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

Fig. 1. Multi-layer well schematic

q = \sum_{k=1}^N q_k

p_{wf} = p_e - q/J

J = \sum_{k=1}^N J_k

p_e = J^{-1} \cdot \sum_{k=1}^N J_k \, (p_k- \delta p_k)

where

	total subsurface flowrate of the well
	total well productivity Index
	apparent formation pressure of dual-layer formation
	bottom-hole pressure at the top of the reference layer
	bottom-hole pressure at the top of the -th layer
	wellbore pressure loss between -th layer and reference layer
	total subsurface flowrate of the -th layer
	formation pressure of the -th layer
	productivity Index of the -th layer

The above equations are valid for both producers and injectors .

In many practical cases:

\delta p_k = \rho \, g \, h_k

where

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

See Also