摘要
我国煤层气储量丰富,煤层气的抽采不仅可以缓解我国能源紧缺的局面,同时可以保护环境和防治瓦斯灾害,目前,煤层气的“高储低渗”的特点一直制约我国煤层气工业的发展。当前如何提高低渗透煤层的渗透率是煤层气开采解决的难点,其理论未形成突破。采用微积分、模糊数学、结构元理论,结合渗流力学、岩石力学对煤层气输运进行了建模和求解。通过分析煤层气在煤层中的运移是吸附、解吸、扩散、渗流的过程,建立了煤层气、水两相双重介质的渗流数学模型,稳态、拟稳态、非稳态情况下的煤层气、水两相数学模型,考虑渗透率为模糊数,建立了稳态、拟稳态、非稳态煤层气、水两相稳态运移的模糊数学模型,分别求出解析解、模糊解析解、隶属度、渐进解、短时渐进解和长时渐进解。主要研究成果如下:
考虑孔隙、裂隙双重介质,分析气相、水相、固体骨架发展过程,建立煤层气输运的数学模型,进行稳态渗流假设,通过化简建立煤层气稳态输运模型,求得稳态解析解。
对稳态解析解进行数值处理得到压力分布图,图线表明稳态条件下,随着半径的增加,气相压力成等差级数变化。这个规律与国内外已有研究成果相似,也就说明了该解析解的可靠性。而包括流量、渗流速度等影响煤层气生产的重要参数均与压力有直接关系,解释求得压力的重要性。
由于实际渗透率的不可测定性,将渗透率视为模糊数,建立煤层气、水两相运移稳态模糊数学模型,基于模糊结构元方法进行分析,由于模糊限定微分方程式的解是可表示的,由此求得模糊解析解,并籍此求得隶属度分布。
在研究水相非稳态渗流时,考虑两种情况,一种是无限大地层,第二种是圆形封闭井。分别建立了无限大地层非稳态渗流数学模型和圆形封闭地层非稳态渗流数学模型,基于波尔兹曼变换法并采用幂积分求得煤层中非稳态水相输运压力和产量的解析解,进而建立了无限大地层非稳态渗流模糊数学模型和圆形封闭地层非稳态渗流模糊数学模型。并求出解析解和模糊解析解。带入实际参数,则可根据每一个隶属度求出符合隶属度范围的渗透率范围,进一步可以求得压力的范围;反之,当给定一个渗透率,就可以知道它的隶属度,从而求出压力的隶属度,即执行值。
采用拉普拉斯变换和反演方法对建立的无限大地层双重介质煤层气拟稳态渗流数学模型进行研究,在求得解析解的同时求得渐进解为。解析解图线显示当半径值一定的情况下,拟压力是随着时间的增加而增加,井筒附近的压力梯度大,也就是说井筒附近的压力降得很快,气体流动快,而远处地层压力变化较慢,井筒对远处煤层中的煤层气影响较小。当时间值一定的情况下,拟压力是随着半径的增加出现三个区段,首先拟压力出现下降,即初始阶段压力会有一个瞬时提升过程。这是由于打井初期井周突然卸压造成气流急速运动,气相压力骤增。第二阶段孔隙气体开始向裂隙扩散,是一个过渡阶段,压力出现下降,最后压力趋于常值,体现煤层气与骨架处于相对稳定状态。相同时间段气相压力随半径的增大而减小,远处地层压力变化较慢,井筒对远处煤层中的煤层气影响较小。ω因子对压力值具有直接影响。特定因子越小,压力越大。它直接决定不同区段拟压力曲线值,可以加快实现较大压力降。
渐进解显示立井初期,随着时间的增加拟压力上升,压力下降梯度明显。固定时刻,随着半径增加,拟压力呈递减对数曲线形式。时间较长时,固定位置气相压力稳定,但远处地层受压力影响很小,基本不发生变化。
建立无限大地层煤层气拟稳态渗流模糊数学模型,分别求得短时、长时渐进模糊解。通过模糊解析求值可以得到不同隶属度下渗透率在不同时间、不同半径的范围,并可得拟压力范围,进而推得压力的范围。这些数据为实际工程提供有利参考。
研究双重介质煤层气非稳态渗流过程,建立数学模型,求得解析解和渐进解。
本文的研究为煤层气的输运提供了可靠的理论研究,解析解的求得为煤层气的商业化开发具有很大的实用价值。
Consider the pores, cracks dual media, analysis of the development of gas, water phase and solid skeleton. Establish the mathematical model of methane transport, assumption the steady flow, establishment the model of CBM steady-state transport by simplification, and obtained the steady-state analytical solution.
Consider the pores, cracks dual media, analysis of the development of gas, water phase and solid skeleton. Establish the mathematical model of methane transport, assumption the steady flow, establishment the model of CBM steady-state transport by simplification, and obtained the steady-state analytical solution.
Numerical treatment the steady-state analytical solution and got the pressure distribution, the chart shows that under the steady state conditions, as the radius increases, gas pressure changes into the arithmetic progression, this rule similar to the existing research results at home and abroad. Also shows the reliability of the analytical solution. The important parameters of coal bed methane production which including flow, flow speed, etc. are directly related with the pressure. Explain the importance of the pressure obtained.
As the unpredictable qualitative of actual penetration, take the permeability as a fuzzy number, establishing coal bed methane, water, transport steady-state two-phase mathematical model of fuzzy. Base on the fuzzy structure element method. The solution of fuzzy constraint differential equations can be expressed. Obtain the fuzzy analytical solution, and take calculated distribution of membership.
In study of non-steady seepage of water phase, two cases considered, one is the infinite ground, the second is a well closed circular. Establish the coal bed methane formation infinite and closed circle formation mathematical model of steady flow. Get the analytical solution of non-steady state transport of water-phase pressure and produce in coal based on Boltzmann transformation and power integrator. Furthermore, establish the coal bed methane formation infinite and closed circle formation fuzzy mathematical model of steady flow. And get the analytical solutions and the fuzzy analytic solution. Take into the actual parameter, can calculated the permeability range consistent with the scope of membership according to each membership. Otherwise, give a penetration to know that it’s membership, and get the membership of pressure, that the implementation of value.
Based on Laplace transform and inversion, the analytical solution and asymptotic solution were found by studying on the unsteady state percolation mathematical model of double-medium CBM at infinity stratum. The analytical solutions show the quasi-pressure increases along the time pass when radius is definite. The pressure gradient become large what mean the pressure fall down fast nearby the gas well. Gas flowing rapidly and pressure variation slowly in the distance, so the effect on the coal seams by CBM is less. Quasi-pressure appears three sections when time is certain. First, because of the sudden pressure relief, airflow makes haste, quasi-pressure decrease and pressure increase. Then, there will be a transition moment, pore gas diffuse to crack, pressure become less. Finally, pressure becomes constant. At the same time, in-situ rock stress change slowly in the distance. There is straight effect on the pressure byωfactor. Pressure becomes large along the smallω. It decides the quasi-pressure and achieves bigger differential pressure.
The asymptotic solutions show that at the beginning of vertical shaft construction, the pseudo pressure to be increased as the time increased. The press gradient decreased significantly. At a fixed time, the pseudo pressure decreased by logarithmic curve with the radius increases. As the time longer, gas pressure is stable at a fixed position, but the pressure has little effect formation by far away. Basically does not change.
Established the coal bed methane formation infinite fuzzy mathematical model of steady flow, obtained the solution of short-time asymptotic solutions and the long-time asymptotic solutions. Through fuzzy analysis evaluated we can got the range of permeability under different membership degrees in different times and different radius. And get the range of pseudo pressure, further push the range of pressure. The data provide a favorable reference to the actual project.
Study on the unsteady flow process of coal bed gas in double-porosity media. Found mathematical model, got the analytical solution and the asymptotic solution.
This study provided a reliable theoretical study for the transport of coal bed methane. The obtained of analytical solutions has great practical value for the commercial development of CBM.
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