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Excerpt

Despite of terminological similarity there is a difference in the way Dynamic Modelling (DM),  Well Flow Performance (WFP) and Well Testing (WT) usually define formation pressure and productivity index.



Formation pressure,

LaTeX Math Inline
bodyp_e

Flowrate,

LaTeX Math Inline
bodyq

Productivity Index,

LaTeX Math Inline
bodyJ


WFP

Drain-area formation pressure estimate 
within the drainage area 

LaTeX Math Inline
bodyA_e

LaTeX Math Block
anchor1
alignmentleft
p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS


Surface flowrates:

Oil surface flowrate

LaTeX Math Inline
bodyq_O

Gas surface flowrate

LaTeX Math Inline
bodyq_G

Water surface flowrate

LaTeX Math Inline
bodyq_W

Liquid surface flowrate

LaTeX Math Inline
bodyq_L


Drain-area surface Productivity Index: 

LaTeX Math Inline
bodyJ_r

Oil Surface Productivity Index

LaTeX Math Inline
body\displaystyle J_{r, O} = \frac{q_O}{p_r - p_{wf}}

Gas Surface Productivity Index

LaTeX Math Inline
body\displaystyle J_{r, G} = \frac{q_G}{p_r - p_{wf}}

Water Surface Productivity Index

LaTeX Math Inline
body\displaystyle J_{r, W} = \frac{q_W}{p_r - p_{wf}}

Liquid Surface Productivity Index

LaTeX Math Inline
body\displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}}

WT

Drain-boundary formation pressure estimate 
along the boundary of drainage area 

LaTeX Math Inline
bodyA_e

LaTeX Math Block
anchor1
alignmentleft
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 sandface flowrate:

LaTeX Math Inline
bodyq_t = q_w+q_o+q_g


Total Sandface Productivity Index:

LaTeX Math Inline
body\displaystyle J_t = \frac{q_t}{p_e - p_{wf}}

DM

9-cell formation pressure

LaTeX Math Block
anchor1
alignmentleft
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
anchor1
alignmentleft
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
bodyp_{e9,o}, \, p_{e9,g}, \, p_{e9,w}

Sandface Flowrates:

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:

Oil Sandface Productivity Index

LaTeX Math Inline
body\displaystyle J_o = \frac{q_o}{p_{e,o} - p_{wf}}

Gas Sandface Productivity Index

LaTeX Math Inline
body\displaystyle J_g = \frac{q_g}{p_{e,g} - p_{wf}}

Water Sandface Productivity Index

LaTeX Math Inline
body\displaystyle J_ w = \frac{q_q}{p_{e,w} - p_{wf}}




Sometimes the wrong estimations of flowrate stem form the wrong inputs (

LaTeX Math Inline
bodyJ
or
LaTeX Math Inline
bodyp_e
).


See Also

Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management

Subsurface E&P Disciplines / Production Technology / Productivity Index