Water hammer oscillation blocking removal method based on disturbance equation modeling

Abstract

The invention discloses a water hammer oscillation blockage removal method based on disturbance equation modeling, and relates to the technical field of oil and gas field exploitation and shaft physical blockage removal. Constructing boundary conditions of the negative pulse return-to-zero type switching valve; constructing a disturbance continuity equation and a disturbance momentum equation; the gravity influence is eliminated, and a water hammer wave disturbance equation set is built in combination with the pipeline friction coefficient; according to the interval and the time step length when the target shaft is dispersed, on the basis of the boundary condition of the negative pulse return-to-zero type switching valve, finite difference discrete processing is conducted on the water hammer wave disturbance equation set, and water hammer wave transient control equation sets corresponding to all depth nodes are obtained and solved in parallel; and pressure distribution and speed distribution of the water hammer waves in the propagation process in the target shaft are obtained, and then parameters of water hammer oscillation unblocking operation of the target shaft are designed or adjusted. According to the method, the water hammer wave disturbance equations suitable for different well types are constructed, the gravity effect requirement is eliminated, well depth and channel friction factors are uniformly incorporated into a modeling framework, and high-precision description of the transient propagation process of the water hammer waves is achieved.

Description

Technical Field

[0001] This application relates to the field of oil and gas field development and wellbore physical unblocking technology, and in particular to a water hammer oscillation unblocking method based on perturbation equation modeling. Background Technology

[0002] Water hammer (also known as water surge) is a transient pressure fluctuation in a fluid system caused by abrupt changes in boundary conditions (such as rapid opening and closing of valves), and is a typical unsteady flow problem. This phenomenon is widespread in the oil and gas industry, commonly found in water injection wells, oil and gas pipelines, and wellhead equipment, especially during the rapid valve closure phase after hydraulic fracturing operations. In recent years, in addition to its use in fracture assessment and pipeline monitoring, water hammer has been gradually introduced into wellbore clogging operations, demonstrating advantages such as low cost, environmental friendliness, and strong penetration. During oil and gas well production, the wellbore and adjacent reservoirs are prone to blockage due to inorganic scale deposition, cuttings accumulation, poor sand-carrying return, or chemical residue deposition, leading to reduced production and limited fluid transport. Currently, commonly used unclogging methods include chemical acidizing, mechanical well washing, and hydraulic fracturing, but these methods generally suffer from high costs, high operational risks, severe environmental pollution, and poor applicability. In contrast, physical unblocking technology based on water hammer can generate periodic high-intensity water hammer pressure waves in the wellbore by rapidly opening and closing wellhead valves, thereby creating strong disturbances to the blocked area and achieving non-invasive, high-frequency dynamic unblocking.

[0003] Numerous studies and field practices have demonstrated the promising application prospects of this technology. Representative publications include: Yi Fei et al., 2024, "Research and Application of Multi-stage Hydraulic Impact Unblocking Technology"; Sun Lin et al., 2022, "Optimization of Hydraulic Impact Tools and Downhole Experiments"; Li Liang, 2015, "Application of Hydraulic Impact Fracturing and Strong Negative Pressure Unblocking Technology in Shuguang Oilfield"; and Wei Bin, 2009, "Development and Application of Oil Well Hydraulic Impact Unblocking Device." These studies primarily focus on the structural optimization, experimental testing, and engineering applications of downhole hydraulic impact tools. Some studies have provided preliminary descriptions of the water hammer wave propagation mechanism and unblocking mechanism. However, the transient characteristics and propagation complexity of water hammer waves pose significant challenges to parameter design in actual unblocking operations. Accurate description of water hammer wave propagation behavior is crucial for optimizing unblocking parameters. Although computational fluid dynamics (CFD) can currently be used to establish transient models for simulating complex pipe networks, its high computational cost and complex model construction make it unsuitable for real-time field analysis. In engineering, the one-dimensional Euler equation is usually used to model the propagation process of water hammer waves, and combined with inverse problem analysis for blockage diagnosis and unblocking optimization. Common solution methods include the method of characteristics, the finite difference method, the finite volume method, and the finite element method. Although current research has achieved certain results in device design and experimental verification, there are still obvious shortcomings in the following key technologies: (1) Lack of water hammer wave propagation modeling methods applicable to different well types: Current research mostly uses traditional water hammer wave models, which fail to fully consider the disturbance characteristics and the differences in gravity effects in different well types (such as vertical wells and horizontal wells), and lack adaptability. (2) Water hammer parameter design relies on experience and lacks a systematic optimization mechanism: In existing unblocking operations, key parameters such as water hammer frequency, injection pressure, and opening and closing cycle mostly rely on empirical formulas or on-site trial and error, resulting in poor stability of unblocking effect and lack of a scientific parameter optimization framework. Summary of the Invention

[0004] The purpose of this application is to provide a water hammer oscillation unblocking method based on perturbation equation modeling, which aims to overcome the problems of weak modeling ability and reliance on experience in the field of well water hammer unblocking in existing technologies. By constructing water hammer wave perturbation models suitable for different well working conditions, the method improves modeling accuracy while ensuring computational efficiency, and optimizes parameter configuration in combination with on-site working conditions, thereby improving the efficiency and operational adaptability of well unblocking.

[0005] To achieve the above objectives, this application provides the following solution: This application provides a water hammer oscillation unblocking method based on perturbation equation modeling, including: Discretize the target wellbore into multiple depth nodes along the direction of the target wellbore pipeline, and obtain the spacing and time step when discretizing the target wellbore. Construct the boundary conditions for a negative pulse zero-type switching valve in the water hammer pulse simulation process; Based on the mass conservation equation of the Euler equation, the density variable is decomposed into background ground state and perturbation quantity, and a first-order linear expansion is performed to eliminate the background ground state density field and construct the perturbation continuity equation. Based on the momentum conservation equation of the Euler equation, the velocity variable is decomposed into the background ground state and the perturbation quantity, the background ground state momentum field is eliminated, and the perturbation momentum equation is constructed. Based on the disturbance term, the pipe friction coefficient of the target well is introduced into the disturbance momentum equation and combined with the disturbance continuity equation to obtain the water hammer wave disturbance equation set. Based on the spacing and time step when the target wellbore is discrete, the water hammer wave disturbance equations are discretized according to the boundary conditions of the negative pulse zero-type switching valve. The transient control equations of water hammer waves corresponding to all depth nodes are obtained and solved simultaneously to obtain the pressure distribution and velocity distribution of water hammer waves during their propagation in the target wellbore. Based on the pressure and velocity distribution during the propagation of water hammer waves in the target wellbore, the parameters for water hammer oscillation unblocking operations in the target wellbore are dynamically designed or adjusted.

[0006] Optionally, the process of constructing the boundary conditions for the negative pulse zero-type switching valve is as follows: Based on the rock parameters of the formation in the area where the target well is located, the resonant frequency of the formation in the area where the target well is located is determined using the resonant frequency determination formula; the rock parameters include: formation porosity, empirical constant of rock elastic modulus, and empirical constant of formation porosity; Based on the resonant frequency, the ideal time period for valve switching operation during water hammer pulse simulation is determined using the ideal time period determination formula. Based on the ideal time period, the main frequency parameters for generating the disturbance waveform are determined using the main frequency parameter determination formula. Based on the main frequency parameters, a continuous valve switching boundary disturbance input of “attenuation -> zeroing -> negative pulse -> zeroing again” is constructed for the valve closing stage based on the Mexican hat function; Based on the spacing and time step of the discrete target wellbore, the spacing and time step of the discrete target wellbore are discretized to obtain the discretized switch valve boundary disturbance input; The discrete switching valve boundary disturbance input is determined to be a single-period disturbance negative pulse zero-return type switching valve boundary condition; By introducing a time offset index into the boundary conditions of a single-period negative pulse zero-return switching valve, the boundary conditions of a multi-periodic negative pulse zero-return switching valve are obtained.

[0007] Optionally, the formula for determining the resonant frequency is: ; in, The resonant frequency of the formation in the area where the target well is located; This is an empirical constant for the elastic modulus of rock; Formation porosity; This is an empirical constant for formation porosity; Formation density in the area where the target well is located; The formula for determining the ideal time period is: ; in, The ideal time period for valve switching operation during water hammer pulse simulation; The time adjustment parameter for the water hammer pulse simulation process; The formula for determining the main frequency parameter is: ; in, The main frequency parameters generated for the disturbance waveform; The boundary condition disturbance input for the continuous negative pulse zeroing type switching valve is: ; in, ρ is the wellhead pressure of the target wellbore; ρ is the density of the fluid in the target wellbore; and c is the velocity of sound in the fluid. For time parameters; The discrete switching valve boundary disturbance input is: ; in, For discretized switching valve boundary disturbance input; Δt is the integer index of the time step; Δt is the time step size when the target wellbore is discrete. Peak frequency; The zero time corresponds to the integer index of the time. The boundary conditions for the multiple periodic negative pulse zeroing type switching valve are: ; ; ; ; in, Boundary conditions for a zero-reset type switching valve with multiple periodic negative pulses; As a variable; Indexed by time offset; The time interval for continuously opening and closing the valve; It is an adjustable repetition periodicity factor; The basic period of a single water hammer pressure wave's round-trip propagation; The target wellbore pipe length.

[0008] Optionally, based on the mass conservation equation of the Euler equation, the density variable is decomposed into the background ground state and the perturbation quantity, expanded linearly in the first order, the background ground state density field is eliminated, and the perturbation continuity equation is constructed, specifically including: The fluid density is expressed as the sum of the steady-state ground-state component and the transient disturbance component, and then substituted into the mass conservation equation of the Euler equation. Substituting the disturbance term of the negative pulse zero-type switching valve gate into the mass conservation equation of the Euler equation, we obtain the first-order equation for the continuity of the disturbance. Substituting the equation of state into the first-order perturbation continuity equation, and linearizing the perturbations of pressure and density, yields the second-order perturbation continuity equation. By setting the fluid background velocity term of the steady-state flow in the perturbation continuity second-order equation to zero, the perturbation continuity equation is obtained.

[0009] Optionally, the fluid density is: ; in, The density of the fluid in the target wellbore; The background density of the fluid in steady-state flow; This is the change in fluid density; The velocity of the fluid in the target wellbore; The background velocity of the fluid in steady-state flow; The change in velocity; The mass conservation equation of the Euler equation is: ; in, Let x be the position variable along the wellbore, at the wellhead x=0; It is a time variable; The continuous first-order equation for the perturbation is: ; The equation of state is: ; in, The speed of sound in a fluid; For disturbance pressure; The perturbation continuous second-order equation is: ; The perturbation continuity equation is: .

[0010] Optionally, based on the momentum conservation equation of the Euler equation, the velocity variable is decomposed into the background ground state and the perturbation quantity, the background ground state momentum field is eliminated, and the perturbation momentum equation is constructed, specifically including: Substituting the switch disturbance formula into the momentum conservation equation of the Euler equation, we obtain the first-order equation of disturbance momentum. By setting the fluid background velocity term of the steady-state flow in the first-order equation of the disturbance momentum to zero, the disturbance momentum equation is obtained.

[0011] Optionally, the momentum conservation equation of the Euler equation is: ; The first-order equation for the perturbation momentum is: ; The equation for the perturbation momentum is: .

[0012] Optionally, the water hammer wave disturbance equations are: ; in, For the target wellbore pipe diameter, The coefficient of friction of the target wellbore is denoted as .

[0013] Optionally, the transient control equations for the water hammer wave are: ; ; in, The next time index is n+1, the current position index is x, and the disturbed fluid velocity value is used. The current time index is n, the current position index is x, and the disturbed fluid velocity value is x. Index for the current time The pressure value at the next position index x+1; Index for the current time The pressure value at current position index x; Index for the current time Current position index x disturbed fluid velocity value; The perturbation suppression value is set as the index of the current position x at the next time step (n+1). Index for the current time Current location index x disturbance pressure value; Index for the current time Current position index x fluid velocity value; Index for the current time The fluid velocity value at the previous position index x-1; The depth node spacing.

[0014] Optionally, based on the spacing and time step when discretizing the target wellbore, the water hammer wave disturbance equations are discretized according to the boundary conditions of the negative pulse zero-type switching valve. This yields the transient control equations for the water hammer wave corresponding to all depth nodes, which are then solved simultaneously to obtain the pressure and velocity distributions of the water hammer wave during its propagation in the target wellbore. Specifically, this includes: The negative pulse zeroing type switching valve boundary condition is applied at the wellhead of the target well to complete the disturbance source term injection; Based on the spacing and time step when the target wellbore is discrete, the water hammer wave disturbance equation set is discretized to obtain the water hammer wave transient control equation set corresponding to all depth nodes. The perturbation velocity is assigned at the target wellbore boundary, and the corresponding pressure is updated using a correction format. Apply a non-absorbing boundary at the bottom end of the target wellbore; The pressure and velocity disturbance values ​​are updated alternately at each time step, and the transient control equations of the water hammer wave corresponding to each time step are solved to obtain the instantaneous pressure distribution and the instantaneous velocity distribution of the water hammer wave during its propagation in the target wellbore. Based on the instantaneous pressure distribution corresponding to all time steps, the pressure distribution during the propagation process in the target wellbore is determined. Based on the instantaneous velocity distribution corresponding to all time steps, the velocity distribution during the propagation process in the target wellbore is determined.

[0015] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a water hammer oscillation unblocking method based on perturbation equation modeling. For vertical and inclined wells, the direction of water hammer waves needs to consider the influence of gravity. A perturbation equation is established to eliminate the gravity term in the background equation, considering only the perturbation pressure requirements in the unblocking scenario. Therefore, it is suitable for any well setup. For water hammer wave unblocking systems in vertical, horizontal, and multi-branch wells, the perturbation equation of the water hammer pulse is simulated to estimate the design of water hammer wave unblocking pulse parameters (maximum pulse amplitude, main frequency, and pulse operation period). Based on the design parameters, the effective unblocking radius is calculated, providing on-site operation parameters for wellbore water hammer wave pressure unblocking systems and improving unblocking operation capabilities. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1This is a flowchart of a water hammer oscillation unblocking method based on perturbation equation modeling in one embodiment of this application; Figure 2 This is a schematic diagram of vertical well unblocking in one embodiment of this application; Figure 3 This is a schematic diagram of the boundary of a single-cycle opening and closing gate in one embodiment of this application; Figure 4 This is a schematic diagram of the boundary between two opening and closing gates in one embodiment of this application; Figure 5 This is a schematic diagram of the pressure change at the unblocking point of the gate boundary during a single opening and closing operation, as shown in one embodiment of this application. Figure 6 This is a schematic diagram of the pressure change at the unblocking point of the double-switching gate boundary in one embodiment of this application. Detailed Implementation

[0018] 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 embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0019] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] In one exemplary embodiment, such as Figure 1 As shown, a water hammer oscillation unblocking method based on perturbation equation modeling is provided, including: Step 101: Discretize the target wellbore into multiple depth nodes along the direction of the target wellbore pipeline, and obtain the spacing and time step when discretizing the target wellbore.

[0021] Step 102: Construct the boundary conditions for the negative pulse zeroing type switching valve in the water hammer pulse simulation process.

[0022] Step 103: Based on the mass conservation equation of the Euler equation, the density variable is decomposed into the background ground state and the perturbation quantity, expanded linearly in the first order, the background ground state density field is eliminated, and the perturbation continuity equation is constructed.

[0023] Step 104: Based on the momentum conservation equation of the Euler equation, decompose the velocity variable into the background ground state and the perturbation quantity, eliminate the background ground state momentum field, and construct the perturbation momentum equation.

[0024] Step 105: Based on the disturbance term, the pipe friction coefficient of the target well is introduced into the disturbance momentum equation and combined with the disturbance continuity equation to obtain the water hammer wave disturbance equation set.

[0025] Step 106: Based on the spacing and time step when discretizing the target wellbore, the water hammer wave disturbance equations are discretized according to the boundary conditions of the negative pulse zero-type switching valve. The transient control equations of the water hammer wave corresponding to all depth nodes are obtained and solved simultaneously to obtain the pressure distribution and velocity distribution of the water hammer wave during its propagation in the target wellbore.

[0026] Step 107: Based on the pressure and velocity distribution during the propagation of water hammer waves in the target wellbore, dynamically design or adjust the parameters for water hammer oscillation unblocking operations in the target wellbore.

[0027] Before step 101, the method also includes: determining the input parameters of the simulation system and making preliminary estimates of the main design parameters.

[0028] Determine the input parameters for the simulation system: In the water hammer wave propagation simulation system, the user needs to input a set of parameters related to the wellbore structure, fluid properties, boundary disturbance conditions, and numerical discretization to achieve numerical simulation of the propagation process of transient pressure waves and velocity waves in the wellbore and output of pressure at key points. These input parameters specifically include: (1) Porosity φ, rock elastic modulus and empirical constants a, b of porosity.

[0029] (2) Wellhead pressure (Unit: megapascals, MPa) represents the maximum pressure amplitude generated at the wellhead at the instant the valve is closed or opened; this value directly controls the intensity of the disturbance source.

[0030] (3) The inner diameter D of the pipe (in meters, m) needs to be entered to define the geometric channel size inside the well, which affects the propagation characteristics of flow inertia and wave velocity.

[0031] (4) At the same time, the total length L of the well shaft (in meters, m) also needs to be input, which determines the spatial scale of the propagation path.

[0032] (5) To describe the time characteristics of valve operation, switching time parameters need to be provided. (Unit: seconds).

[0033] (6) In order to accurately simulate the actual flow resistance, a friction coefficient also needs to be input. (Dimensionless) is used to reflect energy loss caused by turbulence or boundary layer within the pipe.

[0034] (7) In numerical simulation, the total recording time T (in seconds) needs to be set to define the total duration of the simulation calculation. (8) In numerical simulation, it is also necessary to set the time step Δt and the spatial step Δx (in seconds and meters, respectively) to discretize the time axis and the spatial axis. These parameters together determine the accuracy and scale of the computational grid.

[0035] (9) Regarding the fluid itself, the system requires the input of fluid density ρ (in kilograms per cubic meter) and fluid bulk modulus K (in Pascals per kilogram) to solve for the propagation velocity of pressure waves in the fluid. (i.e., speed of sound, measured in meters per second) Density and speed of sound determine the inertial and compressibility characteristics of a medium and affect the intrinsic speed of wave propagation.

[0036] (10) In addition, the system also allows selection of the sampling point location x, which is usually located at different depths in the wellbore, to display the pressure and velocity response at a specific location.

[0037] All the above input parameters together constitute the initial boundary conditions and physical basis of the simulation model, ensuring that the system can accurately simulate the propagation dynamics of water hammer waves caused by valve disturbances in the wellbore.

[0038] Preliminary estimates of key design parameters: (1) Estimation of the resonant frequency of the strata.

[0039] The elastic modulus of geological formations is closely related to their porosity and can be estimated using empirical formulas. Given the porosity φ and empirical constants a and b of a particular region's formations, the elastic modulus of the geological formations can be calculated using the following formula. Based on this, the resonance frequency (Hz) between the water hammer wave unblocking process and the bottom layer formation can be calculated by the following formula: .

[0040] in, This represents the formation density. This frequency reflects the formation's natural response to the unblocking water hammer wave and serves as the boundary valve switching time parameter for subsequent excitation. (Its reciprocal is related to this) The design provides a basis.

[0041] (2) Pulse operation period estimation The propagation period of water hammer waves within a pipe is primarily influenced by the pipe length L and the sound wave propagation velocity c in the fluid. The basic period of a single water hammer pressure wave's round-trip propagation is: .

[0042] In practical engineering applications of this invention, to enhance interference from repetitive excitation or prevent interference dissipation, the time interval between continuous valve switching is typically designed to be an integer multiple of the fundamental period. .

[0043] M is an adjustable repetition period factor, which is a key control parameter used in this application to optimize the pulse interference effect.

[0044] (3) Estimation of maximum disturbance velocity Applying Bernoulli's equation, between the high-pressure point inside the water pipe and the atmospheric outlet point: .

[0045] in, The maximum disturbed fluid velocity is defined as 2% of the maximum wellbore pressure (this parameter is set in this application and can be modified in practice). When the valve is closed, the fluid is stationary, and the background fluid velocity is... Atmospheric pressure is set here. Then, the maximum disturbed flow velocity is obtained. .

[0046] (4) Estimation of maximum disturbance pressure and power When water hammer waves propagate within a wellbore, they generate a significant pressure response due to boundary disturbances. The disturbance pressure generated by a single pulse... With change in disturbance velocity The relationship of v is .

[0047] Where ρ is the fluid density and c is the speed of sound in the fluid. Maximum perturbation velocity.

[0048] Meanwhile, the maximum instantaneous energy power (unit: W) carried by this pulse can be estimated as follows: .

[0049] Where D is the pipe diameter. This expression represents the fluid power output under disturbed pressure. The two expressions are primarily used to represent the maximum unblocking capacity of the water hammer wave.

[0050] Disturbance velocity change With disturbance pressure They are positively correlated, while The system is influenced by both fluid properties and valve boundary control conditions. Therefore, the design of the boundary disturbance velocity will become one of the key parameters for optimizing the subsequent pulse system regulation and unblocking effect.

[0051] The process for constructing the boundary conditions for the negative pulse zero-type switching valve is as follows: Based on the rock parameters of the formation in the area where the target well is located, the resonant frequency of the formation in the area where the target well is located is determined using the resonant frequency determination formula; the rock parameters include: formation porosity, empirical constant of rock elastic modulus, and empirical constant of formation porosity; Based on the resonant frequency, the ideal time period for valve switching operation during water hammer pulse simulation is determined using the ideal time period determination formula. Based on the ideal time period, the main frequency parameters for generating the disturbance waveform are determined using the main frequency parameter determination formula. Based on the main frequency parameters, a continuous valve switching boundary disturbance input of “attenuation -> zeroing -> negative pulse -> zeroing again” is constructed for the valve closing stage based on the Mexican hat function; Based on the rock parameters of the formation in the area where the target well is located, the resonant frequency of the formation in that area is determined using the resonant frequency determination formula. The rock parameters include: formation porosity, empirical constant of rock elastic modulus, and empirical constant of formation porosity.

[0052] Based on the resonant frequency, the ideal time period for valve switching operation during water hammer pulse simulation is determined using the ideal time period determination formula.

[0053] Based on the ideal time period, the dominant frequency parameters for generating the disturbance waveform are determined using the formula for determining the dominant frequency parameters. To adapt to the numerical simulation system, this period... This is further converted into a master frequency parameter (peak frequency) for generating the disturbance waveform. This master frequency is used to control the frequency characteristics of the input disturbance source (switching valve) in the simulation.

[0054] Based on the dominant frequency parameters, a boundary disturbance input for a continuously switching valve is constructed using a Mexican hat function. To simulate the transient velocity disturbance waveform caused by rapid valve closure, a modified Mexican hat function with central symmetry, concentrated frequency, and smooth shape is used as the idealized boundary disturbance input. This boundary disturbance exhibits a short-duration positive disturbance in the time domain, which then rapidly decreases to zero, generates a negative disturbance at a symmetrical position, and finally recovers to zero, simulating the typical characteristics of "positive impact – reverse echo" in actual water hammer. Although this idealized waveform cannot completely reproduce the fluid dynamics of real valve operation, its shape is sufficient to drive the system into an unsteady response and effectively excite water hammer propagation behavior in the wellbore.

[0055] Given that the total recording time T and the time step Δt need to be set, then T = (N-1)Δt, t = nΔt, where n is the integer index of the time step (n = 0, 1, 2, ..., N-1); N is the total number of integer indices.

[0056] Based on the spacing and time step of the discrete target wellbore, the spacing and time step of the discrete target wellbore are discretized to obtain the discretized switch valve boundary disturbance input; The discrete switching valve boundary disturbance input is determined to be a single-period disturbance negative pulse zero-return type switching valve boundary condition; By introducing a time offset index into the boundary conditions of a single-period negative pulse zero-return switching valve, the boundary conditions of a multi-periodic negative pulse zero-return switching valve are obtained.

[0057] When it is necessary to simulate non-single disturbances (such as multiple periodic valve switching), a time offset can be introduced into the waveform generation. Therefore, a time offset index is introduced into the boundary condition of the single-period negative pulse zero-return type switching valve to obtain the boundary condition of the multi-periodic negative pulse zero-return type switching valve. In this way, multi-excitation perturbation velocity input boundary conditions can be constructed to simulate the unblocking behavior of periodic operation. The relevant parameter M is set by studying the impact of continuous excitation on unblocking efficiency and interference mechanism.

[0058] Specifically, the formula for determining the resonant frequency is: .

[0059] in, The resonant frequency of the formation in the area where the target well is located. is an empirical constant for the elastic modulus of rock. This refers to the porosity of the formation. This is an empirical constant for formation porosity. Formation density in the area where the target well is located.

[0060] The formula for determining the ideal time period is: .

[0061] in, This is the ideal time period for valve switching operations during water hammer pulse simulation. The time adjustment parameter is used for the water hammer pulse simulation process.

[0062] The formula for determining the main frequency parameter is: .

[0063] in, The main frequency parameters generated for the disturbance waveform.

[0064] The boundary disturbance input for the continuous switching valve is: .

[0065] in, ρ is the wellhead pressure of the target wellbore. ρ is the density of the fluid in the target wellbore, and c is the velocity of sound in the fluid. This is a time parameter.

[0066] The boundary disturbance input for the discretized switching valve is: .

[0067] in, This is the input for the boundary disturbance of the discretized switching valve. Δt is the integer index of the time step. Δt is the time step size when the target wellbore is discrete. This is the peak frequency, which is related to the speed at which the valve switches on and off. The zero time corresponds to the integer index of the time.

[0068] The boundary conditions for a zero-reset type switching valve with multiple periodic negative pulses are: .

[0069] .

[0070] .

[0071] .

[0072] in, This is the boundary condition for a zero-reset switching valve with multiple periodic negative pulses. For variables. This is the time offset index. This is the time interval for continuously opening and closing the valve. It is an adjustable repetition periodicity factor. This is the basic period of a single water hammer pressure wave's round-trip propagation. The target wellbore length (well depth).

[0073] Based on the input parameters and the boundary conditions of pressure disturbances caused by valve opening and closing, the propagation process of water hammer waves at different locations within the wellbore can be further simulated, providing a basis for evaluating the unblocking effect and optimizing parameters at the target depth. To achieve this goal, this application constructs a system for simulating the propagation of water hammer wave pulses to characterize the dynamic response characteristics of pressure waves in the wellbore under valve disturbance. The core of this simulation system is a set of transient flow control differential equations for water hammer waves, established based on the principles of mass and momentum conservation in the Euler equations, combined with state equations. When describing the complete flow process, the gravity term has a significant impact on the static pressure distribution in vertical or inclined wellbores. However, this application focuses on the small disturbances caused by valve disturbances. Compared to the original steady-state field, these disturbances do not involve gravity terms in the modeling process; therefore, the disturbance control equations naturally do not include gravity influence terms.

[0074] Step 103 specifically includes: expressing the fluid density as the sum of the steady-state ground-state component and the transient disturbance component, and substituting it into the mass conservation equation of the Euler equation; substituting the negative pulse zero-type switching valve disturbance term into the mass conservation equation of the Euler equation to obtain the first-order continuous disturbance equation; substituting the equation of state into the first-order continuous disturbance equation, and linearizing the disturbance quantities of pressure and density to obtain the second-order continuous disturbance equation; setting the fluid background velocity term of the steady-state flow in the second-order continuous disturbance equation to zero to obtain the continuous disturbance equation.

[0075] Water hammer is caused by gate disturbances; therefore, the formula for the gate disturbance term is: .

[0076] in, The density of the fluid in the target wellbore. The background density of the fluid in steady-state flow. This represents the change in fluid density. The velocity of the fluid in the target wellbore. The background velocity of the fluid in steady-state flow. This represents the change in velocity.

[0077] The mass conservation equation of the Euler equation is: .

[0078] in, Let x be the position variable along the wellbore, with x=0 at the wellhead. It is a time variable.

[0079] The first-order equation for the continuity of the perturbation is: .

[0080] The equation of state is: .

[0081] in, The speed of sound in the fluid. This is a pressure disturbance.

[0082] The second-order equation for the perturbation continuity is: .

[0083] The perturbation continuity equation is: .

[0084] Step 104 specifically includes: substituting the switch disturbance formula into the momentum conservation equation of the Euler equation to obtain the first-order equation of disturbance momentum. Setting the fluid background velocity term of the steady-state flow in the first-order equation of disturbance momentum to zero, to obtain the disturbance momentum equation.

[0085] The momentum conservation equation of the Euler equation is as follows: .

[0086] g is the acceleration due to gravity. It refers to the dip angle. In practical applications, whether to add a dip angle item depends on the well type. ).

[0087] The first-order equation for the perturbation momentum is: .

[0088] The equation for the perturbation momentum is: .

[0089] The transient flow perturbation equations for water hammer waves describe physical phenomena similar to those in wave theory—the propagation of pressure waves in a pipe caused by sudden changes (such as valve closure or pump stoppage). The main difference lies in the following: the transient flow equations are more comprehensive, encompassing the physical behavior of the fluid in the transient state (such as friction, pipe elasticity, and fluid compressibility), while the wave equations, through a simplified idealized model, primarily focus on the wave propagation mechanism. The water hammer wave perturbation equations considering pipe friction are as follows: .

[0090] in, For the target wellbore pipe diameter, The pipe friction coefficient of the target wellbore. The perturbation term in step 105, and the (small) perturbation quantities in steps 103 and 104, are background quantities. +δv.

[0091] The transient governing equations for water hammer waves are: .

[0092] .

[0093] in, The next time index is n+1, the current position index is x, and the disturbed fluid velocity value is used. The current time index is n, the current position index is x, and the disturbed fluid velocity value is x. Index for the current time The pressure value at the next position index x+1; Index for the current time The pressure value at current position index x; Index for the current time Current position index x disturbed fluid velocity value; The perturbation suppression value is set as the index of the current position x at the next time step (n+1). Index for the current time Current location index x disturbance pressure value; Index for the current time Current position index x fluid velocity value; Index for the current time The fluid velocity value at the previous position index x-1; The depth node spacing.

[0094] Step 106 specifically includes: Apply a negative pulse zero-type switching valve boundary condition at the wellhead of the target well to complete the disturbance source term injection.

[0095] Based on the spacing and time step when discretizing the target wellbore, the water hammer wave disturbance equations are discretized to obtain the transient control equations for all depth nodes.

[0096] The perturbation velocity is assigned at the wellhead boundary of the target wellbore, and the corresponding pressure is updated using a correction format.

[0097] Apply a non-absorbing boundary at the bottom end of the target wellbore.

[0098] The pressure and velocity disturbance values ​​are updated alternately at each time step, and the transient control equations of the water hammer wave corresponding to each time step are solved to obtain the instantaneous pressure distribution and the instantaneous velocity distribution of the water hammer wave during its propagation in the target wellbore.

[0099] Based on the instantaneous pressure distribution corresponding to all time steps, the pressure distribution during the propagation process in the target wellbore is determined.

[0100] Based on the instantaneous velocity distribution corresponding to all time steps, the velocity distribution during the propagation process in the target wellbore is determined.

[0101] To solve for the pressure and velocity distribution of water hammer waves excited by valve disturbances during their propagation in the wellbore, a set of transient control equations for water hammer waves based on the disturbance quantity was established. This set of equations is derived from the one-dimensional incompressible Euler equations with linearization of the disturbance quantity, includes the coupling relationship between pressure and velocity disturbances, and is solved discretly by combining friction loss and boundary source terms.

[0102] The simulation domain is spatially discretized into several depth nodes along the wellbore length, with a spacing of Δx; it is iterated in time with a fixed step size Δt, and the solution time is T. The fluid density in the wellbore is ρ, the wave velocity is c, the inner diameter is D, and the friction coefficient is... fr The model solution process is as follows: Disturbance source term injection: Boundary conditions are applied at the wellhead (shallowest depth point), and the simulation of the opening and closing gate is formed using the modified Mexican hat function.

[0103] The disturbance equations are discretized to obtain the following transient control equations for water hammer waves.

[0104] .

[0105] .

[0106] Boundary condition handling: The disturbance velocity is directly assigned at the wellhead (x=0) boundary. And update the corresponding pressure using the corrected format; The bottom of the well (x=L) uses a non-absorbing boundary (such as a fixed zero velocity) to avoid the accumulation of interference echoes.

[0107] Numerical Iteration and Storage: At each time step, the pressure and velocity disturbance values ​​are updated alternately, and the instantaneous distribution of the entire wellbore is stored in a two-dimensional array for subsequent visualization or inversion analysis.

[0108] Output result: The model outputs two tensors: δp(x,t) represents the pressure perturbation (in Pa) at each depth point at each time step; δv(x,t) represents the velocity perturbation (in m / s) at each depth point.

[0109] The numerical solution process for this simulation coefficient can accurately characterize the dynamic process of pressure wave propagation, reflection, and attenuation within the pipe under valve disturbance, and supports subsequent analysis of water hammer intensity at the target location and valve opening / closing time. Perform parameter optimization design. This mainly involves selecting appropriate parameters. In ,as well as The size of M in the text.

[0110] Below, with Figure 2 The target formation shown has a porosity of φ=0.1, and the empirical constants for rock elastic modulus and porosity are a=3.0e6 and b=2.64, respectively. The formation density is 2.3 x 10⁻⁶. 3 kg / m 3 Taking a vertical oil well with a pipeline length of 1500m and a pipeline diameter of 0.076m as an example, the unblocking method provided in this application will be specifically explained.

[0111] Because the bulk modulus of the fluid is 2.25 x 10⁻⁶. 9 Pa, fluid density is 1000 kg / m³ 3 ,according to We obtain c = 1500 m / s. Maximum wellhead pressure. .

[0112] Step 1: Preliminary estimation of key design parameters.

[0113] (1) Estimate the formation resonance frequency: .

[0114] (2) The basic period of the round-trip propagation of water hammer pressure waves: .

[0115] (3) Estimation of maximum disturbance velocity: .

[0116] (4) Estimation of maximum disturbance pressure and power: . .

[0117] Step 2: Representation of boundary conditions for negative pulse zero-type switching valve.

[0118] (1) Valve switching time setting, initial attempt . .

[0119] (2) Boundary conditions for the switching valve: .

[0120] The boundary conditions for a single opening and closing gate are as follows: Figure 3 The boundary conditions for the two gate opening and closing are as follows: Figure 4 , Figure 3 and Figure 4 The vertical axis represents the flow velocity, in meters per second. M=1.

[0121] Step 3: Adjust the parameters to perform a simulation of the pressure at the reading point.

[0122] The pressure changes at the unblocking points of single-switch and double-switch gates are as follows: Figure 5 and Figure 6 As shown, the gate's opening and closing mechanism can supplement the attenuated energy through the interference of reflected water hammer waves, thus continuously unblocking the blockage point. The currently set continuous operation time (Toperation) and gate opening / closing time (t) are... c It can achieve unblocking, and other pre-designed unblocking parameters meet the working conditions.

[0123] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, memory, input / output interfaces (I / O), and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is connected to the system bus via the I / O interfaces. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The I / O interfaces of the computer device are used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a water hammer oscillation unblocking method based on perturbation equation modeling.

[0124] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0125] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0126] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0127] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0128] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0129] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0130] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A water hammer oscillation unblocking method based on perturbation equation modeling, characterized in that, include: Discretize the target wellbore into multiple depth nodes along the direction of the target wellbore pipeline, and obtain the spacing and time step when discretizing the target wellbore. Construct the boundary conditions for a negative pulse zero-type switching valve in the water hammer pulse simulation process; Based on the mass conservation equation of the Euler equation, the density variable is decomposed into background ground state and perturbation quantity, and a first-order linear expansion is performed to eliminate the background ground state density field and construct the perturbation continuity equation. Based on the momentum conservation equation of the Euler equation, the velocity variable is decomposed into the background ground state and the perturbation quantity, the background ground state momentum field is eliminated, and the perturbation momentum equation is constructed. Based on the disturbance term, the pipe friction coefficient of the target well is introduced into the disturbance momentum equation and combined with the disturbance continuity equation to obtain the water hammer wave disturbance equation set. Based on the spacing and time step when the target wellbore is discrete, the water hammer wave disturbance equations are discretized according to the boundary conditions of the negative pulse zero-type switching valve. The transient control equations of water hammer waves corresponding to all depth nodes are obtained and solved simultaneously to obtain the pressure distribution and velocity distribution of water hammer waves during their propagation in the target wellbore. Based on the pressure and velocity distribution during the propagation of water hammer waves in the target wellbore, the parameters for water hammer oscillation unblocking operations in the target wellbore are dynamically designed or adjusted.

2. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 1, characterized in that, The process of constructing the boundary conditions for the negative pulse zeroing type switching valve is as follows: Based on the rock parameters of the formation in the area where the target well is located, the resonant frequency of the formation in the area where the target well is located is determined using the resonant frequency determination formula; the rock parameters include: formation porosity, empirical constant of rock elastic modulus, and empirical constant of formation porosity; Based on the resonant frequency, the ideal time period for valve switching operation during water hammer pulse simulation is determined using the ideal time period determination formula. Based on the ideal time period, the main frequency parameters for generating the disturbance waveform are determined using the main frequency parameter determination formula. Based on the main frequency parameters, a continuous valve switching boundary disturbance input of "attenuation -> zeroing -> negative pulse -> zeroing again" is constructed for the valve closing stage based on the Mexican hat function; Based on the spacing and time step of the discrete target wellbore, the spacing and time step of the discrete target wellbore are discretized to obtain the discretized switch valve boundary disturbance input; The discrete switching valve boundary disturbance input is determined to be a single-period disturbance negative pulse zero-return type switching valve boundary condition; By introducing a time offset index into the boundary conditions of a single-period negative pulse zero-return switching valve, the boundary conditions of a multi-periodic negative pulse zero-return switching valve are obtained.

3. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 2, characterized in that, The formula for determining the resonance frequency is: ; in, The resonant frequency of the formation in the area where the target well is located; This is an empirical constant for the elastic modulus of rock; Formation porosity; This is an empirical constant for formation porosity; Formation density in the area where the target well is located; The formula for determining the ideal time period is: ; in, The ideal time period for valve switching operation during water hammer pulse simulation; The time adjustment parameter for the water hammer pulse simulation process; The formula for determining the main frequency parameter is: ; in, The main frequency parameters generated for the disturbance waveform; The boundary condition disturbance input for the continuous negative pulse zeroing type switching valve is: ； in, ρ is the wellhead pressure of the target wellbore; ρ is the density of the fluid in the target wellbore; and c is the velocity of sound in the fluid. For time parameters; The discrete switching valve boundary disturbance input is: ； in, For discretized switching valve boundary disturbance input; Δt is the integer index of the time step; Δt is the time step size when the target wellbore is discrete. Peak frequency; The zero time corresponds to the integer index of the time. The boundary conditions for the multiple periodic negative pulse zeroing type switching valve are: ； ； ； ； in, Boundary conditions for a zero-reset type switching valve with multiple periodic negative pulses; As a variable; Indexed by time offset; The time interval for continuously opening and closing the valve; It is an adjustable repetition periodicity factor; The basic period of a single water hammer pressure wave's round-trip propagation; The target wellbore pipe length.

4. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 1, characterized in that, Based on the mass conservation equation of the Euler equation, the density variable is decomposed into background ground state and perturbation quantity. A first-order linear expansion is performed to eliminate the background ground state density field, and a perturbation continuity equation is constructed, specifically including: The fluid density is expressed as the sum of the steady-state ground-state component and the transient disturbance component, and then substituted into the mass conservation equation of the Euler equation. Substituting the disturbance term of the negative pulse zero-type switching valve gate into the mass conservation equation of the Euler equation, we obtain the first-order equation for the continuity of the disturbance. Substituting the equation of state into the first-order perturbation continuity equation, and linearizing the perturbations of pressure and density, yields the second-order perturbation continuity equation. By setting the fluid background velocity term of the steady-state flow in the perturbation continuity second-order equation to zero, the perturbation continuity equation is obtained.

5. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 4, characterized in that, The disturbance term of the switching valve gate is: ； in, The density of the fluid in the target wellbore; The background density of the fluid in steady-state flow; This is the change in fluid density; The velocity of the fluid in the target wellbore; The background velocity of the fluid in steady-state flow; The change in velocity; The mass conservation equation of the Euler equation is: ； in, Let x be the position variable along the wellbore, at the wellhead x=0; It is a time variable; The continuous first-order equation for the perturbation is: ； The equation of state is: ； in, The speed of sound in a fluid; For disturbance pressure; The perturbation continuous second-order equation is: ； The perturbation continuity equation is: 。 6. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 5, characterized in that, Based on the momentum conservation equation of the Euler equation, the velocity variable is decomposed into the background ground state and the perturbation quantity. The background ground state momentum field is eliminated, and the perturbation momentum equation is constructed, specifically including: Substituting the switch disturbance formula into the momentum conservation equation of the Euler equation, we obtain the first-order equation of disturbance momentum. By setting the fluid background velocity term of the steady-state flow in the first-order equation of the disturbance momentum to zero, the disturbance momentum equation is obtained.

7. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 6, characterized in that, The momentum conservation equation of the Euler equation is: ； The first-order equation for the perturbation momentum is: ； The equation for the perturbation momentum is: 。 8. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 7, characterized in that, The water hammer wave disturbance equations are as follows: ； in, For the target wellbore pipe diameter, The coefficient of friction of the target wellbore is denoted as .

9. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 8, characterized in that, The transient control equations for the water hammer wave are as follows: ； ； in, The next time index is n+1, the current position index is x, and the disturbed fluid velocity value is used. The current time index is n, the current position index is x, and the disturbed fluid velocity value is x. Index for the current time The pressure value at the next position index x+1; Index for the current time The pressure value at current position index x; Index for the current time Current position index x disturbed fluid velocity value; The perturbation suppression value is set as the index of the current position x at the next time step (n+1). Index for the current time Current location index x disturbance pressure value; Index for the current time Current position index x fluid velocity value; Index for the current time The fluid velocity value at the previous position index x-1; The depth node spacing.

10. The water hammer oscillation unblocking method based on perturbation equation modeling according to claim 1, characterized in that, Based on the spacing and time step when discretizing the target wellbore, the water hammer wave disturbance equations are discretized according to the boundary conditions of the negative pulse zero-type switching valve. This yields the transient control equations for all depth nodes, which are then solved simultaneously to obtain the pressure and velocity distributions of the water hammer wave during its propagation in the target wellbore. Specifically, this includes: The negative pulse zeroing type switching valve boundary condition is applied at the wellhead of the target well to complete the disturbance source term injection; Based on the spacing and time step when the target wellbore is discrete, the water hammer wave disturbance equation set is discretized to obtain the water hammer wave transient control equation set corresponding to all depth nodes. The perturbation velocity is assigned at the target wellbore boundary, and the corresponding pressure is updated using a correction format. Apply a non-absorbing boundary at the bottom end of the target wellbore; The pressure and velocity disturbance values ​​are updated alternately at each time step, and the transient control equations of the water hammer wave corresponding to each time step are solved to obtain the instantaneous pressure distribution and the instantaneous velocity distribution of the water hammer wave during its propagation in the target wellbore. Based on the instantaneous pressure distribution corresponding to all time steps, the pressure distribution during the propagation process in the target wellbore is determined. Based on the instantaneous velocity distribution corresponding to all time steps, the velocity distribution during the propagation process in the target wellbore is determined.

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