# A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model

## TL;DR

This paper introduces a novel well model for one-phase flow in anisotropic porous media, utilizing distributed source terms to improve accuracy and robustness across various orientations and anisotropy ratios.

## Contribution

The paper presents a new, consistent well model based on distributed sources, independent of discretization, with analytical derivation and numerical validation for anisotropic media.

## Key findings

- Model is robust to well and permeability orientation
- Increased accuracy over Peaceman-type models
- Independent of discretization method

## Abstract

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 R3 , 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. 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.