Fig. 1. Dual-layer well schematic

(1)	$\begin{array}{l}\displaystyle q = q_1 + q_2\end{array}$

(2)	$\begin{array}{l}\displaystyle p_{wf} = p_e - q/J\end{array}$

(3)	$\begin{array}{l}\displaystyle J = J_1 + J_2\end{array}$

(4)	$\begin{array}{l}\displaystyle p_e = \frac{J_1 \cdot p_1 + J_2 \cdot (p_2- \rho \, g \, h)}{J_1 + J_2}\end{array}$

where

Well
	$\begin{array}{l}q\end{array}$	total subsurface flowrate of the well
	$\begin{array}{l}J\end{array}$	total well productivity Index
	$\begin{array}{l}p_e\end{array}$	apparent formation pressure of dual-layer formation
	$\begin{array}{l}h\end{array}$	true vertical height between the layers tops
	$\begin{array}{l}\rho\end{array}$	wellbore fuid density
	$\begin{array}{l}g\end{array}$	gravity constant
Layer #1
	$\begin{array}{l}p_{wf}\end{array}$	bottom-hole pr4essure at Layer #1 top
	$\begin{array}{l}q_1\end{array}$	total subsurface flowrate of the Layer #1
	$\begin{array}{l}p_1\end{array}$	formation pressure of the Layer #1
	$\begin{array}{l}J_1\end{array}$	productivity Index of the Layer #1
Layer #2
	$\begin{array}{l}p_{wf2} = p_{wf} + \rho \, g\, h\end{array}$	bottom-hole pr4essure at Layer #2 top
	$\begin{array}{l}q_2\end{array}$	total subsurface flowrate of the Layer #2
	$\begin{array}{l}p_2\end{array}$	formation pressure of the Layer #2
	$\begin{array}{l}J_2\end{array}$	productivity Index of the Layer #2

The above equations are valid for both producers and injectors.

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See Also