Forecasting method and system for catenary riser slug flow-induced vibration

Abstract

The invention relates to a catenary riser slug flow-induced vibration forecasting method and system. The method comprises the following steps: constructing a catenary riser vibration equation under the action of a slug flow based on specific geometric parameters, material parameters and fluid parameters of a catenary riser and considering the influence of the internal flow force of the slug flow; acquiring slug flow main parameters such as liquid holdup of a liquid slug area, slug flow unit length and liquid slug area length, constructing a slug flow space-time distribution model in a pulse wave form, and calculating slug flow space-time distribution; performing spatial discretization on a catenary riser vibration equation, and converting a partial differential equation into an ordinary differential equation set by using a second-order precision finite difference method; according to the method, the calculated space-time distribution of the slug flow is substituted into the ordinary differential equation set, then the fourth-order Runge-Kutta method is adopted to carry out time integration on the ordinary differential equation set, the slug flow-induced vibration response of the flexible catenary riser can be rapidly and efficiently solved, the calculation efficiency is high, the engineering applicability is high, and the safety and reliability of deep sea oil and gas development can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean engineering, and in particular to a method and system for predicting slug flow-induced vibration of a catenary riser section. Background Art

[0002] With the continuous development of science and technology and the increasing demand for energy by humans, the scope of offshore oil and gas resource development has gradually expanded from shallow waters to deep waters, becoming an important energy growth pole. The riser in the offshore oil and gas exploration and development system is an important transportation channel connecting offshore floating devices and subsea wellheads, and most of them adopt the oil-gas mixed transportation method. There is an interface between the multiphase media and flow instability is accompanied. The flow states and parameters of each phase of the two-phase flow mainly composed of oil and gas will evolve dynamically, and the two-phase flow patterns are also diverse under different transportation conditions; the interface in the multiphase media will lead to an increase in flow instability. Especially under the influence of factors such as density difference, viscosity difference, and surface tension, these factors act together, making the two-phase flow (such as oil-gas mixed flow) exhibit diverse flow patterns under different transportation conditions (such as different temperatures, pressures, flow velocities, etc.), such as slug flow, bubbly flow, annular flow, mist flow, and other different types. Among them, slug flow is a typical flow pattern with gas-liquid alternating characteristics. The characteristics of slug flow are that gas and liquid appear alternately, forming a flow pattern of a section of gas followed by a section of liquid. This pattern not only affects flow parameters such as fluid pressure drop and velocity distribution, but also has a significant impact on the design and safety of the pipeline system. Due to the periodicity of this flow pattern itself, the load exerted on the pipe body is extremely likely to induce pipe body vibration. When the slug frequency is close to the structural natural frequency, resonance may occur, threatening the safety of the oil and gas production system. Therefore, accurately and quickly predicting the dynamic response of the two-phase flow mixed transportation pipeline system is an indispensable important technical means in pipeline structure design.

[0003] At present, the research on the problem of slug flow-induced vibration of marine risers is relatively scarce. The relevant research mainly focuses on the excitation problems of single-phase flow transportation pipelines or gas-liquid two-phase flows in heat exchangers. The existing theories cannot meet the actual needs of deep-sea oil and gas exploration projects. On the other hand, most of the research on in-pipe flow excitation considers the dynamic response induced by slug flow in relatively simple straight pipes such as top-tensioned risers. Compared with top-tensioned risers, steel catenary risers have the advantages of being economical and reliable, without the need for top tension compensation, and being better adapted to the movement of floating bodies. They have been widely used in actual projects and have gradually become the preferred riser form in deep-sea oil and gas development projects. Due to the free hanging and catenary shape of this pipe type, its dynamic characteristics are more complex than those of top-tensioned risers; at the same time, the periodic load generated by the in-pipe flow gravity is extremely likely to cause pipe body vibration. However, the current research on slug flow-induced vibration of catenary risers is relatively blank. Summary of the Invention

[0004] In order to solve the problem that there are relatively few studies on slug-flow-induced vibration of catenary risers in the prior art and there is a lack of effective prediction methods, the present invention proposes a method for predicting slug-flow-induced vibration of catenary risers, which can quickly and efficiently solve the slug-flow-induced vibration response of flexible catenary risers, has high calculation efficiency and strong engineering applicability, and can improve the safety and reliability of deep-sea oil and gas development. The present invention also relates to a system for predicting slug-flow-induced vibration of catenary risers.

[0005] The technical solution of the present invention is as follows:

[0006] A method for predicting slug-flow-induced vibration of catenary risers, characterized by comprising the following steps:

[0007] Steps for constructing the vibration equation of the catenary riser: Establish a flexible catenary riser model with a specific length in the X-Y-Z Cartesian global coordinate system. The two ends of the pipe body of the catenary riser model are fixed with hinged boundary conditions and freely hang in the X-Y plane. Obtain the geometric parameters of the catenary riser including the inner and outer diameters, cross-sectional area, and moment of inertia of the cross-section, the material parameters of the catenary riser including Young's modulus, bending stiffness, and tensile and compressive stiffness, and the fluid parameters of the catenary riser including the gas velocity inside the pipe, the liquid velocity inside the pipe, the liquid density inside the pipe, and the gas density inside the pipe. And construct the catenary riser vibration equation under the action of slug flow, which involves the obtained geometric parameters, material parameters, and fluid parameters of the catenary riser, and simultaneously includes the internal flow gravity, centrifugal force, Coriolis force of the catenary riser to be solved, and the unknown vibration displacements of the catenary riser in the X and Y directions.

[0008] Steps for constructing the spatio-temporal distribution model of slug flow: By unitizing the slug flow, a slug flow unit includes a gas slug zone and a liquid slug zone, and the gas slug zones and liquid slug zones are arranged alternately in sequence. Then, use the pulsed wave Fourier series expansion to construct the periodic spatio-temporal distribution model of the slug flow holdup, and obtain the main parameters of the slug flow including the holdup of the liquid slug zone, the length of the slug flow unit, and the length of the liquid slug zone, and then input them into the spatio-temporal distribution model of the slug flow to calculate the periodic spatio-temporal distribution of the slug flow holdup.

[0009] Steps for discretizing the catenary riser vibration equation: Divide the catenary riser axially into several segments, calculate the spatial step size, and discretize the spatial nodes divided by the second-order accurate finite difference method based on the spatial step size. At the same time, combine the catenary riser vibration equation to obtain an ordinary differential equation system with the second-order time derivative term of the vibration displacement on one side of the equal sign and the internal flow gravity, centrifugal force, Coriolis force, and vibration displacement of the catenary riser on the other side of the equal sign.

[0010] Steps for solving the slug flow excitation equations in the pipe: Substitute the calculated periodic spatio-temporal distribution of the slug flow holdup into the ordinary differential equations, and then integrate the ordinary differential equations with the periodic spatio-temporal distribution of the slug flow holdup in time by the fourth-order Runge-Kutta method to obtain the catenary riser vibration displacement of the spatio-temporal distribution, so as to realize the vibration prediction of the catenary riser caused by slug flow.

[0011] Preferably, in the step of constructing the catenary riser vibration equation, the obtained catenary riser material parameters further include the mass per unit length of the pipe, the attached water mass per unit length, and the viscous damping coefficient. The horizontal tension at the top of the catenary and the catenary inclination are also obtained to calculate the effective tension. The constructed catenary riser vibration equation also includes the effective tension, as well as the catenary geometric-related slope and catenary geometric-related curvature calculated by the catenary static equation expressing the initial geometric shape of the catenary.

[0012] Preferably, in the step of constructing the catenary riser vibration equation, the used catenary static equation includes a first parameter and a second parameter related to the hinged boundary conditions. The first parameter is an additional term inside the hyperbolic cosine function of the catenary static equation. The first parameter includes the inverse hyperbolic sine function based on the effective gravity per unit length of the catenary, the horizontal distance from the top to the bottom of the catenary, and the vertical distance from the top to the bottom of the catenary. The second parameter is another additional term outside the hyperbolic cosine function of the catenary static equation. The second parameter includes the hyperbolic cosine function of the first parameter.

[0013] Preferably, in the step of constructing the slug flow spatio-temporal distribution model, the constructed periodic slug flow spatio-temporal distribution model of the slug flow holdup is:

[0014]

[0015] where A s is the amplitude of the holdup in the slug zone, L s is the slug flow unit length, L f is the length of the slug zone, N is a positive integer, k is the number of slug units per unit length, U t is the slug flow unit velocity, U t The expression is:

[0016] U t = 1.2(U ls + U gs )

[0017] where U gs is the gas superficial velocity, obtained from the gas velocity in the pipe; U ls is the liquid superficial velocity, obtained from the liquid velocity in the pipe.

[0018] Preferably, in the step of solving the slug flow excitation equations in the pipe, when performing integral calculation in terms of time, the calculation time nodes are divided according to the total duration. First, the vibration displacements of the catenary riser in the X and Y directions at the initial moment are solved, and then the vibration displacements of the catenary riser in the X and Y directions at the next time node are solved. All time nodes are calculated in turn to obtain the vibration displacements of the catenary riser with spatio-temporal distribution.

[0019] Preferably, after the step of solving the slug flow excitation equations in the pipe, an extended analysis step is further included. By changing the hinged boundary conditions of the catenary riser vibration equation, the initial geometric shape of the catenary, and / or the environmental load mode, and combining with the existing external flow vortex-induced vibration model of the catenary riser, the vibration response of the catenary riser under the combined action of internal and external flows is extendedly analyzed.

[0020] A slug flow-induced vibration prediction system for a catenary riser, characterized in that it includes a module for constructing a catenary riser vibration equation, a module for constructing a slug flow spatio-temporal distribution model, a module for discretizing the catenary riser vibration equation, and a module for solving the slug flow excitation equations in the pipe, which are connected in sequence.

[0021] The module for constructing a catenary riser vibration equation establishes a flexible catenary riser model with a specific length in the X-Y-Z Cartesian global coordinate system. The two ends of the pipe body of the catenary riser model are fixed with hinged boundary conditions and freely hang in the X-Y plane. The geometric parameters of the catenary riser including the inner and outer diameters, cross-sectional area, and cross-sectional moment of inertia are obtained, the material parameters of the catenary riser including Young's modulus, bending stiffness, and tensile and compressive stiffness are obtained, and the fluid parameters of the catenary riser including the gas velocity in the pipe, the liquid velocity in the pipe, the liquid density in the pipe, and the gas density in the pipe are obtained. And a catenary riser vibration equation under the action of slug flow is constructed, which involves the obtained geometric parameters, material parameters, and fluid parameters of the catenary riser, and simultaneously includes the internal flow gravity, centrifugal force, and Coriolis force of the catenary riser to be solved, as well as the unknown vibration displacements of the catenary riser in the X and Y directions.

[0022] The module for constructing a slug flow spatio-temporal distribution model unitizes the slug flow. A slug flow unit includes a gas slug zone and a liquid slug zone, and each gas slug zone and liquid slug zone are arranged alternately in sequence. Then, a periodic slug flow spatio-temporal distribution model of the slug flow holdup is constructed by using the pulse wave Fourier series expansion, and the main parameters of the slug flow including the holdup in the liquid slug zone, the length of the slug flow unit, and the length of the liquid slug zone are obtained and then input into the slug flow spatio-temporal distribution model to calculate the periodic spatio-temporal distribution of the slug flow holdup.

[0023] The discrete catenary riser vibration equation module divides the catenary riser axially into several segments, calculates the spatial step size, and discretizes the spatial nodes divided based on the spatial step size by the second-order accurate finite difference method. At the same time, in combination with the catenary riser vibration equation, a system of ordinary differential equations is obtained, with the second-order time derivative term based on the vibration displacement on one side of the equal sign and including the in-flow gravity, centrifugal force, Coriolis force, and vibration displacement of the catenary riser on the other side of the equal sign;

[0024] The module for solving the excitation equation system of slug flow in the pipe substitutes the calculated periodic spatio-temporal distribution of the slug flow holdup into the system of ordinary differential equations, and then integrates the system of ordinary differential equations with the periodic spatio-temporal distribution of the slug flow holdup in time by the fourth-order Runge-Kutta method to obtain the spatio-temporal distribution of the catenary riser vibration displacement, so as to realize the prediction of the vibration of the catenary riser caused by slug flow.

[0025] Preferably, in the module for constructing the catenary riser vibration equation, the horizontal tension at the top of the catenary and the catenary inclination are also obtained, and then the effective tension under the combined action of gravity, buoyancy, and tension is calculated. The constructed catenary riser vibration equation also includes the effective tension, as well as the catenary geometric-related slope and catenary geometric-related curvature calculated by the catenary static equation expressing the initial geometric shape of the catenary; the catenary static equation includes a first parameter and a second parameter related to the hinged boundary conditions. The first parameter is an additional term inside the hyperbolic cosine function of the catenary static equation, and the first parameter includes the inverse hyperbolic sine function based on the effective gravity per unit length of the catenary, the horizontal distance from the top to the bottom of the catenary, and the vertical distance from the top to the bottom of the catenary. The second parameter is another additional term outside the hyperbolic cosine function of the catenary static equation, and the second parameter includes the hyperbolic cosine function of the first parameter.

[0026] Preferably, in the module for constructing the slug flow spatio-temporal distribution model, the constructed periodic slug flow spatio-temporal distribution model of the slug flow holdup is:

[0027]

[0028] where A s is the amplitude of the holdup in the slug zone, L s is the slug flow unit length, L f is the length of the slug zone, N is a positive integer, k is the number of slug units per unit length, U t is the slug flow unit velocity, U t The expression is:

[0029] U t = 1.2(U ls + U gs )

[0030] where Ugs is the gas superficial velocity, which is obtained according to the gas flow velocity in the pipe; U ls is the liquid superficial velocity, which is obtained according to the liquid flow velocity in the pipe.

[0031] Preferably, a further extended analysis module is connected after the module for solving the slug flow excitation equations in the pipe. The extended analysis module jointly uses the existing external flow vortex-induced vibration model of the catenary riser to extend the analysis of the vibration response under the combined action of the internal and external flows of the catenary riser by changing the hinged boundary conditions of the catenary riser vibration equation, the initial geometric shape of the catenary, and / or the environmental load mode.

[0032] The technical effects of the present invention are as follows:

[0033] The present invention relates to a prediction method for the slug flow-induced vibration of a catenary riser. A vibration equation of the catenary riser under the action of slug flow is constructed. Based on the specific geometric parameters, material parameters, and fluid parameters of the catenary riser and considering the influence of the internal flow forces of the slug flow, namely the gravity, centrifugal force, and Coriolis force of the internal fluid, this vibration equation of the catenary riser can accurately describe the dynamic behavior of the catenary riser, or more precisely, can accurately describe the dynamic response of the catenary riser under the action of complex fluids, providing a solid theoretical basis for subsequent vibration analysis and prediction, making the research on the vibration characteristics of the catenary riser more scientific and systematic, and being able to adapt to the vibration analysis of the riser under different working conditions; by unitizing the slug flow and using the Fourier series expansion of the pulse wave to construct a periodic spatio-temporal distribution model of the slug flow holdup, and obtaining the main parameters of the slug flow including the holdup in the liquid slug region, the slug flow unit length, and the liquid slug region length and then inputting them into the spatio-temporal distribution model of the slug flow, the periodic spatio-temporal distribution of the slug flow holdup can be calculated, which can describe the dynamic characteristics of the slug flow. Through the Fourier series expansion of the pulse wave, the change of the slug flow holdup in space and time can be accurately described, capturing the periodic and alternating characteristics of the slug flow, providing the necessary hydrodynamic information for calculating the gravity, centrifugal force, and Coriolis force of the fluid in the pipe, making the calculation of these forces more accurate, and being able to adapt to the changes of different slug flow parameters (such as the slug flow unit length, the liquid slug region length, etc.), improving the generality and applicability of the spatio-temporal distribution model of the slug flow; spatially discretizing the vibration equation of the catenary riser, dividing it into several segments along the axial direction of the catenary riser, calculating the spatial step size, and using the second-order accurate finite difference method to discretize the vibration equation, transforming the partial differential equation into a system of ordinary differential equations. By discretizing the continuous vibration equation, the complex partial differential equation can be solved by numerical methods, improving the feasibility and efficiency of the calculation, being able to accurately capture the vibration response of the catenary riser at different spatial positions, providing detailed spatial information for subsequent time integration, and being able to adapt to the complex geometric shape of the catenary riser to ensure that the vibration characteristics at different positions can be accurately calculated; combining with the spatio-temporal distribution model of the slug flow, using the fourth-order Runge-Kutta method to perform time integration on the system of ordinary differential equations to solve the vibration displacement response of the catenary riser under the action of slug flow. This response includes the vibration displacement of the catenary riser at different time points. The fourth-order Runge-Kutta method is a high-precision numerical integration method that can accurately calculate the vibration response of the riser at different time points, that is, a high-precision time response, improving the accuracy of the prediction, and being able to completely describe the dynamic process of the riser vibration, including the transient response and the steady-state response, providing a comprehensive analysis tool for engineering applications. By reasonably dividing the time step size, the calculation efficiency can be improved while ensuring the calculation accuracy, and it is applicable to large-scale engineering calculations.Each step of the present invention is executed in sequence and integrated with each other to analyze the vibration characteristics of a flexible catenary riser for internal gas-liquid slug flow. By combining the catenary riser vibration equation with the internal flow gravity, centrifugal force, and Coriolis force, the excitation response of the internal flow in the flexible pipeline can be calculated, and the slug flow excitation displacement of the flexible catenary riser can be calculated quickly and efficiently to achieve the vibration prediction caused by slug flow in the catenary riser. Compared with the traditional computational fluid dynamics method, the prediction method of the present invention has high calculation efficiency, strong engineering applicability, can accurately predict the vibration displacement induced by slug flow, avoid the resonance risk, and can be used as a technical means for pipeline structure design, response rapid prediction, vibration control, and fatigue analysis in deep-sea oil and gas exploration and development systems to meet the actual engineering needs.

[0034] The present invention also relates to a vibration prediction system for a catenary riser caused by slug flow. This system corresponds to the above-mentioned vibration prediction method for a catenary riser caused by slug flow and can be understood as a system for implementing the above-mentioned vibration prediction method for a catenary riser caused by slug flow. This system is provided with a module for constructing the catenary riser vibration equation, a module for constructing the slug flow spatio-temporal distribution model, a module for discretizing the catenary riser vibration equation, and a module for solving the excitation equation set of the slug flow in the pipe. Each module is connected in sequence and works together synergistically. On the technical level, the catenary riser vibration equation under the action of the Coriolis force, centrifugal force, and gravity of the internal flow in the pipe is constructed. The slug flow is unitized and a slug flow spatio-temporal distribution model (or called the slug flow spatio-temporal distribution function) is constructed in the form of a pulse wave. Based on the known main parameters of the slug flow, the slug flow excitation displacement of the flexible catenary riser can be calculated quickly and efficiently, with high calculation efficiency and accurate prediction. On the application level, it fills the technical gap in the analysis and prediction of the vibration of a catenary riser induced by slug flow, has strong engineering applicability, high model expandability, supports multi-physical field coupling analysis, is flexible in application, realizes the rapid prediction of the vibration response of a flexible catenary riser caused by slug flow, and improves the prediction effect, and can improve the safety and reliability of deep-sea oil and gas development. Brief Description of the Drawings

[0035] Figure 1 It is a flowchart of the vibration prediction method for a catenary riser caused by slug flow according to the present invention.

[0036] Figure 2 It is a schematic diagram of the vibration of a flexible catenary riser under the action of slug flow and a slug flow unit according to the present invention.

[0037] Figure 3a and Figure 3b It is a comparison and verification diagram of the vibration displacements of the catenary riser in the X and Y directions calculated by the method of the present invention and the experimentally measured vibration displacements.

[0038] Figure 4 It is a preferred structural block diagram of the vibration prediction system for a catenary riser caused by slug flow according to the present invention. Detailed Embodiment

[0039] The present invention will be described below with reference to the accompanying drawings.

[0040] The present invention relates to a method for predicting slug flow-induced vibration of a catenary riser. As shown in the Figure 1 flow chart, it includes the following steps:

[0041] I. Steps for constructing the vibration equation of the catenary riser: Establish a flexible catenary riser model with a specific length in the X-Y-Z Cartesian global coordinate system, calculate the initial pipe shape according to the structural parameters of the catenary riser, and construct the vibration equation of the catenary riser under the action of slug flow.

[0042] Specifically, establish a flexible catenary riser model with a length of L in the X-Y-Z Cartesian global coordinate system. The two ends of the pipe body of the catenary riser model are fixed with hinged boundary conditions and freely hang in the X-Y plane. X is the horizontal direction, Y is the vertical direction, Z is perpendicular to the X-Y plane, and a local coordinate s with the origin o is established along the pipe axis direction, where 0 ≤ s ≤ L. Obtain the geometric parameters of the catenary riser including the outer diameter, inner diameter, cross-sectional area, moment of inertia of the cross-section, etc., the material parameters of the catenary riser including Young's modulus, bending stiffness, tensile and compressive stiffness, mass per unit length of the pipe, mass of attached water per unit length, and viscous damping coefficient, etc., and the fluid parameters of the catenary riser including the gas velocity inside the pipe, liquid velocity inside the pipe, liquid density inside the pipe, gas density inside the pipe, etc. Assume that the catenary riser is a linear elastic material along the s direction and has a uniform cross-section, that is, Young's modulus (E), outer diameter (D), inner diameter (d), outer area (A o ), inner area (A i ), cross-sectional area (A r ), moment of inertia of the cross-section (I), mass per unit length of the pipe (m), mass of attached water per unit length (m a ), viscous damping coefficient c, flexural rigidity (EI), and tensile and compressive stiffness (EA r ) are uniform along the pipe length. Considering the vibration equation of the catenary riser under the action of slug flow inside the pipe as follows:

[0043]

[0044] In the formula, u and v are the displacements of the catenary riser in the X and Y directions respectively; m i is the mass of the internal flow per unit length, U i is the internal flow velocity, i = 1 or 2 corresponds to the gas slug region or the liquid slug region, g is the acceleration due to gravity, and t is the time; and are the centrifugal forces generated by the internal flow in the X and Y directions respectively, and are the Coriolis forces in the X and Y directions respectively, m ig is the force caused by the gravity of slug flow in the pipe, that is, the weight of the slug zone per unit length m1g = ρ G (1 - R)A i g, the weight of the liquid slug zone per unit length m2g = ρ L RA i g, ρ G and ρ L are the gas and liquid densities in the pipe, and R is the liquid holdup of slug flow; that is, a vibration equation of the catenary riser under slug flow is constructed, which involves the obtained geometric parameters, material parameters, and fluid parameters of the catenary riser, and simultaneously includes the internal flow gravity, centrifugal force, and Coriolis force of the catenary riser to be solved, as well as the unknown vibration displacements u and v of the catenary riser in the X and Y directions. Further, the constructed three-dimensional vibration equation of the catenary riser also includes t, T e , etc., where t is time, and T e is the effective tension under the combined action of gravity, buoyancy, and tension; is the slope related to the catenary geometry, is the curvature related to the catenary geometry, which can be calculated from the static equation of the catenary:

[0045]

[0046] In the x - y coordinates in the X - Y plane, the initial geometric shape of the catenary can be calculated from the static equation of the catenary, and then the parameters related to the catenary geometry are obtained for solving the vibration equation. In the formula, the parameters C1 and C2 are related to the hinged boundary conditions:

[0047]

[0048] In the formula, W e is the effective gravity per unit length of the riser, that is, the difference between gravity and buoyancy. X H is the horizontal distance from the top to the bottom of the catenary, Y H is the vertical distance from the top to the bottom of the catenary, T H is the horizontal tension at the top of the catenary, β is the catenary inclination angle, and the effective tension T e in the vibration equations (1) - (2) of the catenary riser can be calculated by T e = T H / cosβ. That is to say, the static equation of the catenary in formula (3) includes the first parameter C1 and the second parameter C2 related to the hinged boundary conditions. The first parameter C1 is an additional term inside the hyperbolic cosine function cosh in the static equation of the catenary, and the second parameter C2 is another additional term outside the hyperbolic cosine function cosh in the static equation of the catenary. The first parameter C1 in formula (4) includes the effective gravity W per unit length of the catenary e, the horizontal distance X from the top to the bottom of the catenary H , the vertical distance Y from the top to the bottom of the catenary H The inverse hyperbolic sine function sinh -1 , the second parameter C2 of Equation (5) includes the hyperbolic cosine function cosh of the first parameter C1. Calculated from Equation (3), the coordinates of the catenary in the X-Y plane can be obtained, that is, the static line shape y(x) of the catenary riser. The pipe section with a length of ds can be calculated by the Pythagorean theorem from the length dx in the X direction and the length dy in the Y direction , and then the geometric parameters of the catenary related in Equations (1) and (2) can be obtained

[0049] Second, the steps for constructing the slug flow spatio-temporal distribution model. Unitize the slug flow and obtain the main parameters of the slug flow such as the liquid holdup in the slug zone, the slug flow unit length, and the slug zone length. Construct the slug flow spatio-temporal distribution model (i.e., the periodic spatio-temporal distribution function of the slug flow liquid holdup) in the form of a pulse wave and calculate the slug flow spatio-temporal distribution.

[0050] Assuming that the slug flow already exists in the catenary riser and is transported from the low end to the high end, unitize the slug flow, as Figure 2 shown. A slug flow unit is composed of a gas slug zone and a liquid slug zone. Each gas slug zone and liquid slug zone are arranged alternately in sequence. The periodic spatio-temporal distribution model of the slug flow liquid holdup R in the catenary riser (also called the slug flow spatio-temporal distribution model) can be expressed by the Fourier series expansion of the pulse wave as:

[0051]

[0052] In the formula, A s is the amplitude of the function, that is, the amplitude of the liquid holdup in the liquid slug zone; L s is the slug flow unit length, that is, the wavelength; L f is the liquid slug zone length; N is a positive integer, k is the number of slug units per unit length, that is, the wave number, U t is the slug flow unit velocity, and the expression is:

[0053] U t = 1.2(U ls + U gs ) (7)

[0054] In the formula, U gs and U ls are the gas superficial velocity and the liquid superficial velocity respectively, and can be obtained from the gas velocity U1 in the gas slug zone and the liquid velocity U2 in the liquid slug zone respectively:

[0055] U gs = U1(1 - A s ) (8)

[0056] U ls = U2A s (9)

[0057] Input the obtained slug flow main parameters including the liquid holdup A in the slug zone s , the slug flow unit length L s and the slug zone length L f into the slug flow spatio-temporal distribution model of Equation (6) to calculate the periodic spatio-temporal distribution of the slug flow liquid holdup.

[0058] III. Steps of the catenary riser vibration equation for spatially discretizing the catenary riser vibration equation: Divide the catenary riser axially into several segments, calculate the spatial step size, and discretize the spatial nodes divided by the second-order accurate finite difference method based on the spatial step size. At the same time, combine the catenary riser vibration equation to obtain an ordinary differential equation system with the second-order time derivative term of the vibration displacement on one side of the equal sign and including the in-flow gravity, centrifugal force, Coriolis force, and vibration displacement of the catenary riser on the other side of the equal sign.

[0059] Specifically, divide the catenary riser axially into M segments on average, that is, the spatial calculation step size Δs = L / M, the total number of spatial discrete points is M + 1, and the discrete points are s i , numbered i = 0, 1, 2... M. The second-order accurate finite difference formulas for the partial derivatives of displacements u and v in Equations (1) and (2) are:[[]]

[0060]

[0061]

[0062] Substitute Equations (10)-(17) into Equations (1)-(2), and keep the second-order time derivative term of the vibration displacement on the left side of the equal sign, and organize the remaining terms to the right side of the equal sign. It can be organized into an ordinary differential equation system in the following ordinary differential form, that is, the ordinary differential equation system of Equations (1)-(2) at any spatial node s i :

[0063]

[0064] Where C x1 to C x11 , C y1 to C y11 are several coefficients of the riser displacements u, v and the riser velocities du / dt, dv / dt after organization; F x is the centrifugal force exerted by the slug flow on the pipe body in the X direction related to the initial curvature of the pipeline F y is the centrifugal force exerted by the slug flow on the pipe body in the Y direction related to the initial curvature of the pipeline and the gravity The resultant force, other forces, such as and have been discretized into forms related to u, v, du / dt, and dv / dt. Therefore, Eqs. (18)-(19) are ordinary differential equation systems including the gravity, centrifugal force, Coriolis force, and vibration displacement of the internal flow in the catenary riser.

[0065] IV. Steps for solving the excitation equation system of slug flow in the pipe: Substitute the calculated periodic spatio-temporal distribution of the slug flow holdup into the ordinary differential equation system, and then perform time integration on the ordinary differential equation system with the periodic spatio-temporal distribution of the slug flow holdup substituted by using the fourth-order Runge-Kutta method to obtain the spatio-temporal distribution of the catenary riser vibration displacement, so as to realize the prediction of the catenary riser vibration caused by slug flow.

[0066] Specifically, divide the total calculation time t total evenly into J segments, that is, t = t j (j = 0, 1, 2, 3..., J), to obtain J + 1 time nodes; under the conditions of known parameters such as the holdup amplitude in the slug zone, the slug flow unit length, the slug zone length, the number of slug units per unit length, and the two-phase flow velocity, obtain the spatio-temporal distribution of the slug flow through Eq. (6) and substitute it into Eqs. (18)-(19), and then use the fourth-order Runge-Kutta method to integrate Eqs. (18)-(19) in time to obtain the vibration displacements u and v of the riser in the spatio-temporal distribution. The steps for solving the excitation equation system of slug flow in the pipe can first solve the vibration displacements of the catenary riser in the X and Y directions at the initial moment, and then solve the vibration displacements of the catenary riser in the X and Y directions at the next time node, and calculate all time nodes in turn to obtain the spatio-temporal distribution of the catenary riser vibration displacements u and v.

[0067] Specifically, Eqs. (18)-(19) are ordinary differential equations including the gravity, centrifugal force, Coriolis force, and vibration displacement in the catenary riser. The gravity, centrifugal force, and Coriolis force of the fluid in the pipe are related to the density and velocity of the fluid. In slug flow, since the density and velocity in the gas slug region and liquid slug region are different, these forces will also change with the change of R(s,t). That is, the spatio-temporal distribution R(s,t) of slug flow describes the change of the liquid holdup of the fluid in the riser with space and time, and this change will directly affect the gravity, centrifugal force, and Coriolis force of the fluid in the pipe, and further affect the vibration characteristics of the catenary riser. Specifically, the density in the liquid slug region is relatively large, so in the liquid slug region, the gravity and centrifugal force are relatively large; the density in the gas slug region is relatively small, so in the gas slug region, the gravity and centrifugal force are relatively small. Therefore, by substituting R(s,t) into the ordinary differential equations (18)-(19), the changes of the gravity, centrifugal force, and Coriolis force with space and time can be calculated, and thus the vibration response of the riser under slug flow can be obtained. Therefore, by relating the spatio-temporal distribution R(s,t) of slug flow to the gravity, centrifugal force, and Coriolis force in the ordinary differential equations, the vibration response of the riser under slug flow can be solved. That is to say, the calculation of the gravity, centrifugal force, and Coriolis force is realized by substituting the spatio-temporal distribution R(s,t) of slug flow into the ordinary differential equations. These forces will change in real time with the vibration response of the riser, rather than being calculated only once at the initial state. This real-time updated calculation method ensures the accuracy and reliability of the vibration analysis of the catenary riser.

[0068] V. Expansion analysis steps: By changing the hinged boundary conditions of the catenary riser vibration equation, the initial catenary geometry, and / or the environmental load mode, and combining with the existing external flow vortex-induced vibration model of the catenary riser, the vibration response under the combined action of the internal and external flows of the catenary riser is expanded for analysis. The applicable range is wider, and it can provide support for the vibration analysis of the riser under different working conditions. The relevant model of the slug flow-induced vibration prediction method for the catenary riser of the present invention can simulate the internal flow excitation. According to actual needs, it can be expanded for analysis by combining with another external flow vortex-induced vibration model of the catenary riser (or by combining with the external flow vortex-induced vibration prediction technology / method of the catenary riser). By changing the hinged boundary conditions of the catenary riser vibration equation, the initial catenary geometry, and / or the environmental load mode, the vibration response under the combined action of the internal and external flows of the catenary riser is expanded for analysis. This makes the prediction method of the present invention highly scalable and supports multi-physical field coupling analysis. For example, the vibration characteristics of the catenary riser under different flow velocities and different environmental load conditions can be analyzed, so as to provide more comprehensive theoretical support for the design and operation of the catenary riser.

[0069] Calculation example

[0070] For the numerical values of the parameters shown in Table 1, the method of the present invention is adopted to realize the rapid prediction of the slug flow-induced vibration response of the flexible catenary riser.

[0071] Table 1

[0072] Parameter Name Symbol Value Catenary Riser Length L 1.28 m Outer Diameter D 0.006 m Inner Diameter d 0.004 m Young's Modulus E 7.15 MPa Effective Gravity <![CDATA[W e > 0.16 N / m Horizontal Tension <![CDATA[T H > 0.1 N Liquid Phase Density in Pipe <![CDATA[ρ L > 1000 kg / m³ Gas Phase Density in Pipe <![CDATA[ρ G > 1.225 kg / m³ Gas Phase Flow Velocity in Pipe <![CDATA[U1]]> 0.2 m / s Liquid Phase Flow Velocity in Pipe <![CDATA[U2]]> 0.1 m / s Liquid Holdup in Liquid Plug Zone R 1 Liquid Holdup in Gas Plug Zone R 0 Length of Slug Flow Unit Ls 0.32 m Length of Liquid Plug Zone <![CDATA[L f > 0.16 m Spatial Step Size Δs 0.005 m Time Step Size Δt 0.001 s Total Calculation Duration <![CDATA[t total > 1000 s

[0073] First, determine the structural parameters of the catenary riser: Taking a certain actual project as an example, assume that the length L of the catenary riser is 1.28 m, the outer diameter D is 0.006 m, the inner diameter d is 0.004 m, the Young's modulus E is 7.15 MPa, the effective gravity We is 0.16 N / m, and the horizontal tension T H is 0.1 N, the liquid phase density ρ L in the pipe is 1000 kg / m³, and the gas phase density ρ G in the pipe is 1.225 kg / m³. The gas phase flow velocity U1 in the pipe is 0.2 m / s, and the liquid phase flow velocity U2 in the pipe is 0.1 m / s.

[0074] Calculate the initial pipe shape: According to the catenary static equation shown in Equation (3), combined with the parameters related to the hinged boundary conditions, calculate the coordinates of the catenary in the X - Y plane, and then obtain the initial geometric shape of the catenary. By calculating the horizontal distance X H from the top to the bottom of the catenary, the vertical distance Y H , and the parameters C1 and C2 related to the boundary conditions, determine the specific shape of the catenary.

[0075] Construct the vibration equation of the catenary riser under slug flow action: Based on the above - determined parameters, substitute them into the catenary riser vibration equations (1) - (2) considering the gravity, centrifugal force, and Coriolis force of the fluid in the pipe under slug flow action to form a specific catenary riser vibration equation.

[0076] Obtain the main parameters of slug flow: Determine the main parameters of slug flow such as the liquid - slug zone liquid - hold - up amplitude As, slug flow unit length Ls, liquid - slug zone length L f , and the number of slug flow units per unit length k. Assume that the liquid - slug zone liquid - hold - up amplitude As is 1 (i.e., the liquid - hold - up rate R in the liquid - slug zone is 1 and the gas - hold - up rate R in the gas - slug zone is 0), the slug flow unit length Ls is 0.32 m, and the liquid - slug zone length L f is 0.16 m.

[0077] Construct the slug flow model and calculate the spatio - temporal distribution: Adopt the pulse - wave form to construct the spatio - temporal distribution model of slug flow Equation (6), and calculate the periodic spatio - temporal distribution of the liquid - hold - up rate of slug flow according to the known parameters. Through the calculation formula of the slug flow unit velocity U t , combined with the gas phase superficial velocity U gs and the liquid phase superficial velocity U ls , determine the liquid - hold - up rate distribution of slug flow at different times and positions.

[0078] Discrete catenary riser vibration equation: Divide the catenary riser axially into M segments on average, determine the spatial step size Δs (such as Δs = 0.005 m), and discretize the partial derivative of displacement in the catenary riser vibration equation using a second-order accurate finite difference formula to obtain an ordinary differential equation system at any spatial node s i where.

[0079] Solving for vibration displacement: Divide the total calculation time t total into J segments on average (such as the time step size Δt = 0.001 s, and the total calculation time t total is 1000 s), to obtain J + 1 time nodes. Given the spatio-temporal distribution of slug flow, use the fourth-order Runge-Kutta method to integrate the ordinary differential equation system in time, and sequentially solve the riser vibration displacements u and v at the initial moment and the next time node until all time nodes are calculated to obtain the vibration displacements of the riser at different times and positions.

[0080] Analyzing the results: Based on the calculated vibration displacements, analyze the vibration characteristics of the catenary riser under the action of slug flow, such as vibration amplitude, frequency, etc.

[0081] Such as Figure 3a and Figure 3b shown in the comparison and verification diagrams of the vibration displacements u and v of the catenary riser in the X and Y directions simulated and calculated by the method of the present invention based on an example with the experimentally measured vibration displacements. The ordinate s / L in the figure normalizes the length of the catenary riser, and the range of s / L is from 0 to 1, Figure 3a represents the X direction, and the abscissa u rms / d normalizes the vibration displacement of the catenary riser in the X direction. After normalization, Figure 3a the curve in is the vibration displacement of the catenary riser in the X direction simulated and calculated by the method of the present invention, and the circle points are the vibration displacements in the X direction measured by several experimental points in each catenary riser; Figure 3b represents the Y direction, and the abscissa v rms / d normalizes the vibration displacement of the catenary riser in the Y direction. After normalization, Figure 3b the curve in is the vibration displacement of the catenary riser in the Y direction simulated and calculated by the method of the present invention, and the circle points are the vibration displacements in the Y direction measured by several experimental points in each catenary riser. Through the comparison of the results, the rationality and accuracy of the method for predicting the vibration of the catenary riser caused by slug flow are verified, and the rapid prediction of the vibration response of the flexible catenary riser caused by slug flow is realized, providing a basis for pipeline structure design and vibration control.

[0082] The present invention also relates to a prediction system for slug flow-induced vibration of a catenary riser. This system corresponds to the above-mentioned prediction method for slug flow-induced vibration of a catenary riser and can be understood as a system for implementing the above-mentioned prediction method for slug flow-induced vibration of a catenary riser. The preferred structure of this system is as Figure 4 shown, and it includes a module for constructing the vibration equation of the catenary riser, a module for constructing the spatio-temporal distribution model of slug flow, a module for discretizing the vibration equation of the catenary riser, a module for solving the excitation equation set of the slug flow in the pipe, and an extended analysis module, which work together in coordination.

[0083] Among them, the module for constructing the vibration equation of the catenary riser establishes a flexible catenary riser model with a specific length in the X-Y-Z Cartesian global coordinate system. The two ends of the pipe body of the catenary riser model are fixed with hinged boundary conditions and freely hang in the X-Y plane. Geometric parameters of the catenary riser including inner and outer diameters, cross-sectional area, and cross-sectional moment of inertia, material parameters of the catenary riser including Young's modulus, bending stiffness, and tensile and compressive stiffness, and fluid parameters of the catenary riser including gas flow velocity in the pipe, liquid flow velocity in the pipe, liquid density in the pipe, and gas density in the pipe are obtained. And a vibration equation of the catenary riser under the action of slug flow is constructed, which involves the obtained geometric parameters, material parameters, and fluid parameters of the catenary riser, and simultaneously includes the internal flow gravity, centrifugal force, and Coriolis force of the catenary riser to be solved, as well as the unknown vibration displacements of the catenary riser in the X and Y directions.

[0084] The module for constructing the spatio-temporal distribution model of slug flow unitizes the slug flow. A slug flow unit includes a gas slug zone and a liquid slug zone, and the gas slug zones and liquid slug zones are arranged alternately in sequence. Then, a periodic spatio-temporal distribution model of the slug flow holdup is constructed by using the pulse wave Fourier series expansion, and the main parameters of the slug flow including the holdup of the liquid slug zone, the length of the slug flow unit, and the length of the liquid slug zone are obtained and then input into the spatio-temporal distribution model of the slug flow to calculate the periodic spatio-temporal distribution of the slug flow holdup.

[0085] The module for discretizing the vibration equation of the catenary riser is divided into several segments along the axial direction of the catenary riser, the spatial step size is calculated, and based on the spatial step size, the spatial nodes divided are discretized by the second-order accurate finite difference method. At the same time, in combination with the vibration equation of the catenary riser, an ordinary differential equation set is obtained, with the second-order derivative term of time based on the vibration displacement on one side of the equal sign and including the internal flow gravity, centrifugal force, Coriolis force, and vibration displacement of the catenary riser on the other side of the equal sign.

[0086] The module for solving the slug flow excitation equations in the pipe section substitutes the calculated periodic spatio-temporal distribution of the slug flow liquid holdup into the ordinary differential equations, and then integrates the ordinary differential equations with the periodic spatio-temporal distribution of the slug flow liquid holdup in time by the fourth-order Runge-Kutta method to obtain the catenary riser vibration displacement in the spatio-temporal distribution, so as to realize the prediction of the vibration of the catenary riser caused by slug flow.

[0087] Preferably, in the module for constructing the catenary riser vibration equation, the horizontal tension at the top of the catenary and the catenary inclination are also obtained, and then the effective tension under the combined action of gravity, buoyancy and tension is calculated. The constructed catenary riser vibration equation also includes the effective tension and the catenary geometric-related slope and catenary geometric-related curvature calculated by the catenary static equation expressing the initial geometric shape of the catenary. Further, the catenary static equation includes a first parameter and a second parameter related to the hinged boundary conditions. The first parameter is an additional term inside the hyperbolic cosine function of the catenary static equation. The first parameter includes the inverse hyperbolic sine function based on the effective gravity per unit length of the catenary, the horizontal distance from the top to the bottom of the catenary, and the vertical distance from the top to the bottom of the catenary. The second parameter is another additional term outside the hyperbolic cosine function of the catenary static equation. The second parameter includes the hyperbolic cosine function of the first parameter.

[0088] Preferably, in the module for constructing the slug flow spatio-temporal distribution model, the constructed periodic slug flow spatio-temporal distribution model of the slug flow liquid holdup is as follows:

[0089]

[0090] where A s is the amplitude of the liquid holdup in the slug zone, L s is the slug flow unit length, L f is the slug zone length, N is a positive integer, k is the number of slug units per unit length, U t is the slug flow unit velocity, U t The expression is:

[0091] U t = 1.2(U ls + U gs )

[0092] where U gs is the gas superficial velocity, obtained from the gas velocity in the pipe; U ls is the liquid superficial velocity, obtained from the liquid velocity in the pipe.

[0093] Preferably, an extended analysis module is further connected after the module for solving the slug flow excitation equations in the pipe. The extended analysis module jointly uses the existing external flow vortex-induced vibration model of the catenary riser to extend the analysis of the vibration response of the catenary riser under the combined action of internal and external flows by changing the hinged boundary conditions of the catenary riser vibration equation, the initial geometric shape of the catenary, and / or the environmental load mode.

[0094] The slug flow-induced vibration prediction method and system for the catenary riser of the present invention constructs the vibration equation of the catenary riser under the action of the Coriolis force, centrifugal force, and gravity of the internal flow in the technical aspect, unitizes the slug flow and constructs the slug flow spatio-temporal distribution model (or called the slug flow spatio-temporal distribution function) in the form of pulse waves. Based on the known main parameters of the slug flow, the slug flow excitation displacement of the flexible catenary riser can be calculated quickly and efficiently, with high calculation efficiency and accurate prediction. From the application aspect, it fills the technical gap in the analysis and prediction of the slug flow-induced vibration of the catenary riser, has strong engineering applicability, high model extensibility, supports multi-physical field coupling analysis, is flexible in application, realizes the rapid prediction of the slug flow-induced vibration response of the flexible catenary riser, improves the prediction effect, and can improve the safety and reliability of deep-sea oil and gas development.

[0095] It should be noted that the above specific embodiments can enable those skilled in the art to understand the present invention more comprehensively, but do not limit the present invention in any way. Therefore, although this specification has described the present invention in detail with reference to the drawings and embodiments, those skilled in the art should understand that the present invention can still be modified or equivalently replaced. In short, all technical solutions and their improvements that do not depart from the spirit and scope of the present invention should be covered by the protection scope of the patent of the present invention.

Claims

1. A method for predicting vibration caused by catenary riser slug flow, characterized in that: The steps include: The catenary riser vibration equation is constructed, a flexible catenary riser model of a specific length is established in an XYZ Cartesian global coordinate system, both ends of the catenary riser model are fixed by hinged boundary conditions and freely suspended in the XY plane, the catenary riser geometric parameters including inner and outer diameters, cross-sectional areas, and cross-sectional inertia moments, the catenary riser material parameters including Young's modulus, bending stiffness, and tensile and compressive stiffness, and the catenary riser fluid parameters including gas phase flow rate in the pipe, liquid phase flow rate in the pipe, liquid phase density in the pipe, and gas phase density in the pipe are obtained, and the catenary riser vibration equation under the action of slug flow involving the obtained catenary riser geometric parameters, material parameters, and fluid parameters, as well as the catenary riser internal flow gravity, centrifugal force, and Coriolis force to be solved, and the unknown catenary riser vibration displacement in the X and Y directions is constructed; The step of constructing a slug flow spatiotemporal distribution model comprises: unitizing the slug flow, wherein a slug flow unit comprises a gas plug area and a liquid plug area, and each gas plug area and liquid plug area are arranged alternately in sequence; then a pulse wave Fourier series expansion is used to construct a periodic slug flow spatiotemporal distribution model of the slug flow liquid holdup; and main slug flow parameters including the liquid plug area liquid holdup, the slug flow unit length and the liquid plug area length are obtained and then input into the slug flow spatiotemporal distribution model to calculate the periodic spatiotemporal distribution of the slug flow liquid holdup; The catenary riser vibration equation is discretized, and the catenary riser is divided into a plurality of segments along the axial direction, and the spatial step length is calculated, and the divided spatial nodes are discretized by a second-order precision finite difference method based on the spatial step length, and at the same time, the catenary riser vibration equation is combined to obtain a group of ordinary differential equations with a time second-order derivative term based on the vibration displacement on one side of the equal sign and a group of ordinary differential equations including gravity, centrifugal force, Coriolis force and vibration displacement of the internal flow of the catenary riser on the other side of the equal sign; The step of solving the slug flow excitation equation group in the pipe is to substitute the calculated periodic spatiotemporal distribution of the slug flow holdup into the ordinary differential equation group, and then integrate the ordinary differential equation group into which the periodic spatiotemporal distribution of the slug flow holdup is substituted in time by the fourth-order Runge-Kutta method to obtain the spatiotemporal distribution of the catenary riser vibration displacement, so as to realize the prediction of the catenary riser slug flow-induced vibration.

2. The method for predicting vibration caused by catenary riser slug flow according to claim 1, characterized in that: In the step of constructing the catenary riser vibration equation, the obtained catenary riser material parameters also include the pipe mass per unit length, the attached water mass per unit length and the viscous damping coefficient. The horizontal tension at the top of the catenary and the inclination of the catenary are also obtained to calculate the effective tension. The constructed catenary riser vibration equation also includes the effective tension and the catenary geometry-related slope and catenary geometry-related curvature calculated by the catenary static equation expressing the initial geometric shape of the catenary.

3. The method for predicting vibration caused by catenary riser slug flow according to claim 2, characterized in that: In the step of constructing the catenary riser vibration equation, the catenary static equation used includes a first parameter and a second parameter related to the uniformly hinged boundary condition, the first parameter is an added term located inside the hyperbolic cosine function of the catenary static equation, the first parameter includes an inverse hyperbolic sine function based on the effective gravity per unit length of the catenary, the horizontal distance from the top end of the catenary to the bottom end, and the vertical distance from the top end to the bottom end of the catenary, the second parameter is another added term located outside the hyperbolic cosine function of the catenary static equation, the second parameter includes the hyperbolic cosine function of the first parameter.

4. The method for predicting catenary riser slug flow-induced vibration according to any one of claims 1 to 3, characterized in that: In the step of constructing the spatiotemporal distribution model of the slug flow, the periodic spatiotemporal distribution model of the slug flow liquid holdup is constructed as follows: Among them, A s is the liquid holdup amplitude in the liquid plug area, L s is the slug flow unit length, L f is the length of the liquid plug area, N is a positive integer, k is the number of slug units per unit length, U t is the unit velocity of the slug flow, U t The expression is: IN t =1.2(U ls +U gs ) Among them, U gs is the gas phase superficial velocity, which is obtained according to the gas phase flow rate in the tube; U ls is the liquid superficial velocity, which is obtained based on the liquid flow rate in the tube.

5. The method for predicting catenary riser slug flow-induced vibration according to any one of claims 1 to 3, characterized in that: In the step of solving the set of equations for the slug flow excitation in the pipe, the time nodes are divided according to the total time length when the time integral calculation is performed, and the vibration displacement of the catenary riser in the X and Y directions at the initial moment is first solved, and then the vibration displacement of the catenary riser in the X and Y directions at the next time node is solved, and all time nodes are calculated in sequence to obtain the catenary riser vibration displacement distributed in time and space.

6. The method for predicting vibration caused by catenary riser slug flow according to claim 2 or 3, characterized in that: After the step of solving the set of equations for the plug flow excitation in the pipe, an extended analysis step is also included, in which the vibration response of the catenary riser under the combined action of the internal and external flows is extended and analyzed by combining the existing catenary riser external flow vortex-induced vibration model by changing the hinged boundary conditions of the catenary riser vibration equation, the initial geometric shape of the catenary, and / or the environmental load mode.

7. A catenary riser slug flow induced vibration prediction system, characterized in that: It includes a module for constructing catenary riser vibration equations, a module for constructing a slug flow time-space distribution model, a module for discretizing catenary riser vibration equations, and a module for solving the slug flow excitation equations in the pipe, which are connected in sequence. The module for constructing catenary riser vibration equations is used to establish a flexible catenary riser model of a specific length in an XYZ Cartesian global coordinate system, wherein both ends of the tube body of the catenary riser model are fixed by hinged boundary conditions and freely suspended in the XY plane, and catenary riser geometric parameters including inner and outer diameters, cross-sectional areas, and cross-sectional inertia moments, catenary riser material parameters including Young's modulus, bending stiffness, and tensile and compressive stiffness, and catenary riser fluid parameters including gas phase flow rate in the tube, liquid phase flow rate in the tube, liquid phase density in the tube, and gas phase density in the tube are obtained, and a catenary riser vibration equation under the action of slug flow involving the obtained catenary riser geometric parameters, material parameters, and fluid parameters, as well as the catenary riser internal flow gravity, centrifugal force, and Coriolis force to be solved, and unknown catenary riser vibration displacements in the X and Y directions is constructed; The module for constructing a slug flow spatiotemporal distribution model is to unitize the slug flow, wherein a slug flow unit includes a gas plug area and a liquid plug area, and each gas plug area and liquid plug area are arranged alternately in sequence, and then a pulse wave Fourier series expansion is used to construct a periodic slug flow spatiotemporal distribution model of the slug flow liquid holdup, and main slug flow parameters including the liquid holdup of the liquid plug area, the slug flow unit length and the liquid plug area length are obtained and then input into the slug flow spatiotemporal distribution model to calculate the periodic spatiotemporal distribution of the slug flow liquid holdup; The discrete catenary riser vibration equation module divides the catenary riser into several sections along the axial direction, calculates the spatial step length, and discretizes the divided spatial nodes based on the spatial step length by a second-order precision finite difference method, and combines the catenary riser vibration equation to obtain a group of ordinary differential equations with a time second-order derivative term based on the vibration displacement on one side of the equal sign and a group of ordinary differential equations including the gravity of the internal flow of the catenary riser, centrifugal force, Coriolis force and vibration displacement on the other side of the equal sign; The module for solving the slug flow excitation equation group in the pipe substitutes the calculated periodic spatiotemporal distribution of the slug flow liquid holdup into the ordinary differential equation group, and then integrates the ordinary differential equation group into which the periodic spatiotemporal distribution of the slug flow liquid holdup is substituted in time by the fourth-order Runge-Kutta method to obtain the spatiotemporal distribution of the catenary riser vibration displacement, so as to realize the prediction of the catenary riser slug flow-induced vibration.

8. The catenary riser slug flow induced vibration prediction system according to claim 7, characterized in that: In the module for constructing the catenary riser vibration equation, the horizontal tension at the top of the catenary and the inclination of the catenary are also obtained to calculate the effective tension under the combined action of gravity, buoyancy and tension. The constructed catenary riser vibration equation also includes the effective tension and the catenary geometry-related slope and catenary geometry-related curvature calculated by the catenary static equation expressing the initial geometric shape of the catenary; the catenary static equation includes a first parameter and a second parameter related to the uniformly hinged boundary condition, the first parameter is an added term inside the hyperbolic cosine function of the catenary static equation, the first parameter includes an inverse hyperbolic sine function based on the effective gravity per unit length of the catenary, the horizontal distance from the top of the catenary to the bottom, and the vertical distance from the top of the catenary to the bottom, the second parameter is another added term outside the hyperbolic cosine function of the catenary static equation, and the second parameter includes the hyperbolic cosine function of the first parameter.

9. The catenary riser slug flow induced vibration prediction system according to claim 7 or 8, characterized in that: In the module for constructing the spatiotemporal distribution model of slug flow, the periodic spatiotemporal distribution model of slug flow liquid holdup is constructed as follows: Among them, A s is the liquid holdup amplitude in the liquid plug area, L s is the slug flow unit length, L f is the length of the liquid plug area, N is a positive integer, k is the number of slug units per unit length, U t is the unit velocity of the slug flow, U t The expression is: IN t =1.2(U ls +U gs ) Among them, U gs is the gas phase superficial velocity, which is obtained according to the gas phase flow rate in the tube; U ls is the liquid superficial velocity, which is obtained based on the liquid flow rate in the tube.

10. The catenary riser slug flow induced vibration prediction system according to claim 8, characterized in that: The module for solving the in-pipe plug flow excitation equation group is also connected to an extended analysis module. The extended analysis module combines the existing catenary riser external flow vortex-induced vibration model with the catenary riser to expand and analyze the vibration response of the catenary riser under the combined action of the internal and external flows by changing the hinged boundary conditions of the catenary riser vibration equation, the initial geometric shape of the catenary, and / or the environmental load mode.

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