Motivation
The stabilized water injection profile satisfies the assumptions of the Stationary Quasi-Isothermal Incompressible Isoviscous Pipe Flow Pressure Profile @model.
For the stabilized flow the wellbore pressure profile is constant and wellbore temperature profile is changing very slowly.
This allows solving the pressure-temperature problem iteratively:
- Iterations
- Iteration
- Iteration ...
Inputs & Outputs
Inputs | Outputs | ||
---|---|---|---|
T_s | Intake temperature | p(l) | Pressure distribution along the pipe |
p_s | Intake pressure | q(l) | |
q_s | Intake flowrate | u(l) | Flow velocity distribution along the pipe |
z(l) | Pipeline trajectory TVDss | ||
\theta (l) | Pipeline trajectory inclination, \displaystyle \cos \theta (l) = \frac{dz}{dl} | ||
T(l) | Along-pipe temperature profile | ||
\rho(T, p) | |||
\mu(T, p) | |||
d | Flow pipe diameter (tubing or casing depending on where flow occurs) | ||
\epsilon | Inner pipe wall roughness |
Assumptions
Stationary fluid flow | Homogenous fluid flow | Isothermal or Quasi-isothermal conditions | Constant cross-section pipe area A along hole |
Incompressible fluid \rho(T, p)=\rho_s = \rm const | Isoviscous \mu(T, p) = \mu_s = \rm const |
Equations
Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
|
where
f_s = f({\rm Re}, \, \epsilon) | Darcy friction factor |
\displaystyle {\rm Re}_s = \frac{4 \rho_s q_s}{\pi d} \frac{1}{\mu_s} | Reynolds number |
A = 0.25 \, \pi \, d^2 | flow pipe cross-section area (tubing or casing depending on where flow occurs) |
See Also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Production Technology / Well Flow Performance / Lift Curves (LC) / Water Injection Wellbore Profile @model
[ Stationary Quasi-Isothermal Incompressible Isoviscous Pipe Flow Pressure Profile @model ]