页岩气藏双重介质模型的解的结构

发布时间：2018-09-14 10:24

【摘要】：基于解的相似构造理论,以求解微分方程边值问题为出发点;作为预备知识,直接给出二阶线性齐次微分方程的相似构造法理论,利用Laguerre方程边值问题和Gegenbauer方程边值问题进一步解释和论证该理论,发现这两种方程边值问题的解都可以用连分式的形式表达,给出了这两种方程边值问题的解的相似结构的求解步骤,进一步说明解的相似构造理论运用于这类问题的有效性。本文的主题研究的是页岩气藏双重介质模型的解的相似结构:首先,根据页岩气渗流理论,以页岩气藏双重介质模型为研究对象,针对页岩气藏解吸吸附、应力敏感、气体扩散、滑脱效应以及启动压力梯度等复杂的渗流问题,以解吸吸附为前提,建立了如下三种数学模型:(1)应力敏感性天然裂缝页岩气藏双孔渗流模型;(2)考虑启动压力梯度裂缝性页岩气藏双孔渗流模型;(3)分别从考虑基质孔隙滑脱效应、考虑基质微孔隙滑脱效应和气体扩散两种因素以及综合考虑基质微孔隙应力敏感、滑脱效应和气体扩散三种因素共同作用的三个角度出发的页岩气藏双渗透渗流模型。接着,利用线性化方法、摄动法、常数变易法以及Laplace变换等数学方法,将建立的三个页岩气藏渗流模型转化为相应的变型Bessel方程边值问题,得到三个模型在Laplace空间下的解。最后,利用变型Bessel方程的解的相似构造理论,对三个模型的解进行进一步研究和分析,发现三个模型的解具有相似的结构。这不仅扩展了解的相似构造理论的应用范围,证明了解的相似构造理论在页岩气双重介质模型的有效性,而且提供了求解页岩气藏渗流模型的一种新方法,为进行页岩气藏渗流模型的进一步研究提供便利。
[Abstract]:Based on the theory of similarity construction of solutions, the similarity construction theory of second order linear homogeneous differential equations is directly given as a preliminary knowledge to solve boundary value problems of differential equations. By using the boundary value problem of Laguerre equation and the boundary value problem of Gegenbauer equation, the theory is further explained and proved. It is found that the solutions of these two boundary value problems can be expressed in the form of continuous fractions. The steps of solving the similar structure of the solutions of the boundary value problems of the two equations are given. The validity of the similarity construction theory of the solutions applied to this kind of problems is further illustrated. The theme of this paper is to study the similar structure of the solution of shale gas reservoir dual medium model. Firstly, according to the shale gas percolation theory, taking the shale gas reservoir dual medium model as the research object, aiming at the shale gas reservoir desorption and adsorption, the stress is sensitive. The complex seepage problems, such as gas diffusion, slippage effect and starting pressure gradient, are based on desorption and adsorption. Three mathematical models are established as follows: (1) stress sensitive natural fractured shale gas reservoir dual pore seepage model; (2) considering starting pressure gradient fracture shale gas reservoir dual pore seepage model; (3) considering matrix pore slippage effect, Considering two factors of matrix micropore slippage and gas diffusion, and considering the three factors of matrix micropore stress sensitivity, slippage effect and gas diffusion, the double permeability seepage model of shale gas reservoir is developed. Then, by means of linearization method, perturbation method, constant variation method and Laplace transformation, the three shale gas reservoir seepage models are transformed into the corresponding modified Bessel equation boundary value problem, and the solutions of the three models in Laplace space are obtained. Finally, by using the similarity construction theory of the solutions of the modified Bessel equation, the solutions of the three models are further studied and analyzed, and it is found that the solutions of the three models have similar structures. This not only extends the scope of application of the similar structure theory, but also proves the validity of the similar structure theory in the shale gas dual medium model, and provides a new method to solve the seepage model of shale gas reservoir. It is convenient for further study on seepage model of shale gas reservoir.
【学位授予单位】：西华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TE37;O175.8

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