GeophysicalResearchLetters
RESEARCHLETTER Effect of fracture roughness on seismic source
10.1002/2013GL058683 and fluid transport responses
Key Points: S. Raziperchikolaee1, V. Alvarado1, and S. Yin1
• Hydromechanical-seismic model is
applied to study fracture deformation 1Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming, USA
• Volumetric deformation of fracture is
affected by its geological properties
• Fracture roughness affect its trans- Abstract To explain how fracture roughness affects seismic source and transport response of deformed
port and seismic source responses
fractured rock, we developed a microscale fluid flow-geomechanics-seismicity model. The modeling
method considers comprehensive grains and cement interactions. Fluid flow behavior is obtained
Correspondence to: through realistic network models of the pore space in the compacted assembly. In addition, forces and
V. Alvarado,
valvarad@uwyo.edu displacements in the grains involved in the bond breakage are measured to determine seismic moment
tensor. The results of our work show that in addition to stress conditions in the target formation, geological
properties of preexisting fractures affect volumetric deformation of the seismic source as well. The results
Citation:
Raziperchikolaee, S., V. Alvarado, of the model proves that roughness of fractures, applied in a Berea sample, causes deviation of source
and S. Yin (2014), Effect of frac- mechanism of acoustic emission events toward opening tensile part and enhances the permeability of the
ture roughness on seismic source sample significantly during its failure even under confining pressure.
and fluid transport responses,
Geophys. Res. Lett., 41, 1530–1536,
doi:10.1002/2013GL058683.
1. Introduction
Received 12 NOV 2013 Moment tensor solution is an approach to study complex mechanisms involved in rock fracturing. With
Accepted 24 JAN 2014 nonzero volumetric deformation of a seismic source considered, the moment tensor represents all types of
Accepted article online 28 JAN 2014 crack propagation that have contribution to rock damage [Aki and Richards, 2002]. Characterizing source
Published online 12 MAR 2014 mechanism of induced seismicity by moment tensor inversion [Baig and Urbancic, 2010] reveals that
microearthquakes with volumetric components have been found in different environments [Miller et al.,
1998]. Tensile microearthquakes were recorded at volcanic and geothermal areas under high fluid pressure
[Julian et al., 2010]. In addition, microearthquakes with volumetric component could be induced during
hydraulic stimulation operation intended to increase permeability in oil and gas reservoirs [Šílenỳ et al.,
2009]. Volumetric changes related to microseismic events are a function of combined shear and tensile
forces in the source of events. In a recent work, Fischer and Guest [2011] showed that the presence of ten-
sile deformation in the source of microseismic events depends on differential stress along the preexisting
fracture exhibiting failure tendency.
While it is proven that geomechanical conditions could cause volumetric deformation in the source of
microseismic events, the impact of geological properties of fractures on generating events with tensile com-
ponent has been neglected. In this sense, could fracture roughness affect volumetric deformation in the
source of event? Conversely, is its effect on seismic source and transport response of deformed fracture
significant? In our research, a microscale hydromechanical-seismic model has been developed to address
effects of fracture roughness on fluid flow and seismic source behavior of deformed fractured samples. By
modeling pore structure between grains realistically, we are able to predict fluid flow behavior of the rock
sample under different stress conditions. In addition, forces and displacements around microcracks are
investigated to determine seismic source behavior of microfractures. A fractured Berea sandstone sample is
simulated based on its geological and geomechanical properties. The roughness of fracture is modeled by
assigning dilation angle and asperity on the grains involved in the fracture. The simulation results show that
sources of acoustic emission (AE) events generated during deformation of rough fractures have volumetric
component toward tensile crack opening, in contrast to smooth plane fractures. In addition, permeability of
the rock sample with a rough fracture enhances significantly during its failure under confining pressure in
the numerical triaxial tests.
2. NumericalModel
2.1. Microscale Geomechanical Behavior Modeling
In microscale modeling of rocks, constitutive elements such as grains, cracks, and pores are explicitly
modeled, enabling us to better understand rock mechanical behavior. The bonded particle model (BPM)
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Geophysical Research Letters 10.1002/2013GL058683
represents the rock as a compacted bonded assembly of rigid particles interacting at soft contacts and
can be used to predict macroscopic rock behavior from micromechanical properties. BPM can also model
and track damage formation inside a rock sample due to progressive development and coalescence of
microcracks to predict failure behavior of rocks [Potyondy and Cundall, 2004].
2.2. Modeling Fluid Flow Behavior at Microscale
An accurate representation of pore space is needed to predict fluid flow behavior in sedimentary rocks.
To study the effect of rock deformation on transport properties, we build a dynamic pore network model
regenerated as a function of grain deformation. To construct the network of pores and pipes, tetrahedral
cells are made by grouping nearest four neighbor particles together in the rock sample. Cell interior
corresponds to the pore, and the location of each pore is the geometric center of the cell. The cell face cor-
responds to the pipe and represents the flow path between two adjacent connected pores. Conductivity of
pipes is the main parameter used to calculate permeability of the network. The length of the pipe is the dis-
tance between pores, and the effective radius of each cylindrical pipe is calculated as an average of two radii
[Bryant et al., 1993]. The first radius, rc, corresponds to the largest circle that can be inscribed in the cross
section among three particles. The second radius, re, corresponds to the equivalent circle radius with the
same total area as the cross section among three particles. Since the inscribed circle always covers a smaller
area than the cross section, a cylindrical tube of radius rc has lower hydraulic conductivity than the conduit.
On the other hand, a circle is the most efficient cross section for fluid flow, a cylindrical tube of radius of re
has larger conductivity than a conduit. reff is bounded by these two radii. The schematic of the radii used to
calculate effective radius of each pipe is shown in Figure 1a.
The Hagen-Poiseuille law is used for calculation of hydraulic conductance of each pipe.
r4𝜋
g = effij (1)
𝜇8z
where g is the hydraulic conductance, reff and z are the effective radius and length, and 𝜇 is the fluid viscos-
ity. Steady state pressure distribution is applied in the network by calculating flow through each pipe and
solving the resulting set of equations representing mass conservation to measure permeability of network.
By applying the steady state pressure distribution and assuming the instantaneous response of an incom-
pressible fluid, effects of fluid pressure on further rock deformation are not considered for calculation of rock
permeability. Effect of pore pressure decrement due to rock expansion on further deformation is a compli-
cated function of initial permeability of sample, pore pressure inside it, and geological properties of sample,
which is not considered in our work. In our hydromechanical model, the one-way coupling occurs through
geometrical constrains of pore structure of the sample in each time step as a function of rock deformation.
To calculate the permeability of the sample, pressure boundary conditions are applied to the inlet and out-
let sections of the sample as to estimate pressure inside the sample. Zero-flux condition is imposed on the
remaining boundaries along the main direction of flow.
2.3. Modeling of Seismic Source Deformation
AE data provide valuable information to study the mechanics of microcrack generation and coalescence
leading to developing of the macrofracture in the rock sample [Lockner et al., 1991]. By measuring the forces
in the contacts around the source particles and the distance between the contact location and the centroid
of an AE event, and by considering microcracks that develop close together in space and time as one event,
seismic moment of AE events can be calculated to study the complex behavior of mechanisms involved in
fracturing in detail [Hazzard and Young, 2002].
In this letter, components of unbalanced forces developed in the source particles and concentrated in the
particle center are measured at each time step of crack development. By measuring the distance between
the contact where bond breakage occurred and the particle center involved in the bond breakage as well,
the components of the moment tensor of each microcrack are calculated. The summation of different com-
ponents of moment tensor of the microcracks that make up one AE event is used to calculate moment
tensor of the whole event. Components of moment tensor for an event consist of a cluster of microcracks,
calculated as follows:
∑N
M = Fk ∗ Rkij i j (2)
k=1
RAZIPERCHIKOLAEE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1531
Geophysical Research Letters 10.1002/2013GL058683
Figure 1. (a) Schematic of circles for calculation of pipes effective radius. (b) Joint plane and pore network in the Berea
sample.
where N is number of grains involved in making an event, Fki is the ith component of unbalanced force con-
centrated in the center of Kth grain, and Rkj is the jth component of distance between contact point and
center of kth grain. To interpret the induced seismicity, the moment tensor is decomposed and the source
mechanism is displayed in a source-type plot, Hudson diagram [Hudson et al., 1989].
Equal area source-type plot provides graphical presentation of source mechanism of events. The Hudson
diagram, as a source-type plot, shows the opening and closure of tensile fractures as well as shearing of frac-
tures. Double couple mechanism represents pure shear displacement along the fracture plane with zero
volumetric component at the source map to the center of the diagram. Explosion and implosion type repre-
sents pure volumetric change at source map at the top and bottom of the diagram. Mechanisms correspond
to the opening and closing of cracks map to top right and bottom left of Hudson diagram. By applying
Hudson diagram, a variety of source mechanisms involved in fracture deformation could be distinguished.
2.4. Construction of a Fractured Berea Sample
In this letter, we demonstrate the usefulness of our approach by building a Berea sample through assigning
a uniform grain size distribution of particles with an average grain radius of 0.13 mm [Zhu and Wong, 1997].
Packing and cementation of grains are simulated by a material genesis procedure [Potyondy and Cundall,
2004] to make the initial distribution of grains packed yield an initial porosity of 21% [Zhu and Wong, 1997].
We find appropriate micromechanical properties of the modeled sample by comparing the mechanical
response of a synthetic sample in the numerical triaxial test to the response of the rock measured in labo-
ratory. The micromechanical properties assigned to simulate mechanical behavior of Berea sandstone are
shown in Table 1. The model is calibrated using published experimental rock mechanical data of Berea sand-
stone [Zhu and Wong, 1997]. A Berea specimen with dimensions 3 mm × 4.5 mm × 3 mm is constructed.
The geomechanical domain in the sample is larger than the fluid flow domain, and the pore network is
only built at the center of geomechanical domain to avoid large computation time associated with the
pore network. Smooth joint contact model is applied to simulate smooth interface between grains and to
model discontinuities [Mas Ivars et al., 2008]. In this method, orientation of contacts between particles is
neglected to model joint without considering roughness of interface. By applying this method, particles do
not move around each other; instead, they slide along each other and experience shearing in the smooth
frictional surface.
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Geophysical Research Letters 10.1002/2013GL058683
3. Results andDiscussion
Table 1. Properties of the Berea Sandstone Sample
Berea’s Properties A smooth fracture is applied to the Berea
sample with a dip angle of 45◦ and dip
Grain distribution Uniform grain size ◦
Grain density(kg/m3) 2650 direction of 0 , shown in Figure 1b. The joint
Inter-grain friction 0.4 particles have the same stiffness as that of
Microscale Young modulus(GPa) 5.25 intact particles and have the microstrength
Normal/Tangential stiffness 2
R (mm) 0.13 of one fifth of intact grains. We performed aave
Rmax∕Rmin 1.85 numerical triaxial test under confining pres-
Grain number 6505 sure of 5 MPa, shown in Figure 2a, to study
Intergranular mean tensile strength(MPa) 55
Intergranular mean shear strength(MPa) 55 the effect of deformation of plane fracture
Normal strength deviation(MPa) 15 on transport and seismic source behavior
Shear strength deviation(MPa) 15 of the sample, shown in Figures 2b and 3c.
Peak strength at 5 Mpa 85
Young Modulus at 5 MPa 5 Due to application of axial load, the sample
Permeability(Darcy) 0.348 is compacted before losing its strength and
Sample porosity 0.21 the size of the pore structure decreases as
well. After reaching the peak strength, the
rock experiences expansion. This expansion of the rock is mainly due to shearing along the fracture plane,
which causes enhancement of the sample permeability. The mechanism of AE events during deformation of
plane fracture is concentrated in the middle of DC and closure of cracks shown in Hudson diagram, proving
presence of negative volumetric component in the source of AE events, shown in Figure 3c. We performed
the same numerical triaxial test on the fractured samples with different roughness to study how transport
and seismic source responses change inside the fractured rock as a function of fracture properties.
3.1. Effect of Dilation Angles
Dilation angle represents the volumetric expansion of rock materials during its failure. Dilation of fracture
could be modeled indirectly by assigning dilation angle in the smooth joint model. To consider dilation of
the fracture in the smooth joint model, we added dilation angle to the parameter list of the grains that make
the joint. Based on the amount of shear deformation in the grains on the joint plane, we are able to apply
normal displacements on the grains as a function of assigned grain dilation angle. Dilation of fracture could
be modeled directly by considering grains roughness along the joint in the natural joint model. To study the
real dilation of the Berea sample, we applied a natural joint to the intact Berea sample as well with the same
orientation and micromechanical properties of the smooth joint, already studied in this work. Then, we
investigate its effect on mechanical behavior of the Berea sandstone sample. In this approach to represent
a discontinuity, roughness, and bumpiness of particles on either side of the joint will affect its mechanical
behavior, such as its peak strength and dilation, naturally. As shown in Figure 2a, the sample with natural
joint has lower peak strength in comparison to the intact sample due to the lower microstrength of grains
Figure 2. (a) Effect of smooth and natural joint on mechanical behavior of sample. (b) Effect of smooth joint on transport properties of sample.
RAZIPERCHIKOLAEE ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1533
Geophysical Research Letters 10.1002/2013GL058683
Figure 3. (a) Volumetric deformation of sample with natural and smooth joint. (b) Effect of dilation angle on transport properties of sample. (c) Effect of dilation
angle on source mechanism of AE events plotted in Hudson diagram.
along the joint. On the other hand, it has higher peak strength in comparison to the sample with the smooth
joint due to considering the effect of roughness of joint. We made a comparison between volumetric expan-
sion of sample with natural joint and sample with smooth joint having dilation angle of 5◦, Figure 3a. In
both cases, after movement of the fracture plane by applying shear force to it, the volume of the sample
increases. Although the failure of sample with smooth joint occurs at lower strain, the amounts of volumet-
ric deformation of both samples after failure are near to each other. The variation of dilation angle in the
fractured sample with the smooth joint sample is chosen around this value.
The models with different dilation angles have nearly the same peak strength, and the main impact of apply-
ing dilation angle occurs during the shearing of the fracture. Effect of rock deformation on the permeability
of the fractured sample is shown in Figure 3b. Due to shearing of the fracture surface, the pipes radii in the
updated pore network increase inside the sample and enhance the permeability. The total expansion of
the rock is significantly higher in the case of fractured samples with a higher dilation angle that results in
larger permeability of sample, as shown in Figure 3b. The source mechanism of AE events in the sample after
shearing of fractures is shown in Figure 3c under confining pressure of 5 MPa. In the case with zero dila-
tion angle, the source mechanism of AE events are concentrated in the middle of DC and closure of cracks.
By applying dilation angle to the joint particles, the source mechanism of AE events shows more disperse
behavior and move toward opening of cracks. This proves that roughness of the fracture, represented by
dilation angle, could generate tensile forces in the source of failure resulting in deviation of source mecha-
nism of acoustic emission events toward opening tensile part and enhances the permeability of the sample
significantly during its failure under confining pressure.
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Geophysical Research Letters 10.1002/2013GL058683
Figure 4. (a) Asperities with deviation of 10 and 20◦ applied to the plane joint. (b) Effect of joint asperities on mechanical behavior of sample. (c) Effect of joint
asperities on transport behavior of sample. (d) Effect of joint asperities on source mechanism of AE events plotted in Hudson diagram.
3.2. Effect of Asperity of Fracture
To study the effect of asperity of fractures on mechanical behavior, i.e., deformation and peak strength of
a fractured sample, a deviation of 10 and 20◦ from original dip angle of fracture is applied to the different
parts of the plane joint. A schematic of the fractured sample with two different asperity angles is shown
in Figure 4a. Its effect on mechanical and fluid flow properties of the fractured sample is shown in Figures
4b and 4c. By presence of asperity on the fracture, the fracture becomes rougher. Both peak and residual
strength of sample is a function of asperity angle. In fact, the asperity resist shearing along the fracture, lead-
ing to higher strength of the sample. By applying higher deviation of asperity angles, the peak strength of
the sample increases and occurs at higher strain. In addition, the residual stress of the sample is increased
leading to higher sample dilation. The fluid flow and seismic source response of fractured samples follow
its mechanical behavior. The permeability is higher after shearing of fractures in the case of sample with a
rough fracture due to larger natural dilation of sample after rock deformation. By increasing the asperity
angle, this effect is more pronounced and lead to more increment of permeability of the sample. By fur-
ther shear deformation, degradation of asperity may happen, affecting its dilation. In our work, the asperity
is as strong as in intact rock. Our model does not consider damage evolution of the asperities and gouge
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Geophysical Research Letters 10.1002/2013GL058683
generation which may lead to reduction of permeability. The dilation of fracture shows its effect on seismic
source mechanism of AE events in Figure 4d. In the case of rough fracture, AE source mechanism deviates
from concentrated zone in the plane fracture and shows its tendency toward opening crack part of Hudson
diagram. Asperity of the fracture could generate tensile force during its deformation leading to opening of
the microcracks and permeability enhancement.
Hydraulic stimulation of geological formations in oil and gas fields or geothermal reservoirs could lead to
induced microseismicity. Spatial mapping of the microseismic events enables imaging of the pattern of
activated fracture networks that in turn enhances the prediction of fluid flow in subsurface formation [Baig
and Urbancic, 2010]. Activation of natural fractures could happen under confining pressure, which resist
enhancement of permeability. The result of analyzing source mechanism of AE events during failure of
rough fracture in our work proves that tensile component in the source of failure can be induced because
of fracture surface properties, i.e., its roughness. In addition, the fracture roughness can lead to permeability
enhancement in the natural fractures under confining pressure. Changes in permeability of activated frac-
tures in the stimulated reservoir volume correlate with significant improvement in well productivity [Cipolla
et al., 2011]. Based on our study on evolution of transport behavior of sample with rough fracture, the
roughness of fracture surface could dilate fracture and increase the aperture normal to the fracture surface
under confining pressure. Fracture roughness could resist against sliding back of fracture to the initial posi-
tion, and it could be the main source of fracture permanent dilation when the closure stress is applied after
hydraulic stimulation.
4. Conclusions
By applying the hydromechanical-seismic modeling, we are able to study seismic source mechanism and
transport behavior of deformed fractured rock samples and the connection between them as a function of
fracture properties. Roughness of fracture, leading to shear dilation and aperture variation, was modeled
to show its greatest influence on permeability increment and deviation of source mechanism of AE events
toward crack opening in the sample. While the AE events generated during deformation of plane fractures
have volumetric component toward crack closure and the permeability of a fractured sample could be
increased insignificantly, the AE events generated during deformation of rougher fractures have volumet-
ric component toward tensile crack opening, and the permeability of a fractured sample could be increased
significantly during its failure, when performing the same triaxial compression test.
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