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The pressure interference test with multiple homogeneous layers staying in a permeable contact with each other will honour the following equations:

LaTeX Math Block
anchorsigma
alignmentleft
\left< \sigma \right > = \sum_m \sigma_m


LaTeX Math Block
anchorstorage
alignmentleft
\left< c_t \phi h A\right > = \sum_m c_{tm} \phi_m h_m A_m

where

LaTeX Math Inline
bodym

number of layers

LaTeX Math Inline
body\left< \sigma \right >

transmissibility of the multilayer system

LaTeX Math Inline
body\left< c_t \, \phi \, h \, A \right>

total reservoir storage of the multilayer system

LaTeX Math Inline
bodyA_m

reservoir drainage area of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
body\sigma_m =M_m h_m

transmissibility of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
bodyh_m

reservoir thickness of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
bodyM_m = k_m M_{rm}

reservoir fluid mobility of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
bodyM_{rm} =\left< \frac{k_r}{\mu} \right>_m

relative reservoir fluid mobility of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
bodyk_m

absolute permeability to air of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
body\phi_m

reservoir porosity of the

LaTeX Math Inline
bodym
-th layer

LaTeX Math Inline
bodyc_{tm}

 total compressibility of the

LaTeX Math Inline
bodym
-th layer


The equations 

LaTeX Math Block Reference
anchorsigma
 and 
LaTeX Math Block Reference
anchorstorage
 define the 3D → 2D upscaling algorithm for pressure calculations.


See Also


Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing / Pressure Interference Test (PIT)