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:
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DM | field-average pressure within the 9-cell area 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} ) |
| 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}{p_r - p_{wf}} |
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, 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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WFP | field-average pressure within the drainage area LaTeX Math Block |
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| p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
| surface component flowrate (each fluid component separately) and sometimes liquid flowrate | fluid component productivity index: LaTeX Math Inline |
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body | J_W = \frac{q_W}{p_r - p_{wf}} |
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, 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_{OW} = \frac{q_{OW}}{p_r - p_{wf}} |
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WT | average pressure value along 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}} |
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