GLOSSARY

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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.

The most typical definitions (although they do not cover the full variety of definitions referred in petroleum literature) are summarised in the table below:


Formation pressure,

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bodyp_e

Flowrate,

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bodyq

Productivity Index,

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bodyJ


WFP

Drain-area formation pressure estimate 
within the drainage area 

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bodyA_e

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


Surface flowrates:

Oil surface flowrate

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bodyq_O

Gas surface flowrate

LaTeX Math Inline
bodyq_G

Water surface flowrate

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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 

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bodyA_e

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anchor1
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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:

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bodyq_t = q_w+q_o+q_g


Total Sandface Productivity Index:

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

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:

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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}}



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