A method and system for determining the drag of a deep water riser based on recursive convolution

Abstract

The application provides a deepwater riser friction loss determination method and system based on recursive convolution, relates to the technical field of deepwater drilling riser dynamics modeling, and comprises the following steps: obtaining riser structure parameters and fluid parameters, establishing a full fluid column model and solving to obtain baseline friction resistance data; constructing a multi-stage recursive convolution state function containing to-be-identified attenuation parameters; setting to-be-identified output weights for the second stage and above state functions and linearly combining to establish a fluid leakage friction resistance approximation model; determining state differential relationships according to the recursive relationships of the state functions and establishing a linear outer system model; taking the baseline friction resistance data as a fitting target, performing parameter identification on the attenuation parameters and the output weights to obtain an identified linear outer system model; and determining the fluid leakage friction resistance based on the model and forming a friction resistance time sequence result. The application effectively improves leakage friction loss representation accuracy and reduces model complexity.

Description

Technical Field

[0001] This invention relates to the field of dynamic modeling technology for deepwater drilling risers, and in particular to a method and system for determining the discharge friction of deepwater risers based on recursive convolution. Background Technology

[0002] The riser in deepwater drilling is a crucial channel connecting the offshore drilling platform and the subsea wellhead, responsible for functions such as drilling fluid circulation, drill string delivery, and wellhead pressure control. In emergency situations such as typhoons, internal waves, or dynamic positioning system failure, the bottom assembly of the riser must quickly separate from the subsea blowout preventer (BOP) to ensure operational safety. After emergency separation, the drilling fluid inside the riser is discharged under gravity, while seawater enters. The movement of the drilling fluid and seawater relative to the riser wall generates fluid leakage friction resistance. This friction resistance directly acts on the riser and is a key factor affecting its backflush displacement, velocity, and overall dynamic response. To support the analysis of the riser's backflush response and the design of the control system, a mathematical model that accurately describes the time-varying nature of this friction resistance is needed. In existing technologies, the full-fluid column model is based on fluid dynamics equilibrium equations and has clear physical meaning; sinusoidal function approximation models and exponential polynomial approximation models fit the friction resistance variation trend through parameterized functions to reduce computational complexity.

[0003] However, the aforementioned existing technologies all have significant limitations. The full-fluid column model involves time-varying parameters such as fluid length, velocity, and acceleration, requiring simultaneous numerical solutions to nonlinear fluid dynamics equations, making the calculation process complex. More importantly, after drilling fluid discharge, if the original equations are continued to be numerically solved, the fluid length or motion state may exceed the actual physical range, making it difficult for the model output to automatically and smoothly remain at zero. Typically, additional discharge termination conditions or zeroing of frictional resistance are required, making it difficult to achieve a self-consistent expression of frictional resistance naturally decaying to zero. The sinusoidal function approximation model uses a superposition of several sinusoidal functions to fit the frictional resistance, but due to the continuous oscillating characteristics of sinusoidal functions, significant periodic oscillations may still be output after drilling fluid discharge, making it difficult to guarantee that frictional resistance naturally decays to zero, which does not match the actual physical state. Furthermore, when converting it to a linear external system, each sinusoidal function term usually requires the introduction of two states; if an s-term sinusoidal function is used, a 2s-order external system is formed, and the number of parameters to be identified and the order of the external system increase significantly with the number of terms. Although the exponential polynomial approximation model can use the exponential decay term to gradually reduce the frictional resistance to zero, when converting it into a linear external system, it is necessary to introduce corresponding auxiliary states according to the order of the time polynomial. In order to ensure the fitting accuracy, a higher order polynomial is often required, which still forms a higher order external system, and the order reduction effect is limited.

[0004] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for determining the discharge friction of deep-water risers based on recursive convolution, which effectively improves the accuracy of discharge friction characterization and reduces model complexity.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows: This invention provides a method for determining the discharge friction of deep-water riser pipe based on recursive convolution, including the following steps: Step S1: Obtain the structural and fluid parameters of the deep-water drilling riser, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain the benchmark friction resistance data. Step S2: Construct a multi-level recursive convolutional state function containing several attenuation parameters to be identified; each level of the recursive convolutional state function corresponds to an attenuation parameter to be identified; wherein, the first-level recursive convolutional state function is an exponential decay function determined by its corresponding attenuation parameter to be identified, and the second-level and above recursive convolutional state functions are obtained by convolving the previous level recursive convolutional state function with the exponential decay function determined by the attenuation parameter to be identified in the current level; Step S3: Introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and perform linear combination based on the recursive convolution state functions of the second level and above and the corresponding output weights to be identified to establish an approximate model of fluid discharge friction resistance. Step S4: Determine the corresponding state differential relationship based on the recursive relationship between the recursive convolution state functions at each level, and establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance; the order of the linear external system model is consistent with the order of the multi-level recursive convolution state function. Step S5: Using the benchmark friction resistance data as the fitting target, the parameters to be identified and the output weights to be identified are identified based on the fluid leakage friction resistance approximation model. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. Step S6: Determine the fluid discharge frictional resistance based on the identified linear external system model, and form the time series results of the fluid discharge frictional resistance changing with time during the emergency disconnection of the baffle.

[0007] Preferably, step S1 specifically includes: Obtain the structural and fluid parameters of the riser in deepwater drilling; the structural parameters include the total length of the riser, the inner diameter of the riser, and the internal flow cross-sectional area of ​​the riser; the fluid parameters include the density of seawater, the density of drilling fluid, the friction coefficient of seawater, and the friction coefficient of drilling fluid. Based on structural and fluid parameters, the drilling fluid inside the riser and the seawater entering from the lower end of the riser are considered as a whole fluid column. A whole fluid column model is established based on the balance between the gravity, inertial force and friction of the fluid column. The frictional resistance generated by the drilling fluid section and the frictional resistance generated by the seawater section are determined based on the full-fluid column model, and the fluid discharge frictional resistance is determined based on the frictional resistance generated by the drilling fluid section and the frictional resistance generated by the seawater section. The full liquid column model is numerically solved according to the preset sampling time to obtain the fluid discharge friction resistance corresponding to each preset sampling time, and the reference friction resistance data is formed based on each preset sampling time and the corresponding fluid discharge friction resistance.

[0008] Preferably, in step S2, the construction A series of recursive convolution state functions are defined, and corresponding attenuation parameters to be identified are set for each level of the recursive convolution state function. It is a positive integer not less than 2; The first-level recursive convolution state function is represented as:

[0009] in, For a moment The corresponding first-level recursive convolution state function value, The decay parameter to be identified corresponds to the first-level recursive convolution state function. Represents the natural exponential function; The state functions of recursive convolutions at levels two and above are expressed as follows:

[0010] in, Let be the order number of the recursive convolution state function, and ; For a moment The corresponding number Level recursive convolution state function value, For the integration time The corresponding number Level recursive convolution state function value, For the first The decay parameter to be identified corresponding to the recursive convolution state function. For the first The decay parameter to be identified corresponding to the recursive convolution state function; The identified decay parameter corresponding to the first-level recursive convolution state function and the identified decay parameter corresponding to the second-level and above recursive convolution state functions are all greater than 0.

[0011] Preferably, in step S3, when the number of levels of the multi-level recursive convolution state function is... At that time, it was the second level to the third level. The recursive convolution state functions of the second to third stages each set the corresponding output weights to be identified, and then... Each recursive convolutional state function is multiplied by its corresponding output weight to be identified, and the resulting products are summed to establish an approximate model of the fluid discharge friction resistance.

[0012] Preferably, in step S4, the state differential relationship corresponding to the first-level recursive convolution state function is determined based on the recursive relationship between the recursive convolution state functions at each level, as expressed by the following formula:

[0013] Level 2 to Level 1 The state differential relationship corresponding to the recursive convolution state function is expressed by the following formula:

[0014] in, For a moment The corresponding first-level recursive convolution state function value, This is the time derivative of the first-order recursive convolution state function. Let be the order number of the recursive convolution state function, and ; For a moment The corresponding number Level recursive convolution state function value, For the first The time derivative of the recursive convolution state function. For a moment The corresponding number Level recursive convolution state function value, For the first The decay parameter to be identified corresponding to the recursive convolution state function. For the first The decay parameter to be identified corresponding to the recursive convolution state function; Level 1 to Level 2 The state vector is composed of recursive convolutional state functions. The linear relationship between the derivative of the state vector and the state vector is determined based on the state differential relationship, and the state equation of the linear external system model is constructed. The linear relationship between the approximate output of the fluid discharge friction resistance and the state vector is determined based on the approximate model of fluid discharge friction resistance, and the output equation of the linear external system model is constructed. The linear external system model is established based on the state equation and the output equation.

[0015] Preferably, in step S5, the reference friction resistance at each preset sampling time is determined based on the reference friction resistance data, and the approximate value of the friction resistance at each preset sampling time is determined based on the fluid leakage friction resistance approximation model. The parameter identification target is to minimize the sum of squared errors between the reference friction resistance and the approximate value of friction resistance at each preset sampling time. The attenuation parameters to be identified corresponding to each level of recursive convolution state function and the output weights to be identified corresponding to each level of recursive convolution state function above the second level are jointly identified to obtain the corresponding attenuation parameters and output weights. Substitute the identified attenuation parameters and output weights into the linear external system model to determine the corresponding parameters in the linear external system model, thus obtaining the identified linear external system model.

[0016] Preferably, in step S5, for multi-level recursive convolutional state functions of different orders, parameter identification is performed using the same set of benchmark friction resistance data as the fitting target. The fitting effect and model complexity of the approximate fluid discharge friction resistance models corresponding to different orders are compared, and the target order is determined based on the comparison results. The identified linear external system model corresponding to the target order is taken as the target linear external system model; wherein, the order of the target linear external system model is consistent with the target order. In step S6, the initial state of the target linear external system model is used as the starting point for state evolution. The state evolution is carried out according to the state equation of the target linear external system model to obtain the recursive convolution state at different times. The fluid discharge friction resistance at each time is determined according to the output equation of the target linear external system model. The state evolution and fluid discharge friction resistance determination process are executed continuously in time sequence to form the time sequence result of the fluid discharge friction resistance changing with time during the emergency disconnection of the water pipe.

[0017] The present invention also provides a system for determining the friction of deep-water riser discharge based on recursive convolution, comprising: The benchmark data acquisition module is used to acquire the structural and fluid parameters of the riser in deep water drilling, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain benchmark friction resistance data. The state function construction module is used to construct a multi-level recursive convolutional state function containing several decay parameters to be identified. The approximate model building module is used to introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and to establish an approximate model of fluid discharge friction resistance by linearly combining the recursive convolution state functions of the second level and above and the corresponding output weights to be identified. The external system establishment module is used to determine the corresponding state differential relationship based on the recursive relationship between the state functions at each level of recursive convolution, and to establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance. The parameter identification module is used to identify the attenuation parameters and output weights to be identified based on the approximate model of fluid leakage friction resistance, using the benchmark friction resistance data as the fitting target. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. The friction determination module is used to determine the fluid discharge friction resistance based on the identified linear external system model, and to generate a time-series result of the fluid discharge friction resistance changing over time during the emergency disconnection of the riser.

[0018] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method for determining the friction of deep-water riser discharge based on recursive convolution.

[0019] The present invention also provides a computer storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for determining the discharge friction of a deep-water riser based on recursive convolution.

[0020] The beneficial effects of this invention are: effectively improving the accuracy of the characterization of downward leakage friction and reducing model complexity. By constructing multi-level recursive convolutional state functions and introducing identification decay parameters that satisfy positive value constraints to each level of state function, the recursive convolutional state functions at each level have a stable decay trend after time increases. On this basis, the state functions at the second level and above are linearly combined according to the output weights. By utilizing the difference in the decay rate of each level of state function, a non-monotonic change pattern from zero to a peak value and then gradually decaying to zero can be formed. Since the eigenvalues ​​of the linear external system state matrix are determined by the negative values ​​of each decay parameter, all eigenvalues ​​are negative real numbers, giving the system asymptotic stability. After the fluid discharge ends, the friction resistance output can naturally approach zero without the need to set additional discharge termination conditions or cutoff functions. The recursive relationship between the recursive convolutional state functions is converted into a state differential relationship, and a standard linear state space form of the external system model is established. For the s-level recursive convolutional model, an s-order linear external system is directly formed without the need to introduce additional auxiliary states; the parameters to be identified only include s decay parameters and s-1 output weights, for a total of 2s-1. Compared to sinusoidal function models, which require introducing two states for each sinusoidal function term (2s-order external system, 3s-order parameters), and exponential polynomial models, which require introducing auxiliary states as the polynomial order increases, this invention significantly reduces the computational burden of parameter identification and the complexity of controller design. By setting different recursive convolution state function series to form linear external systems of different orders, and using the same set of benchmark friction resistance data as the fitting target for models of different orders, parameter identification is performed. The appropriate model order is determined based on fitting accuracy and model complexity. In practical applications, the model with the lowest order that meets the preset accuracy requirements can be selected, achieving a flexible balance between fitting accuracy and computational complexity. Attached Figure Description

[0021] Figure 1 This is a diagram illustrating the method steps of the present invention.

[0022] Figure 2 This is a system module diagram of the present invention.

[0023] Figure 3 This is a comparison diagram of the fluid discharge friction resistance of different orders of recursive convolution models and the full liquid column model in Embodiment 3 of the present invention.

[0024] Figure 4 This is a comparison chart of the calculation results of different approximate friction resistance models in Embodiment 3 of the present invention.

[0025] Figure 5 This is a diagram of the internal structure of a computer device according to Embodiment 4 of the present invention. Detailed Implementation

[0026] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0027] Example 1: See Figure 1 As shown, this embodiment is a method for determining the discharge friction of a deep-water riser based on recursive convolution, including the following steps: Step S1: Obtain the structural and fluid parameters of the deep-water drilling riser, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain the benchmark friction resistance data. Specifically, deepwater drilling risers are used to connect offshore drilling platforms to the subsea wellhead. During normal drilling, the riser is filled with drilling fluid. When the drilling platform is in a situation requiring emergency riser disconnection, the bottom assembly of the riser is separated from the subsea blowout preventer (BOP). After emergency disconnection, the drilling fluid inside the riser is discharged from the lower end under gravity, while seawater enters the riser from the lower end. During this process, the drilling fluid and seawater move relative to the riser and rub against the inner wall of the riser. As the drilling fluid is discharged, the seawater enters, and the fluid movement changes, a fluid discharge frictional resistance that varies over time is formed. This fluid discharge frictional resistance acts directly on the riser and affects the dynamic backflush response after emergency disconnection.

[0028] Furthermore, the structural and fluid parameters of the deepwater drilling riser are obtained. The structural parameters include the total length of the riser. Inner diameter of the riser pipe and the internal flow cross-sectional area of ​​the riser pipe Fluid parameters include seawater density. Drilling fluid density Seawater friction coefficient coefficient of friction with drilling fluid and obtain gravitational acceleration. The above parameters are determined based on the structure of the riser pipe to be analyzed and the corresponding fluid conditions. The specific parameter values ​​can be set according to the actual modeling object.

[0029] During the fluid discharge process, Indicates time The length of the seawater section inside the riser is equal to the corresponding length of the drilling fluid section. ;by Indicates the velocity of the fluid relative to the riser pipe, in Represents the acceleration of the fluid relative to the riser pipe, in Indicates the drilling fluid discharge rate, in Indicates time The corresponding total frictional resistance of fluid discharge. As drilling fluid is discharged and seawater enters, the length of the seawater section, the length of the drilling fluid section, and the fluid motion state change over time.

[0030] Furthermore, considering the drilling fluid inside the riser and the seawater entering from the lower end of the riser as a single fluid column, a dynamic model of the entire fluid column is established based on the balance between gravity, inertial force, and frictional force of the fluid column, specifically expressed as follows:

[0031] in, This is the total length of the riser pipe. For a moment The length of the seawater section This represents the length of the drilling fluid section at the corresponding moment. and These are the densities of seawater and drilling fluid, respectively. The cross-sectional area of ​​the water pipe for internal flow. This refers to the drilling fluid discharge rate. The acceleration of the fluid relative to the riser pipe. It is the acceleration due to gravity. The total frictional resistance during fluid discharge is given. The above dynamic relationships describe the fluid motion processes under conditions of drilling fluid discharge, seawater inflow, and the time-varying lengths of both fluid types.

[0032] Furthermore, the total frictional resistance of fluid discharge. Frictional resistance generated by drilling fluid section Frictional resistance generated with seawater section Together they constitute, that is:

[0033] Among them, the frictional resistance generated by the drilling fluid section for:

[0034] Frictional resistance generated in the seawater section for:

[0035] In the formula, and These are the friction coefficients of drilling fluid and seawater, respectively. The velocity of the fluid relative to the riser pipe. The inner diameter of the riser is given. From the above relationships, it can be seen that the frictional resistance of the drilling fluid section and the frictional resistance of the seawater section are related to the density, friction coefficient, relative velocity of the fluid, and length of the corresponding fluid section, respectively. Therefore, during the fluid discharge process after the riser is detached in an emergency, as the fluid composition and motion state change, the two frictional resistances change accordingly, and the total frictional resistance of the fluid discharge obtained by combining them also changes with time.

[0036] It should be noted that in this step, the full-fluid column model is used to describe the process of drilling fluid discharge and seawater ingress after emergency riser detachment from a fluid dynamics perspective. Unlike directly using a fixed-form approximation function to describe frictional resistance, the full-fluid column model calculates the fluid discharge frictional resistance through the dynamic relationship between fluid length, motion state, and fluid property parameters. The calculated frictional resistance data serves as the benchmark data for parameter identification in the subsequent recursive convolution model. The full-fluid column model can comprehensively describe the processes of drilling fluid discharge, seawater ingress, and the time-varying lengths of both fluids. However, its numerical solution process is relatively complex. Therefore, the benchmark frictional resistance data is subsequently used to identify a low-order linear external system model, and the identified linear external system model is used to determine the time-varying fluid discharge frictional resistance during the emergency riser detachment process.

[0037] Furthermore, the full-fluid column model is numerically solved according to preset sampling times. During the numerical solution process, the lengths of the seawater section and drilling fluid section, as well as the fluid motion state, are determined based on the full-fluid column dynamic model at each time point. The frictional resistance generated by the drilling fluid section and the frictional resistance generated by the seawater section are calculated based on the fluid state at the corresponding time point, and these two are added together to obtain the fluid discharge frictional resistance at that time point. The fluid discharge process is solved sequentially over time to obtain the fluid discharge frictional resistance at multiple sampling times.

[0038] Correlating each sampling time with the corresponding fluid discharge frictional resistance generates discrete reference frictional resistance data:

[0039] in, For the preset sampling time, For the full liquid column model at the sampling time The corresponding fluid discharge frictional resistance is obtained. By sequentially obtaining the fluid discharge frictional resistance at multiple sampling times, the resulting benchmark frictional resistance data characterizes the process of fluid discharge frictional resistance changing over time after the emergency disconnection of the riser.

[0040] It should be noted that the calculation time range used to generate the baseline frictional resistance data should cover the fluid discharge process to be analyzed, so that the obtained data can reflect the rise, peak value, and decay characteristics of the fluid discharge frictional resistance. The specific values ​​of the riser structure size, fluid property parameters, sampling step size, and calculation time can be set according to the riser to be analyzed and its corresponding fluid conditions. This embodiment does not impose fixed limitations on them.

[0041] Furthermore, the baseline frictional resistance data serves as the fitting target for the subsequent parameter identification process. Through subsequent steps, a multi-level recursive convolutional state function is constructed, and the corresponding decay parameters and output weights are identified. A low-order linear external system that can characterize the time-varying process of fluid discharge frictional resistance is established. Based on the state evolution of the linear external system after parameter identification, the fluid discharge frictional resistance that changes with time during the emergency detachment of the baffle is determined.

[0042] Step S2: Construct a multi-level recursive convolutional state function containing several attenuation parameters to be identified; each level of the recursive convolutional state function corresponds to an attenuation parameter to be identified; wherein, the first-level recursive convolutional state function is an exponential decay function determined by its corresponding attenuation parameter to be identified, and the second-level and above recursive convolutional state functions are obtained by convolving the previous level recursive convolutional state function with the exponential decay function determined by the attenuation parameter to be identified in the current level; Specifically, to construct a recursive dynamic state for characterizing the time-varying process of fluid discharge frictional resistance, a common... The first level of recursive convolution state function is defined, and corresponding attenuation parameters to be identified are set for each level of the recursive convolution state function. The first level... The level recursive convolution state function is denoted as , will the The attenuation parameter to be identified is denoted as... ,in, , Let be the series of the recursive convolution state function, and It is a positive integer not less than 2. The recursive convolution state functions at each level are constructed in a manner that iterates step by step from the first level to the second level and all levels above the second level.

[0043] Furthermore, the first-level recursive convolution state function adopts an exponentially decaying form, which is expressed as:

[0044] in, This is the first-level recursive convolution state function. The decay parameter to be identified corresponds to the first-level recursive convolution state function. For time, Represented by natural constant The base is an exponential function. Therefore, the first-level recursive convolution state function serves as the starting state for the progressive construction of subsequent levels of recursive convolution state functions.

[0045] Furthermore, for the second level and above recursive convolution state functions, the previous level's recursive convolution state function is used as the construction basis for the current level's recursive convolution state function, and the previous level's recursive convolution state function is convolved with the exponential decay function determined by the decay parameter to be identified in the current level. The state function of a level recursive convolution is expressed as:

[0046] in, For the first Level recursive convolution state function, The state function of the previous recursive convolution at the integration time The corresponding state value, For the first The decay parameter to be identified corresponding to the recursive convolution state function. The decay parameter to be identified corresponds to the state function of the previous recursive convolution. This is the variable for the convolution integral. In the exponent term... This represents the time interval between the current moment and the integration moment, determined by the decay parameter corresponding to this stage. Determine the exponential decay relationship corresponding to this time interval.

[0047] According to the above recursive relationship, the first-level recursive convolution state function is directly determined by its corresponding exponential decay function; the second-level recursive convolution state function is obtained by convolving the aforementioned first-level recursive convolution state function; the third-level recursive convolution state function is obtained by convolving the aforementioned second-level recursive convolution state function; and so on, until the third-level recursive convolution state function is formed. The recursive convolution state functions are arranged in a series, with each level forming a sequential, interconnected recursive relationship. Furthermore, any recursive convolution state function at the second level or higher is related to the recursive convolution state function at the previous level.

[0048] It should be noted that each attenuation parameter to be identified satisfies:

[0049] The positive value constraint causes the corresponding exponential terms in the recursive convolution state functions at each level to decay over time, and serves as a constraint condition for subsequent decay parameter identification. At the same time, this parameter constraint provides a parameter basis for establishing a linear external system with stable decay characteristics based on the state differential relationship of the recursive convolution state functions at each level.

[0050] It should also be noted that in this step... All parameters are to be identified. This step only determines the parameterized construction relationship between the recursive convolutional state functions at each level, and does not determine the specific values ​​of each attenuation parameter at this stage. The specific values ​​of each attenuation parameter will be determined in the subsequent parameter identification process, using the benchmark friction resistance data formed in step S1 as the fitting target. Therefore, this step yields a multi-level recursive convolutional state function that includes the attenuation parameters to be identified and has a hierarchical recursive relationship.

[0051] Furthermore, when setting When performing a level-wise recursive convolution state function, the corresponding state function is formed. A recursive state; the series of the recursive convolution state function corresponds to the order of the subsequent linear external system built upon these states, i.e., constructing... When performing a multi-level recursive convolution state function, it can be further formed This is a linear external system. Therefore, different orders of recursive convolution models can be formed by setting different levels of the recursive convolution state function. The specific model order can be determined by considering the fitting effect and complexity of the corresponding model.

[0052] Furthermore, the second-level and higher recursive convolutional state functions constructed in this step are used in step S3 to establish an approximate model of fluid discharge frictional resistance; the recursive relationship between each level of recursive convolutional state functions is used in step S4 to further determine the corresponding state differential relationship; the attenuation parameters to be identified in this step are identified in step S5 in combination with the reference frictional resistance data, so that the recursive convolutional state function structure formed in this step forms a continuous technical chain with the subsequent frictional resistance approximate model, linear external system model and parameter identification process.

[0053] Step S3: Introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and perform linear combination based on the recursive convolution state functions of the second level and above and the corresponding output weights to be identified to establish an approximate model of fluid discharge friction resistance. Specifically, in step S2, the following is constructed: After the first level of recursive convolution state function, it becomes the second to the third level. Each level of recursive convolutional state function introduces a corresponding output weight to be identified. The first level... The output weights to be identified corresponding to the recursive convolution state function are denoted as follows: ,in, Therefore, when the series of the recursive convolution state function is... At that time, a total of Each output weight to be identified is associated with the second to the third level. The corresponding state function is a level recursive convolution.

[0054] Furthermore, the second level to the third level Each recursive convolutional state function is multiplied by its corresponding output weight to be identified, and the results are linearly combined to establish an approximate model of fluid leakage friction resistance:

[0055] in, For a moment The corresponding approximate value of fluid discharge frictional resistance, The first step constructed for step S2 Level recursive convolution state function, For the first The output weights to be identified corresponding to the recursive convolution state function. Let be the series of the recursive convolutional state function. For any given time... They respectively obtained the second to the third level. The state values ​​corresponding to the recursive convolution state function are summed according to the corresponding output weights to obtain the approximate value of the fluid discharge friction resistance at that moment.

[0056] It should be noted that in the above approximate model of fluid discharge frictional resistance, the first-order recursive convolution state function It does not directly participate in the linear combination of the approximate output of frictional resistance, but serves as the starting state for constructing the second-level recursive convolutional state function in step S2; the second level to the... The recursive convolutional state function is used to form an approximate output of fluid discharge frictional resistance. Therefore, in the case of... In the case of a multi-level recursive convolution state function, the corresponding settings are... Each output weight.

[0057] Furthermore, the output weights to be identified satisfy the following:

[0058] The positive value condition serves as a constraint for parameter identification when using output weights. In this step, each output weight only determines its correspondence and parameter properties in the approximate model of fluid discharge friction resistance; its specific values ​​are not yet determined and will be identified in subsequent step S5 in conjunction with the baseline friction resistance data formed in step S1.

[0059] It should be noted that the identified decay parameter in step S2 is used to determine the time variation relationship of the recursive convolution state function at each level, and the identified output weights introduced in this step are used to determine the second to the third level. The weighted relationship between the recursive convolutional state function and the approximate output of fluid discharge frictional resistance. Therefore, for a given system containing... The model of the hierarchical recursive convolution state function includes a total of One attenuation parameter to be identified and There are 16 output weights to be identified, i.e., a total of 160 weights. One parameter to be identified.

[0060] Furthermore, for any sampling time in step S1 Based on the approximate model of fluid discharge frictional resistance established in this step, the approximate frictional resistance corresponding to the same sampling time can be obtained:

[0061] in, For the total liquid column model in step S1 at the sampling time The obtained reference frictional resistance, This step approximates the frictional resistance at the same sampling time using the recursive convolution approximation model. Step S5 uses the benchmark frictional resistance data as the fitting target, and uniformly identifies the attenuation parameter to be identified in step S2 and the output weight to be identified in this step, so as to minimize the fitting error between the approximate frictional resistance at the corresponding sampling time and the benchmark frictional resistance.

[0062] Furthermore, the approximate model of fluid discharge frictional resistance established in this step determines the linear relationship between the recursive convolution state and the approximate output of frictional resistance. In step S4, the corresponding state differential relationship is further determined based on the recursive relationship between the recursive convolution state functions at each level in step S2. The state differential relationship is used to construct the state relationship of the linear external system, and the approximate model of fluid discharge frictional resistance established in this step is used to construct the corresponding output relationship, thereby representing the recursive convolution model in the form of a linear external system.

[0063] Step S4: Determine the corresponding state differential relationship based on the recursive relationship between the recursive convolution state functions at each level, and establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance; the order of the linear external system model is consistent with the order of the multi-level recursive convolution state function. Specifically, step S2 constructs the first level to the second level. The recursive convolutional state functions have a sequentially connected recursive relationship. To represent the recursive convolutional state functions in a linear state-space form, the time derivative of each level of the recursive convolutional state function is calculated, and the corresponding state differential relationship is determined based on their recursive convolutional relationship.

[0064] Furthermore, for the first-level recursive convolution state function:

[0065] Taking its derivative with respect to time, we get:

[0066] in, This represents the time derivative of the first-level recursive convolution state function. This represents the decay parameter to be identified for the first-level recursive convolution state function. Therefore, the change in the first-level recursive convolution state is determined by its current state and the corresponding decay parameter.

[0067] For level two and above The time derivative of the recursive convolution state function in step S2 is obtained by taking the time derivative of the convolution recursion relationship:

[0068] in, Indicates the first The time derivative of the state function of a recursive convolution. This is the state function of the previous recursive convolution. The decay parameter to be identified corresponds to the state function of the previous recursive convolution. The attenuation parameter to be identified corresponds to the recursive convolution state function of this level. Therefore, for any recursive convolution state at the second level and above, its state change is jointly determined by the previous level recursive convolution state and the current level recursive convolution state, thus transforming the convolution integral recursive relationship in step S2 into a sequentially connected state differential relationship.

[0069] It should be noted that the above state differential relationship directly corresponds to the recursive convolution construction relationship in step S2. The change of the first-level recursive convolution state is only related to its own state; the second-level and above recursive convolution states retain the state decay relationship of the current level while inheriting the previous level's recursive convolution state, thereby maintaining a step-by-step recursive structure between the states.

[0070] Furthermore, the first to the second level constructed in step S2 are... The recursive convolution state functions sequentially form the state vector:

[0071] in, The state vector of the linear external system contains a total of There are 1 state component, and each state component corresponds to a first-level recursive convolution state function.

[0072] Based on the state differential relationship corresponding to the state functions of each level of recursive convolution, the dynamic changes of the state vector are uniformly represented as:

[0073] in, The state matrix of the linear external system is specifically represented as follows:

[0074] As can be seen from the state matrix above, its main diagonal elements are the negative decay parameters corresponding to each level of the recursive convolution state function, the elements on the adjacent sub-diagonal positions are the decay parameters corresponding to the previous level of the recursive convolution state function, and the remaining elements are zero. Therefore, the first-level state determines its state change only through its corresponding negative decay parameter, and the second to... Each level state establishes a connection with the adjacent previous level state through the negative attenuation parameter of the current level and the attenuation parameter of the previous level, so that the structural relationship in the state matrix corresponds to the step-by-step serial recursive relationship in step S2.

[0075] Furthermore, the approximate model of fluid discharge frictional resistance established in step S3 is as follows:

[0076] Among them, the second level to the third level The recursive convolutional state functions are used to approximate the fluid discharge frictional resistance output according to their corresponding output weights. Based on the linear combination relationship, the output matrix of the linear external system is constructed as follows:

[0077] The approximate output of the fluid discharge frictional resistance is expressed as:

[0078] in, The output matrix of the linear external system has a first term of zero, corresponding to the first-level recursive convolution state function not directly participating in the approximate output of fluid discharge frictional resistance; the second term to the... The items are respectively the second level to the first level. The output weights to be identified corresponding to the recursive convolution state function Therefore, this output relationship is consistent with the approximate model of fluid leakage friction resistance established in step S3.

[0079] Based on the above state differential relationship and the approximate output relationship of frictional resistance, a linear external system model of fluid discharge frictional resistance is established:

[0080] Therefore, the multi-level recursive convolutional state function constructed in the form of convolution integral in step S2 and the approximate output relationship of fluid discharge frictional resistance established in step S3 are uniformly represented in a linear state-space form. The state equations describe the dynamic evolution of each level of recursive convolutional state over time, and the output equations obtain approximate values ​​of fluid discharge frictional resistance based on each level of recursive convolutional state. Thus, the linear external system model is not another frictional resistance model independently established in steps S2 and S3, but rather the state-space representation of the aforementioned recursive convolutional model.

[0081] Furthermore, based on the definition of the recursive convolution state function at each level, the initial state of the linear external system is set as follows:

[0082] That is, the state value corresponding to the first-level recursive convolution state function at the initial time is 1, and the state value corresponding to the second level and so on is 1. The state values ​​corresponding to the first-order recursive convolution state function are all 0 at the initial time. The initial state serves as the initial condition for calculating the state evolution of the linear external system.

[0083] It should be noted that when step S2 is constructed When performing a multi-level recursive convolution of the state function, the state vector Include Each state component, and the corresponding state matrix for The matrix is ​​of order n, therefore the established linear external system model is: This constructs a linear external system of order 1. Therefore, the order of the recursive convolutional state function is consistent with the order of the linear external system model. By setting different orders of the recursive convolutional state function, linear external systems of different orders can be constructed without adding auxiliary states to constitute the order of the external system in addition to the recursive convolutional states. This structure allows the model order to be directly determined by the number of recursive convolutional states.

[0084] Furthermore, due to the state matrix It is in lower triangular form, and its eigenvalues ​​are determined by the elements of the main diagonal. Therefore, the eigenvalues ​​are... The feature values ​​are:

[0085] The attenuation parameters to be identified in step S2 satisfy the following:

[0086] therefore:

[0087] That is, the state matrix All eigenvalues ​​are negative real numbers, thus giving the linear external system asymptotic stability. As time increases, each recursive convolution state gradually decays under the constraints of the recursive structure and the positive value of the decay parameter. The corresponding approximate output of the fluid discharge frictional resistance also gradually approaches zero, thus eliminating the need for additional truncation functions or additional decay processing in the linear external system to force the frictional resistance to zero. This stable decay characteristic is formed by the model structure and the constraints of the decay parameter.

[0088] It should be noted that the linear external system model established in this step is still a parameterized model containing parameters to be identified at this stage. Among them, the state matrix... Includes the attenuation parameter to be identified set in step S2 Output matrix Includes the output weights to be identified introduced in step S3 This step determines the structural position of the attenuation parameters and output weights in the linear external system, as well as their corresponding state and output relationships. The specific values ​​of each parameter have not yet been determined.

[0089] Step S5: Using the benchmark friction resistance data as the fitting target, the parameters to be identified and the output weights to be identified are identified based on the fluid leakage friction resistance approximation model. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. Specifically, for series of The recursive convolution model, step S2 sets up the following: One attenuation parameter to be identified Step S3 is set with Output weights to be identified The aforementioned attenuation parameters and output weights to be identified are combined to form a parameter vector to be identified:

[0090] in, for The parameter vector to be identified corresponding to the multi-level recursive convolution model contains a total of One parameter to be identified; attenuation parameter This is used to determine the temporal variation relationship of the recursive convolution state functions at each stage in step S2, and to determine the state matrix in step S4 accordingly. The relevant elements; the output weights are used to determine the weighted relationship between the recursive convolution state functions at each level in step S3 and the approximate output of the fluid discharge friction resistance, and to determine the relevant elements of the output matrix in step S4 accordingly.

[0091] Furthermore, step S1 has already obtained the data at each sampling time. Corresponding reference friction resistance And form reference friction resistance data; for the same sampling time, according to the recursive convolution state function constructed in step S2 and the approximate model of fluid discharge friction resistance established in step S3, the corresponding approximate friction resistance is obtained:

[0092] in, For the full liquid column model at the sampling time The calculated reference frictional resistance, This is the approximate frictional resistance corresponding to the recursive convolution approximation model at the same sampling time. For the first Level recursive convolution state function at sampling time The corresponding state value, For the first The output weights to be identified correspond to the recursive convolution state function. Therefore, a correspondence between the reference frictional resistance and the approximate frictional resistance is established at each sampling time.

[0093] Furthermore, using the baseline frictional resistance data obtained in step S1 as the fitting target, a nonlinear least squares method is employed to identify the parameter vector. Parameter identification is performed, and the sum of squared errors between the reference frictional resistance and the approximate frictional resistance at each sampling time is used as the fitting error. The parameter identification objective is expressed as:

[0094] in, Let S be the sum of squared fitting errors corresponding to the parameter vector to be identified. The number of sampling points for the reference friction resistance data used in parameter identification. The sampling point number is used. By jointly identifying the attenuation parameters and output weights to be identified, the sum of squared errors between the output of the recursive convolution approximation model at each sampling time and the corresponding reference friction resistance is minimized, thereby obtaining the corresponding attenuation parameters and output weights.

[0095] It should be noted that the attenuation parameter to be identified and the output weight to be identified jointly affect the output of the approximate model of fluid discharge friction resistance. Specifically, when the value of the attenuation parameter changes, the recursive convolution state function defined in step S2 changes accordingly, thereby altering the recursive state values ​​corresponding to different sampling times; when the value of the output weight changes, the weighting relationship of each recursive convolution state in the approximate output of friction resistance changes accordingly. Therefore, this step uses the same fitting objective to jointly identify the above two types of parameters to determine the model parameters corresponding to the benchmark friction resistance data obtained in step S1.

[0096] Furthermore, during the parameter identification process, each attenuation parameter to be identified satisfies:

[0097] Each output weight to be identified satisfies:

[0098] That is, nonlinear least squares parameter identification is performed under the aforementioned positive value constraints. For the decay parameter, the positive value constraint also makes the main diagonal elements of the state matrix in step S4 negative, so that the linear external system after parameter identification maintains the asymptotic stability characteristics of step S4; the output weights participate in parameter identification according to the positive value constraints.

[0099] It should be noted that during parameter identification in this step, the recursive convolution state level and state recursion relationship determined in step S2, the frictional resistance output combination relationship determined in step S3, and the linear external system structure determined in step S4 all remain unchanged. Parameter identification is used to determine the specific values ​​of the attenuation parameters and output weights to be identified in the above model structure. Therefore, for a given level... The recursive convolution model is obtained through parameter identification. Each attenuation parameter and The output weights are adjusted without changing the number of states and the order of the linear external system of the recursive convolutional model.

[0100] Furthermore, after parameter identification is completed, the identified attenuation parameters are substituted into the state matrix established in step S4, and the identified output weights are substituted into the output matrix. Simultaneously, the recursive convolution state function in step S2 and the approximate model of fluid discharge friction resistance in step S3 are determined accordingly. This transforms the parameterized linear external system containing the parameters to be identified in step S4 into a linear external system model where the attenuation parameters and output weights are already determined, resulting in the identified linear external system model.

[0101] The identified linear external system model serves as the model basis for determining the time-varying fluid leakage frictional resistance during the emergency disconnection of the riser in step S6.

[0102] It should also be noted that when using different levels of recursive convolution state functions, the parameters of the recursive convolution models of different levels can be identified using the same set of benchmark friction resistance data formed in step S1 as the fitting target, following the parameter identification method described above. The fitting accuracy and model complexity of each recursive convolution model can then be compared under the same benchmark conditions. The fitting accuracy can be determined by considering how each recursive convolution model characterizes the main changes in the benchmark friction resistance during the rising, peak, and decay phases. The model complexity can be determined based on the number of parameters to be identified and the order of the linear external system. The comparison is made in ascending order of the recursive convolution state function series. When increasing the model series can improve the representation of the main changing characteristics of the reference friction resistance, the model series can be further increased. When the current series model can already represent the main changing characteristics of the reference friction resistance well, and the improvement in fitting effect obtained by further increasing the model series no longer has a significant comprehensive advantage compared with the increased number of parameters to be identified and the order of the linear external system, the target series is determined based on the comprehensive comparison of fitting accuracy and model complexity, and the identified linear external system model corresponding to the target series is taken as the target linear external system model.

[0103] Step S6: Determine the fluid discharge frictional resistance based on the identified linear external system model, and form the time series results of the fluid discharge frictional resistance changing with time during the emergency disconnection of the baffle.

[0104] Specifically, after identifying the attenuation parameters and output weights to be identified in step S5, and substituting the identification results into the linear external system model established in step S4, the state matrix and output matrix in the linear external system model are determined by the corresponding identification parameters. Taking the initial state of the linear external system determined in step S4 as the starting point of state evolution, the state evolution calculation is performed on the linear external system according to the state differential relationship between the recursive convolution states at different times after the emergency detachment of the riser.

[0105] Furthermore, the initial state of the identified linear external system adopts the initial state determined in step S4, namely:

[0106] Starting from the initial moment, based on the identified state matrix For the state vector Perform state evolution. At any time to be determined... Obtain the first to the second level corresponding to that moment. The recursive convolutional state is processed, and the state vector is input into the identified output relationship, which is then processed by the output matrix. For the second level to the third level The recursive convolution states are weighted and combined according to the output weights identified in step S5 to obtain the fluid discharge frictional resistance at that moment:

[0107] in, The first one identified in step S5 The output weights corresponding to the recursive convolution state function. For a moment The corresponding number The state values ​​are obtained through hierarchical recursive convolution. Therefore, for any analysis point after the emergency disconnection of the riser, the corresponding fluid discharge frictional resistance can be obtained based on the current state of the identified linear external system.

[0108] Furthermore, the aforementioned state evolution and output calculations are continuously executed in chronological order. Between adjacent moments, the state evolution result of the previous moment is used as the basis for subsequent state changes. The fluid discharge frictional resistance at different moments is obtained sequentially, and each moment is correlated with its corresponding fluid discharge frictional resistance in chronological order to form a time-series result of the fluid discharge frictional resistance changing over time during the emergency riser disconnection process. This time-series result describes the change in fluid discharge frictional resistance over time caused by drilling fluid discharge, seawater inflow, and changes in fluid motion state after the emergency riser disconnection.

[0109] Furthermore, since the eigenvalues ​​of the state matrix in step S4 are determined by the decay parameters, and the parameter identification in step S5 is performed under the constraint that all decay parameters are positive, the identified state matrix maintains asymptotic stability. Combined with the parameter identification results obtained in step S5 based on the reference friction resistance data, the identified linear external system can approximate the rise, peak, and decay processes reflected by the reference friction resistance data. Simultaneously, as time increases, the recursive convolution states at each stage gradually decay, and the fluid discharge friction resistance obtained from the output matrix gradually approaches zero, thus maintaining stable decay in the later stages of the fluid discharge process without the need for a separate cutoff function or additional decay processing to force the friction resistance to zero.

[0110] It should be noted that the fluid discharge frictional resistance determined in this step has a different technical function than the baseline frictional resistance data formed in step S1. The baseline frictional resistance data in step S1 is obtained by solving the full liquid column model at multiple sampling times, and is used in step S5 for attenuation parameter and output weight identification. After the parameter identification is completed, the identified linear external system is used to perform state evolution according to the state equation, and the fluid discharge frictional resistance corresponding to different times is continuously obtained through the output equation. Therefore, after the parameter identification is completed, it is not necessary to repeatedly perform the numerical solution of the full liquid column model for each time to be determined, thereby reducing the computational burden caused by repeated numerical solutions while maintaining the ability to characterize the time-varying process of fluid discharge frictional resistance.

[0111] It should also be noted that the fluid discharge frictional resistance determined in this step has a clear physical meaning, characterizing the time-varying frictional effect acting on the riser during the drilling fluid discharge and seawater ingress process after the riser emergency detachment. After obtaining the time-series results of the fluid discharge frictional resistance changing over time, it can be further used as the input for the time-varying fluid action in the dynamic analysis after the riser emergency detachment, to analyze the influence of the change in fluid discharge frictional resistance on the riser backlash motion.

[0112] Example 2: See Figure 2As shown, this embodiment is a deep-water riser discharge friction determination system based on recursive convolution, including: The benchmark data acquisition module is used to acquire the structural and fluid parameters of the riser in deep water drilling, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain benchmark friction resistance data. The state function construction module is used to construct a multi-level recursive convolutional state function containing several decay parameters to be identified. The approximate model building module is used to introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and to establish an approximate model of fluid discharge friction resistance by linearly combining the recursive convolution state functions of the second level and above and the corresponding output weights to be identified. The external system establishment module is used to determine the corresponding state differential relationship based on the recursive relationship between the state functions at each level of recursive convolution, and to establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance. The parameter identification module is used to identify the attenuation parameters and output weights to be identified based on the approximate model of fluid leakage friction resistance, using the benchmark friction resistance data as the fitting target. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. The friction determination module is used to determine the fluid discharge friction resistance based on the identified linear external system model, and to generate a time-series result of the fluid discharge friction resistance changing over time during the emergency disconnection of the riser.

[0113] Example 3: To verify the effectiveness of the deep-water riser discharge friction determination method based on recursive convolution of the present invention, and to analyze the approximate effect of friction resistance and model complexity under different recursive convolution model levels, numerical simulation was used for verification.

[0114] This embodiment uses MATLAB for simulation, with a simulation time of 100 s and a simulation step size of 0.01 s. A deep-water drilling riser with a length of 1000 m is used as the simulation object. The friction coefficient of the drilling fluid is set to 0.004, the friction coefficient of seawater is set to 0.002, the density of the drilling fluid is set to 1537 kg / m³, the density of seawater is set to 1025 kg / m³, the inner diameter of the riser is set to 0.4826 m, the internal flow cross-sectional area of ​​the riser is set to 0.1829 m², and the gravitational acceleration is set to 9.8 m / s².

[0115] First, following the method described in step S1 of Example 1, a full-fluid column model was established based on the aforementioned structural and fluid parameters. Numerical solutions were then performed to calculate the drilling fluid discharge and seawater ingress processes after the emergency detachment of the riser. The frictional resistance generated in the drilling fluid section and the seawater section were determined separately. Based on these results, the fluid discharge frictional resistance at each sampling time was obtained, and the results were used as baseline frictional resistance data. Under the aforementioned simulation conditions, the drilling fluid was discharged in approximately 51.12 s. To fully examine the drilling fluid discharge process and the characteristics of frictional resistance changes after discharge, the simulation time was set to 100 s.

[0116] Following the steps S2-S5 of Example 1, second-order, third-order, and fourth-order recursive convolutional models were established respectively. Using the same full-liquid column model as the baseline frictional resistance data as the fitting target, the attenuation parameters and output weights in each recursive convolutional model were identified. Specifically, the second-order recursive convolutional model includes 2 attenuation parameters and 1 output weight, requiring the identification of 3 parameters, and correspondingly forming a second-order linear external system; the third-order recursive convolutional model includes 3 attenuation parameters and 2 output weights, requiring the identification of 5 parameters, and correspondingly forming a third-order linear external system; the fourth-order recursive convolutional model includes 4 attenuation parameters and 3 output weights, requiring the identification of 7 parameters, and correspondingly forming a fourth-order linear external system.

[0117] See Figure 3 As shown, Figure 3 This is a comparison of fluid discharge frictional resistance between recursive convolution models of different orders and the full liquid column model. Figure 3 It can be seen that the second-order recursive convolution model can reflect the overall trend of fluid discharge frictional resistance increasing from zero to a peak and then gradually decreasing. However, there are still significant deviations from the full liquid column model in the rising phase, near the peak, and attenuation phase. After improving the recursive convolution model to the third order, its calculation curves are closer to the calculation results of the full liquid column model in the rising phase, peak phase, and attenuation phase, thus improving its ability to characterize the main changes in fluid discharge frictional resistance.

[0118] Further increasing the recursive convolution model to the fourth order resulted in further changes in its calculation curve compared to the third-order model. However, both the third-order and fourth-order models were able to effectively characterize the main changes in fluid discharge frictional resistance reflected by the full liquid column model. Meanwhile, the fourth-order recursive convolution model required identifying seven parameters and establishing a fourth-order linear external system, while the third-order recursive convolution model only required identifying five parameters and establishing a third-order linear external system. Considering the representational effects of different orders of recursive convolution models on the main changes in the baseline frictional resistance, as well as the number of parameters to be identified and the order of the linear external system, this embodiment determined the third order as the target order for this simulation condition and used the third-order recursive convolution model for subsequent comparative verification.

[0119] After determining the third-order recursive convolution model, in order to further verify the effectiveness of the method of the present invention in the dynamic characterization of fluid discharge friction resistance and model complexity, the third-order recursive convolution model was compared with the sinusoidal function model and the exponential polynomial model under the same working conditions as the aforementioned simulation.

[0120] The sinusoidal model used in this embodiment is formed by superimposing eight sinusoidal functions with different amplitudes, frequencies, and phases. Each sinusoidal function contains amplitude, frequency, and phase parameters, requiring the identification of a total of 24 parameters, and corresponding to the formation of a 16th-order linear external system. The exponential polynomial model used in this embodiment is formed by combining an exponential decay function with a time polynomial, requiring the identification of a total of 6 parameters, and corresponding to the formation of a 6th-order linear external system. The aforementioned third-order recursive convolution model requires the identification of 3 decay parameters and 2 output weights, totaling 5 parameters, and corresponding to the formation of a 3rd-order linear external system.

[0121] See Figure 4 As shown, Figure 4 This is a comparison chart of calculation results for different approximate models of frictional resistance. Figure 4 It can be seen that during the drilling fluid discharge process from 0 to 51.12 s, the third-order recursive convolution model, the sinusoidal function model, and the exponential polynomial model can all reflect the main trend of the fluid discharge friction resistance increasing from zero, reaching a peak, and then gradually decreasing. This indicates that the third-order recursive convolution model can use a lower-order linear external system to characterize the main friction resistance variation characteristics during the drilling fluid discharge process.

[0122] When the time exceeded approximately 51.12 seconds and the drilling fluid discharge was completed, the sinusoidal model still exhibited significant oscillations, with its output continuously changing in both positive and negative directions over time, making it difficult to reflect the gradual decay of the fluid discharge frictional resistance after discharge. In contrast, the exponential polynomial model and the third-order recursive convolution model both maintained a gradually decaying trend. For the third-order recursive convolution model of this invention, since the decay parameters corresponding to each level of the recursive convolution state function are all positive, the resulting linear external system maintains asymptotic stability. Therefore, as time increases, each level of the recursive convolution state gradually decays, and the fluid discharge frictional resistance obtained by linearly combining the output weights gradually approaches zero, thus reflecting the decay process of frictional resistance after the drilling fluid discharge is completed.

[0123] Further comparison of the structural complexity of different approximation models reveals that the third-order recursive convolution model in this embodiment only requires identifying 5 parameters and establishing a third-order linear external system; the exponential polynomial model requires identifying 6 parameters and establishing a sixth-order linear external system; and the eight-term sine function model requires identifying 24 parameters and establishing a sixteenth-order linear external system. Therefore, while all models can characterize the main changing trend of fluid discharge friction resistance during the drilling fluid discharge stage, the third-order recursive convolution model of this invention can achieve dynamic characterization of fluid discharge friction resistance with fewer parameters to be identified and a lower-order linear external system. Simultaneously, it can maintain stable attenuation after drilling fluid discharge, thereby reducing the complexity of parameter identification and linear external system modeling.

[0124] In summary, under this simulation condition, by comparing the fitting effects and model complexity of second-order, third-order, and fourth-order recursive convolution models, the third-order recursive convolution model was selected as the target model. This third-order recursive convolution model can effectively characterize the rise, peak, and decay processes of fluid discharge frictional resistance, requiring only 5 parameters to be identified and a third-order linear external system. Compared with the sinusoidal and exponential polynomial models used in this embodiment, it maintains an effective characterization of the main changes in fluid discharge frictional resistance while having a lower model order and parameter scale, and can ensure a stable decay of frictional resistance after fluid discharge, thus achieving a better overall balance between the approximation effect of frictional resistance and model complexity.

[0125] Example 4: This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0126] This computer device can be a server, and its internal structure diagram can be as follows: Figure 5 As shown, the computer device includes a processor, internal memory, non-volatile storage medium, I / O interface, and communication interface. The processor, internal memory, non-volatile storage medium, and I / O interface are connected via a system bus, and the communication interface is connected to the I / O interface. The processor provides computing and control capabilities; the non-volatile storage medium stores the operating system, computer programs, and a database; the internal memory provides the environment for the operation of the operating system and computer programs; the database stores relevant data; and the communication interface enables communication between the computer device and external terminals. When executed by the processor, the computer program implements a method for determining the friction of a deep-water riser pipe based on recursive convolution.

[0127] Those skilled in the art will understand that Figure 5The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0128] Example 5: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0129] If the functions implemented by the method are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art or the current technical solution, can be embodied in the form of a software product. This current computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0130] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0131] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0132] The technical features of this invention not described can be implemented by or using existing technology, and will not be repeated here. Of course, the above description is not a limitation of this invention, and this invention is not limited to the examples above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of this invention should also be within the protection scope of this invention.

Claims

1. A method for determining the discharge friction of a deep-water riser based on recursive convolution, characterized in that, Includes the following steps: Step S1: Obtain the structural and fluid parameters of the deep-water drilling riser, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain the benchmark friction resistance data. Step S2: Construct a multi-level recursive convolutional state function containing several attenuation parameters to be identified; each level of the recursive convolutional state function corresponds to an attenuation parameter to be identified; wherein, the first-level recursive convolutional state function is an exponential decay function determined by its corresponding attenuation parameter to be identified, and the second-level and above recursive convolutional state functions are obtained by convolving the previous level recursive convolutional state function with the exponential decay function determined by the attenuation parameter to be identified in the current level; Step S3: Introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and perform linear combination based on the recursive convolution state functions of the second level and above and the corresponding output weights to be identified to establish an approximate model of fluid discharge friction resistance. Step S4: Determine the corresponding state differential relationship based on the recursive relationship between the recursive convolution state functions at each level, and establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance; the order of the linear external system model is consistent with the order of the multi-level recursive convolution state function. Step S5: Using the benchmark friction resistance data as the fitting target, the parameters to be identified and the output weights to be identified are identified based on the fluid leakage friction resistance approximation model. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. Step S6: Determine the fluid discharge frictional resistance based on the identified linear external system model, and form the time series results of the fluid discharge frictional resistance changing with time during the emergency disconnection of the baffle.

2. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, Step S1 specifically includes: Obtain the structural and fluid parameters of the riser in deepwater drilling; the structural parameters include the total length of the riser, the inner diameter of the riser, and the internal flow cross-sectional area of ​​the riser; the fluid parameters include the density of seawater, the density of drilling fluid, the friction coefficient of seawater, and the friction coefficient of drilling fluid. Based on structural and fluid parameters, the drilling fluid inside the riser and the seawater entering from the lower end of the riser are considered as a whole fluid column. A whole fluid column model is established based on the balance between the gravity, inertial force and friction of the fluid column. The frictional resistance generated by the drilling fluid section and the frictional resistance generated by the seawater section are determined based on the full-fluid column model, and the fluid discharge frictional resistance is determined based on the frictional resistance generated by the drilling fluid section and the frictional resistance generated by the seawater section. The full liquid column model is numerically solved according to the preset sampling time to obtain the fluid discharge friction resistance corresponding to each preset sampling time, and the reference friction resistance data is formed based on each preset sampling time and the corresponding fluid discharge friction resistance.

3. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, In step S2, construct A series of recursive convolution state functions are defined, and corresponding attenuation parameters to be identified are set for each level of the recursive convolution state function. It is a positive integer not less than 2; The first-level recursive convolution state function is represented as: in, For a moment The corresponding first-level recursive convolution state function value, The decay parameter to be identified corresponds to the first-level recursive convolution state function. Represents the natural exponential function; The state functions of recursive convolutions at levels two and above are expressed as follows: in, Let be the order number of the recursive convolution state function, and ; For a moment The corresponding number Level recursive convolution state function value, For the integration time The corresponding number Level recursive convolution state function value, For the first The decay parameter to be identified corresponding to the recursive convolution state function. For the first The decay parameter to be identified corresponding to the recursive convolution state function; The identified decay parameter corresponding to the first-level recursive convolution state function and the identified decay parameter corresponding to the second-level and above recursive convolution state functions are all greater than 0.

4. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, In step S3, when the number of levels of the multi-level recursive convolution state function is At that time, it was the second level to the third level. The recursive convolution state functions of the second to third stages each set the corresponding output weights to be identified, and then... Each recursive convolutional state function is multiplied by its corresponding output weight to be identified, and the resulting products are summed to establish an approximate model of the fluid discharge friction resistance.

5. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, In step S4, the state differential relationship corresponding to the first-level recursive convolution state function is determined based on the recursive relationship between the recursive convolution state functions at each level. The formula is as follows: Level 2 to Level 1 The state differential relationship corresponding to the hierarchical recursive convolution state function is expressed by the following formula: in, For a moment The corresponding first-level recursive convolution state function value, This is the time derivative of the first-order recursive convolution state function. Let be the order number of the recursive convolution state function, and ; For a moment The corresponding number Level recursive convolution state function value, For the first The time derivative of the recursive convolution state function. For a moment The corresponding number Level recursive convolution state function value, For the first The decay parameter to be identified corresponding to the recursive convolution state function. For the first The decay parameter to be identified corresponding to the recursive convolution state function; Level 1 to Level 2 The state vector is composed of recursive convolutional state functions. The linear relationship between the derivative of the state vector and the state vector is determined based on the state differential relationship, and the state equation of the linear external system model is constructed. The linear relationship between the approximate output of the fluid discharge friction resistance and the state vector is determined based on the approximate model of fluid discharge friction resistance, and the output equation of the linear external system model is constructed. The linear external system model is established based on the state equation and the output equation.

6. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, In step S5, the reference friction resistance at each preset sampling time is determined based on the reference friction resistance data, and the approximate value of the friction resistance at each preset sampling time is determined based on the fluid leakage friction resistance approximation model. The parameter identification target is to minimize the sum of squared errors between the reference friction resistance and the approximate value of friction resistance at each preset sampling time. The attenuation parameters to be identified corresponding to each level of recursive convolution state function and the output weights to be identified corresponding to each level of recursive convolution state function above the second level are jointly identified to obtain the corresponding attenuation parameters and output weights. Substitute the identified attenuation parameters and output weights into the linear external system model to determine the corresponding parameters in the linear external system model, thus obtaining the identified linear external system model.

7. The method for determining the discharge friction of deep-water riser pipe based on recursive convolution according to claim 1, characterized in that, In step S5, for multi-level recursive convolution state functions of different orders, the same set of benchmark friction resistance data is used as the fitting target for parameter identification. The fitting effect and model complexity of the approximate models of fluid discharge friction resistance corresponding to different orders are compared, and the target order is determined based on the comparison results. The identified linear external system model corresponding to the target order is taken as the target linear external system model. The order of the target linear external system model is consistent with the target order. In step S6, the initial state of the target linear external system model is used as the starting point for state evolution. The state evolution is carried out according to the state equation of the target linear external system model to obtain the recursive convolution state at different times. The fluid discharge friction resistance at each time is determined according to the output equation of the target linear external system model. The state evolution and fluid discharge friction resistance determination process are executed continuously in time sequence to form the time sequence result of the fluid discharge friction resistance changing with time during the emergency disconnection of the water pipe.

8. A system for determining the frictional resistance of a deep-water riser pipe based on recursive convolution, characterized in that, The steps for performing the deepwater riser discharge friction determination method based on recursive convolution as described in any one of claims 1 to 7 include: The benchmark data acquisition module is used to acquire the structural and fluid parameters of the riser in deep water drilling, establish a full liquid column model based on the structural and fluid parameters, and numerically solve the fluid discharge process after the riser is detached in an emergency to obtain benchmark friction resistance data. The state function construction module is used to construct a multi-level recursive convolutional state function containing several decay parameters to be identified. The approximate model building module is used to introduce corresponding output weights to be identified for the recursive convolution state functions of the second level and above, and to establish an approximate model of fluid discharge friction resistance by linearly combining the recursive convolution state functions of the second level and above and the corresponding output weights to be identified. The external system establishment module is used to determine the corresponding state differential relationship based on the recursive relationship between the state functions at each level of recursive convolution, and to establish a linear external system model based on the state differential relationship and the approximate model of fluid leakage friction resistance. The parameter identification module is used to identify the attenuation parameters and output weights to be identified based on the approximate model of fluid leakage friction resistance, using the benchmark friction resistance data as the fitting target. The identification results are then substituted into the linear external system model to obtain the identified linear external system model. The friction determination module is used to determine the fluid discharge friction resistance based on the identified linear external system model, and to generate a time-series result of the fluid discharge friction resistance changing over time during the emergency disconnection of the riser.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method for determining the discharge friction of a deep-water riser based on recursive convolution as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for determining the discharge friction of a deep-water riser based on recursive convolution as described in any one of claims 1 to 7.

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