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.
Outputs
Inputs & Outputs
T_s | Intake temperature | T(l) | Along-pipe temperature profile |
p_s | Intake pressure | \rho(T, p) | Fluid density |
q_s | Intake flowrate | \mu(T, p) | |
z(l) | Pipeline trajectory TVDss | A | Pipe cross-section area |
\theta (l) | Pipeline trajectory inclination, \displaystyle \cos \theta (l) = \frac{dz}{dl} | \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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where
f({\rm Re}, \, \epsilon) | Darcy friction factor |
\displaystyle {\rm Re} = \frac{u(l) \cdot d}{\nu(l)} = \frac{4 \rho_s q_s}{\pi d} \frac{1}{\mu(T, p)} | Reynolds number |
\displaystyle d = \sqrt{ \frac{4 A}{\pi}} | characteristic linear dimension of the pipe |
See Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model.
Approximations
Incompressible pipe flow \rho(T, p) = \rho_s with constant viscosity \mu(T, p) = \mu_s
Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate | ||||||||
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The first term in the right side of (8) 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 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 ]