A shale gas horizontal well borehole sand accumulation amount calculation method and system

Abstract

The application discloses a shale gas horizontal well wellbore sand accumulation amount calculation method and system, and the calculation method comprises the following steps: determining wellhead sand flow based on the obtained cumulative sand production amount of the wellhead in a calculation period; determining a dimensionless number based on the obtained gas well structure parameters and real-time production parameters; determining the cumulative inflow sand amount at the well bottom in the calculation period based on the wellhead sand flow and the dimensionless number; and calculating the cumulative sand accumulation amount in the wellbore in the calculation period according to the cumulative sand production amount of the wellhead and the cumulative inflow sand amount at the well bottom. The application is suitable for any sand production horizontal gas well, and the cumulative sand accumulation amount in the wellbore is calculated to determine the sand production state of the gas well and the severity of the wellbore sand accumulation, predict the sand plugging risk, and then guide the development of a reasonable and feasible production system, sand cleaning period and sand control cleaning measures, effectively strengthen the wellbore sand control and plugging removal, and ensure the stable production of the gas well.

Description

Technical Field

[0001] This application relates to the field of fluid and sand removal technology in oil and gas development, and in particular to a method and system for calculating the amount of sand accumulated in a shale gas horizontal well. Background Technology

[0002] The rapid development of the national economy has increased the demand for energy. Shale gas, as an unconventional natural gas, is the cleanest fossil energy source. my country has abundant shale gas reserves, and in recent years, shale gas development has achieved significant breakthroughs, becoming an important source for increasing my country's natural gas reserves and production. Due to its geological formation, shale gas wells will produce formation sand after large-scale sand fracturing. Most shale gas wells are water-producing wells, so the wellbore often experiences a complex process where shale gas carries water and sand together. When gas production is low or sand production is severe, not all sand can be carried out and large amounts accumulate in the wellbore. If the accumulated sand is not removed in time, it will seriously endanger gas well production, including:

[0003] 1. Blockage of the wellbore can cause reduced gas well production, and in severe cases, can lead to a complete shutdown.

[0004] 2. Erosion damages the well casing and shortens its service life;

[0005] 3. Abrasion damages downhole equipment;

[0006] 4. Causes accidents such as sand jamming in the well;

[0007] Therefore, during gas well production, it is often necessary to monitor the sand accumulation in the wellbore and take timely measures to remove the sand to prevent blockages and other harmful phenomena, eliminate the hazards of sand accumulation, and ensure gas well production. Existing wellbore sand carrying prediction and sand prevention and removal technologies include: Patent application CN117145404A, entitled "A Sand-sinking Sand Prevention and Gas Drainage Machine Pulling String", which is used for coalbed methane extraction and solves the problems of gas lock, sand jamming, sand burial, and ball valve leakage encountered by conventional drainage pumps in coalbed methane well mechanical extraction. The main method involves using packers to suspend the production tubing, allowing produced gas and water to pass through wire mesh screens into the production tubing while preventing sand particles from entering the tubing and thus avoiding sand jamming and burial hazards. Patent application CN116856908A, entitled "An Experimental Method for Determining the Critical Sand-Carrying Velocity of Shale Gas Wells," has been published. Based on fluid mechanics similarity criteria and the Gray model, physical simulation experiments are conducted to obtain sand holding capacity and sand holding rate under different conditions, and the critical sand-carrying production rate is calculated. The calculation of the critical sand-carrying production rate can clarify the sand-carrying state of the gas well, determine whether sand accumulation has occurred within the well, and provide a theoretical basis for drainage process design. Patent application CN113657050A, entitled "A Method for Calculating the Critical Sand-Carrying Velocity Considering the Influence of Slug Bubbles and Multiple Parameters," has also been published. Based on a detailed consideration of the gas-liquid two-flow pattern, a method for calculating the critical sand-carrying velocity is provided. The calculation of the critical sand-carrying production rate can clarify the sand-carrying state of the gas well; when the gas phase velocity is less than the critical velocity, sand accumulation will occur within the gas well.

[0008] Existing technologies can determine sand accumulation conditions and whether sand has formed in the wellbore by calculating the critical sand-carrying velocity or flow rate. However, they cannot quantitatively predict the amount of sand accumulated in the wellbore, leading to inaccurate sand removal operations. Excessive sand removal frequency results in high costs, while insufficient frequency prevents timely sand removal, causing severe sand blockage and impacting production. Therefore, qualitative evaluation and quantitative prediction of sand accumulation in shale gas wellbores under specific conditions are crucial for developing reasonable and feasible production systems, sand removal systems, and sand control technologies. This helps prevent sand blockage and other harmful phenomena, reduces negative factors affecting gas well productivity, and is of great significance for ensuring shale gas production. Summary of the Invention

[0009] This application provides a method and system for calculating the amount of sand accumulated in the wellbore of shale gas horizontal wells. This solves the problem in existing technologies where the inability to calculate the amount of sand accumulated in the wellbore leads to high costs when the sand removal frequency is too high, or serious sand blockage when the sand removal frequency is too low, severely impacting production. The method enables quantitative calculation of the amount of sand accumulated in the wellbore during a specific time period in the liquid-carrying sand production process of gas wells. Through online or intermittent sand removal by the wellhead desander, the cumulative sand output from the wellhead during a specific time period is statistically analyzed. Based on the wellhead sand output and combined with a horizontal well liquid-carrying sand calculation model, a series of calculations are performed to obtain the cumulative amount of sand accumulated in the wellbore within a specific time period. This clarifies the degree of sand accumulation in the wellbore, assesses the sand-carrying status of the wellbore, and predicts the hazards of sand blockage. This provides a basis for optimizing production systems and sand control measures, as well as for sand removal and unblocking work, ensuring stable gas well production.

[0010] In a first aspect, embodiments of this application provide a method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well, the calculation method comprising:

[0011] The wellhead sand flow rate is determined based on the cumulative sand production at the wellhead during the calculated time period.

[0012] The dimensionless numbers are determined based on the acquired gas well structure parameters and real-time production parameters. The dimensionless numbers include: gas phase Reynolds number, liquid phase Reynolds number and gas phase Froude number.

[0013] The cumulative sand inflow to the bottom of the well during the calculation period is determined based on the wellhead sand flow rate and the dimensionless number.

[0014] The cumulative sand accumulation in the wellbore during the calculation period is calculated based on the cumulative sand output at the wellhead and the cumulative sand inflow at the bottom of the well.

[0015] Preferably, the gas well structural parameters include at least: tubing inner diameter, total well depth, vertical well section length, and horizontal well section length.

[0016] The real-time production parameters include at least: real-time wellhead oil pressure, wellhead temperature, real-time natural gas standard condition volumetric flow rate, and real-time liquid phase standard condition volumetric flow rate. The liquid phase is generally water, but may contain a small amount of impurities in actual production.

[0017] Preferably, determining the dimensionless number based on the acquired gas well structure parameters and real-time production parameters includes:

[0018] Based on the real-time production parameters, determine the real-time natural gas operating density, real-time natural gas operating volume flow rate, real-time liquid phase operating density, and real-time liquid phase operating volume flow rate.

[0019] The real-time apparent gas phase velocity and real-time apparent liquid phase velocity are determined based on the gas well structure parameters and the real-time production parameters.

[0020] Based on the real-time apparent gas flow rate, real-time apparent liquid flow rate, real-time natural gas operating density, and real-time liquid operating density, the real-time converted gas flow rate and the real-time converted liquid flow rate are determined.

[0021] The dimensionless number is determined based on the real-time conversion gas phase flow rate and the real-time conversion liquid phase flow rate.

[0022] Preferably, the real-time natural gas operating condition density is determined according to the following formula:

[0023]

[0024] in, For real-time natural gas operating condition density, Z The gas compressibility factor under wellhead temperature and pressure conditions. P For real-time wellhead oil pressure, T The wellhead temperature, The relative density of natural gas;

[0025] The real-time natural gas operating condition volumetric flow rate is determined according to the following formula:

[0026]

[0027] in, This refers to the real-time volumetric flow rate of natural gas under operating conditions. T The wellhead temperature, P For real-time wellhead oil pressure, This refers to the real-time standard volumetric flow rate of natural gas.

[0028] The real-time liquid phase density is determined according to the following formula:

[0029]

[0030] in, For liquid phase operating conditions, This is the standard density of the liquid phase.

[0031] The real-time liquid phase volumetric flow rate is determined according to the following formula:

[0032]

[0033] in, This represents the real-time volumetric flow rate under liquid phase operating conditions. This represents the real-time standard volumetric flow rate of the liquid phase.

[0034] Preferably, the real-time apparent gas velocity is determined according to the following formula:

[0035]

[0036] in, For real-time apparent gas phase velocity, This refers to the real-time volumetric flow rate of natural gas under operating conditions. d This refers to the inner diameter of the oil pipe.

[0037] The real-time apparent flow rate of the liquid phase is determined according to the following formula:

[0038]

[0039] in, For real-time apparent flow rate of the liquid phase, This represents the real-time volumetric flow rate under liquid phase operating conditions. d This refers to the inner diameter of the oil pipe.

[0040] Preferably, the real-time conversion gas phase flow rate is determined according to the following formula:

[0041]

[0042] in, To convert gas phase flow rate in real time, For real-time apparent gas phase velocity, The density is the standard liquid phase density. For real-time liquid phase operating conditions, For natural gas standard condition density, Real-time natural gas operating condition density;

[0043] The real-time conversion liquid phase flow rate is determined according to the following formula:

[0044]

[0045] in, To convert the liquid phase flow rate in real time, This represents the real-time apparent flow rate of the liquid phase.

[0046] Preferably, the dimensionless gas-phase Reynolds number is determined according to the following formula:

[0047]

[0048] in, For gas phase Reynolds number, For natural gas standard condition density, Real-time conversion of gas phase flow rate, d The inner diameter of the oil pipe. This refers to the dynamic viscosity of natural gas under standard conditions.

[0049] The dimensionless liquid phase Reynolds number is determined according to the following formula:

[0050]

[0051] in, For liquid phase Reynolds number, For the standard density of water, To convert the liquid phase flow rate in real time, d The inner diameter of the oil pipe. The standard dynamic viscosity of water;

[0052] The dimensionless gas-phase Froude number is determined based on the Lockhart-Martinelli method according to the following formula:

[0053]

[0054] in, For the phase of Froude number, For natural gas standard condition density, To convert gas phase flow rate in real time, For the standard density of water, It is the acceleration due to gravity. d This refers to the inner diameter of the oil pipe.

[0055] Preferably, the cumulative sand output at the wellhead is obtained by the amount of sand discharged through the wellhead desander within the calculated time period;

[0056] The wellhead sand flow rate is determined according to the following formula:

[0057]

[0058] in, For wellhead sand flow rate, To calculate the cumulative sand production at the wellhead within a given time period, t To calculate the duration of a time period.

[0059] Preferably, the step of determining the cumulative sand inflow at the bottom of the well during the calculation period based on the wellhead sand flow rate and the dimensionless number includes:

[0060] The sand flow rate at the bottom of the well is determined based on the wellhead sand flow rate and the dimensionless number.

[0061] The cumulative sand inflow at the bottom of the well is obtained by statistically analyzing the sand flow rate at the bottom of the well during the calculation period.

[0062] Preferably, the flow rate of sand flowing into the bottom of the well is determined according to the following formula:

[0063]

[0064]

[0065] in, This represents the flow rate of sand flowing into the well bottom. For wellhead sand flow rate, d The inner diameter of the oil pipe. h The length of the vertical well section. l For the total well depth, c The length of the horizontal well section. It is a function of the dimensionless gas-phase Reynolds number, liquid-phase Reynolds number, and gas-phase Froude number. For gas phase Reynolds number, For liquid phase Reynolds number, For the gas phase Froude number;

[0066] The cumulative amount of sand flowing into the bottom of the well is determined according to the following formula:

[0067]

[0068] in, For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. t To calculate the time period, dt It is the derivative of the calculation time period.

[0069] Preferably, the cumulative amount of sand accumulated in the wellbore during the calculation period is determined according to the following formula:

[0070]

[0071] in, For calculating time periods t The cumulative amount of sand accumulated inside the inner wellbore. For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. This is to calculate the cumulative sand output from the wellhead within a given time period.

[0072] Secondly, embodiments of this application also provide a shale gas horizontal wellbore sand accumulation calculation system, the calculation system comprising:

[0073] The data acquisition module is used to obtain the well structure parameters and real-time production parameters of shale gas horizontal wells;

[0074] The central control module is used to calculate the cumulative sand accumulation in the wellbore during the calculation period based on the gas well structure parameters and the real-time production parameters.

[0075] The output prompt module is used to output the calculation results of the central control module and / or remind users to deal with the sand accumulation in the wellbore.

[0076] Thirdly, embodiments of this application provide a device, including:

[0077] processor;

[0078] Memory used to store processor-executable instructions;

[0079] When the processor executes the executable instructions, it implements the method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well as described above.

[0080] Fourthly, a storage medium includes a computer program or instructions for storing a method for calculating the amount of sand accumulated in a shale gas horizontal wellbore, as described above, when the computer program or instructions are executed.

[0081] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0082] This application provides a method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well. This method utilizes a technique where, during the production of liquid-carrying sand in a gas well, sand is discharged online or intermittently through a sand collector at the wellhead. The cumulative sand output at the wellhead is statistically analyzed over a specific time period. Based on this sand output and combined with a horizontal well liquid-carrying sand calculation model, a series of calculations are performed to obtain the cumulative amount of sand accumulated in the wellbore within that specific time period. This effectively solves the technical problem in existing technologies where it is impossible to quantitatively calculate the amount of sand accumulated in the wellbore, enabling the quantitative calculation of the cumulative amount of sand accumulated in the wellbore of a horizontal well within any given time period. Attached Figure Description

[0083] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 A flowchart illustrating the method for calculating sand accumulation in a shale gas horizontal wellbore provided in this embodiment of the application;

[0085] Figure 2 This is a schematic diagram illustrating the principle of online calculation of well sand accumulation in an embodiment of this application.

[0086] Figure 3 This is a schematic diagram of the structure of the shale gas horizontal well sand accumulation calculation system provided in the embodiments of this application;

[0087] Figure 4 A graph showing the calculation results of production parameters and sand accumulation during a calculation period provided for an exemplary embodiment of this application. Detailed Implementation

[0088] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0089] It should be understood that although the steps in the flowcharts of this application's embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0090] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0091] refer to Figure 1 As shown in the embodiments of this application, the method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well includes:

[0092] S1. Determine the wellhead sand flow rate based on the cumulative sand production at the wellhead during the obtained calculation period.

[0093] In the embodiments of this application, before determining the wellhead sand flow rate, it is necessary to obtain the cumulative sand production at the wellhead of a single gas well within the calculation period, referring to... Figure 2 The diagram illustrates a sand separation process in a gas well. A sand separator installed at the wellhead separates the sand produced by the shale gas well and collects the separated sand in a sand collection cylinder. In the embodiments of this application, the sand discharge through the sand collection cylinder allows for the statistical calculation of the time period. t Cumulative sand output from the inner wellhead The wellhead sand flow rate of this gas well can be calculated using the following formula:

[0094]

[0095] in, For wellhead sand flow rate, To calculate the cumulative sand production at the wellhead within a given time period, t To calculate the duration of the time period. In this embodiment, the unit of the calculated time period can be seconds, minutes, hours, or even days, weeks, months, etc. Since sand removal from the sand collection cylinder in actual shale gas production environments usually does not have a strict, fixed time pattern, its operation mainly depends on well conditions, production systems, and on-site management. In order to obtain the cumulative sand production at the wellhead within a predetermined time period, the date, time, and amount of sand removed (volume or mass) for each sand removal are accurately recorded and included in the calculation of the time period. t The cumulative sand production at the wellhead within the specified time period is calculated by... t The amount of sand discharged is obtained by summing up the sand discharge volumes of all records within a given period. For example, the sand discharge volumes for a day, a week, and a month are summed up, corresponding to the calculation period. t The calculation period can be one day, one week, or one month, etc. In this embodiment, the wellhead sand flow rate is simplified to the average sand output within the calculation period, that is, the cumulative sand output at the wellhead is calculated. Divide by the calculation period t The wellhead sand flow rate was obtained. This is used to accommodate the discontinuity of sand removal.

[0096] S2. Determine dimensionless numbers based on the acquired gas well structure parameters and real-time production parameters. The dimensionless numbers include: gas phase Reynolds number, liquid phase Reynolds number, and gas phase Froude number.

[0097] In the embodiments of this application, the obtained gas well structural parameters include: tubing inner diameter. d Total well depth l Vertical well section length h and the length of the horizontal well section c The real-time production parameters acquired include: real-time wellhead oil pressure P, wellhead temperature T, and natural gas standard condition volumetric flow rate. Real-time standard liquid volumetric flow rate .

[0098] In this embodiment, before determining the dimensionless number, it is necessary to calculate some real-time production parameters to obtain the real-time natural gas operating condition density, real-time natural gas operating condition volumetric flow rate, real-time liquid phase operating condition density, and real-time liquid phase volumetric flow rate. In this embodiment, the calculation of the real-time natural gas operating condition density is performed according to the following formula:

[0099]

[0100] in, For real-time natural gas operating condition density, Z The gas compressibility factor under wellhead temperature and pressure conditions.P For real-time wellhead oil pressure, T The wellhead temperature, This represents the relative density of natural gas.

[0101] The following formula is used to calculate the real-time volumetric flow rate of natural gas under operating conditions:

[0102]

[0103] in, This refers to the real-time volumetric flow rate of natural gas under operating conditions. T The wellhead temperature, P For real-time wellhead oil pressure, This refers to the standard volumetric flow rate of natural gas.

[0104] The following formula is used to calculate the real-time liquid phase volumetric flow rate:

[0105]

[0106] in, This represents the real-time volumetric flow rate under liquid phase operating conditions. This represents the real-time standard volumetric flow rate of the liquid phase.

[0107] The real-time liquid phase operating condition volumetric flow rate is equal to the real-time liquid phase standard condition volumetric flow rate. The obtained real-time liquid phase standard condition volumetric flow rate can be used as the real-time liquid phase operating condition volumetric flow rate without any transformation calculations, due to the incompressibility of liquids. Since the standard density of any medium is a fixed value under specific pressure and temperature conditions, the required natural gas standard density in this embodiment... Since it is a fixed value, it can be looked up using a standard value without calculation. Similarly, the standard density of the liquid phase in this embodiment... This is also a fixed value, obtainable simply by querying. Since the density variation of the liquid is minimal within the temperature and pressure range at the shale gas wellhead, the resulting error is within acceptable engineering limits. Therefore, provided the core calculation logic is correct, the results are sufficiently accurate, and the model is made more concise and practical, the real-time liquid phase density can be determined. Liquid phase standard density .

[0108] In the embodiments of this application, before determining the dimensionless number, calculations are required based on some gas well structural parameters and some real-time production parameters to obtain the real-time apparent gas flow rate. and real-time apparent liquid flow rate Among these, determining the real-time apparent gas velocity... When completing the task, follow the formula below:

[0109]

[0110] in, For real-time apparent gas phase velocity, This refers to the real-time volumetric flow rate of natural gas under operating conditions. d This refers to the inner diameter of the oil pipe.

[0111] Determining the real-time apparent flow rate of the liquid phase When completing the task, follow the formula below:

[0112]

[0113] in, For real-time apparent flow rate of the liquid phase, This represents the real-time volumetric flow rate under liquid phase operating conditions. d This refers to the inner diameter of the tubing. During gas well production, the produced liquid phase is generally formation water, but in some cases it may contain impurities such as foaming agents.

[0114] Furthermore, the real-time apparent gas flow rate obtained through the above steps... Real-time apparent flow rate of liquid phase Natural gas standard condition density Real-time natural gas operating density Liquid phase standard density To determine the real-time conversion gas phase flow rate. and real-time conversion liquid phase flow rate Specifically, real-time conversion of gas phase flow rate Calculated using the following formula:

[0115]

[0116] in, To convert gas phase flow rate in real time, For real-time apparent gas phase velocity, The density is the standard liquid phase density. For real-time liquid phase operating conditions, For natural gas standard condition density, Real-time natural gas operating condition density;

[0117] In this embodiment, the real-time conversion velocities of the gas and liquid phases are actually the real-time gas-liquid velocities of a wellbore gas-liquid sand-carrying experiment constructed based on fluid mechanics similarity. It should be noted that the wellbore diameter of the gas-liquid sand-carrying experiment is consistent with that of the actual gas well, and the lengths of the horizontal and vertical well sections are proportional to those of the actual gas well. The temperature and pressure of the experimental environment are under standard conditions, and the gas and liquid media used are air and water. The calculation method for the real-time conversion velocities is as follows: under the principle of ensuring that the experiment and the production site meet the gravity similarity, the Froude numbers of production and experiment are calculated based on the Lockhart-Martinelli method and made equal, thereby obtaining the real-time conversion gas phase velocity. As for the liquid phase, due to its incompressibility, the real-time conversion liquid phase velocity is equal to the real-time liquid phase apparent velocity.

[0118] =

[0119] In this embodiment, after obtaining information such as the real-time conversion gas phase flow rate, real-time conversion liquid phase flow rate, real-time natural gas operating condition density, real-time liquid phase operating condition density, and natural gas standard condition density based on the above steps, the dimensionless number is determined. In this embodiment, the dimensionless number includes: the gas phase Reynolds number. Liquid phase Reynolds number And the gas phase Froude number, where, in determining the gas phase Reynolds number When completing the task, follow the formula below:

[0120]

[0121] in, For gas phase Reynolds number, For natural gas standard condition density, Real-time conversion of gas phase flow rate, d The inner diameter of the oil pipe. The standard dynamic viscosity of natural gas is given, with air as the experimental gaseous medium, at 1.73. For standard air density, The viscosity is the standard dynamic viscosity of air. In this embodiment, the gas phase Reynolds number is... The Reynolds number in the gas phase represents the ratio of inertial forces to viscous forces in a fluid. It is a dimensionless number used to determine the flow state of a fluid. As a quantitative and dynamic kinetic indicator, the abstract "airflow sand-carrying capacity" is concretized and digitized, and embedded into the mathematical model as the core input. This enables the accurate back-calculation of the unmeasurable bottom-hole sand inflow and the final wellbore sand accumulation based on the measurable wellhead sand output.

[0122] Determining the Reynolds number in the liquid phase When completing the task, follow the formula below:

[0123]

[0124] in, For liquid phase Reynolds number, For the standard density of water, To convert the liquid phase flow rate in real time, d The inner diameter of the oil pipe. This represents the standard dynamic viscosity of water. In this embodiment, the liquid phase Reynolds number is... It has the ability to quantify liquid phase carrying capacity, that is, to independently evaluate the lifting and carrying effect of liquid on sand particles in flow; to improve flow pattern judgment, that is, to work in conjunction with gas phase Reynolds number to help the model identify the real gas-liquid two-phase flow pattern in the wellbore; and to ensure the comprehensiveness of the model, that is, as a necessary input for the core model, to prevent large calculation deviations under low gas volume conditions, and to keep the sand accumulation calculation high-precision at all stages of gas well production.

[0125] The determination of the gas-phase Froude number is based on the Lockhart-Martinelli method and is performed according to the following formula:

[0126]

[0127] in, For the phase of Froude number, For natural gas standard condition density, To convert gas phase flow rate in real time, For the standard density of water, It is the acceleration due to gravity. d The inner diameter of the oil pipe is 1.73, and the experimental gaseous medium is air. That is, the standard density of air. In this embodiment, the gas phase Froude number... The Froude number represents the ratio of inertial force to gravity in a fluid. In the context of sand-carrying in horizontal wells, gravity is the most direct and primary force causing sand settling and sand accumulation. Therefore, determining the gas phase Froude number is crucial. Its function is to determine the suspension and migration state of sand particles:

[0128] Among them, the high gas phase Froude number The value indicates that the inertial force of the airflow is much greater than the gravity. The airflow has enough energy to lift the sand particles off the bottom of the well and keep them suspended, so that they are continuously carried out of the wellhead. Therefore, it is not easy for sand to accumulate inside the well.

[0129] Low gas phase Froude number The value indicates that gravity is dominant and the energy of the airflow is insufficient to resist gravity. The sand particles will settle from the airflow, roll and slide at the bottom of the well, and eventually stop to form a sand bed. At this time, the sand carrying efficiency is extremely low and the risk of sand accumulation is high.

[0130] Gas phase Froude number Its role also lies in serving as a key input to the mathematical model of sand-carrying capacity, providing the mathematical model with information about the direction of gravity that cannot be provided by the gas phase Reynolds number and the liquid phase Reynolds number.

[0131] S3. Determine the cumulative sand inflow at the bottom of the well during the calculation period based on the wellhead sand flow rate and the dimensionless number.

[0132] In the embodiments of this application, when calculating the cumulative sand inflow at the bottom of the well, it is necessary to first determine the sand inflow rate at the bottom of the well, and then determine the cumulative sand inflow at the bottom of the well based on the sand inflow rate at the bottom of the well. This is specifically achieved according to the following steps:

[0133] The sand flow rate at the bottom of the well is determined based on the wellhead sand flow rate and the dimensionless number.

[0134] The cumulative sand inflow at the bottom of the well is obtained by statistically analyzing the sand flow rate at the bottom of the well during the calculation period.

[0135] In the embodiments of this application, the determination of the sand inflow rate at the bottom of the well is accomplished according to the following formula:

[0136]

[0137]

[0138] In this embodiment, the formula for calculating the sand inflow rate at the bottom of the well is obtained through a wide range of wellbore gas-water sand-carrying experiments, wherein, This represents the flow rate of sand flowing into the well bottom. For wellhead sand flow rate, d The inner diameter of the oil pipe. h The length of the vertical well section. l For the total well depth, c The length of the horizontal well section. It is a function of the dimensionless gas-phase Reynolds number, liquid-phase Reynolds number, and gas-phase Froude number. For gas phase Reynolds number, For liquid phase Reynolds number, It is the Froude number for the gas phase.

[0139] In the embodiments of this application, the determination of the cumulative sand inflow at the bottom of the well is performed according to the following formula:

[0140]

[0141] in, For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. t To calculate the time period, dt This is the differential of the calculation time period.

[0142] S4. Calculate the cumulative sand accumulation in the wellbore during the calculation period based on the cumulative sand output at the wellhead and the cumulative sand inflow at the bottom of the well.

[0143] In the embodiments of this application, the calculation time period is obtained through the above steps. t Cumulative sand output from the inner wellhead and calculation time period t After accumulating the amount of sand flowing into the bottom of the well, the calculation time period is obtained according to the following formula. t Cumulative sand accumulation inside the well shaft:

[0144]

[0145] in, For calculating time periods t The cumulative amount of sand accumulated inside the inner wellbore. For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. This is to calculate the cumulative sand output from the wellhead within a given time period.

[0146] refer to Figure 3 As shown in the embodiment of this application, the shale gas horizontal well shaft sand accumulation calculation system includes: a data acquisition module, a central control module, and an output prompt module. The data acquisition module sends the acquired data information to the central control module for processing, and the output prompt module outputs the output results of the central control module and reminds users to maintain the shale gas production system.

[0147] In the embodiments of this application, when calculating the amount of sand accumulated in the wellbore of a shale gas well, the calculation system first collects the well structure parameters of the shale gas well through the data acquisition module, such as the inner diameter of the tubing, the total well depth, the length of the vertical well section, and the length of the horizontal well section, as well as the real-time production parameters of the shale gas well, such as the real-time wellhead oil pressure, wellhead temperature, real-time natural gas standard volumetric flow rate, and real-time liquid phase standard volumetric flow rate. Further, the central control module processes the well structure parameters and real-time production parameters collected by the data acquisition module according to the processing steps of the shale gas horizontal well sand accumulation calculation method described above, ultimately obtaining the calculation result of the shale gas horizontal well sand accumulation. The calculation result is then output through the output prompt module, for example, wirelessly or wiredly to the monitoring center or the terminal device of the relevant user, and further controls the monitoring center or terminal device to issue corresponding prompts to enable maintenance of the shale gas production system, such as processing the accumulated sand in the wellbore.

[0148] In one exemplary embodiment:

[0149] In this exemplary embodiment, the shale gas well is a sand-producing and water-producing gas well, with a total well depth of [missing information]. l =4023m, of which the length of the horizontal well section is c =1553m, length of vertical well section h =2043m, using the inner diameter of the oil pipe d The well uses a 50mm tubing and a desander is installed at the wellhead for sand removal. The shale gas well produced 1.6 to 1.9 Nm³ of gas in a certain month. 3 / d, water production is 5 Nm 3 / d, wellhead oil pressure P =2.0~2.3MPa, wellhead temperature T =40℃, standard condition density of natural gas is = 0.7174kg / m 3 The standard density of liquid water is = 1000kg / m 3 The gas-liquid interfacial tension σ is 0.072 N / m, and the standard dynamic viscosity of natural gas is... =11.6 μPa·s. The shale gas well was in continuous production for a certain month and no wellbore sand flushing was carried out during that month. The cumulative sand accumulation in the wellbore during that month was calculated.

[0150] Following the specific implementation steps, calculations were performed. The daily real-time production parameters and the cumulative sand accumulation in the wellbore were obtained within one month, as shown in Table 1. The final cumulative sand accumulation for one month was 0.7545 m³. 3 The changes in gas phase velocity, liquid phase velocity, and cumulative sand accumulation within that month are as follows: Figure 4 As shown.

[0151] Table 1 shows the calculated daily real-time production parameters and cumulative sand accumulation.

[0152]

[0153] In the production process of shale gas horizontal wells carrying liquid and sand, the technical method of this application can quantitatively calculate the cumulative sand accumulation in the wellbore within any calculation period, and the calculation period can cover the dynamic changes of production parameters such as gas production, liquid production, and wellhead pressure throughout the entire life cycle. By calculating the sand accumulation, the sand-carrying production status and the severity of sand accumulation in the wellbore can be clarified, the risk of sand blockage can be predicted, and then the formulation of reasonable and feasible production systems, sand removal cycles, and sand prevention and cleaning measures can be guided, effectively strengthening wellbore sand prevention and unblocking, and ensuring stable gas well production.

[0154] While this application provides the method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in this embodiment is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the methods shown in this embodiment or the accompanying drawings can be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0155] Some modules of the system described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via communication networks. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0156] The modules described in the above embodiments can be implemented by computer chips or physical entities, or by products with certain functions. For ease of description, the above systems are described by dividing them into various modules based on their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0157] The methods, systems, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, such as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. Memory controllers can also be implemented as part of the control logic of memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.

[0158] This application also provides an apparatus, including: a processor; a memory for storing processor-executable instructions; when the processor executes the executable instructions, it implements the method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well as described above.

[0159] This application also provides a storage medium, including a computer program or instructions for storing a computer program or instructions that, when executed, enable the method for calculating the amount of sand accumulated in a shale gas horizontal wellbore as described above.

[0160] Furthermore, in the various embodiments of the present invention, each functional module can be integrated into a processing module, or each module can exist independently, or two or more modules can be integrated into a single module.

[0161] The aforementioned storage media include, but are not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Cache, Hard Disk Drive (HDD), or Memory Card. The memory can be used to store computer program instructions.

[0162] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0163] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0164] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for calculating the amount of sand accumulated in the wellbore of a shale gas horizontal well, characterized in that, The calculation method includes: The wellhead sand flow rate is determined based on the cumulative sand production at the wellhead during the calculated time period. The dimensionless numbers are determined based on the acquired gas well structure parameters and real-time production parameters. The dimensionless numbers include: gas phase Reynolds number, liquid phase Reynolds number and gas phase Froude number. The cumulative sand inflow to the bottom of the well during the calculation period is determined based on the wellhead sand flow rate and the dimensionless number. Based on the cumulative sand output at the wellhead and the cumulative sand inflow at the bottom of the well, the cumulative sand accumulation in the wellbore during the calculation period is calculated. The step of determining the cumulative sand inflow at the bottom of the well during the calculation period based on the wellhead sand flow rate and the dimensionless number includes: The bottom-hole sand inflow rate is determined based on the wellhead sand flow rate and the dimensionless number, and the bottom-hole sand inflow rate is determined according to the following formula: in, This represents the flow rate of sand flowing into the well bottom. For wellhead sand flow rate, d The inner diameter of the oil pipe. h The length of the vertical well section. l For the total well depth, c The length of the horizontal well section. It is a function of the dimensionless gas-phase Reynolds number, liquid-phase Reynolds number, and gas-phase Froude number. For gas phase Reynolds number, For liquid phase Reynolds number, It is the Froude number for the gas phase.

2. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 1, characterized in that, The determination of dimensionless numbers based on acquired gas well structure parameters and real-time production parameters includes: Based on the aforementioned real-time production parameters, determine the real-time natural gas operating density, real-time natural gas operating volume flow rate, real-time liquid phase operating density, and real-time liquid phase operating volume flow rate. The real-time apparent gas phase velocity and real-time apparent liquid phase velocity are determined based on the gas well structure parameters and the real-time production parameters. The real-time gas phase flow rate and the real-time liquid phase flow rate are determined based on the real-time apparent gas phase flow rate, the real-time apparent liquid phase flow rate, the real-time natural gas operating density, and the real-time liquid phase operating density. The dimensionless number is determined based on the real-time conversion gas phase flow rate and the real-time conversion liquid phase flow rate.

3. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 2, characterized in that, The real-time natural gas operating density is determined according to the following formula: in, For real-time natural gas operating condition density, Z The gas compressibility factor under wellhead temperature and pressure conditions. P For real-time wellhead oil pressure, T The wellhead temperature, The relative density of natural gas; The real-time natural gas operating condition volumetric flow rate is determined according to the following formula: in, This refers to the real-time volumetric flow rate of natural gas under operating conditions. T The wellhead temperature, P For real-time wellhead oil pressure, This refers to the real-time standard volumetric flow rate of natural gas. The real-time liquid phase density is determined according to the following formula: in, For real-time liquid phase operating conditions, This is the standard density of the liquid phase; The real-time liquid phase volumetric flow rate is determined according to the following formula: in, This represents the real-time volumetric flow rate under liquid phase operating conditions. This represents the real-time standard volumetric flow rate of the liquid phase.

4. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 2, characterized in that, The real-time apparent gas velocity is determined according to the following formula: in, For real-time apparent gas phase velocity, This refers to the real-time volumetric flow rate of natural gas under operating conditions. d This refers to the inner diameter of the oil pipe. The real-time apparent flow rate of the liquid phase is determined according to the following formula: in, For real-time apparent flow rate of the liquid phase, This represents the real-time volumetric flow rate under liquid phase operating conditions. d This refers to the inner diameter of the oil pipe.

5. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 2, characterized in that, The real-time conversion gas phase flow rate is determined according to the following formula: in, To convert gas phase flow rate in real time, For real-time apparent gas phase velocity, The density is the standard liquid phase density. For real-time liquid phase operating conditions, For natural gas standard condition density, Real-time natural gas operating condition density; The real-time conversion liquid phase flow rate is determined according to the following formula: in, To convert the liquid phase flow rate in real time, This represents the real-time apparent flow rate of the liquid phase.

6. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 2, characterized in that, The dimensionless gas-phase Reynolds number is calculated according to the following formula: in, For gas phase Reynolds number, Real-time conversion of gas phase flow rate, For natural gas standard condition density, d The inner diameter of the oil pipe. This refers to the dynamic viscosity of natural gas under standard conditions. The dimensionless liquid phase Reynolds number is determined according to the following formula: in, For liquid phase Reynolds number, For the standard density of water, To convert the liquid phase flow rate in real time, d The inner diameter of the oil pipe. The standard dynamic viscosity of water; The dimensionless gas-phase Froude number is determined based on the Lockhart-Martinelli method according to the following formula: in, For the phase of Froude number, For natural gas standard condition density, To convert gas phase flow rate in real time, For the standard density of water, It is the acceleration due to gravity. d This refers to the inner diameter of the oil pipe.

7. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 1, characterized in that, The cumulative sand output at the wellhead is obtained by the amount of sand discharged through the wellhead desander during the calculation period. The wellhead sand flow rate is determined according to the following formula: in, For wellhead sand flow rate, To calculate the cumulative sand production at the wellhead within a given time period, t To calculate the duration of a time period.

8. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 1, characterized in that, The step of determining the cumulative sand inflow at the bottom of the well during the calculation period based on the wellhead sand flow rate and the dimensionless number further includes: The cumulative amount of sand flowing into the bottom of the well is determined according to the following formula: in, For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. t To calculate the time period, dt This is the derivative of the computation time.

9. The method for calculating the amount of sand accumulated in a shale gas horizontal wellbore according to claim 1, characterized in that, The cumulative amount of sand accumulated in the wellbore during the calculation period is determined according to the following formula: in, For calculating time periods t The cumulative amount of sand accumulated inside the inner wellbore. For calculating time periods t The cumulative amount of sand flowing into the bottom of the well. This is to calculate the cumulative sand output from the wellhead within a given time period.

10. A system employing the method for calculating the amount of sand accumulated in a shale gas horizontal wellbore as described in any one of claims 1-9, characterized in that, include: The data acquisition module is used to obtain the well structure parameters and real-time production parameters of shale gas horizontal wells; The central control module is used to calculate the cumulative sand accumulation in the wellbore during the calculation period based on the gas well structure parameters and the real-time production parameters. The output prompt module is used to output the calculation results of the central control module and / or remind users to deal with the sand accumulation in the wellbore.

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