Abstract
ABSTRACT A new Porous Media Momentum (PMM) equation has been developed to account for unsteady flow through porous media. The equation contains not only the familiar permeability and non-Darcy factor terms but includes acceleration terms as well. For one-dimensional flow in the x-direction the equation takes the form − ∂ p ∂ x = μ v k + β ρ v 2 + ρ φ 2 v ∂ v ∂ x + ρ φ ∂ v ∂ t For gases this equation was put in dimensionless form by considering the ideal gas equation of state and neglecting the Klinkenberg effect. The PMM equation was solved for an instantaneous pressure step change at one end of a porous core (1-D flow). The PMM solutions were compared with the Forchheimer equation and the Darcy equation. At very small time (high accelerations) the PMM solutions correlated much better with experimental data than either the Forchheimer or Darcy equations. At large time (low accelerations) there was little difference between the PMM and Forchheimer solutions and experimental data. A bonus of this work is that the model develops an expression for the non-Darcy factor.
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