Patent ID: 7930926

Claim:
A method of determining permeability of liquid through a liquid-saturated solid material, the method comprising: a) performing vibration testing of a sample of said liquid in said liquid-saturated solid material, wherein said vibration testing provides porosity of the sample, mass of the liquid, mass of the solid material, and a measured Kevin-Voigt (KV) damping ratio for the sample, wherein damping ratio and dashpot are related by equation (1): Damping ratio=Dashpot/(2√{square root over ( k×m )}) (1), wherein m=total mass of liquid and solid material, and k=stiffness defined by equation (2), k =(shear modulus of solid material· A )/ L (2), wherein A=cross-sectional area of said sample volume, and L=length of said sample volume; b) Mapping multiple calculated Kelvin-Voigt-Maxwell-Biot (KVMB)-determined equivalent KV damping ratio versus multiple assumed trial KVMB-dashpots, by the steps of: assuming multiple trial KVMB dashpot values d, and calculating the three eigenvalues corresponding to a decoupled version of equation (3) for each assumed trial KVMB dashpot value: ⅆ ⅆ t ⁡ [ u f u . f u . w ] = [ 0 1 0 - k M f - d M f + d M f 0 + d M w - d M w ] · [ u f u . f u . w ] , ( 3 ) wherein u f =solid-material-mass displacement, {dot over (u)} f =solid-material-mass velocity, and {dot over (u)} w =liquid-mass velocity, M f =mass of said solid material, M w =mass of said liquid, and d=assumed trial KVMB dashpot value, and wherein k is defined by equation (2); retaining two complex conjugate eigenvalues λ 1 and λ 2 of said three eigenvalues of said decoupled version of equation (3) for each assumed trial KVMB dashpot, inserting said two complex conjugate eigenvaluves into equation (4) to compute a KVMB-determined equivalent KV damping ratio ξ, and discarding the third of said three eigenvalues: ξ = ( λ 1 + λ 2 ) 2 2 ⁢ λ 1 ⁢ λ 2 =  λ 1 + λ 2  2 ⁢ λ 1 ⁢ λ 2 ; ( 4 ) mapping said KVMB-determined equivalent KV damping ratios ξ versus the multiple assumed trial KVMB dashpots, determining the KVMB-determined equivalent KV damping ratio that most-closely matches the observed KV damping ratio and determining from said mapping a coupled KVMB dashpot solution and an uncoupled KVMB dashpot solution for said most-closely matched KVMB-determined equivalent KV damping ratio; c) computing permeability K d of said liquid through said liquid-saturated solid material by inserting said coupled KVMB dashpot solution into equation (5): K d = n 2 ⁢ g ⁢ ⁢ ρ liquid ⁢ A · L d , ( 5 ) wherein n=said porosity, g=acceleration due to gravity, ρ liquid =mass density of said liquid, d=said coupled KVMB dashpot solution, A=cross-sectional area of said sample volume, and L=length of said sample volume.