Motivation
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The stabilized water injection profile satisfies the assumptions of the Pressure Profile in Incompressible Stationary Quasi-Isothermal Incompressible Isoviscous Pipe Flow Pressure Profile @model.
Inputs & Outputs
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For the stabilized flow the wellbore pressure profile is constant and wellbore temperature profile is changing very slowly.
This allows solving the pressure-temperature problem iteratively:
- Iterations
- Iteration
- Iteration ...
Outputs
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distribution along | | LaTeX Math Inline |
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body | | distribution along the pipe |
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p_s | distribution along distribution along the pipe |
| LaTeX Math Inline |
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body | q_s | distribution along distribution along the pipe |
Inputs
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| Pipeline trajectory TVDss | \theta (l) | Pipeline trajectory inclination, | LaTeX Math Inline |
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body | --uriencoded--\displaystyle \cos \theta (l) = \frac%7Bdz%7D%7Bdl%7D
Assumptions
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fluid fluid Incompressible fluid Constant cross-section pipe area along hole| LaTeX Math Inline |
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| body | \rho(T, p)=\rho_s = \rm const |
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Isoviscous
Equations
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| Pressure profile | Pressure gradient profile | Fluid velocity | Fluid rate |
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| LaTeX Math Block |
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| anchor | PPconst |
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| alignment | left |
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| p(l) = p_s + \rho_s \, g \, z(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s \, l |
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| LaTeX Math Block |
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| \frac{dp}{dl} = \rho_s \, g \cos \theta(l) - \frac{\rho_s \, q_s^2 }{2 A^2 d} \, f_s |
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| LaTeX Math Block |
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| q(l) =q_s = \rm const |
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| LaTeX Math Block |
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| u(l) = u_s = \frac{q_s}{A} = \rm const |
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where
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Production Technology / Well Flow Performance / Lift Curves (LC) / Water Injection Wellbore Profile @model
[ Pressure Profile in Incompressible Stationary Quasi-Isothermal Incompressible Isoviscous Pipe Flow Pressure Profile @model ] [ Darcy friction factor in water producing/injecting wells @model ]
[ Water Injection Wellbore Temperature Profile @model ]
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