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
	Intake temperature		Pressure distribution along the pipe
	Intake pressure		Flowrate distribution along the pipe
	Intake flowrate		Flow velocity distribution along the pipe
	Pipeline trajectory TVDss
	Pipeline trajectory inclination,
	Along-pipe temperature profile
	Fluid density
	Fluid viscosity
	Pipe cross-section area
	Inner pipe wall roughness

Assumptions

Equations

p(l) = p_s + \rho_s \, g \, z(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s \, l

\frac{dp}{dl} = \rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s

q(l) =q_s = \rm const

u(l) = u_s = \frac{q_s}{A} = \rm const

where

\frac{dp}{dl} = \rho_s \, g \, \frac{dz}{dl}  - \frac{\rho_s \, q_s^2 }{2 A^2 d} f_s

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  along-hole ( see  Darcy friction factor in water producing/injecting wells ).

References