Motivation

The pipeline and wellbore flow simulations require a model of fluid pressure variation as a function of elevation :

p = p(z)

Output

	Elevation

The static balance equation for fluid column is:

\frac{dp}{dz}= \rho(p) \cdot g

where

p(z) = p_0 + \rho \cdot g \cdot (z-z_0)

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

\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:

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)