GLOSSARY > Dual-layer IPR > image2020-4-19_14-50-24.png

Fig. 1. Dual-layer well schematic

q = q_1 + q_2

p_{wf} = p_e - q/J

J = J_1 + J_2

p_e = \frac{J_1 \cdot p_1 + J_2 \cdot (p_2- \delta p_2)}{J_1 + J_2}

where

Well
		total subsurface flowrate of the well
		total well productivity Index
		apparent formation pressure of dual-layer formation
		wellbore pressure loss between the tips of two layers
		true vertical height between the layers tops
		wellbore fuid density
		gravity constant
Layer #1
		bottom-hole pr4essure at Layer #1 top
		total subsurface flowrate of the Layer #1
		formation pressure of the Layer #1
		productivity Index of the Layer #1
Layer #2
		bottom-hole pr4essure at Layer #2 top
		total subsurface flowrate of the Layer #2
		formation pressure of the Layer #2
		productivity Index of the Layer #2

In many practical cases:

\delta p_2 = \rho \, g \, h

where

	wellbore fuid density
	gravity constant
	true vertical height between -th layer and reference layer

The above equations are valid for both producers and injectors.

p_{wf} = p_1 - q_1/J_1

p_{wf,2} = p_2 - q_2/J_2

p_{wf2} = p_{wf} + \delta p_2

This leads to

p_1 - q_1/J_1 = p_2 - \delta p_2 - q_2/J_2

See Also