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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

Productivity Index, J


Drain-area formation pressure estimate 
within the drainage area A_e

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

Surface flowrates:

Oil surface flowrate q_O

Gas surface flowrate q_G

Water surface flowrate q_W

Liquid surface flowrate q_L

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 
along the boundary of drainage area A_e

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

where L_e is the boundary of drainage area A_e

Total sandface flowrate:

q_t = q_w+q_o+q_g

Total Sandface Productivity Index: \displaystyle J_t = \frac{q_t}{p_e - p_{wf}}


9-cell formation pressure

(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} )

for each fluid phase individually: p_{e9,o}, \, p_{e9,g}, \, p_{e9,w}

Sandface Flowrates:

Oil sandface flowrate q_o

Gas sandface flowrate q_g

Water sandface flowrate q_w

Sandface Productivity Index:

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}}

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

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