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

This difference is summarized The most typical definitions (although they do not cover the full variety of definitions referred in petroleum literature) are summarised in the table below:

Formation pressure,

LaTeX Math Inline

body	p

Flow rate,

LaTeX Math Inline

body	q

_e

Flowrate,

LaTeX Math Inline

body	q

Productivity Index,

LaTeX Math Inline

body	J

WFP

Drain-area formation pressure estimate
within the drainage area

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body	A_e

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anchor	1
alignment	left

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

Surface flowrates:

Oil surface flowrate

LaTeX Math Inline

body	q_O

Gas surface flowrate

LaTeX Math Inline

body	q_G

Water surface flowrate

LaTeX Math Inline

body	q_W

Liquid surface flowrate

LaTeX Math Inline

body	q_L

Drain-area surface Productivity Index:

LaTeX Math Inline

body	J_r

Oil Surface Productivity Index

LaTeX Math Inline

body	\displaystyle J_{r, O} = \frac{q_O}{p_r - p_{wf}}

Gas Surface Productivity Index

LaTeX Math Inline

body	\displaystyle J_{r, G} = \frac{q_G}{p_r - p_{wf}}

Water Surface Productivity Index

LaTeX Math Inline

body	\displaystyle J_{r, W} = \frac{q_W}{p_r - p_{wf}}

Liquid Surface Productivity Index

LaTeX Math Inline

body	\displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}}

WT

Drain-boundary formation pressure estimate
along the boundary of drainage area

LaTeX Math Inline

body	A_e

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anchor	1
alignment	left

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

where

LaTeX Math Inline

body	L_e

is the boundary of drainage area

LaTeX Math Inline

body	A_e

Total sandface flowrate:

LaTeX Math Inline

body	q_t = q_w+q_o+q_g

Total Sandface Productivity Index:

LaTeX Math Inline

body	\displaystyle J_t = \frac{q_t}{p_e - p_{wf}}

Productivity Index LaTeX Math InlinebodyJ

DM

9-cell formation pressure

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anchor	1
alignment	left

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

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anchor	1
alignment	left

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} )

oil sandface flowrate

LaTeX Math Inline

body	q_o

gas sandface flowrate

LaTeX Math Inline

body	q_g

water sandface flowrate

LaTeX Math Inline

body	q_w

sandface productivity index

for each fluid phase individually:

LaTeX Math Inline

body

J_ w = \frac{q_q}{p_r -

p_{

wf}

e9,o}

,

LaTeX Math InlinebodyJ_o = \frac{q_o}{p_r -

\, p_{

wf}

e9,g}

,

LaTeX Math InlinebodyJ_g = \frac{q_g}{p_r -

\, p_{

wf}

e9,w}

WFP

Field-average formation pressure estimate within the drainage area Ae

LaTeX Math Block

anchor	1
alignment	left

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

Sandface Flowrates:

Oil sandface

oil surface

flowrate

LaTeX Math Inline

body	q_

O

o

gas surface

Gas sandface flowrate

LaTeX Math Inline

body	q_

G

g

water surface surface productivity index:

Water sandface flowrate

LaTeX Math Inline

body	q_

W

liquid flowrate

LaTeX Math Inline

body	q_L

w

Sandface Productivity Index:

Oil Sandface Productivity Index

LaTeX Math Inline

body	\displaystyle J_

W

o = \frac{q_

W

o}{p_

r

{e,o} - p_{wf}}

,

Gas Sandface Productivity Index

LaTeX Math Inline

body	\displaystyle J_

O

g = \frac{q_

O

g}{

p_r -

p_{

wf}} , LaTeX Math InlinebodyJ_G = \frac{q_G}{p_r

e,g} - p_{wf}}

and sometimes liquid productivity index:

Water Sandface Productivity Index

LaTeX Math Inline

body	\displaystyle J_

{OW}

w = \frac{q_

{OW}

q}{p_

r

{e,w} - p_{wf}}

WT

Boundary-average formation pressure estimate along the boundary of drainage area Ae

LaTeX Math Block

anchor	1
alignment	left

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

where

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