Despite of terminological similarity there is a big difference in the way Dynamic Modelling (DM), Well Flow Performance (WFP) and Well Testing deal with (WT) usually define formation pressure and flowrates which results in a difference in productivity index definition and corresponding analysis.. The most typical definitions (although they do not cover the full variety of definitions referred in petroleum literature) are summarised This difference is summarized in the table below: Flow rateProducivity DMfieldaverage within the 9-cell area {e9}{e9, \ i,j} 9sumk=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: | LaTeX Math Inline |
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| body | \{ q_w, \, q_o, \, q_g \} |
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(each fluid phase separately) | phase productivity index: | LaTeX Math Inline |
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body | J_ w = \frac{q_q , o o , g gWFPfieldaverage pressure within the rAiintAdSsurface component flowrate \{ q_W, q_O, q_G \} | (each fluid component separately) is the boundary of drainage area | |
and sometimes liquid flowrate {\rm liq} W Ofluid component productivity indexW Wr , | LaTeX Math Inline |
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| body | J_O = \frac{q_O}{p_r - p_{wf}} |
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, | LaTeX Math Inline |
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| body | J_G = \frac{q_G}{p_r - p_{wf}} |
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and sometimes liquid productivity index: | LaTeX Math Inline |
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| body | J_{\rm liq} = \frac{q_{\rm liq}}{p_r - p_{wf}} |
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WT | average pressure value at the boudary of drainage area | LaTeX Math Block |
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| p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl |
where is the boundary of drainage area | total flowrate at sandface: | | DM | 9-cell formation pressure | LaTeX Math Block |
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| p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l} |
| LaTeX Math Block |
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| 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: | LaTeX Math Inline |
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| body | p_{e9,o}, \, p_{e9,g}, \, p_{e9,w} |
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– for Black Oilt = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O)qt = B_w \, q_W + B - R_s B_g1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G – for Volatile Oilor { W, \, O, \, G \} pseudo-components of Compositional Modeltotal multiphase productivity index: t t
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