Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
Title
On Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Rock
Fractures
Permalink
https://escholarship.org/uc/item/5j291513
Authors
Pruess (ed), K.
Tsang, Y.W.
Publication Date
1989-09-01
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University of California
LBL-27449
Preprint
LawrenceBerkeleyLaboratory
UNIVERSITY OF CALIFORNIA
EARTH SCIENCES DIVISION
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Submitted to Water Resources Research
On Two-Phase Relative Permeability and Capillary Pressure
of Rough-Walled Rock Fractures
K. Pruessand Y.W.Tsang
September 1989
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LBL-27449
On Two-Phase Relative Permeability and
Capillary Pressure of Rough-Walled Rock Fractures
K. Pruess and Y. W. Tsang
Earth SciencesDivision
Lawrence Berkeley Laboratory
1 Cyclotron Road
Berkeley, California 94720
September 1989
This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of
Renewable Energy Technologies, Geothermal Technology Division; by the Director, Office of Civilian
Radioactive Waste Management, Repository Technology Division; and by the Director, Office of Energy
Research, Office of Basic Energy Sciences, Engineering & Geosciences Division, of the U.S. Department
of Energy under Contract No. DE-AC03-76SFOOO98.Additional funding was provided by NAGRA.
-1 -
ON TWO-PHASE RELATIVE PERMEABILITY AND CAPILLARY
PRESSURE OF .ROUGH- WALLED ROCK FRACTURES
K. Pruess and Y. W. Tsang
Earth Sciences Division
Lawrence Berkeley Laboratory
. 1CyclotronRoad
Berkeley, California 94720
ABSTRACT
This paper presents a con~eptual and numerical model of multiphase flow in fractures.
The void space of real rough-walled rock fractures is conceptualized as a two-
dimensional heterogeneous porous medium, characterized by aperture as a function of
position in the fracture plane. Portions of a fracture are occupied by wetting and non-
wetting phase, respectively, according to local capillary pressure and accessibility cri-
teria. Phase occupancy and permeability are derived by assuming a parallel-plate
approximation for suitably small subregions in the fracture plane. For log-normal aper-
ture distributions, a simple approximation to fracture capillary pressure is obtained in
closed fonn; it is found to resemble the typical shape of Leverett's j-function. Wetting
and non-wetting phase relative permeabilities are calculated by numerically simulating
single phase flows separately in the wetted and non-wetted pore spaces. illustrative
examples indicate that relative penneabilities depend sensitively on the nature and range
of spatial correlation betWeen apertures. It is also observed that interference between
fluid phases flowing in a fracture tends to be strong, with the sum of wetting and non-
wetting phase relative permeabilities being considerably less than 1 at intermediate
saturations.
- 2-
INTRODUCTION
Fluid flow in geologic media is often dominated by the highly permeable pathways pro-
vided by rock fractures and joints. Multiphase flow through fractures occurs in many
subsurface flow systems that are of engineering interest in the context of energy resource
recovery (petroleum, natural gas, geothermal water and steam) and environmental pro-
tection (chemical and radiation contamination in groundwater aquifers, partially
saturated zones). It also plays a crucial role in petroleum migration and ore deposition,
and in the evolution of hydrothermal convection systems.
From a practical viewpoint, the most important example of multiphase flow is in
petroleum reservoirs, many of which are situated in fractured-porous formations (Weber
and Bakker, 1981). In these reservoirs, two- and three-phase flow of oil, water, and gas
occurs naturally and in response to production and injection operations. Many natural
gas reservoirs with two-phase flow of gas and water are located in tight rocks with
predominant fracture permeability. A different kind of two-phase flow, namely,
water/vapor flow with strong phase change and latent heat effects, occurs in geothermal
reservoirs and in hydrothermal convection systems. Most of these systems are found in
fractured rocks with low matrix permeability (typically of order IO-18m2= 1 micro-
darcy). Strong two-phase flow effects of water/vapor and water/noncondensible gas are
expected near geologic repositories for heat-generating or corroding radioactive wastes
(Pruess, 1989).
In the analysis of multiphase flows it is important to carefully distinguish between fluid
phases and components. Phases are the "physical" and components the "chemical" build-
ing blocks of a fluid system. Throughout a fluidphase, thermophysical propenies such as
pressure, temperature, and viscosity vary continuously and smoothly from point to point,
while these properties will undergo discontinuous jumps at phase boundaries. The sur-
face tension effects at the interface between fluid phases give rise to capillary pressure
phenomena. Fluid components distribute themselves among phases according to solubil-
ity and volatility. For example, in a high-pressure mixture of water, a heavy hydrocarbon