【摘要】：基于解的相似構(gòu)造理論,以求解微分方程邊值問(wèn)題為出發(fā)點(diǎn);作為預(yù)備知識(shí),直接給出二階線性齊次微分方程的相似構(gòu)造法理論,利用Laguerre方程邊值問(wèn)題和Gegenbauer方程邊值問(wèn)題進(jìn)一步解釋和論證該理論,發(fā)現(xiàn)這兩種方程邊值問(wèn)題的解都可以用連分式的形式表達(dá),給出了這兩種方程邊值問(wèn)題的解的相似結(jié)構(gòu)的求解步驟,進(jìn)一步說(shuō)明解的相似構(gòu)造理論運(yùn)用于這類(lèi)問(wèn)題的有效性。本文的主題研究的是頁(yè)巖氣藏雙重介質(zhì)模型的解的相似結(jié)構(gòu):首先,根據(jù)頁(yè)巖氣滲流理論,以頁(yè)巖氣藏雙重介質(zhì)模型為研究對(duì)象,針對(duì)頁(yè)巖氣藏解吸吸附、應(yīng)力敏感、氣體擴(kuò)散、滑脫效應(yīng)以及啟動(dòng)壓力梯度等復(fù)雜的滲流問(wèn)題,以解吸吸附為前提,建立了如下三種數(shù)學(xué)模型:(1)應(yīng)力敏感性天然裂縫頁(yè)巖氣藏雙孔滲流模型;(2)考慮啟動(dòng)壓力梯度裂縫性頁(yè)巖氣藏雙孔滲流模型;(3)分別從考慮基質(zhì)孔隙滑脫效應(yīng)、考慮基質(zhì)微孔隙滑脫效應(yīng)和氣體擴(kuò)散兩種因素以及綜合考慮基質(zhì)微孔隙應(yīng)力敏感、滑脫效應(yīng)和氣體擴(kuò)散三種因素共同作用的三個(gè)角度出發(fā)的頁(yè)巖氣藏雙滲透滲流模型。接著,利用線性化方法、攝動(dòng)法、常數(shù)變易法以及Laplace變換等數(shù)學(xué)方法,將建立的三個(gè)頁(yè)巖氣藏滲流模型轉(zhuǎn)化為相應(yīng)的變型Bessel方程邊值問(wèn)題,得到三個(gè)模型在Laplace空間下的解。最后,利用變型Bessel方程的解的相似構(gòu)造理論,對(duì)三個(gè)模型的解進(jìn)行進(jìn)一步研究和分析,發(fā)現(xiàn)三個(gè)模型的解具有相似的結(jié)構(gòu)。這不僅擴(kuò)展了解的相似構(gòu)造理論的應(yīng)用范圍,證明了解的相似構(gòu)造理論在頁(yè)巖氣雙重介質(zhì)模型的有效性,而且提供了求解頁(yè)巖氣藏滲流模型的一種新方法,為進(jìn)行頁(yè)巖氣藏滲流模型的進(jìn)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.
【學(xué)位授予單位】：西華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TE37;O175.8

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