Velocity of viscous fingers in miscible displacement: Intermediate concentration
arxiv(2023)
摘要
We investigate one-phase flow in porous medium corresponding to a miscible
displacement process in which the viscosity of the injected fluid is smaller
than the viscosity in the reservoir fluid, which frequently leads to the
formation of a mixing zone characterized by thin fingers. The mixing zone grows
in time due to the difference in speed between its leading and trailing edges.
The transverse flow equilibrium (TFE) model provides estimates of these speeds.
We propose an enhancement for the TFE estimates, and provide its theoretical
justification. It is based on the assumption that an intermediate concentration
exists near the tip of the finger, which allows to reduce the integration
interval in the speed estimate. Numerical simulations were conducted that
corroborate the new estimates within the computational fluid dynamics model.
The refined estimates offer greater accuracy than those provided by the
original TFE model.
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