Motivation


The stabilized water injection profile satisfies the assumptions of the Pressure Profile in Incompressible Stationary Quasi-Isothermal Isoviscous Pipe Flow @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:

  1. Iterations
  2. Iteration
  3. Iteration ...


Outputs

Pressure distribution along the pipe

Flowrate distribution along the pipe

Flow velocity distribution along the pipe


Inputs 

Intake temperature 

Along-pipe temperature profile 

Intake pressure 

Fluid density 

Intake flowrate 

Fluid viscosity 

Pipeline trajectory TVDss

Flow pipe diameter

(tubing or casing depending on where flow occurs)


Pipeline trajectory inclination,

Inner pipe wall roughness


Assumptions

Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Incompressible fluid  

Isoviscous flow  

Constant cross-section pipe area along hole


Equations

Pressure profilePressure gradient profileFluid velocityFluid rate


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

Darcy friction factor (see Darcy friction factor in water producing/injecting wells @model) at intake point

Reynolds number at intake point

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

[ Pressure Profile in Incompressible Stationary Quasi-Isothermal Isoviscous Pipe Flow @model ] [ Darcy friction factor in water producing/injecting wells @model ]

[ Water Injection Wellbore Temperature Profile @model ]