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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 summarised 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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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} )

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
bodyJ_o = \frac{q_o}{p_{e,o} - p_{wf}}

Gas sandface productivity index

LaTeX Math Inline
bodyJ_g = \frac{q_g}{p_{e,g} - p_{wf}}

Water sandface productivity index

LaTeX Math Inline
bodyJ_ w = \frac{q_q}{p_{e,w} - 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


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


Surface productivity index:

Oil surface productivity index

LaTeX Math Inline
bodyJ_O = \frac{q_O}{p_r - p_{wf}}

Gas surface productivity index

LaTeX Math Inline
bodyJ_G = \frac{q_G}{p_r - p_{wf}}

Water surface productivity index

LaTeX Math Inline
bodyJ_W = \frac{q_W}{p_r - p_{wf}}

Liquid surface productivity index

LaTeX Math Inline
bodyJ_L = \frac{q_L}{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 sandface flowrate:

LaTeX Math Inline
bodyq_t = q_w+q_o+q_g

Total sandface productivity index:

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


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