In certain production scenarios of multi-fractured unconventional wells, it appears that there exists the unexpected possibility that increasing the well's flowing pressure (decreasing the drawdown) can result in improved productivity and in larger Estimated Ultimate Recovery (EUR). This has been attributed to the pressure- dependence of permeability. This consideration provided the motivation for this study, namely to understand under what conditions pressure-dependent permeability affects the recovery and production performance.

The effect of pressure-dependent permeability is frequently modelled using the function: k(p)=kieγ(ppi), where, γ is the pressure-dependent permeability coefficient. Production at constant flowing pressure is studied for linear-flow geometry of systems with pressure-dependent permeability, representing matrix flow into a stimulated-reservoir volume (SRV) and/or a finite conductivity fracture.

It is shown that when the permeability is a function of the pressure in the reservoir, the production rate increases continuously as the drawdown is increased, and no reversal of productivity is observed. However, when the fracture conductivity is a function of the well flowing pressure, there will be an operating point beyond which a reversal of production behavior is observed, and the production rate decreases as the drawdown is increased.

Steady-state and transient models are developed to explore the conditions that lead to such a reversal. A numerical simulator is used to generate the behaviour of a system in which the fracture conductivity varies with respect to the flowing pressure. It demonstrates that the path of the producing pressure can be optimized so that oil recovery is maximized.

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