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Excerpt

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:


Formation pressure,

LaTeX Math Inline
bodyp

Flow rate,

LaTeX Math Inline
bodyq

Productivity Index

LaTeX Math Inline
bodyJ


DM

9-cell formation pressure

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anchor1
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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} )


oil sandface flowrate

LaTeX Math Inline
bodyq_o

gas sandface flowrate

LaTeX Math Inline
bodyq_g

water sandface flowrate

LaTeX Math Inline
bodyq_w



sandface productivity index:


LaTeX Math Inline
bodyJ_ w = \frac{q_q}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_o = \frac{q_o}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_g = \frac{q_g}{p_r - p_{wf}}


WFP

Field-average formation pressure estimate within the drainage area Ae

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p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS


oil surface flowrate

LaTeX Math Inline
body\{ q_W, q_O,

gas surface flowrate

LaTeX Math Inline
bodyq_G \}

(each fluid component separately)

water surface flowrate

LaTeX Math Inline
bodyq_W

and sometimes liquid flowrate

LaTeX Math Inline
bodyq_{OW} = q_O + q_WL


surface productivity index:

LaTeX Math Inline
bodyJ_W = \frac{q_W}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_O = \frac{q_O}{p_r - p_{wf}}
,
LaTeX Math Inline
bodyJ_G = \frac{q_G}{p_r - p_{wf}}

and sometimes liquid productivity index:

LaTeX Math Inline
bodyJ_{OW} = \frac{q_{OW}}{p_r - p_{wf}}


WT

Boundary-average formation pressure estimate along the boundary of drainage area Ae

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p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl

where

LaTeX Math Inline
bodyL_e
is the boundary of drainage area
LaTeX Math Inline
bodyA_e

total flowrate at sandface:

LaTeX Math Inline
bodyq_t = B_w \, q_W + \frac{(B_o - R_s v \, B_g}{1 - R_v R_s} ) \, q_O + \frac{(B_g - R_v s \, B_o}{1 - R_v R_s} ) \, q_G

total sandface productivity index:

LaTeX Math Inline
bodyJ_t = \frac{q_t}{p_e - p_{wf}}


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