# Reservoir flow through the wellbore of a geothermal well

## Input(s)

\(n\): Performance Exponent for Flow in the wellbore (dimensionless)

\(P_{t f}\): Wellhead Flowing Pressure \((\mathrm{psi})\)

\(P_{w f}\): Bottomhole Flowing Pressure (psi)

\(C_{1}\): Performance Coefficient for Flow upwards in the Wellbore (bbl/d psi)

## Output(s)

\(W\): Flow Rate \((\mathrm{bbl} / \mathrm{d})\)

## Formula(s)

\[
\mathrm{W}=\mathrm{C}_{1}\left(\mathrm{P}_{\mathrm{wf}}^{2}-\mathrm{P}_{\mathrm{tf}}^{2}\right)^{\mathrm{n}}
\]

## Reference(s)

Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 8.8.