An optimized design method for controlling the leakage pressure rise of production strings

Abstract

The present application relates to an optimized design method for controlling the leakage pressure buildup of a production string, including: determining whether there is leakage of the annulus fluid in the casing-tubing annulus of a target gas well; if there is no leakage of the annulus fluid in the casing-tubing annulus of the target gas well, determining the depth of the leakage point of the production string; based on the determined depth of the leakage point, determining Curve 1 of the variation of the maximum pressure in the casing-tubing annulus with the density of the annulus fluid; according to the pressure-bearing capacities of the tubing head, production string, production casing and packer, determining Curve 2 of the variation of the maximum pressure control range in the casing-tubing annulus with the density of the annulus fluid; optimizing and determining the density of the annulus fluid according to Curve 1 and Curve 2 to reduce the pressure in the casing-tubing annulus to within the safety threshold. The present application can reduce the pressure in the casing-tubing annulus to within the safety threshold without replacing the production string or performing major well repairs, effectively controlling the phenomenon of pressure buildup due to string leakage, avoiding exceeding the wellbore pressure-bearing capacity, and reducing the control cost and maintenance cycle.

Description

Technical Field

[0001] The present application relates to the field of natural gas wellbore safety control, and particularly to an optimized design method for controlling the pressure rise caused by the leakage of a production string. Background Art

[0002] With the rapid development of the national economy and the continuous improvement of environmental protection requirements, the consumption of natural gas has been increasing continuously, which has promoted the exploration and development of natural gas into deep formations. At the same time, the supply and price of natural gas are greatly affected by the international situation and there are seasonal peaks in consumption. A large number of underground gas storage facilities need to be built to ensure the balance between supply and demand of natural gas. The production of natural gas depends on wellbores and production strings. The production string, also known as the tubing string, is formed by screwing together metal tubing and other components. As the channel for natural gas to flow from underground to the surface, the production string bears complex loads and harsh temperature and pressure conditions. In some cases, it is also accompanied by corrosive gases such as hydrogen sulfide and carbon dioxide, which can cause various forms of leakage phenomena such as corrosion perforation of the pipe wall, stress cracking, coupling disengagement, and thread seal failure, forming a gas-liquid interaction channel between the casing-tubing annulus and the tubing string, and then leading to an increase in the pressure in the casing-tubing annulus, resulting in the phenomenon of pressure rise caused by the leakage of the production string.

[0003] The safety hazards brought about by the pressure rise caused by the leakage of the production string are extremely large. Especially when the pressure in the casing-tubing annulus exceeds the bearing capacity of the wellbore, the safety hazards are mainly reflected in three aspects: First, the safety barrier of the wellbore is damaged. The high pressure in the casing-tubing annulus can cause accidents such as wellhead lifting, cement sheath cracking, and pipe string extrusion; Second, a large amount of combustible gas accumulates in the annulus, posing a risk of leakage and fire; Third, environmental pollution. Natural gas will enter the shallow soil or groundwater along the leakage channel in the wellbore, and in some cases, continuously release methane into the atmosphere, forming a source of greenhouse gas leakage. Therefore, when the production string leaks, effective measures need to be taken to reduce the pressure in the casing-tubing annulus caused by the leakage and prevent the pressure in the casing-tubing annulus from exceeding the bearing capacity of the wellbore.

[0004] However, the existing risk control of production string leakage relies heavily on workover operations. The pressure rise caused by leakage is mainly controlled by replacing the production string, which incurs high operating costs. Moreover, there are risks of pipe string fracture, reservoir pollution, and well control during the workover process. Chemical plugging faces challenges such as high temperature and pressure, pipe wall pollution, and lack of pressure-bearing barriers, making it difficult to achieve effective plugging.

[0005] Therefore, there is an urgent need to provide an optimized design method for controlling the pressure rise caused by the leakage of the production string to solve the above-mentioned technical problems. Summary of the Invention

[0006] The present application provides an optimized design method for controlling the pressure rise caused by leakage of the production string, which can reduce the annulus pressure between the tubing and the casing to within the safety threshold without replacing the production string or conducting major well repairs, thereby effectively controlling the pressure rise caused by leakage of the production string, avoiding exceeding the bearing capacity of the wellbore, reducing the control cost and the maintenance period, and realizing the continuous high-intensity production of gas wells.

[0007] In a first aspect, the present application provides an optimized design method for controlling the pressure rise caused by leakage of the production string, including the following steps:

[0008] Step 1: Determine whether the annulus fluid in the annulus between the tubing and the casing of the target gas well leaks; wherein, the annulus between the tubing and the casing is composed of a tubing head, a production string, a production casing, and a packer;

[0009] Step 2: If the annulus fluid in the annulus between the tubing and the casing of the target gas well does not leak, determine the depth of the leakage point of the production string;

[0010] Step 3: According to the determined depth of the leakage point, determine Curve 1 of the maximum pressure of the annulus between the tubing and the casing changing with the density of the annulus fluid;

[0011] Step 4: According to the bearing capacities of the tubing head, the production string, the production casing, and the packer, determine Curve 2 of the maximum value of the pressure control range of the annulus between the tubing and the casing changing with the density of the annulus fluid;

[0012] Step 5: Optimize and determine the density of the annulus fluid according to Curve 1 and Curve 2 to reduce the pressure of the annulus between the tubing and the casing to within the safety threshold.

[0013] Preferably, determining whether the annulus fluid in the annulus between the tubing and the casing of the target gas well leaks includes: based on the target gas well where the production string leaks, determining whether the annulus fluid leaks by monitoring the height of the annulus liquid level in the annulus between the tubing and the casing, and defining the amplitude of the annulus liquid level fluctuation according to the difference between the maximum value and the minimum value of the annulus liquid level depth monitored within a specific time divided by the maximum well depth; when the amplitude of the annulus liquid level fluctuation within a specific time does not exceed the threshold, it is considered that the annulus fluid does not leak; when the amplitude of the annulus liquid level fluctuation within a specific time exceeds the threshold, it is considered that the annulus fluid leaks.

[0014] Preferably, if the annulus fluid in the annulus between the tubing and the casing of the target gas well does not leak, determining the depth of the leakage point of the production string includes:

[0015] Step 2.1: Obtain the pressure profile inside the production string under the well shut-in condition;

[0016] Step 2.2: Calculate and determine the pressure profile in the annulus between the tubing and the casing according to the gas column and liquid column pressures;

[0017] Step 2.3: Based on the pressure difference between the pressure profile in the production string and the pressure profile in the casing - annulus as the driving force for leakage, analyze and determine the variation law of the maximum casing - annulus pressure with the depth of the leakage point, and obtain Curve Three;

[0018] Step 2.4: According to the casing - annulus pressure calculated under the well - shut - in condition, the depth of the leakage point corresponding to the pressure value of the casing - annulus pressure on Curve Three is the depth of the leakage point of the production string.

[0019] Preferably, in Step 2.1: Obtaining the pressure profile in the production string under the well - shut - in condition includes: closing the wellhead of the target gas well, recording the corresponding casing - annulus pressure and wellhead oil pressure, and then lowering a pressure gauge into the well to obtain the pressure profile in the production string;

[0020] Alternatively, segment the production string, calculate the gas density within each segment according to pressure and temperature, and then calculate the pressure within the production string at the corresponding depth.

[0021] Preferably, the segmenting the production string, calculating the gas density within each segment according to pressure and temperature, and then calculating the pressure within the production string at the corresponding depth includes:

[0022] According to the PVT equation of the gas, obtain the gas density, and the gas density can be described by the following formula:

[0023]

[0024] where ρ gi is the gas density of the i - th segment, g / cm 3 ; p ti is the pressure within the production string of the i - th segment, MPa; p s is the standard - condition pressure, Pa; T s is the standard - condition temperature, K; T ti is the temperature within the production string of the i - th segment, i.e., the formation temperature, K; ρ gs is the standard - condition gas density, g / cm 3 ; i is the segment number, dimensionless, i = 1, 2, 3....;

[0025] Calculate the temperature within the production string of the i - th segment, i.e., the formation temperature, which is expressed by the following formula:

[0026] T ti = T t0 + g e × i × H F (4) where T t0 is the wellhead temperature, K; g e is the geothermal gradient, K / 100m; H Fis the sectional length, m;

[0027] Calculate the pressure in the production string at the corresponding sectional depth according to the gas density, as shown in the formula:

[0028] p ti+1 = p ti + 10 -3 × ρ gi × g × H F (5)

[0029] In the formula, p ti+1 is the pressure in the production string at the (i + 1)-th section, MPa; g is the acceleration of gravity, m / s 2 ; According to the above steps, calculate from the wellhead to the bottom of the well in sequence to obtain the pressure in the production string at the corresponding depth.

[0030] Preferably, in step 2.2: Calculate the pressure profile in the casing-tubing annulus according to the gas column and liquid column pressures, including: Calculate the gas density in the casing-tubing annulus. Since the length of the gas column in the casing-tubing annulus is short, the influence of formation temperature on the gas density is no longer considered. The gas density in the casing-tubing annulus is expressed by the following formula:

[0031]

[0032] In the formula, ρ ga is the gas density in the casing-tubing annulus, g / cm 3 ; T ta is the wellhead temperature of the casing-tubing annulus, K;

[0033] According to the pressure profile in the casing-tubing annulus above the liquid level in the casing-tubing annulus, which is only related to the gas column in the annulus, and the pressure profile in the casing-tubing annulus below the liquid level in the annulus is affected by both the gas column and liquid column pressures. Calculate the pressure profile in the casing-tubing annulus separately. Among them, when calculating this profile, assume that the pressure in the casing-tubing annulus is zero, and it is expressed by the following formula:

[0034]

[0035] In the formula, H ta is the depth of the casing-tubing annulus, m; p ta is the value of the pressure profile in the casing-tubing annulus at the depth H ta , MPa; ρ ga is the gas density in the casing-tubing annulus, g / cm 3 , ρ L is the density of the annulus liquid in the casing-tubing annulus, g / cm 3 ; pa is the pressure in the casing-tubing annulus, MPa.

[0036] Preferably, in step 2.3: based on the pressure difference between the pressure profile in the production string and the pressure profile in the casing annulus as the driving force for leakage, analyze and determine the variation law of the maximum annulus pressure with the depth of the leakage point, and obtain curve three, including: according to the driving force for leakage coming from the pressure difference on both sides of the leakage point, the pressure inside the leakage point depends on the pressure profile in the production string at the depth of the leakage point, and the pressure outside the leakage point depends on the pressure profile in the casing annulus at the depth of the leakage point, which is expressed by the following formula:

[0037]

[0038] In the formula, p ln represents the pressure inside the leakage point, MPa; p lw represents the pressure outside the leakage point, MPa; H is the well depth, m; H L is the well depth where the leakage point is located, m; p tL is the pressure value corresponding to the pressure profile in the production string at the depth of the leakage point, MPa; p taL is the pressure value corresponding to the pressure profile in the casing annulus at the depth of the leakage point, MPa;

[0039] After the production string leaks, the production string, the leakage point and the casing annulus form a U-tube. According to the U-tube principle, when the annulus pressure reaches the maximum value, the pressures inside and outside the leakage point are equal. Determine the maximum annulus pressure corresponding to the leakage points at different depths, which is expressed by the following formula;

[0040] p anmax = p ln - p lw |H = H L (9)

[0041] In the formula, p anmax is the maximum annulus pressure, MPa;

[0042] According to the depth from the wellhead to the packer of the target gas well, change the depth of the leakage point, and obtain curve three according to the variation law of the maximum annulus pressure with the depth of the leakage point.

[0043] Preferably, in step 3: based on the determined depth of the leakage point, determine curve one of the variation of the maximum annulus pressure with the density of the annulus liquid, including: when the depth of the leakage point is below the annulus liquid level, the pressure outside the leakage point is affected by the pressure of the annulus liquid column, and the pressure of the annulus liquid column is related to the density of the annulus liquid;

[0044] According to the known depth of the leakage point, establish the relationship between the maximum annulus pressure caused by the leakage starting pressure and the density of the annulus liquid, which is expressed by the following formula:

[0045] p amaxL = p lnL - 10 -3 × [(ρ ga × g × H max ) + ρ L × g × (H LD - H max )] (11)

[0046] In the formula, p anmaxL is the maximum value of the annulus pressure between the tubing and the casing under the condition of determining the depth where the actual leakage point of the gas well is located, MPa, ρ ga is the gas density in the annulus between the tubing and the casing, g / cm3, ρ L is the annulus liquid density in the annulus between the tubing and the casing, g / cm3; p lnL is the inner pressure of the leakage point when the known leakage point depth is HL, MPa; By changing the density of the annulus liquid, the first curve of the change of the maximum value of the annulus pressure between the tubing and the casing with the annulus liquid density is obtained.

[0047] Preferably, in step 4: according to the pressure-bearing capacities of the tubing head, production string, production casing and packer, determine the second curve of the change of the maximum value of the pressure control range of the annulus between the tubing and the casing with the annulus liquid density, including: Based on the fact that the maximum value of the pressure control range of the annulus between the tubing and the casing needs to ensure the pressure-bearing capacities of the tubing head, production string, production casing and packer, calculate the pressure-bearing capacities of the tubing head, production string, production casing and packer respectively to determine the maximum value of the pressure control range of the annulus between the tubing and the casing; Among them, the maximum value of the pressure control range of the annulus between the tubing and the casing determined by the tubing head is 80% of its rated pressure resistance capacity, and is expressed by the following formula:

[0048] p1 = 0.8 × p 额 (12)

[0049] In the formula, p1 is the maximum value of the pressure control range of the annulus between the tubing and the casing determined by the tubing head, MPa; p 额 is the rated pressure resistance capacity of the tubing head, MPa;

[0050] The maximum value of the pressure control range of the annulus between the tubing and the casing determined by the production string is the external extrusion resistance strength of the production string under open well production and shut-in well conditions, and is expressed by the following formula:

[0051]

[0052] In the formula, p2 is the maximum value of the pressure control range of the annulus between the tubing and the casing determined by the production string, MPa; p 挤 is the minimum external extrusion resistance strength of the production string in the gas well, MPa; S2 is the external extrusion safety factor, dimensionless; p t2p1 is the inner pressure of the tubing string corresponding to the depth where the minimum external extrusion strength of the production string is located, MPa; h2 is the depth where the minimum external extrusion strength of the production string is located, m;

[0053] The maximum value of the control range of the annulus pressure determined by the production casing is the internal pressure resistance of the production casing, which is expressed by the following formula:

[0054]

[0055] In the formula, p3 is the maximum value of the control range of the annulus pressure determined by the production casing, MPa; p 内 is the minimum internal pressure resistance of the production casing, MPa; S3 is the internal pressure safety factor of the production casing, dimensionless; p b is the pressure value in annulus B, MPa; ρ b is the equivalent brine density of annulus B, g / cm 3 ; h3 is the depth where the minimum internal pressure resistance of the production casing is located, m;

[0056] The maximum value of the pressure control range of the annulus determined by the packer is the limit of the packer setting pressure, which is expressed by the following formula;

[0057] p4 = p 封 + p 下 - 10 -3 ρ Lg h4 (15)

[0058] In the formula, p4 is the maximum value of the pressure control range of the annulus determined by the packer, MPa; p 封 is the working differential pressure for setting the packer, MPa; p 下 is the pressure at the lower end of the packer, MPa; h4 is the depth from the liquid level of the annulus protection fluid to the packer, m;

[0059] The maximum value of the pressure control range of the annulus is obtained according to the minimum value among the maximum values of the pressure control ranges of the annulus determined by the tubing head, production string, production casing and packer, which is expressed by the following formula;

[0060] Δp aA = min(p1, p2, p3, p4) (16)

[0061] In the formula, △p aA is the maximum value of the pressure control range of the annulus, MPa;

[0062] By changing the density of the annulus fluid, the variation curve two of the maximum value of the pressure control range of the annulus with the density of the annulus fluid is obtained.

[0063] Preferably, step 5: Optimize and determine the annulus fluid density according to the first change curve and the second change curve to reduce the pressure in the oil-casing annulus to within the safety threshold, including: Plotting the first change curve of the maximum pressure in the oil-casing annulus with respect to the annulus fluid density and the second change curve of the maximum value of the pressure control range in the oil-casing annulus with respect to the annulus fluid density in the same coordinate system;

[0064] When the pressure in the oil-casing annulus is less than the pressure control range in the oil-casing annulus, the corresponding annulus fluid density is the optimized annulus fluid density value required;

[0065] When this density value does not exist or is too large, the depth of the annulus liquid level is increased, and then steps 2 to 5 are repeated above to re-determine the annulus fluid density.

[0066] This application has at least the following advantages:

[0067] (1) Effectively control the phenomenon of pressure rise caused by leakage of the production string without major overhaul of the production string, avoid exceeding the wellbore pressure-bearing capacity, thereby reducing the control cost and maintenance cycle, and realizing continuous high-intensity production of gas wells;

[0068] (2) No additional device is required, no need to lift the production string for major overhaul, low cost, long-lasting effect, and the annulus pressure will not rise repeatedly;

[0069] (3) Wide application range, applicable to injection-production wells in gas storage reservoirs and high-pressure gas wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram showing the wellbore structure in an embodiment;

[0071] Figure 2 It is a schematic diagram of the steps of an optimized design method for controlling pressure rise caused by leakage of the production string in an embodiment;

[0072] Figure 3 It is a schematic diagram for positioning the leakage point of the first change curve of the maximum pressure in the oil-casing annulus with respect to the depth of the leakage point in an embodiment;

[0073] Figure 4 It is a schematic diagram of the optimized design of the density value of the annulus fluid in an embodiment;

[0074] Figure 5 It is a schematic structural diagram of a computer device in an embodiment.

[0075] Reference numerals: 1, formation; 2, cement sheath; 3, production casing; 4, production string; 5, packer; 6, reservoir; 7, wellhead; 8, annulus fluid; 9, annulus gas; 10, oil-casing annulus liquid level. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0076] The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present application and are not intended to limit the present application.

[0077] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form also

[0078] includes the plural form. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. However, those of ordinary skill in the art can understand that in the embodiments of the present application, many technical details are provided to help readers better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can still be implemented. The markings of the following embodiments are for convenience of description and should not constitute any limitation on the specific implementation manner of the present application. The various embodiments can be combined with each other and cross-referenced on the premise of not being contradictory.

[0080] Please refer to Figure 1 As shown, the wellbore serves as a channel for oil and gas production and carbon energy injection / production. The wellbore structure generally includes a production casing 3 disposed in the wellhead 7. The lower end of the production casing 3 extends into the reservoir 6. A space is formed between the production casing 3 and the formation 1 (the sidewall of the wellhead 7), which is the casing annulus. The casing annulus is filled with a cement sheath 2. The cement sheath 2 plays a role in fixing the production casing 3, preventing the corrosion of the production casing 3, and preventing the fluid of different layers from flowing through each other to achieve the cementing effect. A production string 4 is disposed at the middle position of the production casing 3. The area enclosed between the production string 4 and the production casing 3 is the tubing-casing annulus. The tubing-casing annulus is filled with an annulus fluid 8 and an annulus gas 9. The interface between the annulus fluid 8 and the annulus gas 9 is the tubing-casing annulus liquid level 10. A packer 5 is disposed at the bottom inside the production casing 3. The lower end of the production string 4 passes through the packer 5. It can be understood that the tubing-casing annulus is composed of a tubing head, the production casing 3, the production string 4, and the packer 5.

[0081] Please refer to Figure 2 As shown, the present application provides an optimized design method for controlling the leakage pressure rise of a production string, including the following steps:

[0082] S201: Determine whether there is leakage of the annulus fluid in the tubing-casing annulus of the target gas well; wherein, the tubing-casing annulus is composed of a tubing head, a production string, a production casing, and a packer;

[0083] S202: If there is no leakage of the annulus fluid in the tubing-casing annulus of the target gas well, determine the depth of the leakage point of the production string;

[0084] S203: According to the determined depth of the leakage point, determine Curve 1 of the variation of the maximum pressure in the tubing-casing annulus with the density of the annulus fluid;

[0085] S204: According to the pressure-bearing capacity of the tubing head, production string, production casing, and packer, determine Curve 2 of the variation of the maximum value of the pressure control range in the tubing-casing annulus with the density of the annulus fluid;

[0086] S205: Optimize and determine the density of the annulus fluid according to Curve 1 and Curve 2 to reduce the pressure in the tubing-casing annulus to within the safety threshold.

[0087] In the embodiment of the present application, by optimizing the density of the annulus fluid in the tubing-casing annulus, the pressure in the tubing-casing annulus is reduced to within the safety threshold, thereby effectively controlling the safety risks caused by the pressure rise at the leakage point of the production string. More importantly, on the premise of not moving the production string and avoiding major repairs, the phenomenon of pressure rise at the leakage point of the production string is effectively managed, avoiding exceeding the pressure-bearing capacity of the wellbore, thereby reducing the management and control cost and the maintenance period, and realizing the continuous high-intensity production of the gas well.

[0088] The following elaborates on each step in detail:

[0089] S201: Determine whether there is leakage of the annulus fluid in the tubing-casing annulus of the target gas well; wherein, the tubing-casing annulus is composed of a tubing head, a production string, a production casing, and a packer;

[0090] In this embodiment, it should be noted that first, it is necessary to determine whether there is leakage of the annulus fluid in the tubing-casing annulus of the target gas well to determine the applicability of the optimization design method of the present application. Specifically, for the target gas well with a leaking production string, the leakage of the annulus fluid is determined by monitoring the height of the annulus liquid level in the tubing-casing annulus, and the monitoring method can be, but is not limited to, acoustic liquid level monitoring, etc. Define the amplitude of the annulus liquid level fluctuation as: the difference between the maximum value and the minimum value of the monitored annulus liquid level depth within a specific time divided by the maximum well depth. Among them, the specific time can be, but is not limited to, 24h, and the monitoring frequency can be, but is not limited to, 12h. However, the total number of monitoring times within the specific monitoring time should not be less than 2 times, and it is expressed by the following formula (1):

[0091]

[0092] In the formula, F1 is the amplitude of the annular fluid level fluctuation, dimensionless; H max is the maximum value of the annular fluid level depth, m; H min is the minimum value of the annular fluid level depth, m; H W is the maximum value of the well depth, m;

[0093] When the amplitude of the annular fluid level fluctuation does not exceed the threshold within a specific time, it is considered that there is no leakage of the annular fluid; when the amplitude of the annular fluid level fluctuation exceeds the threshold within a specific time, it is considered that there is leakage of the annular fluid. Among them, the threshold can be, but is not limited to, 0.01.

[0094] Since this application controls the leakage starting pressure of the production string by optimizing the density of the annular fluid, when there is leakage of the annular fluid, the control effect will be weakened. Therefore, the optimization design method provided in this application is not applicable to the case of leakage of the annular fluid. When there is no leakage of the annular fluid, the optimization design scheme provided in this application can be used to control the leakage starting pressure of the production string.

[0095]

[0096] In the formula, F is the threshold for judging whether the method is applicable, dimensionless.

[0097] S202: If there is no leakage of the annular fluid in the oil casing annulus of the target gas well, determine the depth of the leakage point of the production string; specifically including:

[0098] S202.1: Obtain the pressure profile inside the production string under the well shut-in condition;

[0099] S202.2: Calculate the pressure profile in the oil casing annulus according to the gas column and liquid column pressures;

[0100] S202.3: Based on the pressure difference between the pressure profile inside the production string and the pressure profile in the oil casing annulus as the driving force for leakage, determine the variation law of the maximum oil casing annulus pressure with the leakage point depth, and obtain the third variation curve;

[0101] S202.4: According to the calculated oil casing annulus pressure under the well shut-in condition, the leakage point depth corresponding to the pressure value of the oil casing annulus pressure on the third variation curve is the leakage point depth of the production string.

[0102] The following is a detailed description. In this embodiment, it should be noted that for a gas well to which this optimized design method applicable to the present application is applied, the depth of the leakage point is first determined, mainly by plotting the curve of the maximum annulus pressure varying with the depth of the leakage point. To plot this variation curve, it is first necessary to determine the pressure profile inside the production string and the pressure profile of the tubing-casing annulus under the shut-in condition. Specifically, close the wellhead of the target gas well, and record the corresponding tubing-casing annulus pressure and wellhead oil pressure. Then, lower a pressure gauge into the well to obtain the pressure profile inside the production string; alternatively, in the case where it is not possible to lower a pressure gauge, the pressure profile inside the production string at the corresponding depth can be obtained by calculation. First, segment the production string, and the segment length can be but is not limited to 1 m. Then, calculate the gas density within the segment according to the pressure and temperature. Then, calculate the pressure inside the production string at the corresponding depth. According to the PVT equation of the gas, the gas density can be obtained, and the gas density can be expressed as:

[0103]

[0104] where ρ gi is the gas density of the i-th segment, g / cm3; p ti is the pressure inside the production string of the i-th segment, MPa; p s is the standard condition pressure, Pa; Ts is the standard condition temperature, K; T ti is the temperature inside the production string of the i-th segment, i.e., the formation temperature, K; ρ gs is the gas standard condition density, g / cm3; i is the segment number, dimensionless, i = 1, 2, 3....;

[0105] The temperature inside the production string of the i-th segment, i.e., the formation temperature, is calculated by the following formula:

[0106] T ti = T t0 + g e × i × H F (4)

[0107] where T t0 is the wellhead, K; g e is the geothermal gradient, K / 100 m; H F is the segment length, m;

[0108] The pressure inside the production string at the corresponding segment depth is calculated according to the gas density as shown in the formula:

[0109] p ti+1 = p ti + 10 -3 × ρ gi × g × H F (5)

[0110] where pti+1 is the pressure inside the production string for the (i + 1)-th section, in MPa; g is the acceleration due to gravity, in m / s 2 ;

[0111] According to the above formulas (3) to (5), calculating from the wellhead to the bottom of the well in sequence can obtain the pressure profile inside the production string at the corresponding depths.

[0112] After obtaining the pressure profile inside the production string, calculate the annulus pressure profile between the tubing and the casing. When the annulus pressure between the tubing and the casing is zero, the annulus pressure profile between the tubing and the casing is affected by the pressure of the gas column and the liquid column. First, calculate the gas density inside the annulus between the tubing and the casing. Since the length of the gas column inside the annulus between the tubing and the casing is short, the influence of the formation temperature on the gas density is no longer considered. Then, the gas density inside the annulus between the tubing and the casing is as shown in the formula:

[0113]

[0114] In the formula, ρ ga is the gas density inside the annulus between the tubing and the casing, in g / cm 3 ; T ta is the wellhead temperature of the annulus between the tubing and the casing, in K;

[0115] According to the annulus pressure profile between the tubing and the casing above the liquid level in the annulus, which is only related to the gas column in the annulus, and the annulus pressure profile between the tubing and the casing below the liquid level in the annulus is affected by the pressure of the gas column and the liquid column. Calculate the annulus pressure profile between the tubing and the casing respectively. Among them, when calculating this profile, it is assumed that the annulus pressure between the tubing and the casing is equal to zero, and it is expressed by the following formula:

[0116]

[0117] In the formula, H ta is the depth of the annulus between the tubing and the casing, in m; p ta is the numerical value of the annulus pressure profile between the tubing and the casing at the depth Hta, in MPa; ρ ga is the gas density inside the annulus between the tubing and the casing, in g / cm 3 ; ρ L is the density of the annulus liquid inside the annulus between the tubing and the casing, in g / cm 3 .

[0118] After obtaining the pressure profile inside the production string and the annulus pressure profile between the tubing and the casing, analyze the variation law of the maximum annulus pressure between the tubing and the casing with the depth of the leakage point. The driving force for leakage comes from the pressure difference on both sides of the leakage point. The pressure inside the leakage point depends on the pressure profile inside the production string at the depth where the leakage point is located, and the pressure outside the leakage point depends on the annulus pressure profile between the tubing and the casing at the depth where the leakage point is located, and it is expressed by the following formula:

[0119]

[0120] Wherein, p ln represents the pressure inside the leakage point, in MPa; p lw represents the pressure outside the leakage point, in MPa; H is the well depth, in m; H L is the well depth where the leakage point is located, in m; p tL is the pressure value corresponding to the pressure profile inside the production string at the depth where the leakage point is located, in MPa; p taL is the pressure value corresponding to the pressure profile in the tubing-casing annulus at the depth where the leakage point is located, in MPa;

[0121] After the production string leaks, the production string, the leakage point, and the tubing-casing annulus form a U-tube. According to the U-tube principle, when the pressure in the tubing-casing annulus reaches the maximum value, the pressures inside and outside the leakage point are equal. The maximum value of the pressure in the tubing-casing annulus corresponding to leakage points at different depths is determined and expressed by the following formula;

[0122] p anmax = p ln - p lw |H = H L (9)

[0123] Wherein, p anmax is the maximum value of the pressure in the tubing-casing annulus, in MPa;

[0124] By changing the depth of the leakage point according to the depth from the wellhead to the bottom packer of the target gas well, the variation law of the maximum value of the pressure in the tubing-casing annulus with the depth of the leakage point can be obtained, and the variation curve three is drawn.

[0125] According to the pressure in the tubing-casing annulus recorded under the above-mentioned shut-in conditions, the depth of the leakage point corresponding to this pressure value on the curve is the actual depth where the leakage point of the gas well production string is located, and is expressed by the following formula:

[0126] H LD = H L1 |p anmax = p as (10)

[0127] Wherein, H LD is the actual depth where the leakage point of the gas well is located, in m; p as is the pressure in the tubing-casing annulus recorded after shut-in, in MPa; H L1 is the depth of the leakage point corresponding to the pressure in the tubing-casing annulus under the shut-in conditions of the leakage point, in m.

[0128] S203: According to the determined depth of the leakage point, determine the variation curve one of the maximum value of the pressure in the tubing-casing annulus with the density of the annulus fluid;

[0129] In this embodiment, it should be noted that according to the depth of the leakage point, when determining the leakage point with a fixed depth, the curve of the maximum pressure in the oil-casing annulus varying with the density of the annulus liquid is obtained. When the depth of the leakage point is below the liquid level in the annulus, the pressure outside the leakage point is affected by the pressure of the liquid column in the annulus, and the pressure of the liquid column in the annulus is related to the density of the annulus liquid. Under the condition that the depth of the leakage point is known, the relationship between the maximum annulus pressure caused by the leakage starting pressure and the density of the annulus liquid can be established and expressed by the following formula:

[0130] p amaxL = p lnL - 10 -3 ×[(ρ ga ×g×H max ) + ρ L ×g×(H LD - H max )] (11)

[0131] In the formula, p anmaxL is the maximum pressure in the oil-casing annulus under the condition of determining the depth where the actual leakage point of the gas well is located, in MPa; ρ ga is the density of the gas in the oil-casing annulus, in g / cm³; ρ L is the density of the annulus liquid in the oil-casing annulus, in g / cm³;

[0132] By changing the density of the annulus liquid, the curve of the maximum pressure in the oil-casing annulus varying with the density of the annulus liquid can be obtained.

[0133] S204: Determine the curve of the maximum value of the pressure control range in the oil-casing annulus varying with the density of the annulus liquid according to the pressure-bearing capacities of the tubing head, production string, production casing and packer;

[0134] In this embodiment, it should be noted that the curve of the maximum value of the pressure control range in the oil-casing annulus varying with the density of the annulus liquid is determined. First of all, the maximum value of the pressure control range in the oil-casing annulus needs to ensure the pressure-bearing capacities of the tubing head, production string, production casing and packer. Among them, the maximum value of the pressure control range in the oil-casing annulus determined by the tubing head is 80% of its rated pressure resistance, and is expressed by the following formula:

[0135] p1 = 0.8×p 额 (12)

[0136] In the formula, p1 is the maximum value of the pressure control range in the oil-casing annulus determined by the tubing head, in MPa; p rated is the rated pressure resistance of the tubing head, in MPa;

[0137] The maximum value of the pressure control range in the oil-casing annulus determined by the production string mainly considers the external extrusion resistance of the production string under the conditions of open-well production and shut-in well conditions, and is expressed by the following formula:

[0138]

[0139] Wherein, p2 is the maximum value of the control range of the annulus pressure between the production tubing and the casing determined by the production tubing, in MPa; pextrusion is the minimum external extrusion resistance of the production tubing in the gas well, in MPa; S2 is the external extrusion safety factor, dimensionless; p t2 is the internal pressure of the tubing string corresponding to the depth where the minimum external extrusion resistance of the production tubing is located, in MPa; h2 is the depth where the minimum external extrusion resistance of the production tubing is located, in m;

[0140] The maximum value of the control range of the annulus pressure between the production tubing and the casing determined by the production casing mainly considers the internal pressure resistance of the casing and is expressed by the following formula:

[0141]

[0142] Wherein, p3 is the maximum value of the control range of the annulus pressure between the production tubing and the casing determined by the production casing, in MPa; pinner is the minimum internal pressure resistance of the production casing, in MPa; S3 is the internal pressure safety factor of the production casing, dimensionless; p b is the pressure value in annulus B, in MPa; ρ b is the equivalent brine density of annulus B, in g / cm 3 ; h3 is the depth where the minimum internal pressure resistance of the production casing is located, in m;

[0143] The maximum value of the control range of the annulus pressure between the production tubing and the casing determined by the packer mainly considers the limitation of the setting pressure of the packer and is expressed by the following formula;

[0144] p4 = p 封 + p 下 - 10 -3 ρ L gh4 (15)

[0145] Wherein, p4 is the maximum value of the control range of the annulus pressure between the production tubing and the casing determined by the packer, in MPa; p 封 is the setting working pressure difference of the packer, in MPa; p 下 is the pressure at the lower end of the packer, in MPa; h4 is the depth from the liquid level of the annulus protection fluid to the packer, in m;

[0146] The maximum value of the control range of the annulus pressure between the production tubing and the casing is taken as the minimum value among the maximum values of the control ranges of the annulus pressure between the production tubing and the casing determined by the tubing head, the production tubing, the production casing and the packer, and is expressed by the following formula;

[0147] Δp aA = min(p1, p2, p3, p4) (16)

[0148] Wherein, △p aAis the maximum value of the pressure control range in the annulus between the tubing and the casing, MPa;

[0149] By varying the density of the annulus fluid, the curve of the maximum value of the pressure control range in the annulus between the tubing and the casing versus the density of the annulus fluid can be obtained.

[0150] Please refer to Figure 3 and Figure 4 shown in Figure S205: Optimally determine the density of the annulus fluid according to the first curve and the second curve to reduce the pressure in the annulus between the tubing and the casing to within the safety threshold.

[0151] In this embodiment, it should be noted that the first curve of the maximum pressure in the annulus between the tubing and the casing versus the density of the annulus fluid and the second curve of the maximum value of the pressure control range in the annulus between the tubing and the casing versus the density of the annulus fluid are plotted in the same coordinate system; when the pressure in the annulus between the tubing and the casing is less than the pressure control range in the annulus between the tubing and the casing, the corresponding density of the annulus fluid is the optimized density value of the annulus fluid required; when this density value does not exist or is too large, the depth of the annulus liquid level is increased, and then the above steps S202 to S205 are repeated to re-determine the density of the annulus fluid.

[0152] As Figure 5 shown in Figure, it is a block diagram of a computer device according to an embodiment of the present application. The computer device is intended to represent various forms of digital computers or mobile devices. Among them, the digital computer may include a desktop computer, a portable computer, a workbench, a personal digital assistant, a server, a mainframe computer, and other suitable computers. The mobile device may include a tablet computer, a smart phone, a wearable device, etc.

[0153] As Figure 5 shown in Figure, the device 600 includes a computing unit 601, a ROM 602, a RAM 603, a bus 604, and an input / output (I / O) interface 605. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other through the bus 604. The input / output (I / O) interface 605 is also connected to the bus 604.

[0154] The computing unit 601 can perform various processes in the method embodiments of this application according to computer instructions stored in the read-only memory (ROM) 602 or computer instructions loaded from the storage unit 608 into the random access memory (RAM) 603. The computing unit 601 can be various general-purpose and / or dedicated processing components with processing and computing capabilities. The computing unit 601 can include, but is not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. In some embodiments, the method provided in the embodiments of this application can be implemented as a computer software program, which is tangibly contained in a computer-readable storage medium, such as the storage unit 608.

[0155] The RAM 603 can also store various programs and data required for the operation of the device 600. Part or all of the computer programs can be loaded and / or installed onto the device 600 via the ROM 602 and / or the communication unit 609.

[0156] The input unit 606, output unit 607, storage unit 608, and communication unit 609 in the device 600 can be connected to the I / O interface 605. Among them, the input unit 606 can be, such as, a keyboard, a mouse, a touch screen, a microphone, etc.; the output unit 607 can be, such as, a display, a speaker, an indicator light, etc. The device 600 can exchange information, data, etc. with other devices through the communication unit 609.

[0157] It should be noted that this device can also include other components necessary for normal operation. It can also only include the components necessary to implement the solution of this application, and does not necessarily include all the components shown in the figure.

[0158] The various embodiments of the systems and technologies described herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGA), application-specific integrated circuits (ASIC), application-specific standard products (ASSP), systems-on-a-chip (SOC), complex programmable logic devices (CPLD), computer hardware, firmware, software, and / or combinations thereof.

[0159] The computer instructions for implementing the method of this application can be written in any combination of one or more programming languages. These computer instructions can be provided to the computing unit 601, such that when the computer instructions are executed by a computing unit 601 such as a processor, the steps involved in the method embodiments of this application are executed.

[0160] The computer-readable storage medium provided by this application can be a tangible medium that can contain or store computer instructions for executing the various steps involved in the method embodiments of this application. The computer-readable storage medium can include, but is not limited to, storage media in the form of electronic, magnetic, optical, electromagnetic, etc.

[0161] The above specific embodiments do not constitute a limitation on the protection scope of this application. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application shall be included within the protection scope of this application.

Claims

1. An optimization design method for controlling the pressure rise due to leakage of a production tubing, characterized in that: The following steps are involved: Step 1: Determine whether the annular space liquid in the oil-casing annulus of the target gas well is lost; wherein the oil-casing annulus is composed of a tubing head, a production string, a production casing and a packer; Step 2: If the annular space liquid in the oil casing annulus of the target gas well does not leak, then determine the leakage point depth of the production string; including: Step 2.1: Obtain the pressure profile in the production string under shut-in conditions; Step 2.2: Calculate the pressure profile in the casing annulus based on the gas column and liquid column pressures; Step 2.3: Based on the pressure difference between the pressure profile in the production string and the pressure profile in the casing annulus as the driving force of the leakage, the variation law of the maximum value of the casing annulus pressure with the depth of the leakage point is analyzed and determined to obtain the variation curve 3; Step 2.4: According to the casing annulus pressure calculated under the shut-in condition, the leakage point depth corresponding to the pressure value of the casing annulus pressure on the variation curve 3 is the leakage point depth of the production string; Step 3: Determine the maximum pressure of the casing annulus as the density of the annulus liquid changes curve 1 according to the determined leakage point depth; including: When the depth of the leakage point is below the annular liquid surface, the pressure outside the leakage point is affected by the pressure of the annular liquid column, and the pressure of the annular liquid column is related to the density of the annular liquid. According to the known depth of the leakage point, the relationship between the maximum annular pressure caused by the leakage pressure and the annular liquid density is established; According to the density of the annular space liquid, a curve 1 of the maximum pressure of the oil casing annular space and the change of the density of the annular space liquid is obtained; Step 4: According to the pressure bearing capacity of the tubing head, production string, production casing and packer, determine the second curve of the maximum value of the pressure control range of the casing annulus as the density of the annulus liquid changes; including: Based on the maximum value of the pressure control range of the casing annulus, the pressure bearing capacity of the tubing head, the tubing, the production casing and the packer must be guaranteed, and the pressure bearing capacity of the tubing head, the production tubing string, the production casing and the packer is calculated respectively to determine the maximum value of the casing annulus pressure control range; The maximum value of the pressure control range of the casing annulus is obtained according to the minimum value of the maximum values ​​of the pressure control range of the casing annulus determined by the tubing head, the production string, the production casing and the packer; According to the transformation of the annular space liquid density, a second curve of the maximum value of the pressure control range of the casing annular space and the change of the annular space liquid density is obtained; Step 5: Optimizing and determining the annular space liquid density according to the change curve 1 and the change curve 2 to reduce the pressure of the oil casing annulus to within the safety threshold; including: In the same coordinates, a first curve of the maximum pressure of the casing annulus and the change of the annular liquid density and a second curve of the maximum pressure control range of the casing annulus and the change of the annular liquid density are drawn; when the casing annulus pressure is less than the casing annulus force control range, the corresponding annular liquid density is the required optimized annular liquid density value; When the density value does not exist or is too large, the depth of the annular liquid surface is increased, and then the above steps 2 to 5 are repeated to redetermine the annular liquid density.

2. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: The step of determining whether the annular space liquid in the oil casing annulus of the target gas well has been lost comprises: based on the target gas well having a leak in the production string, determining whether the annular space liquid has been lost by monitoring the annular space liquid level in the oil casing annulus; The annular liquid level fluctuation amplitude is defined by dividing the difference between the maximum and minimum annular liquid level depths within a specific monitoring period by the maximum well depth; When the fluctuation amplitude of the annular space liquid level does not exceed the threshold value within a specific time, it is considered that the annular space liquid has not been lost; When the annular space liquid level fluctuation amplitude exceeds a threshold value within a specific time, it is considered that the annular space liquid is lost.

3. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: The step 2.1: obtaining the pressure profile in the production string under the shut-in condition, comprises: The wellhead of the target gas well is closed, the corresponding casing annulus pressure and wellhead oil pressure are recorded, and then a pressure gauge is lowered into the well to obtain the pressure profile in the production string; or, The production string is divided into sections, and the gas density in the sections is calculated based on the pressure and temperature, and then the pressure in the production string at the corresponding depth is calculated.

4. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 3 is characterized in that: The production string is segmented, and the gas density in the segment is calculated according to the pressure and temperature, and then the pressure in the production string at the corresponding depth is calculated, including: According to the PVT equation of the gas, the gas density is obtained, and the gas density can be described by the following formula: In the formula, ρ gi is the gas density of the i-th segment, g / cm 3 , p ti is the pressure in the production string of the i-th segment, MPa, p s is the standard pressure, Pa; T s is the standard temperature, K, T ti is the temperature in the production string of the i-th segment, i.e., the formation temperature, K, ρ gs is the standard density of the gas, g / cm 3 , i is the segment number, dimensionless, i = 1, 2, 3...; The temperature inside the production string of the i-th segment, that is, the formation temperature, is calculated using the following formula: T ti =T t0 +g e ×i×H F (4), Where, T t0 is the wellhead, K, g e is the geothermal gradient, K / 100m, H F is the segment length, m; The pressure in the production string at the corresponding segment depth is calculated according to the gas density, as shown in the formula: p ti+1 =p ti +10 -3 ×ρ gi ×g×H F (5), In the formula, p ti+1 is the pressure in the production string of the i+1th segment, MPa; g is the acceleration of gravity, m / s 2 According to the above steps, the pressure in the production string at the corresponding depth is calculated from the wellhead to the well bottom.

5. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: The step 2.2: calculating the pressure profile in the casing annulus according to the gas column and liquid column pressures, includes: calculating the gas density in the casing annulus. Since the length of the gas column in the casing annulus is short, the influence of the formation temperature on the gas density is no longer considered. The gas density in the casing annulus is expressed by the following formula: In the formula, ρ ga is the gas density in the casing annulus, g / cm 3 , T ta is the wellhead temperature of the casing annulus, K; According to the casing annulus pressure profile located above the casing annulus liquid level, it is only related to the annular gas column, and the casing annulus pressure profile located below the annular liquid level is affected by both the gas column and the liquid column pressure. The casing annulus pressure profile is calculated respectively, wherein, when calculating the profile, the casing annulus pressure is preset to be zero, which is expressed by the following formula: In the formula, H ta is the casing annulus depth, m, p ta Depth H ta The value of the casing annulus pressure profile, MPa, ρ ga is the gas density in the casing annulus, g / cm 3 , ρ L is the density of the annular liquid in the casing annulus, g / cm 3 ;p a Casing annulus pressure, MPa.

6. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: The step 2.3: based on the pressure difference between the pressure profile in the production string and the pressure profile in the casing annulus as the driving force of the leakage, the variation law of the maximum value of the casing annulus pressure with the depth of the leakage point is analyzed and determined to obtain the variation curve 3, including: The driving force of leakage comes from the pressure difference on both sides of the leakage point. The pressure inside the leakage point depends on the pressure profile inside the production string at the depth of the leakage point. The pressure outside the leakage point depends on the pressure profile of the casing annulus at the depth of the leakage point, which is expressed by the following formula: In the formula, p ln Indicates the pressure inside the leak point, MPa, p lw Indicates the pressure outside the leak point, MPa, H is the well depth, m, H L is the well depth of the leak point, m, p tL is the pressure value corresponding to the pressure profile in the production string at the depth of the leak point, MPa, p taL is the pressure value corresponding to the casing annulus pressure profile at the depth of the leakage point, MPa; After the production string leaks, the production string, the leak point and the casing annulus form a U-shaped tube. According to the U-shaped tube principle, when the casing annulus pressure reaches the maximum value, the pressure inside and outside the leak point are equal. The maximum casing annulus pressure corresponding to the leak points at different depths is determined and expressed by the following formula; p anmax =p ln –p lw |H=H L (9) In the formula, p anmax is the maximum value of casing annulus pressure, MPa; According to the depth from the wellhead to the packer of the target gas well, the depth of the leakage point is changed, and the variation law of the maximum value of the casing annulus pressure with the depth of the leakage point is analyzed to obtain the variation curve 3.

7. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: According to the known depth of the leakage point, the relationship between the maximum annular pressure caused by the leakage pressure and the annular liquid density is established and expressed by the following formula: p amaxL =p lnL -10 -3 ×[(ρ ga ×g×H max )+r L ×g×(H LD -H max )] (11) In the formula, p anmaxL To determine the maximum annular pressure of the casing at the depth of the actual leakage point of the gas well, MPa, ρ ga is the gas density in the casing annulus, g / cm3, ρ L It is the density of the annular liquid in the casing annulus, g / cm3.

8. The optimization design method for controlling the pressure rise due to leakage of a production tubing according to claim 1, characterized in that: The maximum value of the pressure control range of the casing annulus determined by the tubing head is 80% of its rated pressure resistance capacity, which is expressed by the following formula: p1=0.8×p 额 (12) Where p1 is the maximum value of the casing annulus pressure control range determined by the tubing head, MPa, p 额 is the rated pressure resistance of the tubing head, MPa; The maximum value of the pressure control range of the casing annulus determined by the tubing is the anti-external collapse strength of the tubing under the conditions of well opening and well shut-in, which is expressed by the following formula: Where p2 is the maximum value of the casing annulus pressure control range determined by the tubing, MPa, p 挤 is the minimum anti-external collapse strength of the oil pipe in the gas well, MPa, S2 is the anti-external collapse safety factor, dimensionless, p t2 is the pressure in the tubing string corresponding to the depth of the minimum anti-external collapse strength of the tubing, MPa, h2 is the depth of the minimum anti-external collapse strength of the tubing, m; The maximum value of the control range of the casing annulus pressure determined by the production casing is the internal pressure resistance of the production casing, which is expressed by the following formula: Where p3 is the maximum value of the casing annulus pressure control range determined by the production casing, MPa, p 内 is the minimum internal pressure strength of the production casing, MPa, S3 is the safety factor of the production casing against internal pressure, dimensionless, p b is the pressure value of annulus B, MPa, ρ b is the equivalent brine density of annulus B, g / cm 3 ; h3 is the depth of the minimum internal pressure resistance of the production casing, m; The maximum value of the pressure control range of the casing annulus determined by the packer is the limit of the packer setting pressure, which is expressed by the following formula: p4=p 封 +p 下 -10 -3 r L gh4 (15) Where p4 is the maximum value of the casing annulus pressure control range determined by the packer, MPa, p 封 is the packer setting working pressure difference, MPa, p 下 is the pressure at the lower end of the packer, MPa, h4 is the depth from the annulus protection fluid level to the packer, m; The maximum value of the pressure control range of the casing annulus is obtained by the minimum value among the maximum values ​​of the pressure control range of the casing annulus determined by the tubing head, the production string, the production casing and the packer, and is expressed by the following formula; Δp aA =min(p1,p2,p3,p4) (16) In the formula, △p aA It is the maximum value of the pressure control range of the casing annulus, MPa.

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