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Despite of terminological similarity there is a big difference in the way Dynamic Modelling,  Well Flow Performance and Well Testing define formation pressure and productivity index.

This difference is summarized in the table below:


Formation pressure,

LaTeX Math Inline
bodyp

Flow rate,

LaTeX Math Inline
bodyq

Producivity Index,

LaTeX Math Inline
bodyJ

DM

field-average pressure within the 9-cell area

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bodyA_{e9}

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anchor1
alignmentleft
p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l}


LaTeX Math Block
anchor1
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p_{e9, \ i,j} = \frac{1}{9} ( p_{i,j}
+ p_{i, \, j+1} + p_{i, \, j-1}
+ p_{i-1, \, j} + p_{i-1, \, j}
+ p_{i-1 \, j-1} + p_{i+1, \, j+1}
+ p_{i-1 \, j+1} + p_{i+1, \, j-1} )


phase flowrate at sandface:

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body\{ q_w, \, q_o, \, q_g \}

(each fluid phase separately)

phase productivity index:


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bodyJ_ w = \frac{q_q}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_o = \frac{q_o}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_g = \frac{q_g}{p_r - p_{wf}}

WFP

field-average pressure within the drainage area

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bodyA_e

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anchor1
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p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS


surface component flowrate

LaTeX Math Inline
body\{ q_W, q_O, q_G \}

(each fluid component separately)

and sometimes liquid flowrate

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bodyq_{OW} = q_O + q_W

fluid component productivity index:

LaTeX Math Inline
bodyJ_W = \frac{q_W}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_O = \frac{q_O}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_G = \frac{q_G}{p_r - p_{wf}}

and sometimes liquid productivity index:

LaTeX Math Inline
bodyJ_{OW} = \frac{q_{OW}}{p_r - p_{wf}}

WT

average pressure value along the boudary of drainage area

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bodyA_e

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anchor1
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p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl

where

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bodyL_e
is the boundary of drainage area
LaTeX Math Inline
bodyA_e

total flowrate at sandface:

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bodyq_t = B_w \, q_W + \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G

where

LaTeX Math Inline
body\{ W, \, O, \, G \}
are pseudo-components of Compositional Model

total multiphase productivity index:

LaTeX Math Inline
bodyJ_t = \frac{q_t}{p_e - p_{wf}}


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