rockphypy.Fluid

Module Contents

Classes

Fluid

Fluid subsitution approaches and models describing velocity dispersion and attenuation due to the fluid effect.
class rockphypy.Fluid.Fluid[source]

Fluid subsitution approaches and models describing velocity dispersion and attenuation due to the fluid effect.

static Brie(Kw, Kgas, Sw, e)[source]

Brie empirical fluid mixing law

Parameters:

  • Kw (float) – bulk modulus of fluid phase

  • Kgas (float) – bulk modulus of gas phase

  • Sw (float or array) – water saturation

  • e (int) – Brie component

Returns:

float or array – Kf: effective fluid propertie

static Biot(Kdry, Gdry, K0, Kfl, rho0, rhofl, eta, phi, kapa, a, alpha, freq)[source]

Compute Biot dispersion and velocity attenuation

Parameters:

  • Kdry (float or array-like) – dry frame bulk modulus

  • Gdry (float or array-like) – dry frame shear modulus

  • K0 (float) – bulk modulus of mineral material making up rock

  • Kfl (float) – effective bulk modulus of pore fluid

  • rho0 (float) – grain density

  • rhofl (float) – pore fluid density

  • eta (float) – η is the viscosity of the pore fluid

  • phi (float) – porosity

  • kapa (float) – absolute permeability of the rock

  • a (float) – pore-size parameter. Stoll (1974) found that values between 1/6 and 1/7 of the mean grain diameter

  • alpha (float) – tortuosity parameter, always greater than or equal to 1.

  • freq (float or array-like) – frequency range, e.g 10^-3 to 10^3 Hz

Returns:

float or array-like – Vp_fast, fast P-wave velocities at all frequencies,km/s Vp_slow, slow P-wave velocities at all frequencies,km/s Vs, S-wave velocities,km/s QP1_inv, fast P-wave attenuation QP2_inv, slow P-wave attenuation Qs_inv, S-wave attenuation

static Biot_HF(Kdry, Gdry, K0, Kfl, rho0, rhofl, phi, alpha)[source]

Biot high-frequency limiting velocities in the notation of Johnson and Plona (1982)

Parameters:

  • Kdry (float or array-like) – dry frame bulk modulus

  • Gdry (float or array-like) – dry frame shear modulus

  • K0 (float) – bulk modulus of mineral material making up rock

  • Kfl (float) – effective bulk modulus of pore fluid

  • rho0 (float) – grain density

  • rhofl (float) – pore fluid density

  • phi (float) – porosity

  • alpha (float) – tortuosity parameter, always greater than or equal to 1.

Returns:

float or array-like – Vp_fast,Vp_slow,Vs: high-frequency limiting velocities,km/s

static Geertsma_Smit_HF(Kdry, Gdry, K0, Kfl, rho0, rhofl, phi, alpha)[source]

Approximation of Biot high-frequency limit of the fast P-wave velocity given by Geertsma and Smit (1961), This form predicts velocities that are too high (by about 3%–6%) compared with the actual high-frequency limit.

Parameters:

  • Kdry (float or array-like) – dry frame bulk modulus

  • Gdry (float or array-like) – dry frame shear modulus

  • K0 (float) – bulk modulus of mineral material making up rock

  • Kfl (float) – effective bulk modulus of pore fluid

  • rho0 (float) – grain density

  • rhofl (float) – pore fluid density

  • phi (float) – porosity

  • alpha (float) – tortuosity parameter, always greater than or equal to 1.

Returns:

float or array-like – Vp_fast,Vs: high-frequency limiting velocities, km/s

static Geertsma_Smit_LF(Vp0, Vpinf, freq, phi, rhofl, kapa, eta)[source]

Low and middle-frequency approximations of Biot wave given by Geertsma and Smit (1961). Noticed that mathematically this approximation is valid at moderate-to-low seismic frequencies, i.e. f<fc

Parameters:

  • Vp0 (float) – Biot−Gassmann low-frequency limiting P-wave velocity, km/s or m/s

  • Vpinf (float) – Biot highfrequency limiting P-wave velocity, km/s or m/s

  • freq (float or array-like) – frequency

  • phi (float) – porosity

  • rhofl (float) – fluid density

  • kapa (float) – absolute permeability of the rock.

  • eta (float) – viscosity of the pore fluid

Returns:

float or array-like – Vp: frequency-dependent P-wave velocity of saturated rock

static Gassmann(K_dry, G_dry, K_mat, Kf, phi)[source]

Computes saturated elastic moduli of rock via Gassmann equation given dry-rock moduli.

Parameters:

  • K_dry (float or array-like) – dry frame bulk modulus

  • G_dry (float or array-like) – dry frame shear modulus

  • K_mat (float) – matrix bulk modulus

  • Kf (float) – fluid bulk modulus

  • phi (float or array-like) – porosity

Returns:

float or array-like – K_sat, G_sat: fluid saturated elastic moduli

static Gassmann_sub(phi, K0, Ksat1, Kfl1, Kfl2)[source]

Fluid subsititution using Gassmann equation, thr rock is initially saturated with a fluid, compute the saturated moduli for tge rock saturated with a different fluid

Parameters:

  • phi (float or array-like) – porosity

  • K0 (float) – mineral modulus

  • Ksat1 (float or array-like) – original bulk modulus of rock saturated with fluid of bulk modulus Kfl1

  • Kfl1 (float) – original saturant

  • Kfl2 (float) – new saturant

Returns:

float or array-like – Ksat2: new satuarted bulk modulus of the rock

static vels(K_dry, G_dry, K0, D0, Kf, Df, phi)[source]

Computes Vp,Vs and densities of saturated rock using Gassmann relations from elastic moduli of rock. See also Gassmann_vels.

Parameters:

  • K_dry (float) – dry frame bulk modulus

  • G_dry (float) – dry frame shear modulus

  • K0 (float) – mineral matrix bulk modulus

  • D0 (float) – mineral matrix density

  • Kf (float) – fluid bulk modulus

  • Df (float) – fluid density in g/cm3

  • phi (float or array) – porosity

Returns:

float or array – Vp, Vs, rho

static Gassmann_vels(Vp1, Vs1, rho1, rhofl1, Kfl1, rhofl2, Kfl2, K0, phi)[source]

Gassmann fluid substituion with velocities

Parameters:

  • Vp1 (float or array-like) – saturated P velocity of rock with fluid 1

  • Vs1 (float or array-like) – saturated S velocity of rock with fluid 1

  • rho1 (float) – bulk density of saturated rock with fluid 1

  • rhofl1 (float) – density of fluid 1

  • Kfl1 (float) – bulk modulus of fluid 1

  • rhofl2 (float) – density of fluid 2

  • Kfl2 (float) – bulk modulus of fluid 2

  • K0 (float) – mineral bulk modulus

  • phi (float or array-like) – porosity

Returns:

float or array-like – Vp2, Vs2: velocities of rock saturated with fluid 2

static Gassmann_approx(Msat1, M0, Mfl1, phi, Mfl2)[source]

Perform gassmann fluid subsititution using p wave modulus only

Parameters:

  • Msat1 (float or array-like) – in situ saturated p wave modulus from well log data

  • M0 (float) – p wave modulus of mineral

  • Mfl1 (float) – p wave modulus of in situ fluid

  • phi (float) – porosity

  • Mfl2 (float) – p wave modulus of new fluid for susbtitution

Returns:

float or array-like – Msat2: p wave modulus of rock fully saturated with new fluid

static Brown_Korringa_dry2sat(Sdry, K0, G0, Kfl, phi)[source]

Compute fluid saturated compliances from dry compliance for anisotropic rock using Brown and Korringa (1975). See eq. 32 in the paper.

Parameters:

  • Sdry (2d array) – comliance matrix of the dry rock

  • K0 (float) – Isotropic mineral bulk modulus

  • G0 (float) – Isotropic mineral shear modulus

  • Kfl (float) – Isotropic fluid bulk modulus

  • phi (float) – porosity

Returns:

2d array – Ssat (6x6 matrix): Saturated compliance of anisotropic rock

static Brown_Korringa_sat2dry(Ssat, K0, G0, Kfl, phi)[source]

Compute dry compliance from fluid saturated compliances for arbitrarily anisotropic rock using Brown and Korringa (1975). See eq. 32 in the paper.

Parameters:

  • Ssat (2d array) – comliance matrix (6x6) of the saturated rock

  • K0 (float) – Isotropic mineral bulk modulus

  • G0 (float) – Isotropic mineral shear modulus

  • Kfl (float) – Isotropic fluid bulk modulus

  • phi (float) – porosity

Returns:

2d array – Sdry (6x6 matrix): Dry compliance of anisotropic rock

static Brown_Korringa_sub(Csat, K0, G0, Kfl1, Kfl2, phi)[source]

Fluid substitution in arbitrarily anisotropic rock using Brown and Korringa (1975). the rock is originally saturated by fluid 1. After fluid subsititution, the rock is finally saturated by fluid 2.

Parameters:

  • Csat (6x6 matrix) – comliance matrix of the saturated rock

  • K0 (float) – Isotropic mineral bulk modulus

  • G0 (float) – Isotropic mineral shear modulus

  • Kfl1 (float) – bulk modulus of the original fluid

  • Kfl2 (float) – bulk modulus of the final fluid

  • phi (float) – porosity

Returns:

2d array – Csat2, Ssat2 (6x6 matrix): Dry stiffness and compliance matrix of anisotropic rock saturated with new fluid

static Mavko_Jizba(Vp_hs, Vs_hs, Vpdry, Vsdry, K0, rhodry, rhofl, Kfl, phi)[source]

Predicting the very high-frequency moduli and velocities of saturated rocks from dry rock properties using the Squirt flow model derived by Mavko and Jizba (1991).

Parameters:

  • Vp_hs (float) – P wave velocity of the dry rock measured at very high effective pressure in the unit of m/s

  • Vs_hs (float) – S wave velocity of the dry rock measured at very high effective pressure in the unit of m/s

  • Vpdry (array) – P wave velocity of the dry rock measured at different effective pressure in the unit of m/s

  • Vsdry (array) – S wave velocity of the dry rock measured at different effective pressure in the unit of m/s

  • K0 (float) – mineral bulk moduli

  • rhodry (float) – bulk density of the dry rock

  • rhofl (float) – bulk density of the pore fluid

  • Kfl (float) – bulk moduli of the pore fluid

  • phi (float) – porosity

Returns:

float or array-like – Kuf_sat (float):GPa, predicted high frequency bulk moduli of saturated rock Guf_sat (array): GPa, predicted high frequency shear moduli of saturated rock at different pressure Vp_hf (array): m/s, predicted high frequency P wave velocities of saturated rock Vs_hf (array): m/s, predicted high frequency S wave velocities of saturated rock

static Squirt_anisotropic(Sdry, Sdry_hp)[source]

Predict wet unrelaxed frame compliances at very high frequency from dry frame compliances for transversely isotropic rocks using theoretical formula derived by Mukerji and Mavko, (1994)

Parameters:

  • Sdry (list or array) – dry rock compliances [S11 S12 S13 S33 S44]

  • Sdry_hp (array) – dry rock compliances at very high effective stress [S11 S12 S13 S33 S44]

Returns:

array – The wet-frame compliances [S11 S12 S13 S33 S44]

static White_Dutta_Ode(Kdry, Gdry, K0, phi, rho0, rhofl1, rhofl2, Kfl1, Kfl2, eta1, eta2, kapa, a, sg, freq)[source]

Dispersion and Attenuation of partial saturation using White and Dutta–Odé Model.

Parameters:

  • Kdry (float) – bulk modulus of the dry rock

  • Gdry (float) – shear modulus of the dry rock

  • K0 (float) – Isotropic mineral bulk modulus

  • phi (float) – porosity

  • rho0 (float) – mineral density

  • rhofl1 (float) – density of the fluid opcupying the central sphere

  • rhofl2 (float) – density of the fluid opcupying the outer sphere

  • Kfl1 (float) – bulk modulus of the fluid opcupying the central sphere

  • Kfl2 (float) – bulk modulus of the fluid opcupying the outer sphere

  • eta1 (float) – viscousity of the fluid opcupying the central sphere

  • eta2 (float) – viscousity of the fluid opcupying the outer sphere

  • kapa (float) – absolute permeability of the rock

  • a (float) – radius of central sphere , sg=a3/b3

  • sg (float) – saturation of fluid opcupying the central sphere

  • freq (float or array-like) – frequencies

Returns:

float, array-like – Vp (m/s): P wave velocity km/s a_w: attenuation coefficient K_star: complex bulk modulus