Motivation
The pipeline and wellbore flow simulations require a model of fluid pressure p variation as a function of elevation z:
(1) | p = p(z) |
Output
Intput
Equation
The static balance equation for fluid column is:
(2) | \frac{dp}{dz}= \rho(p) \cdot g |
where
Approximations
Incompressible fluids
(3) | p(z) = p_0 + \rho \cdot g \cdot (z-z_0) |
Ideal gases
(4) | p(z) = p_0 \cdot \exp \left[ - \frac{M \, g}{R \, T} \cdot (z-z_0) \right] |
Also known as Hydrostatic Boltzmann pressure distribution
Full-range model
(5) | \frac{1+ c_0 \, p(z)}{1 + c_0 \, p_0} = \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z-z_0)}{1+c_0 \, p_0} \right] |
The pressure drop between two points is going to be:
(6) | p_2 - p_1 = \frac{ (1+c_0 \, p_1)}{c_0} \cdot \left( \exp \left[ \frac{ с_0 \cdot \rho_0 \cdot g \cdot (z_2-z_1)}{1+c_0 \, p_0} \right] - 1 \right) |
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics
[ Fluid Dynamics ]