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Pipeline Flow Pressure Model is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.

Inputs & Outputs

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Outputs

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Intake temperature  LaTeX Math Inlinebody

LaTeX Math Inline
body

T_s

Intake pressure 

LaTeX Math Inlinebody

p(l)

Pressure distribution along the pipe

LaTeX Math Inline
body

p_s

q(l)

Flowrate distribution along the pipe

LaTeX Math Inlinebodyq_s

Intake flowrate 

LaTeX Math Inline
bodyu(l)

Flow velocity distribution along the pipe

Inputs & Outputs

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LaTeX Math Inline
bodyz(l)

Pipeline trajectory TVDss

LaTeX Math Inline
body

\theta (l)

T_s

Intake temperature 
Pipeline trajectory inclination, LaTeX Math Inlinebody--uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D

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)

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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