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试井是指弱可压缩流体在多孔介质中的流动,而多孔介质的性质通常是由一类非线性的偏微分方程组来描述。方程组通常利用拉普拉斯变换或拉普拉斯变换的数值反演来求解,如Stehfest反演和Crump反演。然而并不是所有的试井问题都可以通过这些方法得到解决,一种新的变换方法如正交配置法和伽勒金法,可以更加有效、简便地对此类方程进行求解。但是,迄今为止,这些方法在实际应用上仍然受到限制。首要的任务是研究在理想的径向流系统中,正交配置法在弱可压缩流体的试井分析中应用的可行性。现在,不规则边界的非均质油藏的试井模拟技术得到了发展。由于主要关注的是正交配置模拟的可行性,所以没有必要研究更多的试井问题。然而,本文还是给出了一些典型实例的应用,并且将一些结果和数值反演所得到的结果进行了比较。给出了一种新的方法来数值模拟弱可压缩流体的流动,而且这种流动考虑了井筒储集和表皮效应的影响。同时,还表明了运用正交配置法进行试井模拟是切实可行的,并且在许多情况下,正交配置法得到的解要比拉普拉斯变换的数值反演所得到的解更加理想,但也有一定的不足之处。例如,压力导数的波动要是通过有限元的正交配置法来解决,那么就需要在编制程序时额外考虑到有限差分或者是拉普拉斯的数值反演。
Well testing refers to the flow of weakly compressible fluids in porous media, whereas the properties of porous media are usually described by a class of nonlinear partial differential equations. Equations are usually solved using numerical inversion of the Laplace transform or Laplace transform, such as Stehfest inversion and Crump inversion. However, not all of the well testing problems can be solved by these methods. A new transformation method such as orthogonal collocation method and Galerkin method can solve these equations more effectively and easily. However, these methods have so far been limited in practical application. The primary task is to investigate the feasibility of using the orthogonal configuration method in well test analysis of weakly compressible fluids in an ideal radial flow system. Well test simulation techniques for heterogeneous reservoirs with irregular boundaries have now been developed. Since the main concern is the feasibility of the orthogonal configuration simulation, there is no need to study more well testing problems. However, this article also gives some typical examples of applications, and some results and numerical inversion of the results obtained were compared. A new method is presented to numerically simulate the flow of weakly compressible fluids, and this flow considers the effects of wellbore storage and skin effect. At the same time, it is shown that it is practicable to use Orthogonal Collocation method for well test simulation. And in many cases, the solution obtained by orthogonal collocation method is more ideal than the numerical inversion of Laplace transform. But there are some shortcomings. For example, if the derivative of the pressure derivative is solved by the orthogonal configuration of the finite element, then additional consideration of finite difference or Laplace’s numerical inversion is required when programming.