Blowdown time in unsteady gas flow

Input(s)

$\mathrm{V}$: Volume $\left(\mathrm{ft}^{3}\right)$

$\boldsymbol{C}_{\boldsymbol{d}}$: Valve Discharge Coefficient (dimensionless)

$\boldsymbol{A}_{\boldsymbol{v}}$: Valve Area (in. ${ }^{2}$ )

$\boldsymbol{\gamma}$: Gas Specific Density (dimensionless)

z: Average Gas Compressibility (dimensionless)

$\mathrm{T}$: Temperature $(\mathrm{K})$

$\boldsymbol{P}_{\boldsymbol{a}}$: Initial Pressure (psi)

$\boldsymbol{P}_{\boldsymbol{b}}$: Output Pressure (psi)

B: Constant

Output(s)

t: Interstitial Velocity2 $(\mathrm{cm} / \mathrm{s})$

Formula(s)

$$ t=\left(\frac{B * V}{C_{d} * A_{v}}\right) *\left(\frac{\gamma}{z * T}\right)^{0.5} * \ln \left(\frac{P_{a}}{P_{b}}\right) $$

Reference(s)

John M. Campbell, Gas Conditioning and Processing, Campbell Petroleum Series, Oklahoma, 1992, Vol. 2, Page 29.