Motivation
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Pipeline flow simulator is addressing this problem. It should account for the varying pipeline trajectory, gravity effects, fluid friction with pipeline walls and varying heat exchange with surroundings.
One of the key problems in designing the pipelines and wells and controlling the fluid transport along is to predict the temperature along-hole pressure distribution during the stationary fluid transport.
In many cases the flow can be considered as Isothermal or Quasi-isothermal.
Pipeline flow simulator is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.
One of the key challenges in Pipe Flow Dynamics is to predict the along-hole pressure distribution during the stationary fluid transport.
In many practical cases the pressure distribution can be approximated by Isothermal or Quasi-isothermal model of fluid flow
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Motivation
One of the key problems in designing the pipelines and controlling the pipeline fluid transport is to predict the temperature and pressure losses during the stationary fluid transport.
Pipeline flow simulator is addressing this problem . It should with account for of the varying varying pipeline trajectory, gravity effects, effects and fluid friction with pipeline walls and varying heat exchange with surroundings.
Definition
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Given
- space coordinates are with -ccordinate facing down to the Earth Centre
- inflow pipeline coordinates
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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- pipeline trajectory
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| body | \{ x_w(l), \, y_w(l), \, z_w(l) \} |
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, where | LaTeX Math Inline |
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| body | l = \int_0^l \sqrt{dx^2 + dy^2 + dz^2} = \int_0^l \sqrt{\dot x^2 + \dot y^2 + \dot z^2} dl |
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, is pipeline length from inflow point | LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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- pipeline cross-section area
- earth gravity vector
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| body | {\bf g} = (0, \, 0, \, g) |
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where
- inflow temperature , inflow pressure , inflow rate
- PVT properties of water ,
- surroundings initial temperature , thermal diffusivity , thermal conductivity of surrounding media
- heat exchange coefficient based on pipeline schematics
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Таким образов формула
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работает в широких пределах дебетов и имеет правильные асимптоты и вполне пригодна для различного рода оценок.
References
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https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae
https://neutrium.net/fluid_flow/pressure-loss-in-pipe/
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