5.4.2.4: 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:

or,

Substituting Equation 5.42b into Equation 5.39 results in:

Again, we evaluate the $c_g{\mu }_g$ product at either the initial pressure, $p_i$ , or the average pressure, $\overline{p}$. In this development, we have:

• $\text{0.006328}$ 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
• $m\left(p\right)$ is the real gas pseudo-pressure, psi²/cp
• $\varphi$ is the porosity of the reservoir, fraction
• $c_g$ is the gas compressibility, 1/psi
• ${\mu }_g$ is the gas viscosity, cp
• $k_g$ is the effective permeability to gas, md
• $t$ is time, days