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Motivation

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Outputs

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LaTeX Math Inline
bodyT(l)

Temperature distribution along the flow pipe

LaTeX Math Inline
bodyq(l)

Flowrate distribution along the flow pipe

LaTeX Math Inline
bodyp(l)

Pressure distribution along the flow pipe

LaTeX Math Inline
bodyu(l)

Flow velocity distribution along the flow pipe

where

LaTeX Math Inline
bodyl

wellbore Measured Depth (MD)


Inputs

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LaTeX Math Inline
bodyT_s

Intake temperature 

LaTeX Math Inline
body\rho(T, p)

Fluid density 

LaTeX Math Inline
bodyp_s

Intake pressure 

LaTeX Math Inline
body\mu(T, p)

Fluid viscosity 

LaTeX Math Inline
bodyq_s

Intake flowrate 

LaTeX Math Inline
bodyd

Flow pipe diameter (tubing or casing depending on where flow occurs)

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness
LaTeX Math Inline
body\theta (l)


Pipeline trajectory inclination,

LaTeX Math Inline
body--uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D



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Equations

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Approximations

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For the stabilized flow the In stabilised wellbore flow the wellbore pressure profile is constant and wellbore temperature profile is changing very slowly.

This allows solving the pressure-temperature problem iteratively:

  1. IterationIterations
  2. Iteration
  3. Iteration ...

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