Despite of terminological similarity there is a big difference in the way Dynamic Modelling, Well Flow Performance and Well Testing define formation pressure and productivity index definition and corresponding analysis.
This difference is summarized in the table below:
| | | |
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| DM | field-average pressure within the 9-cell area
A_{e9}
| (1) |
p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l} |
| (2) |
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} ) |
| 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_g = \frac{q_g}{p_r - p_{wf}}
|
|---|
| WFP | field-average pressure within the drainage area
A_e
| (3) |
p_r = \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
| (4) |
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}} |
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