Analysis of Development Methods for Gravel Envelope Wells   -   17

Appendix A

Mathematical Models for Development Methods

All the mathematical models are based on the well-known potential theory of flow in porous media. The basic equation for the velocity potential (r, z, t) is



where the velocity in the z-direction is



and in the radial direction



k  is the hydraulic conductivity,
= k/S where  S  is the specific storativity for the medium. In general, S is small (10^-4 - 10^-6). For steady flow = 0, and we have

For layered media we have two such potential functions and , and these satisfy conditions



where  n  is the normal direction to the interface between region 1 and region 2. We consider each problem in turn.

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