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