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