Despite of terminological similarity there is a big difference in the way Dynamic Modelling, Well Flow Performance and Well Testing deal with formation pressure and flowrates which results in a difference in productivity index definition and corresponding analysis. This difference is summarized in the table below:
p_R field-average pressure within the 9-cell area
A_{e9}
q phase flowrate at sandface:
\{ q_w, \, q_o, \, q_g \} (each fluid phase separately)
J phase productivity index:
p_R field-average pressure within the drainage area
A_e
p_e = \frac{1}{A_e} \int \int_{A_e} p(x,y,z) dS
q surface component flowrate
\{ q_W, q_O, q_G \} (each fluid component separately) and sometimes liquid flowrate
q_{LIQ} = q_W + q_O
J_s fluid component productivity index:
J_W = \frac{q_W}{p_R - p_{wf}} ,
J_O = \frac{q_O}{p_R - p_{wf}} ,
J_G = \frac{q_G}{p_R - p_{wf}} and sometimes liquid productivity index:
J_{liq} = \frac{q_{LIQ}}{p_R - p_{wf}}
p_e average pressure value at the boudary of drainage area
A_e
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
q total flowrate at sandface:
q_t = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O) – for Black Oil
q_t =
B_w \, q_W
+ \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O
+ \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G – for Volatile Oil or
\{ W, \, O, \, G \} pseudo-components of Compositional Model
J_t total multiphase productivity index:
J_t = \frac{q_t}{p_e - p_{wf}}Formation pressure Flow rate Prroducivity Index DM
J_ w = \frac{q_q}{p_R - p_{wf}} ,
J_o = \frac{q_o}{p_R - p_{wf}} ,
J_o = \frac{q_o}{p_R - p_{wf}}WFP WT