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 summarised in the table below:


Formation pressure,

Flow rate,

Productivity Index


DM

9-cell formation pressure

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


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} )

for each fluid phase individually:

Sandface Flowrates:

Oil sandface flowrate

Gas sandface flowrate

Water sandface flowrate



Sandface Productivity Index:

Oil sandface productivity index

Gas sandface productivity index

Water sandface productivity index


WFP

Field-average formation pressure estimate 
within the drainage area Ae

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


Surface flowrates:

Oil surface flowrate

Gas surface flowrate

Water surface flowrate

Liquid surface flowrate


Surface productivity index:

Oil surface productivity index

Gas surface productivity index

Water surface productivity index

Liquid surface productivity index


WT

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

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

where is the boundary of drainage area

Total sandface flowrate:

Total sandface productivity index: