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, $\begin{array}{l}p_e\end{array}$

Flowrate, $\begin{array}{l}q\end{array}$

Productivity Index, $\begin{array}{l}J\end{array}$

WFP

Drain-area formation pressure estimate
within the drainage area $\begin{array}{l}A_e\end{array}$

(1)	$\begin{array}{l}\displaystyle p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS\end{array}$

Surface flowrates:

Oil surface flowrate $\begin{array}{l}q_O\end{array}$

Gas surface flowrate $\begin{array}{l}q_G\end{array}$

Water surface flowrate $\begin{array}{l}q_W\end{array}$

Liquid surface flowrate $\begin{array}{l}q_L\end{array}$

Drain-area surface Productivity Index: $\begin{array}{l}J_r\end{array}$

Oil Surface Productivity Index $\begin{array}{l}\displaystyle J_{r, O} = \frac{q_O}{p_r - p_{wf}}\end{array}$

Gas Surface Productivity Index $\begin{array}{l}\displaystyle J_{r, G} = \frac{q_G}{p_r - p_{wf}}\end{array}$

Water Surface Productivity Index $\begin{array}{l}\displaystyle J_{r, W} = \frac{q_W}{p_r - p_{wf}}\end{array}$

Liquid Surface Productivity Index $\begin{array}{l}\displaystyle J_{r, L} = \frac{q_L}{p_r - p_{wf}}\end{array}$

WT

Drain-boundary formation pressure estimate
along the boundary of drainage area $\begin{array}{l}A_e\end{array}$

(2)	$\begin{array}{l}\displaystyle p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl\end{array}$

where $\begin{array}{l}L_e\end{array}$ is the boundary of drainage area $\begin{array}{l}A_e\end{array}$

Total sandface flowrate:

$\begin{array}{l}q_t = q_w+q_o+q_g\end{array}$

Total Sandface Productivity Index: $\begin{array}{l}\displaystyle J_t = \frac{q_t}{p_e - p_{wf}}\end{array}$

DM

9-cell formation pressure

(3)	$\begin{array}{l}\displaystyle p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l}\end{array}$

(4)	$\begin{array}{l}\displaystyle p_{e9, \ i,j} = \frac{1}{9} ( p_{i,j} + p_{i, \, j+1} + p_{i, \, j-1} + p_{i-1, \, j} + p_{i-1, \, j} + p_{i-1 \, j-1} + p_{i+1, \, j+1} + p_{i-1 \, j+1} + p_{i+1, \, j-1} )\end{array}$

for each fluid phase individually: $\begin{array}{l}p_{e9,o}, \, p_{e9,g}, \, p_{e9,w}\end{array}$

Sandface Flowrates:

Oil sandface flowrate $\begin{array}{l}q_o\end{array}$

Gas sandface flowrate $\begin{array}{l}q_g\end{array}$

Water sandface flowrate $\begin{array}{l}q_w\end{array}$

Sandface Productivity Index:

Oil Sandface Productivity Index $\begin{array}{l}\displaystyle J_o = \frac{q_o}{p_{e,o} - p_{wf}}\end{array}$

Gas Sandface Productivity Index $\begin{array}{l}\displaystyle J_g = \frac{q_g}{p_{e,g} - p_{wf}}\end{array}$

Water Sandface Productivity Index $\begin{array}{l}\displaystyle J_ w = \frac{q_q}{p_{e,w} - p_{wf}}\end{array}$

Sometimes the wrong estimations of flowrate stem form the wrong inputs ( $\begin{array}{l}J\end{array}$ or $\begin{array}{l}p_e\end{array}$ ).

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See Also

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Definition specifics on formation pressure (Pe) and productivity index (PI)

See Also