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


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

1 r r ( rp p r )= ϕ c g μ g p 0.006328  k g p dt
Equation 5.39

Now, we can use the identity:

p 2 =2pp
Equation 5.40a


p= 1 2p p 2
Equation 5.40b

Substituting Equation 5.40b into Equation 5.39 results in:

1 r r ( r p 2 r )= ϕ c g μ g 0.006328  k g p 2 dt
Equation 5.41

This is the diffusivity equation for real gases in terms pressure-squared, p 2 . Again, the c g μ g product represents a non-linear term which we evaluate at either the initial pressure, p i , or the average pressure, p ¯ .