³ of kill fluid needs to be injected to discharge the remaining gas in the annulus. As the pit gain increases, the difficulty of the kill operation will correspondingly rise, and the requisite total time will also be significantly extended. When the increment of the mud pit increases to 30 m³ and 50 m³, three and four kill cycles are required to do that, respectively. The total time of the corresponding kill operation is extended to 350 min and 460 min, respectively, which is 54 min and 164 min longer than that when pit gain is 20 m³. Furthermore, as the gas column rises within the circulating drilling fluid, it will undergo an expansion in volume and experience a surge in pressure, further posing a threat to the safety of drilling operations. The more gas that invades the annulus, the greater the threat it poses to drilling safety [51]. Therefore, it is crucial to monitor the drilling parameters, such as casing pressure during the drilling process, and promptly address the drilling accidents, such as gas kick [52].

It can also be seen from Figure 10 that when the pit gain is low, the minimum casing pressure of each cycle during the entire kill operation will decrease rapidly. When the pit gain is only 20 m³, the casing pressure decreased to 1.8 MPa at the end of the first kill cycle (i.e., when the first gas discharge is completed). By the end of the second gas discharge, the casing pressure was close to zero. However, when the pit gain is high, this casing pressure drop is not so rapid, but gradual. As observed in Figure 10a, if the mud pit gain increases to 30 m³, the minimum casing pressure at the end of the first kill operation is 5.1 MPa. By the end of the second round of the kill cycle, it dropped to the level at the first round of kill operation in the previous case (i.e., the case where the pit gain is 20 m³). For the case where the pit gain is 50 m³, this phenomenon is more significant. Attributed to the low casing pressure at the end of the initial kill cycle under low pit gain, the gas discharge stage in each kill cycle requires an extremely long duration. However, due to the small volume of kill fluid required in each cycle, the time required for injection of kill fluid is significantly short. On the contrary, when the pit gain is high, the injection time and gas discharge time in kill cycle are opposite to it.

5.2. Effect of the Shut-In Casing Pressure

Shut-in casing pressure is another factor affecting the kill parameters of the kill operation in the displacement kill method [53,54]. The effect of shut-in casing pressure on the kill operation in the displacement kill method was investigated, and the results were presented in Figure 11. As can be seen in Figure 11, if the shut-in casing pressure is high, more kill cycles are required. Correspondingly, the duration of the entire kill operation will be long. When the shut-in casing pressure is only 5.0 MPa, only two kill cycles are needed to discharge the gas in the annulus, and the duration of the entire kill operation is 313 min. If the shut-in casing pressure increases to 10 MPa, the number of complete well killing cycles required becomes three, and the duration of the well killing operation is extended to 350 min. When the shut-in casing pressure continues to increase to an astonishing 20 MPa, the required number of complete kill cycles and the duration of the kill operation increases to 4 and 414 min, respectively. This is because a higher shut-in casing pressure means more reservoir gas is locked in the gas column within the annulus. The discharge of more gas from the wellbore will inevitably take longer. Meanwhile, the casing pressure does not decrease instantaneously, but gradually decreases with the reciprocating cycle of fluid injection and gas discharge. Therefore, for the case of higher shut-in casing pressure, more instances of step-by-step pressure reduction (i.e., kill cycles) are required.

This also illustrates a fact from another perspective, namely that the drilling process of an abnormal high-pressure reservoir should be well monitored to avoid uncontrollable gas kick or blowout. In addition to the above-mentioned difference in the time required for kill operation, there is another difference that needs to be noted: the first kill cycle. As observed in Figure 11, when the shut-in casing pressure is low, it takes a long time to increase the casing pressure to the permissible value by injecting the kill fluid. If the shut-in casing pressure is only 5.0 MPa, it takes 138 min for the casing pressure to increase from the shut-in casing pressure to its permissible value. Even when the shut-in casing pressure is 10 MPa, this time still lasts for 91 min. On the contrary, if the shut-in casing pressure is high, the process of increasing the casing pressure to the allowable safe casing pressure by injecting the well control fluid is very simple. Accordingly, this process will not take a long time. When the shut-in casing pressure is 20.0 MPa (which is close to the permissible value), the injection of 1.7 m³ of kill fluid within 10 min allows the casing pressure to reach the permissible value.

6. Conclusions

In the present work, the method for determining the kill parameters in the kill operation with the displacement method was developed, and its applicability was then verified. Moreover, evolution characteristics of kill parameters when killing fluid leakage occurs and when it does not occur were analyzed, and factors affecting kill operation were also investigated. The main conclusions obtained are as follows:

(1)

The method for determining kill parameters mentioned in the study is applicable for the corresponding simulation analysis. In simulation and experiment, it takes 856 s and 900 s, respectively for the gas inside the annulus to be completely discharged, with a time difference of only 44 s. This is due to fluctuations in the control of experimental conditions during the experimental process. So, this time difference is acceptable.

(2)

The fluid leakage during the kill process will not only increase the cost but also cause an increase in the number of well killing cycles and an extension of the operation time. When there is no leakage of kill fluid, injecting 30 m³ of kill fluid three times within 350 min can completely discharge the gas and relieve the danger. However, the total operation time is extended to 420 min, and the total volume of injected fluid also increases to 32.4 m³ in the presence of fluid leakage.

(3)

A high pit gain indicates a significant amount of gas and a long gas column in the annulus, thereby complicating the kill operations. If the pit gain increases from 20 m³ to 50 m³, the total time used for the kill operation extends by 164 min, and the decrease in casing pressure significantly slows down. This indicates that accurate and real-time monitoring of drilling parameters, such as mud pit increment, during the drilling process is of great significance for ensuring drilling safety.

(4)

For high shut-in casing pressure, although the casing pressure can be raised to its permissible value in a very short time in the first kill cycle, the total operation time was long. This occurs because the casing pressure gradually decreases with each successive kill cycle during the kill process by using the displacement method.

Nevertheless, there are still many deficiencies that need to be supplemented in subsequent studies within this study. Among them, it is necessary to compare the results of this study with those of other kill methods (such as operation time, etc.) in order to highlight the superiority of this research method. In addition, the authors also want to take into account the rheological properties of the gas and liquid phases involved in study for further analysis. In sensitivity analysis, some factors can have an impact on the cost (direct and indirect) of the well killing process. Finally, in future research, the authors will also take economic analysis into consideration.