PNG 301
Introduction to Petroleum and Natural Gas Engineering The Diffusivity Equation for a Gas in Radial-Cylindrical Coordinates in Terms of Pressure


As we have already seen, in the pressure range of p>3,000 psi , the group p μ g Z can be considered to be approximately constant. With this simplification, we can remove the group from the spatial derivative on the left-hand side of Equation 5.37 to obtain:

1 r r ( r p r )= ϕ c g μ g 0.006328  k g p dt
Equation 5.38

This is the diffusivity equation for real gases in terms pressure, p. While this may at first glance appear to be linearized, it is not. Both the gas compressibility term, c g = 1 p 1 Z dZ dp , and the gas viscosity term, μ g , are pressure dependent. When using the pressure formulation, we typically evaluate these terms at either the initial pressure condition, p i , or the average condition, p ¯ . (Note: other more rigorous methods are available for the evaluation of the c g μ g product; however, they are beyond the scope of this course.)