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titleDefinition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Tests

Despite of terminological similarity there is a big difference in the 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

LaTeX Math Inline
bodyp_{R9}

field-average pressure within the 9-cell area

LaTeX Math Inline
bodyA_{e9}

LaTeX Math Inline
bodyq

phase flowrate at sandface:

LaTeX Math Inline
body\{ q_w, \, q_o, \, q_g \}

(each fluid phase separately)

LaTeX Math Inline
bodyJ

phase 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_o = \frac{q_o}{p_R - p_{wf}}

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
body\{ q_W, q_O, q_G \}

(each fluid component separately)

LaTeX Math Inline
bodyJ_s

fluid component 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}}

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

or

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}}