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 rate | Prroducivity Index | DMp_Rfieldaverage within the 9-cell area {e9}{e, \ 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 at sandface: \{ (each fluid phase separately)w, \, q_o, \, q_g \}phase productivity index: w qR , o oR , o oR WFPfield-average pressure within the drainage area p_R | | \displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}} |
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| WT | |
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| p_e = \frac{1}{ |
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AiintAdSq | surface component flowrate is the boundary of drainage area |
\{ q_W, q_O, q_G \} | (each fluid component separately) and sometimes liquid flowrate {\rm liq} W O | fluid 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_{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: | LaTeX Math Inline |
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| body | q_t = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O) |
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– for Black Oil| LaTeX Math Inline |
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| body | 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 |
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– for Volatile Oilor pseudo-components of Compositional Model | | total multiphase productivity index: | LaTeX Math Inline |
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body | J_t = \frac{q_t}{p_e - p_{wf}} | | 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} |
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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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| | Sandface Productivity Index: Oil Sandface Productivity Index | LaTeX Math Inline |
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| body | \displaystyle J_o = \frac{q_o}{p_{e,o} - p_{wf}} |
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Gas Sandface Productivity Index | LaTeX Math Inline |
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| body | \displaystyle J_g = \frac{q_g}{p_{e,g} - p_{wf}} |
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Water Sandface Productivity Index | LaTeX Math Inline |
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| body | \displaystyle J_ w = \frac{q_q}{p_{e,w} - p_{wf}} |
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