Mathematical model of Gradiomanometer G_p tool readings.
In case of stationary homogenous isothermal pipeline fluid flow the pressure gradient G_p can be correlated to volumetric flowrate q as (see model):
| (1) | G_p = G_{p0} + K \cdot q \cdot (1 + (q/q_{\infty})^n)^{1/n} |
where
q | volumetric flowrate around the gradiomanometer |
G_{p0} | pressure gradient in static fluid column |
K | a number defining the pipe flow productivity |
q_{\infty} | correction factor for strong-turbulent fluid flow |
n | turbulence curvature with default value n=12 |
Equation
(1) suggests that pressure gradient depends on flowrate:
- linearly
\sim q from laminar to slightly turbulent flow regimes
- and develops a stronger almost quadratic dependence \sim q^2 at strong-turbulent fluid flow
The model parameters \{ G_{p0}, \, K, \, q_{\infty} \} should be calibrated in-situ as they strongly depend on fluid type and the location specifics of the tool in a pipe.
The parameter G_{p0} can be directly measure from static surveys if these are available.
Alternatively it maybe assessed as:
| (2) | G_{p0} = \rho \, g \, \cos \theta |
where
\rho | Fluid density at a given location with pressure p and temperature T |
g | standard gravity constant |
\cos \theta | correction factor for trajectory deviation |
The parameter K is very sensitive to in-situ conditions but can be roughly estimated as:
| (3) | K = \frac{8 \pi \, \mu}{A^2} |
where
For non-isothermal flow the model parameters \{ G_{p0}, \, K, \, q_{\infty} \} should be calibrated at different temperature values.
See also
[ Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model ]