Motivation

One of the key challenges in Pipe Flow Dynamics is to predict the along-hole pressure distribution during the stationary fluid transport.

In many practical cases the stationary pressure distribution can be approximated by Isothermal or Quasi-isothermal model of fluid flow.

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

Assumptions

Equations

\bigg( 1 -  \frac{c(p) \, \rho_0^2 \, q_0^2}{A^2}   \bigg )  \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl}  - \frac{\rho_0^2 \, q_0^2 }{2 A^2 d} \frac{f(p)}{\rho(p)}

u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A(l)}

q(l) = \frac{\rho_0 \cdot q_0}{\rho(p)}

(see Derivation of Stationary Isothermal Homogenous Pipe Flow Pressure Profile @model )

Approximations

Incompressible fluid with constant friction

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

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

u(l) = \frac{q_0}{A(l)}

q(l) =q_0 = \rm const

where

The first term in  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 the water can be considered as incompressible and friction factor  an be assumed constant  along-hole ( see  Darcy friction factor in water producing/injecting wells ).

References