Prediction of fluid occupancy in fractures using network modeling and x-ray microtomography.
I: Data conditioning and model description
Zuleima T. Karpyn
Department of Energy and Mineral Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802-5000, USA
Mohammad Piri
*
Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071-2000, USA
Received 25 November 2006; published 31 July 2007
This paper presents a two-dimensional pore-scale network model of a rough-walled fracture whose inner
structure had been mapped using x-ray microtomography. The model consists of a rectangular lattice of
conceptual pores and throats representing local aperture variations. It is a two-phase model that takes into
account capillary, viscous, and gravity forces. Mapping of fluids and fracture topology was done at a voxel
resolution of 0.027 0.027 0.032 mm
3
, which allowed the construction of realistic fracture representations
for modeling purposes. This paper describes the necessary data conditioning for network modeling, a different
approach to determine advancing and receding contact angles from direct x-ray microtomography scans, and
the network model formulation and methods used in the determination of saturation, absolute and relative
permeabilities, capillary pressures, and fluid distributions. Direct comparison of modeled results and experi-
mental observations, for both drainage and imbibition processes, is presented in the companion paper M. Piri
and Z. T. Karpyn, following paper, Phys. Rev. E 76, 016316 2007.
DOI: 10.1103/PhysRevE.76.016315 PACS numbers: 47.56.+r, 47.80.Jk, 91.60.Ba
I. INTRODUCTION
Mapping the distribution of fluids in underground forma-
tions is of great importance for fields such as environmental
remediation, geohazard mitigation, hydrology, geothermal
exploitation, and hydrocarbon recovery. The ability to pre-
dict where fluids will migrate, and the characterization of
fundamental transport properties, has motivated extensive re-
search regarding multiphase flow through geologic forma-
tions. Many formations also present structural discontinuities
that have great impact on the mobilization of fluids. Frac-
tures are the most common form of discontinuity found in
these systems. Fractures control the overall conductivity of
the rock while the porous matrix provides fluid storage ca-
pacity. Understanding transport properties of fractures and
their dependence on structure, fluids, and boundary condi-
tions is essential for the design of effective recovery and
remediation strategies.
Various approaches have been developed for the study of
transport phenomena in fractures. They range from geometri-
cal characterization of single fractures and fracture networks
to transport processes, single and multiphase flow. Early
work on computer-based network modeling dates back to the
late 1950s 1–3. In the past two decades, pore-scale network
modeling has gained vast attention and has improved with
the addition of features such as fluid trapping and wetting
layers 4 –9. Dynamic network models allow the study of
the effect of injection rate on residual saturations, relative
permeabilities and the competition between various driving
forces, i.e., capillary, viscous, and gravity forces, and their
effects on displacement mechanisms, i.e., snapoff, cluster
growth, and frontal advance 10–14. Wetted structures and
gravity fingers have been observed in network simulations of
spontaneous imbibition in porous media including the effect
of gravity 15. Glass et al. 16 studied quasistatic immis-
cible displacement in horizontal, rough-walled fractures us-
ing modified invasion percolation models. They ignored vis-
cous and gravity forces and also assumed that influence of
local convergence or divergence of the fracture walls was
ignorable. They examined the influence of the combined ef-
fect of two principle radii of curvature, in-plane and
aperture-induced. This allowed the authors to model the ex-
perimentally reported saturation fronts. The dependence of
capillary pressure and relative permeability characteristics on
contact angles and void structures has also been investigated
using pore-scale network models 17–20.
Proper characterization of the pore structure is crucial for
the accuracy of multiphase displacement mechanisms imple-
mented in pore network models. Experiments using statisti-
cal approaches, transparent epoxy replicas, and imaging
techniques, e.g., nuclear magnetic resonance, serial section
measurements of porous materials, and high resolution mi-
crotomography, have provided means to characterize aper-
ture distributions and describe preferential flow paths in frac-
tures 21–26. In spite of recent advances in pore-scale
representations of fractures and understanding of their flow
characteristics, additional investigation is still needed. It is
important to have a reliable physically-based tool able to
predict macroscopic flow properties and fluid distributions in
realistic fractures representation.
In this work, a highly detailed aperture distribution map
constructed from x-ray microtomography scans is used to
create a network of conceptual pores and throats representing
the fracture’s void structure. The fracture model presented in
this study is a modified two-dimensional adaptation of a
three-dimensional mixed-wet random pore-scale network
model of two- and three-phase flow in porous media with *mpiri@uwyo.edu
PHYSICAL REVIEW E 76, 016315 2007
1539-3755/2007/761/01631513 ©2007 The American Physical Society 016315-1