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| title | Definition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Tests |
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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
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_{R9} | field-average pressure within the 9-cell area {e9}| LaTeX Math Block |
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| p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
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p_R | | \displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}} |
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WT | |
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(each fluid component separately)
| p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl |
where is the boundary of drainage area | | |
| 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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WT | | average pressure value at the boudary 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} |
| 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: 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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Sometimes the wrong estimations of flowrate stem form the wrong inputs (
or ).
See Also
...
Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management
Subsurface E&P Disciplines / Production Technology / Productivity Index
