A method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection.

Abstract

This invention belongs to the field of oil and gas development engineering technology, specifically relating to a method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection. The method includes the following steps: S1, calculating the wellhead sand production rate based on the amount of sand flushed out; S2, obtaining particle size distribution characteristics; S3, calculating the actual production of each production section based on the wellhead production; S4, calculating the dominant sand-carrying phase velocity of each production section based on the actual production of each production section; S5, calculating the maximum sand-carrying particle size of each production section based on the dominant sand-carrying phase velocity; S6, calculating the sedimentation ratio of each production section based on the particle size distribution characteristics and the maximum sand-carrying particle size of each production section; S7, calculating the sedimentation rate based on the wellhead sand production rate and the sedimentation ratio of each production section; S8, calculating the amount of sediment within the effective production time based on the sedimentation rate. This invention provides a theoretical basis for identifying major sedimentation production sections and formulating sand removal and control measures.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas development engineering technology, specifically relating to a method for calculating the amount of sediment in the production section of a deep natural gas well based on the sediment collection at the wellhead. Background Technology

[0002] Deep and ultra-deep oil and gas resources are one of the important directions for increasing reserves and production in my country's energy sector. In recent years, exploration and development progress has been made in deep and ultra-deep oil and gas areas such as the Kuqa Piedmont, Tarim Basin, Sichuan Basin, and Junggar Basin. Deep clastic gas reservoirs, tight sandstone gas reservoirs, and high-temperature and high-pressure gas reservoirs have gradually become important targets for stabilizing and increasing oil and gas production. However, deep and ultra-deep oil and gas reservoirs generally face sand production problems during development. For some deep gas wells, especially vertical wells with multiple production sections, after the reservoir sand enters the production section wellbore, some of it can be carried to the wellhead with the gas phase or gas-liquid two-phase flow and detected by wellhead sand production monitoring devices, sand collectors, or surface separation systems; the other part settles and accumulates near the production section due to insufficient flow velocity, large particle size, or reduced sand-carrying capacity, forming bottom sand.

[0003] Compared to shallow oil and gas wells, deep and ultra-deep oil and gas wells are characterized by greater depth, more complex wellbore pressure and temperature conditions, and higher operating costs, making conventional mechanical sand control measures less readily adopted on-site. Furthermore, due to their greater depth, bottom sand accumulation is difficult to detect directly and promptly, making it challenging to accurately determine its location and quantity. Continuous accumulation of bottom sand can narrow the effective flow channel in the production section, abnormally increase production pressure differentials, and deteriorate bottom-hole flow conditions. In severe cases, it can lead to sand burial of the production section, reduced production capacity, frequent sand flushing operations, and even affect the long-term stable production of the gas well. Therefore, establishing a method that can indirectly predict the sand accumulation rate and quantity in the production section of deep and ultra-deep gas wells by combining wellhead production data, wellhead sand collector data, and reservoir basic parameters is of significant engineering importance. Currently, the following key issues remain regarding the prediction of sand accumulation in the production section of deep and ultra-deep oil and gas wells: Question 1: Direct detection of sand deposits at the bottom of deep oil and gas wells is costly, and there is a lack of indirect, simple, and engineering-applicable sand deposit prediction techniques. In the field, determining the presence of sand deposits or their height at the bottom of the well typically requires methods such as running tubing for sand exploration, well logging, and sand flushing analysis. These methods are time-consuming, expensive, and risky, and often require production shutdowns or changes to normal production schedules, making them unsuitable as routine monitoring methods for sand deposit dynamics in deep and ultra-deep gas wells.

[0004] Question 2: Even with known wellhead sand production monitoring data or sand discharge from the sand collector, it is still difficult to directly obtain the actual amount of sand settled downhole. For deep gas wells, the migration of formation sand from the production section to the wellhead is influenced by a combination of factors, including flow velocity, gas-liquid ratio, dominant sand-carrying phase, particle size distribution, and variations in sand-carrying capacity across different well sections. Existing methods mostly focus on statistical or qualitative assessments of wellhead sand production, lacking a calculation method that can link the measured sand production rate at the wellhead, the flow velocity distribution in the production section, the sand particle size distribution, and the proportion of sand settled in each production section. This makes it difficult to accurately evaluate the total amount of sand settled at the bottom of the well. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the amount of sand deposited in the production section of deep natural gas wells based on wellhead sand collection, in order to solve the problems of difficulty in directly detecting bottom sand deposits in deep wells and the difficulty in accurately judging the amount of downhole sand deposits from wellhead sand production data. Addressing the issues of deep and ultra-deep oil and gas wells, high sand exploration costs, high construction risks, and difficulty in continuously monitoring bottom sand deposit dynamics, this invention aims to establish an indirect prediction method that does not rely on running tubing for sand exploration. It utilizes readily available data such as wellhead production data, bottomhole flowing pressure, reservoir physical parameters, and produced sand particle size distribution to quickly evaluate the risk and dynamics of sand deposits in the production section. Furthermore, addressing the problem that wellhead sand production monitoring data or sand collection volume can only reflect the amount of sand reaching the surface and cannot directly represent the actual amount of downhole sand deposits, this invention aims to establish a calculation method that combines the measured sand production volume at the wellhead with the sand-carrying capacity of the production section, the produced sand particle size distribution, and the proportion of sand deposits in each section, thereby achieving the conversion from wellhead sand production volume to the total downhole sand deposit volume. This invention enables quantitative prediction of the main sand-laden well sections and downhole sand volume in deep and ultra-deep water-producing gas wells, providing a basis for optimizing production systems, determining the timing of sand flushing operations, and designing sand control and removal measures.

[0006] The specific technical solution of the present invention is as follows: A method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection, comprising the following steps: S1. Calculate the sand discharge rate based on the amount of sand flushed out by the wellhead sand collector; S2. Obtain the particle size distribution characteristics based on the sand produced by the eroded strata; S3. Calculate the actual output of each production section based on the wellhead output; S4. Calculate the dominant sand-carrying phase flow velocity in the production section based on whether the deep natural gas well produces water and the gas-water production rate. S5. Calculate the maximum sand-carrying particle size of each production section based on whether the deep natural gas well produces water and the flow velocity of the dominant sand-carrying phase in the production section. S6. Calculate the sedimentation ratio of each production section based on the obtained particle size distribution characteristics and the maximum sand-carrying particle size of each production section. S7. Calculate the settling rate based on the wellhead sand production rate and the settling ratio of each production section. S8. Calculate the amount of sand settled within the effective production time based on the sand settling rate.

[0007] Furthermore, step S1 specifically includes: S1. Calculate the wellhead sand discharge rate based on the amount of sand flushed out by the wellhead sand collector: Based on the sand collector data, the sand discharge rate M at the wellhead is obtained, and the sand discharge rate at the wellhead during the effective production time is calculated:

[0008] In equation (1), The sand production rate at the wellhead is m. 3 / d; t is the effective production time, in days; M is the amount of sand flushed out of the wellhead within the effective production time t, in meters. 3 .

[0009] S2. Obtain the grain size distribution characteristics based on the sand produced from the eroded strata: Based on experimental data or field test results of reservoir produced sand, obtain the cumulative particle size distribution curve. (D), then the particle size distribution function is:

[0010] In equation (2), F(D) Indicates particle size less than or equal to D The cumulative mass percentage of sand particles; f(D) Indicates the proportion of particles within a unit particle size range; D denoted as the particle size of the sand, in meters (m).

[0011] S3. Calculate the actual output of each production section based on the wellhead output: The wellhead water production and gas production are known. For the aqueous phase, the volume coefficient of water is approximately 1, therefore the total actual water production in the production section can be directly expressed as:

[0012] In equation (3), q w,tot The total actual water production of the production section, in m 3 / d; Q wsc,tot The daily water production at the wellhead, in meters. 3 / d.

[0013] For the gas phase, the daily gas production under standard wellhead conditions is converted to the total actual downhole gas production as follows:

[0014] In equation (4), q g,tot The total actual gas production of the production section, in m 3 / d; Qgsc,tot The daily gas production at the wellhead is expressed in m. 3 / d;B g It represents the gas volume coefficient under the conditions of bottom hole flowing pressure and bottom hole temperature.

[0015] Based on the total actual gas production and total actual water production in the well, and considering the permeability and reservoir thickness of each production section, the actual water production in each production section is calculated:

[0016] Actual gas production in each production section downhole:

[0017] In equations (5) and (6), q w , i Let m be the actual water production in the i-th production section downhole. 3 / d; q g,i Let m be the actual downhole gas production of the i-th production section. 3 / d; n is the total number of production segments (in this patent, the production segment refers to the effective production segment); i The values ​​can be 1, 2, 3, ..., n; k i For the first i Permeability of the reservoir in each production section, mD; H i For the first i The effective thickness of the reservoir in each production section, in meters; It is the sum of the products of the permeability and effective thickness of all production sections, mD·m.

[0018] S4. Calculate the dominant sediment-carrying phase velocity in the production section based on whether water is produced and the gas-water production rate: Suppose there are n production sections in the reservoir from bottom to top. Then, in the well section above the m-th production section, the actual downhole volumetric flow rates of the water phase and gas phase are respectively:

[0019]

[0020] In equations (7) and (8), q w (z m ) Let m be the volumetric flow rate of the downhole water phase at the m-th production section location. 3 / d; q g (z m )Let m be the downhole gas volumetric flow rate at the m-th production section location. 3 / d.

[0021] Based on the drilling and completion data, the cross-sectional area of ​​the production section wellbore is calculated as follows:

[0022] In the formula, A is the cross-sectional area of ​​the well shaft, in meters. 2 L is the inner diameter of the well shaft, in meters (m).

[0023] The apparent velocities of the aqueous and gas phases in the wellbore production section are as follows:

[0024]

[0025] In the formula, v w (z m ) represents the apparent velocity of the liquid phase at the m-th production section location, in m / s; v g (z m ) represents the apparent velocity of the gas phase at the m-th production section location, in m / s.

[0026] When the deep natural gas well produces only gas and not water, the production section is a pure gas phase flow. At this time, the sand-carrying phase is gas, and its sand-carrying velocity is:

[0027] When the deep natural gas well produces water, the production section exhibits a two-phase flow of gas and liquid. At this time, the proppant-carrying phase is the water phase, and its proppant-carrying velocity is:

[0028] In the formula, u c (z m ) The dominant sand-carrying phase flow velocity in the m-th production section is m / s; u g (z m ) Let m be the gas phase sand-carrying velocity in the m-th production section, in m / s; u w (z m ) Let be the water phase sand-carrying flow velocity in the m-th production section, in m / s.

[0029] This production section is a gas-liquid two-phase flow. First, the gas holdup is calculated based on the drift flow model:

[0030] In the formula, V is the gas holdup of the m-th production section, %; C0 is a distributed parameter, dimensionless; d The drift velocity is expressed in m / s. The distribution parameters and drift velocity under high gas-liquid ratio and low gas-liquid ratio conditions can be taken as different values, which can be determined based on wellbore test data, flow pattern identification results, or empirical calibration values ​​in the same block.

[0031] The actual flow velocities of the gas phase and liquid phase are respectively:

[0032]

[0033] Note: m represents the m-th calculation position or production section within the wellbore, where m takes values ​​from 1, 2, 3, ..., n. Preferably, each production section is numbered from bottom to top, then z m This indicates the wellbore location in the m-th production section, where the wellbore flow rate is the cumulative inflow from the 1st production section to the m-th production section.

[0034] S5. Calculate the maximum sand-carrying particle size for each production section based on whether water is produced and the flow velocity of the dominant sand-carrying phase in the production section: When the deep natural gas well produces only gas and not water, the production section of the wellbore is a pure gas phase flow, with the gas phase being the dominant sand-carrying phase. Therefore, the critical sand-carrying velocity of a sand particle with diameter D in this well section is expressed as:

[0035] If we define the maximum carryable particle size of the m-th production section as Dmax,m, then we have:

[0036] Therefore, we can conclude that:

[0037] In the formula, u c (D,z m ) For the m-th production section, the particle size is D The critical sand-carrying velocity of sand particles, m / s; D max,m Let m be the maximum particle size that can be carried in the m-th production section; u cg (D max,m ,z m ) C represents the critical gas-phase sand-carrying velocity of the sand particle with the largest carryable particle size in the m-th production section, in m / s; g ρ is the empirical coefficient for gas-phase sand carrying under pure gas-phase flow conditions; sThe density of sand particles is kg / m³. 3 ;ρ g The density of the gas is kg / m³. 3 g is the acceleration due to gravity, m / s² 2 .

[0038] When the deep natural gas well produces water, the production section of the wellbore is a two-phase flow of gas and liquid, with the liquid phase being the dominant sand-carrying phase. Therefore, the critical sand-carrying velocity of a sand particle with diameter D in this production section is expressed as:

[0039] The maximum carryable particle size of the m-th production section is:

[0040] Therefore, we can conclude that:

[0041] In the formula, u cw (D max,m ,z m ) is the critical sand-carrying velocity in the aqueous phase for the sand particles with the largest carryable particle size in the m-th production section, in m / s; ρ is the empirical coefficient for liquid phase sand carrying under gas-liquid two-phase flow conditions; f The density of water is kg / m³. 3 .

[0042] Preferably, Cg and The calibration can be performed through indoor flow ring experiments, on-site wellhead sand production monitoring data, sand discharge volume from the desander, or sand return data.

[0043] S6. Calculate the proportion of sediment in each production section based on the obtained particle size distribution characteristics of the produced sand from the formation: The relationship between the particle size distribution characteristics obtained in S2 and the maximum carryable particle size is shown in the attached figure. Figure 1 Calculate the conditions for sediment settling:

[0044] For the m-th production section, particles with a diameter larger than the maximum carryable diameter of that section are considered to have deposited. Therefore, the proportion of sediment in this production section is... Represented as: (twenty four) This formula indicates that if the dominant sand-carrying phase velocity in the m-th production section is relatively low, then D max,mIf the velocity of the sand-carrying phase is smaller, more coarse particles cannot be carried away, and the proportion of sedimentation increases accordingly; conversely, if the velocity of the sand-carrying phase is higher, the proportion of sedimentation decreases, and the value of m is 1, 2, 3, ... n.

[0045] S7. Calculate the settling rate based on the wellhead sand production rate and the settling ratio of each production section: Assume that the initial sand output rate is the same for all production sections, denoted as q. s0 If the wellbore has n production sections, then the total initial sand production rate downhole is:

[0046] Let the production sections be numbered 1-n from bottom to top. The sand particles entering the wellbore from the i-th production section must pass through each of the production sections above them sequentially as they move upwards to the wellhead. Therefore, the proportion of sand particles from that production section that ultimately reach the wellhead is:

[0047] S1 calculates the actual sand production rate at the wellhead as q. sw According to the definition of proportion, we have:

[0048] From this, the original sand output rate of each production section can be obtained:

[0049] In the formula, q s,tot The total initial sand production rate downhole, m 3 / d; q s0 The original sand output rate for each production section, m 3 / d; q sw The actual sand production rate at the wellhead, in meters (m) 3 / d; β m Let be the proportion of sediment in the m-th production section; η i This represents the proportion of sand particles that ultimately reach the wellhead in the i-th production section.

[0050] The total downhole sand settling rate is equal to the difference between the total initial downhole sand production rate and the actual wellhead sand production rate. The sand settling rate is calculated by combining the wellhead sand production rate calculated in S1 and the sand settling ratio in S6.

[0051] In the formula, q sd Let m be the settling rate. 3 / d.

[0052] S8. Calculate the amount of sand settled within the effective production time based on the sand settling rate. If the gas well production remains essentially constant during the effective production time t, then the amount of sand settled at the bottom of the well can be calculated based on the effective production time t:

[0053] In the formula, M d The amount of sand settled at the bottom of the well during the effective production time t, m 3 .

[0054] By adopting the above technical solution, the beneficial effects of the present invention are as follows: (1) This invention provides a method for predicting sand settling in the production section of deep and ultra-deep gas wells without relying on downhole sand exploration. This method can indirectly calculate the downhole sand settling rate and amount by using readily available field data such as the amount of sand flushed out by the wellhead sand collector, effective production time, wellhead gas production, water production, reservoir permeability, and reservoir thickness, thereby reducing the cost and construction risk of deep well sand exploration operations.

[0055] (2) This invention establishes a quantitative conversion relationship between wellhead sand production and downhole sand production. By calculating the wellhead sand production rate, the sand production ratio of each production section and the sand particle passing ratio, the original downhole sand production rate and sand production rate are inverted, realizing the conversion from "measurable wellhead sand production" to "actual downhole sand production", solving the problem that wellhead sand production data is difficult to directly evaluate downhole sand production.

[0056] (3) This invention fully considers the distribution characteristics of sand particles produced in the formation and establishes a graded sedimentation judgment method based on the maximum sand-carrying particle size. By comparing the maximum carryable particle size with the distribution of produced sand particle size in different production sections, the sedimentation ratio of each production section can be quantitatively calculated, and the carrying and settling of sand particles of different sizes can be judged. This realizes the transformation from overall experience judgment to particle size-based sedimentation judgment, and provides a basis for identifying the main sedimentation production sections and formulating sand removal and prevention measures. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the pressure and velocity distribution in the production section and the graded sedimentation of the formation sand. Detailed Implementation

[0058] Example 1 To verify the effectiveness of the method of the present invention, a vertical well (6500m deep) of a deep three-layer combined gas production well is analyzed as an example. The formation pressure of this well is 82MPa, the bottom hole flowing pressure is 56MPa, and the known parameters are shown in Table 1: Table 1

[0059] (1) Calculate the sand discharge rate based on the amount of sand flushed out by the wellhead sand collector. Based on the sand collector data, the sand discharge from the wellhead was 480L, and the sand discharge rate at the wellhead was 0.08m / s² within the effective production time of 6 days. 3 / d.

[0060] (2) Obtaining particle size distribution characteristics based on sand produced from the eroded strata Based on the experimental data of the flushed sand samples and the results of field tests, the cumulative distribution of the sand grain size produced by the formation was obtained as follows: 0.02 mm corresponds to 0%, 0.04 mm corresponds to 15%, 0.06 mm corresponds to 35%, 0.08 mm corresponds to 60%, 0.10 mm corresponds to 80%, 0.12 mm corresponds to 92%, and 0.15 mm corresponds to 100%.

[0061] (3) Calculate the actual output of each production section based on the wellhead output. The total actual gas production from the well is:

[0062] Since the water volume factor is taken as 1, the total actual water production in the well is 4m³. 3 / d.

[0063] First, based on the reservoir's overall supply capacity k i H i Initial division of total wellhead production:

[0064] The actual gas production of the three production sections can be obtained as follows: q g1 =66.67m 3 / d, q g2 =333.33m 3 / d, q g3 =300m 3 / d The actual water production was as follows: q w1 =0.381m 3 / d, q w2 =1.905m 3 / d, q w3 =1.714m 3 / d (4) Calculate the dominant sediment-carrying phase velocity in the production section based on whether water is produced and the gas-water output. Assuming three smaller layers form three production sections from bottom to top, the cumulative flow and velocity of each production section are as follows: Production Section 1 (Lowermost Production Section): q g (z1) = 66.67m 3 / d, q w(z1)=0.381m 3 / d v g (z1) = 0.0348 m / s, v w (z1) = 0.000199 m / s Production Section 2 (Middle Production Section): q g (z2) = 66.67 + 333.33 = 400m 3 / d, q w (z2) = 0.381 + 1.905 = 2.286m 3 / d v g (z2) = 0.2088 m / s, v w (z2) = 0.00119 m / s Production Section 3 (Upper Production Section) q g (z3)=700m 3 / d, q w (z3)=4m 3 / d v g (z3) = 0.3655 m / s, v w (z3) = 0.00209 m / s Based on the gas and water production, this operating condition is determined to be a high gas-liquid ratio condition. A high gas-liquid ratio drift flow model is adopted (calibrated using wellbore test data from the same block under high gas-liquid ratio conditions, with drift flow model parameters C0=1.02, V...). d Calculate the gas holdup (=0.002m / s):

[0065] Substituting these values, we get: α(z1) = 0.923, α(z2) = 0.965, α(z3) = 0.967 The actual liquid flow velocities are as follows: u w (z1) = 0.00258 m / s, u w (z2) = 0.0340 m / s, u w (z3) = 0.0634 m / s Since this well is a gas-liquid two-phase flow well, and the liquid phase is the dominant sand-carrying phase under gas-liquid two-phase flow conditions, the flow velocities of the dominant sand-carrying phase in the three production sections are respectively taken as: u c (z1) = 0.00258 m / s, u c (z2) = 0.0340 m / s, u c (z3) = 0.0634 m / s (5) Calculate the maximum sand-carrying particle size and the sand settling ratio of each production section based on the gas and water production. The cumulative grain size distribution of the sand in the producing formation is as follows: 0.02 mm corresponds to 0%, 0.04 mm corresponds to 15%, 0.06 mm corresponds to 35%, 0.08 mm corresponds to 60%, 0.10 mm corresponds to 80%, 0.12 mm corresponds to 92%, and 0.15 mm corresponds to 100%.

[0066] The maximum sand-carrying particle size was calculated using the liquid-phase critical sand-carrying velocity model.

[0067] Then we have: D max,1 ≈0.00029mm, D max,2 ≈0.0527mm, D max,3 ≈0.172mm, From this, the proportion of sediment in each production section can be obtained: Production Section 1: D max,1 <D min =0.02mm Therefore, all sand grains of different sizes in this production section exhibit a depositional tendency: β1=1 Production Section 2: D max,2 ≈0.0527mm Linear interpolation of the cumulative particle size distribution shows that the cumulative proportion of particles smaller than or equal to 0.0527 mm is approximately 27.7%. Therefore: β² = 1 - 0.277 = 0.723 Production Section 3: D max,3 ≈0.172mm>0.125mm This indicates that the third production stage already has the capacity to carry sand of all particle sizes; therefore, β3 = 0. (6) Calculate the settling rate based on the wellhead sand production rate and the settling ratio of each production section. The calculated percentages of sand particles that ultimately reach the wellhead in each production section are as follows: Production Section 1: η1=(1-β1)(1-β2)(1-β3)=0 Production stage 2: η2 = (1-β2)(1-β3) = 0.277 Production Section 3: η3 = (1-β3) = 1 The sand production rate measured at the wellhead can then be calculated as follows:

[0068] The total initial sand production rate downhole is:

[0069] Therefore, the total sand settling rate downhole is:

[0070] (7) Calculate the amount of sand settled within the effective production time based on the sand settling rate. The amount of sand settled at the bottom of the well within 6 days of effective production time is: .

Claims

1. A method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection, characterized in that, Includes the following steps: S1. Calculate the sand discharge rate at the wellhead based on the amount of sand flushed out at the wellhead. S2. Obtain the particle size distribution characteristics based on the sand produced by the eroded strata. The particle size distribution characteristics are characterized by the proportion of particles within a unit particle size range. S3. Calculate the actual output of each production section based on the wellhead output. The actual output of each production section includes the actual water production and the actual gas production in each production section. S4. Calculate the dominant sand-carrying phase flow velocity of each production section based on whether the deep natural gas well produces water and the actual output of each production section calculated in step S3. S5. Calculate the maximum sand-carrying particle size of each production section based on whether the deep natural gas well produces water and the dominant sand-carrying phase flow velocity of each production section calculated in step S4. S6. Based on the particle size distribution characteristics obtained in S2 and the maximum sand-carrying particle size of each production section obtained in step S5, calculate the sand settling ratio of each production section. S7. Calculate the settling rate based on the wellhead sand production rate obtained in S1 and the settling ratio of each production section obtained in step S6. S8. Calculate the amount of sand settled within the effective production time based on the sand settling rate obtained in S7.

2. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 1, characterized in that, Step S4 is as follows: In equations (10) and (11), v w (z m ) Let be the apparent velocity of the liquid phase at the m-th production section location, in m / s; v g (z m ) Let be the apparent velocity of the gas phase at the m-th production section location, in m / s; q w (z m ) Let m be the volumetric flow rate of the downhole water phase at the m-th production section location. 3 / d; q g (z m ) Let m be the downhole gas volumetric flow rate at the m-th production section location. 3 / d, where A is the cross-sectional area of ​​the well shaft, in meters. 2 ; When the deep natural gas well only produces gas and not water: When the deep natural gas well produces water: In equations (12) and (13), u c (z m ) The dominant sand-carrying phase flow velocity in the m-th production section is m / s; u g (z m ) Let m be the gas phase sand-carrying velocity in the m-th production section, in m / s; u w (z m ) Let m be the velocity of the water phase carrying sand in the m-th production section, in m / s; In equation (14), Let be the gas holdup of the m-th production section, %; C0 is a distribution parameter, dimensionless. V d The drift velocity is in m / s; 。 3. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 2, characterized in that, In step S4: In equations (7) and (8), i The values ​​are 1, 2, 3, ..., m; q w , i For the first i Actual water production in each production section, m 3 / d; q g,i For the first i Actual gas production in each production section, m³ 3 / d.

4. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 2, characterized in that, Step S5 is as follows: When the deep natural gas well only produces gas and not water: In equation (19), D max,m Let m be the maximum carryable particle size in the m-th production stage; C g ρ is the empirical coefficient for gas-phase sand carrying under pure gas-phase flow conditions; s The density of sand particles is kg / m³. 3 ; ρ g The density of the gas is kg / m³. 3 g is the acceleration due to gravity, m / s² 2 ; When the deep natural gas well produces water: In equation (22), This is the empirical coefficient for sand carrying in the liquid phase under gas-liquid two-phase flow conditions; ρ f The density of water is kg / m³. 3 .

5. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 4, characterized in that, Step S6 is as follows: For the m-th production section, particles with a diameter larger than the maximum carryable diameter of that section are considered to have deposited. The sedimentation ratio of this production section is expressed as: (24) In equation (24), Let m be the sand settling ratio of the m-th production section, where m takes values ​​of 1, 2, 3, ..., n.

6. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 5, characterized in that, Step S7 is as follows: In equations (26), (27), and (29), q s,tot The total initial sand production rate downhole, m 3 / d; q s0 The original sand output rate for each production section, m 3 / d; n is the total number of production sections; i The values ​​can be 1, 2, 3, ..., n; η i This represents the proportion of sand particles that ultimately reach the wellhead in the i-th production stage. The sand production rate at the wellhead is m. 3 / d; In equation (25), q sd Let m be the settling rate. 3 / d.

7. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 6, characterized in that, Step S8 is as follows: In equation (30), M d The amount of sand settled at the bottom of the well during the effective production time t, m 3 t represents the effective time.

8. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 1, characterized in that, Step S1 is as follows: In equation (1), The sand production rate at the wellhead is m. 3 / d; t is the effective production time, in days; M is the amount of sand flushed out of the wellhead within the effective production time t, in meters. 3 .

9. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 1, characterized in that, Step S2 is as follows: In equation (2), f(d) Indicates the proportion of particles within a unit particle size range; F(D) Indicates particle size less than or equal to D The cumulative mass percentage of sand particles; D denoted as the particle size of the sand, in meters (m).

10. The method for calculating the amount of sediment in the production section of a deep natural gas well based on wellhead sediment collection according to claim 1, characterized in that, Step S3 is as follows: In equation (3), q w,tot The total actual water production of the production section, in m 3 / d; Q wsc,tot The daily water production at the wellhead, in meters. 3 / d; In equation (4), q g,tot The total actual gas production of the production section, in m 3 / d; Q gsc,tot The daily gas production at the wellhead is expressed in m. 3 / d;B g This represents the gas volume coefficient under the conditions of bottom hole flowing pressure and bottom hole temperature. In equations (5) and (6), q w , i For the first i Actual water production in each production section, m 3 / d; q g,i Let m be the actual downhole gas production of the i-th production section. 3 / d; n is the total number of production sections; i The values ​​can be 1, 2, 3, ..., n; k i For the first i Permeability of the reservoir in each production section, mD; H i For the first i The effective thickness of the reservoir in each production section, in meters; It is the sum of the products of the permeability and effective thickness of all production sections, mD·m.

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