Deep sea dry tree floating platform and riser full coupling hydrodynamic analysis method

Abstract

The application provides a kind of deep sea dry tree floating platform and riser full coupling hydrodynamic analysis method, it includes: 1) according to the potential flow theory, establish the hydrodynamic calculation model of floating platform, obtain the motion response of floating platform;2) establish the tensioner mathematical model considering the influence of gas state and internal friction, obtain the motion equation of tensioner;3) according to three-dimensional lumped mass method, establish riser model, get riser motion control equation;4) establish the overall coupling dynamic model of deep sea dry tree floating platform and riser, connect the riser top with the production deck of floating platform together through the tensioner mathematical model, calculate and transfer tension using the established tensioner mathematical model, for the overall coupling dynamic analysis of floating production system.The application can realize the overall coupling dynamic analysis of deep sea floating platform and tensioner and riser, be used for hydrodynamic calculation of marine engineering structure, solve the problem that there is no detailed model conforming to engineering practice about floating production system at present.

Description

Technical Field

[0001] This invention relates to the field of hydrodynamic calculation of marine engineering structures, specifically to a fully coupled hydrodynamic analysis method for a deep-sea dry tree floating platform and its riser. Background Technology

[0002] Currently, the main types of floating platforms widely used globally in deep-sea oil and gas extraction include Floating Production Storage and Offloading (FPSO) systems, semi-submersible platforms (SEMI), tension leg platforms (TLP), and Spar platforms. These systems primarily consist of a top float, riser, and mooring, forming a coupled dynamic system that generates complex dynamic responses under external environmental loads. Dry tree production systems, which place the production tree on the top float of the floating platform above the wellhead, offer convenient daily maintenance and high economic benefits, making them a research hotspot in recent years. However, this production method places higher demands on the relative motion between the floating platform and the riser; therefore, accurately predicting the coupled motion response of the floating platform and riser has become a key research focus in marine engineering and oil and gas exploration.

[0003] The shortcomings of current methods used both domestically and internationally for analyzing and processing the motion response of coupled deep-sea dry-tree floating platforms and risers are as follows:

[0004] (1) Common decoupling analysis methods consider the floating platform and riser separately. First, the motion of the floating platform is obtained, and then the motion of the floating platform is used as the top boundary condition input to perform further hydrodynamic analysis on the riser structure. This method completely ignores the coupled dynamic effects between the two, including velocity, acceleration and force, which will cause great inaccuracies.

[0005] (2) In the existing fully coupled analysis methods, the connection between the floating platform and the riser is often simplified to a hinge, and relative motion between the two is not allowed, which is inconsistent with the actual engineering. In the treatment of the tensioner model, most of them adopt a simplified tensioner model that ignores the influence of internal friction. However, internal friction is one of the key factors affecting the performance of the tensioner hydraulic cylinder. The simplified model will cause inaccuracy in numerical simulation.

[0006] In conclusion, it is necessary to further innovate existing technologies. Summary of the Invention

[0007] This invention provides a fully coupled analysis method for deep-sea dry tree floating platforms and risers. The purpose is to achieve overall coupled analysis of deep-sea floating platforms, tensioners, and risers, which can be used for hydrodynamic calculations of marine engineering structures to solve the problem of the lack of detailed models that conform to engineering practice for current floating production systems.

[0008] To solve the above-mentioned technical problems, this invention provides a fully coupled hydrodynamic analysis method for a deep-sea dry tree floating platform and riser, which mainly includes the following steps:

[0009] 1) Establish a hydrodynamic calculation model for the floating platform based on potential flow theory to obtain the motion response of the floating platform;

[0010] 2) Establish a mathematical model of the tensioner that considers the effects of gas state and internal friction, and obtain the motion equation of the tensioner;

[0011] 3) Establish a riser model based on the three-dimensional lumped mass method and obtain the riser motion control equations;

[0012] 4) Establish an integrated coupled dynamic model of the deep-sea dry tree floating platform and riser. Connect the riser apex to the production deck of the floating platform through the tensioner mathematical model. Use the established tensioner mathematical model to calculate and transmit tension in order to conduct an integrated coupled dynamic analysis of the floating production system.

[0013] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser includes the following: the hydrodynamic calculation model of the floating platform established in step 1) includes an upper floating body, a heave plate, and mooring; the upper floating body and the heave plate are connected by telescopic columns; the floating platform is considered as a rigid body, and a hydrodynamic calculation model of the floating platform is established. The hydrodynamic calculation model of the floating platform is divided into above-water and below-water sections and meshed; Morison elements are used to compensate for the fluid viscosity force of the floating platform, and the potential flow damping of the wetted surface of the floating platform and the drag force of the Morison elements are used as the total damping of the structure.

[0014] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser includes the following step: Step 1) uses three-dimensional potential flow theory to calculate the wave load on the wetted surface of the floating platform, simplifying the floating platform into a rigid body with six degrees of freedom of motion, namely sway x1, sway x2, heave x3, roll x4, pitch x5 and yaw x6. The six-degree-of-freedom position and six-degree-of-freedom motion of the floating platform are obtained through rigid body dynamics.

[0015] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser, wherein the total velocity potential of the wave load is:

[0016] Φ(x,y,z)=Re[(Φ I (x,y,z)+Φ D (x,y,z)+Φ R (x,y,z))e -iωt (1);

[0017] In equation (1), Φ I(x,y,z) represents the incident potential; Φ D (x,y,z) represents the diffraction potential; Φ R (x,y,z) represents the radiation potential; e -iωt The time factor;

[0018] The following boundary conditions must be met:

[0019]

[0020]

[0021]

[0022]

[0023] In equations (2)-(5), g is the acceleration due to gravity; i is the outward normal vector of the wetted surface of the object; u i The velocity of the object along the i-th direction; h is the water depth; k is the wave number;

[0024] The frequency domain motion control equations for the floating platform are:

[0025] [-ω 2 (M+A(ω))+iω(B(ω) p +B V )+C I +C ij X(ω,β)=F(ω,β) (6);

[0026] In equation (6), M is the mass and inertial mass matrix; A(ω) is the additional mass matrix; B(ω) p B is the potential flow damping matrix; V C is the linearized viscous damping matrix; I For the still water restoring torque; C ij X(ω,β) is the external restoring force coefficient matrix; F(ω,β) is the external excitation force matrix; X(ω,β) includes wave damping, added mass, and wave excitation force.

[0027] The time-domain motion control equations for the floating platform are:

[0028]

[0029] In equation (7), M ij The mass matrix of the floating platform; U ij For the additional mass matrix; L ij (t-τ) is the delay function of the floating platform; C ij This is the still water restoring force coefficient matrix; For first-order wave loads; For second-order wave loads; Fw (t) represents the wind load; F cu (t) represents the flow load; F m (t) represents the force exerted by the mooring on the floating platform.

[0030] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser, wherein the six degrees of freedom positions of the floating platform are:

[0031] POSITION = [xyz θ1 θ2 θ3] T (8);

[0032] The six degrees of freedom motion of the floating platform is as follows:

[0033] VELOCITY=[v1 v2 v3 ω1 ω2 ω3] T (9).

[0034] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser, wherein the establishment of the tensioner mathematical model in step 2) includes the following steps:

[0035] 2.1) Construct the internal pressure change relationship of the high-pressure gas cylinder of the tensioner, specifically as follows:

[0036]

[0037] The change in gas volume in the high-pressure gas cylinder is represented as follows:

[0038] ΔV A =V A1 -V A0 =A r *x p (11);

[0039] Therefore, the pressure change ΔP in the high-pressure gas cylinder caused by the change in gas volume is... A and the pressure change ΔP in the low-pressure gas cylinder B They can be represented as:

[0040]

[0041]

[0042] In equations (12)-(13) above, P A0 P B0 These are the initial pressures in the high-pressure and low-pressure gas cylinders, respectively; V A0 V B0 These are the initial volumes in the high-pressure and low-pressure gas cylinders, respectively; A p A is the cross-sectional area of ​​the piston; rdenoted as φ, where φ is the cross-sectional area of ​​the piston rod side; x is the displacement of the piston within the hydraulic cylinder.

[0043] 2.2) The "Stribeck effect" friction model is selected as the internal friction model of the tensioner; the total friction is simulated as a function of relative velocity and pressure, defined by the following two parts: the velocity-related part F v The part related to pressure F p , is defined as:

[0044] F f =F v +F p (14);

[0045]

[0046] F p =k p |P pr |=F s (16);

[0047] In equations (14)-(16) above, F c F is the Coulomb friction force; s For static friction; v p v is the piston speed. l Piston's limit speed (Stribeck speed) (|v l |≤0.05m / s); P pr For pressure difference; k v a is the coefficient of viscous friction; v Friction index (0 < a) v <1); k p The coefficients are linear.

[0048] 2.3) Tension F provided by the tensioner T It is expressed as the sum of the hydraulic pressure generated by the pressure difference on both sides of the hydraulic cylinder piston and the frictional force generated by the internal friction of the hydraulic cylinder, and its expression is as follows:

[0049] F T =F h +F f (17);

[0050] The hydraulic pressure F generated by the pressure difference on both sides of the tensioner piston in the hydraulic cylinder h It can be represented as:

[0051] F h =P r A r -P p A p (18);

[0052] Depending on the gas state, the pressure difference between the two sides of the tensioner piston in the hydraulic cylinder can also be expressed as:

[0053] P r =P A0 +ΔP A ,P p =P B0 +ΔP B (19);

[0054] Taking into account the internal friction of the hydraulic cylinder, and combining the above equations (12)-(13), the tension F provided by the tensioner in the hydraulic cylinder is... T The equilibrium equation can be rewritten as:

[0055]

[0056] The real-time response of the floating platform and riser at the connection point is input into the tensioner to simulate the coupled dynamic response of the tensioner with the floating platform and riser. Furthermore, the tension calculation formula of the tensioner's mathematical model during the simulation can be rewritten using a parametric formula as follows:

[0057]

[0058] In equation (21), x p This refers to the real-time displacement along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; v p x represents the real-time speed along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; r This refers to the real-time displacement along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner; v r This refers to the real-time speed along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner.

[0059] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser includes the following: In step 3), the dynamic model of the riser is established using the lumped mass method by dividing the riser into n lumped mass nodes and connecting each adjacent mass node with a massless spring segment; the nodes are numbered sequentially from the riser apex to the anchor point as 1, 2, ..., n, R. k and These represent the position coordinates and velocity of the k-th node, respectively.

[0060]

[0061]

[0062] In equations (22)-(23), r i,k Let represent the coordinate component of the three-dimensional coordinate of the k-th mass node on the i-th coordinate axis; Let n represent the velocity component of the three-dimensional coordinates of the k-th mass node on the i-th coordinate axis;i The unit component representing the direction of the i-th coordinate axis;

[0063] The infinitesimal elements between nodes k and k+1 are numbered k+(1 / 2), from R k Point to R k+1 The infinitesimal element is named S. k+(1 / 2) Its length is l k+(1 / 2) The unit vector of the (k+1 / 2)th infinitesimal element, i.e., t k+(1 / 2) , can be represented as S k+(1 / 2) and l k+(1 / 2) The quotient between them; in addition, the tangent direction q at each node. k Approximately, these are directions pointing between two adjacent nodes; these geometric vectors are defined as follows:

[0064]

[0065]

[0066]

[0067]

[0068] The forces acting on the riser's mass point include wet weight, axial tension, axial damping, bending moment, seabed contact force, and hydrodynamic forces.

[0069] Based on the principle of dynamic balance at the nodes, the mass m in the riser is obtained. k The equations of motion for the nodes are:

[0070]

[0071] Using Runge-Kutta to solve for risers, the second-order differential equations are transformed into a system of first-order differential equations before calculation:

[0072]

[0073] When the riser starts the calculation, the initial values ​​are the position coordinates and velocity vectors of n nodes, with a total of 6×n parameters. The first 1 to 3×n parameters are the coordinate positions, and the 3×n+1 to 6×n parameters are the node velocities.

[0074] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser, wherein: in step 4), the overall coupled model of the deep-sea dry tree floating platform and riser is established by calculating the tensioner tension through the position and velocity at the connection point between the floating platform and the tensioner and at the top of the riser, and transferring the tensioner tension as an external load to the floating platform and riser within a relatively short time step to obtain the new motion of the floating platform and riser, and then performing tensioner analysis based on the new boundary conditions at the corresponding connection nodes to obtain the updated tensioner tension, and repeating this process continuously in the next time step until the preset calculation time is reached, thereby performing the overall coupled dynamic analysis of the deep-sea dry tree floating platform and riser.

[0075] The described hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser includes the following: To determine the position and velocity at the connection point between the floating platform and the tensioner, the origin of the global coordinate system O-XYZ is taken as the intersection of the vertical line where the center of gravity of the floating platform is located when it is in equilibrium and the still water surface. The Z-axis is vertically upward, and the X and Y axes satisfy the right-hand rule. The origin of the local coordinate system o-xyz is fixed at the center of mass of the rigid body and moves with the rigid body. The transformation relationship between the global coordinate system O-XYZ and the local coordinate system o-xyz is as follows:

[0076]

[0077] In equation (31) above, E is the Euler angle transformation matrix, and its expression is as follows:

[0078]

[0079] In the formula, θ1, θ2, and θ3 are the angles between the three axes of the local coordinate system and the three axes of the global coordinate system, respectively, and are called Euler angles.

[0080] The fully coupled hydrodynamic analysis method for the deep-sea dry tree floating platform and riser includes the following: when performing real-time motion state analysis on a moving rigid body, the motion of the rigid body needs to be synthesized; the motion of the rigid body can be decomposed into translation following an arbitrary base point and rotation relative to this base point.

[0081] If we assume point M is the center of mass of the rigid body, and point N is any point outside the center of mass, then the velocity composition formula is:

[0082] v N =v M +ω×r MN (32);

[0083] Expressing the vector operation formula using scalar operations yields the velocity conversion relationship as follows:

[0084]

[0085] Expanding, we get:

[0086]

[0087] In equation (34), v NX v NY v NZ Let v be the velocity components of point N along the x, y, and z directions. MX v MY v MZ Let ω be the velocity components of point M along the x, y, and z directions; X ω Y ω Z Let X be the angular velocity components of point N relative to the x, y, and z axes; M Y M Z M Let M be the coordinates of point M, X N Y N Z N The coordinates of point N;

[0088] Therefore, the location of the connection point between the tensioner and the floating platform is:

[0089]

[0090] The velocity at the connection point between the tensioner and the floating platform is:

[0091]

[0092] The expressions for the piston's displacement x and relative velocity v in the hydraulic cylinder are as follows:

[0093]

[0094]

[0095] In equations (37)-(38), Y(1), Y(2), and Y(3) are the coordinate positions of the riser apex in the x, y, and z directions; h is the initial length of the tensioner; Y(379), Y(380), and Y(381) are the velocity components of the riser apex along the x, y, and z directions.

[0096] The expression for the total tension of the tensioner can be obtained as follows:

[0097]

[0098] The expressions for the tension components in the X, Y, and Z directions of the tensioner are as follows:

[0099]

[0100]

[0101]

[0102] By adopting the above technical solution, the present invention has the following beneficial effects:

[0103] The present invention presents a reasonable method for the overall coupling analysis of the deep-sea dry tree floating platform and its riser. By establishing an overall coupling model of the deep-sea dry tree floating platform and its riser, it can effectively perform overall coupling dynamic analysis of the floating production system. This invention employs a tensioner mathematical model that considers the influence of internal friction to calculate and transmit tension. The calculation time is divided into multiple time steps, considering the overall coupling effect of the floating platform and riser within a relatively short time step. This avoids the limitations of solving the floating platform and riser separately, and also avoids the inaccuracies of simplifying the tensioner model without considering the influence of internal friction. Attached Figure Description

[0104] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0105] Figure 1 This is a flowchart illustrating the overall coupling analysis method of the deep-sea dry tree floating platform and riser of the present invention.

[0106] Figure 2 This is a schematic diagram of the overall model structure of the deep-sea dry tree floating platform and riser involved in the overall coupling analysis method of the deep-sea dry tree floating platform and riser of the present invention.

[0107] Figure 3 This is a schematic diagram of the tensioner mathematical model involved in the overall coupling analysis method of the deep-sea dry tree floating platform and riser of the present invention;

[0108] Figure 4 This is a roadmap of the tensioner and riser program solution technology involved in the overall coupling analysis method of the deep-sea dry tree floating platform and riser of this invention. Detailed Implementation

[0109] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0110] The present invention will be further explained below with reference to specific embodiments.

[0111] like Figure 1 , 2 As shown in the figure, this embodiment provides a fully coupled hydrodynamic analysis method for a deep-sea dry tree floating platform and riser, which includes the following steps:

[0112] S100. Based on potential flow theory, establish a hydrodynamic calculation model for the floating platform to obtain the motion response of the floating platform.

[0113] In this invention, the established hydrodynamic calculation model of the floating platform includes an upper floating body, a heave plate, and mooring. The upper floating body and the heave plate are connected by telescopic columns. The floating platform is considered as a rigid body, and a hydrodynamic calculation model of the floating platform is established. The hydrodynamic calculation model of the floating platform is divided into above-water and below-water sections and meshed. Among them, Morison elements are used to compensate for the fluid viscosity force of the floating platform, and the potential flow damping of the wetted surface of the floating platform and the drag force of the Morison elements are used as the total damping of the structure.

[0114] The wave load on the wetted surface of the floating platform is calculated using three-dimensional potential flow theory, and the total velocity potential is:

[0115] Φ(x,y,z)=Re[(Φ I (x,y,z)+Φ D (x,y,z)+Φ R (x,y,z))e -iωt (1);

[0116] In equation (1), Φ I (x,y,z) represents the incident potential; Φ D (x,y,z) represents the diffraction potential; Φ R (x,y,z) represents the radiation potential; e -iωt The time factor.

[0117] The following boundary conditions must be met:

[0118]

[0119]

[0120]

[0121]

[0122] In equations (2)-(5), g is the acceleration due to gravity; i is the outward normal vector of the wetted surface of the object; u i Let be the velocity of the object along the i direction; h be the water depth; and k be the wave number.

[0123] The frequency domain motion control equations for the floating platform are:

[0124] [-ω 2 (M+A(ω))+iω(B(ω) p +B V )+C I +C ij X(ω,β)=F(ω,β) (6);

[0125] In equation (6), M is the mass and inertial mass matrix; A(ω) is the additional mass matrix; B(ω) p B is the potential flow damping matrix; V C is the linearized viscous damping matrix; I For the still water restoring torque; C ij X(ω,β) is the external restoring force coefficient matrix; F(ω,β) is the external excitation force matrix; X(ω,β) includes wave damping, added mass, wave excitation force, etc.

[0126] The time-domain motion control equations for the floating platform are:

[0127]

[0128] In equation (7), M ij The mass matrix of the floating platform; U ij For the additional mass matrix; L ij (t-τ) is the delay function of the floating platform; C ij This is the still water restoring force coefficient matrix; For first-order wave loads; For second-order wave loads; F w (t) represents the wind load; F cu (t) represents the flow load; F m (t) represents the force exerted by the mooring on the floating platform.

[0129] In this invention, the floating platform is simplified as a rigid body with six degrees of freedom of motion, namely sway x1, yaw x2, heave x3, roll x4, pitch x5, and bow x6. The positions of the floating platform with six degrees of freedom are obtained through rigid body dynamics as follows:

[0130] POSITION = [xyz θ1 θ2 θ3] T (8);

[0131] The six degrees of freedom motion of the floating platform is as follows:

[0132] VELOCITY=[v1 v2 v3 ω1 ω2 ω3] T (9).

[0133] S200. Establish a mathematical model of the tensioner that considers the effects of gas state and internal friction, and obtain the motion equation of the tensioner.

[0134] like Figure 3 As shown, the mathematical model of the direct-acting tensioner established in this invention considers the influence of internal friction within the tensioner; ignores pressure loss in the pressure pipeline; ignores the mass of the piston rod and hydraulic oil; satisfies the gas state change law; and ignores the influence of temperature. The establishment of the tensioner mathematical model includes the following steps:

[0135] S201. Construct the internal pressure change relationship of the high-pressure gas cylinder of the tensioner, specifically as follows:

[0136]

[0137] Considering that hydraulic oil is incompressible, the gas volume is assumed to change with the movement of the hydraulic cylinder piston; the change in gas volume in the high-pressure gas cylinder is expressed as follows:

[0138] V A =V A1 -V A0 =A r *x p (11);

[0139] Therefore, the pressure change ΔP in the high-pressure gas cylinder is caused by the change in gas volume. A and the pressure change ΔP in the low-pressure gas cylinder B They can be represented as follows:

[0140]

[0141]

[0142] In equations (12)-(13), P A0 P B0 These are the initial pressures in the high-pressure and low-pressure gas cylinders, respectively; V A0 V B0 These are the initial volumes in the high-pressure and low-pressure gas cylinders, respectively; A p A is the cross-sectional area of ​​the piston; r denoted as , where is the cross-sectional area of ​​the piston rod side; x is the displacement of the piston within the hydraulic cylinder.

[0143] S202. The internal friction model of the tensioner adopts the "Stribeck effect" friction model; the total friction is simulated as a function of relative velocity and pressure, defined by the following two parts: the velocity-related part F. v The part related to pressure F p , is defined as:

[0144] F f =F v +F p (14);

[0145]

[0146] F p =k p |P pr |=F s (16);

[0147] In equations (14)-(16), F c F is the Coulomb friction force; s For static friction; v p v is the piston speed. l Piston's limit speed (Stribeck speed) (|v l |≤0.05m / s); P pr For pressure difference; k v a is the coefficient of viscous friction; v Friction index (0 < a) v <1); k p These are linear coefficients.

[0148] S203, tension F provided by the tensioner T It is expressed as the sum of the hydraulic pressure generated by the pressure difference on both sides of the hydraulic cylinder piston and the frictional force generated by the internal friction of the hydraulic cylinder, and its expression is as follows:

[0149] F T =F h +F f (17);

[0150] The hydraulic pressure F generated by the pressure difference on both sides of the tensioner piston in the hydraulic cylinder h It can be represented as:

[0151] F h =P r A r -P p A p (18);

[0152] Depending on the gas state, the pressure difference between the two sides of the tensioner piston in the hydraulic cylinder can also be expressed as:

[0153] P r =P A0 +ΔP A ,P p =P B0 +ΔP B (19);

[0154] Taking into account the internal friction of the hydraulic cylinder, according to equations (12)-(13), the tension F provided by the tensioner in the hydraulic cylinder is... T The equilibrium equation can be rewritten as:

[0155]

[0156] In this invention, the real-time response of the floating platform and riser at the connection point is input into the tensioner to simulate the dynamic coupling response of the tensioner with the floating platform and riser. Therefore, the calculation formula of the tensioner mathematical model during the simulation can be rewritten using a parametric formula:

[0157]

[0158] In equation (21), x p This refers to the real-time displacement along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; v p x represents the real-time speed along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; r This refers to the real-time displacement along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner; v r This refers to the real-time speed along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner.

[0159] S300. Establish the riser model based on the three-dimensional lumped mass method and obtain the riser motion control equation.

[0160] In this invention, a lumped mass method is used to establish the dynamic model of the riser. This method divides the riser into n lumped mass nodes and connects each adjacent mass node with a massless spring segment. The nodes are numbered sequentially from the riser apex to the anchor point as 1, 2, ..., n, R. k and These represent the position coordinates and velocity of the k-th node, respectively.

[0161]

[0162]

[0163] In equations (22)-(23), r i,k Let represent the coordinate component of the three-dimensional coordinate of the k-th mass node on the i-th coordinate axis; Let n represent the velocity component of the three-dimensional coordinates of the k-th mass node on the i-th coordinate axis; i This represents the unit component in the direction of the i-th coordinate axis.

[0164] The infinitesimal elements between nodes k and k+1 are numbered k+(1 / 2), from R k Point to R k+1 The infinitesimal element is named S. k+(1 / 2) Its length is l k+(1 / 2) The unit vector of the (k+1 / 2)th infinitesimal element, i.e., t k+(1 / 2) , can be represented as S k+(1 / 2) and l k+(1 / 2)The quotient between them; in addition, the tangent direction q at each node. k Approximately, these are directions pointing between two adjacent nodes; these geometric vectors are defined as follows:

[0165]

[0166]

[0167]

[0168]

[0169] The forces acting on the riser's mass point include wet weight, axial tension, axial damping, bending moment, seabed contact force, and hydrodynamic forces. Torque has a negligible effect on the riser's response and is therefore disregarded here.

[0170] Based on the principle of dynamic balance at the nodes, the mass m in the riser is obtained. k The equations of motion for the nodes are:

[0171]

[0172] Using Runge-Kutta to solve for risers, the second-order differential equations are transformed into a system of first-order differential equations before calculation:

[0173]

[0174] In this invention, the riser is divided into 126 concentrated mass nodes. When the riser starts to be calculated, the initial values ​​are the position coordinates and velocity vectors of the 126 nodes, with a total of 6×126 parameters. The first 1 to 3×126 parameters are the coordinate positions, and the 3×126+1 to 6×126 parameters are the node velocities.

[0175] Writing the parameters into the matrix yields:

[0176] Y(756)=[x1 y1 z1 ... x 126 y 126 z 126 v x1 v y2 v y3 ... v x126 v y126 v z126 ] T (30);

[0177] S400. Establish an integrated coupled dynamic model of the deep-sea dry tree floating platform and riser. Connect the riser apex to the production deck of the floating platform through the tensioner mathematical model. Use the established tensioner mathematical model to calculate and transmit tension in order to conduct an integrated coupled dynamic analysis of the floating production system.

[0178] To determine the position and velocity at the connection point between the floating platform and the tensioner, the origin of the global coordinate system O-XYZ is defined as the intersection of the vertical line containing the center of gravity of the floating platform in its equilibrium position and the still water surface. The Z-axis points vertically upward, and the X and Y axes follow the right-hand rule. The origin of the local coordinate system o-xyz is fixed at the center of mass of the rigid body and moves with the rigid body. The transformation relationship between the two coordinate systems is as follows:

[0179]

[0180] Where E is the Euler angle transformation matrix, expressed as follows:

[0181]

[0182] In the formula, θ1, θ2, and θ3 are the angles between the three axes of the local coordinate system and the three axes of the global coordinate system, respectively, and are called Euler angles.

[0183] In this invention, when performing real-time motion state analysis on a moving rigid body, the motion of the rigid body needs to be synthesized. The motion of a rigid body can generally be decomposed into two aspects: one is translation following an arbitrary base point, and the other is rotation relative to this base point.

[0184] If we assume point M is the center of mass of the rigid body, and point N is any point outside the center of mass, then the velocity composition formula is:

[0185] v N =v M +ω×r MN (32);

[0186] Expressing the vector operation formula using scalar operations yields the velocity conversion relationship as follows:

[0187]

[0188] Expanding, we get:

[0189]

[0190] In equation (34), v NX v NY v NZ Let v be the velocity components of point N along the x, y, and z directions. MX v MY v MZ Let ω be the velocity components of point M along the x, y, and z directions; X ω Y ω Z Let X be the angular velocity components of point N relative to the x, y, and z axes; M Y M ZM Let M be the coordinates of point M, X N Y N Z N Let N be the coordinates of point N.

[0191] Therefore, the location of the connection point between the tensioner and the floating platform is:

[0192]

[0193] The velocity at the connection point between the tensioner and the floating platform is:

[0194]

[0195] In this invention, the initial length of the tensioner is set to 4m, therefore the displacement x and relative velocity v of the piston in the hydraulic cylinder are:

[0196]

[0197]

[0198] In the formula, Y(1), Y(2), and Y(3) are the coordinate positions of the riser apex in the x, y, and z directions; Y(379), Y(380), and Y(381) are the velocity components of the riser apex along the x, y, and z directions.

[0199] The total tension of the tensioner can be obtained as:

[0200]

[0201] The tension components of the tensioner in the X, Y, and Z directions are:

[0202]

[0203]

[0204]

[0205] like Figure 4As shown, this invention selects to call a dynamic link library subroutine developed within the FORTRAN language to add the tensioner and riser to the AQWA model. In each time step, firstly, the position and velocity of the connection point between the floating platform and the tensioner are calculated based on the current position of the floating platform and its transpose matrix. Then, the velocity and position of the riser apex are obtained by calling the configuration of the riser from the previous time step (initial values ​​are assigned at the initial moment). The tensioner tension is updated by combining the relative displacement and velocity between the connection point of the floating platform and the tensioner and the riser apex. Finally, the tensioner tension is used as the boundary condition at the top of the riser to update the riser motion state and save the data. Simultaneously, the tensioner tension is fed back to AQWA. This process is repeated continuously in the next time step until the preset calculation time is reached. This invention divides the calculation time into multiple time steps and considers the coupled dynamic response between the floating platform, tensioner, and riser in each time step.

[0206] This invention considers the overall coupling effect between the floating platform and the riser within a fairly short time step, avoiding the limitations of solving the floating platform and riser separately, and also avoiding the inaccuracies of simplifying the tensioner model without considering the influence of internal friction.

[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fully coupled hydrodynamic analysis method for a deep-sea dry tree floating platform and its riser, characterized in that, Includes the following steps: 1) Establish a hydrodynamic calculation model for the floating platform based on potential flow theory to obtain the motion response of the floating platform; 2) Establish a mathematical model of the tensioner that considers the effects of gas state and internal friction, and obtain the motion equation of the tensioner; 3) Establish a riser model based on the three-dimensional lumped mass method and obtain the riser motion control equations; 4) Establish an integrated coupled dynamic model of the deep-sea dry tree floating platform and riser. Connect the riser apex to the production deck of the floating platform through the tensioner mathematical model. Use the established tensioner mathematical model to calculate and transmit tension in order to conduct an integrated coupled dynamic analysis of the floating production system. The hydrodynamic calculation model of the floating platform established in step 1) includes an upper floating body, a heave plate, and mooring; the upper floating body and the heave plate are connected by telescopic columns; the floating platform is considered as a rigid body, and a hydrodynamic calculation model of the floating platform is established. The hydrodynamic calculation model of the floating platform is divided into above-water and below-water sections and meshed; Morison elements are used to compensate for the fluid viscosity force of the floating platform, and the potential flow damping of the wetted surface of the floating platform and the drag force of the Morison elements are used as the total damping of the structure. Step 3) involves establishing the dynamic model of the riser using the lumped mass method. This involves dividing the riser into n lumped mass nodes and connecting each adjacent node with a massless spring segment. The nodes are numbered sequentially from the riser apex to the anchor point as 1, 2, ..., n. and These represent the position coordinates and velocity of the k-th node, respectively. （22）； (23)； In equations (22)-(23), Let represent the coordinate component of the three-dimensional coordinate of the k-th mass node on the i-th coordinate axis; Let represent the velocity component of the three-dimensional coordinate of the k-th mass node on the i-th coordinate axis; The unit component representing the direction of the i-th coordinate axis; The infinitesimal elements between nodes k and k+1 are numbered k+(1 / 2), from... point to The infinitesimal element is named Its length is The unit vector of the (k+1 / 2)th infinitesimal element, i.e. , can be represented as and The quotient between them; in addition, the tangent direction at each node. Approximately, these are directions pointing between two adjacent nodes; these geometric vectors are defined as follows: (24); (25); (26); (27)； The forces acting on the riser's mass point include wet weight, axial tension, axial damping, bending moment, seabed contact force, and hydrodynamic forces. Based on the principle of dynamic balance at the nodes, the mass in the riser is... The equations of motion for the nodes are: (28); Using Runge-Kutta to solve for risers, the second-order differential equations are transformed into a system of first-order differential equations before calculation: (29)； When the riser starts the calculation, the initial values ​​are the position coordinates and velocity vectors of n nodes, with a total of 6×n parameters. The first 1 to 3×n parameters are the coordinate positions, and the 3×n+1 to 6×n parameters are the node velocities. In the overall coupling model of the deep-sea dry tree floating platform and riser established in step 4), the tensioner tension is calculated by the position and velocity at the connection point between the floating platform and the tensioner and at the top of the riser. Within a relatively short time step, the tensioner tension is transferred as an external load to the floating platform and the riser to obtain the new motion of the floating platform and the riser. Then, the tensioner is analyzed according to the new boundary conditions at the corresponding connection nodes to obtain the updated tensioner tension. This process is repeated continuously in the next time step until the preset calculation time is reached, thereby performing the overall coupling dynamic analysis of the deep-sea dry tree floating platform and the riser.

2. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 1, characterized in that: Step 1) involves using three-dimensional potential flow theory to calculate the wave load on the wetted surface of the floating platform, simplifying the floating platform into a rigid body with six degrees of freedom of motion, namely sway x1, sway x2, heave x3, roll x4, pitch x5 and yaw x6. The six-degree-of-freedom position and six-degree-of-freedom motion of the floating platform are obtained through rigid body dynamics.

3. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 2, characterized in that, The total velocity potential of the wave load is: ; In equation (1), For the incident potential; This is a diffraction pattern; Radiation potential; The time factor; The following boundary conditions must be met: ; ; ; ; In equations (2)-(5), It is the acceleration due to gravity; The external normal vector of the wetted surface of the object; For the object along The speed of movement in the direction; For water depth; Wave number; The frequency domain motion control equations for the floating platform are: ; In equation (6), For mass and inertial mass matrices; For the additional mass matrix; The potential flow damping matrix; This is the linearized viscous damping matrix; For still water restoring torque; This is the external restoring force coefficient matrix; The external excitation force matrix; This includes wave damping, added mass, and wave excitation force; The time-domain motion control equations for the floating platform are: ; In equation (7), The mass matrix of the floating platform; For the additional mass matrix; For the delay function of the floating platform; This is the still water restoring force coefficient matrix; For first-order wave loads; It is a second-order wave load; For wind load; For flow load; The force exerted by the mooring on the floating platform.

4. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 2, characterized in that, The six degrees of freedom positions of the floating platform are: ; The six degrees of freedom motion of the floating platform is as follows: 。 5. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 1, characterized in that, The establishment of the tensioner mathematical model in step 2) includes the following steps: 2.1) Construct the internal pressure change relationship of the high-pressure gas cylinder of the tensioner, specifically as follows: ; The change in gas volume in the high-pressure gas cylinder is represented as follows: ; Therefore, the pressure change in the high-pressure gas cylinder is caused by the change in gas volume. Pressure changes in low-pressure gas cylinders They can be represented as: ; ; In equations (12)-(13) above, These are the initial pressures in the high-pressure and low-pressure gas cylinders, respectively. These are the initial volumes in the high-pressure gas cylinder and the low-pressure gas cylinder, respectively. This represents the cross-sectional area of ​​the piston. This is the cross-sectional area of ​​the piston rod side; This represents the displacement of the piston within the hydraulic cylinder. 2.2) The "Stribeck effect" friction model is selected as the internal friction model of the tensioner; the total friction is simulated as a function of relative velocity and pressure, defined by the following two parts: velocity-related part. stress-related parts , is defined as: ; ; ; In equations (14)-(16) above, Coulomb friction; It is static friction; Piston speed; The piston's maximum speed (Stribeck speed) ); For pressure difference; It is the coefficient of viscous friction; Friction index ( ); The coefficients are linear. 2.3) Tension provided by the tensioner It is expressed as the sum of the hydraulic pressure generated by the pressure difference on both sides of the hydraulic cylinder piston and the frictional force generated by the internal friction of the hydraulic cylinder, and its expression is as follows: ; The hydraulic pressure generated by the pressure difference on both sides of the tensioner piston in the hydraulic cylinder It can be represented as: ; Depending on the gas state, the pressure difference between the two sides of the tensioner piston in the hydraulic cylinder can also be expressed as: ; Taking into account the internal friction of the hydraulic cylinder, and combining the above equations (12)-(13), the tension provided by the tensioner in the hydraulic cylinder is... The equilibrium equation can be rewritten as: ; The real-time response of the floating platform and riser at the connection point is input into the tensioner to simulate the coupled dynamic response of the tensioner with the floating platform and riser. Furthermore, the tension calculation formula of the tensioner's mathematical model during the simulation can be rewritten using a parametric formula as follows: ; In equation (21), The real-time displacement along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; The real-time speed along the tensioner hydraulic cylinder at the connection point between the floating platform and the tensioner; The real-time displacement along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner; This refers to the real-time speed along the tensioner hydraulic cylinder at the connection point between the riser and the tensioner.

6. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 1, characterized in that: To determine the position and velocity at the connection point between the floating platform and the tensioner, the origin of the global coordinate system O-XYZ is taken as the intersection of the vertical line containing the center of gravity of the floating platform when it is in equilibrium and the still water surface. The Z-axis points vertically upward, and the X and Y axes follow the right-hand rule. The origin of the local coordinate system o-xyz is fixed at the center of mass of the rigid body and moves with the rigid body. The transformation relationship between the global coordinate system O-XYZ and the local coordinate system o-xyz is as follows: （31）； In equation (31) above, E is the Euler angle transformation matrix, and its expression is as follows: ； In the formula, , , These are the angles between the three axes of the local coordinate system and the three axes of the global coordinate system, and are called Euler angles.

7. The hydrodynamic analysis method for the fully coupled deep-sea dry tree floating platform and riser as described in claim 1, characterized in that: When performing real-time motion state analysis on a rigid body, the motion of the rigid body must be synthesized; the motion of the rigid body can be decomposed into translation following an arbitrary base point and rotation relative to that base point. If we assume point M is the center of mass of the rigid body, and point N is any point outside the center of mass, then the velocity composition formula is: (32); Expressing the vector operation formula using scalar operations yields the velocity conversion relationship as follows: (33); Expanding, we get: (34); In equation (34), Let N be the velocity components along the x, y, and z directions. Let M be the velocity components along the x, y, and z directions; Let N be the angular velocity components relative to the x, y, and z axes; Let M be the coordinates of point M. The coordinates of point N; Therefore, the location of the connection point between the tensioner and the floating platform is: (35); The velocity at the connection point between the tensioner and the floating platform is: (36); piston displacement in hydraulic cylinder and relative velocity The expressions are as follows: (37); (38); In equations (37)-(38), , , These are the coordinates of the riser's apex in the x, y, and z directions. This is the initial length of the tensioner; , , The velocity components of the riser apex along the x, y, and z directions; The expression for the total tension of the tensioner can be obtained as follows: (39); The expressions for the tension components in the X, Y, and Z directions of the tensioner are as follows: (40); (41); (42)。

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