Role of inertia in falling head permeability test

Abstract

SUMMARYThis paper discusses the role of macro-and micro-inertial forces in the falling head permeability test. The model of flow including viscous and dynamic interaction forces is formulated. Then, the model is used to perform numerical simulations of the tests for high-permeability soils. The presented results prove the existence of a level of permeability of materials above which macro-and micro-inertial forces are important and that in all cases the latter forces are dominant. The results suggest limited validity of the standard interpretation of the falling head permeability test and possible usefulness of the test to determine both permeability and the parameter characterizing non-linear interactions of fluid and solid skeleton.

Identification of Drag Parameters of Flow in High Permeability Materials by U-Tube Method

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A method for the estimation of dual transmissivities from slug tests

“…The most common analytic models used to interpret slug tests were developed by Bouwer and Rice (1976), Bredehoeft and Papadopulos (1980), Cooper et al (1965Cooper et al ( , 1967 and Hvorslev (1951). These models, however, usually assume homogeneity of the analyzed water-bearing formations, when many of them are, in fact, characterized by the presence of different systems of void space which may lead to preferential flow (Beckie and Harvey 2002;Copty et al 2011;Pechstein et al 2016).…”

Forchheimer and added mass effects in the flow towards a well

“…In higher velocity flows, differently from usual seepage problems, the force exerted by the soil particles on the moving water is not well described by a linear function of the velocity (e.g., ). In order to model such flows, more complex expressions for the interaction force have been proposed as, for instance, the following quite general law , obtained from the traditional linear Darcy force by the addition of a Forchheimer term (quadratic in the velocity) and an added mass term (linear in the acceleration): valid only for incompressible fluids. In the aforementioned equation, f is the interaction force per unit volume, v is the velocity (‖ v ‖ denotes the norm of v ), a is the acceleration, and α , β , and λ are positive constants (only homogeneous soils will be treated here).…”

“…In order to illustrate the magnitude of these numbers in a particular case, consider the following values: r 0 = 0.10 m, Q / D = 10 − 2 m 3 /s/m, n = 0. 3, ρ = 10 3 kg/m 3 , γ = 9.81 × 10 3 N/m 3 , and, for a coarse sand : α = 2 × 10 4 Pa m − 2 s, β = 3 × 10 5 Pa m − 3 s 2 , λ = 2 × 10 3 Pa m − 2 s 2 . In this case: B ∞ ≅ 8.6 × 10 − 3 m, C ∞ ≅ 4.3 × 10 − 4 m, b 0 ≅ 8 × 10 − 1 , c 0 = 8 × 10 − 2 .…”