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

	Intake temperature		Along-pipe temperature profile
	Intake pressure		Fluid density
	Intake flowrate		Fluid viscosity
	Pipeline trajectory TVDss		Pipe cross-section area
	Pipeline trajectory inclination,		Inner pipe wall roughness

Assumptions

Equations

p(l) = p_0 + \rho_s \, g \, \Delta z(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0 \, l

\frac{dp}{dl} = \rho_0 \, g \cos \theta(l) - \frac{\rho_0 \, q_0^2 }{2 A^2 d} \, f_0

j_m = \rho_0 \cdot \sqrt{\frac{2 \, d}{f_0 \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_0 - p)/ \rho_0}

\dot m = j_m \cdot A = \rho_0 \cdot A \cdot \sqrt{\frac{2 \, d}{f_0 \, l }} \cdot \sqrt{g \, \Delta z(l) + (p_0 - p)/ \rho_s}

q_0 = \dot m / \rho_0 = A \cdot \sqrt{\frac{2 \, d }{ f_0 \, l }} \cdot \sqrt{  g \, \Delta z(l) + (p_0 - p)/ \rho_s }

u_0 = j_m/ \rho_0 =q_0 / A = \sqrt{\frac{2 \, d }{ f_0 \, l }} \cdot \sqrt{  g \, \Delta z(l) + (p_0 - p)/ \rho_s }

where

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