#!/usr/bin/env python
# -*-coding:utf-8 -*-
'''
Recreation and modifcations of the Permeabilities models in Rock physics handbook matlab tools.
'''
[docs]class Permeability:
"""
Different permeability models.
"""
[docs] @staticmethod
def Kozeny_Carman(phi,d):
"""Describe the permeability in a porous medium using Kozeny-Carman equation assuming the turtuosity tau=sqrt(2), 1/B=2.5 for unconsolidated monomodal sphere pack.
Parameters
----------
phi : float or array-like
porosity
d : float
pore diameter in m.
Examples
--------
>>> phi= np.linspace(0.01,0.35,100)
>>> d= 250
>>> k= Kozeny_Carman(phi, d)
>>> plt.semilogy(phi, k )
Returns
-------
float or array-like
k (m^2): the resulting permeability is in the same units as d^2
"""
k= d**2/180 *phi**3/(1-phi)**2
return k
[docs] @staticmethod
def Kozeny_Carman_Percolation(phi,phic, d, B):
"""The Kozeny−Carman relations incorporating the percolation effect
Parameters
----------
phi : float or array-like
porosity
phic : float
percolation porosity
d : float
pore diameter
B : float
geometric factor that partly accounts for the irregularities of pore shapes.
Returns
-------
float or array-like
k (m^2): the resulting permeability is in the same units as d^2
"""
k= B*d**2* (phi-phic)**3/(1+phic-phi)**2
return k
[docs] @staticmethod
def Owolabi(phi, Swi):
"""Estimate the permeability in uncosonlidated sands of Pleistocene to Oligocene age in Eastern Niger Delta from log derived porosityand irreducible water saturation.
Parameters
----------
phi : float or array-like
porosity
Swi : float or array-like
irreducible water-saturation from welllogs
Returns
-------
float or array-like
k_oil, k_gas: permeabilities in mD for oil and gas sand reservoir, respectively
"""
#For Oil Sand
k_oil = 307 + (26552*(phi**2))-(34540*(phi*Swi)**2)
#For Gas Sand
k_gas = 30.7 + (2655*(phi**2))-(3454*(phi*Swi)**2)
return k_oil, k_gas
[docs] @staticmethod
def Perm_logs(phi, Swi):
"""Various empirical correlations of between permeability, porosity and irreducible water-saturation from welllogs. Models includs Tixier, Timur, Coates and Coates-Dumanoir.
Parameters
----------
phi : float or array-like
porosity
Swi : float or array-like
irreducible water-saturation from welllogs
Returns
-------
float or array-like
k_tixier, k_Timur , k_coates, k_coates_Dumanoir: different permeability estimations, in the unit of mD
Assumptions
-----------
- The functional forms used in these equations have to be calibrated, whenever possible, to site-specific data.
- The rock is isotropic.
- Fluid-bearing rock is completely saturated.
"""
k_tixier = 62500*phi**6/Swi**2
k_Timur = 10000*phi**4.5/Swi**2
k_coates = 10000*phi**4*(1-Swi)**2/Swi**2
k_coates_Dumanoir = 352*phi**4/Swi**4
return k_tixier, k_Timur , k_coates, k_coates_Dumanoir
[docs] @staticmethod
def Panda_Lake(d, C,S,tau,phi):
"""Modified Kozeny-carman relation incorpating the contribution of grain size variation and sorting using Manmath N. Panda and Larry W. Lake relation.
Parameters
----------
d : float
mean particles size in um.
C : float
coefficient of variation of particles size distribution
S : float
skewness of particles size distribution
tau : float
tortuosity factor
phi : float or array-like
porosity
Returns
-------
float or array-like
k (md): permeability
References
----------
- Estimation of Single-Phase permeability from parameters of particle-Size Distribution, Manmath N. Panda and Larry W. Lake, AAPG 1994.
"""
k= d**2*phi**3*(C**3*S+3*C**2+1)**2/(72*tau*(1-phi)**2*(C**2+1)**2)
return k
[docs] @staticmethod
def Panda_Lake_cem(phi,d):
"""Quantify the effects of cements on the single phase permeability estimate of unconsolidated sand using Panda & Lake model
Parameters
----------
phi : float or array-like
porosity
d : float
mean particles size in um
Returns
-------
float or array-like
k (md): permeability
"""
K =3.34*(d**2)*((phi**3)/(1-phi)**2)
return K
[docs] @staticmethod
def Revil(phi, d):
"""Estimate permeability in very shaly rock using Revil et al. 1997
Parameters
----------
phi : float or array-like
porosity
d : float
mean particles size in um
Returns
-------
float or array-like
k (md): permeability
"""
k = 1000*(d**2)*(phi**4.5)/24
return k
[docs] @staticmethod
def Fredrich(phi, d, b):
"""Compute permability considering Pore Geometry and Transport Properties of Fontainebleau Sandstone
Parameters
----------
phi : float or array-like
porosity>10%
d : float
_description_
b : float
shape factor b is equal to 2 for circular tubes and equal to 3 for cracks.
Returns
-------
float or array-like
k (md): permeability
References
----------
- Fredrich, J. T., Greaves, K. H., & Martin, J. W. (1993, December). Pore geometry and transport properties of Fontainebleau sandstone. In International journal of rock mechanics and mining sciences & geomechanics abstracts (Vol. 30, No. 7, pp. 691-697). Pergamon.
"""
# formation factor assuming tau^2=2.5
F= 2.5/phi
# pore surface area per unit sample volume
Sv= 6*(1-phi)*d
# permeability
k= 1/(b*F) * (phi/Sv)**2
return k
[docs] @staticmethod
def Bloch(S,C,D):
"""Predict porosity and permeability in sandstones prior to drilling using Bloch empirical relations obtain in Yacheng field.
Parameters
----------
S : float
Trask sorting coefficient
C : float
Rigid grain content in frac
D : float
Grain size in mm
Returns
-------
float or array-like
phi, k: porosity (frac) and permeability (mD), respectively
"""
# Porosity Calculation
phi = -6.1 + (9.8/S) + (0.17*C)
# Permeability Calculation
k = 10**(-4.67 + (1.34*D) + (4.08/S)+ 3.42*(C/100))
return phi, k
[docs] @staticmethod
def Bernabe(phi, crf,w, r):
"""Bernabe models permit to compute the permeability and porosity of strongly pressure dependent pores such as cracks and approximately constant pores associated with tubes and nodal pores.
Parameters
----------
phi : float or array-like
total porosity
crf : float
crack fraction in pore volume
w : float
width or aperture of the equivalent crack in um
r : float
radius of the tube in um
Returns
-------
float or array-like
k (md): total permeability
References
----------
- Bernabe, Y. (1991). Pore geometry and pressure dependence of the transport properties in sandstones. Geophysics, 56(4), 436-446.
"""
#Crack porosity
phicrack = phi*crf
#Crack permeability
# Kcrack = (w^2)*Phicrack/(12*Taucrack^2); (w^2)*(crf*phi)/30 , Taucrack = crack tortuosity, Taucrack^2 = 2.5,
kcrack = (w**2)*phicrack/30
#Tube porosity Ktube = (r^2)*Phitube/(8*Tautube^2); (r^2)*((1-CrackFraction)*Phi)/20; tube tortuosity Tautube^2 = 2.5
phitube = phi - phicrack
#Tube permeability
ktube = (r**2)*phitube/20
#Total permeability
k = kcrack+ktube
return k
