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For the pressure diffusion with constant diffusion coefficients and linear homogeneous boundary conditions the pressure response 

LaTeX Math Inline
bodyp(t)
in one well to a complex flowrate history 
LaTeX Math Inline
bodyq(t)
in the same well honours the convolution equation:

...

LaTeX Math Inline
bodyp_{n, \, 0}

Initial formation pressure at zero time

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bodyt=0
for the
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bodyn
-th well

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bodyp_{u,nm}(\tau)

Drawdown Transient Response in the

LaTeX Math Inline
bodyn
-th well to the unit-rate production


LaTeX Math Inline
bodyp_{u,nm}(\tau)



Cross-well Transient Response
in the

LaTeX Math Inline
bodyn
-th well to the unit-rate production in
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bodym
-th well


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body\dot q_m(\tau) = \frac{dq_m}{d\tau}


A speed of

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bodyn
-th well total sandface flow rate variation

...


The pressure convolution principle has some limitations and may not be adequate for some practical cases.

For example, changing reservoir conditions, high compressibility – everything which breaks linearity of diffusion equations.

There are some workarounds on these cases but the best practice is to check the validity of pressure convolution (and therefore the applicability of MDCV) on the simple synthetic 2-well Dynamic Flow Model (DFM) with the typical for the given case  reservoir-fluid-production conditions.


See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing

Well & Reservoir Surveillance ] [ Pressure Diffusion ] [ Pressure drawdown ]

[ Pressure Deconvolution  ] MDCV ]

Convolution @math ]

References

...

Arthur Aslanyan, Mathematical aspects of Multiwell Deconvolution and its relation to Capacitance Resistance Model, arxiv.org/abs/2203.01319