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
T_0 | Intake temperature | T(l) | Along-pipe temperature profile |
p_0 | Intake pressure |
\rho(T, p) | |
q_0 | 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 flow | Homogenous flow | Isothermal or Quasi-isothermal conditions |
Constant cross-section pipe area A along hole |
Equations
Pressure profile along the pipe | ||
---|---|---|
| ||
Mass Flowrate | ||
| ||
Intake Volumetric Flowrate | ||
| ||
Mass Flux | ||
|
where
\rho_0 = \rho(T_0, p_0) | Intake fluid density |
j_m = \dot m / A | Intake mass flux |
\displaystyle \dot m = \frac{dm }{ dt} | mass flowrate |
\displaystyle q_0 = \frac{dV_0}{dt} = \dot m / \rho_0 | Intake flowrate |
\Delta z(l) = z(l)-z(0) | elevation drop along pipe trajectory |
f_s = f({\rm Re}_s, \, \epsilon) | Darcy friction factor at intake point |
\displaystyle {\rm Re} = \frac{u(l) \cdot d}{\nu(l)} = \frac{4 \rho_0 q_0}{\pi d} \frac{1}{\mu} | Reynolds number at intake point |
\displaystyle d = \sqrt{ \frac{4 A}{\pi}} | characteristic linear dimension of the pipe |
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 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 / Pressure Profile in Stationary Quasi-Isothermal Homogenous Pipe Flow @model
[ Darcy friction factor ] [ Darcy friction factor @model ]
[ Homogenous Pipe Flow Temperature Profile @model ]