rockphypy.GM

Module Contents

Classes

GM

Contact based granular medium models and extensions.
class rockphypy.GM.GM[source]

Contact based granular medium models and extensions.

static ThomasStieber(phi_sand, phi_sh, vsh)[source]

Thomas-Stieber porosity model for sand-shale system.

Parameters:

  • phi_sand (float) – clean sand porosity

  • phi_sh (float) – shale porosity

  • vsh (float or array-like) – volume faction of shale in the mixture

Returns:

float or array-like – phi_ABC,phi_AC (frac): porosity line as shown in Fig 5.3.2 in (Mavko,2020)

static silty_shale(C, Kq, Gq, Ksh, Gsh)[source]

Dvorkin–Gutierrez silty shale model: model the elastic moduli of decreasing clay content for shale.

Parameters:

  • C (float or array-like) – volume fraction of clay

  • Kq (float) – bulk modulus of silt grains

  • Gq (float) – shear modulus of silt grains

  • Ksh (float) – saturated bulk modulus of pure shale

  • Gsh (float) – saturated shear modulus of pure shale, * Ksh and Gsh could be derived from well-log measurements of VP, VS and density in a pure shale zone.

Returns:

float or array-like – K_sat, G_sat: elastic moduli of the saturated silty shale.

static shaly_sand(phis, C, Kss, Gss, Kcc, Gcc)[source]

Modeling elastic moduli for sand with increasing clay content using LHS bound rather than using Gassmann relation.

Parameters:

  • phis (float) – critical porosity of sand composite

  • C (float or array-like) – clay content

  • Kss (float) – saturated bulk moduli for clean sandstone using e.g. HM

  • Gss (float) – saturated shear moduli for clean sandstone using e.g. HM

  • Kcc (float) – saturated bulk moduli calculated from the sandy shale model at critical clay content using silty shale model

  • Gcc (float) – saturated shear moduli calculated from the sandy shale model at critical clay content using silty shale model

Returns:

float or array-like – K_sat,G_sat: saturated rock moduli of the shaly sand

static contactcement(K0, G0, Kc, Gc, phi, phic, Cn, scheme)[source]

Compute dry elastic moduli of cemented sandstone via Contact cement model by Dvorkin &Nur (1996).

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • Kc (float) – Bulk modulus of cement

  • Gc (float) – Shear modulus of cement

  • phi (float or array-like) – Porosity

  • phic (float) – Critical Porosity

  • Cn (float) – coordination number

  • scheme (int) –

    Scheme of cement deposition

    1=cement deposited at grain contacts 2=cement deposited at grain surfaces

Returns:

_type_ – K_dry, G_dry (GPa): Effective elastic moduli of dry rock

References

  • Dvorkin & Nur, 1996, Geophysics, 61, 1363-1370

static hertzmindlin(K0, G0, phic, Cn, sigma, f)[source]

Compute effective dry elastic moduli of granular packing under hydrostatic pressure condition via Hertz-Mindlin approach. Reduced shear factor that honours the non-uniform contacts in the granular media is implemented.

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa phic : float Critical Porosity

  • Cn (float) – coordination number

  • sigma (float or array-like) – effective stress

  • f (float) – reduced shear factor between 0 and 1 0=dry pack with inifinitely rough spheres; 1=dry pack with infinitely smooth spheres

Returns:

  • K_dry, G_dry (float or array-like) – effective elastic moduli of dry pack

  • References – ———-

  • - Rock physics handbook section 5.5.

  • - Bachrach, R. and Avseth, P. (2008) Geophysics, 73(6), E197–E209.

static softsand(K0, G0, phi, phic, Cn, sigma, f)[source]

Soft-sand (unconsolidated sand) model: model the porosity-sorting effects using the lower Hashin-Shtrikman-Walpole bound. (Also referred to as the ‘friable-sand model’ in Avseth et al. (2010).

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • phi (float or array like) – Porosity phic : float Critical Porosity

  • Cn (float) – coordination number

  • sigma (float or array-like) – effective stress

  • f (float) – reduced shear factor between 0 and 1 0=dry pack with inifinitely rough spheres; 1=dry pack with infinitely smooth spheres

Returns:

  • float or array-like – K_dry, G_dry (GPa): Effective elastic moduli of dry pack

  • References – ———-

  • - The Uncemented (Soft) Sand Model in Rock physics handbook section 5.5

  • - Avseth, P.; Mukerji, T. & Mavko, G. Cambridge university press, 2010

static Walton(K0, G0, phic, Cn, sigma, f)[source]

Compute dry rock elastic moduli of sphere packs based on the Walton (1987)’ thoery. Reduced shear factor that honours the non-uniform contacts in the granular media is implemented.

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa phic : float Critical Porosity

  • Cn (float) – coordination number

  • sigma (float or array-like) – effective stress

  • f (float) – reduced shear factor between 0 and 1 0=dry pack with inifinitely rough spheres; 1=dry pack with infinitely smooth spheres

Returns:

  • float or array-like – K_w, G_w: Effective elastic moduli of dry pack

  • References – ———-

  • - Walton model in Rock physics handbook section 5.5

  • - Walton, K., 1987, J. Mech. Phys. Solids, vol.35, p213-226.

  • - Bachrach, R. and Avseth, P. (2008) Geophysics, 73(6), E197–E209

static johnson(K0, G0, n, phi, epsilon, epsilon_axial, path='together')[source]

effective theory for stress-induced anisotropy in sphere packs. The transversely isotropic strain is considered as a combination of hydrostatic strain and uniaxial strain.

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • n (float) – coordination number

  • phi (float or array like) – porosity

  • epsilon (float or array like) – hydrostatic strain (negative in compression)

  • epsilon_axial (float or array like) – uniaxial strain (along 3-axis)

  • path (str, optional) – ‘together’: the hydrostatic and uniaxial strains are applied simultaneously ‘uni_iso’: the uniaxial strain is applied first followed by a hydrostatic strain ‘iso_uni’: the hydrostatic strain is applied first followed by a uniaxial strain by default ‘together’

Returns:

  • array and float – C: (matrix): VTI stiffness matrix sigma33: non zero stress tensor component sigma11: non zero stress tensor component, sigma11=sigma22

  • References – ———-

  • - Norris, A. N., and Johnson, D. L., 1997, ASME Journal of Applied Mechanics, 64, 39-49.

  • - Johnson, D.L., Schwartz, L.M., Elata, D., et al., 1998. Transactions ASME, 65, 380–388.

static stiffsand(K0, G0, phi, phic, Cn, sigma, f)[source]

Stiff-sand model: Modified Hashin-Shtrikman upper bound with Hertz-Mindlin end point, counterpart to soft sand model. model the porosity-sorting effects using the lower Hashin–Shtrikman–Walpole bound.

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • phi (float or array like) – Porosity phic : float Critical Porosity

  • Cn (float) – coordination number

  • sigma (float or array-like) – effective stress

  • f (float) – reduced shear factor between 0 and 1 0=dry pack with inifinitely rough spheres; 1=dry pack with infinitely smooth spheres

Returns:

float or array-like – K_dry, G_dry (GPa): Effective elastic moduli of dry pack

static constantcement(phi_b, K0, G0, Kc, Gc, phi, phic, Cn, scheme)[source]

Constant cement (constant depth) model according to Avseth (2000)

Parameters:

  • phi_b (_type_) – adjusted high porosity end memeber

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • Kc (float) – Bulk modulus of cement

  • Gc (float) – Shear modulus of cement

  • phi (float or array-like) – Porosity

  • phic (float) – Critical Porosity

  • Cn (float) – coordination number

  • scheme (int) –

    Scheme of cement deposition

    1=cement deposited at grain contacts 2=cement deposited at grain surfaces

Returns:

  • float or array-like – K_dry, G_dry (GPa): Effective elastic moduli of dry rock

  • References – ———-

  • - Avseth, P.; Dvorkin, J.; Mavko, G. & Rykkje, J. Geophysical Research Letters, Wiley Online Library, 2000, 27, 2761-2764

static MUHS(K0, G0, Kc, Gc, phi, phi_b, phic, Cn, scheme)[source]

Increasing cement model: Modified Hashin-Strikmann upper bound blend with contact cement model. For elastically stiff sandstone modelling.

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • Kc (float) – Bulk modulus of cement

  • Gc (float) – Shear modulus of cement

  • phi (float or array-like) – Porosity

  • phi_b (_type_) – adjusted high porosity end memeber

  • phic (float) – Critical Porosity

  • Cn (float) – coordination number

  • scheme (int) –

    Scheme of cement deposition

    1=cement deposited at grain contacts 2=cement deposited at grain surfaces

Returns:

  • float or array-like – K_dry, G_dry (GPa): Effective elastic moduli of dry rock

  • References – ———-

  • - Avseth, P.; Mukerji, T. & Mavko, G. Cambridge university press, 2010

static Digby(K0, G0, phi, Cn, sigma, a_R)[source]

Compute Keff and Geff using Digby’s model

Parameters:

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • phi (float) – Porosity

  • Cn (float) – coordination number

  • sigma (float or array-like) – stress

  • a_R (float) – a_R (unitless): ratio of the radius of the initially bonded area to the grain radius

Returns:

  • float or array-like – Keff, Geff (Gpa): effective medium stiffness

  • References – ———-

  • - Digby, P.J., 1981. Journal of Applied Mechanics, 48, 803–808.

static pcm(f, sigma, K0, G0, phi, phic, v_cem, v_ci, Kc, Gc, Cn, mode, scheme, f_)[source]

Computes effective elastic moduli of patchy cemented sandstone according to Avseth (2016).

Parameters:

  • f (float) – volume fraction of cemented rock in the binary mixture

  • sigma (float or array-like) – effective stress

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • phi (float) – Porosity

  • phic (float) – Critical Porosity

  • v_cem (float) – cement fraction in contact cement model. phi_cem= phic-vcem

  • v_ci (float) – cement threshold above which increasing cement model is applied

  • Kc (float) – bulk modulus of cement

  • Gc (float) – shear modulus of cement

  • Cn (float) – coordination number

  • mode (str) – ‘stiff’ or ‘soft’. stiffest mixing or softest mixing. Defaults to ‘stiff’.

  • scheme (int) – contact cement scheme. 1=cement deposited at grain contacts 2=cement deposited at grain surfaces

  • f – slip factor in HM modelling. Defaults to 0.5.

Note

(Avseth,2016): If 10% is chosen as the “critical” cement limit, the increasing cement model can be used in addition to the contact cement model. (Torset, 2020): with the increasing cement model appended at 4% cement”

Returns:

  • float or array-like – K_DRY, G_DRY (GPa): effective elastic moduli of the dry rock

  • References – ———- - Avseth, P.; Skjei, N. & Mavko, G. The Leading Edge, GeoScienceWorld, 2016, 35, 868-87.

static diluting(k, sigma0, sigma, m)[source]

stress dependent diluting parameter used in varying patchiness cement model.

Parameters:

  • k (float) – cement crushing factor. k<=1: no cement crumbling; k>1: cement crumbling.

  • sigma0 (float) – reference stress, e.g. maximum effective stress, stress at which unloading begins.

  • sigma (array-like) – effective stress

  • m (float) – curvature parameter that defines diluting rate.

Returns:

array-like – stress dependent diluting parameter

static vpcm(alpha, f, sigma, K0, G0, phi, phic, v_cem, v_ci, Kc, Gc, Cn, scheme, f_)[source]

Compute effective elastic moduli using varying patchiness cement model (VPCM) as proposed by Yu et al. (2023).

Parameters:

  • alpha (float or array-like) – diluting parameters

  • f (float) – volume fraction of cemented rock in the binary mixture

  • sigma (float or array-like) – effective stress

  • K0 (float) – Bulk modulus of grain material in GPa

  • G0 (float) – Shear modulus of grain material in GPa

  • phi (float) – Porosity

  • phic (float) – Critical Porosity

  • v_cem (float) – cement fraction in contact cement model. phi_cem= phic-vcem

  • v_ci (float) – cement threshold above which increasing cement model is applied

  • Kc (float) – bulk modulus of cement

  • Gc (float) – shear modulus of cement

  • Cn (float) – coordination number

  • scheme (int) – contact cement scheme. 1=cement deposited at grain contacts 2=cement deposited at grain surfaces

  • f – slip factor in HM modelling.

  • Note – (Avseth,2016): If 10% is chosen as the “critical” cement limit, the increasing cement model can be used in addition to the contact cement model. (Torset, 2020): with the increasing cement model appended at 4% cement”

Returns:

array-like – K_DRY, G_DRY (GPa): effective elastic moduli of the dry rock