Construction method of submarine pipeline inter-span erosion prediction model under wave current condition

Abstract

The invention relates to a method for constructing a submarine pipeline inter-span erosion prediction model under a wave current condition, and the method comprises the steps: introducing a flow velocity ratio and a KC number based on the previous research, and calibrating the influence of the flow velocity ratio m, the KC number and different burial depth ratios e / D on the suspended span expansion speed of a submarine pipeline under different hydrodynamic forces, and a pipeline suspended span expansion speed prediction formula considering the wave flow effect under the seabed clear water condition is constructed. The method is suitable for a suspended span expansion prediction formula under pure flow, pure wave and wave flow effects under the clear water condition, fills the blank in the field of three-dimensional scour prediction under the clear water condition, and has important practical significance for design, maintenance and protection of submarine pipelines.

Description

Technical Field

[0001] The present invention relates to a method for constructing a prediction model for inter-span erosion of submarine pipelines under wave-current conditions, belonging to the technical field of submarine pipeline design. Background Art

[0002] In the field of ocean engineering, submarine pipelines, as key facilities for transporting important energy sources such as oil and natural gas, their safety and stability are of crucial importance. However, for a long time, the scour problem of the bed around the pipeline has been the main reason threatening the safety of submarine pipelines and leading to frequent accidents. The situation of submarine pipeline damage due to scour is relatively complex, and the main influencing factor is the length of the span. In contrast, the relationship with the scour depth is relatively small. When the bed around the submarine pipeline is scoured, it will cause the loss of soil under the pipeline, and then form a pipeline span. As the span length increases, the stress borne by the pipeline continuously increases. Once it exceeds the bearing limit of the pipeline material, it is extremely easy to cause serious accidents such as pipeline rupture and leakage, which will not only cause huge economic losses, but also bring catastrophic damage to the marine ecological environment.

[0003] At present, although certain achievements have been made in the research on submarine pipeline scour, such as predecessors proposed a span extension prediction model for three-dimensional scour of submarine pipelines under pure flow and a span extension prediction model for scour of submarine pipelines under three-dimensional wave-current combination in a movable bed condition, there is still a blank in the prediction of wave-current combination scour under clear water conditions. In the actual marine environment, the situation of wave-current combination widely exists, and the clear water condition is not rare. It is of great necessity and obvious benefits to predict the wave-current combination scour under clear water conditions. On the one hand, this can complement the existing prediction system and form a unified and comprehensive prediction model, enabling the model to cover the span extension situations of clear water and movable bed under pure flow, pure wave, and wave-current actions, providing a more perfect theoretical basis for the safety assessment of submarine pipelines; on the other hand, accurate prediction can help engineers understand the stress and deformation conditions of the pipeline under different working conditions in advance, so as to formulate more targeted and economical protection measures, effectively reducing the risk of accidents caused by scour damage of submarine pipelines and ensuring the safety and stability of marine energy transportation.

[0004] To sum up, carrying out the prediction research on wave-current combination scour under clear water conditions has important practical significance and application value, and it is urgent to deeply explore and innovate in related fields. Summary of the Invention

[0005] The present invention provides a method for constructing a prediction model for inter-span erosion of submarine pipelines under wave-current conditions, which is applicable to the span extension prediction formulas under pure flow, pure wave, and wave-current actions under clear water conditions, filling the blank in the field of three-dimensional scour prediction under clear water conditions, and having important practical significance for the design, maintenance, and protection of submarine pipelines.

[0006] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0007] A method for constructing a prediction model of submarine pipeline spanwise erosion under wave and current conditions specifically includes the following steps:

[0008] Step S1, during the pipeline scouring process, the lateral expansion speed V of the free span at the bottom of the pipeline h is related to the following eleven physical quantities: V h = f(g(s - 1), D, υ, d, e, n, h, T, U c , U w ), where V h is the lateral expansion speed of the free span at the bottom of the pipeline, g(s - 1) is the submerged unit weight of sediment, s = 2.65 is the relative specific gravity of sediment, D is the pipeline diameter, υ = 10 -6 m 2 / s is the viscosity of water, d is the median grain size of sediment, e is the depth of the pipeline buried in the seabed, n is the porosity of the seabed, h is the water depth, T is the wave period, U c is the near-bottom current velocity, U w is the near-bottom oscillatory velocity;

[0009] Simplify the functional dependence relationship between the eleven physical quantities into a function involving nine dimensionless quantities: Among them, θ cw is the Shields number, representing the relationship between the seabed shear stress and sediment incipience, e / D is the ratio of the pipeline burial depth to the pipeline diameter, the critical Shields number θ crit is a parameter for distinguishing between movable bed and clear water, θ crit is calculated through the Reynolds number Re of the sediment particle size, and the existing functional dependence relationship between the two is θ crit = 0.165(Re + 0.6) -0.8 + 0.045exp(-40Re -1.3 ), Re ≥ 1, Fr is the Froude number, KC is the Keulegan - Carpenter number, n is the porosity, m is the flow velocity intensity, m = U c / (Uc + U w ), KC = U w T p / D, T p is the period;

[0010] The effect of the Shields number is considered through the Shields number ratio to further simplify the function of the nine dimensionless quantities into:

[0011] Under the condition of clear water on the seabed, θ cw < θ crit , 0.01 < Fr <0.15;

[0012] Step S2. Based on the physical scouring process, there is a relationship between the difference in sediment transport rate between entering and leaving the scour pit, the lateral expansion speed of the pipeline bottom span, and the scouring depth: Δq is the difference in sediment transport rate, and S’ is the scouring depth under clear water conditions on the seabed;

[0013] Step S3. The expression for the difference in sediment transport rate between leaving and entering the span shoulder area is:

[0014]

[0015] where α is the shear stress amplification factor,

[0016] Based on the Shields number ratio under clear water conditions in Step S1, we get:

[0017]

[0018] where, represents the ratio of the seabed scouring depth under clear water conditions below the pipeline to the seabed scouring depth under movable bed conditions below the pipeline, that is, S’ is the scouring depth under clear water conditions on the seabed, and S is the scouring depth under movable bed conditions on the seabed;

[0019] Step S4. Based on the dependency analysis between the lateral expansion speed V of the pipeline bottom span h and the difference in sediment transport rate, we get:

[0020]

[0021] Step S5. The maximum vertical two-dimensional scouring depth at the pipeline bottom is expressed as: Continuing, the exponential function of the maximum scouring depth in the hydrodynamic environment including pure flow, pure wave, and wave-current at the pipeline bottom is: where B is determined by the actual test data rate;

[0022] Step S6. Based on the three-dimensional equilibrium scouring depth exponential function obtained in Step S5 and combining the flow velocity intensity m and the Keulegan Carpenter number dependency Φ(KC) introduced in Step S1 and Step S3, the formula for the span expansion speed is:

[0023]

[0024] Furthermore, in Step S5, set B = -6;

[0025] Furthermore, in Step S6, set A = 3;

[0026] Further, in step S6, in the obtained formula for the overhang expansion speed,

[0027]

[0028] Further, for the formula for the overhang expansion speed the formula for measuring the prediction accuracy is:

[0029]

[0030] where R 2 is the fitting performance of the overhang expansion speed formula relative to the average prediction, N is the number of data sets, j is the measured value, p is the predicted value, is the average value of the overhang expansion speed measurement values;

[0031] Further, the value range of R 2 is from 0 to 1. When R 2 = 1, it indicates the best prediction accuracy. If R 2 > 0, it indicates an improvement in the prediction close to the average prediction.

[0032] Through the above technical solutions, compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The method for constructing a prediction model for submarine pipeline inter-span erosion under wave-current conditions provided by the present invention predicts the combined wave-current scouring under clear water conditions, can further complement relevant content, thereby forming a new unified prediction model, enabling the model to predict the clear water and movable bed overhang expansion under pure flow, pure wave, and wave-current actions, making the prediction model more perfect and comprehensive;

[0034] 2. The method for constructing a prediction model for submarine pipeline inter-span erosion under wave-current conditions provided by the present invention, based on previous research, introduces the flow velocity ratio to predict the combined wave-current scouring under clear water conditions, thereby better protecting pipelines that face unstable overhang expansion factors due to being designed to move laterally to adapt to thermal expansion, avoiding pipeline sagging and damage caused by the enlargement of scouring pits, and reducing losses and risks caused by pipeline damage;

[0035] 3. The method for constructing a prediction model for submarine pipeline inter-span erosion under wave-current conditions provided by the present invention predicts the combined wave-current scouring under clear water conditions, which can better fit the actual marine environment and meet the requirements for submarine pipeline protection and management in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention will be further described below in conjunction with the drawings and embodiments.

[0037] Figure 1 It is a schematic diagram of the dimensionless span extension velocity considering the flow velocity intensity dependence provided by the present invention. Specific embodiments

[0038] Now, the present invention will be further described in detail with reference to the accompanying drawings. In the description of the present application, it should be understood that the orientation or positional relationship indicated by terms such as "left side", "right side", "upper part", "lower part", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not represent the importance of components, so they cannot be understood as limitations on the present invention. The specific dimensions adopted in this embodiment are only for illustrating the technical solution by way of example, and do not limit the protection scope of the present invention.

[0039] This application is based on the span extension prediction models for three-dimensional scour of submarine pipelines under pure flow and the span extension prediction models for three-dimensional wave-current combined scour of submarine pipelines under movable bed conditions proposed by predecessors, and further complements the prediction of wave-current combined scour under clear water conditions, thus forming a new unified prediction model that can predict the clear water span extension under pure flow, pure wave, and wave-current action.

[0040] Regarding the prediction models proposed by predecessors, the present application adopts the research by Hansen et al. (1991) who first studied the expansion speed of the suspended span length under the pipeline based on the sediment conservation equation at the cross-shoulder under steady flow. The research found that there is a significant relationship between the suspended span expansion and the sag of the pipeline. It was also found that the burial depth also affects the suspended span expansion speed. The formula they proposed shows that the suspended span expansion speed decreases with the increase of the pipeline burial depth. Wu and Chiew (2012) studied the lateral expansion speed of the suspended span caused by steady flow under clear water conditions (less than the critical Shields number, θ < θc) through a physical experimental model. Starting from four dimensionless parameters that may have an impact (steady force: the ratio of pipeline burial depth, water depth to pipe diameter; environmental force: Shields number (θ), Froude number (Fr)), they studied the influencing factors of the suspended span expansion speed. The study pointed out that the Froude number (Fr) closely related to the fluid depth is the key factor determining the suspended span expansion speed. The first and second suspended span expansion speeds also appeared in their research experiments, and they were defined as the rapid development stage (a rapid phase of development, where the suspended span develops at a relatively fast speed) and the slack development stage (a slack phase of development, where the suspended span develops at a relatively slow speed), and it was shown that the duration of the two stages is related to the balance between the steady force and the environmental force. Dogan et al. (2021) studied the prediction formula for the suspended span expansion speed under clear water scour under wave loads through physical experiments. The study showed that the relationship between the suspended span expansion speed under pure wave action in the clear water state and the Shields number is weakly correlated, but strongly correlated with the KC number. Sui et al. (2021) proposed a prediction formula for the suspended span expansion speed caused by steady flow under unified clear water and movable bed conditions by combining dimensional analysis and physical experimental data analysis. The effective Shields number was introduced into the formula to explore the relationship between the suspended span expansion and the Shields number. Among them, for the movable bed condition, it is the difference between the Shields number and the critical Shields number (θ - θcrit), and for the clear water condition, it is the ratio of the Shields number to the critical Shields number (θ / θcrit). The study showed that the first and second suspended span expansion speeds also appeared in the suspended span expansion speed, and it was also demonstrated that the Shields number is the most important factor affecting the suspended span expansion speed rather than the Froude number (Fr).

[0041] In these models studied by predecessors, if the reason for the weak dependence on the Shields number cannot be clarified and the clear water data from multiple studies cannot be compared in the same framework to predict the result of no scour. To improve the above problems, the present application studied the mechanism of suspended span expansion after superimposing water flow and waves under clear water conditions, provided a method for constructing a prediction model for submarine pipeline inter-span erosion under wave-current conditions, and finally was able to derive an ideal prediction formula. Specifically, it includes the following steps:

[0042] Step S1, during the pipeline scour process, the lateral expansion speed V of the suspended span at the bottom of the pipelineh is related to the following eleven physical quantities: V h = f(g(s - 1), D, υ, d, e, n, h, T, U c , U w ), where V h is the lateral expansion velocity of the pipeline bottom suspension span, g(s - 1) is the buoyant unit weight of sediment, s = 2.65 is the relative specific gravity of sediment, D is the pipeline diameter, υ = 10 -6 m 2 / s is the viscosity of water, d is the median grain size of sediment, e is the pipeline burial depth into the seabed, n is the seabed porosity, h is the water depth, T is the wave period, U c is the near - bed current velocity, U w is the near - bed fluctuating velocity;

[0043] The functional dependencies among the eleven physical quantities are simplified to a function involving nine dimensionless quantities: where θ cw is the Shields number, representing the relationship between the seabed shear stress and sediment incipient motion, e / D is the ratio of pipeline burial depth to pipeline diameter, the critical Shields number θ crit is a parameter for distinguishing movable bed and clear water, θ crit is calculated through the Reynolds number Re of the sediment particle size, and the existing functional dependency between them is θ crit = 0.165(Re + 0.6) -0.8 + 0.045exp(-40Re -1.3 ), Re ≥ 1, Fr is the Froude number, KC is the Keulegan - Carpenter number, n is the porosity, m is the velocity intensity, m = U c / (U c+ U w ), KC = U w T p / D, T p is the period;

[0044] The effect of the Shields number is considered through the Shields number ratio , which defines the comparison of the current intensity with the initial motion condition of sediments. Under the clear - water condition on the seabed, θ cw < θ crit , 0.01 < F r < 0.15. Therefore, the dependence of the Froude number can be ignored, while the dependence on the KC number is relatively large. So, under the clear - water condition, the KC number cannot be ignored. As for the porosity, it is usually a constant (about 0.4) in sandy soil and can also be ignored. Then, the function of the nine dimensionless quantities is further simplified to:

[0045]

[0046] In step S2, based on the physical scouring process, there is a relationship between the difference in sediment transport rate between entering and leaving the scour pit and the lateral expansion velocity and scouring depth at the bottom of the pipeline: Δq is the difference in sediment transport rate, and S’ is the scouring depth under clear water conditions on the seabed.

[0047] In step S3, the expression for the difference in sediment transport rate between leaving and entering the span shoulder area is:

[0048]

[0049] where α is the shear stress amplification factor,

[0050] Based on the Shields number ratio under clear water conditions in step S1, we get:

[0051]

[0052] where, represents the ratio of the seabed scouring depth under clear water conditions below the pipeline to the seabed scouring depth under moving bed conditions below the pipeline, that is S’ is the scouring depth under clear water conditions on the seabed, and S is the scouring depth under moving bed conditions on the seabed.

[0053] In step S4, based on the dependency analysis between the lateral expansion velocity V h at the bottom of the pipeline and the difference in sediment transport rate, we get:

[0054]

[0055] In step S5, the maximum vertical two-dimensional scouring depth at the bottom of the pipeline is expressed as: Continuing, the exponential function of the maximum scouring depth in the hydrodynamic environment including pure flow, pure wave, and wave-current at the bottom of the pipeline is: where B is determined from the experimental data rate. For clear water conditions, B = -6.

[0056] In step S6, based on the three-dimensional equilibrium scouring depth exponential function obtained in step S5 and combining the flow velocity intensity m and the Keulegan Carpenter number dependency Φ(KC) introduced in step S1 and step S3, the formula for the span expansion velocity is:

[0057]

[0058] The coefficient A = 3.

[0059] Regarding the span expansion velocity formula obtained in step S6, Υ c (m), the dependency of the span expansion velocity on m is introduced, specifically The KC number is still retained, with its limit being and the cross-span lateral expansion speed V h The dependence on the difference in sediment transport rate is specifically

[0060] After forming the above unified prediction model, it is necessary to test its prediction performance. The formula for measuring prediction accuracy is as follows:

[0061]

[0062] where R 2 is the fitting performance of the cross-span expansion speed formula relative to the average prediction, N is the number of data sets, j is the measured value, p is the predicted value, is the average value of the cross-span expansion speed measured values. R 2 ranges from 0 to 1. When R 2 = 1, it indicates the best prediction accuracy. If R 2 > 0, it indicates an improvement in the prediction close to the average prediction.

[0063] To more intuitively see the accuracy of the prediction model provided by this application, Figure 1 As shown, this application compares the aforementioned previous model with the prediction model of this application in the same frame. A total of 82 experimental data of clear-water scouring cross-span expansion speed are used in the whole figure. These data consist of 16 experimental cases of wave-current experiments under clear water provided by this application, 3 pure-current experimental cases of Hansen et al. (1991), 1 pure-current experimental case of Sui et al. (2021), 47 pure-current experimental cases of Wu and Chiew (2012), and 15 pure-wave experimental cases of Dogan and Arisoy (2021).

[0064] Among them, regarding the formula for the clear-water cross-span expansion speed under the action of unidirectional steady flow load proposed by Sui et al. (2021) through a combination of dimensional analysis and physical experimental data analysis

[0065]

[0066] The prediction formula for cross-span expansion under the action of wave load under clear-water conditions proposed by Dogan et al. (2021) is:

[0067]

[0068] Incorporating the data of Dogan et al. (2021) into the prediction model provided by this application can explain the reason for the weak dependence on the Shields number under the condition of combined wave and current action, that is, the data they provided are exactly near the critical value of sediment incipient motion

[0069] As for Hansen et al. (1991), he derived a general semi-theoretical formula for predicting the migration speed of the free span under a submarine pipeline, and this formula is

[0070]

[0071] However, the clear water dataset proposed by Wu and Chiew (2012) cannot be compared within the framework proposed by Hansen et al. (1991). It can be obtained from the formula derived by Hansen et al. (1991) that the water flow intensity of the clear water dataset proposed by Wu and Chiew (2012) is too weak to obtain (αθ - θ c ) < 0, that is, the result of predicting no scouring has been improved in the prediction model provided in this application.

[0072] Figure 1 As shown, the solid line represents the model prediction, and the dotted line represents the threshold of the prediction model as ±2 (that is, the experimental data distributed within the dotted line conforms to the prediction model). The flow intensity m is represented by the color gradually changing from blue to yellow, and the yellow dataset (pure flow) is completely distributed around the predicted value. Obviously, this application shows in the figure that the predicted R 2 = 0.53, verifying that the formula of this model and the expression of Υ c (m) can predict the cross-span lateral expansion rate under pure wave, wave-current, and pure flow conditions, and the prediction performance is good.

[0073] In summary, based on the previous research, this application introduces the flow velocity ratio and the KC number, calibrates the influence of the flow velocity ratio m, KC number, and different burial depth ratios e / D on the cross-span expansion speed of the submarine pipeline under different hydrodynamic actions, and constructs a prediction formula for the cross-span expansion speed of the pipeline considering wave-current action under clear water conditions on the seabed.

[0074] Those skilled in the art of this technology can understand that unless otherwise defined, all terms (including technical terms and scientific terms) used here have the same meaning as the general understanding of those of ordinary skill in the field to which this application belongs. It should also be understood that terms defined in general dictionaries should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as here.

[0075] The meaning of "and / or" described in this application refers to the situation where each exists alone or both exist simultaneously.

[0076] The meaning of "connection" described in this application can be a direct connection between components or an indirect connection between components through other components.

[0077] Inspired by the above-described ideal embodiments of the present invention, through the above description, relevant staff can make various changes and modifications completely within the scope without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions, characterized in that: The specific steps include: Step S1: During the pipeline flushing process, the lateral expansion speed V of the suspended span at the bottom of the pipeline h Related to the following eleven physical quantities: V h =f(g(s-1),D,υ,d,e,n,h,T,U c ,U w ), where V h is the lateral expansion velocity of the suspended span at the bottom of the pipeline, g(s-1) is the floating density of the sediment, s=2.65 is the relative density of the sediment, D is the pipeline diameter, υ=10 -6 m 2 / s is the viscosity of water, d is the median particle size of sediment, e is the depth of the pipeline buried in the seabed, n is the porosity of the seabed, h is the water depth, T is the wave period, U c is the velocity of the water flow near the bottom, U w is the near-bottom fluctuating velocity; The functional dependencies between the eleven physical quantities are simplified to functions involving nine dimensionless quantities: Among them, θ cw is the Shields number, which represents the relationship between seabed shear stress and sediment initiation, e / D is the ratio of pipeline burial depth to pipeline diameter, and the critical Shields number θ crit is the parameter that distinguishes the moving bed from the clean water, θ crit The functional dependence between the two is calculated by the Reynolds number Re of the sediment particle size. crit =0.165(Re+0.6) -0.8 +0.045exp(-40Re -1.3 ), Re ≥ 1, Fr is the Froude number, KC is the KeuleganCarpenter number, n is the porosity, m is the velocity intensity, m = U c / (U c+ U w ), KC=U w T p / D,T p For the cycle; The effect of Shields number is through the Shields number ratio Considering this, the function of the nine dimensionless quantities can be further simplified as follows: Under clear seawater conditions, θ cw <θ crit , 0.01 <F r <0.15; Step S2, based on the physical scouring process, the difference in sediment transport rate between entering the scouring pit and leaving the scouring pit is related to the lateral expansion speed of the suspended span at the bottom of the pipeline and the scouring depth: Δq is the difference in sediment transport rate, S' is the scouring depth under clear seabed conditions; Step S3, the difference expression of sediment transport rate between leaving the shoulder area and entering the shoulder area is: Where α is the shear stress amplification factor, Based on the Shields number ratio under the clear water condition in step S1, we obtain: in, It represents the ratio of the scouring depth of the seabed below the pipeline under the condition of clear seabed water to the scouring depth of the seabed below the pipeline under the condition of moving bed, that is, S' is the scouring depth under seabed clear water conditions, and S is the scouring depth under seabed moving bed conditions; Step S4, based on the lateral expansion speed V of the suspended span at the bottom of the pipeline h The dependence analysis between the difference of sediment transport rate and the value of the sediment transport rate shows that: Step S5, the maximum vertical two-dimensional scouring depth of the pipeline bottom is expressed as: The exponential function of the maximum scour depth under the hydrodynamic environment of pure flow, pure wave and wave flow at the bottom of the pipeline is obtained as follows: Among them, B is determined by the actual test data rate; Step S6, based on the three-dimensional balanced scour depth index function obtained in step S5, combined with the velocity intensity m and Keulegan Carpenter number dependency Φ(KC) introduced in steps S1 and S3, the formula for the span extension velocity is obtained as follows:

2. The method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions according to claim 1 is characterized by: In step S5, B=-6 is set.

3. The method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions according to claim 1, characterized in that: In step S6, A=3 is set.

4. The method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions according to claim 1, characterized in that: In step S6, the formula for the span extension speed is obtained:

5. The method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions according to claim 1, characterized in that: Formula for span extension speed The prediction accuracy measurement formula is: Among them, R 2 is the fitting performance of the span extension velocity formula relative to the average prediction, N is the number of data sets, j is the measured value, p is the predicted value, is the average value of the span extension velocity measurements.

6. The method for constructing a prediction model for inter-span erosion of submarine pipelines under wave and current conditions according to claim 1, characterized in that: R 2 The value range is from 0 to 1. 2 =1, indicating the best prediction accuracy. 2 >0, indicating that the forecast is close to the improvement of the mean forecast.

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