A method, medium and system for calculating dynamic response of an offshore oil and gas string system

Abstract

The application provides a kind of marine oil and gas string system dynamic response calculation method, medium and system, belong to marine oil and gas engineering technical field, the method includes establishing marine oil and gas string system dynamics theoretical model, and based on dynamics theoretical model establishes marine oil and gas string system finite element model;Adopt implicit numerical calculation method to solve marine oil and gas string system finite element model, obtain marine oil and gas string system dynamic response, using marine oil and gas string system adaptive grid strategy, grid adaptive adjustment is carried out to marine oil and gas string system finite element model;Adopt marine oil and gas string system adaptive step strategy, carry out adaptive step dynamic response analysis to marine oil and gas string system;The displacement, velocity, acceleration and other dynamic response data of marine oil and gas string system are post-processing operation, obtain the strain, stress, bending moment and other data of each node of marine oil and gas string system and analyze marine oil and gas string safety, guide safe operation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of offshore oil and gas engineering, and in particular, relates to a kind of offshore oil and gas string system dynamic response calculation method, medium and system. BACKGROUND

[0002] Offshore oil and gas string mainly includes drilling string, testing string, production string, specifically refers to drilling riser, production riser, underwater wellhead and other string-shaped oil and gas equipment, is the "throat" of offshore oil and gas exploration and development. The actual work of offshore oil and gas string system bears dynamic load such as wave, platform movement, etc. These dynamic loads drive the offshore oil and gas string to produce dynamic response, and excessive dynamic response will cause instantaneous damage of offshore oil and gas string. Fatigue damage accumulation caused by long-term dynamic response will cause fatigue fracture of offshore oil and gas string, leading to failure of the whole offshore oil and gas string system, and eventually causing leakage and other serious accidents. In order to ensure the safety of offshore oil and gas string during service, it is necessary to analyze the dynamic response of offshore oil and gas string system.

[0003] The commonly used offshore oil and gas string system dynamic response analysis method mainly includes the following steps: first, the offshore oil and gas string system is meshed and the offshore oil and gas string system finite element model is established, then the implicit numerical integration method such as Houbolt method, Wilson-θ method, Newmark-β method is used for dynamic response analysis. However, there are still several problems in the efficiency of offshore oil and gas string system dynamic response analysis: (1) In order to ensure the accuracy of dynamic response analysis results and reduce spatial discretization error, a relatively dense uniform mesh is generally used for finite element meshing when establishing the offshore oil and gas string system finite element model, which makes the offshore oil and gas string system dynamic response model matrix dimension high and the solving workload large; (2) Large sparse linear equations need to be solved in each iteration step of offshore oil and gas string system dynamic response analysis, and the linear equation solving usually directly uses Gauss elimination method without reasonably using the sparse characteristics of offshore oil and gas string system linear equation, so the dynamic response model iteration solving is slow; (3) In order to ensure the accuracy of dynamic response analysis results and reduce time discretization error, offshore oil and gas string system dynamic response analysis usually uses a small fixed step, which causes low efficiency of dynamic response analysis process. Under the background of offshore oil and gas development, more and more offshore oil and gas strings need to carry out dynamic response analysis, even the whole life cycle dynamic response analysis, the demand for offshore oil and gas string system dynamic response analysis is large, and the problem of low efficiency of dynamic response analysis is increasingly prominent. Therefore, it is of great significance to carry out offshore oil and gas string system dynamic response efficient calculation method research and improve its analysis efficiency for offshore oil and gas string system dynamic response analysis, design and safe operation. SUMMARY

[0004] The main purpose of the present application is to overcome the shortcomings and deficiencies of the prior art, and provide a marine oil and gas string system dynamic response efficient calculation method, processor, execution device and storage medium. For problem (1), a marine oil and gas string system adaptive grid method is proposed, the matrix order of the marine oil and gas string system dynamic response analysis is controlled through spatial discrete error estimation, and the balance between the accuracy and the calculation efficiency of the dynamic response analysis in the spatial scale is realized; for problem (2), a large sparse linear equation system solving method of the marine oil and gas string system dynamic response model is proposed, so as to reduce the iterative solving time of the dynamic response model; for problem (3), a marine oil and gas string system adaptive step method is proposed, the total iteration step number of the marine oil and gas string system dynamic response analysis is controlled through local truncation error, and the balance between the accuracy and the calculation efficiency of the dynamic response analysis in the time scale is realized. Thus, on the basis of constraining the element discrete error and the local truncation error of each time step, the dynamic response solving performance of the marine oil and gas string system is improved, and the efficient calculation of the marine oil and gas string system dynamic response is realized.

[0005] The present application is realized as follows:

[0006] The first aspect of the present application provides a marine oil and gas string system dynamic response calculation method, comprising the following steps:

[0007] S1: a marine oil and gas string system dynamics theoretical model is established, and a marine oil and gas string system finite element model is established based on the dynamics theoretical model;

[0008] S2: an implicit numerical calculation method is used to solve the marine oil and gas string system finite element model, and the marine oil and gas string system dynamic response is obtained, wherein the implicit numerical calculation method at least includes Houbolt method, Wilson-θ method and Newmark-β method;

[0009] S3: a marine oil and gas string system adaptive grid strategy is used to adaptively adjust the grid of the marine oil and gas string system finite element model;

[0010] S4: a marine oil and gas string system adaptive step strategy is used to perform adaptive step dynamic response analysis on the marine oil and gas string system;

[0011] S5: the dynamic response data of the marine oil and gas string system displacement, velocity and acceleration are post-processed to obtain the strain, stress and bending moment data of each node of the marine oil and gas string system;

[0012] S6: according to the obtained dynamic response data of the strain, stress and bending moment of each node of the marine oil and gas string system, the safety of the marine oil and gas string is analyzed to guide the safe operation.

[0013] On the basis of the above technical solutions, the marine oil and gas string system dynamic response calculation method can be further improved as follows:

[0014] The step S1 specifically comprises:

[0015] (1) A marine oil and gas string system dynamics transverse vibration model is established, and is specifically as follows:

[0016]

[0017] In the formula, m is the unit length mass of the marine oil and gas string; c is the damping coefficient; E is the elastic modulus of the marine oil and gas string; I(x) is the cross-sectional moment of inertia; T(x) is the effective axial tension; and F(x,t) is the transverse load applied on the unit length of the marine oil and gas string.

[0018] (2) A marine oil and gas string system dynamics axial vibration model is established, and is specifically as follows:

[0019]

[0020] In the formula, u(x,t) is the axial vibration of the marine oil and gas string; F is the axial hydrodynamic load applied on the marine oil and gas string; and A(x) is the cross-sectional area of the marine oil and gas string.

[0021] (3) The boundary conditions of the marine oil and gas string system model motion are set;

[0022] (4) A marine oil and gas string element finite element model is established, and is specifically as follows:

[0023]

[0024] In the formula, u is the marine oil and gas string element displacement vector; M, C and K are respectively the element mass matrix, the element damping matrix and the element stiffness matrix; and F is the marine oil and gas string element load vector. e e e e e

[0025] (5) A marine oil and gas string system overall finite element model is established, and is specifically as follows:

[0026]

[0027] In the formula, u is the marine oil and gas string displacement vector; M, C and K are respectively the overall mass matrix, the overall damping matrix and the overall stiffness matrix; and F is the marine oil and gas string load vector.

[0028] ​​​​​The step S2 specifically comprises: solving the large sparse linear equation group in the iteration step in the implicit numerical calculation method is an effective stiffness matrix, is an effective load matrix, and the sparse linear equation group calculation method of the marine oil and gas pipe column system is used for solving;

[0029] The step S3 specifically comprises:

[0030] (1) setting an error estimation interval of an adaptive mesh strategy, stress smoothing of discrete units is performed in the estimation interval to construct a continuous unit stress field, and then a spatial discrete error estimator is used to calculate the discrete error estimation of the units, and a maximum error envelope line of the discrete units is calculated, the error estimation interval can be set for several wave periods, and the stress smoothing can use the mass point average method, and the formula is as follows:

[0031]

[0032] In the formula, N e is the number of units connected with the mass point i; is a stress value calculated at the mass point i of the e th unit;

[0033] (2) using a spatial discrete error estimation method and a mesh redrawing strategy, which are specifically as follows:

[0034] The Zienkiewicz-Zhu method is used for unit posterior error estimation. Specifically, the error of the marine oil and gas pipe column system and the energy norm of the error are calculated, which are respectively:

[0035] e σ = σ * - σ h

[0036] ‖e σ ‖ s = [∫ Ω e σ D -1 e σ DΩ] 1 / 2

[0037] In the formula, σ * is a unit stress vector after stress smoothing; and σ h is a numerical calculation stress solution vector;

[0038] Then, for the i th unit, the relative error η s_i is:

[0039]

[0040] In the formula, ‖e σ ‖s_i is the energy error norm of the ith element; ‖u‖ s_i is the displacement response energy norm of the ith element;

[0041] The maximum spatial discretization relative error is set as The maximum allowed error norm of each element is:

[0042]

[0043] where e i is the spatial discretization error of each element, u is the displacement response of the offshore oil and gas column system obtained by numerical analysis method, and m is the number of elements of the offshore oil and gas column system finite element model, is the maximum spatial discretization error allowed for each element;

[0044] The minimum allowed error of the element is α is a coefficient less than 1, in order to balance the efficiency of mesh partitioning and the accuracy of dynamic response analysis, the interval is set to 0.9-1;

[0045] At the same time, in the adaptive mesh partitioning strategy, according to the dynamic response accuracy of the offshore oil and gas column system, the mesh refinement and coarsening limits are set to avoid the calculation burden caused by too fine and too coarse mesh partitioning, which is:

[0046] And the local encryption number of element i mesh ξ i is:

[0047]

[0048] where k refine is the maximum number of mesh refinement defined;

[0049] And the mesh coarsening strategy is to combine two meshes into one, and the execution condition is:

[0050]

[0051] where ‖e σ ‖ s_coarse_i is the energy error norm of the offshore oil and gas column element after adjacent mesh coarsening, k coarse is the number of mesh coarsening;

[0052] (3) When the analysis time exceeds the next time step of the error estimation interval, based on the maximum error envelope line of the discretized element error calculated in the error estimation interval, the adaptive mesh partitioning strategy of the offshore oil and gas column is used to re-partition the finite element mesh of the offshore oil and gas column system;

[0053] (4) According to the grid re-meshing result, the dynamic response parameters of the marine oil and gas string system solved in the current iteration step are recalculated or divided, including vector parameters such as displacement, velocity, acceleration, and matrix parameters such as stiffness matrix, mass matrix, and damping matrix, and are substituted into the next iteration step for numerical calculation.

[0054] The step S4 specifically comprises:

[0055] (1) The local truncation error of the single-step iteration solution of the dynamic response of the marine oil and gas string system is calculated using the time-discrete posterior error estimator, and is specifically as follows:

[0056]

[0057] In the formula, u is the displacement vector of the marine oil and gas string system; is the Taylor expansion of the displacement vector of the marine oil and gas string system at the corresponding previous time, which can be expressed as:

[0058]

[0059] In the formula, is the displacement vector of the marine oil and gas string system at the n+1 time; u n is the displacement vector of the marine oil and gas string system at the n time; and Δt is the corresponding step length;

[0060] The L2 norm of the local truncation error is calculated, and is specifically as follows:

[0061]

[0062] In the formula, η t is a function of the step length, and is denoted as η t =F(Δt);

[0063] (2) After obtaining the local truncation error, a step length optimization strategy is used to calculate a new step length, and subsequent dynamic response analysis of the marine oil and gas string system is performed, and is specifically as follows:

[0064] Let the L2 norm of the local truncation error at the t n time be η t =F(Δt n ), then

[0065]

[0066] According to the Newton-Raphson iteration method, there is

[0067] Δt n+1 =Δt n +F′(Δt n ) -1 F(Δt n)

[0068] where Δt n+1 is the adjusted step size;

[0069] Set tolerance coefficients f1, f2, set when the local truncation error L2 norm is acceptable within a certain range, at this time the step size remains unchanged, namely:

[0070] f1ε≤η t ≤f2ε

[0071] In general, f1 is less than 1, f2 is set to 1, and ε is the maximum allowable local truncation error.

[0072] After meeting the conditions, the iteration is ended to obtain the adjusted step size Δt new_1 ; The step size before adjustment is Δt old ;

[0073] Then, add step size adjustment constraints to prevent the step size from changing too drastically, when the step size decreases, the decrease is not more than half of the original step size, when the step size increases, the increase is not more than twice the original step size, which can be expressed as:

[0074] Δt new ={min{max{0.5,Δt new_1},2}}Δt old

[0075] Where, for the large sparse linear equation system in the implicit numerical calculation method is the effective stiffness matrix, is the effective load matrix, the specific steps for solving the sparse linear equation system of the offshore oil and gas string system include:

[0076] (1) Calculate the effective stiffness matrix according to the numerical calculation method;

[0077] (2) Introduce the sparse linear equation system solving method for the offshore oil and gas string system to calculate the large sparse matrix decomposition, where for the direct solving method of the large sparse linear equation system of the offshore oil and gas string system, Cholesky decomposition is used to decompose the large sparse matrix and Gaussian elimination is used to solve the linear equation system, which is shown as follows:

[0078] K=LL T

[0079] Where, L is a lower triangular matrix; L T is the transpose matrix of L;

[0080] For the iterative solution method of large sparse linear equations of the marine oil and gas string system, the incomplete Cholesky decomposition method is used to decompose the large sparse matrix, and the preconditioned conjugate gradient method is used to solve the linear equations, as shown in the following:

[0081] K=L I L I T +R

[0082] In the formula, L I is a lower triangular matrix; L I T is the transpose matrix of L I ; R is the residual vector after incomplete Cholesky decomposition;

[0083] Further,

[0084] For the Houbolt method, the effective stiffness matrix is:

[0085]

[0086] In the formula, c H0 , c H1 are constant parameters of the Houbolt method;

[0087] For the Wilson-θ method, the effective stiffness matrix is:

[0088]

[0089] In the formula, c W0 , c W1 are constant parameters of the Wilson-θ method;

[0090] For the Newmark-β method, the effective stiffness matrix is:

[0091]

[0092] In the formula, c N0 , c N1 are constant parameters of the Newmark-β method.

[0093] The second aspect of the present application provides a computer readable storage medium, the computer readable storage medium has computer program instructions stored thereon; the computer program instructions are executed by a processor to realize the marine oil and gas string system dynamic response calculation method.

[0094] The third aspect of the present application provides a marine oil and gas string system dynamic response calculation system, comprising the code of the computer readable storage medium described above.

[0095] Compared with the prior art, the marine oil and gas string system dynamic response calculation method, medium and system provided by the present application has the following advantages: (1) the marine oil and gas string system adaptive mesh method is proposed, the matrix order of the marine oil and gas string system dynamic response analysis is controlled through spatial discrete error estimation, the matrix order is reduced under the premise of ensuring the modeling accuracy of the marine oil and gas string dynamic response, and the workload of solving the dynamic response model is reduced; (2) the large sparse linear equation system solving method of the marine oil and gas string system dynamic response model is proposed, and the iterative solving time of the dynamic response model is reduced; (3) the marine oil and gas string system adaptive step method is proposed, the total iteration step number of the marine oil and gas string system dynamic response analysis is controlled through local truncation error, and the dynamic response analysis is recursively propagated with the optimal step, so that the marine oil and gas string system dynamic response solving process can be greatly optimized, and the marine oil and gas string system dynamic response efficient calculation is realized. BRIEF DESCRIPTION OF DRAWINGS

[0096] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the description of the embodiments of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0097] Among them, Figure 1 is a step flow chart of the marine oil and gas string system dynamic response calculation method provided by the present application.

[0098] Figure 2 is a detailed step flow chart of the marine oil and gas string system dynamic response calculation method provided by the present application. DETAILED DESCRIPTION

[0099] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0100] Therefore, the following detailed description of the embodiments of the application provided in the drawings is not intended to limit the scope of the application claimed, but merely represents selected embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.

[0101] It should be noted that similar reference numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0102] In the description of the application, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the application.

[0103] In addition, the terms "first" and "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first" and "second" can explicitly or implicitly include one or more of the features. In the description of the application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0104] As Figure 1 shown, is a flow chart of a marine oil and gas string system dynamic response calculation method provided by the first aspect of the application, which comprises the following steps:

[0105] S1: establishing a marine oil and gas string system dynamics theoretical model, and establishing a marine oil and gas string system finite element model based on the dynamics theoretical model;

[0106] S2: solving the marine oil and gas string system finite element model by using an implicit numerical calculation method to obtain the dynamic response of the marine oil and gas string system, the implicit numerical calculation method at least comprising: Houbolt method, Wilson-θ method, Newmark-β method;

[0107] Among them, the Newmark-β method is a method of generalizing the linear acceleration method; the Newmark-β method can be considered as a generalized algorithm which generalizes the average constant acceleration and linear acceleration algorithm. The Newmark-β method has a pseudo-static incremental equation form and different types of pseudo-static total equation forms;

[0108] Among them, the Wilson-θ method is an extension of the linear acceleration method, and its basic idea and implementation method are to change linearly in the time period [t, t+θ△t], first calculate the motion at time ti+θ△t, wherein θ>1, and then obtain the motion at time ti+△t through interpolation. It can be proved that when θ≥1.37, the Wilson-θ method is unconditionally stable;

[0109] Among them, the Houbolt method is an implicit calculation method, and its numerical damping increases quickly with the increase of △t / T, so the oscillation of the solution decays quickly; when △t→∞, the spectral radius of the Houbolt method tends to 0, and the key problem of using the Houbolt method is that in the Houbolt method, the rounding error of the Houbolt method will not become larger and larger in the calculation regardless of the value of △t, and the Houbolt method is unconditionally stable. When M=C=0, the recursive equation of the method can be converted into a static equation, so the Houbolt method can be used to solve the static solution when the load changes with time;

[0110] S3: Adopting the self-adaptive grid strategy of the marine oil and gas string system, the grid of the finite element model of the marine oil and gas string system is self-adaptively adjusted; by setting the upper limit and lower limit of the allowable value of the unit discretization error, when the unit error exceeds the upper limit of the error allowance, the unit size is reduced by grid refinement; when the unit error is lower than the lower limit of the error allowance, the grid size is increased by grid coarsening, so that the unit error is kept within the allowable range;

[0111] S4: Adopting the self-adaptive step strategy of the marine oil and gas string system, the self-adaptive step dynamic response analysis is carried out on the marine oil and gas string system; first, the local truncation error corresponding to the current step of the dynamic model of the marine oil and gas string system is calculated using the time discretization posterior error estimator; then the L2 norm of the local truncation error is compared with the local truncation error tolerance set in advance, if the L2 norm of the local truncation error is within the tolerance range, the current step is used to continue the next step of the marine oil and gas string system dynamic response calculation; if the L2 norm of the local truncation error is outside the tolerance range, the step optimization strategy is used to adjust the next step of the dynamic response calculation step, and return to the previous time for the next step of the dynamic response iteration calculation, so that the corresponding local truncation error and L2 norm are always kept within the tolerance;

[0112] S5: post-processing the dynamic response data of the marine oil and gas string system displacement, velocity, acceleration and the like, to obtain the strain, stress, bending moment and the like of each node of the marine oil and gas string system;

[0113] S6: analyzing the safety of the marine oil and gas string according to the obtained dynamic response data of the strain, stress, bending moment and the like of each node of the marine oil and gas string system, to guide the safe operation.

[0114] On the basis of the above technical solution, the marine oil and gas string system dynamic response calculation method of the application can be further improved as follows:

[0115] The step S1 specifically comprises:

[0116] (1) establishing a marine oil and gas string system dynamic transverse vibration model, which is specifically as follows:

[0117]

[0118] In the formula, m is the unit length mass of the marine oil and gas string; c is the damping coefficient; E is the elastic modulus of the marine oil and gas string; I(x) is the cross-sectional moment of inertia; T(x) is the effective axial tension; and F(x, t) is the transverse load applied on the unit length of the marine oil and gas string.

[0119] (2) establishing a marine oil and gas string system dynamic axial vibration model, which is specifically as follows:

[0120]

[0121] In the formula, u(x, t) is the axial vibration of the marine oil and gas string; F is the axial hydrodynamic load applied on the marine oil and gas string; and A(x) is the cross-sectional area of the marine oil and gas string.

[0122] (3) setting the boundary conditions of the marine oil and gas string system model motion;

[0123] (4) establishing a marine oil and gas string element finite element model, which is specifically as follows:

[0124]

[0125] In the formula, u e is the marine oil and gas string element displacement vector; M e , C e and K e are respectively the element mass matrix, the element damping matrix and the element stiffness matrix; and F e is the marine oil and gas string element load vector.

[0126] (5) establishing a marine oil and gas string system overall finite element model, which is specifically as follows:

[0127]

[0128] where u is the displacement vector of the offshore oil and gas pipe column; M, C and K are the overall mass matrix, overall damping matrix and overall stiffness matrix, respectively; and F is the load vector of the offshore oil and gas pipe column.

[0129] wherein the step S2 specifically comprises: solving the large sparse linear equation group in the iteration step in the implicit numerical calculation method is an effective stiffness matrix, is an effective load matrix, and the sparse linear equation group calculation method of the offshore oil and gas pipe column system is used for solving;

[0130] wherein the step S3 specifically comprises:

[0131] (1) setting an error estimation interval of an adaptive mesh strategy, constructing a continuous element stress field by stress smoothing of discrete elements in the estimation interval, and then calculating the element discrete error estimation by a spatial discrete error estimator, and simultaneously calculating the maximum error envelope line of the discrete elements, the error estimation interval can be set for several wave periods, and the stress smoothing can use the mass point average method, and the formula is as follows:

[0132]

[0133] wherein N e is the number of elements connected to the mass point i; is the stress value of the e-th element calculated at the mass point i;

[0134] (2) using a spatial discrete error estimation method and a mesh redrawing strategy, which are specifically as follows:

[0135] The Zienkiewicz-Zhu method is used for element posterior error estimation. Specifically, the error of the offshore oil and gas pipe column system and the energy norm of the error are calculated, which are respectively:

[0136] e σ = σ * - σ h

[0137] ‖e σ ‖ s = [∫ Ω e σ D -1 e σ dΩ] 1 / 2

[0138] wherein σ * is the element stress vector after stress smoothing; and σ h is the numerical calculation stress solution vector;

[0139] Then, for the i-th element, its relative error η s_i is:

[0140]

[0141] where, ‖e σ ‖ s_i is the energy error norm of the i-th element; ‖u‖ s_i is the displacement response energy norm of the i-th element;

[0142] The maximum spatial discretization relative error is set as The maximum allowed error norm of each element is:

[0143]

[0144] where, e i is the spatial discretization error of each element, u is the displacement response of the offshore oil and gas string system obtained by numerical analysis method, m is the number of elements of the offshore oil and gas string system finite element model, is the maximum spatial discretization error allowed for each element; the minimum allowed error of the element is α is a coefficient less than 1, in order to balance the efficiency of mesh partitioning and the accuracy of dynamic response analysis, the interval is set to 0.9-1;

[0145] At the same time, in the adaptive mesh partitioning strategy, according to the dynamic response accuracy of the offshore oil and gas string system, the mesh refinement and coarsening limits are set to avoid the calculation burden caused by too fine and too coarse mesh partitioning, which is:

[0146] And the local encryption number of element i mesh ξ i is:

[0147]

[0148] where, k refine is the defined maximum number of mesh refinement;

[0149] And the mesh coarsening strategy is to combine two meshes into one, and the execution condition is:

[0150]

[0151] where, ‖e σ ‖ s_coarse_i is the energy error norm of the adjacent mesh coarsened offshore oil and gas string element, k coarse is the number of mesh coarsening;

[0152] (3) When the analysis time exceeds the next time step of the error estimation interval, based on the maximum envelope line of the discrete element error calculated in the error estimation interval, the adaptive meshing strategy of the marine oil and gas string is used to perform finite element mesh redivision of the marine oil and gas string system;

[0153] (4) According to the mesh redivision result, the marine oil and gas string system dynamic response parameters obtained by solving the current iteration step are recalculated or divided, including displacement, velocity, acceleration and other vector parameters, and stiffness matrix, mass matrix, damping matrix and other matrix parameters, and are substituted into the next iteration step for numerical calculation.

[0154] The step S4 specifically comprises:

[0155] (1) The local truncation error of the marine oil and gas string system dynamic response after one-step iteration solving is calculated using a time-discrete posterior error estimator, which is specifically as follows:

[0156]

[0157] In the formula, u is a marine oil and gas string system displacement vector; is a Taylor expansion of the marine oil and gas string system displacement vector at the corresponding previous time, which can be expressed as:

[0158]

[0159] In the formula, is the n+1 time marine oil and gas string system displacement vector; u n is the n time marine oil and gas string system displacement vector; and Δt is the corresponding step length;

[0160] The L2 norm of the local truncation error is calculated, which is specifically as follows:

[0161]

[0162] In the formula, η t is a function of the step length, and η t =F(Δt) is recorded.

[0163] (2) After obtaining the local truncation error, a step length optimization strategy is used to calculate a new step length, and subsequent marine oil and gas string system dynamic response analysis is performed, which is specifically as follows:

[0164] Let the L2 norm of the local truncation error at time t n be η t =F(Δt n ), then

[0165]

[0166] According to Newton-Raphson iteration method, there are

[0167] Δt n+1 = Δt n +F'(Δt n ) -1 F(Δt n )

[0168] In the formula, Δt n+1 is the adjusted step size;

[0169] The tolerance coefficients f1, f2 are set, and the local truncation error L2 norm is set to be acceptable within a certain range, at which time the step size remains unchanged, that is:

[0170] f1ε≤η t ≤f2ε

[0171] In general, f1 is less than 1, f2 is set to 1, and ε is the maximum allowable local truncation error.

[0172] After meeting the conditions, the iteration is ended to obtain the adjusted step size Δt new_1 ; and the step size before adjustment is Δt old ;

[0173] Subsequently, a step size adjustment constraint is added to prevent the step size from changing too drastically, and when the step size decreases, the decrease is not more than half of the original step size, and when the step size increases, the increase is not more than twice the original step size, which can be expressed as:

[0174] Δt new ={min{max{0.5,Δt new_1},2}}Δt old

[0175] Where, for the large sparse linear equations in the iteration step of the implicit numerical calculation method is the effective stiffness matrix, is the effective load matrix, and the specific steps for solving the sparse linear equations of the offshore oil and gas string system include;

[0176] (1) Calculate the effective stiffness matrix according to the numerical calculation method;

[0177] (2) Introduce the sparse linear equation solving method of the offshore oil and gas string system to calculate the large sparse matrix decomposition, wherein for the direct solving method of the large sparse linear equations of the offshore oil and gas string system, Cholesky decomposition is used to decompose the large sparse matrix and Gaussian elimination is used to solve the linear equations, which is specifically shown as follows:

[0178] K = LL T

[0179] In the formula, L is a lower triangular matrix; L T is the transpose matrix of L;

[0180] For the iterative solution method of large sparse linear equations of the marine oil and gas string system, the incomplete Cholesky decomposition method is used to decompose the large sparse matrix, and the preconditioned conjugate gradient method is used to solve the linear equations, as shown in the following:

[0181] K = LL T + R

[0182] In the formula, L I is a lower triangular matrix; L I T is the transpose matrix of L I ; R is the residual vector after incomplete Cholesky decomposition;

[0183] Further,

[0184] For the Houbolt method, the effective stiffness matrix is:

[0185]

[0186] In the formula, c H0 , c H1 are constant parameters of the Houbolt method;

[0187] For the Wilson-θ method, the effective stiffness matrix is:

[0188]

[0189] In the formula, c W0 , c W1 are constant parameters of the Wilson-θ method;

[0190] For the Newmark-β method, the effective stiffness matrix is:

[0191]

[0192] In the formula, c N0 , c N1 are constant parameters of the Newmark-β method.

[0193] The second aspect of the present application provides a computer readable storage medium, the computer readable storage medium has computer program instructions stored thereon; the computer program instructions are executed by a processor to realize the marine oil and gas string system dynamic response calculation method.

[0194] A third aspect of the present application provides a marine oil and gas string system dynamic response calculation system, comprising the code of the computer readable storage medium described above.

[0195] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for calculating dynamic response of a marine oil and gas string system, characterized by, The method comprises the following steps: S1: establishing a dynamic theoretical model of the offshore oil and gas string system, and establishing a finite element model of the offshore oil and gas string system based on the dynamic theoretical model; S2: solving the finite element model of the offshore oil and gas string system by using an implicit numerical calculation method to obtain the dynamic response of the offshore oil and gas string system, wherein the implicit numerical calculation method at least comprises: Houbolt method, Wilson-θ method and Newmark-β method; S3: adopting an adaptive mesh strategy of the offshore oil and gas string system to adaptively adjust the finite element model of the offshore oil and gas string system; S4: adopting an adaptive step strategy of the offshore oil and gas string system to adaptively analyze the dynamic response of the offshore oil and gas string system in steps; S5: performing post-processing operation on the dynamic response data of the displacement, velocity and acceleration of the offshore oil and gas string system to obtain the strain, stress and bending moment data of each node of the offshore oil and gas string system; S6: analyzing the safety of the offshore oil and gas string system according to the obtained dynamic response data of the strain, stress and bending moment of each node of the offshore oil and gas string system to guide safe operation. The step S2 further comprises: solving the large sparse linear equation group in the iteration step in the implicit numerical calculation method is an effective stiffness matrix, is an effective load matrix, and the sparse linear equation group calculation method for the marine oil and gas pipe column system is used for solving; specifically comprising the following steps: (1) calculating the effective stiffness matrix according to the numerical calculation method; (2) introducing a sparse linear equation solving method for the offshore oil and gas string system to perform large sparse matrix decomposition calculation, wherein for the direct solving method of the large sparse linear equation of the offshore oil and gas string system, Cholesky decomposition method is used to decompose the large sparse matrix and Gaussian elimination method is used to solve the linear equation, which is specifically as follows: K = LL T ; where L is a lower triangular matrix; L T is the transpose matrix of L; For the iterative solving method of the large sparse linear equation of the offshore oil and gas string system, incomplete Cholesky decomposition method is used to decompose the large sparse matrix and preconditioned conjugate gradient method is used to solve the linear equation, which is specifically as follows: K = L I L I T + R; where L I is a lower triangular matrix; L I T is the transpose of L I ; R is the residual vector after incomplete Cholesky decomposition. (3) after the sparse matrix decomposition, the preconditioned conjugate gradient method is used to solve the large sparse linear equation of the offshore oil and gas string system to obtain the next displacement result u.

2. The method of claim 1, wherein, The step S1 specifically comprises: (1) establishing a dynamic transverse vibration model of the offshore oil and gas string system, which is specifically as follows: In the formula, m(x) is the unit length mass of the offshore oil and gas string; c is the damping coefficient; E is the elastic modulus of the offshore oil and gas string; I(x) is the cross-sectional moment of inertia; T(x) is the effective axial tension; and F(x, t) is the transverse load applied on the unit length of the offshore oil and gas string; (2) establishing a dynamic axial vibration model of the offshore oil and gas string system, which is specifically as follows: In the formula, u(x, t) is the axial vibration of the offshore oil and gas string; F is the axial hydrodynamic load applied on the offshore oil and gas string; and A(x) is the cross-sectional area of the offshore oil and gas string; (3) setting the boundary conditions of the offshore oil and gas string system model motion; (4) establishing a finite element model of the offshore oil and gas string unit, which is specifically as follows: wherein u e is the ocean oil and gas string unit displacement vector; M e , C e and K e are the unit mass matrix, unit damping matrix and unit stiffness matrix, respectively; and F e is the ocean oil and gas string unit load vector. (5) establishing a global finite element model of the offshore oil and gas string system, which is specifically as follows: In the formula, u is the displacement vector of the offshore oil and gas string; M, C and K are the global mass matrix, global damping matrix and global stiffness matrix respectively; and F is the load vector of the offshore oil and gas string.

3. The method of claim 2, wherein, The step S3 specifically comprises: (1) Set the error estimation interval of adaptive mesh strategy, and construct a continuous element stress field by stress smoothing of discrete elements in the estimation interval. Then calculate the element discretization error estimation by spatial discretization error estimator, and calculate the maximum envelope of discretization error at the same time. The error estimation interval is set for several wave periods, and the stress smoothing uses the particle average method, which is as follows: where N is the number of elements connected to particle i e N is the number of elements connected to particle i N is the number of elements connected to particle i (2) The spatial discretization error estimation method and mesh refinement strategy are used, which are as follows: The Zienkiewicz-Zhu method is used for element posterior error estimation, which is as follows: the error and energy norm of the error of the offshore oil and gas pipe column system are calculated, respectively: e σ = σ * - σ h ; || e σ || s = [∫ Ω e σ D -1 e σ dΩ] 1 / 2 ; where σ * is the smoothed element stress vector; σ h is the numerical computed stress solution vector; Then for the i-th cell, its relative error η s_i is: where ||e|| is the energy norm of the error vector e. σ ‖ s_i ||u|| is the energy norm of the displacement response vector u. s_i ||u|| is the energy norm of the displacement response vector u. The maximum spatially-discrete relative error is set to The maximum allowable error norm for each cell is: In the formula, e i is the spatial discretization error of each element, u is the displacement response of the offshore oil and gas pipe string system obtained by numerical analysis method, m is the number of elements of the finite element model of the offshore oil and gas pipe string system, is the maximum spatial discretization error allowed for each element; The minimum allowable error of the unit is α is a coefficient less than 1, and is set in the interval of 0.9-1 in order to balance the efficiency of meshing and the accuracy of dynamic response analysis. At the same time, in the adaptive mesh division strategy, according to the dynamic response accuracy of the offshore oil and gas pipe column system, the mesh refinement and coarsening limits are set to avoid the calculation burden caused by too fine or too coarse mesh, which is as follows: And the unit i grid local encryption number ξ i Is: In the formula, k refine is the maximum number of refinements of the defined grid; And the mesh coarsening strategy is to combine two meshes into one, and the execution condition is: where ‖e σ ‖ s_coarse_i is the energy error norm of the adjacent mesh coarsening ocean oil and gas string unit, k coarse is the number of mesh coarsening times; (3) When the analysis time exceeds the next time step of the error estimation interval, based on the maximum envelope of discretization error calculated in the error estimation interval, the adaptive mesh division strategy of the offshore oil and gas pipe column is used to refine the finite element mesh of the offshore oil and gas pipe column system; (4) According to the mesh refinement result, the dynamic response parameters of the offshore oil and gas pipe column system obtained by solving this iteration step are recalculated or divided, including the vector parameters of displacement, velocity and acceleration, and the matrix parameters of stiffness matrix, mass matrix and damping matrix, which are substituted into the next iteration step for numerical calculation.

4. The method of claim 3, wherein, The step S4 specifically includes: (1) Calculate the local truncation error of the offshore oil and gas pipe column system dynamic response after single step iteration solution by using time discretization posterior error estimator, which is as follows: In the formula, u is the displacement vector of the marine oil and gas string system; The Taylor expansion of the displacement vector of the marine oil and gas string system at the corresponding previous moment can be expressed as: wherein is the displacement vector of the offshore oil and gas string system at the n+1 time; u n is the displacement vector of the offshore oil and gas string system at the n time; Δt is the corresponding step length; Calculate the L2 norm of the local truncation error, which is as follows: where η t is a function of the step size, denoted η t = F(Δt). (2) After obtaining the local truncation error, use the step length optimization strategy to calculate the new step length, and perform subsequent offshore oil and gas pipe column system dynamic response analysis, which is as follows: Let t n be the local truncation error at time t t = F(Δt n ), then According to the Newton-Raphson iteration method, we have Δt n+1 = Δt n + F'(Δt n ) -1 F(Δt n ) In the formula, Δt n+1 is the adjusted step size; Set the tolerance coefficients f1 and f2, and set the local truncation error L2 norm within a certain range as acceptable, at which time the step length remains unchanged, that is: f1ε≤η t ≤f2ε; In the formula, f1 is less than 1, f2 is set to 1, and ε is the maximum allowable local truncation error; After meeting the conditions, the iteration ends to obtain the adjusted step size Δt new_1 ; the pre-adjustment step size is Δt old ; Then, add the step length adjustment constraint to prevent the step length from changing too drastically. When the step length decreases, the decrease amplitude does not exceed half of the original step length, and when the step length increases, the increase amplitude does not exceed twice the original step length, which can be expressed as: Δt new = {min{max{0.5, Δt new_1}, 2}} Δt old .

5. The offshore oil and gas pipe column system dynamic response calculation method according to claim 4, characterized in that: For the Houbolt method, the effective stiffness matrix is: wherein c H0 , c H1 is a Houbolt method constant parameter; For the Wilson-θ method, the effective stiffness matrix is: wherein c W0 , c W1 are Wilson-θ method constant parameters; For the Newmark-β method, the effective stiffness matrix is: In the formula, c N0 , c N1 are constant parameters of the Newmark-β method.

6. A computer-readable storage medium, characterized in that: The computer readable storage medium stores computer program instructions; the computer program instructions are executed by the processor to realize the offshore oil and gas pipe column system dynamic response calculation method according to any one of claims 1-5.

7. A system for calculating dynamic response of a marine oil and gas riser system, the system comprising: The code containing the computer readable storage medium of claim 6.

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