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The stabilized water injection profile satisfies the assumptions of the Stationary Quasi-Isothermal Incompressible Isoviscous Pipe Flow Pressure Profile @model.
Motivation
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Inputs & Outputs
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Assumptions
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Equations
| 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
| LaTeX Math Inline |
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| body | --uriencoded--f_s = f(%7B\rm Re%7D, \, \epsilon) |
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| Darcy friction factor |
| LaTeX Math Inline |
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| 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 |
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| Reynolds number |
| LaTeX Math Inline |
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| body | --uriencoded--A = 0.25 \, \pi \, d%5e2 |
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| flow pipe cross-section area (tubing or casing depending on where flow occurs) |
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
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