Gas well annulus gas leakage monitoring method and system

Abstract

The invention relates to a gas well annulus gas leakage monitoring method and system. The method comprises the steps that the casing side pressure of an initial leakage point is determined; determining the gas leakage flow of the leakage point; determining a time step length required for generating a single bubble under the gas leakage flow; sampling by taking the time step length as a time interval, and obtaining a gas column volume and a liquid column volume in the annulus protection liquid in the current time step length; determining a target wellhead oil sleeve annulus pressure; the casing side pressure of the target leakage point is determined; if the casing side pressure of the target leakage point is smaller than the pressure in the pipe column at the leakage point, the gas column volume and the liquid column volume are updated and serve as the gas column volume and the liquid column volume of the next time step respectively; and the casing side pressure of the target leakage point is repeatedly obtained till the casing side pressure of the target leakage point is larger than or equal to the pressure in the pipe column at the leakage point, and it is determined that gas leakage in the gas well annulus is stopped. The problem that the leakage point casing side pressure detection result error is large due to the fact that the migration process of leaked gas in a liquid column section is ignored in the detection process is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of pipe column leakage detection, and in particular to a method and system for monitoring gas leakage in the annulus of a gas well. Background Art

[0002] Many in-service gas wells and newly developed complex gas wells have experienced casing damage and abnormal annular pressure to varying degrees, which seriously threatens the operational safety of oil and gas production and has gradually become a major safety hazard. Annular pressure refers to the phenomenon of abnormal pressure at the wellhead in the space outside the gas well completion string. The gas well is composed of multiple layers of casing, which constitutes several annular spaces. Among them, the possibility of abnormal annular high pressure and the accident consequences of the A annulus formed by the gas well completion string (tubing) and the production casing are much higher than those of other annuli, so the research on the pressure relief and recovery of the A annulus is particularly important. The annulus of the gas well is filled with a certain height of annular protection fluid. During normal production, the liquid surface pressure remains constant and the wellhead pressure relief valve is closed. However, due to the complex internal environment of the gas well, which is often in a high temperature and high pressure state, the downhole packer or tubing joint will leak and fail, causing the production layer gas to enter the annulus, flow through the annular protection fluid, and then rise to the top of the annulus, and continue to accumulate at the annular wellhead, causing annular pressure holding. In severe cases, it will cause wellhead lifting or blowout accidents, causing huge economic losses and environmental damage.

[0003] The existing monitoring of gas leakage in the annulus pressure of gas wells is mainly through calculating the gas flow rate of downhole leakage, ignoring the migration process of the leaking gas in the liquid column section, that is, the leaking gas directly migrates to the wellhead and gathers at the wellhead. Finally, a wellhead annulus gas state equation considering the liquid column compression is established to solve the annulus pressure at the wellhead. The disadvantage of the above method is that it ignores the migration process of the leaking gas in the liquid column section, and the result has a large error. Summary of the invention

[0004] In order to overcome the problem of ignoring the migration process of the leaking gas in the liquid column section, resulting in large error in the results, the present invention provides a method and system for monitoring gas leakage in the annulus of a gas well.

[0005] In a first aspect, in order to solve the above technical problems, the present invention provides a method for monitoring gas leakage in the annulus of a gas well, comprising:

[0006] S1, obtaining the initial wellhead casing annulus pressure, and determining the casing side pressure at the initial leakage point according to the initial wellhead casing annulus pressure;

[0007] S2, determining the gas leakage flow rate at the leakage point according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure;

[0008] S3, determining the time step required to generate a single bubble under the gas leakage flow rate according to the bubble volume after the multiple bubbles are separated from the leakage point;

[0009] S4, sampling with the time step as the time period, and obtaining the gas column volume and liquid column volume in the annular protection liquid at the end time corresponding to the current time period;

[0010] S5, determining the target wellhead casing annulus pressure according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the current end time;

[0011] S6. Determine the casing side pressure at the target leakage point according to the target wellhead casing annulus pressure;

[0012] S7. If the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, the gas column volume and the liquid column volume continue to be updated and used as the gas column volume and the liquid column volume of the next time period respectively;

[0013] S8. Repeat steps S5 to S7 until the casing pressure at the target leakage point is greater than or equal to the pressure in the tubing string at the leakage point, and determine that the gas leakage in the annulus of the gas well stops.

[0014] In a second aspect, the present invention further provides a gas well annulus gas leakage monitoring system, comprising:

[0015] The module for determining the casing side pressure at the initial leakage point is used to obtain the initial wellhead casing annulus pressure and determine the casing side pressure at the initial leakage point according to the initial wellhead casing annulus pressure;

[0016] A gas leakage flow determination module is used to determine the gas leakage flow of the leakage point according to the casing side pressure of the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure;

[0017] A time step determination module, used for determining a time step required for generating bubbles under a gas leakage flow rate according to the bubble volumes after the multiple bubbles are separated from the leakage point;

[0018] The initial value acquisition module is used to sample at time step intervals to obtain the gas column volume and liquid column volume gas column volume in the annular protection fluid at the end time corresponding to the current time step period;

[0019] A target wellhead casing annulus pressure determination module is used to determine the target wellhead casing annulus pressure gas column volume according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the end of the current time step;

[0020] A target leakage point casing side pressure determination module is used to determine the target leakage point casing side pressure according to the target wellhead casing annulus pressure;

[0021] An updating module is used for continuing to update the gas column volume and the liquid column volume if the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, and using them as the gas column volume and the liquid column volume gas column volume gas column volume of the next time step period respectively;

[0022] The end judgment module is used to repeatedly execute the corresponding functions of the target wellhead casing annulus pressure determination module, the target leakage point casing side pressure determination module and the update module until the casing side pressure of the target leakage point is greater than or equal to the pressure in the tubing at the leakage point, and it is determined that the gas leakage in the gas well annulus has stopped.

[0023] The beneficial effects of the present invention are as follows: the initial wellhead casing annulus pressure is obtained, the casing side pressure at the initial leakage point is obtained, and then the gas leakage flow rate at the leakage point is determined according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure, and then the bubble diameter and bubble volume after multiple bubbles are separated from the leakage point are studied to obtain the time step for bubble generation at the leakage point, and then the time step is used as the time period for sampling to detect gas leakage in the annulus of the gas well. Within the time period, the change in the liquid column volume and the gas column volume caused by the migration of bubbles in the annulus protection fluid are taken into account. Changes are obtained, and the changes in the wellhead casing annulus pressure caused by bubble migration during this period are obtained, the target wellhead casing annulus pressure is obtained, and then the casing side pressure of the target leakage point is recalculated according to the target wellhead casing annulus pressure. The gas leakage situation in the gas well annulus can be obtained by comparing the casing side pressure of the target leakage point with the pressure in the tubing at the leakage point. In this embodiment, the influence of bubbles migrating in the annulus protection fluid on the wellhead casing annulus pressure is taken into account, the accuracy of the detection results is improved, and the problem that the prior art ignores the migration process of the leaking gas in the liquid column section and the result has a large error is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0025] Figure 1 A schematic flow chart of a method for monitoring gas leakage in the annulus of a gas well provided by one embodiment of the present invention;

[0026] Figure 2 A schematic flow chart of a method for monitoring gas leakage in the annulus of a gas well provided by another embodiment of the present invention;

[0027] Figure 3 The present invention is a schematic structural diagram of a gas leakage monitoring system in the annulus of a gas well according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The following examples are provided to further explain and supplement the present invention and do not constitute any limitation to the present invention.

[0029] A method and system for monitoring gas leakage in the annulus of a gas well according to an embodiment of the present invention will be described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, an embodiment of the present invention provides a method for monitoring gas leakage in the annulus of a gas well, comprising:

[0031] S1. Obtain the initial wellhead casing annulus pressure, and determine the casing side pressure at the initial leakage point according to the initial wellhead casing annulus pressure.

[0032] It should be noted that when gas leakage monitoring is performed, gas leakage may or may not occur. Therefore, if gas leakage does not occur, the default initial value can be set to 0 or the initial value can be added manually. If gas leakage has occurred, the wellhead casing annulus pressure in the current state is obtained and used as the initial wellhead casing annulus pressure.

[0033] S2. Determine the gas leakage flow rate at the leakage point according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure.

[0034] S3. Determine the time step required to generate bubbles under the gas leakage flow rate according to the bubble volumes after the multiple bubbles leave the leakage point.

[0035] The time step required for bubble generation refers to the time required from bubble generation to bubble detachment from the leakage point.

[0036] S4. Sampling is performed with the time step as the time period to obtain the gas column volume and liquid column volume in the annular space protection liquid at the end time corresponding to the current time period.

[0037] When sampling is performed in time periods, since gas leakage has occurred before the initial sampling moment, the initial value of the gas column volume may not be 0, but the liquid column volume is not 0.

[0038] S5. Determine the target wellhead casing annulus pressure according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the current end time.

[0039] S6. Determine the casing side pressure at the target leakage point according to the target wellhead casing annulus pressure.

[0040] S7. If the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, the gas column volume and the liquid column volume continue to be updated and used as the gas column volume and the liquid column volume of the next time period, respectively.

[0041] S8. Repeat steps S5 to S7 until the casing pressure at the target leakage point is greater than or equal to the pressure in the tubing string at the leakage point, and determine that the gas leakage in the annulus of the gas well stops.

[0042] In this embodiment, the initial wellhead casing annulus pressure is obtained, the initial leakage point casing side pressure is obtained, and then the gas leakage flow rate of the leakage point is determined according to the initial leakage point casing side pressure, the pressure in the tubing string at the leakage point and the preset critical pressure. Then, the bubble diameter and bubble volume after multiple bubbles leave the leakage point are studied, and the time step of bubble generation at the leakage point can be obtained. Then, the time step is used as the time interval for sampling, and the gas leakage in the gas well annulus is detected. In this time period, the change of the liquid column volume and the change of the gas column volume caused by the annulus protection fluid due to the bubble migration are considered, and the change of the wellhead casing annulus pressure caused by the bubble migration during this period is obtained to obtain the target wellhead casing annulus pressure, and then the target leakage point casing side pressure is recalculated by the target wellhead casing annulus pressure. The gas leakage in the gas well annulus can be obtained by comparing the target leakage point casing side pressure with the pressure in the tubing string at the leakage point. In this embodiment, the influence of the bubbles on the wellhead casing annulus pressure when migrating in the annulus protection fluid is considered, the accuracy of the detection result is improved, and the problem that the migration process of the leaked gas in the liquid column section is ignored in the prior art, resulting in large error in the result is solved.

[0043] It should be noted that the method should meet the following assumptions:

[0044] (1) The gas leaking from the leakage hole moves vertically upward in the annulus in the form of spherical bubbles;

[0045] (2) All bubbles generated are considered small bubbles;

[0046] (3) The bubbles move upward at a constant speed from the leak hole;

[0047] (4) A single bubble is taken as the research object, and the interference between adjacent bubbles is not considered.

[0048] In addition, this embodiment mainly includes two stages. The first stage is the process of leaking gas generating bubbles, and the second stage is the process of bubble migration. This embodiment will monitor the gas leakage in the annulus of the gas well from two stages.

[0049] Optionally, the casing side pressure at the initial leakage point corresponding to the initial moment is determined according to the initial wellhead casing annulus pressure, and the formula is as follows:

[0050]

[0051] in, Indicates the casing side pressure at the initial leakage point. represents the initial wellhead casing annulus pressure, ρ 1 It represents the density of the annular protection fluid, g represents the acceleration of gravity, h represents f Indicates the distance from the leakage point to the wellhead, hg Indicates the length of the air column in the wellhead ring.

[0052] Optionally, determining the gas leakage flow rate at the leakage point according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point, and a preset critical pressure includes:

[0053] According to the casing side pressure at the initial leakage point, the pressure in the string at the leakage point and the preset critical pressure, the gas flow state is determined. The gas flow state includes critical flow and subcritical flow. The formula is as follows:

[0054]

[0055]

[0056] in, Indicates the casing side pressure at the leak point, P 1 Indicates the pressure in the column at the leak point, P c represents the preset critical pressure, K represents the gas adiabatic index;

[0057] When the gas flow state is critical flow, according to the equivalent diameter of the leak hole, the relative density of natural gas, the temperature in the annulus at the leak point, the gas deviation factor and the gas adiabatic index, the formula for determining the gas leakage flow rate under standard conditions is as follows:

[0058]

[0059] in, Indicates the gas leakage flow corresponding to the critical flow under standard conditions, Indicates the equivalent diameter of the leakage hole, γ g Represents the relative density of natural gas, T 1k Indicates the temperature in the annulus at the leak point, Z 1 represents the gas deviation factor;

[0060] When the gas flow state is subcritical flow, the formula for determining the gas leakage flow rate under standard conditions is as follows based on the equivalent diameter of the leak hole, the relative density of natural gas, the temperature in the annulus at the leak point, the gas deviation factor, the preset critical pressure and the gas adiabatic index:

[0061]

[0062] in, Indicates the gas leakage flow rate corresponding to the subcritical flow under standard conditions;

[0063] According to the gas leakage flow rate corresponding to the critical flow state under standard conditions or the gas leakage flow rate corresponding to the subcritical flow state under standard conditions, as well as the temperature in the annulus at the leakage point, the gas pressure under standard conditions, the gas temperature under standard conditions and the casing side pressure at the initial leakage point, the gas leakage flow rate at the leakage point is determined by the following formula:

[0064]

[0065] in, Indicates the gas leakage flow rate at the leak point. When the gas flow state is critical flow When the gas flow state is subcritical P sc Indicates the gas pressure under standard conditions, T sc Indicates the gas temperature under standard conditions.

[0066] In order to solve the instantaneous change data of the wellhead annulus pressure, the entire bubble migration process is discretized in time. Using the nozzle flow principle, formula (4) and formula (5) can be obtained in the i-th time period. However, the gas leakage obtained by formula (4) and formula (5) is the gas leakage under standard conditions, and the unit is cubic meter per day. For the convenience of calculation, the gas leakage under standard conditions is converted into the gas leakage under actual working conditions, and the unit is cubic meter per second, which is formula (6).

[0067] Optionally, the time step required to generate a single bubble under the gas leakage flow rate is determined according to the bubble volume after the multiple bubbles leave the leakage point, and the formula is as follows:

[0068]

[0069] in, represents the bubble volume corresponding to the jth bubble generated in the i-th time period, Indicates the time step corresponding to the i-th time period.

[0070] The derivation process of formula (7) is as follows:

[0071] First, the force analysis of the bubble generation stage is carried out. The gas in the pipe string enters the annular protection fluid through the leakage hole. Due to the surface tension of the annular protection fluid, the gas entering the annular protection fluid will form bubbles. The bubbles will experience a growth process from small to large. At this time, the bubbles are affected by the upward buoyancy and the orifice resistance. When the bubbles reach a certain volume, the upward buoyancy is greater than the orifice resistance. At this time, the bubbles will leave the orifice and drift upward. When the bubbles just pass through the leakage hole, the flow rate is small, and the influence of viscous resistance and inertia can be ignored. The bubbles are mainly affected by gravity, buoyancy and additional surface force. Therefore, the formulas for buoyancy, gravity and additional surface force are as follows:

[0072]

[0073]

[0074]

[0075] Among them, F l represents buoyancy, d b represents the equivalent diameter of the bubble when it detaches, ρ 1 Indicates the density of the annular protection fluid, F G represents gravity, ρ g Indicates the density of the gas at the leak point, F σ represents the additional surface force, σ represents the surface tension of the bubble, θ represents the angle between the bubble at the leak hole and the horizontal direction, and d ch Indicates the equivalent diameter of the leak hole.

[0076] As the bubble grows, the buoyancy it experiences increases. When the buoyancy, gravity, and additional surface forces that maintain the bubble shape and hinder bubble generation are balanced, the bubble is considered to be detached. At this time:

[0077]

[0078] in:

[0079]

[0080]

[0081] Among them, T 1k Indicates the temperature in the annulus at the leak point, P 2 Indicates the casing side pressure at the leak point, γ g represents the relative density of natural gas, and R represents the gas molar constant.

[0082] Therefore, the formula for the bubble diameter when the bubble leaves the leak hole can be obtained from formula (11) as follows:

[0083]

[0084] Among them, d b Indicates the bubble diameter.

[0085] When the bubble leaves the leakage hole, its migration process in the annular protection fluid does not merge or split, that is, the volume formula of the jth bubble generated in the i-th time period is as follows:

[0086]

[0087] in, represents the bubble volume corresponding to the jth bubble generated in the i-th time period, Indicates the bubble diameter corresponding to the j-th bubble generated in the i-th time period.

[0088] Based on a single bubble, the time it takes for each bubble to grow larger and escape from the leak hole is set as the time step, that is, the time step, and formula (7) can be obtained.

[0089] Optionally, it also includes judging whether any bubble among all bubbles detached from the leakage point in the time period has reached the wellhead according to the distance from the leakage point to the wellhead, the length of the air column around the wellhead, the displacement of the bubble in the time period, and the rising speed of the bubble. The formula is as follows:

[0090]

[0091]

[0092] Among them, h f Indicates the distance from the leakage point to the wellhead, h g Indicates the length of the air column at the wellhead, S (i,j) represents the displacement of the jth bubble in the ith time period, represents the time step corresponding to the i-th time period, represents the rising speed of the jth bubble.

[0093] The whole process of gas well annulus pressure recovery can be divided into two stages according to whether the total amount of gas in the annulus wellhead changes: the first stage is that the bubbles separated from the leakage hole are still migrating upward in the liquid column and have not reached the wellhead; the second stage is that the bubbles have migrated to the wellhead annulus. The displacement of the bubbles can be used to determine whether the bubbles are in the protection fluid migration stage or in the wellhead annulus stage.

[0094] The derivation process of formula (18) is as follows:

[0095] In actual gas wells, the leakage aperture is very small. It can be assumed that the bubbles are in the form of small bubbles when the annular protection fluid migrates, and basically remain spherical during the rising process. Therefore, the dynamic characteristics of the bubbles can be analyzed by studying the force conditions of the bubbles. The bubbles are mainly affected by buoyancy, gravity and viscous resistance during the rising process. The formulas for buoyancy and gravity are known above, and the calculation of viscous resistance is as follows:

[0096]

[0097] Among them, F f represents the viscous resistance, C D represents the drag coefficient, Indicates the rising speed of the bubble.

[0098] The approximate values ​​of the drag coefficient at different Reynolds numbers are:

[0099]

[0100] Among them, R e Reynolds number representing the moving bubble.

[0101] Assuming that the rising trajectory of the bubble is a straight line, according to Newton's law of motion, the dynamic equation of the bubble is:

[0102]

[0103] Among them, m g a represents the kinetic equation.

[0104] in,

[0105]

[0106] so,

[0107]

[0108] When the acceleration a is equal to zero, the velocity of the bubble tends to be stable, and its final rising velocity is:

[0109]

[0110] According to formulas (12), (13) and (14), the bubble diameter when the jth bubble leaves the leak hole in the i-th time period is calculated, where the minimum value of j is 1, and when i=0, j=1, indicating the first bubble at the initial time. When the diameter of the jth bubble when it leaves the leak hole is determined, its constant rising speed formula is as follows:

[0111]

[0112] in, The rising speed of the jth bubble.

[0113] Let the initial stage S (0，1) =0, that is, the first bubble has no displacement when it is just generated. Combining formula (7) and (25), we can get formula (18).

[0114] Optionally, if no bubbles reach the wellhead, the target wellhead casing annulus pressure is determined according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the current end time, and the formula is as follows:

[0115]

[0116] in, Indicates that when no bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column in the i-th time period, represents the volume of the liquid column at the end time i, Indicates the wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annulus protection fluid.

[0117] When bubbles migrate in the annular protection fluid, the total amount of gas in the wellhead gas column remains unchanged. In the process of bubbles in the liquid column from generation to migration and growth, the liquid column is continuously squeezed, so that the liquid level of the annular protection fluid becomes higher, the volume of the gas column decreases, and the annular pressure increases. Therefore, the derivation process of formula (26) is as follows:

[0118] Taking the gas column section at the wellhead as the research object, in the i-th time period, according to the mass conservation equation and the gas state equation, we get:

[0119]

[0120] in, Indicates the wellhead casing annulus pressure, represents the volume of the air column at the i+1th ending time, represents the volume of the air column at the i-th end time.

[0121] because, and is a known quantity. If the initial value is known, the change value can be calculated later. The wellhead volume is decreasing continuously, and the decrease is:

[0122]

[0123] in, represents the increase of all bubbles in the liquid column in the i-th time period, It represents the volume compression of the liquid column due to the increase of wellhead annulus pressure in the i-th time period.

[0124] in addition:

[0125]

[0126]

[0127] Among them, c m Indicates the volume compression coefficient of the annular protection fluid, represents the bubble volume of the kth bubble before the jth bubble in the i-th time period, represents the bubble volume of the kth bubble before the jth bubble in the i-1th time period, Denotes the bubble volume corresponding to the j-th bubble in the i-th time period.

[0128] In the i-th time period, during the upward migration of the previously generated bubbles, the bubble volume will change. The main factors affecting the bubble volume are the changes in temperature and pressure. According to the mass conservation formula of the bubble and the gas state equation, the pressure and temperature at the position of the k-th (0 < k < j) bubble at this time can be obtained as follows:

[0129]

[0130]

[0131] Among them, Denotes the pressure at the position of the k-th bubble in the i-th time period, Denotes the temperature at the position of the k-th bubble in the i-th time period, T wh Denotes the standard temperature.

[0132] Thus, the bubble volume of the k-th (0 < k < j) bubble after the i-th time period can be obtained as:

[0133]

[0134] Among them, Denotes the bubble volume corresponding to the j-th bubble in the i-th time period, Denotes the pressure at the position of the k-th bubble in the i-th time period, Denotes the pressure at the position of the k-th bubble in the (i - 1)-th time period, Denotes the temperature at the position of the k-th bubble in the i-th time period, Denotes the temperature at the position of the k-th bubble in the (i - 1)-th time period.

[0135] Substitute formulas (18), (27) - (32) into the formula corresponding to the situation where no bubble reaches the wellhead in formula (17), and obtain a quadratic equation of one variable about the target wellhead tubing-casing annulus pressure corresponding to the situation where no bubble reaches the wellhead, that is, the following formula:

[0136]

[0137] Solve formula (34) to obtain formula (26).

[0138] Optionally, if no bubble reaches the wellhead, if no bubble reaches the wellhead, then update the gas column volume and liquid column volume, and the formula for the gas column volume is as follows:

[0139]

[0140]

[0141] in, represents the updated gas column volume, Indicates the updated liquid column volume.

[0142] Alternatively, if bubbles reach the wellhead, the target wellhead casing annulus pressure is determined based on the initial wellhead casing annulus pressure, the gas column volume, and the liquid column volume, and the formula is as follows:

[0143]

[0144] in, Indicates that when bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column during the i-th time period, represents the total volume of bubbles entering the wellhead gas column, The volume of the liquid column at the i-th end time, Indicates the wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annular protection fluid, They represent the total amount of gas in the wellhead gas column in the i-th time period and the i+1-th time period respectively.

[0145] When the existing bubbles migrate to the wellhead gas column, the integration of the bubbles not only increases the total amount of material in the wellhead gas column, but also increases the volume of the gas column. Therefore, the derivation process of formula (37) is as follows:

[0146] When the existing bubbles migrate to the wellhead gas column, the integration of the bubbles not only increases the total amount of material in the wellhead gas column, but also increases the volume of the gas column. Therefore, the volume change of the wellhead gas column at this time is:

[0147]

[0148] in, represents the increase of all bubbles in the liquid column during the i-th time period, represents the volume of the air column at time i, It represents the volume compression of the liquid column due to the increase of wellhead annular pressure in the i-th time period, Represents the total volume of bubbles entering the wellhead gas column.

[0149] For bubbles still in the liquid column, it is necessary to calculate their total volume change (same as formula (30)), and for the bubbles that have reached the wellhead gas column, it is necessary to calculate the bubble volume (same as formula (33)) and the amount of substance at the wellhead. The formula for the amount of substance is as follows:

[0150]

[0151] Among them, represents the amount of substance, represents the pressure on the casing side at the initial leakage point, and k represents the adiabatic index of the gas.

[0152] During the i-th time period, a total of the a-th to b-th bubbles enter the wellhead gas column (0 < k < j), so the total volume of the bubbles entering the wellhead gas column is:

[0153]

[0154] Among them, represents the total volume of the bubbles entering the wellhead gas column.

[0155] Since the total amount of substance of the wellhead gas column changes, so:

[0156]

[0157]

[0158]

[0159] Among them, respectively represent the total amount of substance of the wellhead gas column gas during the i-th time period and the (i + 1)-th time period, represents the amount of substance of the k-th bubble, represents the initial wellhead oil-casing annulus pressure, represents the initial gas column volume calculated through the annulus liquid height and the wellbore inner diameter, R represents the gas molar constant, Z represents the gas deviation factor, and T wh represents the standard temperature.

[0160] Substituting formulas (29), (33), (38), (40), (42), and (39) into formula (41) gives a quadratic equation of one variable about the target wellhead oil-casing annulus pressure as:

[0161]

[0162] Solving formula (44) can obtain formula (37).

[0163] Optionally, if bubbles reach the wellhead, update the gas column volume and the liquid column volume. The formula for the gas column volume is as follows:

[0164]

[0165]

[0166] Among them, represents the updated gas column volume, Indicates the updated liquid column volume.

[0167] The present invention is described in detail with a specific example below. Figure 2 As shown, a method for monitoring gas leakage in the annulus of a gas well comprises the following steps:

[0168] S1. Input initial conditions, which include initial time t, initial time node i, initial bubble generation sequence j and preset value n.

[0169] S2. Assign values ​​to each initial condition, where t=0, i=0, j=1 and n=1.

[0170] S3. Calculate the casing side pressure at the initial leakage point.

[0171] S4. Calculate various required parameters, including the bubble diameter, rising speed, amount of substance, bubble volume, pressure at the bubble location, and temperature at the bubble location when the bubble detaches.

[0172] S5. Determine the gas flow state.

[0173] S6. If the gas flow state is critical flow, calculate the gas leakage corresponding to the critical flow state.

[0174] S7. If the gas flow state is a subcritical flow, the gas leakage corresponding to the subcritical flow state is calculated.

[0175] S8. Calculate time step

[0176] S9. If i=0, it is necessary to determine whether there are gas columns and bubbles, and whether there is gas leakage at this moment, and directly jump to S20.

[0177] S10. If the time step i≠0, then according to the bubble migration process in the i-th time period, solve the parameters of the increase of all bubbles in the liquid column in the i-th time period or the volume of bubbles entering the wellhead gas column and the volume of the gas column at the i-th end time.

[0178] S11. For the j-1th generated bubble, calculation starts from the ath bubble in the corresponding air column.

[0179] S12. Calculate the displacement of the ath bubble.

[0180] S13. Determine whether the bubble has reached the wellhead based on the displacement of the ath bubble.

[0181] S14. If the ath bubble does not reach the wellhead, i.e., the first stage, then solve the parameter for the increase of all bubbles in the liquid column during the i-th time period.

[0182] S15. If the ath bubble reaches the wellhead, i.e. the second stage, the parameter n needs to be increased by 1.

[0183] S16. Solve the parameters for the total volume of bubbles entering the wellhead gas column and the total amount of gas in the wellhead gas column.

[0184] S17. Determine the size of a and n at this time, so as to determine whether all bubbles are considered in the migration stage.

[0185] S18. If a>n, it indicates that all bubbles in the i-th time period have not yet been judged to be in the migration stage, and the next bubble is judged, and S12 to S18 are repeatedly executed.

[0186] S19. If a≤n, the gas leakage in the annulus of the gas well can be judged.

[0187] S20, determining whether bubbles have reached the wellhead within the i-th time period.

[0188] S21. If no bubbles reach the wellhead, i.e., the first stage, the target wellhead casing annulus pressure corresponding to the first stage is updated.

[0189] S22. If bubbles reach the wellhead, i.e., the second stage, the target wellhead casing annulus pressure corresponding to the second stage is updated.

[0190] S23. Calculate the updated gas column volume and the updated liquid column volume.

[0191] S24. If the casing pressure at the target leak point is less than the pressure in the tubing string at the leak point, set the parameters i=i+1, j=j+1, And repeat S3 to S24.

[0192] S25. If the casing side pressure at the target leakage point is greater than or equal to the pressure in the tubing string at the leakage point, it is determined that the gas leakage in the annulus of the gas well has stopped.

[0193] like Figure 3 As shown, the present invention provides a gas leakage monitoring system in the annulus of a gas well, comprising:

[0194] The initial leakage point casing side pressure determination module 101 is used to obtain the initial wellhead casing annulus pressure and determine the initial leakage point casing side pressure according to the initial wellhead casing annulus pressure;

[0195] The gas leakage flow determination module 102 is used to determine the gas leakage flow of the leakage point according to the casing side pressure of the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure;

[0196] A time step determination module 103, used to determine the time step required for generating bubbles under the gas leakage flow rate according to the bubble volumes after the multiple bubbles leave the leakage point;

[0197] The initial value acquisition module 104 is used to perform sampling with the time step as the time period, and obtain the gas column volume and liquid column volume gas column volume in the annular protection liquid at the end time corresponding to the current time period;

[0198] The target wellhead casing annulus pressure determination module 105 is used to determine the target wellhead casing annulus pressure gas column volume according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the end time corresponding to the current time period;

[0199] A target leakage point casing side pressure determination module 106 is used to determine the target leakage point casing side pressure according to the target wellhead casing annulus pressure;

[0200] An updating module 107 is used for updating the gas column volume and the liquid column volume if the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, and using them as the gas column volume and the liquid column volume gas column volume gas column volume in the next time period respectively;

[0201] The end judgment module 108 is used to repeatedly execute the corresponding functions of the target wellhead oil casing annulus pressure determination module, the target leakage point casing side pressure determination module and the update module until the casing side pressure of the target leakage point is greater than or equal to the pressure in the tubing at the leakage point, and it is determined that the gas leakage in the gas well annulus has stopped.

[0202] Optionally, the initial leakage point casing side pressure determination module 101 is specifically used for:

[0203] The casing side pressure at the initial leakage point corresponding to the initial moment is determined according to the initial wellhead casing annulus pressure. The formula is as follows:

[0204] in, Indicates the casing side pressure at the initial leakage point. represents the initial wellhead casing annulus pressure, ρ 1 It represents the density of the annular protection fluid, g represents the acceleration of gravity, h represents f Indicates the distance from the leakage point to the wellhead, h g Indicates the length of the air column in the wellhead ring.

[0205] Optionally, the gas leakage flow determination module 102 is specifically used for:

[0206] According to the casing side pressure at the initial leakage point, the pressure in the string at the leakage point and the preset critical pressure, the gas flow state is determined. The gas flow state includes critical flow and subcritical flow. The formula is as follows:

[0207]

[0208]

[0209] in, Indicates the casing side pressure at the leak point, P 1 Indicates the pressure in the column at the leak point, P c represents the preset critical pressure, K represents the gas adiabatic index;

[0210] When the gas flow state is critical flow, according to the equivalent diameter of the leak hole, the relative density of natural gas, the temperature in the annulus at the leak point, the gas deviation factor and the gas adiabatic index, the formula for determining the gas leakage flow rate under standard conditions is as follows:

[0211]

[0212] in, Indicates the gas leakage flow corresponding to the critical flow under standard conditions, Indicates the equivalent diameter of the leakage hole, γ g Represents the relative density of natural gas, T 1k Indicates the temperature in the annulus at the leak point, Z 1 represents the gas deviation factor;

[0213] When the gas flow state is subcritical flow, the formula for determining the gas leakage flow rate under standard conditions is as follows based on the equivalent diameter of the leak hole, the relative density of natural gas, the temperature in the annulus at the leak point, the gas deviation factor, the preset critical pressure and the gas adiabatic index:

[0214]

[0215] in, Indicates the gas leakage flow rate corresponding to the subcritical flow under standard conditions;

[0216] According to the gas leakage flow rate corresponding to the critical flow state under standard conditions or the gas leakage flow rate corresponding to the subcritical flow state under standard conditions, as well as the temperature in the annulus at the leakage point, the gas pressure under standard conditions, the gas temperature under standard conditions and the casing side pressure at the initial leakage point, the gas leakage flow rate at the leakage point is determined by the following formula:

[0217]

[0218] in, Indicates the gas leakage flow rate at the leak point. When the gas flow state is critical flow When the gas flow state is subcritical P sc Indicates the gas pressure under standard conditions, T scIndicates the gas temperature under standard conditions.

[0219] Optionally, the time step determination module 103 is specifically used for:

[0220] According to the bubble volume after multiple bubbles leave the leakage point, the time step required to generate a single bubble under the gas leakage flow rate is determined. The formula is as follows:

[0221]

[0222] in, represents the bubble volume corresponding to the jth bubble in the i-th time period, Indicates the time step corresponding to the i-th time period.

[0223] Optionally, a judgment module is also included, which is specifically used to:

[0224] According to the distance from the leakage point to the wellhead, the length of the air column around the wellhead, the displacement of the bubbles within the time period, and the rising speed of the bubbles, it is determined whether there are bubbles that have reached the wellhead among all the bubbles that have separated from the leakage point within the time period. The formula is as follows:

[0225]

[0226]

[0227] Among them, h f Indicates the distance from the leakage point to the wellhead, h g Indicates the length of the air column at the wellhead, S (i,j) represents the displacement of the jth bubble in the ith time period, Indicates the time step corresponding to the i-th time period, represents the rising speed of the jth bubble.

[0228] Optionally, the target wellhead casing annulus pressure determination module is specifically used for:

[0229] If no bubbles reach the wellhead, the target wellhead casing annulus pressure is determined based on the initial wellhead casing annulus pressure, the current gas column volume and the liquid column volume. The formula is as follows:

[0230]

[0231] in, Indicates that when no bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column during the i-th time period, The volume of the liquid column at the i-th ending time, represents the initial wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annulus protection fluid.

[0232] Optionally, the update module is specifically used for:

[0233] If no bubbles reach the wellhead, the gas column volume and liquid column volume are updated and the gas column volume is shown as follows:

[0234]

[0235]

[0236] in, represents the updated gas column volume, Indicates the updated liquid column volume.

[0237] Optionally, the target wellhead casing annulus pressure determination module is specifically used for:

[0238] If bubbles reach the wellhead, the target wellhead casing annulus pressure is determined based on the initial wellhead casing annulus pressure, gas column volume and liquid column volume. The formula is as follows:

[0239]

[0240] in, Indicates that when bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column during the i-th time period, represents the total volume of bubbles entering the wellhead gas column, The volume of the liquid column at the i-th ending time, Indicates the wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annular protection fluid, They represent the total amount of gas in the wellhead gas column in the i-th time period and the i+1-th time period respectively.

[0241] Optionally, the update module is specifically used for:

[0242] If bubbles reach the wellhead, the gas column volume and liquid column volume are updated and displayed as follows:

[0243]

[0244]

[0245] in, represents the updated gas column volume, Indicates the updated liquid column volume.

[0246] An electronic device according to an embodiment of the present invention comprises a memory, a processor and a program stored in the memory and running on the processor. When the processor executes the program, some or all steps of the above-mentioned method for monitoring gas leakage in the annulus of a gas well are implemented.

[0247] Among them, the electronic device can be a computer, and correspondingly, its program is computer software. The above-mentioned parameters and steps in an electronic device of the present invention can refer to the parameters and steps in an embodiment of a gas leakage monitoring method in the annulus of a gas well, and will not be repeated here.

[0248] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0249] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for monitoring gas leakage in the annulus of a gas well, characterized in that: include: S1, obtaining the initial wellhead casing annulus pressure, and determining the casing side pressure at the initial leakage point according to the initial wellhead casing annulus pressure; S2, determining the gas leakage flow rate at the leakage point according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure; S3, determining the time step required to generate a single bubble at the gas leakage flow rate according to the bubble volume after the multiple bubbles are separated from the leakage point; S4, sampling with the time step as the time period, and obtaining the gas column volume and liquid column volume in the annular space protection liquid at the end time corresponding to the current time period; S5, determining a target wellhead casing annulus pressure according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the current end time; S6, determining the casing side pressure at the target leakage point according to the target wellhead casing annulus pressure; S7, if the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, continue to update the gas column volume and liquid column volume, and use them as the gas column volume and liquid column volume of the next time period respectively; S8, repeating steps S5 to S7 until the casing side pressure at the target leakage point is greater than or equal to the pressure in the tubing string at the leakage point, and determining that the gas leakage in the annulus of the gas well stops.

2. The method according to claim 1, characterized in that The casing side pressure at the initial leakage point corresponding to the initial moment is determined according to the initial wellhead casing annulus pressure, and the formula is as follows: in, Indicates the casing side pressure at the initial leakage point. represents the initial wellhead casing annulus pressure, ρ1 represents the density of the annulus protection fluid, g represents the gravity acceleration, h f Indicates the distance from the leakage point to the wellhead, h g Indicates the length of the air column in the wellhead ring.

3. The method according to claim 2, characterized in that The method of determining the gas leakage flow rate at the leakage point according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure includes: The gas flow state is determined according to the casing side pressure at the initial leakage point, the pressure in the tubing string at the leakage point and the preset critical pressure. The gas flow state includes critical flow and subcritical flow. The formula is as follows: in, represents the casing side pressure at the initial leakage point, P1 represents the pressure inside the string at the leakage point, P c represents the preset critical pressure, K represents the gas adiabatic index; When the gas flow state is critical flow, the formula for determining the gas leakage flow rate under standard conditions is as follows based on the equivalent diameter of the leakage hole, the relative density of natural gas, the temperature in the annulus at the leakage point, the gas deviation factor and the gas adiabatic index: in, Indicates the gas leakage flow rate corresponding to the critical flow under standard conditions, d ch Indicates the equivalent diameter of the leakage hole, γ g Represents the relative density of natural gas, T 1k represents the temperature in the annulus at the leak point, and Z1 represents the gas deviation factor; When the gas flow state is subcritical flow, according to the equivalent diameter of the leak hole, the relative density of natural gas, the temperature in the annulus at the leak point, the gas deviation factor, the preset critical pressure and the gas adiabatic index, the formula for determining the gas leakage flow rate under standard conditions is as follows: in, Indicates the gas leakage flow rate corresponding to the subcritical flow under standard conditions; According to the gas leakage flow rate corresponding to the critical flow state under standard conditions or the gas leakage flow rate corresponding to the subcritical flow state under standard conditions, as well as the temperature in the annulus at the leakage point, the gas pressure under standard conditions, the gas temperature under standard conditions and the casing side pressure at the initial leakage point, the gas leakage flow rate at the leakage point is determined by the following formula: in, Indicates the gas leakage flow rate at the leak point. When the gas flow state is critical flow When the gas flow state is subcritical P sc Indicates the gas pressure under standard conditions, T sc Indicates the gas temperature under standard conditions.

4. The method according to claim 3, characterized in that The time step required to generate a single bubble under the gas leakage flow rate is determined according to the bubble volume after the multiple bubbles are separated from the leakage point. The formula is as follows: in, represents the bubble volume corresponding to the jth bubble generated in the i-th time period, Indicates the time step corresponding to the i-th time period.

5. The method according to any one of claims 1 to 4, characterized in that: It also includes judging whether any bubble among all bubbles separated from the leakage point in the time period has reached the wellhead according to the distance from the leakage point to the wellhead, the length of the air column around the wellhead, the displacement of the bubble in the time period, and the rising speed of the bubble. The formula is as follows: Among them, h f Indicates the distance from the leakage point to the wellhead, h g Indicates the length of the air column at the wellhead, S (i,j) represents the displacement of the jth bubble in the ith time period, represents the time step corresponding to the i-th time period, represents the rising speed of the jth bubble.

6. The method according to claim 5, characterized in that If no bubbles reach the wellhead, the target wellhead casing annulus pressure is determined according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume at the current time step, and the formula is as follows: in, Indicates that when no bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column in the i-th time period, The volume of the liquid column at the i-th ending time, represents the initial wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annulus protection fluid.

7. The method according to claim 6, characterized in that If no bubbles reach the wellhead, the gas column volume and liquid column volume are updated and the gas column volume is shown as follows: in, represents the updated gas column volume, Indicates the updated liquid column volume.

8. The method according to claim 5, characterized in that If bubbles reach the wellhead, the target wellhead casing annulus pressure is determined according to the initial wellhead casing annulus pressure, the gas column volume and the liquid column volume. The formula is as follows: in, Indicates that when bubbles reach the wellhead, the corresponding target wellhead casing annulus pressure is updated. represents the volume of the air column at the i-th end time, represents the increase of all bubbles in the liquid column during the i-th time period, represents the total volume of bubbles entering the wellhead gas column, The volume of the liquid column at the i-th end time, Indicates the wellhead casing annulus pressure, c m Indicates the volume compression coefficient of the annular protection fluid, They represent the total amount of gas in the wellhead gas column in the i-th time period and the i+1-th time period respectively.

9. The method according to claim 8, characterized in that If bubbles reach the wellhead, the gas column volume and liquid column volume are updated and displayed as follows: in, represents the updated gas column volume, Indicates the updated liquid column volume.

10. A gas leakage monitoring system in the annulus of a gas well, characterized in that: include: The module for determining the casing side pressure at the initial leakage point is used to obtain the initial wellhead casing annulus pressure and determine the casing side pressure at the initial leakage point according to the initial wellhead casing annulus pressure; A gas leakage flow determination module, used to determine the gas leakage flow of the leakage point according to the casing side pressure of the initial leakage point, the pressure in the tubing string at the leakage point and a preset critical pressure; A time step determination module, used to determine the time step required to generate bubbles under the gas leakage flow rate according to the bubble volumes after the multiple bubbles leave the leakage point; An initial value acquisition module is used to perform sampling with the time step as a time period, and obtain the gas column volume and liquid column volume in the annular space protection liquid at the end time corresponding to the current time period; A target wellhead casing annulus pressure determination module is used to determine the target wellhead casing annulus pressure gas column volume according to the initial wellhead casing annulus pressure, the gas column volume at the current end time, and the liquid column volume; A target leakage point casing side pressure determination module, used to determine the target leakage point casing side pressure according to the target wellhead casing annulus pressure; An updating module, for updating the gas column volume and the liquid column volume if the casing side pressure at the target leakage point is less than the pressure in the tubing string at the leakage point, and using them as the gas column volume and the liquid column volume gas column volume gas column volume in the next time period respectively; The end judgment module is used to repeatedly execute the corresponding functions of the target wellhead oil casing annulus pressure determination module, the target leakage point casing side pressure determination module and the update module until the casing side pressure of the target leakage point is greater than or equal to the pressure in the tubing at the leakage point, and it is determined that the gas leakage in the gas well annulus has stopped.

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