Mechanical energy balance for wellbore fluids


\(p_{1}, p_{2}\): Pressure at positions 1 and 2 (\mathrm{psi})$

\(\rho_{f}\): Fluid Density (lbm/ft3)

\(g_{c}\): Gravitational System Conversion Constant \(\left(32.17(\mathrm{lbm} / \mathrm{ft}) /\left(\mathrm{lbf} / \mathrm{s}^{2}\right)\right)\)

\(g\): Acceleration of Gravity \(\left(\mathrm{ft} / \mathrm{s}^{2}\right.\) )

\(Z_{1}, Z_{2}\): Fluid elevation at Positions 1 and \(2(\mathrm{ft})\)

\(v_{1}, v_{2}\): Fluid velocity at Positions 1 and \(2(\mathrm{ft} / \mathrm{s})\)

\(E_{l}\): Irreversible Energy Loss between Positions 1 and 2 (ft lbf/lbm)


\(W\): Work done by the Fluid while in Flow (ft lbf/lbm)


\[ W=-\left[\int_{P_{1}}^{P_{2}} \frac{d p}{\rho_{f}}+\frac{g}{g_{c}}\left(Z_{2}-Z_{1}\right)+\frac{\rho_{f}\left(v_{2}^{2}-v_{1}^{2}\right)}{2 g_{c}}+E_{l}\right] \]


Watson, D., Brittenham, T., & Moore, P. L. (2003). Advanced Well Control (Vol. 10). Society of Petroleum Engineers, Page: 8.

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