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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 summarised in the table below:
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DM | 9-cell formation pressure
(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} ) |
for each fluid phase individually:
p_{e9,o}, \, p_{e9,g}, \, p_{e9,w} | | |
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WFP | Field-average formation pressure estimate within the drainage area Ae
(3) |
p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
| | surface 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}} |
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WT | Boundary-average formation pressure estimate along the boundary of drainage area Ae
(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 sandface flowrate:
q_t = B_w \, q_W + (B_o - R_v \, B_g) \, q_O + (B_g - R_s \, B_o) \, q_G
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