Difference between revisions of "6/π stimulated well potential"
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− | :<math> | + | :<math>\frac{dP}{dx}|_{x=x_e/2} = \frac{dP}{dx}|_{x=-x_e/2} = 0</math> |
:<math> \frac{dP}{dt} =const\ for \ \forall x </math> | :<math> \frac{dP}{dt} =const\ for \ \forall x </math> |
Revision as of 10:29, 12 September 2018
Brief
6/π is the maximum possible stimulation potential for pseudo steady state linear flow in a square well spacing.
Math & Physics
Pseudo steady state flow boundary conditions:
From Diffusivity Equation:
- ( 1 )
From Material Balance:
- ( 2 )
( 2 ) - > ( 1 ) :
- ( 3 )
Integrating ( 3 ):
- must satisfy boundary condition:
- ( 4 )
Integrating ( 4 ):
- ( 5 )
Since average pressure is: :
Diff eq
From Mass conservation:
- ( 1 )
From Darcy's law:
- ( 2 )
( 2 ) →( 1 ):
- ( 3 )
- ( 4 )
- ( 5 )
( 5 ) -> ( 4 ):
- ( 6 )
- ( 7 )
Assumption that viscosity is constant cancels out first term in left hand side of (7):
- ( 8 )
- ( 9 )
( 9 ) -> ( 8 ):
- ( 10 )
Term in (10) is second order of magnitude low and can be cancelled out, which yields:
- ( 11 )
See also
optiFrac
fracDesign
Production Potential
Nomenclature
- = cross-sectional area, cm2
- = thickness, m
- = permeability, d
- = pressure, atm
- = initial pressure, atm
- = average pressure, atm
- = flow rate, cm3/sec
- = length, m
- = drinage area length, m
- = drinage area width, m
Greek symbols
- = oil viscosity, cp