Motivation
One of the key challenges in Pipe Flow Dynamics is to predict the along-hole pressure distribution during the stationary fluid transport.
The
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.
Inputs & Outputs
Inputs | Outputs |
---|---|
Intake pressure p_0 | |
Intake rate q_0 | |
Pipeline trajectory inclination \theta (l) as function of | |
pipeline trajectory {\bf r} = {\bf r}(l) = \{ x(l), \, y(l), \, z(l) \} | along-pipe stabilized pressure distribution p(l) |
along-pipe stabilized flowrate distribution q(l) | |
Along-pipe temperature profile T(l) | along-pipe stabiliszed average flow velocity distribution u(l) |
Fluid density \rho(T, p) and fluid viscosity \mu(T, p) | |
Inner pipe wall roughness \epsilon |
Assumptions
Stationary fluid flow | Homogenous fluid flow | Isothermal or Quasi-isothermal conditions | Constant cross-section pipe area A along hole |
Equations
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(see Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model )
Approximations
Incompressible pipe flow with constant friction
Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
where
\displaystyle \cos \theta(l) = \frac{dz(l)}{dl} | correction factor for trajectory inclination |
The first term in (5) 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 the water can be considered as incompressible and friction factor an be assumed constant f(l) = f_s = \rm const along-hole ( see Darcy friction factor in water producing/injecting wells ).
See also
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 ]