Motivation

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

p = p(z)

Output

Input

	Elevation		Fluid density at Logging reference point
	Logging reference point (usually at surface)		Fluid Compressibility at Logging reference point
	Standard gravity constant

The static balance equation for fluid column is:

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

Full-range model

p(z) = p_0 + \rho_0 \cdot g \cdot (z-z_0)

p(z) = p_0 \cdot \exp \left[ - \frac{\rho_0 \, g}{p_0} \cdot (z-z_0) \right]

\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]

p_2 - p_1 = \rho_0 \cdot g \cdot (z_2-z_1)

p_2 - p_1  = p_1  \cdot \left( \exp \left[ \frac{  \rho_0 \cdot g \cdot (z_2-z_1)} {p_0}  \right] - 1 \right)

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)