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Transient flow in Radial Composite Reservoir



Equations

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LaTeX Math Block
anchor
CT
1
alignmentleft
q^{\downarrow}_{AQ}(t)= J \cdot \frac{\partial p_a}{\partial r}



LaTeX Math Block
anchorRC
alignmentleft
\frac{\partial p_1}{\partial t_D} = 
\chi
 \
cdot \left[ \
frac{\partial^2 p_
a
1}{\partial 
r^2
r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_
a
1}{\partial r_D}
\right]



LaTeX Math Block
anchor1
alignmentleft
q^{
\
downarrow}_{AQ}(t)=\
frac{d Q^{\downarrow}_{AQ}}{dt} = q^{\downarrow}_{AQ}(t)


LaTeX Math Block
anchorCT
alignmentleft
p_
a
1(t = 0, r)
|_{r=r_e}
= 
p(r)
0



LaTeX Math Block
anchor
1
CT
alignmentleft
q^{\downarrow}_{AQ}
p_a(t, r)= p(0) 
B
+ \
cdot \frac{\partial p}{\partial r}
int_0^t p_1(t-\tau) \dot p(\tau) d\tau



LaTeX Math Block
anchorCT
alignmentleft
p_
a
1(t, r=r
)|_{r=\infty
_e)} = 
p_ior
1




LaTeX Math Block
anchor1
alignmentleft
\frac{\partial p_
a
1}{\partial r
}|_{
_D}(t, r=r_a
}
) = 0




Expand
titleDerivation


LaTeX Math Block
anchorRC
alignmentleft
\frac{\partial p_a}{\partial t} = \chi \cdot \left[ \frac{\partial^2 p_a}{\partial r^2} + \frac{1}{r}\cdot \frac{\partial p_a}{\partial r} \right]
123



See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer Drive / Aquifer Drive Models

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