A method for calculating annular pressure during cement slurry weight loss process

Abstract

The present invention belongs to the technical field of oil and gas well cementing engineering, and specifically relates to a method for calculating the annular pressure during the waiting and weight loss process of cement slurry. The method includes the steps of calculating the temperature change of cement slurry, calculating the weight loss pressure of cement slurry; and calculating the law of the annular pressure change during the waiting and weight loss process of cement slurry: finally, the law of the annular pressure change during the waiting and weight loss process of cement slurry is obtained from the wellbore annular pressure during the entire waiting and weight loss process. The present invention provides a method for calculating the annular pressure during the waiting and weight loss process of cement slurry in a large temperature difference well. The method takes into account the law of hydration heat release during the waiting and weight loss of cement slurry, so that the calculation of the wellbore temperature field is more accurate, thereby providing an accurate calculation method for the annular pressure during the waiting and weight loss process, and provides a theoretical basis for the formulation of annular back pressure compensation scheme during the waiting and weight loss of cement slurry, which is of great significance for the safe cementing construction of large temperature difference and narrow density window oil and gas wells.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas well cementing engineering, and in particular relates to a method for calculating annular space pressure in a cement slurry weight loss process. Background Art

[0002] High-pressure gas wells, especially those with large temperature differences, usually have complex geological structures and many vertical oil, gas and water displays. The annular air channeling after cementing is a difficult problem that needs to be solved urgently. Studies have shown that the hydration of cement slurry during the waiting period will lead to a decrease in the pressure acting on the gas layer, resulting in the phenomenon of cement slurry weight loss, which causes pressure imbalance, which is one of the reasons for early gas channeling after cementing. In order to solve this technical problem, relevant workers have conducted a series of related studies. It mainly focuses on the investigation of weight loss pressure. For example, Chinese patent CN111287688A discloses a method for determining the weight loss value of cement slurry and a method for holding annular pressure in different time periods after cementing. This patent solves the pressure balance problem after the weight loss of cement slurry by replenishing annular pressure in stages, avoids the pressure value exceeding the high pressure leakage formation caused by one-time holding pressure waiting, effectively achieves pressure stability throughout the waiting process, and better solves the problem of short-term channeling after cementing.

[0003] For example, patent CN111042801A focuses on the weight loss of cement slurry under different cement slurry systems. It discloses a device and a method for measuring the weight loss of annular cement slurry. The device includes a kettle, a pressure pump and a computer. The kettle is provided with coaxial casing and formation baffles. The bottom of the casing is provided with a heating rod and a temperature sensor. The bottom of the annular gap between the casing and the formation baffle is provided with an annular pressure sensor. The annular pressure sensor and the temperature sensor transmit data to the computer. The top of the kettle is provided with three flanges connected in sequence, and the flanges are provided with pressure valves and pressure gauges. The device can simulate the weight loss of cement slurry, well wall and casing under actual working conditions, and can analyze the weight loss of cement slurry under different formations and different cement slurry systems, and can also simulate the weight loss at different well depths and different temperatures and pressures.

[0004] The document "Research and Application of Cement Slurry Weight Loss Pressure Evaluation Technology" (Liu Yang, Drilling Fluids and Completion Fluids, Vol. 36, No. 6, November 2009, 749-753) uses the proportional reduction method to develop a set of high-temperature and high-pressure cement slurry weight loss pressure evaluation experimental equipment, and conducts typical cement slurry weight loss pressure experiments in vertical and inclined wells. At the same time, a method for calculating the cement slurry weight loss pressure in sections is proposed, which has been tested in the field and provides guidance for the annulus pressure holding and setting.

[0005] The above-mentioned literature mainly focuses on the experimental test method of weight loss pressure. Due to the limitation of the length of the cement slurry column in the laboratory, the maximum test temperature is only 120°C, which cannot meet the requirements of high temperature and high pressure. Although the calculation method of the annular pressure during the weight loss process of cement slurry is involved, the weight loss of cement slurry is greatly affected by temperature, and the existing research has not considered the changes in the wellbore temperature field during the cement slurry setting process.

[0006] Therefore, how to provide a method for calculating the annular pressure during the cement slurry waiting to set process with higher calculation accuracy so that it can be applied to wells with large temperature differences and to apply accurate annular pressure to the cement slurry waiting to set process is a technical problem faced by this application. Summary of the invention

[0007] In order to solve the defects of the prior art, the purpose of the present invention is to provide a method for calculating the annular pressure during the cement slurry waiting for setting weight loss process, and adopt this calculation method to provide theoretical guidance for the accurate application of annular back pressure during the waiting for setting process.

[0008] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0009] A method for calculating annular pressure during cement slurry weight loss process comprises the following steps:

[0010] Calculation steps for cement slurry temperature-time variation curve:

[0011] According to the static temperature T at the bottom of the well sb , cement slurry return depth temperature T st The wellbore is divided into n sections according to the allowable temperature variation range ΔT. The wellbore sections are recorded as sections 1, 2, 3...i...n from top to bottom. The vertical depth of the i-th wellbore from the wellhead is recorded as H i ; The time when cement slurry hydration heat release begins is recorded as t 0 , the end of hydration exothermicity is recorded as t ∞ , any time in the heat release process from the beginning to the end of heat release is recorded as t m ;

[0012] Determine the well depth H during the cement slurry setting process according to parameters 1), 2) and 3) i The time variation curve of the wellbore temperature at ;

[0013] 1) is the functional relationship of cement slurry hydration exothermic temperature, 2) is the wellbore depth H i 3) is the change in cement slurry temperature caused by heat exchange between the formation and the cement slurry; 4) is the change in cement slurry temperature caused by heat exchange between the casing and the cement slurry;

[0014] Calculation steps of cement slurry weight loss pressure:

[0015] According to the experimental data of cement slurry weight loss pressure at different temperatures, combined with the wellbore temperature distribution data determined by the cement slurry temperature change calculation step, the cement slurry weight loss pressure data is fitted every t°C within the wellbore temperature distribution range, where t takes a value not exceeding 5;

[0016] The calculation steps of the annular pressure change law during the cement slurry setting weight loss process are as follows:

[0017] According to the cement slurry weight loss pressure data obtained by fitting in the cement slurry weight loss pressure calculation step and the static liquid column pressure calculation formula, the temperature T of the i-th section of the wellbore of the cement slurry within the wellbore temperature field is inverted. i The corresponding density ρ i ; Then the temperature T i The corresponding density ρ i , and the temperature data T of the bottom of the annular cement slurry in the i-th section i ', using cubic spline difference, we get t m Cement slurry density ρ at the i-th well section at time i '; Then the bottom depth H of the i-th well section i ' and t m Cement slurry density ρ at the i-th well section at time i ' and the gravitational acceleration constant g determine t m The wellbore annulus pressure Pf(t m ), and finally, the annular pressure variation law of the cement slurry during the whole process of waiting for setting weight loss is obtained from the wellbore annular pressure during the whole process of waiting for setting weight loss.

[0018] Preferably, the cement slurry temperature change calculation steps are as follows:

[0019] The calculation formula for the change of wellbore temperature at any well depth with time is shown in formula (1):

[0020] T s =T e -T t +T c (1)

[0021] In formula (1), Ts is the wellbore temperature in the weightless state, K; Te is the change in cement slurry temperature caused by the heat exchange between the formation and cement slurry at the i-th wellbore depth, K; Tc is the hydration temperature rise of cement slurry, K; Tt is the change in cement slurry temperature caused by the heat exchange between casing and cement slurry, K;

[0022] The change in cement slurry temperature Te caused by heat exchange between the formation and cement slurry at the i-th wellbore depth in formula (1) is obtained by the following formula (2):

[0023]

[0024] In formula (2), T eis the change in cement slurry temperature caused by heat exchange between the formation and cement slurry at the i-th wellbore depth, K; r w is the wellbore radius, m; U a is the formation thermal conductivity, W / m 2 ·K;c c is the specific heat capacity of cement slurry in the annulus, J / kg·K; ρ c is the density of cement slurry in the annulus, kg / m 3 ; A a is the cross-sectional area of ​​the annulus, m 2 ; T e,0 is the temperature at the interface between the wellbore and the formation, K;

[0025] The hydration temperature rise of cement slurry at the depth of the i-th section of the wellbore is T c It is calculated by the cement slurry hydration exothermic function formula (3):

[0026]

[0027] In formula (3), Q ∞ is the final hydration heat of cement paste per unit mass; c c is the specific heat capacity of cement slurry in the annulus, J / (kg·K); α is the hydration degree of cement slurry;

[0028] The cement slurry temperature change Tt caused by the heat exchange between the casing and the cement slurry satisfies the functional relationship shown in formula (4):

[0029]

[0030] In formula (4), T t is the change in cement slurry temperature caused by heat exchange between casing and cement slurry, r ci is the inner diameter of the casing, m; U c is the total heat transfer coefficient from casing to annulus, W / (m 2 ·K); T f is the drilling fluid temperature in the casing, K.

[0031] Preferably, T e,0 is the temperature at the interface between the wellbore and the formation, which is obtained by the following formula (2-1):

[0032]

[0033] In formula (2-1), T 0 is the surface temperature, °C; G is the geothermal gradient, °C·hm -1 ;H i is the wellbore depth, m, K; T c is the hydration temperature rise of cement slurry, K.

[0034] Preferably, Aa is the cross-sectional area of ​​the annulus, which is calculated as (π(wellbore radius 2 -Casing radius 2 )).

[0035] Preferably, α is the hydration degree of cement slurry, which is obtained by formula (3-2):

[0036] In formula (3-2), Q(t) is t m The hydration of unit mass of cement slurry releases heat at this moment.

[0037] The heat released by cement slurry hydration can be measured using conventional temperature measuring instruments in the art.

[0038] Preferably, the cement slurry weight loss pressure is calculated using the following formula (5):

[0039]

[0040] In formula (5), T s is the wellbore temperature in weightless state, T S It is calculated by formula (1).

[0041] Preferably, in the step of calculating the annular pressure variation law during the cement slurry setting weight loss process, the static liquid column pressure calculation formula is as shown in formula (6):

[0042] P(T i )=ρ i gH (6)

[0043] In formula (6), P(T i ) is the hydrostatic column pressure, MPa; ρ i For cement paste at T i Density of temperature; H is the depth of the wellbore.

[0044] Preferably, the temperature data T at the bottom of any i-th section of the annular cement slurry is i The calculation formula of ' is shown in formula (8):

[0045] T′ i =T sb -(i-1)ΔT (8)

[0046] In formula (8), T sb is the bottom hole temperature, K; ΔT is the allowable temperature variation range, generally 1-2°C, and i refers to the cement slurry in the ith well section.

[0047] Preferably, for any segment of annular cement slurry, the i-th segment refers to the segment according to the bottom hole temperature T sb , the temperature of cement slurry at the deep end T stand the allowable temperature variation range ΔT divide the annular cement slurry into n sections;

[0048] The calculation formula of n is shown in formula (8-1),

[0049]

[0050] In formula (8-1), T sb is the bottom hole temperature, K; T st is the temperature of cement slurry at the depth, K.

[0051] Preferably, the bottom depth H of the i-th well section i The calculation formula is shown in formula (10):

[0052] H′ i =f -1 (T′ i )=f -1 [T sb -(i-1)ΔT] (10)

[0053] In formula (10), T sb is the bottom hole temperature, K, and ΔT is the allowable temperature variation range, which is generally 1-2℃.

[0054] Preferably, t m The wellbore annulus pressure Pf(t m ) The calculation formula is shown in formula (11):

[0055]

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] (1) The present invention provides a method for calculating the annular pressure during the waiting-for-setting process of cement slurry in a large temperature difference well. The method takes into account the heat release law of hydration during the waiting-for-setting of cement slurry, making the calculation of the wellbore temperature field more accurate, thereby providing an accurate calculation method for the annular pressure during the waiting-for-setting weight loss process, providing a theoretical basis for the formulation of annular back pressure compensation scheme during the waiting-for-setting of cement slurry, and having important significance for the safe cementing construction of large temperature difference and narrow density window oil and gas wells;

[0058] (2) Existing research is limited by the length of the cement slurry column in the laboratory, and can only test the weightlessness pressure data of 1-3 temperature points, and the highest test temperature is only 120°C. The research object of this patent is aimed at wells with large temperature differences, which meets the requirements of high temperature and high pressure;

[0059] (3) The existing methods for compensating annular pressure still have much room for improvement, especially for wells with large temperature differences. This patent provides a method for accurately calculating the annular pressure during the cement slurry weight loss process, which has important guiding significance for the application of annular compensation pressure. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0061] Figure 1 This is the cement slurry hydration exothermic curve in Example 1.

[0062] Figure 2 This is the cement slurry weight loss pressure process curve.

[0063] Figure 3 Figure 3 is a segmentation diagram of annulus cement slurry based on temperature step size.

[0064] Figure 4 This is the annular pressure change curve during the cement slurry setting weight loss process in Example 1.

[0065] In the figure, 1. producing layer, 2. tail slurry, 3. lead slurry, 4. cement slurry return depth, 5. pre-fluid, 6. production casing. DETAILED DESCRIPTION

[0066] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0067] Example 1

[0068] This embodiment takes a certain oil and gas well as an example to illustrate the calculation method of annular pressure during cement slurry weight loss process:

[0069] It includes the steps of calculating the temperature change of cement slurry:

[0070] According to the static temperature T at the bottom of the well sb , cement slurry return depth temperature T st The wellbore is divided into n sections according to the allowable temperature variation range ΔT. The wellbore sections are recorded as sections 1, 2, 3...i...n from top to bottom. The vertical depth of the i-th wellbore from the wellhead is recorded as H i ; The time when cement slurry hydration heat release begins is recorded as t 0 , the end of hydration exothermicity is recorded as t ∞ , any time in the heat release process from the beginning to the end of heat release is recorded as t m ;

[0071] Determine the well depth H during the cement slurry setting process according to parameters 1), 2) and 3) i The time variation curve of the wellbore temperature at ;

[0072] 1) is the functional relationship of cement slurry hydration exothermic temperature, 2) is the wellbore depth H i 3) is the change in cement slurry temperature caused by heat exchange between the formation and the cement slurry; 4) is the change in cement slurry temperature caused by heat exchange between the casing and the cement slurry;

[0073] That is, the calculation function of cement slurry temperature change is as shown in formula (1):

[0074] T s =T e -T t +T c (1)

[0075] In formula (1), T s is the wellbore temperature in weightless state, K; T e is the change in cement slurry temperature caused by heat exchange between the formation and cement slurry at the i-th wellbore depth, K; T c is the hydration temperature rise of cement paste, K; T t is the temperature change of cement slurry caused by heat exchange between casing and cement slurry, K.

[0076] In this embodiment, the change in cement slurry temperature Te caused by heat exchange between the formation and cement slurry at the i-th wellbore depth is obtained by the following formula (1a):

[0077]

[0078] In formula (2), T e is the change in cement slurry temperature caused by heat exchange between the formation and cement slurry at the i-th wellbore depth, K; r w is the wellbore radius, m; U a is the formation thermal conductivity, W / (m 2 ·K); c c is the specific heat capacity of cement slurry in the annulus, J / (kg·K); ρ c is the density of cement slurry in the annulus, kg / m 3 ; A a is the cross-sectional area of ​​the annulus, which is calculated as (π×(wellbore radius 2 -Casing radius 2 )), m 2 ; T e,0 is the temperature at the interface between the wellbore and the formation, which is obtained by the following formula (2-1):

[0079]

[0080] In formula (2-1), T 0 is the surface temperature, °C; G is the geothermal gradient, °C·hm -1 ;H i is the wellbore depth, m; T c is the hydration temperature rise of cement slurry, K.

[0081] In this embodiment, the hydration temperature rise of cement slurry at the depth of the i-th section of the wellbore is T c It is calculated by the cement slurry hydration exothermic function formula (3):

[0082]

[0083] In formula (3), Q ∞ is the final hydration heat per unit mass of cement slurry, which is obtained by formula (3-1); c c is the specific heat capacity of cement slurry in the annulus, J / (kg·K); α is the hydration degree of cement slurry, which is obtained by formula (3-2);

[0084]

[0085] In formula (1)-2a, Q' is the heat released by cement slurry hydration, J / kg, and m is the mass of cement slurry;

[0086]

[0087] In formula (3-2), Q(t) is t m The hydration of unit mass of cement slurry releases heat at this moment.

[0088] The heat released by cement slurry hydration can be measured using conventional temperature measuring instruments in the art.

[0089] In this embodiment, the change in cement slurry temperature caused by heat exchange between the casing and the cement slurry is T t The functional relationship is as shown in formula (4):

[0090]

[0091] In formula (4), T t is the change in cement slurry temperature caused by heat exchange between casing and cement slurry, r ci is the inner diameter of the casing, m; U c is the total heat transfer coefficient from casing to annulus, W / (m 2 ·K); T f is the drilling fluid temperature in the casing, K.

[0092] In this embodiment, the parameters of the oil and gas well are: well type: vertical well, well depth: 1950m, wellbore diameter: 660mm, casing diameter: 508mm, cement slurry density: 1800kg / m 3, surface temperature: 25℃, thermal conductivity of the formation: 1.83W / (m 2 ·K), formation specific heat capacity: 710J / (kg·K), geothermal gradient: 3℃·hm -1 , thermal conductivity of cement slurry: 0.72W / (m 2 ·K), cement slurry specific heat capacity: 780J / (kg·K), casing thermal conductivity: 43.2W / (m 2 ·K).

[0093] like Figure 1 As shown, it is a curve of the change of the wellbore temperature at any depth of the well with time during the cement slurry setting process calculated in this embodiment.

[0094] Calculation steps of cement slurry weight loss pressure :

[0095] According to the experimental data of cement slurry weight loss pressure at different temperatures, combined with Calculation steps for cement slurry temperature change The determined wellbore temperature distribution data is used to fit the cement slurry weight loss pressure data every t°C within the wellbore temperature distribution range: t takes a value not exceeding 5, such as 2-5, and 2 is taken in this embodiment.

[0096] Where P s is the weight loss pressure of cement slurry at different temperatures, and its calculation formula is shown in formula (5):

[0097]

[0098] In formula (5), T s is the wellbore temperature in weightless state, T S Calculated from formula (1), in this embodiment, P S The fitting results are as follows Figure 2 shown.

[0099] Calculation steps of annular pressure variation law during cement slurry weight loss process :

[0100] according to Calculation steps of cement slurry weight loss pressure The cement slurry weight loss pressure data obtained by fitting and the static liquid column pressure calculation formula are used to invert the cement slurry temperature T in the wellbore temperature field range. i The corresponding density ρ i ; Then the temperature T i The corresponding density ρ i , and the temperature data T at the bottom of any i-th section of the annular cement slurry i ', using cubic spline difference, we get t m Cement slurry density ρ at the i-th well section at time i '; Then the bottom depth H of the i-th well section i ' and t m Cement slurry density ρ at the i-th well section at time i' and the gravitational acceleration constant g determine t m Wellbore annulus pressure P f (t m ), and finally, the annular pressure variation law of the cement slurry during the whole process of waiting for setting weight loss is obtained from the wellbore annular pressure during the whole process of waiting for setting weight loss.

[0101] In this step , hydrostatic column pressure calculation formula As shown in formula (6):

[0102] P(T i )=ρ i HkDJ i (6)

[0103] In formula (6), P(T i ) is the hydrostatic column pressure, MPa; ρ i is the cement paste at temperature T i The density at time H i is the wellbore depth.

[0104] In the present invention, the hydrostatic column pressure P(T i ) can be measured by a pressure detection device.

[0105] The temperature field of cement slurry in the wellbore is inverted by the hydrostatic column pressure. Density ρ corresponding to temperature Ti i , the calculation formula is shown in formula (7),

[0106] ρ i =g(T i ) (7)

[0107] Temperature data T at the bottom of the i-th section of annular cement slurry i ' The calculation formula is shown in formula (8):

[0108] T′ i =T sb -(i-1)ΔT (8)

[0109] In formula (8), T sb is the bottom hole temperature, K; ΔT is the allowable temperature variation range, generally 1-2°C,

[0110] i refers to the cement slurry in the i-th well section, such as Figure 3 As shown, according to the bottom hole temperature T sb , the temperature of cement slurry at the deep end T st and the allowable temperature variation range ΔT divide the annular cement slurry into n sections;

[0111] The calculation formula of n is shown in formula (8-1),

[0112]

[0113] In formula (8-1), T sbis the bottom hole temperature, K; T st is the temperature of cement slurry at the depth, K.

[0114] According to the density data ρ corresponding to any temperature i , and the temperature data of the bottom of any i-th section of the annular cement slurry T i ', through polynomial fitting, we can get any t m Cement slurry density ρ at the i-th well section at time i ' The calculation formula is shown in formula (9):

[0115]

[0116] The bottom depth of the i-th well section is H i ' The calculation formula is shown in formula (10):

[0117] H′ i =f -1 (T′ i )=f -1 [T sb -(i-1)ΔT] (10);

[0118] In formula (10), T sb is the bottom hole temperature, K, and ΔT is the allowable temperature variation range, which is generally 1-2℃.

[0119] t m Wellbore annulus pressure P f (t m ) The calculation formula is shown in formula (11):

[0120]

[0121] like Figure 4 FIG. 1 is a curve showing the change of annular pressure with well depth calculated by the above method of this embodiment.

[0122] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating annular pressure during cement slurry weight loss during setting, characterized in that: The steps include: Calculation steps for cement slurry temperature-time variation curve: According to the static temperature T at the bottom of the well sb , cement slurry return depth temperature T st The wellbore is divided into n sections according to the allowable temperature variation range ΔT. The wellbore sections are recorded as sections 1, 2, 3...i...n from top to bottom. The vertical depth of the i-th wellbore from the wellhead is recorded as H i The start time of cement slurry hydration heat release is recorded as t0, and the end time of hydration heat release is recorded as t ∞ , any time in the heat release process from the beginning to the end of heat release is recorded as t m ; Determine the wellbore depth H during the cement slurry waiting process according to parameters 1), 2) and 3) i The time variation curve of the wellbore temperature at ; 1) is the functional relationship of cement slurry hydration exothermic temperature, 2) is the wellbore depth H i 3) is the change in cement slurry temperature caused by heat exchange between the formation and the cement slurry; 4) is the change in cement slurry temperature caused by heat exchange between the casing and the cement slurry; Calculation steps of cement slurry weight loss pressure: According to the experimental data of cement slurry weight loss pressure at different temperatures, combined with the wellbore temperature distribution data determined by the cement slurry temperature change calculation step, the cement slurry weight loss pressure data is fitted every t℃ within the wellbore temperature distribution range, where t takes a value not exceeding 5; The calculation steps of the annular pressure change law during the cement slurry setting weight loss process are as follows: According to the cement slurry weight loss pressure data obtained by fitting in the cement slurry weight loss pressure calculation step and the static liquid column pressure calculation formula, the temperature T of the i-th section of the wellbore of the cement slurry within the wellbore temperature field is inverted. i The corresponding density ρ i ; Then the temperature T i The corresponding density ρ i , and the temperature data T of the bottom of the annular cement slurry in the i-th section i ', using cubic spline difference, we get t m Cement slurry density ρ at the i-th well section at time i '; Then the bottom depth H of the i-th well section i ' and t m Cement slurry density ρ at the i-th well section at time i ' and the gravitational acceleration constant g determines t m The wellbore annulus pressure Pf(t m ), and finally, the annular pressure variation law of the cement slurry during the whole process of waiting for setting weight loss is obtained from the wellbore annular pressure during the whole process of waiting for setting weight loss; The calculation steps of the cement slurry temperature change are as follows: The calculation formula for the change of wellbore temperature at any well depth with time is shown in formula (1): T s =T e -T t +T c (1) In formula (1), Ts is the wellbore temperature in the weightless state, K; Te is the change in cement slurry temperature caused by heat exchange between the formation and cement slurry at a certain wellbore depth, K; Tc is the hydration temperature rise of cement slurry, K; Tt is the change in cement slurry temperature caused by heat exchange between casing and cement slurry, K; The change in cement slurry temperature Te caused by heat exchange between the formation and cement slurry at a certain wellbore depth in formula (1) is obtained by the following formula (2): In formula (2), T e is the change in cement slurry temperature caused by heat exchange between the formation and cement slurry at a certain wellbore depth, K; r w is the wellbore radius, m; U a is the formation thermal conductivity, W / m 2 ·K;c c is the specific heat capacity of cement slurry in the annulus, J / kg·K; ρ c is the density of cement slurry in the annulus, kg / m 3 ; A a is the cross-sectional area of ​​the annulus, m 2 ; T e,0 is the temperature at the interface between the wellbore and the formation, K; Cement slurry hydration temperature rise T at a certain depth c It is calculated by the cement slurry hydration heat release function as shown in formula (3); In formula (3), Q ∞ is the final hydration heat of cement paste per unit mass; c c is the specific heat capacity of cement slurry in the annulus, J / (kg·K); α is the hydration degree of cement slurry; The cement slurry temperature change Tt caused by the heat exchange between the casing and the cement slurry satisfies the functional relationship shown in formula (4): In formula (4), T t is the change in cement slurry temperature caused by heat exchange between casing and cement slurry, r ci is the inner diameter of the casing, m; U c is the total heat transfer coefficient from casing to annulus, W / (m 2 ·K); T f is the drilling fluid temperature in the casing, K.

2. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1 is characterized in that: T e,0 is the temperature at the interface between the wellbore and the formation, which is obtained by the following formula (2-1): In formula (2-1), T0 is the surface temperature, °C; G is the geothermal gradient, °C·hm -1 ;H i is the wellbore depth, m, K; T c is the hydration temperature rise of cement slurry, K.

3. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: α is the hydration degree of cement slurry, which is obtained by formula (3-2): In formula (3-2), Q(t) is t m The hydration of unit mass of cement slurry releases heat at this moment.

4. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: The weight loss pressure of cement slurry is calculated using the following formula (5): In formula (5), T s is the wellbore temperature in weightless state, T S It is calculated by formula (1).

5. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: In the step of calculating the annular pressure variation law during the cement slurry setting weight loss process, the static liquid column pressure calculation formula is shown in formula (6): P(T i )=ρ i gH (6) In formula (6), P(T i ) is the hydrostatic column pressure, MPa; ρ i is the temperature T of the cement slurry in the i-th section of the wellbore i The corresponding density; H is the wellbore depth.

6. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: Temperature data T at the bottom of any i-th section of annular cement slurry i The calculation formula of ' is shown in formula (8): T i ′=T sb -(i-1)ΔT (8) In formula (8), T sb is the bottom hole temperature, K; ΔT is the allowable temperature variation range, generally 1-2°C, i refers to the cement slurry in the i-th well section.

7. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 6, characterized in that: The calculation formula of n is shown in formula (8-1), In formula (8-1), T sb is the bottom hole temperature, K; T st is the temperature of cement slurry at the depth, K.

8. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: The bottom depth of the i-th well section is H i The calculation formula is shown in formula (10): H i ′=f -1 (T i ′)=f -1 [T sb -(i-1)ΔT] (10) In formula (10), T sb is the bottom hole temperature, K, and ΔT is the allowable temperature variation range, which is generally 1-2℃.

9. The method for calculating annular pressure during cement slurry weight loss during setting according to claim 1, characterized in that: t m The wellbore annulus pressure Pf(t m ) The calculation formula is shown in formula (11):

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