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  1. Iterations
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Inputs & Outputs


Inputs 

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InputsOutputs

LaTeX Math Inline
bodyT_s

Intake temperature 

LaTeX Math Inline
body

p

T(l)

Pressure distribution along the pipe
Along-pipe temperature profile 

LaTeX Math Inline
bodyp_s

Intake pressure 

LaTeX Math Inline
body

q(l

\rho(T, p)

Flowrate distribution along the pipe
Fluid density 

LaTeX Math Inline
bodyq_s

Intake flowrate 

LaTeX Math Inline
body

u(l)Flow velocity distribution along the pipe

\mu(T, p)

Fluid viscosity 

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
bodyd

Flow pipe diameter

(tubing or casing depending on where flow occurs)

LaTeX Math Inline
body\theta (l)


Pipeline trajectory inclination,

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

LaTeX Math Inline
body

T(l)Along-pipe temperature profile 

\epsilon

Inner pipe wall roughness


Outputs

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LaTeX Math Inline
body

\rho(T, p)Fluid density 

p(l)

Pressure distribution along the pipe

LaTeX Math Inline
body

\mu(T, p

q(l)

Fluid viscosity 

Flowrate distribution along the pipe

LaTeX Math Inline
body

d

Flow pipe diameter

(tubing or casing depending on where flow occurs)

LaTeX Math Inline
body\epsilon

Inner pipe wall roughness

u(l)

Flow velocity distribution along the pipe

Assumptions

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Stationary fluid flowHomogenous fluid flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole

Incompressible fluid  

LaTeX Math Inline
body\rho(T, p)=\rho_s = \rm const

Isoviscous  

LaTeX Math Inline
body\mu(T, p) = \mu_s = \rm const



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LaTeX Math Inline
body--uriencoded--f_s = f(%7B\rm Re%7D, \, \epsilon)

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

LaTeX Math Inline
body--uriencoded--\displaystyle %7B\rm Re%7D_s = \frac%7B4 \rho_s q_s%7D%7B\pi d%7D \frac%7B1%7D%7B\mu_s%7D

Reynolds number

LaTeX Math Inline
body--uriencoded--A = 0.25 \, \pi \, d%5e2

flow pipe cross-section area  (tubing or casing depending on where flow occurs)

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