Taking Qinhuangdao 32-6 Oilfield as an example, the analysis and calculation of annual extreme factors such as wind, wave, current and tide in the sea area are reported by numerical calculation. Based on the historical sea surface pressure field and weather map during the typhoon and strong cold wave weather that affected the sea area during 197\0 1993, the numerical calculation model jointly developed by China Offshore Oil Corporation and Qingdao Ocean University is adopted. That is, the calculation model of sea surface wind field (including two-layer diagnosis model, planetary boundary layer dynamic model and typhoon model), shallow water wave-current coupling numerical calculation model and three-dimensional model of water level flow field. The calculation area is divided by 1/8 grid distance, and the wind speed of each grid point in the process of strong cold wave and typhoon weather affecting the sea area every year is calculated by using the numerical calculation model of sea surface wind field. The wave height, period, water level, wind increase and water decrease of each grid point are calculated by the numerical model of wave-current coupling and the three-dimensional model of water level field and flow field, which are used as the sample sequence for calculating the design environment elements. Then, according to the sample sequence, the design wave element values of each recurrence period of the engineering point are calculated by Weibull distribution.
Case selection of (1) disastrous weather process
During the 24 years from 1970 to 1993, the severe weather process that swept the Bohai Sea exceeded 120 times, but only 82 weather processes could affect the wind, waves, currents and water levels in Qinhuangdao (QHD)32-6 oilfield, with an average of about 3 or 4 times a year. They can't all cause annual extremes. Only by simulating the weather processes one by one can we determine which weather processes are desirable.
(2) Other results obtained from the simulation results.
Various average wind speeds at 1. 10m height.
According to the requirements of ocean engineering and API standards, the extreme annual average wind speed at the height of 10m is converted into the extreme annual average wind speed at the same height according to the following formula:
1h average wind speed = = 30 minutes average wind speed/1.03
3h average wind speed = = 1h average wind speed/1.05.
10min average wind speed = = 1h average wind speed × 1.07.
1 minute average wind speed = = 1 hour average wind speed × 1.20
3sec average wind speed = = 1h average wind speed×1.60.
2. The relationship between wave elements
Wave simulation gives the effective wave height Hs and the corresponding period Ts.
A. assume that the single wave height h and the effective wave height Hs satisfy Rayleigh distribution:
High-tech and Practice of Offshore Oil in China
F(H) is the cumulative probability of wave height ≥H, then the maximum single wave height Hmax has the following relationship with Hs:
High-tech and Practice of Offshore Oil in China
N is the number of wave sequences that constitute Hs. N is the number of big waves in a stable state for a certain period of time. As we all know, the steady process of big waves does not last long. If the average period of this wave is N=800 waves, the duration is τ =10s× 800 = 8000s = 2.22h. If this wave meets the requirements of the stable process, the following formula is given:
High-tech and Practice of Offshore Oil in China
The maximum single wave height Hmax is calculated according to the formula (17- 13).
B. characteristic period:
The average period is the circular frequency corresponding to the spectral peak period S(ωp); Spectral peak period
Maximum wave period Tmax= 1.06Ts (according to the relation provided by Gotha).
(3) High and low water levels that occur once in many years
For places with long-term water level observation, the annual extreme high and low water levels of measured data and the annual extreme storm increase and decrease can be used to calculate the annual extreme water level, which can be obtained according to the long-term extreme distribution. For places where there is no long-term water level observation, the annual extreme wind water increase and wind water decrease can be calculated by simulating the weather process, and the annual high and low water levels can only be obtained by the linear combination of the annual extreme wind water increase and wind water decrease and the characteristic water levels (such as the highest astronomical tide level and the lowest astronomical tide level).
See Table 17-5 for annual high and low water levels and annual wind-driven increase (decrease) water in Bohai Sea, and the highest and lowest astronomical tide levels obtained by major water stations based on the measured tide level data.
Select the following linear combinations to calculate the high and low water levels with the annual wind increase and decrease and the highest and lowest astronomical tide levels:
Annual high water level = 0.72m (annual wind increasing water+highest astronomical tide level)
Low water level with annual return period = =0.9 1m (annual return period with reduced wind and water+lowest astronomical tide level)
Table 17-5 Annual High and Low Water Levels and Astronomical Maximum and Minimum Tidal Levels at Bohai Tidal Level Observatory
The results are close to the annual high and low water levels calculated from the measured water levels. Table 17-6 lists the results of 100 for comparison. Therefore, for places where there is no long-term measured water level, this form of linear combination can be used to obtain high and low water levels close to the actual annual return period.
In order to obtain high and low water levels by the above method, it is necessary to obtain reliable annual wind power increase and decrease. Table 17-7 gives the annual rainstorm increase and decrease in Qinhuangdao and Tanggu calculated according to the simulated strong weather process and measured data. It is found that the results are quite close, so the reliable annual increase and decrease of Qinhuangdao 32-6 Oilfield can be obtained by using the above linear combination.
Table 17-6 Estimated values of high and low water levels and wind-induced water reduction at main water level observation stations in Bohai Sea
Table 17-7 Comparison Results of Measured and Calculated Rainstorm Increase and Decrease Water in Qinhuangdao and Taigu
Using eight main harmonic constants (m2, S2, N2, K2, K 1, D 1, P 1, Q 1) obtained by numerical simulation of tidal waves in Bohai Sea and the harmonic constants of long-term tidal components in nearby areas, the highest (lowest) astronomical tidal level is calculated as/kloc-0. The expression of tidal level is:
High-tech and Practice of Offshore Oil in China
According to the harmonic constants of the main tidal components, the theoretical water depth datum is calculated by Ferrara Kierski method, and the near lowest tidal level is calculated by BPF method. In order to maintain unity, the chart depth datum adopts the theoretical depth datum.
2. Calculation of design parameters of environmental factors in different return periods
According to the engineering design requirements of QHD32-6 Oilfield, the extreme value sample sequence of wind, wave, water level and ocean current is calculated by the above-mentioned 1970- 1993 strong weather process, and the once-in-a-year design parameters are calculated by Weibull extreme value probability distribution.
Weibul 1 probability distribution:
High-tech and Practice of Offshore Oil in China
Where: a, b and c are parameters to be determined, and a > 0 is the position parameter; B > 0 is the proportional parameter; C > 0 is the shape parameter. When a=0, the above formula is a two-parameter Weibull 1 distribution. You can get the logarithm of the above formula:
High-tech and Practice of Offshore Oil in China
Move items from the above formula:
High-tech and Practice of Offshore Oil in China
On the Weibull probability grid, ln(x-a) is the abscissa and ln [- 1n (1-f (x))] is the ordinate.
Rewrite the above formula:
High-tech and Practice of Offshore Oil in China
Because x > a in 1n(x-a) is necessary, so take a=Xn, that is, take the smallest element in the sequence as the position parameter, and then estimate the parameters of e and d by least square method. The design parameters of environmental elements with multi-year return period are obtained by the following formula:
High-tech and Practice of Offshore Oil in China
From this, the design parameters such as wind speed, wave, current and tidal level in the sea area of Qinhuangdao 32-6 Oilfield can be calculated.
Three, wind, wave, tide and current joint probability calculation technology
The disastrous offshore dynamic environment such as wind, wave, tide and current directly causes disastrous damage and casualties to offshore, coastal engineering, estuaries and coastal cities, thus causing huge economic losses. In order to optimize the evaluation method of coastal dynamic environment, we must first consider its "simultaneous appearance" and "simultaneous effect" on offshore and coastal engineering. Because a typhoon (or storm) process, its greatest harm is the consequences caused by the simultaneous occurrence of various disastrous dynamic environments. However, how to consider the characteristics of "simultaneous occurrence", the traditional evaluation method at home and abroad is to analyze the probability of various disasters' dynamic environment, select the dynamic factors in different return periods, and then superimpose them as the evaluation method of extreme sea conditions in offshore and coastal engineering as the "design standard". For example, the 50-year wave height and 50-year tide level are used as design criteria in coastal engineering design, and the 100 wave height, 100 wind speed and 100 ocean current are used as design criteria in offshore engineering design. Obviously, the events in which the extreme values of various factors of coastal disaster dynamic environment are combined under certain probability conditions are small probability events, which are very conservative as design standards. Especially, some oilfields in China belong to "marginal oilfields". Using too high disaster dynamic environment as the design standard will lead to too high economic investment and make many oilfields lose their development value. Traditional evaluation methods are not desirable.
The norms and DNV norms widely used in the world have made corresponding provisions on extreme sea conditions caused by wind, waves, tides and currents. China offshore oil development project takes this code as the industry standard, and this code puts forward three different solutions for extreme sea conditions:
Firstly, the once-in-a-century wind speed, once-in-a-century wave height and once-in-a-century ocean current speed are adopted as design standards respectively.
Secondly, the once-in-a-century wave height and related wind speed are adopted;
Thirdly, the wind, wave and current values reappeared simultaneously with the once-in-a-century joint probability are adopted.
The API specification points out that the first method is too conservative and recommends the second method. However, it is pointed out in the Code that the word "correlation" of "wind current value associated with once-in-a-century wave height" is ambiguous. The third method is difficult to use because the joint probability is not a single solution. Therefore, the second method is still widely used in ocean engineering.
The starting point of this study is that it is a correct and practical method to study the joint probability of wind, wave and current during a gale or typhoon at the same time, because the first method essentially regards wind, wave and current as independent random variables, and it is unreasonable to use the once-in-a-century probability as the product of the three probabilities. The disadvantage of the second method is that the word "association" pointed out in API specification is "ambiguous"; Secondly, the once-in-a-century wave height and its associated wind speed and joint probability of wind speed (both of which have corresponding probability grades) must be a return period of more than once in a hundred years. Some conclusions of this study also prove this point.
(A) joint probability stochastic simulation method
The derivation of multidimensional joint probability is actually to solve the formula (17-20):
High-tech and Practice of Offshore Oil in China
Equation (17-20) can only be solved analytically if all random variables are normally distributed. The stochastic simulation method is effective for non-Gaussian functions and joint probability density functions of multidimensional random variables with different correlations.
Stochastic simulation method is a method of repeating some processes by computer based on real data and some assumptions. The commonly used simulation method is Monte Carlo method, but the M-C method takes a long time to solve the small failure probability, and the result accuracy is not high, so we must find a new method. Critical sampling method is an effective method to reduce machine time and variance. Its basic principle is to focus on the most important area sampling of distribution, that is, the part that makes the main contribution to the failure probability, instead of extending it to the whole definition domain for uniform sampling.
Figure 17- 1 two-dimensional joint probability diagram
Is the design point coordinates; Fx(x) is the joint probability density; Is the weight function density.
In order to illustrate the characteristics of the key sampling method, the diagram 17- 1 is shown in two dimensions. The curve running through the x 1 and x2 planes in the figure represents the joint probability curve simulating the joint probability state, and the distribution exceeding the joint probability is on the right side of the curve. On the left is the part below the joint probability, and a point closest to the origin can be found on the surface, called "design point", as its coordinates. The key sampling method is characterized by sampling around the design point; Another feature is the introduction of the weight density function hy(x), through which the simulation is directed to the area centered on the design point, so as to achieve the purpose of reducing the variance of the simulation results.
The formula (17-20) is calculated as follows:
High-tech and Practice of Offshore Oil in China
Among them:
The probability density function fx(x) represents the true joint probability density of the weight density function under special circumstances.
As can be seen from the above formula, the weight density is not important, therefore, the expected value of joint probability can be written as:
High-tech and Practice of Offshore Oil in China
Where: n is the number of simulations; Is the ith analog vector.
The advantage is that it is suitable for the original space without considering the distribution type of basic random variables. For correlated random variables, it is difficult to transform basic random variables into independent standard normal variable vectors. But in fact, the calculation of joint probability uses the original distribution, and any non-Gaussian distribution will not affect the weighted samples. When using any non-Gaussian distribution and related random variables, the following transformations are required:
High-tech and Practice of Offshore Oil in China
Where Fxi(ixi) is the original cumulative distribution function of the basic random variable x; φ- 1 (.) is the inverse of the standard Gaussian cumulative distribution function. Assuming that z is standard normal, the joint probability density function can be written as:
High-tech and Practice of Offshore Oil in China
Where Zi is the calculation result of formula (17-23); φ (.) is the standard normal density function; φn(Z，R？ ) is a multidimensional standard Gaussian density function with a mean of 0 and a standard deviation of1; r？ A modified correlation matrix is formed by the following formula: is a value defined by a series of correlation coefficients.
High-tech and Practice of Offshore Oil in China
For each pair of edge distributions, the equation (17-25) can be solved iteratively.
It should be pointed out that the edge distribution density and covariance are not one-to-one corresponding to the joint density of non-Gaussian random variables, but in most cases the available information is limited to the edge distribution and covariance. Therefore, as long as it does not contradict the data, any suitable model can be adopted, and its application scope depends on the correlation coefficient between variables, and has nothing to do with the mathematical basis of any model.
(2) Development of joint probability stochastic simulation software.
JOPAP, a joint probabilistic stochastic simulation software based on critical sampling method, consists of two parts.
1. Calculation of design point
In this way, random points can be sampled in the effective area centered on the design point, which reduces the calculation time and improves the simulation efficiency.
2. Focus on sampling and calculate the joint probability.
Before executing the main program, different basic equations of joint probability model should be designed according to the different practical problems to be calculated, which are called limit state equations. The simulated limit state equation is:
High-tech and Practice of Offshore Oil in China
Different joint probabilities can be obtained by adjusting different set values (A 1, A2, A3). For example, if an Ai is given to the eigenvalues (such as once-in-a-century value and once-in-a-decade value) obtained by independent statistics of each variable Xi, the probability that each variable Xi exceeds its once-in-a-century (once-in-50-year) value can be obtained. This study has completed the development of the above software.
(3) The solution method of non-single solution of joint probability stochastic simulation and its engineering application.
Joint probability calculation of maximum wave height and corresponding simultaneous wind speed and current velocity. For fixed offshore structures, from the load analysis, when the maximum wave height and corresponding simultaneous wind speed and current velocity are used as random simulation samples, the load effect under the combined action is the most unfavorable to the platform structure, as shown in the following figure.
1. Find the individual extreme value of each element in a hundred years.
The distributions of wave height, wind speed and current velocity usually conform to some probability distribution, such as Gumbel distribution, Weibull distribution (1 distribution) and lognormal distribution. Therefore, the above distribution can be fitted according to the data of wave height, wind speed and flow velocity in the process of multiple gale. According to the maximum wave height, a set of corresponding wind and wave current combinations can be selected, thus forming a series of wind and wave currents dominated by waves, currents and winds. For each sequence, Gambert distribution, Weibull distribution and lognormal distribution are calculated. After the goodness-of-fit test of the distribution curve, the distribution form of wind speed, wave height and velocity corresponding to each combination can be determined by using certain criteria. Kolmogorov test is used here, which is also the commonly used K-S test. The absolute deviation of frequency and the minimum mean square deviation of deviation are used as criteria. See table 17-8 for the calculation results of distribution forms of each element.
From table 17-8, we can also see a seemingly contradictory phenomenon, that is, the once-in-a-century current value based on the maximum flow sequence is less than the once-in-a-century wave height value based on the maximum wind sequence, and the once-in-a-century wave height value based on the maximum wind sequence is less than the once-in-a-century wave height value based on the maximum wind sequence. This phenomenon can be explained by the small variance of velocity series (wave height series). Therefore, although the original series value of current (wave height) dominated by current (wave) is larger than that dominated by wind (wave height), its probability distribution curve is flat, so the once-in-a-century value is lower than that of wind-dominated current (wave height).
Table 17-8 once-in-a-century wind, wave and current distribution forms and extreme values
2. Joint probability stochastic simulation analysis method
Wind, wave and current are interrelated but not independent. The joint probability method takes the wind, waves and currents that occur simultaneously in the process of "storm" or "typhoon" as the basic sequence of random analysis, thus obtaining a group of combinations of wind, waves and currents and corresponding probability levels. That is, the solution formula:
High-tech and Practice of Offshore Oil in China
Where: g (x) < 0 represents the fault domain.
For non-Gaussian and related multidimensional random variables, good results can be obtained by solving the equation with stochastic simulation method. Stochastic simulation method is a method to realize some processes by computer based on some characteristics and assumptions of real data, and Monte Carlo method is one of them. The basic idea is to establish a probability model, so that its mathematical expectation is equal to the failure probability of the structure, and then randomly sample the model, and finally estimate the failure probability with the mean of the sub-samples. However, when solving the small joint probability, using Monte Carlo method directly requires a lot of machine time and will produce large errors. Therefore, Monte Carlo method is only applicable to the case that the failure probability is not too small. "Critical sampling method" can improve the efficiency of Monte Carlo sampling, and its basic principle is to concentrate on sampling the most important areas in the distribution, that is, partial sampling that makes the main contribution to the joint probability, rather than equal sampling extended to the whole definition domain. In the process of solving the formula (17-26) by random simulation, there is a non-single solution problem, that is, using the "key sampling method" random simulation program, taking the distribution form, mean value, variance and correlation coefficient matrix of wind and waves under the action of marine environmental factors as input conditions, after calculation, multiple groups of marine environmental factor combinations with joint probability of once in a hundred years can be obtained. Solving non-single solution problems requires certain control conditions, generally taking the maximum response as the criterion. If the response is represented by y, then Y=f(H, Uc, Uw), where h is the wave height, Uc is the flow velocity and Uw is the wind speed. The sampling of H, Uc and Uw will affect the value of Y, so the corresponding wind and wave series with wave height, current and wind as the main factors are usually selected according to the data for simulation. By using the random simulation program of "key sampling method", the combination of wind, wave and current can be obtained, which is dominated by flow, wave and wind. Based on the platform response criterion, the combination corresponding to the maximum response is taken as the final solution, from which the joint design standard of marine environment equivalent to once in a hundred years can be obtained. See table 17-9 for the calculation results.
Table 17-9 wind, wave and current values under joint probability method
See table 17- 10 for the single factor distribution, once-in-a-century value and response value of wind wave current on jacket platform.
Table 17- 10 Single factor distribution form, once-in-a-century value and response value of wind wave current on jacket platform
(4) Calculate the joint probability of maximum speed and corresponding simultaneous wave height and wind speed.
For a free-floating semi-submersible platform, the platform bears the largest load due to the stable motion caused by waves, so it is appropriate to adopt the combination of maximum wave height and corresponding wind speed as the joint probability selection criterion.
For the semi-submersible platform with strong constraints, as shown in the calculation results, the environmental load on the platform is the largest in this case, as shown in table 17- 1 1.
Table 17- 1 1 Joint Design Standard for Marine Environment of Floating Platforms
(5) The joint probability that the maximum wave height and the maximum flow velocity occur at the same time.
Riser is an important component in the marine engineering structure system, and it is also a weak and vulnerable component. The calculation results show that the joint probability of wind, wave and current with wave or current as the control condition must be used as the design standard. The comparison of various methods is shown in Figure 17-2, Figure 17-3 and Table 17- 12.
Figure 17-2 once-in-a-century curve dominated by speed.
Figure 17-3 once-in-a-century curve dominated by wave height
Table 17- 12 Comparison of various methods
(6) Joint probability of maximum wind speed and corresponding wave height and wind speed.
Due to the large windward area of the important part of jack-up platform, the maximum wind speed and the corresponding wave height and wind speed can lead to the maximum response. See table 17- 13 for example calculation.
Table 17- 13 Comparison of combined probability of once-in-a-century wind waves and currents, corresponding overturning moment and extreme response method
(7) Conclusion
A. The software development of "non-Gaussian process, joint probability of multidimensional random variables with different correlations" random simulation (JOPAP software development) was completed according to the expected plan. Stochastic simulation technology has the advantages of fast convergence (5 ~ 10 times faster than M-C method) and small error (the maximum relative error is less than 10%).
B. Stochastic simulation software can be used for probability distribution modes commonly used in various disastrous dynamic environments (such as extreme value I, II and III distribution, Weibull distribution, lognormal distribution, compound extreme value distribution, etc.). ), and can meet the probability analysis of various engineering disaster prevention.
C. Based on the response of different engineering structures to the most unfavorable combination of disaster environment, this study samples the data of different types of disasters occurring at the same time, so as to achieve the purpose of transforming the non-single solution of joint probability random simulation into a fixed solution.
D. According to American API specification, China specification and other specifications, this project specifically solves the problems existing in the dynamic environment assessment method of simultaneous disasters: ① For fixed platforms, it is suggested to adopt the joint probability of wind, wave and current with wave height as the control condition as the design standard; ② For jack-up platforms, it is suggested that the joint probability of wind, wave and current with wind speed as the control condition should be taken as the design standard; ③ In the sea area with large current, the design standard of platform riser must adopt the joint probability of wind, wave and current controlled by wave or current.
E. The results of this project have solved some vague expressions in the latest version of American API (China Offshore Oil Industry Code), and solved the reasonable determination method of different engineering structure design standards by joint probability method for the first time in the world.