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,
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} )
oil sandface flowrate
gas sandface flowrate
water sandface flowrate
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
oil surface flowrate
gas surface flowrate
water surface flowrate
liquid flowrate
surface productivity index:
and sometimes liquid 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 flowrate at sandface:
total sandface productivity index: