Motivation
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.
Inputs & Outputs
Inputs | Outputs | ||
---|---|---|---|
p_0 | Intake pressure | p(l) | |
q_0 | Intake flowrate | u(l) | Flow velocity distribution along the pipe |
\theta (l) | |||
{\bf r}(l) | |||
T(l) | Along-pipe temperature profile | ||
\rho(T, p) | Fluid density and | ||
\mu(T, p) | |||
A | Pipe cross-section area | ||
\epsilon | Inner pipe wall roughness |
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 \rho(p) = \rho_0 with constant friction f(u) = f_0
Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
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|
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 ]