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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. This difference is summarized The most typical definitions (although they do not cover the full variety of definitions referred in petroleum literature) are summarised in the table below: Flow rate, Gas Surface Productivity Index LaTeX Math Inline |
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body | \displaystyle J_{r, G} = \frac{q_G}{p_r - p_{wf}} |
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Water Surface Productivity Index LaTeX Math Inline |
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body | \displaystyle J_{r, W} = \frac{q_W}{p_r - p_{wf}} |
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Liquid Surface Productivity Index LaTeX Math Inline |
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body | \displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}} |
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| WT | Drain-boundary formation pressure estimate along the boundary 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 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} ) |
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 sandface productivity index sandface productivity indexWFP Field-average formation pressure estimate within the drainage area Ae LaTeX Math Block |
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| p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
Oil surface flowrate Gas surface flowrate Water surface flowrate Liquid flowrate surface productivity index:
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Sometimes the wrong estimations of flowrate stem form the wrong inputs (
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or
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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
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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 - R_v \, B_g) \, q_O + (B_g - R_s \, B_o) \, q_G |
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Total sandface productivity index:
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management
Subsurface E&P Disciplines / Production Technology / Productivity Index