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The word  "Inflow" is misnomer as IPR analysis is applicable for both producers and injectors.


The most general proxy-model is given by LIT (Laminar Inertial Turbulent) IPR model:

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anchor9C1T3
alignmentleft
a \, q + b \, q^2 = \Psi(p_r) - \Psi(p_{wf})

where

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bodyp_r

static pressure

LaTeX Math Inline
bodya

laminar flow coefficient

LaTeX Math Inline
bodyb

turbulent flow coefficient

LaTeX Math Inline
body\Psi

pseudo-pressure function specific to a certain gas PVT model


It needs well tests at least three different rates to assess  

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body--uriencoded--\%7B a \, , \, b, \, p_r \%7D
 but obviously more tests will make assessment more accurate.


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The IPR analysis is closely related to well Productivity Index (PI)  

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bodyJ_s
 which is defined as below:

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where 

LaTeX Math Inline
bodyn
 is the turbulent flow exponent, equal to 0.5 for fully turbulent flow and equal to 1 for laminar flow.

The more accurate approximation is given by LIT (Laminar Inertial Turbulent) IPR model:

LaTeX Math Block
anchor9C1T3
alignmentleft
a \, q + b \, q^2 = \Psi(p_r) - \Psi(p_{wf})

where 

LaTeX Math Inline
body\Psi
 – is pseudo-pressure function specific to a certain gas PVT model,  
LaTeX Math Inline
bodya
 is laminar flow coefficient and 
LaTeX Math Inline
bodyb
 is turbulent flow coefficient.

It needs two well tests at two different rates to assess 

LaTeX Math Inline
body\{ q_{max} \, , \, n \}
 or 
LaTeX Math Inline
body\{ a \, , \, b \}
.  

But obviously more tests will make assessment more accruate.


Saturated Oil IPR

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For saturated oil reservoir the free gas flow inflict the downward trend of IPR plot  similar to dry gas (Fig. 4).

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