Motivation
One of the key problems in designing the pipelines and wells and controlling the fluid transport along is to predict the pressure along-hole pressure distribution during the stationary fluid transport.
In many cases the flow can be considered as isothermal or quasi-isothermal.
Pipeline flow simulator is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.
Inputs & Outputs
| Inputs | Outputs |
|---|---|
Pipeline trajectory {\bf r} = {\bf r}(l) = \{ x(l), \, y(l), \, z(l) \} | along-pipe distribution of stabilised pressure p(l) |
Pipeline cross-section area A(l) | along-pipe distribution of stabilised flow rate q(l) |
Fluid density \rho(T, p) and fluid viscosity \mu(T, p) | along-pipe distribution of stabilised average flow velocity u(l) |
Inner pipe wall roughness \epsilon |
Assumptions
| Stationary flow |
| Homogenous flow |
| Isothermal or quasi-isothermal conditions |
Constant area A(l) along hole |
Equations
| (1) | \bigg( 1 - \frac{c(p) \, \rho_s^2 \, q_s^2}{A^2} \bigg ) \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl} - \frac{\rho_s^2 \, q_s^2 }{2 A^2 d} \frac{f(p)}{\rho(p)} |
Approximations
Incompressible fluid with constant friction
| Pressure profile | Pressure gradient profile | ||||
|---|---|---|---|---|---|
|
|
where
\displaystyle \cos \theta(l) = \frac{dz(l)}{dl} | correction factor for trajectory deviation |
The first term in (3) defines the hydrostatic column of static fluid while the last term defines the friction losses under fluid movement:
In water producing or water injecting wells the 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
Petroleum Industry / Upstream / Pipe Flow Simulation / Water Pipe Flow @model
[ Darcy friction factor ] [ Darcy friction factor @model ]