A new theory for flow computations in a large class of anisotropic media with applications to well productivity modeling

A new theory for calculation of fluid flow in laterally isotropic, spatially anisotropic permeable media is presented. This theory is capable of quantifying fluid flow in such media without the use of cumbersome tensorial calculations involving non-zero off-diagonal elements. Using this theory, we derive analytical models for well productivity of deviated wells in such media, for both steady-state and semi-steady-state flow. The theory developed in this paper relies on a spatial volume preserving transform composed of two rotations and two linear coordinate deformations. This transform is designed such that a prefixed direction aligns with one of the coordinate axes of the transformed space. Furthermore, the transformed medium is isotropic in planes perpendicular to the prefixed direction, and the transformed permeability is diagonal. As a bi-product, the new theory developed in this paper also provides closed formulas for directional permeabilities. These formulas are expressed with a different set of parameters than well known classical formulas for directional permeabilities. Since both approaches are fully analytical without any form of approximation, it is imperative that these formulas are proven identical.

Automated summary

A new theory for calculating fluid flow in laterally isotropic, spatially anisotropic permeable media is presented, which includes analytical models for well productivity in such media. The theory relies on a spatial volume preserving transform and provides closed formulas for directional permeabilities using different parameters than classical formulas. Both approaches are fully analytical and need to be proven identical.