A method for predicting the expansion speed of submarine pipeline span

Abstract

The present invention relates to a method for predicting the expansion speed of a submarine pipeline span. The method introduces flow velocity intensity, calibrates the relationship between flow velocity intensity and span expansion speed under different hydrodynamic effects, and proposes a pipeline span expansion speed prediction formula considering wave and current effects under a unified moving bed condition. The method can accurately predict the lateral expansion speed of the span under pure wave, wave and current and pure current conditions.

Description

Technical Field

[0001] The invention relates to a method for predicting the expansion speed of a submarine pipeline free span, belonging to the technical field of submarine pipeline design, and in particular to the prediction of the free span of a pipeline caused by the action of water flow or waves. Background Art

[0002] Since the world's first submarine pipeline was put into production in the Gulf of Mexico in the United States in 1954, there have been hundreds of oil field shutdowns and marine pollution incidents caused by pipeline damage in various countries around the world. After entering the 1990s, submarine pipeline damage accidents have increased year by year. In 2002 alone, China National Offshore Oil Corporation had four submarine pipeline damage accidents, which not only affected offshore oil and gas production, but also cost tens of millions of yuan to repair. Data shows that the probability of damage / leakage per 1,000 kilometers of pipelines in the world is currently 0.2% per year. These accidents not only bring huge economic losses to oil-producing countries, but also cause serious damage to the local ecology. Therefore, the safety of submarine pipelines has received great attention from the marine engineering community of various countries, and statistics and investigations have begun to be conducted on the causes of pipeline accidents. Relevant departments have conducted statistics on pipeline accidents in the Gulf of Mexico and found that the scouring of the bed around the pipeline is the main cause of the accident.

[0003] The main reason for the damage of submarine pipelines due to scouring is the length of the span. Regarding the span in the prior art, for example, the application with publication number CN107742039B provides a submarine pipeline design method based on the vortex-induced vibration fatigue life of the span. The background of the research on the span is that when the ocean currents and waves flow through the span section, vortex shedding will occur, which will trigger periodic alternating forces, causing vortex-induced vibration of the pipeline and fatigue failure of the pipeline. The evaluation and control parameters involved include pipeline structure size, elastic modulus, structural modal damping ratio, effective wave height, effective wave period, pipeline stress during unit amplitude vibration, gully depth at the span, turbulence intensity, Reynolds number, fatigue life SN curve, pipeline vibration mode function, etc. That is to say, the above-mentioned public application considers the expansion of pipeline span from the perspective of how to avoid vortex-induced vibration combined with fatigue damage accumulation.

[0004] After a deeper understanding of the mechanism of span extension, it is found that the size of the pipeline may range from 20-30 cm to more than 1.0 m, the length of the pipeline may range from hundreds of meters to thousands of meters, the water depth may range from tens of meters to hundreds of meters, the pipeline may be laid on the seabed, may be buried, or may be partially buried. Of course, in most places, the pipeline is required to be buried underground, which can avoid damage from fishing gear or anchors, and also avoid pipeline scouring. When the pipeline is exposed to the action of the current and the seabed is erodible (when it is laid on the seabed or partially buried), scouring may occur around the pipeline under the action of wave currents (waves / currents), which may cause the pipeline to free span (this process we call lateral span extension). The pipeline along the length of the span may or may not sag in the generated scouring holes. If the pipeline sags to a certain extent, it will cause the pipeline to rupture due to excessive deflection, resulting in serious losses. Figure 1 As shown in the auxiliary, as the scour pit becomes larger, the pipeline will sag, and this process is called span extension.

[0005] Obviously, seabed scour caused by the coastal dynamic environment is one of the main causes of pipeline fatigue damage. In the actual environment, scour not only develops vertically downward around the pipeline, but also expands laterally from the middle to both ends along the pipeline. Therefore, it is not comprehensive to only consider the influence of vortex-induced vibration. The formation and development of scour pits under the pipeline have obvious three-dimensional characteristics, and the lateral expansion speed of the suspended span is an important aspect of the study of this three-dimensional scour problem.

[0006] Therefore, it is very necessary to propose a model that can reasonably predict the expansion of the span, which plays an important role in the protection of the pipeline. Summary of the invention

[0007] The present invention provides a method for predicting the expansion velocity of a submarine pipeline span, which predicts the expansion velocity of a pipeline span under pure flow, pure wave and wave-flow under the same moving bed condition, and plays an important role in protecting the pipeline.

[0008] The technical solution adopted by the present invention to solve its technical problem is:

[0009] A method for predicting the expansion speed of a submarine pipeline span includes the following steps:

[0010] Step S1: Under the condition of the moving bed on the seabed, during the pipeline scouring 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 his 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, υ=10 -6 m 2 / s is the viscosity of water, 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;

[0011] Step S2: Simplify the functional dependencies between the eleven physical quantities in step S1 into 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, θ cw With θ crit Combined effective Shields number, 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 );

[0012] Step S3: Further simplify the function involving nine dimensionless quantities in step S2 into a function involving five dimensionless quantities:

[0013] Step S4: Based on the physical scouring process, the difference in sediment transport rate between entering and leaving the scouring pit and the lateral expansion speed of the suspended span at the bottom of the pipeline and the scouring depth have the following relationship: Among them, Δq is the difference in sediment transport rate, and S is the scour depth;

[0014] Step S5: According to the sediment transport rate formula, the sediment transport rate difference is expressed as:

[0015] Among them, 1.5<α<2.2, M=8;

[0016] Step S6: Taylor expansion of the sediment transport rate difference, in θ cw -θ crit =0 is expressed as:

[0017] Δq *=[(α-1)θ crit ] 3 / 2 +O(θ cw -θ crit ) 1 / 2 ;

[0018] Step S7: The Taylor expansion expression in step S6 is obtained at a larger θ cw -θ crit The limit value is:

[0019] Δq * =(α 3 / 2 -1)(θ cw -θ crit ) 3 / 2 ;

[0020] Step S8: According to the limit value in step S7, Δq * Approximate expression is:

[0021]

[0022] Step S9: In the approximate expression of Δq* in step S8, take α=1.88, θ crit =0.045, then the expression is:

[0023]

[0024] Step S10: The maximum vertical two-dimensional scouring depth of the pipeline bottom is expressed as:

[0025] Step S11: According to the expression of step S10, the exponential function of the maximum scouring depth of the pipeline bottom under the hydrodynamic environment including pure flow, pure wave and wave flow is obtained as follows: Among them, B is determined by the actual test data rate;

[0026] Step S12: Combining step S3, step S4, step S9 and step S11, the formula for the span extension speed is obtained as follows:

[0027] Among them, A is determined by the actual test data rate;

[0028] Furthermore, in the function Fr<0.25, the seabed porosity n is set to a constant n=0.4, and the KC number has little effect on the two-dimensional scour time scale under the pipeline. Therefore, it is inferred that the lateral migration velocity V h If the influence of is small, the function involving nine dimensionless quantities can be further simplified to a function involving five dimensionless quantities;

[0029] Further, in step S11, B=-3.2 is set;

[0030] Further, in step S12, A=3 is set;

[0031] Further, based on the span extension velocity formula obtained in step S12, Υ(m) is obtained by calibration in combination with the physical model experimental data.

[0032] When the pipeline scour is in pure flow condition, that is, m = 1, γ(m) = 1;

[0033] When pipeline scour is in wave flow condition, if the flow occupies the dominant area, that is, m>0.5, γ(m) decreases as m decreases;

[0034] When pipeline scour is in wave-current condition, if the wave occupies the dominant area, that is, m<0.5, Υ(m) increases as m decreases;

[0035] In the wave-dominated region, if m < 0.2, γ(m) has an approximately constant value of 0.3, which is lower than that of the pure flow condition;

[0036] Furthermore, the formula of γ(m) is:

[0037]

[0038] Furthermore, for the span expansion speed formula

[0039] The prediction accuracy measurement formula is:

[0040]

[0041] 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;

[0042] Furthermore, R 2 The value range is 0-1. 2 =1, indicating the best prediction accuracy. 2 >1, indicating that the forecast is close to the improvement of the average forecast.

[0043] Through the above technical solution, compared with the prior art, the present invention has the following beneficial effects:

[0044] The method for predicting the expansion speed of a submarine pipeline free span provided by the present invention introduces flow velocity intensity, calibrates the relationship between flow velocity intensity and the expansion speed of the free span under different hydrodynamic effects, and proposes a pipeline free span expansion speed prediction formula considering the wave and current effects under unified moving bed conditions. The method can accurately predict the lateral expansion rate of the free span under pure wave, wave and current and pure current conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0046] Figure 1 This is a schematic diagram of the span expansion caused by the pipeline sagging due to the enlargement of the scour pit;

[0047] Figure 2 It is a schematic diagram of the span extension under the condition of wave superposition and water flow;

[0048] Figure 3 is the critical Shields curve and the Shields number distribution of the data set;

[0049] Figure 4 It is a schematic diagram of dimensionless span extension velocity without considering the velocity intensity dependence;

[0050] Figure 5 It is a schematic diagram of the dependence of flow intensity on the span extension speed;

[0051] Figure 6 These are the experimental result images under pure wave conditions and pure flow conditions, where 6a, 6b, and 6c are the experimental result images of pure wave, and 6d, 6e, and 6f are the experimental result images of pure flow;

[0052] Figure 7 It is a conceptual diagram of sediment transport rate under pure flow, wave flow and pure wave conditions;

[0053] Figure 8 It is a schematic diagram of dimensionless span extension velocity considering the velocity intensity dependence;

[0054] Fig. 9 This is a schematic diagram of the model prediction performance proposed by Professor Cheng;

[0055] Fig.10 It is a schematic diagram of the dependence of KC number on the expansion speed of suspension span;

[0056] Fig.11 It is a schematic diagram of the dependence of function F on the span extension speed. DETAILED DESCRIPTION

[0057] The present invention will now be described in further 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 the terms "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, and "first", "second", etc. do not indicate the importance of the components, and therefore cannot be understood as a limitation on the present invention. The specific dimensions used in this embodiment are only for illustrating the technical solution by example, and do not limit the scope of protection of the present invention.

[0058] As described in the background technology, the length of the span is the main reason for the damage of the submarine pipeline due to scouring. The scouring of the water flow not only develops vertically downward around the pipeline, but also expands horizontally from the middle to both ends along the pipeline. The culprit of the scouring is the water flow. At present, there are very few studies in this direction. The only one is the prediction model for span extension under the action of pure flow. However, the water flow situation is complicated. In addition to pure flow, it also includes pure waves and wave flow (wave and flow combination). Figure 2 The figure shows the schematic diagram of the span extension under the condition of wave superposition flow. It can be seen from the figure that the scouring process can be described as follows: In the initial stage, the small hole (manually dug in the experiment) based on the CC section is the starting point of the scouring. As the scouring progresses, the sediment will move to both sides along the pipe, forming a suspension phenomenon, that is, the S shown in the AA section. h The span gradually expands with the passage of water. When the scouring of the CC section reaches the maximum equilibrium depth (i.e. the scouring no longer continues to expand indefinitely, but reaches a stable state), the BB section has not yet been locally scoured and is still in the initial state. From an engineering point of view, a formula that can reasonably predict the expansion of the span under pure flow, pure wave and wave-flow plays an important role in the protection method of the pipeline.

[0059] Therefore, this application introduces flow velocity intensity, studies the dependence of the span extension velocity under the action of wave and current on the flow velocity intensity, and at the same time studies the influence of different Shields numbers on the span extension velocity, and proposes a prediction method for the span extension velocity of a submarine pipeline considering the action of wave and current under a unified moving bed condition. Through data processing and dimensional analysis research methods, the span extension velocity data under the action of existing wave and current, waves, and pure flow are obtained to obtain data calibration and model comparison, and finally the expected result can be obtained, that is, the three-dimensional span extension prediction formula around the pipeline considering the action of wave and current under moving bed conditions.

[0060] Next, the prediction method provided by this application is described, which specifically includes the following steps:

[0061] Step S1: Under the condition of the moving bed on the seabed, during the pipeline scouring 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, υ=10 -6 m 2 / s is the viscosity of water, 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;

[0062] It should be pointed out here that in addition to the moving bed condition, it also includes the clear water condition. The main difference between these two conditions is whether the seabed is deformed. Under the clear water condition, the seabed is relatively stable and the impact of the water flow on the seabed is small. Under the moving bed condition, the seabed will undergo erosion and siltation changes with the action of the water flow. This change has a greater impact on the speed of the span expansion. Therefore, this step is set to be based on the moving bed condition as a prerequisite.

[0063] Step S2: Step S1 involves a functional dependency relationship between physical variables. Through standard dimensional analysis, the functional dependency relationship between eleven physical quantities in step S1 can be simplified to a function involving nine dimensionless quantities:

[0064] Here, in the function of nine dimensionless quantities, the velocity intensity m is taken into consideration, θ crit The critical Shields number θ can be calculated by the Reynolds number Re of the sediment particle size. crit The specific relationship between Reynolds number Re is Figure 3 It can be seen that Figure 3 The middle curve represents the critical Shields number. The upper part of the curve is the moving bed condition, and the lower part is the clean water condition. The dependence between the two is θ crit =0.165(Re+0.6) -0.8 +0.045exp(-40Re -1.3 ), Re≥1.

[0065] θ cw With θ crit Combined effective Shields number, specifically the variable exceeding the critical Shields number (θ cw -θ crit). Fr is the Froude number. The data used in this application is Fr<0.25, so this item is ignored. We believe that the influence of the Froude number on the pipeline should be minimal. As for the Keulegan Carpenter number KC, it is well known that it has little effect on the time scale of the two-dimensional scour under the pipeline. Therefore, it is reasonable to infer that it has a great influence on the lateral expansion velocity V h The influence of V h It is highly related to the scour time scale (the rate at which scour propagates in the vertical direction) and is therefore discarded in this dimensionless analysis. n is the porosity, which is usually a constant in sand (approximately 0.4) and is therefore discarded. m is the velocity intensity, m = U c / (U c+ U w ).

[0066] Step S3: Based on the considerations in step S2, in step S3, the function involving nine dimensionless quantities is further simplified into a function involving five dimensionless quantities:

[0067] Step S4: Based on the physical process of scouring, the difference in sediment transport rate between entering and leaving the scouring pit and the lateral expansion speed of the suspended span at the bottom of the pipeline and the scouring depth have the following relationship: Among them, Δq is the difference in sediment transport rate, and S is the scouring depth.

[0068] Step S5: According to the sediment transport rate formula, the sediment transport rate difference is expressed as:

[0069]

[0070] Among them, 1.5<α<2.2, M=8 can be degenerated into the Meyer-Peter&Muller formula.

[0071] Step S6: Taylor expansion of the sediment transport rate difference, in θ cw -θ crit =0 is expressed as:

[0072] Δq * =[(α-1)θ crit ] 3 / 2 +O(θ cw -θ crit ) 1 / 2 .

[0073] Step S7: The Taylor expansion expression in step S6 is obtained at a larger θ cw -θ crit The limit value is:

[0074] Δq * =(α 3 / 2 -1)(θcw -θ crit ) 3 / 2 .

[0075] Step S8: According to the limit value in step S7, Δq * Approximate expression is:

[0076]

[0077] Step S9: In the approximate expression of Δq* in step S8, take α=1.88, θ crit =0.045, then the expression is:

[0078]

[0079] Step S10: The maximum vertical two-dimensional scouring depth of the pipeline bottom is expressed as:

[0080] Step S11: According to the expression of step S10, the exponential function of the maximum scouring depth of the pipeline bottom under the hydrodynamic environment including pure flow, pure wave and wave flow is obtained as follows: Wherein, B is determined by the actual test data rate, and in this application, B=-3.2 is set.

[0081] Step S12: Step S12: Combining step S3, step S4, step S9 and step S11, the formula for the span extension speed is:

[0082] Wherein, A is determined by the actual test data rate, wherein A is determined by the actual test data rate, and A=3 is set in this application.

[0083] In the above prediction method, γ(m) is introduced. The dependence of the span extension speed on m is based on actual experiments. Next, the process of determining the expression of γ(m) is specifically derived and explained.

[0084] In order to more intuitively see the accuracy of the prediction model provided by this application, all subsequent figures provided in this application show three modes of data presentation, which are clearly marked in each figure, namely the prediction of the current research data set, the prediction of Professor Sui without considering the velocity intensity m, and the prediction proposed by Professor Cheng with the introduction of superimposed wave factors. Here, Professor Cheng's research considers factors such as scour depth, Shields parameter and slope angle at the shoulder. Based on the pure flow condition, the superimposed wave factor is also introduced, which is the same as this application, and a unified formula is proposed to predict the span extension speed under different hydrodynamic conditions, including pure flow, pure wave and wave and flow combination conditions, which are expressed as follows:

[0085]

[0086] In the above expression, β is the sediment repose angle, α is the incident angle of water, and K wc =148 is the calibration correction factor, whose value is determined from experimental data; the above expression is converted to V h * Similar dimensionless form, in Professor Cheng's study, the specific value of β is not clearly specified, but we assume a typical sand value, such as β = 32°. It should be noted that this work only considers the case of vertical incidence, that is, α = 0°. F represents the functional relationship between m and KC, and mainly studies the correlation between the empirical formulas of equilibrium scour depth under wave and current conditions and equilibrium depth under pure flow conditions. The empirical equation that controls this relationship is shown below:

[0087]

[0088] In the above research framework of Professor Cheng, what is different from the prediction model of this application is that the function F is included in the prediction formula.

[0089] Next, all three prediction models are classified. Figure 4 The prediction formula is given only under pure flow conditions (Professor Sui did not consider the dependence of the flow velocity intensity m, that is, the comparison of the span extension velocity between γ(m) and the data set. In the figure, the solid line represents the model prediction, and the dotted line represents that the threshold of the prediction model is ±1 (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. The yellow data set (pure flow) is completely distributed around the predicted value. Obviously, Professor Sui's prediction model does not obtain ideal results when predicting the data set of pure wave and wave-flow conditions. Figure 4 It can also be seen that for a given (θ cw -θ crit ), the value under wave or wave-flow condition is lower than that under pure flow condition. This means that considering the wave component will greatly reduce the span extension speed, which is different from the actual picture ( Figure 6 ) is consistent with the video record in Figure 6 6a, 6b, and 6c are images of the experimental results of pure waves, and 6d, 6e, and 6f are images of the experimental results of pure flow.

[0090] On the other hand Figure 5 The schematic diagram shows the dependence of flow intensity on span extension speed. as the y-axis and the flow intensity m as the x-axis, by using the experimental data to find the dependence of m, Figure 5In the equation, the y-axis is the dimensionless span extension velocity (also called γ(m)) considering the effective Shields number dependence and the embedment depth dependence, and the x-axis represents different flow velocity intensities. Figure 5 From the schematic diagram of the sediment transport rate around the scour holes that may appear under the pipeline under the flow velocity intensity dependence, it can also be concluded that the dimensionless span extension velocity under wave conditions (y-axis value 0.3) is lower than that under pure flow conditions (0.1).

[0091] Presentation Figure 5 The dependence is because the seafloor hydrodynamic environment formed by pure flow, pure wave and wave flow, as the sediment around the scour hole that may appear at the bottom of the pipeline, its transport rate is directly related to the Shields number θ cw The larger the Shields number, the greater the shear stress of the bed below the pipe, the easier it is for sediment to start, and the greater the sediment transport rate below the pipe. When in pure flow conditions, the Shields number θ cw It continues to maintain its maximum value, and under pure wave and wave-current superposition conditions, due to the periodicity of waves, the Shields number only reaches its maximum value twice in one cycle. Therefore, it is believed that under the same Shields number, pure flow conditions have a higher sediment transport rate.

[0092] Finally, a reasonable expression of γ(m) of this application is obtained. When the pipeline scour is in pure flow condition, that is, m=1, it has the maximum expansion speed, γ(m)=1. As m decreases, that is, the pipeline scour is in wave flow condition, γ(m) shows a decreasing-increasing pattern. Specifically, if the flow occupies the dominant area, that is, m>0.5, γ(m) decreases as m decreases; if the wave occupies the dominant area, that is, m<0.5, the decrease in m corresponds to an increase in the standardized span expansion speed γ(m). For m<0.2, γ(m) has an approximately constant value of about 0.3, which is lower than the pure flow condition.

[0093] Then the formula expression of γ(m) is:

[0094]

[0095] About V h * The relationship distribution with m is also combined Figure 5 , which includes pure flow, pure wave and wave-flow conditions, assuming that the lateral expansion speed of the span is closely related to the sediment transport rate, that is, the greater the sediment transport rate, the faster the lateral expansion speed of the span. Figure 7In the figure, the Shields number changes with time under three working conditions. The red curve represents the pure flow condition, and its Shields number does not change with time, and it always remains at a constant Shields number. This means that the sediment transport rate under the pure flow condition is relatively constant. The black curve represents the pure wave condition. It is well known that waves have periodicity. Waves are a reciprocating flow that acts on the sediment in the scour pit above the x-axis (positive direction, along the wave / flow direction) or below (negative direction, opposite to the wave / flow). Unlike water flow, which only transports sediment along the flow direction, its Shields number also shows periodicity over time. In one cycle, the Shields number will only reach two peaks, that is, it reaches two maximum sediment transport rates. Therefore, the overall level of sediment transport rate under the pure flow condition is higher than that under the pure wave condition. The blue curve represents the wave-flow condition. Due to the influence of waves, it also has periodicity. When waves and currents are superimposed, there are two situations: the waves and currents are in the same direction and the waves and currents are in opposite directions. In the former, the sediment transport capacity is stronger, which means that the Shields number reaches the maximum value at this time; while in the latter, the waves and currents will cancel each other out in opposite directions, and the sediment transport capacity will be greatly reduced, and the Shields number reaches the minimum value at this time. Therefore, the sediment transport rate of wave flow is lower than that of pure wave and pure current conditions.

[0096] from Figure 7 It can be seen that the sediment transport is larger in pure flow conditions compared to wave and flow conditions. This results in a faster lateral expansion rate of the pipeline span in the absence of pure flow than in the presence of waves and pure flow. This is explained as a "pumping effect" in this study. As for the pure wave case, it transports sediments in both directions and therefore has a relatively strong ability to transport sediments from the scouring hole to the outside. This is why the migration rate is faster in the pure wave case compared to the wave and flow case. In addition, it is worth noting that if the Shields parameter is given, there is not much difference in the time scale of scouring in the two-dimensional pipeline between the pure flow and pure wave cases.

[0097] After introducing γ(m), i.e. the dependence of the span extension speed on m, the comparison between the predicted value and the data set is redrawn, as shown in the figure below: Figure 8 As shown, all data sets, including wave flow data points, are well distributed around the prediction line.

[0098] exist Figure 8 The square of the correlation coefficient R is shown in 2 The value of is used as a measure of prediction accuracy, and the formula is:

[0099]

[0100] Among them, R 2is 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 measurement. 2 The value of ranges from 0 to 1, indicating the model's fit performance relative to the average prediction. In addition, R 2 = 1 corresponds to perfect prediction, while R 2 >0 indicates an improvement close to the average forecast. Figure 8 The predicted R is shown in 2 =0.80, which verifies that the formula of this model and the expression of γ(m) can predict the lateral expansion rate of the suspended span under pure wave, wave-flow and pure flow conditions.

[0101] As mentioned above, Professor Cheng also introduced the superimposed wave factor to propose a prediction model. The difference from the prediction model of this application is that the coefficient F is included in the prediction formula. The applicant of this case also conducted relevant research and verification on whether the coefficient F needs to be included in the prediction formula. h * ) is compared with the dataset shown in Fig. 9 In, with Figure 8 is drawn in a similar way, from Fig. 9 It can be seen that relatively Figure 8 Regarding the research in this application, the dataset studied by Professor Cheng is more dispersed than the prediction line, which is also reflected in the two studies R 2 In the comparison, using the prediction method proposed by Professor Cheng, R 2 The performance R of this study is 0.44, which is lower than that of the 2 =0.80. This shows that the present application has made significant improvements over Professor Cheng's research, which also introduces the prediction model of superimposed wave factors.

[0102] The reason for the improvement is that the prediction model proposed in this application excludes the influence of KC number on the prediction effect of the lateral expansion rate of the suspended span. Fig.10 This was verified in both theoretical scale analysis and dataset calibration, indicating that it has little impact on the prediction. Fig.10 In the figure, the data set has little relationship with KC and is around the solid line with a constant value of 1.

[0103] Returning to Professor Cheng's study, it can be seen from the formula that an increase in the coefficient F will lead to an increase in the lateral expansion rate of the suspended span. Next, the dependence of F within the prediction framework provided in this application is examined. Fig.11As shown, the dimensionless migration velocity for different F values ​​is shown based on the prediction formula of this application, and it is found that the data set tends to cluster around a constant value. This suggests that the coefficient F may have little dependence if other dependencies on the effective Shields parameter, pre-embedding depth and flow intensity are properly handled.

[0104] The above can further demonstrate that the prediction method for the expansion speed of the submarine pipeline span provided by the present application processes the experimental data under wave and flow conditions, which is different from the processing of the experimental data of pure flow and wave. It processes it through the existing mature wave and flow theory, studies the main factors affecting the expansion speed of the three-dimensional span of pipeline scouring, and fits the relationship between the main influencing factors and its dimensionless expansion speed, introduces the flow velocity intensity, and studies the different Shields numbers θ. cw , the influence of different flow velocity intensities m and different burial depth ratios e / D on the expansion speed of the suspended span of submarine pipelines, and proposed a three-dimensional suspended span expansion prediction formula around the pipeline under the moving bed condition considering the combined action of pure flow, wave and wave-current. Compared with the research of Professor Sui, which studied the predicted speed of the suspended span expansion of the pipeline under the action of a moving bed (corresponding to the clear water condition) when the pipeline was only affected by the water flow (i.e., without the influence of waves), the prediction formula of this application is more accurate. At the same time, compared with the research of Professor Cheng, which includes the prediction formula of the coefficient F, it can be seen from the judgment of the fitting coefficient that the fitting coefficient of this application is closer to 1, that is, the prediction effect is better.

[0105] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0106] The meaning of "and / or" described in this application means that the situations where each exists alone or both exist at the same time are included.

[0107] The term “connection” as used in this application may mean a direct connection between components or an indirect connection between components via other components.

[0108] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for predicting the extension speed of a submarine pipeline span, characterized by: The specific steps include: Step S1: Under the condition of the moving bed on the seabed, during the pipeline scouring process, the lateral expansion speed of the free span at the bottom of the pipeline Related to the following eleven physical quantities: ,in, is the lateral expansion speed of the bottom span of the pipeline, g(s- 1 ) is the buoyant density of sediment, s = 2.65 is the specific gravity of sediment, is the viscosity of water, e The depth of the pipeline buried in the seabed. n is the seabed porosity, h For water depth, T is the wave period, is the velocity of the water flow near the bottom, is the near-bottom fluctuating velocity; Step S2: Simplify the functional dependencies between the eleven physical quantities in step S1 into functions involving nine dimensionless quantities: ,in, is the Shields number, which represents the relationship between seabed shear stress and sediment initiation, is the ratio of pipeline depth to pipeline diameter, critical Shields number It is the parameter that distinguishes the moving bed from the clean water. Reynolds number by sedimentation particle size Calculation, the functional dependency between the two is , , and Combined effective Shields number, is the Froude number, is the Keulegan Carpenter number, n is the porosity, m is the flow intensity, ; Step S3: Further simplify the function involving nine dimensionless quantities in step S2 into a function involving five dimensionless quantities: ; Step S4: Based on the physical scouring process, the difference in sediment transport rate between entering and leaving the scouring pit and the lateral expansion speed of the suspended span at the bottom of the pipeline and the scouring depth have the following relationship: ,in, is the sediment transport rate difference, is the scour depth; Step S5: According to the sediment transport rate formula, the sediment transport rate difference is expressed as: ,in, , ; Step S6: Taylor expansion of the sediment transport rate difference, θ cw -θ crit = 0 is expressed as: ; Step S7: The Taylor expansion expression in step S6 is θ cw -θ crit The limit value is: ; Step S8: According to the limit value in step S7, Expressed as: ; Step S9: Step S8 In the expression, take α = 1.88, θ crit = 0.045, then the expression is: ; Step S10: The maximum vertical two-dimensional scouring depth of the pipeline bottom is expressed as: ; Step S11: According to the expression of step S10, the exponential function of the maximum scouring depth of the pipeline bottom under the hydrodynamic environment including pure flow, pure wave and wave flow is obtained as follows: ,in, B Determined by actual test data rate; Step S12: Combining steps S3, S4, S9 and S11, the formula for the span extension speed is: ,in, A Determined by the actual test data rate.

2. The method for predicting the span extension speed of a submarine pipeline according to claim 1 is characterized by: In a function , seabed porosity n Set to constant n = 0.4, KC The number has little effect on the two-dimensional scour time scale under the pipeline, so it is inferred that the lateral migration velocity of the suspended span V h If the influence of is small, the function involving nine dimensionless quantities can be further simplified to a function involving five dimensionless quantities.

3. The method for predicting the span extension speed of a submarine pipeline according to claim 1, characterized in that: In step S11, set .

4. The method for predicting the free span extension speed of a submarine pipeline according to claim 1, characterized in that: In step S12, set A = 3.

5. The method for predicting the free span extension speed of a submarine pipeline according to claim 1, characterized in that: Based on the span extension speed formula obtained in step S12, the following is obtained by calibration with the physical model experimental data: , When the pipeline scour is in pure flow condition, that is, m = 1, ; When pipeline scour is in wave flow condition, if the flow occupies the dominant area, that is, , along with m decreases with the decrease of; When pipeline scour is in wave and current conditions, if the wave occupies the dominant area, that is, , along with m decreases and increases; In the wave-dominated area, if , It has a constant value of 0.3, which is lower than the pure flow condition.

6. The method for predicting the free span extension speed of a submarine pipeline according to claim 5, characterized in that: The formula expression is: .

7. The method for predicting the free span extension speed of a submarine pipeline according to claim 1, characterized in that: Formula for span extension speed The prediction accuracy measurement formula is: in, 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.

8. The method for predicting the free span extension speed of a submarine pipeline according to claim 7, characterized in that: The value range is 0 -1. , it indicates that the prediction accuracy is the best.

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