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本文建立了单一介质、双重介质非定常非达西低速渗流的数学模型。用拉氏变换求出了单一介质、双重介质非定常非达西低速渗流无穷大地层的解及其长时渐近解。在求解过程中,拉氏空间的特解用格林函数表示。用有限积分交换与拉氏交换求得了单一介质、双重介质非定常非达西低速渗流有界地层的解。从长时渐近解可知,当起始压力梯度λ_B较大时,即非达西低速渗流参数D较大时,非达西低速渗流的压力曲线呈凹型,没有直线段。D越大,压力曲线越上凹。
In this paper, a mathematical model of single medium and non-Darcy non-Darcy low velocity double seepage flow is established. Using Laplace transform, we obtain the solution and its long-time asymptotic solution of a single medium, an infinite medium of non-Darcy double medium with non-Darcy seepage at low velocity. In the process of solving, the special solution of Lagrange space is expressed by Green’s function. Finite integral solution and Lagrangian exchange are used to obtain the solution of a single medium and a ductile medium with non-Darcy low permeability percolation bounded by double media. As can be seen from the long-time asymptotic solution, when the initial pressure gradient λ B is large, that is, when the non-Darcy low velocity seepage parameter D is large, the pressure curve of non-Darcy low velocity seepage is concave with no straight line segment. The larger the D, the more concave the pressure curve.