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LaTeX Math Block
anchorJ
alignmentleft
J_s(q_{\rm liq}) = \frac{q_{\rm liq}}{p_R-p_{wf}}


for oil producer with surface liquid flowrate

LaTeX Math Inline
bodyq_{liq} = q_o O + q_wW
(water and oil at surface conditions)

LaTeX Math Block
anchorJ
alignmentleft
J_s(q_G) = \frac{q_G}{p_R-p_{wf}}


for gas producer with surface gas flowrate

LaTeX Math Inline
bodyq_G
at surface conditions

LaTeX Math Block
anchorJ
alignmentleft
J_s(q_g) = \frac{q_{GI}}{p_{wf}-p_R}


for gas injector with surface gas flowrate

LaTeX Math Inline
bodyq_{GI}
at surface conditions

LaTeX Math Block
anchorJ
alignmentleft
J_s(q_w) = \frac{q_{WI}}{p_R-p_{wf}}


for water injector with surface water flowrate

LaTeX Math Inline
bodyq_{WI}
at surface conditions

where

LaTeX Math Inline
bodyp_R

field-average formation pressure within the drainage area

LaTeX Math Inline
bodyV_e
of a given well:
LaTeX Math Inline
bodyp_R = \frac{1}{V_e} \, \int_{V_e} \, p(t, {\bf r}) \, dV

...

Note
titleImportant Note


Despite of terminological similarity there is a big difference in the way WFP way Dynamic Modelling,  Well Flow Performance and Well Testing deal with formation pressure and flowrates which results in a difference in productivity index definition and corresponding analysis.

This difference is summarized in the table below:




Formation pressureFlow ratePrroducivity Index
DM





WFP

LaTeX Math Inline
bodyp_R

field-average pressure within the drainage area

LaTeX Math Inline
bodyA_e

LaTeX Math Inline
bodyq

surface liquid rate

LaTeX Math Inline
bodyq_W, q_O, q_G

(each fluid component separately)

LaTeX Math Inline
bodyJ_s

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}}

WT

LaTeX Math Inline
bodyp_e

average pressure value at the boudary of drainage area

LaTeX Math Inline
bodyA_e

LaTeX Math Inline
bodyq

total flowrate at sandface:

LaTeX Math Inline
bodyq_t = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O)
– for Black Oil

LaTeX Math Inline
bodyq_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
– for Volatile Oil

LaTeX Math Inline
bodyq_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
– for
LaTeX Math Inline
body\{ W, \, O, \, G \}
pseudo-components of Compositional Model

LaTeX Math Inline
bodyJ_t

total multiphase productivity index

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




WFPWell Testing
Formation pressure

LaTeX Math Inline
bodyp_R

field-average pressure within the drainage area

LaTeX Math Inline
bodyA_e


LaTeX Math Inline
bodyp_e

average pressure value at the boudary of the drainage area

LaTeX Math Inline
bodyA_e


Flow rate

LaTeX Math Inline
bodyq

surface liquid rate

LaTeX Math Inline
bodyq_W, q_O, q_G

(each fluid component separately)

LaTeX Math Inline
bodyq

total flowrate at sandface:

LaTeX Math Inline
bodyq_t = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O)
– for Black Oil


LaTeX Math Inline
bodyq_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
– for Volatile Oil

LaTeX Math Inline
bodyq_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
– for
LaTeX Math Inline
body\{ W, \, O, \, G \}
pseudo-components of Compositional Model

Prroducivity Index

LaTeX Math Inline
bodyJ_s

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}}

LaTeX Math Inline
bodyJ_t

total multiphase proudcivity productivity index

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



































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