5.4.2.3: The Diffusivity Equation for a Gas in Radial-Cylindrical Coordinates in Terms of Pressure-Squared

In the pressure-squared formulation, we assume that the ${\mu }_{g}Z$ product is constant. We have already seen that this approximation is valid for $p<2,000psi$. With this simplification, Equation 5.37 becomes:

Now, we can use the identity:

or,

Substituting Equation 5.40b into Equation 5.39 results in:

This is the diffusivity equation for real gases in terms pressure-squared, $p^2$. Again, the $c_g{\mu }_g$ product represents a non-linear term which we evaluate at either the initial pressure, $p_i$, or the average pressure, $\overline{p}$.