One of the key challenges in Pipe Flow Dynamics is to predict the pressure distribution along the pipe during the stationary fluid transport.
In many practical cases the stationary pressure distribution can be approximated by Isothermal or Quasi-isothermal homogenous fluid flow model.
Pipeline Flow Pressure Model is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.
Pressure distribution along the pipe | |
Flow velocity distribution along the pipe |
Intake temperature | Along-pipe temperature profile | ||
Intake pressure | Fluid density | ||
Intake flowrate | |||
Pipeline trajectory TVDss | Pipe cross-section area | ||
Inner pipe wall roughness |
Stationary flow | Homogenous flow | Isothermal or Quasi-isothermal conditions | Constant cross-section pipe area along hole |
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where
Darcy friction factor | |
Reynolds number | |
characteristic linear dimension of the pipe |
See Derivation of Pressure Profile in Stationary Isothermal Homogenous Pipe Flow @model.
-\frac{1}{c} \frac{d}{dl} \left( \frac{1}{\rho} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{d}{dl} \left( \frac{1}{\rho^2} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{f}{d} \left( \frac{1}{\rho^2} \right) - g \frac{dz}{dl} = 0 |
See derivation at
Incompressible pipe flow with constant viscosity
Pressure Profile in Incompressible Isoviscous Stationary Quasi-Isothermal Pipe Flow @model
Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate | ||||
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where
Darcy friction factor at intake point | |
Reynolds number at intake point |
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The first term in the right side of defines the hydrostatic column of static fluid while the last term defines the friction losses under fluid movement:
In most practical applications in water producing or water injecting wells, water can be considered as incompressible and friction factor can be assumed constant along-hole ( see Darcy friction factor in water producing/injecting wells ).
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation
[ Darcy friction factor ] [ Darcy friction factor @model ] [ Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model ]
[ Homogenous Pipe Flow Temperature Profile @model ]
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