A calculation method for the liquid holdup height in the wellbore of an underground throttling gas well

Abstract

The present invention relates to a method for calculating the liquid accumulation height in the wellbore of an underground throttling gas well, belonging to the technical field of gas production engineering. Based on the equality relationship of the bottom-hole flowing pressure calculated according to the tubing pressure drop formula and the tubing-casing annulus pressure drop formula, and the geometric ratio relationship between the liquid column height in the tubing and the liquid column height in the tubing-casing annulus, a calculation model for the liquid accumulation height in the wellbore is established. Then, by collecting the inlet pressure value of the downhole throttle and the annulus pressure value at the throttle position; substituting the inlet pressure value of the throttle and the annulus pressure value at the throttle position into the calculation model for the liquid accumulation height in the wellbore, the liquid column height in the tubing and the liquid column height in the tubing-casing annulus are calculated, solving the problems of low accuracy and unreliability of the existing calculation method for the liquid accumulation height in the wellbore of low-pressure gas gathering and transportation wells.

Description

Technical Field

[0001] The present invention relates to a method for calculating the liquid accumulation height in the wellbore of an underground throttling gas well, belonging to the technical field of gas production engineering. Background Art

[0002] An important index for the supporting gas drainage and production technology in a water-bearing gas reservoir is the degree of liquid accumulation in the wellbore. According to the degree of liquid accumulation in the wellbore, an economical and effective gas drainage and production technology can be optimized. Therefore, accurately calculating the liquid accumulation height is of great significance for the efficient and stable development of a water-bearing gas reservoir.

[0003] The development methods of water-bearing natural gas reservoirs mainly include high-pressure gas gathering and low-pressure gas gathering. For high-pressure gas gathering wells, there are currently various methods to judge the liquid accumulation height in the wellbore. For example, the secondary sound wave generated by the high-pressure gas at the wellhead is used to detect the liquid level in the annulus; or an echo sounder is used to monitor the liquid level height in the annulus; or the oil-casing pressure difference method is used to calculate the liquid accumulation height in the wellbore. For example, the Chinese patent application for invention with the application number 201810836603.3 and the name of an automatic monitoring device and method for the liquid accumulation surface in the wellbore of a high-pressure gas well discloses the content of using the secondary sound wave generated by the high-pressure gas at the wellhead to detect the liquid level in the annulus; the Chinese patent application for invention with the application number 201511016002.0 and the name of a method for real-time testing the liquid accumulation volume in the wellbore of a gas well discloses the method of using an echo sounder to monitor the liquid level height in the annulus.

[0004] However, for low-pressure gas gathering and transportation wells, due to the existence of downhole throttles, the liquid accumulation height calculated by using the above several liquid accumulation height calculation methods is not accurate. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the liquid accumulation height in the wellbore of an underground throttling gas well, so as to solve the problems of low accuracy and unreliability of the existing calculation methods for the liquid accumulation height in the wellbore of low-pressure gas gathering and transportation wells.

[0006] The present invention provides a method for calculating the liquid accumulation height in the wellbore of an underground throttling gas well, including the following steps:

[0007] Collect the inlet pressure value of the downhole throttle and the annulus pressure value at the throttle position;

[0008] Substitute the inlet pressure value of the throttle and the annulus pressure value at the throttle position into the wellbore liquid accumulation height calculation model for calculation. The wellbore liquid accumulation height calculation model is established according to the following relationship:

[0009] The bottom-hole flowing pressure calculated based on the tubing pressure drop formula is equal to the bottom-hole flowing pressure calculated based on the oil-casing annulus pressure drop formula;

[0010] The liquid column height in the tubing is in a set ratio to the liquid column height in the oil-casing annulus.

[0011] Furthermore, the calculation model for the height of wellbore liquid accumulation is as follows:

[0012] p 1 + p f1 + ρgH 1 = p 2 + p f2 + ρgH 2

[0013] H 2 = kH 1

[0014] ρg(1 - k)H 1 = (p 2 - p 1 ) + (p f2 - p f1 )

[0015] In the formula: H 1 is the liquid column height in the tubing, m; p 1 is the inlet pressure of the throttle, MPa; p f1 is the pressure loss of the flowing gas - liquid mixture from the liquid level depth in the tubing to the throttle depth, MPa; H 2 is the liquid column height in the annulus between the tubing and the casing, m; p 2 is the annulus pressure value at the throttle position, MPa; p f2 is the pressure loss of the static gas - liquid mixture from the liquid level depth in the annulus to the throttle depth, MPa; ρ is the liquid density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 , and k is the ratio of the liquid column height in the annulus to the liquid column height in the tubing.

[0016] Furthermore, the calculation method is iterative calculation:

[0017] 1) Set the difference of (p f2 - p f1 ) to be 0;

[0018] 2) According to the relevant calculation method, calculate the inlet pressure value of the throttle (p 1 ), the annulus pressure value at the throttle position (p 2 ), and the ratio of the liquid column height in the annulus to the liquid column height in the tubing (k);

[0019] 3) Substitute into the calculation model for the height of wellbore liquid accumulation to calculate the liquid accumulation height in the tubing, denoted as H 1-1 ;

[0020] 4) Back - calculate the value of (p f2 _ p f1 ), denoted as (p f2 - pf1 ) -1 ;

[0021] 5) Substitute p 1 , p 2 , k, (p f2 - p f1 ) -1 into the calculation model again to calculate the liquid accumulation height in the tubing, denoted as H 1-2 ;

[0022] 6) If the difference between H 1-2 and H 1-1 is greater than the set precision threshold, then the initial value of (p f2 _p f1 ) is set to (p f2 _p f1 ), and repeat steps 1)-6) again until the difference between H -1 and H 1-2 is less than the set precision threshold. 1-1

[0023] Further, the inlet pressure value of the throttle is obtained by the following method:

[0024] 1) Construct a wellbore pressure profile curve with a liquid column height of 0 m in the tubing;

[0025] 2) Select the bottom hole flowing pressure value, and calculate the throttle nozzle diameter according to the pipe flow model and the gas-liquid two-phase nozzle flow model;

[0026] 3) Calculate the deviation between the calculated throttle nozzle diameter and the actual throttle nozzle diameter. If the deviation is greater than the set precision threshold, adjust the bottom hole flowing pressure value and return to step 2); if the deviation is less than the set precision threshold, calculate the corresponding throttle inlet pressure according to the bottom hole flowing pressure and the pipe flow model at this time.

[0027] Further, the annulus pressure value at the throttle position is calculated by the following static gas column equation:

[0028]

[0029] Where: p 2 is the annulus pressure value at the throttle position, MPa; p ts is the wellhead casing pressure, MPa; γ g is the relative density of natural gas; H 3 is the vertical depth from the wellhead to the throttle position, m; is the average compression factor of the static gas column in the wellbore; is the average temperature of the static gas column in the wellbore, K.

[0030] Further, the calculation formula for the ratio k of the annulus liquid column height to the tubing liquid column height is:

[0031]

[0032] Where: p ts is the wellhead casing pressure, MPa; WGR is the liquid-gas ratio, m 3 / 10 4 m 3 ; erf is the Gaussian error function.

[0033] Furthermore, when the liquid level depth in the tubing and the depth of the throttle position are known, the pressure loss (p f1 ) of the flowing gas-liquid mixture from the liquid level depth in the tubing to the throttle depth is calculated by the pipe flow model.

[0034] Furthermore, when the liquid level depth in the annulus between the tubing and the casing and the depth of the throttle position are known, the pressure loss (p f2 ) of the static gas-liquid mixture from the liquid level depth in the annulus to the throttle depth is calculated by the static gas column equation.

[0035] Furthermore, it further includes the step of judging whether the calculated wellbore liquid accumulation height is valid: comparing the calculated wellbore liquid accumulation height with the height of the throttle position. If the wellbore liquid accumulation height is lower than the height of the throttle position, the calculation result is valid.

[0036] The present invention fully combines the production characteristics of downhole throttling gas wells. The calculation method simply and reliably quantitatively determines the degree of liquid accumulation in the wellbore, which is beneficial to optimizing the gas drainage and production process and refining the process system parameters. Brief Description of the Drawings

[0037] Figure 1 is the calculation flow chart in Embodiment 1 of the wellbore liquid accumulation height calculation method of the present invention;

[0038] Figure 2 is the bar chart of the calculation results of the application example of the present invention. Detailed Embodiments

[0039] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0040] The features and performance of the present invention will be further described in detail below with reference to the embodiments.

[0041] Embodiment 1 of the wellbore liquid accumulation height calculation method:

[0042] In this embodiment, a method for calculating the wellbore liquid accumulation height of a downhole throttling gas well is provided. Based on the production characteristics of the downhole throttling gas well and starting from theoretical research, a calculation model for the wellbore liquid accumulation height is established to guide the drainage and gas production work of the downhole throttling gas well and ensure the stable production of the gas well.

[0043] In order to meet the calculation needs, in this embodiment, a specific calculation model for the wellbore liquid accumulation height is established in combination with the production characteristics of the downhole throttling gas well.

[0044] Taking the downhole choke as the starting point for node analysis, according to the characteristics of the tubing and the casing annulus, the annulus expression of the bottomhole flow pressure can be combined with the tubing expression of the bottomhole flow pressure to obtain the relationship expression of the choke inlet pressure, pressure loss and liquid column height.

[0045] The pipe expression of flow pressure: p wf =p 1 +p f1 +ρgH 1

[0046] Annular expression of flow pressure: p wf =p 2 +p f2 +ρgH 2

[0047] Simultaneous expression: p 1 +p f1 +ρgH 1 =p 2 +p f2 +ρgH 2

[0048] Where: p wf is the bottom hole flowing pressure, unit: MPa; H 1 is the height of the liquid column in the oil pipe, in m; p 1 is the throttle inlet pressure, unit: MPa; p f1 It is the pressure loss of the flowing gas-water mixture from the liquid level in the oil pipe to the throttle depth, in MPa; H 2 is the height of the liquid column in the casing annulus, in m; p 2 is the annular pressure value at the throttle position, unit: MPa; p f2 is the pressure loss of static gas-water mixture from the liquid surface depth in the annulus to the throttle depth, in MPa; ρ is the liquid density, in kg / m 3 ; g is the acceleration due to gravity, unit is m / s 2 .

[0049] In this embodiment, the annulus is in a set ratio to the height of the liquid column in the tubing, that is,

[0050] H2 = kH 1

[0051] By combining this ratio relationship with the above-mentioned relational formula of the pressure in the tubing and the annulus, a calculation model for the liquid accumulation height in the wellbore in this embodiment is formed:

[0052] ρg(1 - k)H 1 = (p 2 - p 1 ) + (p f2 - p f1 )

[0053] H 2 = kH 1

[0054] Where k is the ratio of the liquid column height in the annulus to the liquid column height in the tubing, dimensionless.

[0055] Based on the above calculation formula for the liquid accumulation height in the wellbore, as Figure 1 shown, the method for calculating the liquid accumulation height in the downhole throttling gas well in this embodiment mainly includes the following steps:

[0056] 1) Set the pressure loss difference between the moving gas column in the tubing and the static gas column in the annulus to 0;

[0057] 1) Collect the inlet pressure value of the downhole throttle and the annulus pressure value at the throttle position;

[0058] 2) Substitute the inlet pressure value of the throttle and the annulus pressure value at the throttle position into the above calculation model for the liquid accumulation height in the wellbore to calculate the liquid column height in the tubing and / or the liquid column height in the tubing-casing annulus;

[0059] 3) Calculate the pressure loss of the moving gas column in the tubing and the pressure loss of the static gas column in the annulus according to the liquid column height in the tubing and the liquid column height in the tubing-casing annulus;

[0060] 4) Substitute the inlet pressure value of the throttle, the annulus pressure value at the throttle position, the pressure loss of the moving gas column in the tubing, and the pressure loss value of the static gas column in the annulus into the above calculation model for the liquid accumulation height in the wellbore to recalculate the liquid column height in the tubing and / or the liquid column height in the tubing-casing annulus;

[0061] 5) Compare whether the tubing height values before and after meet the set accuracy threshold. If not, repeat the above calculation steps.

[0062] Example 2 of the method for calculating the liquid accumulation height in the wellbore:

[0063] The difference between this embodiment and Embodiment 1 of the above method for calculating the liquid accumulation height in the wellbore is that in this embodiment, in order to improve the calculation accuracy, a theoretical calculation formula for the ratio of the liquid column height in the annulus to the liquid column height in the tubing is also summarized based on historical measurement data.

[0064] Based on the measured data such as the wellbore annulus liquid column height, tubing liquid column height, wellhead casing pressure, and liquid-gas ratio, a calculation formula for the ratio of the annulus liquid column height to the tubing liquid column height was established:

[0065]

[0066] In the formula: p ts is the wellhead casing pressure, in MPa; WGR is the liquid-gas ratio, with the unit m 3 / 10 4 m 3 ; erf is the Gaussian error function.

[0067] Example 3 of the calculation method for wellbore liquid accumulation height:

[0068] In the above examples, the inlet pressure value of the downhole throttle is usually directly collected. In this example, it is also proposed that the inlet pressure value of the throttle can be fitted according to the gas-liquid two-phase pipe flow model and the gas-liquid two-phase nozzle flow model, which mainly includes the following steps:

[0069] (1) Construct a wellbore pressure profile with a tubing liquid column height of 0 m in the tubing. This profile has the following characteristics: ① The parameters such as gas production rate, liquid production rate, wellbore structure, pipe flow model, and nozzle flow model are exactly the same as those of the original wellbore; ② Because the conditions are the same, in the wellbore above the tubing liquid accumulation surface, the constructed wellbore pressure profile curve is parallel to the original wellbore pressure profile curve, and the distance between the two is related to the bottom hole flowing pressure; ③ Particularly, there is a bottom hole flowing pressure value such that in the wellbore above the tubing liquid accumulation surface, the constructed wellbore pressure profile coincides completely with the original wellbore pressure profile curve, and the two have the same throttle inlet pressure;

[0070] (2) Select a bottom hole flowing pressure value, calculate the throttle inlet pressure from the pipe flow model, and calculate the throttle outlet pressure from the pipe flow model according to the actual wellhead oil pressure;

[0071] (3) According to the gas-liquid two-phase nozzle flow model, substitute the throttle inlet pressure and throttle outlet pressure of the constructed wellbore pressure profile with a tubing liquid column height of 0 m in the tubing to calculate the throttle nozzle diameter, compare it with the actual throttle nozzle diameter, and calculate the error between the two;

[0072] (4) Taking the error accuracy of 1% as the control standard, continuously adjust the bottom hole flowing pressure to calculate the throttle nozzle diameter. When the error control standard is met, it is judged that the constructed wellbore pressure profile coincides completely with the original wellbore pressure profile curve. At this time, the throttle inlet pressure obtained is the throttle inlet pressure of the true wellbore pressure profile.

[0073] Example 4 of the calculation method for wellbore liquid accumulation height:

[0074] In the above embodiments, the corresponding input parameters are mainly obtained by directly collecting the annular pressure value at the throttle position, for example, by directly collecting the pressure by setting a pressure sensor / pressure gauge.

[0075] In this embodiment, the annular pressure value at the choke position is directly calculated by a theoretical formula using parameters such as the wellhead casing pressure, and the following formula is used for calculation:

[0076]

[0077] Where: p 2 is the annular pressure value at the throttle position, unit: MPa; p ts is the wellhead casing pressure, unit: MPa; γ g is the relative density of natural gas, dimensionless; H 3 is the vertical depth from the wellhead to the choke position, in m; is the average compression factor of the static gas column in the wellbore, dimensionless; is the average temperature of the static gas column in the wellbore, in K. Since the required bottom hole pressure is implicit in the compressibility factor, it cannot be displayed and needs to be solved by an iterative method.

[0078] Example 5 of calculation method for wellbore liquid accumulation height:

[0079] The difference between this embodiment and the above-mentioned embodiment is that, in this embodiment, it also includes the step of judging whether the calculated wellbore liquid accumulation height is valid: comparing the calculated wellbore liquid accumulation height with the height of the throttle position, if the wellbore liquid accumulation height is lower than the height of the throttle position, the calculation result is valid and can be used to guide the drainage and gas production work of the underground throttling gas well to ensure the stable production of the gas well.

[0080] Based on the calculation method in the above-mentioned wellbore liquid accumulation height calculation method embodiment, a specific application example is provided, such as Figure 2 :

[0081] Specifically, taking Well A of Dongsheng Gas Field as an example, the wellbore liquid loading height calculation method in this embodiment is used to analyze the wellbore liquid loading degree of the corresponding well:

[0082] Step 1: According to the empirical formula for calculating the ratio of the annular liquid column height to the tubing liquid column height established above, substitute the casing pressure data and liquid-gas ratio data of the gas well to calculate the ratio of the annular liquid column height to the tubing liquid column height.

[0083] Specifically, select the gas well casing pressure data and liquid-gas ratio data at 11 time nodes between June 13, 2018 and December 6, 2019 of this well, substitute them into the empirical formula, and obtain the ratio of the annulus liquid column height to the tubing liquid column height at 11 time nodes (see Table 1). From the calculation results, the ratio of the annulus liquid column height to the tubing liquid column height of Well A fluctuates between 0.58 and 0.65, with an average of 0.62.

[0084] Step 2: According to the fitting process of the above throttler inlet pressure value, obtain the tubing diameter parameter of the gas well, the actual throttler nozzle diameter and depth parameter, the wellhead oil pressure parameter, the daily gas production parameter, the daily liquid production parameter, and the natural gas component parameter of the gas well, and continuously adjust the bottom hole flowing pressure, and obtain the throttler inlet pressure through the fitting curve process.

[0085] Specifically, according to the fitting steps, the throttler inlet pressure at 11 time nodes between June 13, 2018 and December 6, 2019 was calculated (see Table 1). From the calculation results, the throttler inlet pressure of this well decreased from 11.46 MPa to 2.6 MPa.

[0086] Step 3: According to the established calculation formula for the annulus pressure value at the throttler position, input the throttler depth parameter, wellhead casing pressure parameter, and natural gas component parameter of the gas well, and calculate the annulus pressure value at the throttler position.

[0087] Specifically, the annulus pressure value at the throttler position at 11 time nodes between June 13, 2018 and December 6, 2019 was calculated (see Table 1). From the calculation results, the annulus pressure at the throttler position of Well A decreased from 11.55 MPa to 3.81 MPa.

[0088] Step 4: According to the established calculation formula for the liquid accumulation height in the wellbore of the downhole throttling gas well, input the calculated ratio of the annulus liquid column height to the tubing liquid column height, the throttler inlet pressure value, and the annulus pressure value at the throttler position according to the calculation steps, and calculate the tubing liquid accumulation height and the annulus liquid accumulation height.

[0089] Specifically, the liquid accumulation height in the wellbore at 11 time nodes between June 13, 2018 and December 6, 2019 was calculated, as shown in Table 1.

[0090] Step 5: Back-calculate the pressure loss of the moving gas column in the tubing and the pressure loss of the static gas column in the annulus, and then calculate the tubing liquid accumulation height and the annulus liquid accumulation height again, and determine the calculation round according to the calculation accuracy value.

[0091] Specifically, the pressure losses of the flowing gas column in the tubing and the static gas column in the annulus were calculated at 11 time nodes between June 13, 2018 and December 6, 2019. The liquid accumulation heights in the tubing and the casing were calculated again. From the calculation results, the error values of the wellbore liquid accumulation heights calculated in the first and second rounds were less than 5% at 7 time nodes, meeting the calculation accuracy requirements; at 4 nodes, after 3 - 5 rounds of calculation, the error values of the wellbore liquid accumulation heights met the calculation accuracy.

[0092] Step 6: Determine whether the liquid level in the tubing is below the restrictor to determine whether the calculation result is valid.

[0093] Specifically, the vertical depth of the middle part of the formation of Well A is 3170 m, and the vertical depth of the restrictor is 1849 m. The calculated liquid level depths in the tubing are all greater than 2320 m, and the liquid level is below the restrictor, so the calculation result is valid.

[0094] As mentioned above, only the preferred embodiments of the present invention are provided and are not intended to limit the present invention. The patent protection scope of the present invention is subject to the claims. Any equivalent structural changes made by using the description and drawings of the present invention should be included in the protection scope of the present invention by the same token.

[0095] Table 1:

[0096]

[0097]

Claims

1. A method for calculating the liquid level height in the wellbore of an underground throttling gas well, characterized in that, it includes the following steps: Collect the inlet pressure value of the underground throttler and the annulus pressure value at the throttler position; Substitute the inlet pressure value of the throttler and the annulus pressure value at the throttler position into the wellbore liquid level height calculation model for calculation. The wellbore liquid level height calculation model is established according to the following relationships: The bottom hole flowing pressure calculated based on the tubing pressure drop formula is equal to the bottom hole flowing pressure calculated based on the tubing-casing annulus pressure drop formula; The liquid column height in the tubing is in a set ratio to the liquid column height in the tubing-casing annulus; The wellbore liquid level height calculation model is: p 1 + p f1 + ρgH 1 = p 2 + p f2 + ρgH 2 H 2 = kH 1 ρg(1 - k)H 1 = (p 2 - p 1 ) + (p f2 - p f1 ) Where: H 1 is the liquid column height in the tubing, m; p 1 is the inlet pressure of the restrictor, MPa; p f1 is the pressure loss of the flowing gas-water mixture from the liquid level depth in the tubing to the depth of the restrictor, MPa; H 2 is the liquid column height in the tubing-casing annulus, m; p 2 is the annulus pressure value at the restrictor position, MPa; p f2 is the pressure loss of the static gas-water mixture from the liquid level depth in the annulus to the depth of the restrictor, MPa; ρ is the liquid density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 , and k is the ratio of the height of the annulus liquid column to the height of the tubing liquid column; The calculation method is iterative calculation: 1) Set the difference between (p f2 -p f1 ) to be 0; 2) Calculate the inlet pressure value (p 1 ) of the restrictor, the annulus pressure value (p 2 ) at the restrictor position, and the ratio (k) of the annulus liquid column height to the tubing liquid column height; 3) Substitute the wellbore liquid accumulation height calculation model to calculate the tubing liquid accumulation height, denoted as H 1-1 ; 4) Calculate the value of the inverse calculation (p f2 -p f1 ), and denote it as (p f2 -p f1 ) - 1 ; 5) Substitute p 1 , p 2 , k, (p f2 - p f1 ) -1 into the calculation model again to calculate the liquid accumulation height in the tubing, denoted as H 1-2 ; 6) If H 1-2 and H 1-1 have a difference greater than the set precision threshold, then the initial value of (p f2 - p f1 ) is set to (p f2 - p f1 ), -1 and steps 1)-6) are repeated again until the difference between H 1-2 and H 1-1 is less than the set precision threshold.

2. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, the inlet pressure value of the throttler is obtained by the following method: 1) Construct a wellbore pressure profile curve with a liquid column height of 0 m in the tubing; 2) Select the bottom hole flowing pressure value, and calculate the throttler nozzle diameter according to the pipe flow model and the gas-liquid two-phase orifice flow model; 3) Calculate the deviation between the calculated throttler nozzle diameter and the actual throttler nozzle diameter. If the deviation is greater than the set accuracy threshold, adjust the bottom hole flowing pressure value and return to step 2); If the deviation is less than the set accuracy threshold, calculate the corresponding throttler inlet pressure according to the corresponding bottom hole flowing pressure and the pipe flow model at this time.

3. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, the annulus pressure value at the throttler position is calculated by using the following static gas column equation: Where: p 2 is the annulus pressure value at the choke position, MPa; p ts is the casing pressure at the wellhead, MPa; γ g is the relative density of natural gas; H 3 is the vertical depth from the wellhead to the choke position, m; is the average compressibility factor of the static gas column in the wellbore; is the average temperature of the static gas column in the wellbore, K.

4. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, the calculation formula for the ratio k of the annulus liquid column height to the tubing liquid column height is: Where: p ts is the wellhead casing pressure, MPa; WGR is the liquid-gas ratio, m 3 / 10 4 m 3 ; erf is the Gaussian error function.

5. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, When the liquid level depth in the tubing and the depth of the restrictor position are known, the pressure loss (p f1 ) of the flowing gas-liquid mixture from the liquid level depth in the tubing to the restrictor depth is calculated by the pipe flow model.

6. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, When the liquid level depth in the tubing-casing annulus and the depth of the restrictor are known, the pressure loss (p f2 ) of the static gas-liquid mixture from the liquid level depth in the annulus to the restrictor depth is calculated by the static gas column equation.

7. The method for calculating the liquid level height in the wellbore of an underground throttling gas well according to claim 1, characterized in that, it further includes a step of judging whether the calculated wellbore liquid level height is valid: compare the calculated wellbore liquid level height with the height at the throttler position. If the wellbore liquid level height is lower than the height at the throttler position, the calculation result is valid.

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