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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.
This difference is summarized in the table below:
| | | |
|---|
| 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) | single-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_{OW} = q_O + q_W | 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_{OW} = \frac{q_{OW}}{p_r - p_{wf}} |
|---|
| WT | average pressure value along 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
+ \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 | total multiphase productivity index:
J_t = \frac{q_t}{p_e - p_{wf}} |
|---|
