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

$//<![CDATA[ \begin{array}{l}p_R\end{array} //]]>$

field-average pressure within the 9-cell area $//<![CDATA[ \begin{array}{l}A_{e9}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}q\end{array} //]]>$

phase flowrate at sandface: $//<![CDATA[ \begin{array}{l}\{ q_w, \, q_o, \, q_g \}\end{array} //]]>$

(each fluid phase separately)

$//<![CDATA[ \begin{array}{l}J\end{array} //]]>$

phase productivity index:

$//<![CDATA[ \begin{array}{l}J_ w = \frac{q_q}{p_R - p_{wf}}\end{array} //]]>$ , $//<![CDATA[ \begin{array}{l}J_o = \frac{q_o}{p_R - p_{wf}}\end{array} //]]>$ , $//<![CDATA[ \begin{array}{l}J_o = \frac{q_o}{p_R - p_{wf}}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}p_R\end{array} //]]>$

field-average pressure within the drainage area $//<![CDATA[ \begin{array}{l}A_e\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}p_e = \frac{1}{A_e} \int \int_{A_e} p(x,y,z) dS\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}q\end{array} //]]>$

surface component flowrate $//<![CDATA[ \begin{array}{l}\{ q_W, q_O, q_G \}\end{array} //]]>$

(each fluid component separately)

and sometimes liquid flowrate $//<![CDATA[ \begin{array}{l}q_{LIQ} = q_W + q_O\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}J_s\end{array} //]]>$

fluid component productivity index:

$//<![CDATA[ \begin{array}{l}J_W = \frac{q_W}{p_R - p_{wf}}\end{array} //]]>$ , $//<![CDATA[ \begin{array}{l}J_O = \frac{q_O}{p_R - p_{wf}}\end{array} //]]>$ , $//<![CDATA[ \begin{array}{l}J_G = \frac{q_G}{p_R - p_{wf}}\end{array} //]]>$

and sometimes liquid productivity index: $//<![CDATA[ \begin{array}{l}J_{liq} = \frac{q_{LIQ}}{p_R - p_{wf}}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}p_e\end{array} //]]>$

average pressure value at the boudary of drainage area $//<![CDATA[ \begin{array}{l}A_e\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl\end{array} //]]>$ where $//<![CDATA[ \begin{array}{l}L_e\end{array} //]]>$ is the boundary of drainage area $//<![CDATA[ \begin{array}{l}A_e\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}q\end{array} //]]>$

total flowrate at sandface:

$//<![CDATA[ \begin{array}{l}q_t = B_w \, q_W + B_o \, q_O + B_g \, ( q_G - R_s q_O)\end{array} //]]>$ – for Black Oil

$//<![CDATA[ \begin{array}{l}q_t = B_w \, q_W + \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G\end{array} //]]>$ – for Volatile Oil

or $//<![CDATA[ \begin{array}{l}\{ W, \, O, \, G \}\end{array} //]]>$ pseudo-components of Compositional Model

$//<![CDATA[ \begin{array}{l}J_t\end{array} //]]>$

total multiphase productivity index: $//<![CDATA[ \begin{array}{l}J_t = \frac{q_t}{p_e - p_{wf}}\end{array} //]]>$