Difference between revisions of "4/π stimulated well potential"

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:<math>dP=\frac{q B \mu}{2ky_eh} dx</math>
 
:<math>dP=\frac{q B \mu}{2ky_eh} dx</math>
  
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Integration gives:
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Integration gives: <math>P-P_{wf}=\frac{q B \mu}{2ky_eh} x</math>
−
 
 
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:<math>P-P_{wf}=\frac{q B \mu}{2ky_eh} x</math>
 
−
 
 
−
Since average pressure is:
 
−
 
 
−
:<math>\bar P = \frac{\int P dx}{\int dx}</math>
 
  
 +
Since average pressure is: <math>\bar P = \frac{\int P dx}{\int dx}</math>
  
 +
:<math></math>
  
  

Revision as of 09:38, 10 September 2018

Brief

Stimulated well drainage

4/π is the maximum possible stimulation potential for steady state linear flow in a square well spacing.

Math & Physics

Steady state flow boundary conditions:

P |_{x=x_e/2} = P |_{x=-x_e/2} = P_i
\frac{dp}{dt} =0\ for \ \forall x

From Darcy's law:

\frac{q}{2}=\frac{kA}{B \mu}\ \frac{dP}{dx}
A =y_e*h
dP=\frac{q B \mu}{2ky_eh} dx

Integration gives: P-P_{wf}=\frac{q B \mu}{2ky_eh} x

Since average pressure is: \bar P = \frac{\int P dx}{\int dx}

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