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Motivation

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In many practical cases the reservoir flow created by well is getting aligned with a radial direction towards or away from well.

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titleDerivation



Applications

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Equations 

LaTeX Math Block Reference
anchorp_F
 and  
LaTeX Math Block Reference
anchorpwf
play important methodological role as they are used in many algorithms and express-methods of Pressure Testing.



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titleLine Source Solution


In simplest case of infinite homogeneous reservoir, produced by a vertical well the 

LaTeX Math Inline
bodyF
 function has an exact analytical formula, given by exponential integral 
LaTeX Math Inline
bodyF(z) = {\rm Ei}_1 (z)
 (see Line Source Solution (LSS) @model).



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titlePTA


Pressure Testing – Infinite reservoirPTA – Pressure Transient Analysis



Pressure Drop


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anchor1EWTY
alignmentleft
\delta p = p_i - p_{wf}(t) \sim  \ln t + {\rm const}



Log derivative


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anchorIBA4M
alignmentleft
t \frac{d (\delta p)}{dt}  \sim \rm const







Fig. 2. PTA Diagnostic plot for radial fluid flow



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