Assessment of critical path analyses of the relationship between permeability and electrical conductivity of pore networks

Sep 2, 2026

Critical path analysis (CPA) estimates macroscopic transport coefficients in heterogeneous, micro-scale disordered materials, and has been explored for porous media flow and transport. Prior pore-network studies questioned CPA applicability because predictions degrade with increased heterogeneity in well-connected 3D networks and remain incomplete for 2D networks. This work numerically computes permeability and electrical conductivity for 2D/3D networks with varied pore-size distributions and geometries. A new CPA model links permeability to electrical conductivity, matching simulations closely and improving accuracy over a classical CPA model, especially in sufficiently disordered 3D networks (within ±20%).

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Abstract

Background and motivation

Methods and numerical setup

Results: new CPA model and comparisons

Conclusion and implications

| Assessment of critical path analyses of the relationship between permeability
and electrical conductivity of pore networks Todd H. Skaggs ⇑
US Salinity Laboratory, USDA-ARS, Riverside, CA, United States | | | | --- | --- | --- | | a r t i c l e i n f o | | a b s t r a c t | | Article history:
Received 8 February 2011
Received in revised form 22 June 2011 Accepted 26 June 2011
Available online 13 July 2011 | | Critical path analysis (CPA) is a method for estimating macroscopic transport coefﬁcients of heterogeneous materials that are highly disordered at the micro-scale. Developed originally to model conduction in semiconductors, numerous researchers have noted that CPA might also have relevance to ﬂow and transport processes in porous media. However, the results of several numerical investigations of critical path analysis on pore network models raise questions about the applicability of CPA to porous media. Among other things, these studies found that (i) in well-connected 3D networks, CPA predictions were inaccurate and became worse when heterogeneity was increased; and (ii) CPA could not fully explain the transport properties of 2D networks. To better understand the applicability of CPA to porous media, we made numerical computations of permeability and electrical conductivity on 2D and 3D networks with differing pore-size distributions and geometries. A new CPA model for the relationship between the permeability and electrical conductivity was found to be in good agreement with numerical data, and to be a signiﬁcant improvement over a classical CPA model. In sufﬁciently disordered 3D networks, the new CPA prediction was within ±20% of the true value, and was nearly optimal in terms of minimizing the squared prediction errors across differing network conﬁgurations. The agreement of CPA predictions with 2D network computations was similarly good, although 2D networks are in general not well-suited for evaluating CPA. Numerical transport coefﬁcients derived for regular 3D networks of slit-shaped pores were found to be in better agreement with experimental data from rock samples than were coefﬁcients derived for networks of cylindrical pores.
Published by Elsevier Ltd. | | Keywords:
Critical path analysis
Pore network model | | | | Nomenclature
CPA acronym for critical path analysis CV coefﬁcient of variation
ECb bulk electrical conductivity
ECw electrical conductivity of saturating ﬂuidb breadth of slit-shaped pore
g0 proportionality constant in the pore conductance model d spatial dimension (equals 2 or 3)
fg pore conductance probability density function fd pore-size probability density function g pore conductance
gc critical pore conductance
k ﬂuid permeability
k⁄ normalization constant K hydraulic conductivity
l0 pore length
m exponent in pore conductance model | pc
W
y
a
b d
dc
dmin
dmax
dg
g k
l
m
r | percolation threshold
parameter in log-uniform conductance model CPA conductivity prefactor exponent parameter in power law pore-size distribution
parameter in power law conductance distribution characteristic length of pore cross section (termed‘‘pore-size’’)
critical pore-size
lower bound for d upper bound for d geometric mean pore-size ﬂuid viscosity conductivity length scale mean of lnd
percolation correlation length exponent standard deviation of lnd | | --- | --- | --- |

FAQs

What problem does the paper address about critical path analysis in porous media?

The paper addresses whether CPA can reliably estimate transport properties in porous media, given concerns from earlier numerical studies regarding accuracy in 3D networks and explanatory limits in 2D networks.

What approach does the paper use to test CPA?

It performs numerical computations of permeability and electrical conductivity on 2D and 3D pore networks with differing pore-size distributions and geometries.

How does the new CPA model perform compared with a classical CPA model?

The new CPA model agrees well with numerical data and significantly improves accuracy over the classical CPA model, achieving near ±20% error in sufficiently disordered 3D networks and similarly good agreement for 2D computations.

Sep 2, 2026

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