PNG 301
Introduction to Petroleum and Natural Gas Engineering The Diffusivity Equation for a Gas in Radial-Cylindrical Coordinates in Terms of Real Gas Pseudo-Pressure, m(p)


Finally, we will investigate the use of the real gas pseudo-pressure in the diffusivity equation. For this, we differentiate the definition of the pseudo-pressure integral, Equation 5.19, using the fundamental theorem of calculus:

m( p ) p =2 p μ g Z
Equation 5.42a


p= μ g Z 2p m( p )
Equation 5.42b

Substituting Equation 5.42b into Equation 5.39 results in:

1 r r [ r m( p ) r ]= ϕ c g μ g 0.006328  k g m( p ) dt
Equation 5.43

Again, we evaluate the c g μ g product at either the initial pressure, p i , or the average pressure, p ¯ . In this development, we have:

  • 0.006328 is an equation constant (5.615 x 0.001127)
  • r is the radial coordinate in a radial-cylindrical coordinate system, ft
  • p is the pressure, psi
  • m(p) is the real gas pseudo-pressure, psi2/cp
  • ϕ is the porosity of the reservoir, fraction
  • c g is the gas compressibility, 1/psi
  • μ g is the gas viscosity, cp
  • k g is the effective permeability to gas, md
  • t is time, days