非线性渗流方程解析方法研究及应用

发布时间：2018-05-19 21:18

本文选题：解析方法 + 拟流量　；参考：《中国科学院研究生院(渗流流体力学研究所)》2015年博士论文

【摘要】：随着低渗透油田的大规模开发,生产实际和室内实验都表明,流体在特低渗透储层中的流动属于非线性渗流,已经提出了各种形式的非线性渗流数学方程。但到目前为止,对这些非线性渗流方程只有数值解,还缺乏解析解。对于众多石油科学技术工作者来说,非线性方程的解析解是我们追求的重要目标,它对于我们提升现有计算方法,对于我们更准确地预测油田生产动态,提高石油科技水平,无疑都是非常重要的。为此,我们在这方面进行了探索。一、我们以三参数非线性渗流方程为基础,依据稳态逐次替换法求解非稳态、非线性偏微分方程的基本原理,提出了一套求解非线性偏微分方程的解析方法。分析了油井产量变化规律,分析了影响产量的因素；分析了定产条件下,井底压力变化规律,以及非线性参数对井底压力变化的影响。二、基于同伦变换原理,提出了求解应力敏感耦合非线性偏微分方程的解析方法。分析了压力分布的特点,探讨了影响产量递减规律的因素和井底压力下降的规律。提出了附加表皮因子和附加启动压力梯度两种近似方法。讨论了附加表皮因子法与附加启动压力梯度法井底压力和产量递减规律。三、建立了分段压裂水平井有限导流能力产量递减模型,分析了非线性及应力敏感性的影响。分析了水平井筒压降规律和雷诺数变化规律及对产量的影响。四、基于点源函数理论,提出了统一表征线性与非线性的格林函数及求解方法。论证了非线性渗流解析方法满足纽曼乘积条件,提出了归一化拟时间的概念,初步论证了非线性格林函数的解析方法,讨论了垂向渗透率对产量递减规律的影响。五、利用拉氏变换和数值反演方法分析了有界封闭地层非线性渗流产量递减规律,并将结果同文献进行了对比,得出存在极限供给半径的结论。利用围道积分求解了考虑井筒储存效应和表皮因子情况下,非线性油藏井底压力下降规律,给出了非线性试井图版。
[Abstract]:With the large-scale development of low permeability oil fields, the production practice and laboratory experiments show that the flow of fluid in ultra-low permeability reservoirs is nonlinear seepage, and various forms of nonlinear seepage mathematical equations have been proposed. However, up to now, there are only numerical solutions for these nonlinear seepage equations and no analytical solutions. For many petroleum science and technology workers, the analytical solution of nonlinear equations is an important goal we pursue. It is an important goal for us to upgrade the existing calculation methods, to more accurately predict the oil production performance, and to improve the level of petroleum science and technology. There is no doubt that they are very important. Therefore, we have carried on the exploration in this aspect. Firstly, based on the three parameter nonlinear seepage equation and the basic principle of steady state successive substitution method for solving unsteady and nonlinear partial differential equations, an analytical method for solving nonlinear partial differential equations is proposed. The variation law of oil well production and the factors affecting production are analyzed, and the variation law of bottom hole pressure and the influence of nonlinear parameters on bottom hole pressure change are analyzed under the condition of constant production. Secondly, based on the homotopy transformation principle, an analytical method for solving stress-sensitive coupled nonlinear partial differential equations is proposed. The characteristics of pressure distribution are analyzed, and the factors influencing production decline law and the law of bottom hole pressure decreasing are discussed. Two approximate methods, the additional epidermal factor and the additional starting pressure gradient, are proposed. The law of bottom hole pressure and production decline by adding epidermis factor method and additional starting pressure gradient method are discussed. Thirdly, a production decline model with limited conductivity is established, and the effects of nonlinearity and stress sensitivity are analyzed. The variation law of horizontal wellbore pressure drop and Reynolds number and its influence on production are analyzed. Fourthly, based on the point source function theory, the Green's function and its solution are proposed. This paper proves that the analytical method of nonlinear seepage flow satisfies the Newman product condition, puts forward the concept of normalized quasi-time, preliminarily demonstrates the analytical method of nonlinear Green's function, and discusses the influence of vertical permeability on the law of production decline. Fifthly, by using Laplace transform and numerical inversion method, the law of nonlinear percolation production decline in bounded closed strata is analyzed, and the results are compared with the literature, and the conclusion that the limit supply radius exists is obtained. Considering the wellbore storage effect and skin factor, the downwellbore pressure drop law of nonlinear reservoir is solved by means of confining integral, and the nonlinear well test chart is given.
【学位授予单位】：中国科学院研究生院(渗流流体力学研究所)
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O357.3;O175

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