高压天然气管网动态模拟与壅塞流动特性研究
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摘要
天然气作为优质清洁能源得到世界各国的高度重视,随着我国粗放型经济发展方式的转变,能源政策相应调整,天然气在能源结构中的比重不断增加,输送天然气的长输管线和城市高压管网数量越来越大,储存天然气的设施规模不断增大。对高压天然气管道的科学计算和设计,以及在实际运行中正确的判断和调节,直接决定着高压天然气管网系统的安全稳定运行和保障城市正常供气。在设计过程中,由于缺乏计算高压天然气的有效方法和工具,设计人员在水力计算过程中,往往采用稳定流动状态代替不稳定流动状态进行计算,所设计的管网压力、流量等参数与实际运行数据存在较大偏差。在实际生产运行中,缺乏与实际管网相匹配的模拟工具,不能准确评估出输气管线在各种情况下的工况,不能准确控制管线的安全稳定运行。因此有必要针对我国高压天然气管网的实际情况,深入研究高压天然气管网中的流动状况及影响因素,通过动态模拟找出运行参数的变化规律,并提出相应的控制策略。
鉴于此,本文采用建立高压天然气管网数学模型、数值求解、动态仿真模拟、实例对比分析等方法,对高压天然气管网的水力、热力动态特性、高压储气、以及壅塞流动等方面进行了研究。主要结论如下：
(1)对不稳定流数学模型的建立作了大量简化：①天然气沿程温度按等温考虑；②忽略质量流量随时间的变化；③忽略水平输气过程中沿程线速度变化的影响；④忽略管道位置高差的影响；⑤分别采用恰尔内(И.А.Чарный)线性化法和最小二乘法线性化方法对数学模型进行线性化处理等。本文针对目前天然气管道不稳定流动的计算过程中忽略对流项、惯性项和中立项等问题,首次在没有忽略任何项的连续性方程、动量方程、能量方程、状态方程和焓方程所建立的数学模型的情况下,分别采用了特征线法和隐式中心有限差分法对天然气管网不稳定流进行了求数值解。采用数值解法对高压天然气管网不稳定流动进行研究,不用对模型方程组进行简化和复杂的数学变换,求解出来的结果与管道实际运行数据更为接近。求解时要将待求的时间层次上所有的未知量联立起来同时进行求解,求解的非线性方程组很庞大,方程组过大时求解需要的时间长。为了保证数值解的稳定性,时间步长、距离步长都不能够取得过小。数值解考虑了气体与外界环境的热交换,考虑了天然气沿程温度变化,能够计算出天然气沿线的温度分布。由于供气与用气的不均匀性,管网中天然气的压力、流量与温度也随时间波动。如果管网存在有分气点,则在分气点处气体的压力、温度、密度的变化最为剧烈。
(2)与隐式法相比,特征线法主要优点在于它们能对各种边界条件进行显式处理,且计算占用计算机内存较小,但其时间步长和距离步长的比值受到一定稳定条件的限制,这使得时间步长只能取得很小如果分析时间过长时,就需要消耗很长的计算时间。在采用特征线法对天然气管道进行数值求解时,利用逆步进法差分网格建立起特征差分方程,对常微分方程组结合初始条件和边界条件进行求数值解,由于边界节点的参数随时间的变化比较明显,因此该方法能提高计算精度,求解过程容易实现。本文还采用了适用于慢瞬变流的守恒型求解数学模型的隐式中心有限差分法,并利用Newton-Raphson法对形成的高阶非线性方程组进行了迭代计算。隐式中心有限差分法是隐式格式的有限差分方法,表现出了二阶精度高、计算速度快的优点。
(3)对天然气管网进行模拟时,可以单独采用特征线法或隐式有限差分法。本文综合考虑这两种方法的优点,采用综合法求解。结果表明：在模拟高压天然气管网动态运行工况时,在长管元件的边界点上采用特征线法计算,在其它情况下采用隐式中心有限差分法。根据本文所建模型及提出的解法,用Visual C++编程开发出的高压天然气管网动态模拟软件,利用实例计算验证,计算结果可以满足实际工程需要。
(4)采用SHBWR状态方程替代常用的对比状态方程,采用Newton迭代法求解,大幅度提高了天然气状态参数的计算速度与精度。由于高压天然气管道中天然气的流态一般在紊流区,因此在确定管道摩阻系数时,选择计算较为准确的柯列勃洛克公式,采用牛顿迭代方式可以计算出管道摩阻系数。
(5)对输气管道进行水力分析,从输气管道的天然气流动基本方程出发,结合实际气体状态方程与焓方程建立了动态模拟的数学模型；区别于以往的试算法,采用弦截法进行摩阻系数的求解,提高了计算精度。将摩阻系数公式进行变形改写,使其与管道流量进行关联,随着输气管道流量改变而改变,减少了由于摩阻系数的定值输入而带来的误差。
(6)对输气管道的温度变化进行热力学分析,研究了输气管道内天然气温度的变化规律。通过计算比较表明：单独求解输气管道温度与利用含有能量方程的稳定流模型求解出的管道温度基本吻合,因而单独求解管道温度是可行的,为多点接气不稳定流动数学模型模型中温度初始值的求解提供了有效的方法。
(7)多点接气和单气源高压天然气管网数学模型所依据的连续性方程、动量方程以及能量方程是相同的,区别主要在边界条件的处理上,其初始值的求解方法和所建立的方程个数不同。本文提出了多点接高压天然气管网动态模拟初始值计算方法,区别于单气源动态模型,可以从边界条件和约束条件入手对多点接高压天然气管网动态方程组封闭性进行分析。其封闭性分析来看,每增加一个气源点,就要补充两个关于该气源的方程,一个是流量方程或压力方程,另一个是温度方程。从而构成封闭的方程组,达到可以求解条件。
(8)通过对多点接高压天然气管网的计算,得到各个气源点、各个分气点以及各个管段在不同剖面上不同时刻的压力和流量的变化情况。可根据各点压力要求,对各气源压力进行有效控制,对流量进行合理的调度分配。利用SCADA系统采集的数据作为边界条件,对管网进行动态模拟计算,同时将计算结果与SCADA采集的节点流量数据对比分析,可以作为检测数据采集系统的准确性与可靠性
(9)对天然气流动中的壅塞现象进行研究,建立高压天然气管网壅塞流动的数学模型,分别采用四阶Rung-Kutta法和Newton-Raphson迭代法对模型进行求解,并通过工程实例进行对比验证。结果表明计算结果完全可用于天然气管网的设计、运行及调度管理。
(10)以气体动力学为基础,对径管和等径管天然气管道的壅塞现象进行分析研究,采用四阶Rung-Kutta法对等径管道壅塞模型进行求解。结合工程实例,讨论了壅塞状态下管道内气体参数的变化规律。结果再从压缩机室向CNG槽车内加气以及通过CNG槽车向储罐卸气过程中,开始充气阶段由于加(卸)气管两端的压差较大并且管径较小,天然气在低压端急剧膨胀易发生壅塞流动。产生壅塞流动的判定式为：根据实例计算当管道始末端压力比在0.32-0.41之间时,将发生流动壅塞。在工程设计时,管道流量不能超过壅塞流量,否则正常供气会受到影响。等径输气管道天然气流动发生壅塞时,其压力、温度等参数是沿程变化的；压力、温度沿程降低,马赫数及流速沿程增大,流速趋向于声速；各截面的当地声速与密度和温度有关,沿线降低。长输管道末端门站所连接的城市输气管网的管径不应太小,否则在用气高峰时刻在变径处会产生流动壅塞,导致某个时段内输入城市管网的天然气量小于城市实际用气需求量,造成供气不足,引发供气安全事故。
(11)分别对高压管道的稳态储气和非稳态储气进行研究,通过拟合管道内压力变化规律,推导出稳态储气量的计算公式,并分析了管长、压力等参数对稳态储气的影响；结合非稳态储气的定义与变径管道壅塞流动模型,对长输管道末段流动壅塞及其对管道储气能力的影响进行分析。结果表明：长输管线末段管道储气量计算可以按稳态,也可按非稳态来考虑。稳态储气计算结果偏于保守,计算结果与实际结果有误差。按稳态工况计算管段储气量的时候,通常根据起点最大压力、末端最小压力以及管道的实际长度来计算储气量,未考虑其最大储气量和最优长度。如果管段过长,由于流动阻力加大,不但不能多储气,反而会影响管道的储气。在利用长输管线末段储气的设计中应该注意这一特点。按照非稳态计算结果德更准确。
(12)根据本文提出的动态模型和解法,对第一版天然气管网动态模拟软件进行改进,使其具有多点接气高压天然气管网动态模拟计算功能,改进了历史数据的输入、查询、新数据计算与存储等功能,有利于实现负荷预测与实时模拟的结合。通过对多个实际或设计的高压天然气管网在多种不同运行工况下的计算,并将计算结果与国外同类模拟软件(PIPELINE、TGNET、SPS等)计算结果、城市管网SCADA系统采集的实际运行数据进行对比,结果表明,各个调压站计算压力的变化趋势与采集压力的变化趋势基本一致,与国外软件计算结果的相对偏差在6%以内,与SCADA系统采集的实际运行数据的相对误差在3%以内。改进型软件可对实际管网进行动态模拟计算,模拟结果准确反映出管道压力的变化规律,满足高压管网运行的要求,能够指导管网的智能化运行。
从以上结论来看,研究建立的高压天然气动态模拟数学模型和提出的解法计算结果精度高、计算速度快。揭示了城市高压天然气管网不稳定流动和储、放气的变化规律。结合SCADA系统采集的实际运行数据,可对高压管线进行动态模拟,计算结果可指导高压天然气管线的设计、运行工况模拟和储放气的分析。该研究为高压天然气管网动态研究提供了新的思路,为高压天然气管网的设计、运行、调度调控提供了理论依据,为分析壅塞流动和城市天然气高压储气能力提供了新的方法,为高压天然气安全输送和储存提供了技术支持。
Natural gas is a new clean energy resource, which has been attached great importance all over the world. Following the transition from the extensive economy and the adjustment of energy policy, the ratio of natural gas in the energy structure is increasing constantly with longer transmission pipeline and high-pressure gas pipe, and larger scaled gas storage facilities. The scientific calculation and design of the gas pipeline and the correct judgement and adjustment in the actual operation will directly affect the stable and safe operation of high-pressure gas pipeline and the normal supply of gas. Due to lacking the effective method and software in calculation of high-pressure gas, the hydraulic calculation is usually based on the constant flow in stead of variable flow. Thus there is a marginal difference with the actual pipe pressure and flow. Due to lacking the simulation tool, it is not possible to accurately assess the various working conditions of pipeline and control the pipeline operation. Therefore, it is necessary to conduct a deep study on the actual working conditions of high pressure pipeline, find out the operation laws of various parameters through simulation, and put forward the corresponding control strategy.
This article focuses on the study of flow property of high-pressure gas pipeline, high-pressure gas storage, and chocking flow by adopting the methods of mathematical model, numerical analysis, dynamic simulation, and case studies. The major conclusions are following:
1. The mathematical model is simplified as following:(1) constant temperature for the gas pipeline; (2) ignorance of altitude difference; (3) ignorance of linear velocity changes; (4) ignorance of mass flow changes; (5) linearization based onИ.А.Чарныйlinearization method and least square method. As an usual practice, the convective term, inertia, and neutral are ignored in the calculation of variable flow. In this article, the mathematical model is set up based on momemtum equation and energy equation without ignorance of any terms. Mothods of characteristic curves and implicit centered finite difference are used to solve the variable flow. Numerical analysis is used for the unsteady flow of ling-distance transmission pipeline, which is not necessary to simplify model equations with complicated mathematical conversions and can have better result. It will take longer time to solve the unknown parameters since the system of nonlinear equations is extremely large. In order to ensure numerical solution is absolutely stable, the knot timing and spacing should not be too small. Numerical solution takes the heat exchange between gas and outside environment into consideration and therefore can calculate the temperature distribution along the pipeline. Due to the fluctuations of gas supply and consumption, the pressure, flow, and temperature of the gas pipeline will be fluctuated from time to time. If there are nodes in the network, the changes at the nodes will be the most serious.
2. In contrast with the implicit method, the main advantage of the characteristic method is to display boundary conditions with less required computer storage capacity. But the ratio between time step and pipe section is limited to a certain stable condition, the time step should be very small. If it is too long, it requires more time to calculate. When the characteristic method is used to solve the gas pipeline, difference equation is set up with reverse marching algorith differential grid. The system of ordinary differential equation is solved based on the primary condition and boundary condition. Due to the marginal changes of boundary node with timing, this method can increase the computational accuracy with easier solving process. This article also adopts the centered finite differential method to solve for slow transient flow model, and apply Newton-Raphson method to conduct iterative computation for high order non-linear equation group. The centered finite differential method is a kind of implicit type finite differential method, which has the advantages of high accuracy of second order and fast computation speed.
3. When the gas network is simulated, it can adopts characteristic line method or implicit type finite difference method. This article combines the advantages of these two methods and concludes that the characteristic line method is better used on the boundary node of long-distance pipeline when the dynamic operation conditions of high-pressure gas network are simulated; under other conditions, the implicit type finite difference method is better used. The combination of these two methods can be complimentary with each other. When the dynamic simulation software developed with Visual C++ for branched and ring pipeline is adopted to calculate the example, it is found that the calculating result can satisfy with the actual engineering requirements.
4. To replace usual comparision equation of state with SHBWR equation of state and to solve with Newton iterative method, it can greatly improve the computation speed and. accuracy of gas state paramenters. Due to the fact that the gas state of the outer ring high-pressure pipeline is always in a turbulance zone, relatively accurate Colebrook's Formula is chosen to compute the pipe friction factor with Newton iterative method.
5. To conduct hydraulic analysis on gas transmission line, it can be started with the basic equation of pipeline and combine the actual equation of gas state with enthalpy equation to establish dynamic simulation mathematical model; to solve the friction factor with secant method, it is different from the ususal trial method and can increase the computation accuracy. To deform the formula of friction resistance coefficient and associate with pipe flow, it can be changed with the flow and decrease the error caused by the constant value input of friction resistance coefficient.
6. To conduct thermodynamic analysis on the pipeline temperature, it works out the evolution of gas temperature. The computation result indicates that the pipe temperature solved separately can match with the steady flow model. It further concludes that it is feasible to solve the pipe temperature separately. This provides an effective method to solve the initial value of pipe temperature in multi-resource unsteady flow model.
7. The equation of continuity, equation of momentum, and equation of energy applied to the multi-source and single-source mathematical model are the same. The major differences are treatment of boundary condition, solving method of initial value, and number of equations. This article puts forward the calculation method of initial value for multi-resource dynamic simulation, which is different from the single-resource simulation model. It indicates that the closure analysis of multi-resource dynamic simulation can be started with boundary condition and constraint condition. Based on the closure of euqation of multi-source gas network, it is necessary to add two equations to meet the solving conditions when adding one gas source:one is equation of flow or pressure, another is equation of temperature.
8. The computation of multi-source pipe network can obtain the pressures and flows for the various gas sources, nodes, and pipe section at different profiles and moments. The pressures of various gas sources can be effectively adjusted and the flow can be rationally distributed in reponse to the pressure requirements of different locations. To adopt the data collected with SCADA to conduct simulation computation, and at the same time to compare the calculation result with the data collected, it can inspect the accuracy and reliability of data collection system.
9. To conduct a study on the chocking phenomenon of dynamic simulation and gas flow in the multi-source high-pressure gas network, establish mathematical model of dynamic simulation and chocking flow in the high-pressure gas network, and to solve with Newton iteration method and four orders Rung-Kutta method, the reckoning is verified with actual examples. It indicates that the calculation result can be fully used for the design, construction, and operation control of gas pipe network.
10. Based on the gasdynamics, a study is conducted on the chocking phenomenon at the variable sections and constant sections, and a reckoning is solved with four orders Rung-Kutta method for a constant section chocking model. Combining with an actual example, the evolution of the gas parameters in the chocking state is analyzed. The result indicates that under the conditions of gas-filling from compressor to CNG tanker and then to storage tank, the low-pressure end is inclined to be clogged up due to the rapid expansion because of the greater pressure difference at the two ends and smalller pipe diameter in the initial gas-filling stage. The formula for judgment of chocking is According to the computation, it may produce chocking phenomenon when the pipe terminal pressure ratio is between 0.32-0.41. Therefore, the designed flow shall be no more than the chocking flow, otherwise it may affect the normal gas supply. If the constant section occurred with chocking, the pressure and temperature are changed along the pipeline; if the pressure and temperatureare decreased along the pipeline, the Mach number and flow rate are increased, and the flow rate tends to sound velocity; sectional sound velocity is linked with density and temperature and decreased along the pipeline. The diameter of the pipe connected to the gas distribution station at the end of long-distance pipeline shall be not too small, otherwise it may cause chocking phenomenon and gas shortage at the peak time.
11. A study is conducted on static gas storage and dynamic gas storage of high-pressure pipeline respectively. The computation formula is deduced for static gas storage based on the pipeline pressure evolution. The impacts of pipe length and pressure on static gas storage are also analyzed. Further analysis is conducted on the "emission" chocking phenomenon at the end of long-distance pipeline and its impact on static gas storage in accordance with the definition of dynamic gas storage and variable sections chocking model. The result indicates that the gas storage at the end of long-distance pipeline is usually computed in a static or dynamic state. The reckoning from the static state computation tends to be conservative, and the reckoning from the dynamic state computation is more accurate. The reckoning from the static state computation tends to have error. The static state computation is usually based on the maximum pressure at the starting point and minimum pressure at the end of pipeline, and the actual length of pipeline, which does not include maximum gas storage and optimum pipe length. If the pipeline is too long, it shall not only affect the storage capacity but also the gas storage. Therefore, it should be taken into consideration when the gas storage at the end of long-distance pipeline is designed.
12. According to the dynamic model and computation method proposed in this article, a transient simulation and leakage analysis software is developed for the gas pipe network. The software has a computational simulation function on multi-source high-pressure gas network, realizes the historical data inquiry, new data computation and storage, and lays a foundation for the combination of load prediction and real-time simulation. Based on the computation of various working conditions of several high-pressure gas network, in comparison with the results calculated with foreign pipeline simulation softwares like PIPELINE, TGNET, and SPS, and the actual operation data of the city gas pipe, it indicates that relative deviation is within 6% compared to the foreign software, and within 3% compared to the actual operation data. The reckoning of pipe pressure indicates that the evolution trend of calculated pressures for every regulation stations is in line with the data collected and within 5% of error except for several nodes. It concludes that the software simulated result can reflect the evolution of pipe pressure. The software can be used for the dynamic simulation computation on the actual pipe network, meet the requirements of high-pressure network, and provide guidance to the intelligent operation.
From the conclusions above, we can see that the model established and solution proposed can have higher-accurate computation result with rapid speed and reach the levels of the foreign similar studies. It reveals the evolution process of unsteady flow and gas storage and discharge in the city high-pressure gas network, and provides a theoretical basis for the design and control of high-pressure gas network. In combination with the SCADA data collection system, it can conduct a dynamic simulation on the high-pressure pipeline, and instructs on the design, operation condition simulation, and analysis of gas storage and discharge for the high-pressure gas network. This study has important values both in theory and pratice, which provides a new concept on the flowing of natural gas, theoretical basis for the design of high-pressure gas network, a new method for analysis of chocking phenomenon and high-pressure gas storage, and technical support to the national high-pressure gas transmission and storage.
鉴于此,本文采用建立高压天然气管网数学模型、数值求解、动态仿真模拟、实例对比分析等方法,对高压天然气管网的水力、热力动态特性、高压储气、以及壅塞流动等方面进行了研究。主要结论如下：
(1)对不稳定流数学模型的建立作了大量简化：①天然气沿程温度按等温考虑；②忽略质量流量随时间的变化；③忽略水平输气过程中沿程线速度变化的影响；④忽略管道位置高差的影响；⑤分别采用恰尔内(И.А.Чарный)线性化法和最小二乘法线性化方法对数学模型进行线性化处理等。本文针对目前天然气管道不稳定流动的计算过程中忽略对流项、惯性项和中立项等问题,首次在没有忽略任何项的连续性方程、动量方程、能量方程、状态方程和焓方程所建立的数学模型的情况下,分别采用了特征线法和隐式中心有限差分法对天然气管网不稳定流进行了求数值解。采用数值解法对高压天然气管网不稳定流动进行研究,不用对模型方程组进行简化和复杂的数学变换,求解出来的结果与管道实际运行数据更为接近。求解时要将待求的时间层次上所有的未知量联立起来同时进行求解,求解的非线性方程组很庞大,方程组过大时求解需要的时间长。为了保证数值解的稳定性,时间步长、距离步长都不能够取得过小。数值解考虑了气体与外界环境的热交换,考虑了天然气沿程温度变化,能够计算出天然气沿线的温度分布。由于供气与用气的不均匀性,管网中天然气的压力、流量与温度也随时间波动。如果管网存在有分气点,则在分气点处气体的压力、温度、密度的变化最为剧烈。
(2)与隐式法相比,特征线法主要优点在于它们能对各种边界条件进行显式处理,且计算占用计算机内存较小,但其时间步长和距离步长的比值受到一定稳定条件的限制,这使得时间步长只能取得很小如果分析时间过长时,就需要消耗很长的计算时间。在采用特征线法对天然气管道进行数值求解时,利用逆步进法差分网格建立起特征差分方程,对常微分方程组结合初始条件和边界条件进行求数值解,由于边界节点的参数随时间的变化比较明显,因此该方法能提高计算精度,求解过程容易实现。本文还采用了适用于慢瞬变流的守恒型求解数学模型的隐式中心有限差分法,并利用Newton-Raphson法对形成的高阶非线性方程组进行了迭代计算。隐式中心有限差分法是隐式格式的有限差分方法,表现出了二阶精度高、计算速度快的优点。
(3)对天然气管网进行模拟时,可以单独采用特征线法或隐式有限差分法。本文综合考虑这两种方法的优点,采用综合法求解。结果表明：在模拟高压天然气管网动态运行工况时,在长管元件的边界点上采用特征线法计算,在其它情况下采用隐式中心有限差分法。根据本文所建模型及提出的解法,用Visual C++编程开发出的高压天然气管网动态模拟软件,利用实例计算验证,计算结果可以满足实际工程需要。
(4)采用SHBWR状态方程替代常用的对比状态方程,采用Newton迭代法求解,大幅度提高了天然气状态参数的计算速度与精度。由于高压天然气管道中天然气的流态一般在紊流区,因此在确定管道摩阻系数时,选择计算较为准确的柯列勃洛克公式,采用牛顿迭代方式可以计算出管道摩阻系数。
(5)对输气管道进行水力分析,从输气管道的天然气流动基本方程出发,结合实际气体状态方程与焓方程建立了动态模拟的数学模型；区别于以往的试算法,采用弦截法进行摩阻系数的求解,提高了计算精度。将摩阻系数公式进行变形改写,使其与管道流量进行关联,随着输气管道流量改变而改变,减少了由于摩阻系数的定值输入而带来的误差。
(6)对输气管道的温度变化进行热力学分析,研究了输气管道内天然气温度的变化规律。通过计算比较表明：单独求解输气管道温度与利用含有能量方程的稳定流模型求解出的管道温度基本吻合,因而单独求解管道温度是可行的,为多点接气不稳定流动数学模型模型中温度初始值的求解提供了有效的方法。
(7)多点接气和单气源高压天然气管网数学模型所依据的连续性方程、动量方程以及能量方程是相同的,区别主要在边界条件的处理上,其初始值的求解方法和所建立的方程个数不同。本文提出了多点接高压天然气管网动态模拟初始值计算方法,区别于单气源动态模型,可以从边界条件和约束条件入手对多点接高压天然气管网动态方程组封闭性进行分析。其封闭性分析来看,每增加一个气源点,就要补充两个关于该气源的方程,一个是流量方程或压力方程,另一个是温度方程。从而构成封闭的方程组,达到可以求解条件。
(8)通过对多点接高压天然气管网的计算,得到各个气源点、各个分气点以及各个管段在不同剖面上不同时刻的压力和流量的变化情况。可根据各点压力要求,对各气源压力进行有效控制,对流量进行合理的调度分配。利用SCADA系统采集的数据作为边界条件,对管网进行动态模拟计算,同时将计算结果与SCADA采集的节点流量数据对比分析,可以作为检测数据采集系统的准确性与可靠性
(9)对天然气流动中的壅塞现象进行研究,建立高压天然气管网壅塞流动的数学模型,分别采用四阶Rung-Kutta法和Newton-Raphson迭代法对模型进行求解,并通过工程实例进行对比验证。结果表明计算结果完全可用于天然气管网的设计、运行及调度管理。
(10)以气体动力学为基础,对径管和等径管天然气管道的壅塞现象进行分析研究,采用四阶Rung-Kutta法对等径管道壅塞模型进行求解。结合工程实例,讨论了壅塞状态下管道内气体参数的变化规律。结果再从压缩机室向CNG槽车内加气以及通过CNG槽车向储罐卸气过程中,开始充气阶段由于加(卸)气管两端的压差较大并且管径较小,天然气在低压端急剧膨胀易发生壅塞流动。产生壅塞流动的判定式为：根据实例计算当管道始末端压力比在0.32-0.41之间时,将发生流动壅塞。在工程设计时,管道流量不能超过壅塞流量,否则正常供气会受到影响。等径输气管道天然气流动发生壅塞时,其压力、温度等参数是沿程变化的；压力、温度沿程降低,马赫数及流速沿程增大,流速趋向于声速；各截面的当地声速与密度和温度有关,沿线降低。长输管道末端门站所连接的城市输气管网的管径不应太小,否则在用气高峰时刻在变径处会产生流动壅塞,导致某个时段内输入城市管网的天然气量小于城市实际用气需求量,造成供气不足,引发供气安全事故。
(11)分别对高压管道的稳态储气和非稳态储气进行研究,通过拟合管道内压力变化规律,推导出稳态储气量的计算公式,并分析了管长、压力等参数对稳态储气的影响；结合非稳态储气的定义与变径管道壅塞流动模型,对长输管道末段流动壅塞及其对管道储气能力的影响进行分析。结果表明：长输管线末段管道储气量计算可以按稳态,也可按非稳态来考虑。稳态储气计算结果偏于保守,计算结果与实际结果有误差。按稳态工况计算管段储气量的时候,通常根据起点最大压力、末端最小压力以及管道的实际长度来计算储气量,未考虑其最大储气量和最优长度。如果管段过长,由于流动阻力加大,不但不能多储气,反而会影响管道的储气。在利用长输管线末段储气的设计中应该注意这一特点。按照非稳态计算结果德更准确。
(12)根据本文提出的动态模型和解法,对第一版天然气管网动态模拟软件进行改进,使其具有多点接气高压天然气管网动态模拟计算功能,改进了历史数据的输入、查询、新数据计算与存储等功能,有利于实现负荷预测与实时模拟的结合。通过对多个实际或设计的高压天然气管网在多种不同运行工况下的计算,并将计算结果与国外同类模拟软件(PIPELINE、TGNET、SPS等)计算结果、城市管网SCADA系统采集的实际运行数据进行对比,结果表明,各个调压站计算压力的变化趋势与采集压力的变化趋势基本一致,与国外软件计算结果的相对偏差在6%以内,与SCADA系统采集的实际运行数据的相对误差在3%以内。改进型软件可对实际管网进行动态模拟计算,模拟结果准确反映出管道压力的变化规律,满足高压管网运行的要求,能够指导管网的智能化运行。
从以上结论来看,研究建立的高压天然气动态模拟数学模型和提出的解法计算结果精度高、计算速度快。揭示了城市高压天然气管网不稳定流动和储、放气的变化规律。结合SCADA系统采集的实际运行数据,可对高压管线进行动态模拟,计算结果可指导高压天然气管线的设计、运行工况模拟和储放气的分析。该研究为高压天然气管网动态研究提供了新的思路,为高压天然气管网的设计、运行、调度调控提供了理论依据,为分析壅塞流动和城市天然气高压储气能力提供了新的方法,为高压天然气安全输送和储存提供了技术支持。
Natural gas is a new clean energy resource, which has been attached great importance all over the world. Following the transition from the extensive economy and the adjustment of energy policy, the ratio of natural gas in the energy structure is increasing constantly with longer transmission pipeline and high-pressure gas pipe, and larger scaled gas storage facilities. The scientific calculation and design of the gas pipeline and the correct judgement and adjustment in the actual operation will directly affect the stable and safe operation of high-pressure gas pipeline and the normal supply of gas. Due to lacking the effective method and software in calculation of high-pressure gas, the hydraulic calculation is usually based on the constant flow in stead of variable flow. Thus there is a marginal difference with the actual pipe pressure and flow. Due to lacking the simulation tool, it is not possible to accurately assess the various working conditions of pipeline and control the pipeline operation. Therefore, it is necessary to conduct a deep study on the actual working conditions of high pressure pipeline, find out the operation laws of various parameters through simulation, and put forward the corresponding control strategy.
This article focuses on the study of flow property of high-pressure gas pipeline, high-pressure gas storage, and chocking flow by adopting the methods of mathematical model, numerical analysis, dynamic simulation, and case studies. The major conclusions are following:
1. The mathematical model is simplified as following:(1) constant temperature for the gas pipeline; (2) ignorance of altitude difference; (3) ignorance of linear velocity changes; (4) ignorance of mass flow changes; (5) linearization based onИ.А.Чарныйlinearization method and least square method. As an usual practice, the convective term, inertia, and neutral are ignored in the calculation of variable flow. In this article, the mathematical model is set up based on momemtum equation and energy equation without ignorance of any terms. Mothods of characteristic curves and implicit centered finite difference are used to solve the variable flow. Numerical analysis is used for the unsteady flow of ling-distance transmission pipeline, which is not necessary to simplify model equations with complicated mathematical conversions and can have better result. It will take longer time to solve the unknown parameters since the system of nonlinear equations is extremely large. In order to ensure numerical solution is absolutely stable, the knot timing and spacing should not be too small. Numerical solution takes the heat exchange between gas and outside environment into consideration and therefore can calculate the temperature distribution along the pipeline. Due to the fluctuations of gas supply and consumption, the pressure, flow, and temperature of the gas pipeline will be fluctuated from time to time. If there are nodes in the network, the changes at the nodes will be the most serious.
2. In contrast with the implicit method, the main advantage of the characteristic method is to display boundary conditions with less required computer storage capacity. But the ratio between time step and pipe section is limited to a certain stable condition, the time step should be very small. If it is too long, it requires more time to calculate. When the characteristic method is used to solve the gas pipeline, difference equation is set up with reverse marching algorith differential grid. The system of ordinary differential equation is solved based on the primary condition and boundary condition. Due to the marginal changes of boundary node with timing, this method can increase the computational accuracy with easier solving process. This article also adopts the centered finite differential method to solve for slow transient flow model, and apply Newton-Raphson method to conduct iterative computation for high order non-linear equation group. The centered finite differential method is a kind of implicit type finite differential method, which has the advantages of high accuracy of second order and fast computation speed.
3. When the gas network is simulated, it can adopts characteristic line method or implicit type finite difference method. This article combines the advantages of these two methods and concludes that the characteristic line method is better used on the boundary node of long-distance pipeline when the dynamic operation conditions of high-pressure gas network are simulated; under other conditions, the implicit type finite difference method is better used. The combination of these two methods can be complimentary with each other. When the dynamic simulation software developed with Visual C++ for branched and ring pipeline is adopted to calculate the example, it is found that the calculating result can satisfy with the actual engineering requirements.
4. To replace usual comparision equation of state with SHBWR equation of state and to solve with Newton iterative method, it can greatly improve the computation speed and. accuracy of gas state paramenters. Due to the fact that the gas state of the outer ring high-pressure pipeline is always in a turbulance zone, relatively accurate Colebrook's Formula is chosen to compute the pipe friction factor with Newton iterative method.
5. To conduct hydraulic analysis on gas transmission line, it can be started with the basic equation of pipeline and combine the actual equation of gas state with enthalpy equation to establish dynamic simulation mathematical model; to solve the friction factor with secant method, it is different from the ususal trial method and can increase the computation accuracy. To deform the formula of friction resistance coefficient and associate with pipe flow, it can be changed with the flow and decrease the error caused by the constant value input of friction resistance coefficient.
6. To conduct thermodynamic analysis on the pipeline temperature, it works out the evolution of gas temperature. The computation result indicates that the pipe temperature solved separately can match with the steady flow model. It further concludes that it is feasible to solve the pipe temperature separately. This provides an effective method to solve the initial value of pipe temperature in multi-resource unsteady flow model.
7. The equation of continuity, equation of momentum, and equation of energy applied to the multi-source and single-source mathematical model are the same. The major differences are treatment of boundary condition, solving method of initial value, and number of equations. This article puts forward the calculation method of initial value for multi-resource dynamic simulation, which is different from the single-resource simulation model. It indicates that the closure analysis of multi-resource dynamic simulation can be started with boundary condition and constraint condition. Based on the closure of euqation of multi-source gas network, it is necessary to add two equations to meet the solving conditions when adding one gas source:one is equation of flow or pressure, another is equation of temperature.
8. The computation of multi-source pipe network can obtain the pressures and flows for the various gas sources, nodes, and pipe section at different profiles and moments. The pressures of various gas sources can be effectively adjusted and the flow can be rationally distributed in reponse to the pressure requirements of different locations. To adopt the data collected with SCADA to conduct simulation computation, and at the same time to compare the calculation result with the data collected, it can inspect the accuracy and reliability of data collection system.
9. To conduct a study on the chocking phenomenon of dynamic simulation and gas flow in the multi-source high-pressure gas network, establish mathematical model of dynamic simulation and chocking flow in the high-pressure gas network, and to solve with Newton iteration method and four orders Rung-Kutta method, the reckoning is verified with actual examples. It indicates that the calculation result can be fully used for the design, construction, and operation control of gas pipe network.
10. Based on the gasdynamics, a study is conducted on the chocking phenomenon at the variable sections and constant sections, and a reckoning is solved with four orders Rung-Kutta method for a constant section chocking model. Combining with an actual example, the evolution of the gas parameters in the chocking state is analyzed. The result indicates that under the conditions of gas-filling from compressor to CNG tanker and then to storage tank, the low-pressure end is inclined to be clogged up due to the rapid expansion because of the greater pressure difference at the two ends and smalller pipe diameter in the initial gas-filling stage. The formula for judgment of chocking is According to the computation, it may produce chocking phenomenon when the pipe terminal pressure ratio is between 0.32-0.41. Therefore, the designed flow shall be no more than the chocking flow, otherwise it may affect the normal gas supply. If the constant section occurred with chocking, the pressure and temperature are changed along the pipeline; if the pressure and temperatureare decreased along the pipeline, the Mach number and flow rate are increased, and the flow rate tends to sound velocity; sectional sound velocity is linked with density and temperature and decreased along the pipeline. The diameter of the pipe connected to the gas distribution station at the end of long-distance pipeline shall be not too small, otherwise it may cause chocking phenomenon and gas shortage at the peak time.
11. A study is conducted on static gas storage and dynamic gas storage of high-pressure pipeline respectively. The computation formula is deduced for static gas storage based on the pipeline pressure evolution. The impacts of pipe length and pressure on static gas storage are also analyzed. Further analysis is conducted on the "emission" chocking phenomenon at the end of long-distance pipeline and its impact on static gas storage in accordance with the definition of dynamic gas storage and variable sections chocking model. The result indicates that the gas storage at the end of long-distance pipeline is usually computed in a static or dynamic state. The reckoning from the static state computation tends to be conservative, and the reckoning from the dynamic state computation is more accurate. The reckoning from the static state computation tends to have error. The static state computation is usually based on the maximum pressure at the starting point and minimum pressure at the end of pipeline, and the actual length of pipeline, which does not include maximum gas storage and optimum pipe length. If the pipeline is too long, it shall not only affect the storage capacity but also the gas storage. Therefore, it should be taken into consideration when the gas storage at the end of long-distance pipeline is designed.
12. According to the dynamic model and computation method proposed in this article, a transient simulation and leakage analysis software is developed for the gas pipe network. The software has a computational simulation function on multi-source high-pressure gas network, realizes the historical data inquiry, new data computation and storage, and lays a foundation for the combination of load prediction and real-time simulation. Based on the computation of various working conditions of several high-pressure gas network, in comparison with the results calculated with foreign pipeline simulation softwares like PIPELINE, TGNET, and SPS, and the actual operation data of the city gas pipe, it indicates that relative deviation is within 6% compared to the foreign software, and within 3% compared to the actual operation data. The reckoning of pipe pressure indicates that the evolution trend of calculated pressures for every regulation stations is in line with the data collected and within 5% of error except for several nodes. It concludes that the software simulated result can reflect the evolution of pipe pressure. The software can be used for the dynamic simulation computation on the actual pipe network, meet the requirements of high-pressure network, and provide guidance to the intelligent operation.
From the conclusions above, we can see that the model established and solution proposed can have higher-accurate computation result with rapid speed and reach the levels of the foreign similar studies. It reveals the evolution process of unsteady flow and gas storage and discharge in the city high-pressure gas network, and provides a theoretical basis for the design and control of high-pressure gas network. In combination with the SCADA data collection system, it can conduct a dynamic simulation on the high-pressure pipeline, and instructs on the design, operation condition simulation, and analysis of gas storage and discharge for the high-pressure gas network. This study has important values both in theory and pratice, which provides a new concept on the flowing of natural gas, theoretical basis for the design of high-pressure gas network, a new method for analysis of chocking phenomenon and high-pressure gas storage, and technical support to the national high-pressure gas transmission and storage.
引文
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