Radial Flow of Compressible Fluids, Steady State

The flow of a gas at any radius r of Fig. 8.8, where the pressure is p, may be expressed in terms of the flow in standard cubic feet per day by

Substituting in the radial form of Darcy’s law,

Separating variables and integrating,

or

Finally,

The product μz has been assumed to be constant for the derivation of Eq. (8.23). It was pointed out in section 8.4.3 that this is usually true only for pressures less than about 1500 psia to 2000 psia. For greater pressures, it was stated that a better assumption was that the product μz/p was constant. For this case, the following is obtained:

Applying Eqs. (8.23) and (8.24), the products μz and μz/p should be calculated at the average pressure between p₁ and p₂.

If the real gas pseudopressure function is used, the equation becomes