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Assess how Darcy friction factor is varying along the hole the hole of water producing/injecting wells
Conclusion
For water flow the stationary water flow in a constant diameter pipe the Darcy friction factor along-hole variation is usually not exceeding 10 % and in many practical applications can can be considered as constant along hole:
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| body | f(l)= f_s = \rm const |
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The along-hole variation Darcy friction factor is usually not exceeding 10 % but the contribution of the friction-based pressure loss to the gravity-based pressure build up in vertical and slanted wells is very minor which makes constant friction factor assumption become relevant.
The absolute value is staying between
for the very small flow rates (< 100
cmd) and
for the very high flow rates (> 1,000
cmd)
and this should be taken into account in calculations.
For complex well designs with varying pipe flow diameters and water source/stocks which may lead to substantial variation of flowrate the model can be split in segments each having a constant friction factor.
Derivation
Consider a ration between friction-based pressure gradient
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| body | --uriencoded--\displaystyle \left[ \frac%7Bdp%7D%7Bdl%7D \right]_f =\frac%7B\rho_s \, q_s%5e2 %7D%7B2 A%5e2 d%7D \, f_s |
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and gravity-based pressure gradient in vertical well
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| body | --uriencoded--\displaystyle \left[ \frac%7Bdp%7D%7Bdl%7D \right]_g= \rho_s \, g |
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:
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