A new well model for one-phase flow in anisotropic porous media is introduced, where the mass exchange between well and a porous medium is modeled by spatially distributed source terms over a small neighborhood region. To this end, we first present a compact derivation of the exact analytical solution for an arbitrarily oriented, infinite well cylinder in an infinite porous medium with anisotropic permeability tensor in ${\mathbb{R}}^3$, for constant well pressure and a given injection rate, using a conformal map. The analytical solution motivates the choice of a kernel function to distribute the sources. The presented model is independent from the discretization method and the choice of computational grids. It can be applied to porous media with full anisotropic permeability tensors. In numerical experiments, the new well model is shown to be consistent and robust with respect to rotation of the well axis, rotation of the permeability tensor, and different anisotropy ratios. Finally, a comparison with a Peaceman-type well model suggests that the new scheme leads to an increased accuracy for injection (and production) rates for arbitrarily-oriented pressure-controlled wells.

介绍了一种用于各向异性多孔介质中单相流的新井模型，其中井与多孔介质之间的质量交换通过在较小邻域内的空间分布源项进行建模。为此，我们首先给出在各向异性渗透率张量为0的无限多孔介质中任意取向的无限井筒的精确解析解的紧凑推导。${\mathbb{ř}}^3$对于恒定的井压和给定的注入速率，请使用保形图。分析解决方案促使人们选择内核函数来分配源。所提出的模型独立于离散化方法和计算网格的选择。它可以应用于具有各向异性各向异性张量的多孔介质。在数值实验中，新井模型显示出相对于井轴旋转，渗透率张量旋转以及不同的各向异性比率而言是一致且稳健的。最后，与Peaceman型油井模型进行比较表明，该新方案可提高任意定向压力控制油井的注入（和生产）速率的准确性。