compressibility: Calculate compressibility and strain sensitivity.

In abarbour/hydrogeo: Tools for hydrogeology and poroelasticity

Description

Compressibility is, essentially, the inverse of the bulk modulus of a medium, and the strain sensitivity is the amount of strain produced for unit increments in pressure.

Usage

undrained_compressibility.from.beta(Beta, B., Beta_u = NULL)

undrained_compressibility.from.areal_strain_sens(As., B., ...)

areal_strain_sens.from.undrained_compressibility(Beta_hat, B., ...)

.calc_prat(B., nu_u = NULL, fluid_dens = NULL)

calc_alpha(Beta, Beta_u = NULL)

calc_nu_u(B., Beta, nu = NULL, ...)

Arguments

Beta	numeric; The compressibility of the solid matrix, β
B.	numeric; Skempton's coefficient B
Beta_u	numeric; β for an undrained state
As.	numeric; areal strain sensitivity A[s]
...	additional paramters passed from undrained_compressibility.from.areal_strain_sens and areal_strain_sens.from.undrained_compressibility to .calc_prat calc_nu_u to calc_alpha
Beta_hat	numeric; \hat{β}
nu_u	numeric; undrained Poisson's ratio ν
fluid_dens	numeric; the density ρ of the fluid in consideration
nu	numeric; Poisson's ratio ν

Details

X calculates Equation (6) from Rojstaczer and Agnew (1989): \hat{β} and Equation (10) using strain sensitivity

Assumptions

The intake of the well is assumed to penetrate a porous elastic medium with uniform properties. These properties are those specified by the theory of Biot [1941] (as reexpressed by Rice and Cleary [1976] and Green and Wang [1986]), namely the compressibilities of the solid phase β[u], the fluid phase β[f], and the porous matrix when drained of fluid Beta (the matrix compressibility), together with the Poisson's ratio ν, of the matrix, the porosity φ, and the permeability κ.

The fluid phase is assumed to be water at standard temperature and pressure; this can be severely violated deep in the earth.

Physical parameters

ν[u]

calc_nu_u can be used to calculate ν[u]

α

Rice (1998, "Elasticity of Fluid-Infiltrated Porous Solids (Poroelasticity)") notes:

[...] this constant comes from the stress-strain constitutive relationship, under the following situation: Suppose that all pore space is fluid infiltrated, and that all the solid phase consists of material elements which respond isotropically to pure pressure stress states, with the same bulk modulus Ks . Suppose we simultaneously apply a pore pressure p = p[o] and macroscopic stresses amounting to compression by po on all faces σ[11] = σ[22] = σ[33] = -p[o]. That results in a local stress state of p[o,ij] δ[ij] at each point of the solid phase. So each point of the solid phase undergoes the strain p[o,ij] δ[ij] / 3 K[s] , which means that all linear dimensions of the material, including those characterizing void size, reduce by the (very small) fractional amount p[o] / 3 K[s] , causing the macroscopic strains, and change in porosity, ε[11] = ε[22] = ε[33] = -p[o] / 3 K[s] and Δ[n]/n = -p[o] / K[s]

calc_alpha can be used to calculate α

Author(s)

Andrew J. Barbour <[e-mail]>

See Also

skempton, kinvisc, hydrogeo.p

abarbour/hydrogeo documentation built on May 10, 2019, 4:06 a.m.