Despite of terminological similarity there is a difference in the way Dynamic Modelling (DM), Well Flow Performance (WFP) and Well Testing (WT) usually define formation pressure and productivity index. Flowrate,
q Drain-area formation pressure estimate Drain-area surface Productivity Index:
J_r Oil Surface Productivity Index
\displaystyle J_{r, O} = \frac{q_O}{p_r - p_{wf}} Gas Surface Productivity Index
\displaystyle J_{r, G} = \frac{q_G}{p_r - p_{wf}} Water Surface Productivity Index
\displaystyle J_{r, W} = \frac{q_W}{p_r - p_{wf}} Liquid Surface Productivity Index
\displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}} Drain-boundary formation pressure estimate where
L_e is the boundary of drainage area
A_e
q_t = q_w+q_o+q_g
Total Sandface Productivity Index:
\displaystyle J_t = \frac{q_t}{p_e - p_{wf}} for each fluid phase individually:
p_{e9,o}, \, p_{e9,g}, \, p_{e9,w} Oil Sandface Productivity Index
\displaystyle J_o = \frac{q_o}{p_{e,o} - p_{wf}} Gas Sandface Productivity Index
\displaystyle J_g = \frac{q_g}{p_{e,g} - p_{wf}} Water Sandface Productivity Index
\displaystyle J_ w = \frac{q_q}{p_{e,w} - p_{wf}}
within the drainage area
A_e
(1)
p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS
along the boundary of drainage area
A_e
(2)
p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl
DM
(3)
p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l}
(4)
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} )
Sometimes the wrong estimations of flowrate stem form the wrong inputs ( J or p_e).
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management
Subsurface E&P Disciplines / Production Technology / Productivity Index