Introduction

Sustained casing pressure (SCP) and/or annular pressure build-up after cementing a high-pressure, high-production (HPHP) gas well are rampant, and they gravely affect the safe operations of both oil and gas wells. These casing pressures exist in any well annulus, and they are measurable at the wellhead and replenished after being bled down. However, these pressures differ significantly from other pressure build-ups due to the thermal expansion of trapped liquids (Somassoundirame and Nithiyananthan 2021; Volkov et al. 2019). Excessive SCP has an adverse effect on the safety of gas wells, such as busting or collapsing the casing, causing serious accidents, such as blowouts and explosions (Jiang et al. 2015). SCP constitutes a potential new source of continuous natural gas emission from failed casing heads due to the leaching cement sheath and external gas migration (Kinik and Wojtanowicz 2011).

According to the US Minerals Management Service (Mainguy and Innes 2018), there are approximately 8000 wells on the Gulf of Mexico Outer Continental Shelf of the US that have one or more layers of annular pressure (accounting for nearly 60% of all gas wells in the region), and approximately 50% of them occur in the annulus between the tubing string and the production casing, known as the A-annulus. One possible source of SCP is a leaking cement sheath through which the gas flows through the annulus from a high-pressure formation, causing high casing pressure values other than the A-annulus (Kazemi and Wojtanowicz 2022). For SCP in the A-annulus, cracks in the tubing string, casing string, packer rubber seal, and cement failure are potential culprits (Zeng et al. 2017). These findings warrant identifying downhole leak sources of pressure communication between the A-annulus. Detecting any leak at an early stage is an important element of managing the integrity of wells. There are many approaches for downhole leak detection (Al-Hussain et al. 2015; Baharum et al. 2021), especially utilizing rig-less data based on the full interpretation and evaluation of different logs in the field. These methods can identify not only one leak position but also multiple leaks.

Concerning mitigation measures for reducing A-annulus pressure, Srivastava M et al. advocated for annulus top-ups with heavy fluids (Srivastava et al. 2018). Darmawan (2020) defined a lube and bleed operation and the following detailed procedure: The gas in the top-up is replaced with the required fluid (treated water or brine) to reduce the surface pressure. Lower annular pressure is maintained, followed by close monitoring to determine when another lube and bleed cycle is needed. Polymer plugs used in a case study (Darmawan 2020) proved to be an effective method for sealing perforation intervals. However, these plugs are only applicable to temporary well suspensions or permanent well abandonments. Casing leaks may be another source of SCP in the A-annulus. Many efforts have been made to repair casing leaks over the years, including using chemical agents (Meng et al. 2019) and mechanical tubes (Bargawi et al. 2005). Additionally, production tubing leaks have been an overwhelming challenge in managing well integrity, especially in brownfield developments. Al Zayani et al. (2019) proposed an integrated solution for repairing multiple tubing leaks in a single pass. Recently, Olalere et al. (2021) engineered reinforced thermoplastic pipes (Baharum et al. 2021; Vazquez et al. 2020; Al-Dhafeeri et al. 2020). These approaches are all meant to be cost-effective, thus outperforming the economics of often expensive rig-based workovers.

Downhole throttling technology is a well-established technique. Downhole chokes have been used in lieu of surface chokes (White et al. 2014). By moving the pressure and temperature reduction points downhole, the Joule–Thompson cooling response is geothermally regulated. This regulation mitigates hydrate formation in surface facilities, eliminating the use of surface line heaters and methanol injections. This approach is extensively used in various applications, such as rate restriction, sand plugging mitigation, surface hydrate elimination, and liquid unloading (White et al. 2014; Yap et al. 2021). To abate SCP, some scholars have proposed the utilization of downhole multistage choke technology (Jiang et al. 2015). However, to the best of our knowledge, such critical technical rationales as application preconditions under different pathways of single or double leak points in the tubing string have not yet been explored.

In this paper, using OLGA software (Ganat et al. 2017), the phenomenon of abnormal pressure rise in the tubing/casing annulus is first analysed by building separate physical and software models of a single leak in the tubing string (Wu et al. 2018; Yang et al. 2022; Zhu et al. 2012). Then, the influences on the annulus pressure rise from certain factors, such as the leak point depth, casing head pressure blowdown, production shifts, and annular initial gas column height, are presented. Next, the development of fluid exchange between the tubing and casing and pressure rise in the annulus for two successively leaked points in the tubing string (double leaks) is considered (Al Zayani et al. 2019; Kim 2020; Lazhar et al. 2013; Wang et al. 2019, 2020). Finally, building on the resulting upshot, the adaptability of downhole throttling technology to alleviate SCP is studied under various single or double leak scenarios. The novelty of this paper is to develop a method for mitigating SCP based on a rigorous simulation for a single leak and double leaks in the tubing string. The conclusions presented are notable in terms of cost and ease of operation.

OLGA programme methodology

The OLGA programme is a principal component in the analysis of pipeline operations and wellbore hydrodynamics (Ganat et al. 2017). The OLGA dynamic multiphase flow simulator models time-dependent behaviours, or transient flow, to maximize production potential. Transient modelling is an essential component for feasibility studies and field development design. Dynamic simulation is used extensively in both offshore and onshore developments to investigate transient behaviour in pipelines and wellbores. From wellbore dynamics for any well completions to pipeline systems with all types of process equipment, the OLGA simulator provides an accurate prediction of key operational conditions involving transient flow.

The programme solves separate continuity equations for gas, liquid bulk and liquid droplets while using two momentum equations—one for the liquid bulk or film and one for the combination of gas and possibly liquid droplets (Bendlksen et al. 1991). The programme presents the same temperature for both phases by considering one energy equation for the gas/liquid mixture.

Conservation of Mass: For the gas phase, the following equation is obtained:

$$\frac{\partial }{\partial t}\left( {V_{g} \rho_{g} } \right) = - \frac{1}{A}\frac{\partial }{\partial z}\left( {AV_{g} \rho_{g} v_{g} } \right) + {\Psi }_{g} + G_{g}$$
(1)

For the liquid phase at the pipe wall, the following equation is obtained:

$$\frac{\partial }{\partial t}\left( {V_{L} \rho_{L} } \right) = - \frac{1}{A}\frac{\partial }{\partial z}\left( {AV_{L} \rho_{L} v_{L} } \right) - {\Psi }_{g} \frac{{V_{L} }}{{V_{L} + V_{D} }} - {\Psi }_{e} + {\Psi }_{d} + G_{L}$$
(2)

For liquid droplets, the following equation is obtained:

$$\frac{\partial }{\partial t}\left( {V_{D} \rho_{L} } \right) = - \frac{1}{A}\frac{\partial }{\partial z}\left( {AV_{D} \rho_{L} v_{D} } \right) - {\Psi }_{g} \frac{{V_{D} }}{{V_{L} + V_{D} }} + {\Psi }_{e} - {\Psi }_{d} + G_{D}$$
(3)

Conservation of Momentum: For the liquid phase at the pipe wall, the following equation is obtained:

$$\begin{aligned} \frac{\partial }{\partial t}\left( {V_{L} \rho_{L} v_{L} } \right) = & - V_{L} \left( {\frac{\partial p}{{\partial z}}} \right) - \frac{1}{A}\frac{\partial }{\partial z}\left( {AV_{L} \rho_{L} v_{L}^{2} } \right) - \lambda_{L} \frac{1}{2}\rho_{L} \left| {v_{L} } \right|v_{L} \frac{{S_{L} }}{4A} + \lambda_{i} \frac{1}{2}\rho_{g} \left| {v_{r} } \right|v_{r} \frac{{S_{i} }}{4A} \\ + & V_{L} \rho_{L} g\cos \alpha - \Psi_{g} \frac{{V_{L} }}{{V_{L} + V_{D} }}V_{a} - \Psi_{e} v_{i} + \Psi_{d} V_{D} - v_{L} d\left( {\rho_{L} - \rho_{g} } \right)g\frac{{\partial V_{L} }}{\partial Z}\sin a \\ \end{aligned}$$
(4)

For the gas phase and liquid droplets, the following equation is obtained:

$$\begin{aligned} \frac{\partial }{\partial t}\left( {V_{g} \rho_{g} v_{g} + V_{D} \rho_{L} v_{D} } \right) = & - \left( {V_{g} + V_{D} } \right)\left( {\frac{\partial p}{{\partial z}}} \right) - \frac{1}{A}\frac{\partial }{\partial z}\left( {AV_{g} \rho_{g} v_{g}^{2} + AV_{D} \rho_{D} v_{D}^{2} } \right) - \lambda_{g} \frac{1}{2}\rho_{g} \left| {v_{g} } \right|v_{g} \frac{{S_{g} }}{4A} \\ & - \lambda_{i} \frac{1}{2}\rho_{g} \left| {v_{r} } \right|v_{r} \frac{{S_{i} }}{4A} + \left( {V_{g} \rho_{g} + V_{D} \rho_{L} } \right)g\cos \alpha + \Psi_{g} \frac{{V_{L} }}{{V_{L} + V_{D} }}V_{a} + \Psi_{e} v_{i} - \Psi_{d} v_{D} \\ \end{aligned}$$
(5)

Energy Equation: A mixture energy conservation equation is applied, yielding the following equation:

$$\begin{gathered} \frac{\partial }{\partial t}\left[ {m_{g} \left( {E_{g} + \frac{1}{2}v_{g}^{2} + gh} \right) + m_{L} \left( {E_{L} + \frac{1}{2}v_{L}^{2} + gh} \right) + m_{D} \left( {E_{D} + \frac{1}{2}v_{D}^{2} + gh} \right)} \right] \hfill \\ = \frac{\partial }{\partial z}\left[ {m_{g} v_{g} \left( {H_{g} + \frac{1}{2}v_{g}^{2} + gh} \right) + m_{L} v_{L} \left( {H_{L} + \frac{1}{2}v_{L}^{2} + gh} \right) + m_{D} v_{D} \left( {H_{D} + \frac{1}{2}v_{D}^{2} + gh} \right)} \right] + H_{L} + U \hfill \\ \end{gathered}$$
(6)

All these equations are solved using the finite volume method and semi-implicit time integration. OLGA provides dynamic solutions through the accurate modelling of true dynamics. Transient simulation with the OLGA simulator provides an added dimension to steady-state analyses by predicting system dynamics such as time-varying changes in flow rates, fluid composition, temperatures, and operational changes. Generally, information related to the reservoir, well completion, fluids, and equipment are essential for building a dynamic model in OLGA.

Figure 1 shows the flowchart of the OLGA simulation model structure. At the very start, a well structure model is set up using the OLGA well editor module, preferably drawing up its equivalent well schematic. Then, define key parameters to input, such as wellhead, tubing, and reservoir property data. Formation fluid is one of the primary well-completion-related data, its transport properties being created in a third-party software Multiflash. Next, simulation time step and length of tubing segments are optimized. And next, decide how many leaks in the tubing string the model is intended to explore and its durations. Before the programme is ready to simulate, a check is done to ensure there are no syntax errors. What follows in the flowchart is to retrieve SCP-related trends data and, intoxicatingly, explore all the way to its development patterns. Last, based on preceding findings, propose suitable SCP mitigation schemes with downhole chokes deployed accordingly.

Fig. 1
figure 1

Workflow of the OLGA simulation model structure

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Analysis of annular pressure build-up

Single leak in the tubing string

Physical and virtual models

A physical model and an equivalent OLGA software model exploring anomalous pressure evolution in the A-annulus are shown in Fig. 2, and the process of pressure build-up is as follows (Fig. 2, left): produced gas from the “Reservoir” enters the annulus through a “Tubing Rupture” in the tubing string and travels upwards to accumulate as a gas column, which has a lower density than that of the liquid filled in the annulus, creating anomalously high pressure at the top.

Fig. 2
figure 2

Physical model (left) and equivalent OLGA model (right)

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The implementation of this physical model in OLGA software is illustrated in Fig. 2, right: The gas stream comes out of the “Reservoir”. Then, the gas stream flows upwards along the “O4W-0_Wellbore”. At the “Internal Node”, due to the blockage of the “Packer”, the gas stream travels towards the “TubingValve”. Within “O4W-0_Tubing”, which represents a tubing string, the gas stream exchanges with packer fluids through “TubingRupture”. The flow path titled “O4W-0_Annulus” represents an annulus, on which the “TubingRupture” is connected to the tubing by its key “TOPPOSITION”. Herein, the incoming gas stream from the tubing can flow towards either the “TBG_Head” or “CasingHead” through its boundary component “TubingRupture”, diverting part of the incoming gas stream and building up a gas column in the annulus. The essential data used in setting up this OLGA model are shown in Table 1.

Table 1 Key information used for setting up the OLGA model
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Effect of leak depth on casing pressure rise

Based on well data from the Keshen gas field in the Tarim Oilfield Company, the rise in annular pressure is simulated while production continues after a leak occurs in the tubing string. The depth of the leak point is assumed to be 90 m (259 ft), 2570 m (8432 ft), 5468 m (17,940 ft), and 6552 m (21,496 ft), for which the annular pressure trend is shown in Fig. 3. By examining Fig. 3, it can be concluded that the shallower the depth of the leak point is, the higher the SCP and the greater the risk to well integrity. The reason for this phenomenon is that the shallower the leak point is, the lower the flowing tubing pressure at the leak depth. However, the shallower the leak point is, the shorter the length of the annular liquid column, in part because the gas volume leaking into the annulus is approximately equal for all cases in question. Therefore, elevated casing head pressure correlates to reduced leak depths. For this reason, ensuring the integrity of the wellhead sealing and boosting the qualities of downhole safety valves and hermetically sealed tubing (especially upper sections) made of corrosion-resistant alloys are effective methods for mitigating the safety risks of HPHP wells.

Fig. 3
figure 3

Effect of a leak on the rise in annular pressure

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Effect of bleeding off the annulus on casing head pressure

To assess tubing cracks at depths of 90 m (259 ft), 2570 m (8432 ft), 5468 m (17,940 ft), and 6552 m (21,496 ft) separately, the casing pressure is blown down for half an hour at 30 and 65 h sequentially, while the well continues production. These pressure relief effects on casing head pressure developments are pictured in Fig. 4 (left). From this chart, it is evident that each pressure relief effort causes the casing pressure to dip and rebound relatively instantly, resuming or surpassing the pre-relief value and attaining its highest point at the end of the simulation (when the annulus above the leak is filled with natural gas). For the leak point near the casing head (90 m/259 ft in this case), both pressure relief efforts eliminate rises in SCP, but there are jumps for other leakage depths that occur within a fairly short period of time. And the deeper the leak point is, the slower its pressure build-up. Fluid exchange processes between the tubing and the annular space caused by casing pressure release are illustrated in Fig. 4 (right). At the beginning of the pressure blowdown, the gas encroaches the annulus from the tubing string through the leak caused by the reduction in casing pressure and moves upwards in stagnant liquid. In addition, rising gas bubbles expand and depressurize, displacing packer fluid to the tubing through the leak. Once it enters the tubing, stray fluid is carried upwards with rushed gas. The process of fluid swap continues until both sides are pressure balanced.

Fig. 4
figure 4

Casing blowdown effect on the annular pressure (left) and fluid exchange process (right)

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Impacts of production shifts on annular pressure

When there is a leak in the tubing string, gas wells are intentionally beaned to meet production schemes by adjusting the production choke at the Christmas tree. The effect of this operation on the annular pressure is shown in Fig. 5 (left), from which it can be seen that both the ramp-down and ramp-up of gas wells cause the annular pressure to jump. The shared effect is to reduce the lengths in the annular liquid column.

Fig. 5
figure 5

Effects of production shifts (left) and initial gas column (right) on annular pressure

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Effect of the initial gas column in the annulus on the casing pressure

Some authors (Zhang et al. 2021; Chevarunotai et al. 2017; Kalantariasl et al. 2022; Safar et al. 2018) have proposed that the annular space need not be filled with liquid when the well is put on stream; that is, part of the annular space is reserved for gas so that the aim of mitigating thermal-induced SCP can be achieved. If the gas column in the annulus is initially 200 m (656 ft) or 1500 m (4921 ft), the gas well starts production with a single-point leak in the tubing at 5468 m (17,940 ft). The annular pressure trends are pictured in Fig. 5 (right). From this image, it can be observed that the smaller the height of a gas chamber is, the slower the pressure rises and the lower its final value. Therefore, the longer initial gas column (1500 m/4921 ft) is counterproductive in this case study, resulting in a negative impact on unintended final SCP.

Double leaks in the tubing string

From extensive leak detection data in the field under various production conditions, tubing string leaks are often not in the form of a single fissure but in multiple consecutive fissures (Kim 2020; Wang et al. 2019). In the case of multiple leaks, the pressure rise in the annulus is not regulated by one leak alone but by all leaks interactively. A notable feature of multiple leaks (Mohmad et al. 2021; Safar et al. 2018), as opposed to a single leak, is that the annulus pressure rises while the liquid level drops, as is evident in several high sulphur content gas wells. Once the liquid level settles, the upper section of the sulphur-resistant casing is not protected by annular packer fluid, and serious corrosion from corrosive gas comprising H2S, CO2, and water vapour can lessen the integrity of both casing strings and gas wells. Therefore, it is paramount to analyse the leakage patterns of tubing strings with multiple leakage points and to suggest reasonable mitigation strategies for the safe operation of gas producers. In this paper, the pattern of fluid swap and pressure rise in the annulus are both explored, with an existing leak at 2570 m (8432 ft) and another leak occurring separately in the upper (well depth of 90 m/259 ft) or lower position (well depth of 5468 m/17,940 ft).

Shared features of double leak channels

The pressure rise trend at the wellhead of a double leak is shown in Fig. 6 (left). Whether a secondary leak point is located above (90 m/259 ft) or below (5468 m/17,940 ft) the existent, as the leak develops, the gas volume in the annulus grows gradually. Because its density is less than that of the displaced packer fluid (a polymer with a specific gravity of 1.4), the casing head pressure increases until the pressures on either side of the leak point reach equilibrium and fluid exchange stops at both locations. Once stabilized, the annular space above either leak is fully occupied with natural gas.

Fig. 6
figure 6

Annular pressure rise trend of two leakage channels (left) and its schematic diagram of fluid exchange between the annulus and tubing string (right)

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Differences between two leakage channels

Since secondary leakage can occur at different depths, the fluid swap process between the A-annulus and the tubing varies accordingly, as represented schematically in Fig. 6 (right). If the secondary new leak point is higher than the existent (90 m/259 ft, as shown in the figure), the ingress of natural gas into the annulus occurs at the upper leak point at the start of leakage, and the annulus packer fluid at the low leak point escapes into the tube pipe. If the secondary new leak point occurs in the lower part (5468 m/17,940 ft in this case), the annular liquid moves from the lower leak point into the tubing string and is carried upwards by the gas stream, part of which re-enters the annulus via the upper leak with natural gases. When the flow reaches a steady state, the annulus above either leak is filled exclusively with natural gas. Therefore, the deeper the secondary new leak is, the higher the final pressure in the annulus (Fig. 6, left).

Downhole throttling applicability analysis

Single leak in the tubing string

Based on the results of the previous sections, the effectiveness of a downhole choke in curtailing persistent casing pressure is analysed in the following two subsections, depending on whether the annulus above a single leak is occupied fully with gas.

Gaseous annulus above a single leak

After a leak occurs in the tubing string, the annulus can be filled entirely with natural gas due to synthetically manufactured factors, such as casing pressure relief or production shifts, resulting in high and nearly identical tubing and casing pressure profiles (Fig. 7, left and Table 2). If a downhole choke is placed above the leak (e.g. 4983 m/16,348 ft), its wellbore pressure profile and corresponding fluid exchange are illustrated in Fig. 7 (right). After positioning the downhole choke, its throttling effect causes the upstream pressure to jump; thus, the gas enters the annulus via the leak. As gas expands in the annulus, the pressure above the leak point increases until the pressure equalizes on either side of the leak. Therefore, by the time the flow is stabilized, the annular pressure remains stubbornly high. Notwithstanding, the tubing pressure downstream of the throttle falls significantly. Therefore, the performance of this scheme is poor. However, if the throttle is lowered to the well section below the leak point, improved results can be attained (see Table 2) for Pt and Pc down to 15.7 MPa (2277 psi) and 16.9 MPa (2451 psi), respectively.

Fig. 7
figure 7

Wellbore pressure profiles and fluid swap diagrams before (left) and after (right) installation of the downhole choke with a gaseous annulus above the leak point

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Table 2 Performance comparison in downhole choke with a single leak in the tubing string
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Partial gaseous annulus above a single leak

Since the annulus above the leak is partially gaseous (Fig. 8, left), after the downhole choke is put below the leak point, the flowing pressure in the tubing downstream of the choke drops; thus, the liquid inside the annulus flows out into the tubing through the leak (Fig. 8, right) until pressures equalize at the leak point. However, due to the lack of a beneficial pressure difference across the downhole throttle, the casing wellhead pressure is slightly reduced from 45.1 MPa (6541 psi) to 40.8 MPa (5918 psi) and causes the annular liquid level to drop from 2075 m (6808 ft) to 3465 m (11,368 ft) (Table 2). Accordingly, it is determined that the effect of downhole throttling is poor under such operating conditions. Conversely, for some well conditions where the gas productivity is high, lowering the choke below the leak point can significantly dip both Pt and Pc pressures (see Table 2), although this action invokes a slump in the annular liquid level.

Fig. 8
figure 8

Wellbore pressure profiles and fluid swap diagrams before (left) and after (right) installation of the downhole choke with a partial gaseous annulus above the leak

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Double leaks in the tubing string

Based on the previous sections, after two asynchronous leak points occurred in the tubing string, the channelling effect of the annulus results in it being fully occupied with natural gas above either leak. Therefore, two options of positioning the throttle are considered in this paper, i.e. between the leaks versus below the lower leak point. When a choke is located in between (Table 3), natural gas circumvents a bypass in the annulus; that is, it enters the annulus from the lower leak, flows upwards in the annulus, and finally flows back into the tubing from the upper leak, negating the effect of downhole throttling. Therefore, such a scheme is ineffective and undesirable.

Table 3 Performance comparison in downhole chokes in a double-leak tubing
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While the throttle is lowered into the well section below the lower leak, a pressure drop is provoked in the tubing string downstream of it; thus, fluid flows out of the annulus from both leaks concurrently (Fig. 9, right). For the upper leak, the gas flows from the annulus to the tubing until the internal and external pressures are equal.

Fig. 9
figure 9

Pressure profile (left) and fluid exchange between the tubing string and annular space (right) after placing the downhole choke below the lower leak point

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The lower leak is where both packer fluid and natural gas flow out of the annulus and into the tubing. After sometime, the fluid stops flowing out while natural gas re-enters the annulus from the tubing until the internal and external pressures equalize. When pressure equilibrium is reached at each leak, the pressures of Pt and Pc both dwindle significantly and are equal (Fig. 9, left). Therefore, the throttling performance is superior in such landing schemes.

Summary and conclusions

SCPs were rampant after completing a HPHP gas well and posed grave threats to its safe operation. As a well-established technique, downhole throttling technology was widely utilized in the upstream petroleum industry and proposed to mitigate SCPs in this work. First, a physical model with one single leak in the tubing string was built. Second, equivalent OLGA software models and two asynchronously occurring leaks were set up to observe various parameter effects on annulus pressure. Third, their effects on SCP were analysed. Finally, the adaptability levels of downhole throttling technology during either a single leak or double leaks were studied. Therefore, the following conclusions were obtained. The findings on the rise in annular pressure trends were helpful for rig-less leak detection. The downhole choke technology presented for abating SCPs was notable in terms of cost and ease of operation.

  1. (1)

    For one leak alone, the shallower the leak was, the higher the final SCP; most production operations inflicted worse SCP, such as casing pressure release or production shifts.

  2. (2)

    For two leaks occurring sequentially, fluid interaction between the two leak depths imposed a gaseous A-annulus above either leak; the deeper the secondary new leak was, the higher its final pressure in the A-annulus.

  3. (3)

    For a single leak scenario, a downhole choke seated below it could be effective for mitigating the SCP for high-productivity gas wells, whether a full or partial gaseous annulus.

  4. (4)

    For two leaked points happened asynchronously, a downhole choke deployed beneath the lower leak was effective for abating SCPs.

  5. (5)

    The preceding conclusions were reached based on a high-productivity deep gas well in our oilfield, and its applicability rested to a large extent on the accuracy of leak detection. For further study, a less prolific gas producer with sustained casing pressure was a desirable research target.