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:
| Formation pressure | Flow rate | Prroducivity Index |
---|
DM | | field-average pressure within the 9-cell area
A_{e9}
(1) |
p_{e, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l} = \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} ) |
| | phase flowrate at sandface:
\{ q_w, \, q_o, \, q_g \} (each fluid phase separately) | | phase productivity index:
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 | | field-average pressure within the drainage area
A_e
(2) |
p_e = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
| | surface component flowrate
\{ q_W, q_O, q_G \} (each fluid component separately) and sometimes liquid flowrate
q_{\rm liq} = q_W + q_O | | 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_{\rm liq} = \frac{q_{\rm liq}}{p_r - p_{wf}} |
---|
WT | | average pressure value at the boudary of drainage area
A_e
(3) |
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 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 | | total multiphase productivity index:
J_t = \frac{q_t}{p_e - p_{wf}} |
---|