GLOSSARY

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LaTeX Math Inline
bodyT_s

Intake temperature 

LaTeX Math Inline
bodyT(l)

Along-pipe temperature profile 

LaTeX Math Inline
bodyp_s

Intake pressure 

LaTeX Math Inline
body\rho(T, p)

Fluid density 

LaTeX Math Inline
bodyq_s

Intake flowrate 

LaTeX Math Inline
body\mu(T, p)

Fluid viscosity 

LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
bodyA

Pipe cross-section area  
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\epsilon

Inner pipe wall roughness

Assumptions

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Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole


Equations

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LaTeX Math Block
anchorPP
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\left( 1 -  \frac{\rho_s^2 \, q_s^2}{A^2} \cdot \frac{c(p)}{\rho}   \right)  \frac{dp}{dl} = \rho \, g \, \frac{dz}{dl}  - \frac{\rho_s^2 \, q_s^2 }{2 A^2 d} \frac{f({\rm Re}, \, \epsilon)}{\rho}



LaTeX Math Block
anchor1
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q(l) = \frac{\rho_s \cdot q_0}{\rho}



LaTeX Math Block
anchor1
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u(l) = \frac{\rho_s \cdot q_s}{\rho \cdot A}



LaTeX Math Block
anchorp0
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p(l=0) = p_s



LaTeX Math Block
anchorp0
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q(l=0) = q_s



LaTeX Math Block
anchorp0
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\rho(T_s, p_s) = \rho_s


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