Despite of terminological similarity there is a big difference in the way Dynamic Modelling (DM), Well Flow Performance (WFP) and Well Testing define (WT) usually define formation pressure and 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 the 9-cell {e9}( |
Total Sandface Productivity Index: | LaTeX Math Inline |
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| body | \displaystyle J_t = \frac{q_t}{p_e - p_{wf}} |
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| | 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} ) |
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phase flowrate at sandface: | LaTeX Math Inline |
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| body | \{ q_w, \, q_o, \, q_g \} |
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separately)phase productivity indexJ_ w = \frac{q_q}{field-average pressure within the drainage area r - p_{wf}} , | 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 | | {e9,o}, \, p_{e9,g}, \, p_{e9,w} |
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Ae| LaTeX Math Block |
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| p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
surface component \{ W, q_O, q_G \}(each fluid component separately) and sometimes liquid {\rm liq} = q_W + q_Ofluid component productivity index: W Wr , O Or - p_{wf}} , | LaTeX Math Inline |
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body | J_G = \frac{q_G}{p_r and sometimes liquid productivity index: {\rm liq} {\rm liq}r 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
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