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_s | Intake temperature | T(l) | Along-pipe temperature profile |
p_s | Intake pressure |
\rho(T, p) | |
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 flow | Homogenous flow | Isothermal or Quasi-isothermal conditions |
Incompressible fluid \rho(T, p)=\rho_s = \rm const | Isoviscous flow \mu(T, p) = \mu_s = \rm const | Constant cross-section pipe area A along hole |
Equations
Pressure profile | Pressure gradient profile | ||||
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Mass Flux | Mass Flowrate | ||||
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| ||||
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where
j_m = \dot m / A | Intake mass flux |
\displaystyle \dot m = \frac{dm }{ dt} | mass flowrate |
\displaystyle q_s = \frac{dV_s}{dt} = \dot m / \rho_s | Intake flowrate |
u_s = u(l=0) = q_s / A = j_m / \rho_s | Intake Fluid velocity |
\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}_s = \frac{u(l) \cdot d}{\nu(l)} = \frac{4 \rho_s q_s}{\pi d} \frac{1}{\mu_s} | 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 (2) 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 ]