Document [original]

1. Introduction

Subsurface hydraulic stimulations for geoenergy development aim to increase the reservoir permeability via

hydro-fracturing and hydro-shearing processes. Examples of such applications include fluid injection for

enhanced geothermal systems (Li & Zhang,2023; Olasolo etal., 2016; Schoenball etal.,2020), as well as

oil and shale gas exploitation (Das & Zoback,2013; Kim & Moridis,2015). Rock fractures provide preferen-

tial fluid pathways that can transport thermal energy and shale oil and gas. A wealth of evidence from labora-

tory and field experiments suggests that hydro-shearing, which involves injection-induced slip along fractures

and faults, is the primary contributor to enhancing reservoir permeability even when no proppants or acids are

used (Barton etal.,2009; Cappa, Guglielmi, & De Barros,2022; Cappa, Guglielmi, Nussbaum, etal.,2022;

Guglielmi etal.,2015; Ishibashi etal.,2018; Jalali etal.,2018), but this process may also lead to unintentional

and undesired large-magnitude induced seismic events (Mw>3) (Ji, Hofmann, Duan, & Zang,2022; Keranen

& Weingarten,2018; Schultz etal.,2020; Zang etal.,2014). Thus, the ability to predict the transient permea-

bility evolution of individual fractures is the key to accurately estimating fluid flow and reservoir response with

controlled seismicity during injection.

Permeability measurements in conventional displacement-driven shear experiments in the laboratory have shown

that the fracture permeability evolution can be influenced by the surface roughness (Fang, Elsworth, Ishibashi,

& Zhang,2018; Wu etal.,2017), mineral composition (Fang, Elsworth, Wang, & Jia,2018; Fang etal.,2017),

Abstract We present a series of controlled fluid injection experiments in the laboratory on a pre-stressed

natural rough fracture with a high initial permeability (∼10

−13m

2) in granite using different fluid pressurization

rates. Our results show that fluid injection on a fracture with a slight velocity-strengthening frictional

behavior exhibits dilatant slow slip in association with a permeability increase up to ∼41 times attained at

the maximum slip velocity of 0.085mm/s for the highest-rate injection case. Under these conditions, the slip

velocity-dependent change in hydraulic aperture is a dominant process to explain the transient evolution of

fracture permeability, which is modulated by fluid pressurization rate and fracture surface asperities. This

leads to the conclusion that permeability evolution can be engineered for subsurface geoenergy applications by

controlling the fluid pressurization rate on slowly slipping fractures.

Plain Language Summary Understanding the evolution of fracture permeability during hydraulic

stimulation of subsurface reservoirs is the key to characterizing fluid transport and formulating strategies to

limit induced seismicity. Accordingly, there is a significant interest in deciphering how the fluid pressurization

rate, a constitutive operational parameter during injection, influences the transient permeability change during

fracture slip.We conducted a series of experiments in the laboratory using different fluid pressurization rates

on a natural rough fracture in granite under a pre-stressed state. The fracture had a high initial permeability. Our

findings show that when fluid is injected into a fracture with a slight velocity-strengthening frictional behavior,

it causes slow slipping with significant permeability enhancement. The change in hydraulic aperture caused by

slip velocity is the main reason for the temporary change in permeability, and this effect is modulated by fluid

pressurization rate and fracture surface irregularities. Our results suggest that we can modulate the permeability

of subsurface geoenergy reservoirs by controlling the fluid pressurization rate on slowly slipping fractures.

JI ETAL.

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Fracture Permeability Enhancement During Fluid Injection

Modulated by Pressurization Rate and Surface Asperities

Yinlin Ji1 , Wei Zhang2, Hannes Hofmann1,3 , Frédéric Cappa4 , and Supeng Zhang1,5

1Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, Potsdam, Germany, 2School of Petroleum

Engineering, China University of Petroleum (East China), Qingdao, China, 3Institute of Applied Geosciences, Technische

Universität Berlin, Berlin, Germany, 4Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, IRD, Sophia Antipolis,

France, 5Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of

Sciences, Beijing, China

Key Points:

• We conducted fluid injection

experiments on a pre-stressed natural

rough fracture in granite at different

pressurization rates

• The velocity-strengthening fracture

exhibits slow slip accompanied by a

significant increase in permeability

during fluid injection

• Transient fracture permeability is

controlled by injection-induced slip

velocity, modulated by pressurization

rate and surface asperities

Supporting Information:

Supporting Information may be found in

the online version of this article.

Correspondence to:

Y. Ji,

[email protected]

Citation:

Ji, Y., Zhang, W., Hofmann, H., Cappa,

F., & Zhang, S. (2023). Fracture

permeability enhancement during fluid

injection modulated by pressurization

rate and surface asperities. Geophysical

Research Letters, 50, e2023GL104662.

https://doi.org/10.1029/2023GL104662

Received 22 MAY 2023

Accepted 7 SEP 2023

Author Contributions:

Conceptualization: Yinlin Ji

Data curation: Yinlin Ji

Formal analysis: Yinlin Ji

Funding acquisition: Hannes Hofmann

Methodology: Yinlin Ji

Software: Wei Zhang, Supeng Zhang

Validation: Hannes Hofmann, Frédéric

Cappa

Writing – original draft: Yinlin Ji

Writing – review & editing: Yinlin Ji,

Hannes Hofmann, Frédéric Cappa

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stress state (Gutierrez etal.,2000; Rutter & Mecklenburgh,2018), slip direction (Okazaki etal.,2013; Rutter

& Mecklenburgh,2017), slip velocity (Fang etal.,2017; Ishibashi etal.,2018), as well as slip mode (Almakari

etal.,2020; Rutter & Mecklenburgh,2018). Meanwhile, for injection-induced fracture permeability evolution,

several experimental studies have shown that the fracture permeability increases with decreasing effective normal

stress (i.e., increasing fluid pressure) and dilatant slip has been identified as the key mechanism responsible for

permeability enhancement. Particularly, the fracture permeability in granite shows an irreversible enhancement

by self-propping shear activated by fluid pressurization under typical deep geothermal stress conditions (Ye &

Ghassemi,2018), which is more pronounced at lower confining pressures (Almakari etal.,2020). More recently,

the transient permeability enhancement of slowly slipping faults activated by fluid injection in underground

galleries is found to be controlled by the changes in slip velocity (Cappa, Guglielmi, & De Barros,2022) with

increasing fluid pressure, congruent with the laboratory-derived semi-analytical model relating slip velocity

and aperture change (Fang etal.,2017; Samuelson etal.,2009). However, although these previous experiments

provide important insights into the physics of fluid flow and shear slip in fractures, the effects of fluid pressur-

ization rate and fracture surface asperities on transient permeability change during fracture slip remain poorly

constrained.

Here, we performed a series of controlled laboratory fluid injection experiments on a pre-stressed natural rough

fracture in granite to explore the effects of fluid pressurization rate and fracture surface asperities on transient

fracture permeability change. Three fluid injection experiments with different fluid pressurization rates were

conducted consecutively under the same initial stress conditions. Results give new insights into how the fluid

pressurization rate and fracture surface asperities control the transient fracture permeability change during

injection-induced fracture slip.To the best of our knowledge, this work is the first to link the fluid pressuri-

zation rate and fracture surface asperities with transient fracture permeability enhancement using controlled

laboratory-sized experiments (cf., Ji, Hofmann, Duan, & Zang,2022; Zhuang & Zang,2021).

2. Materials and Methods

The fluid injection experiments were performed at room temperature (∼22°C) on a naturally formed rough frac-

ture in granite (Figure1a) using the triaxial shear-flow setup (Figure1b) in the MTS 815 rock mechanics test

system (Text S1 in Supporting InformationS1). The Bukit Timah granite sample was cored from a depth of

approximately 10m in central Singapore, Asia, which is a potential geothermal reservoir rock. The physical,

mechanical, and hydraulic properties of the granite (Ji,2020; Peng etal.,2017) are summarized in Table S1 of the

Supporting InformationS1. We selected a 50-mm-diameter core sample containing a pre-existing sealed natural

fracture and cut it to ∼123.8mm length. We then compressed the sample until it failed along the fracture plane at

20MPa confining pressure by advancing the axial piston at a velocity of 1μm/s, producing a cylindrical sample

containing a natural rough fracture inclined 27° to the core axis. The minor and major axes of the elliptical planar

fracture measure 110 and 50mm, respectively, resulting in a fracture area of 4,320mm

2. Upon visual inspection

of the fracture surface, it appears that the fracture is most likely a magma cooling-induced break of the surround-

ing granite without obvious mineral intrusion (Zhao,1997). Moreover, the fracture is not filled with granular

material. Analysis of the fracture surface topography using a structured light scanner (Model No.: DAVID SLS-3)

indicates a joint roughness coefficient (JRC) of 12.5 (Table S2 in Supporting InformationS1 and the accompany-

ing notes). This JRC value corresponds to a “rough” fracture, as classified by Barton and Choubey(1977). Two

vertical boreholes with a diameter of ∼2mm were drilled at the short edge of each sample half to facilitate the

fluid communication between the endcap and the fracture surface. Filter paper with a pore size of 0.45μm was

inserted between endcaps and sample ends to inhibit the possible contamination of fluid pipes by the produced

wear particles. The sample was secured on the endcaps by two layers of Teflon jacket to exclude confining

oil. The favorable angle of 27° prevents the fracturing of the granite matrix during axial loading (Brady &

Brown,2013; Ji,2020). The permeability contrast between rock matrix (∼1.3×10

−18m

2, Table S1 in Supporting

InformationS1) and fracture (∼1.0×10

−13m

2, Text S1 and Table S3 in Supporting InformationS1) ensures that

the fluid only flows through the fracture during the experiments.

The sample was vacuum-saturated with distilled water for ∼24 hr before the experiments. Afterward, the

confining pressure was first repeatedly cycled between 2 and 11MPa to stabilize the sample by eliminating any

misalignment of the two rock blocks (cf., Kohli & Zoback,2013; Ji, Kluge, etal.,2022). Then, under 2MPa

confining pressure, pressurized distilled water was injected directly into the fracture to reach a fluid pressure

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of 1MPa, and maintained constant until the full saturation of the sample, signified by negligible fluid volume

intake. After full saturation, we first obtained the apparent steady-state friction coefficient (μ) of the fracture by

conducting a multi-stage shear test under an effective normal stress (i.e., total normal stress σn minus fluid pres-

sure p, σ′n=σn−p) of 1, 2, 3, and 10MPa (Figures1c and1d) each at a constant fluid pressure of 1MPa and an

axial displacement rate of 1μm/s. We then reduced the shear stress to ∼85% peak shear strength under 11MPa

normal stress and 1MPa fluid pressure on the fracture. Following that, we held the shear and normal stresses

on the fracture constant (the five-pointed star in Figure1d), and water was injected at a constant pressurization

rate through the two boreholes, which were connected to the same fluid pump, to induce the opening and slip of

the pre-stressed fracture. The schematic of the stress paths during mechanical loading and fluid injection shows

how the stress state approaches the Mohr-Coulomb failure envelope (Figure S1 in Supporting InformationS1).

Figure 1. Experimental material, setup, loading procedure and failure envelope. (a) Natural rough fracture in Bikit Timah

granite with a joint roughness coefficient of 12.5. (b) Triaxial shear-flow setup, where α=27° is the fracture inclination angle

with respect to the sample axis. (c) Multi-stage shear loading before fluid injection to obtain the peak shear strengths (τp,

denoted by black open circles) under 1, 2, 3, and 10MPa effective normal stresses (σ′n). At 10MPa effective normal stress

(constant fluid pressure=1MPa), the fluid volume change first increases dramatically due to shear dilation, and it remains

unchanged after reaching the yield shear stress of ∼6.6MPa, suggesting that the steady-state fracture aperture becomes

relatively constant with increasing slip displacement beyond this point. (d) Mohr-coulomb failure envelope of the fracture

in terms of shear stress as a function of effective normal stress obtained from the multi-stage shear test. The five-pointed

star and red open circles represent the stress states of the fracture before fluid injection (∼85% τp and σ′n=10MPa) and at

the onset of fracture activation, respectively. The apparent steady-state friction coefficient (μ) of the fracture is estimated

as μ=0.75 with zero cohesion. The stress states at the onset of fracture activation are generally compatible with the

Mohr-coulomb failure envelope, indicating the near-uniform distribution of fluid pressure on the fracture surface.

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A sequence of three fluid injection experiments with different fluid pressurization rates of 0.0004, 0.002, and

0.01MPa/s were performed on the same fracture under the same initial stress conditions. The three pressuri-

zation rates were carefully chosen to achieve a balance: they were neither excessively high, ensuring a consist-

ently near-uniform fluid pressure distribution on the fracture (cf., Passelègue etal.,2018), nor excessively low,

enabling the observation of fracture response to fluid injection within a reasonable testing time. The time interval

between two successive experiments was ∼20min to ensure that the fracture was in a stabilized hydromechanical

state (i.e., equilibrium) before the subsequent fluid injection. In addition, prior to each fluid injection experiment,

we measured the steady-state fracture permeability using the steady state flow technique by imposing a constant

upstream fluid pressure of 1MPa through the bottom borehole with the downstream opening to the atmosphere

and measuring the resulting flow rate (Text S1 in Supporting InformationS1).

3. Results

3.1. Frictional Strength and Fracture Deformation in the Experiments

The three peak shear strengths (τp) obtained from the multi-stage shear test were used to construct the

Mohr-Coulomb failure envelope, yielding an apparent steady-state friction coefficient of 0.75 by setting a zero

cohesion (Figure1d), generally compatible with Byerlee’s rule of rock friction (Byerlee,1978). In the subsequent

three fluid injection experiments, the normal stress and shear stress were held constant at 11 and 6.41MPa

(∼85% τp), respectively (Figure2). The fracture was activated and the slip was initiated once the fluid pressure

approached a critical value. In our experiments, the critical activation fluid pressure pff is predicted as 3.42MPa

based on the Mohr-Coulomb failure criterion incorporating the effective stress law, which is roughly consistent

with the laboratory measurements (Figure1d; Table S3 and Text S2 in Supporting InformationS1), indicative of

a near-uniform fluid pressure distribution over the fracture surface (Ji etal.,2020; Passelègue etal.,2018; Rutter

& Hackston,2017). The near-homogeneous fluid pressure distribution on the fracture surface is also confirmed

by the short characteristic diffusion time (Mavko etal.,2009) (Text S2 in Supporting InformationS1).

In the fluid injection experiments, the normal stress and shear stress remain unchanged under servocontrol during

fluid pressurization (Figure2). The fluid pressure is elevated from 1MPa in all the three fluid injection exper-

iments. Fluid pressurization of the fracture requires injection of fluid volume from the pump, according to the

Figure 2. Temporal changes of hydromechanical parameters during fluid injection experiments. Time-dependent evolution

of normal stress, shear stress, fluid pressure, slip displacement and injected fluid volume in the fluid injection experiments at

a fluid pressurization rate of (a) 0.0004, (b) 0.002, and (c) 0.01MPa/s. The initiation of fracture activation is signified by the

increase of slip displacement along the fracture. The injected fluid volume first increases near linearly with time followed by

abrupt increases. The time when the increase of injected fluid volume deviates from the linear trend is roughly the time at the

onset of fracture activation (see black arrows and dashed lines). Note that the slip displacement is offset to zero at the start of

fluid pressurization in each experiment.

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compression-induced pressurization principle of fluids (Ji, Kluge, etal.,2022; Kestin,1979). Particularly, the

elevation of fluid pressure is linearly correlated with the increase of injected fluid volume when the sample

volume is constant, and thus any changes in sample volume result in variations of the injected fluid volume (cf.,

Ashman & Faulkner,2023; Samuelson etal.,2009). The slip displacement starts to increase when the fluid pres-

sure reaches the critical activation fluid pressure. The injected fluid volume increases near linearly before fracture

activation, suggesting that the injected fluid volume mainly serves to compensate for the compressed volume

during the fluid pressure increase. Hence, the elastic normal opening of the fracture induced by the reducing

effective normal stress is negligible as previously observed in other experimental studies (cf., Cappa, Guglielmi,

& De Barros,2022; Guglielmi etal.,2015). This may be due to the small increase of fluid pressure (<2.51MPa)

as the fracture is already primed close to failure, and the high normal stiffness of the fracture in granite (in the

order of ∼100MPa/mm for clean natural fractures in granite, Zangerl etal.,2008). In particular, the maximum

volume increase associated with elastic fracture opening induced by reducing effective normal stress is estimated

as small as ∼108mm

3, which is smaller than 0.09 times the total injected fluid volume upon fracture activation

(Table S3 in Supporting InformationS1). Upon fracture activation, the increase of injected fluid volume starts

to deviate from the linear trend at the time of 5,222.9, 1,162.5, and 260.7s at the pressurization rate of 0.0004,

0.002, and 0.01MPa/s, respectively, and the excessive injected fluid volume is primarily accommodated by the

fracture dilation associated with shear slip (Figure2) (Ji etal.,2019; Li etal.,2021). At the termination of fluid

injection, the fracture slips by 0.24, 1.34, and 1.25mm in the fluid injection experiments at a pressurization rate

of 0.0004, 0.002, and 0.01MPa/s, respectively.

At the same amount of slip displacement change, the slip velocity generally increases with a higher fluid pres-

surization rate with some large fluctuations especially at larger slip displacement (Figure S2 in Supporting Infor-

mationS1). The peak slip velocity increases by ∼15 times at 0.24mm slip displacement change by elevating

the pressurization rate from 0.0004 to 0.01MPa/s. The increased slip velocity at higher-rate fluid pressurization

cases is ascribed to the larger strength deficit relative to the applied shear stress: the higher the fluid pressuriza-

tion rate, the faster rate of reduction in effective normal stress and thereby shear strength, and the larger the slip

acceleration, resulting in a higher slip velocity. The fluctuation of slip velocity with increasing slip displacement

could be attributed to various sizes and strengths of surface asperities (cf., Goebel etal.,2012; Xu etal.,2023;

Ye & Ghassemi,2020).

The maximum slip velocity in our fluid injection experiments is smaller than 0.1mm/s (Table S3 in Supporting

InformationS1), suggesting that the injection-induced slow slip is mainly aseismic (Tinti etal.,2016). This is

further confirmed by the evolution of the apparent friction coefficient (Figure S3 in Supporting InformationS1),

measured as the ratio of the shear stress to effective normal stress, as a function of the logarithm of the slip velocity

(ln(v/v0), where v is the slip velocity and v0 is the background slip velocity before fracture activation) (Guglielmi

etal.,2015; Marone,1998) (Table S4 in Supporting InformationS1). On average, the fracture exhibits a slight

velocity-strengthening frictional behavior, marked by a positive slope in the friction coefficient-versus-ln(v/

v0) plots in the three injection experiments (Figure S3 in Supporting InformationS1). This is congruent with

previous laboratory results suggesting that rough fractures exhibit more positive velocity-strengthening frictional

behavior than smooth fractures (Fang, Elsworth, Ishibashi, & Zhang,2018), a condition facilitating aseismic slow

slip upon activation.

3.2. Velocity Dependence of Transient Fracture Permeability

First, by assuming that the excessive injected fluid volume is primarily accommodated by the increased fracture

volume due to shear-induced dilation, we can estimate the transient change of hydraulic aperture (Δb) accompa-

nying injection-induced fracture slip from the temporal evolution of the injected fluid volume as (Ji etal.,2019;

Li etal.,2021),

𝑏𝑏=

Δ𝑉𝑉

𝐴𝐴

(1)

where ΔVf is the transient excessive increase of injected fluid volume during dilatant fracture slip relative to that

before fracture activation (see Text S3 in Supporting InformationS1 for detailed calculations); A is the area of

the elliptical fracture. Thus, the result obtained by Equation1 is volume-based hydraulic aperture change. Note

that here we posit that the congruence between alterations in hydraulic aperture and mechanical aperture remains

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steadfast, substantiated by prior investigations of permeable fractures within controlled laboratory settings (Fang

etal.,2017; Li etal.,2021) and natural field conditions (Cappa, Guglielmi, & De Barros,2022).

We then used the laboratory-derived semi-analytical model relating slip velocity (v) with aperture (b) (Fang

etal.,2017; Samuelson etal.,2009) to model the volume-based aperture in our experiments,

𝜀𝜀i= −Ψ ⋅ln

[

𝑣𝑣i−1

𝑣𝑣

(

𝑣𝑣i

𝑣𝑣

i−1

−1

)

⋅𝑒𝑒−𝑣𝑣i⋅𝑡𝑡i∕𝐷𝐷c

)]

(2)

𝑏𝑏

evo =𝑏𝑏n

slip

i=n

∏

i=0

(1+Δ𝜀𝜀i

)

(3)

where i is the ith velocity step; Δε is the dilation parameter; Ψ is the dilation factor; ti is the time since the ith

velocity step; Dc is the critical slip distance;

𝐴𝐴𝐴𝐴

evo

and

𝐴𝐴𝐴𝐴

slip

are the modeled aperture and slip-dependent aperture at

the nth velocity step, respectively.

For the shear test conducted under 11MPa normal stress and 1MPa fluid pressure, the fluid volume change

indicates that the fracture aperture gradually increases with increasing slip displacement initially because of

shear dilation, but remains mostly stable after reaching the yield shear stress of ∼6.6MPa (Figure1c). Therefore,

we assumed that the slip-dependent aperture (

𝐴𝐴𝐴𝐴

slip

) stays unchanged at the initial hydraulic aperture (b0) in each

injection case. The validity of this assumption is bolstered by the fact that the steady-state fracture permeability,

as measured prior to each injection experiment, remains almost unchanged (Table S3 in Supporting Informa-

tionS1). Further, because k=b

2/12 (Snow,1969; Witherspoon etal.,1980), the transient permeability change (k/

k0) can be calculated as the square of the ratio between

𝐴𝐴𝐴𝐴

evo

and b0, where k denotes the transient permeability at

the nth velocity step (kn) and k0 is the initial fracture permeability before activation.

This velocity-dependent fracture permeability model has been successfully used to reproduce the transient

permeability change of fractures/faults in the field-scale fluid injection experiments (Cappa, Guglielmi, &

De Barros,2022) and in the lab-scale shear friction experiments (Fang etal.,2017). Based on Equations2 and3,

the best-fit velocity-dependent aperture models to our experimental aperture data derived from injected fluid

volume (Equation1) were obtained by searching the optimal dilation factor (Ψ) in the range from 0 to 5, and

critical slip distance (Dc) from 0.1 to 5,000μm using the genetic algorithm (Holland,1992; Zbigniew,1996)

(Text S4 in Supporting InformationS1). The root mean square error (RMSE) has a global minimum value at

(Ψ=0.08, Dc=0.4μm), (Ψ=0.93, Dc=0.16μm) and (Ψ=0.84, Dc=2.74μm) in modeling the fluid injec-

tion experiments at a pressurization rate of 0.0004, 0.002 and 0.01MPa/s, respectively (Figure S4 in Supporting

InformationS1). The dilation factors (Ψ) in our best-fit models are comparable to the values obtained in previous

studies on laboratory fractures (Fang etal.,2017) and in-situ faults (Cappa, Guglielmi, & De Barros,2022).

Our modeling results seem less sensitive to the critical slip distance (Dc) within a range of less than one order of

magnitude around the optimal value. This is presumably because the influence of each velocity step tends to reach

the steady state at small optimal Dc (see Equation2), and thus a small change of Dc around the optimal value may

not change much the modeling results.

Figures3a, 3c, and3e show that the aperture change calculated using the velocity-dependent aperture model

(Equations2 and3) demonstrates a satisfactory agreement with the measured aperture change determined from

the injected fluid volume (Equation1), signified by the small RMSE values. Note that the RMSE in the first

fluid injection experiment at a rate of 0.0004MPa/s is ∼3 times that of the other two higher-rate counterparts,

which may be due to the relatively poor constraint on the model by the short slip displacement and noisy slip

velocity data. The transient permeability change (k/k0) is always larger than unity (Figures3b, 3d, and3f) with

the maximum value of ∼41 attained at the maximum slip velocity of 0.085mm/s in the highest-rate injection case

(Figure3f), highlighting that the transient fracture permeability accompanying fracture slip is enhanced relative

to the initial steady-state fracture permeability. The results indicate that the injection-induced slip can cause a

substantial temporary increase in transient fracture permeability, which could considerably facilitate fluid flow.

This transient permeability enhancement appears to be much more significant than the relatively minor changes

(∼1.5 times) in steady-state fracture permeability before each injection experiment (Table S3 in Supporting Infor-

mationS1). The synchronicity of the changes in transient permeability and slip velocity, signified by the high

correlation coefficient (Asuero etal.,1988,2006), further suggests that the transient permeability enhancement

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is dominantly regulated by the injection-induced slip velocity (Figures3b, 3d, and3f). In addition, the primary

control of slip velocity on the change of transient permeability is reaffirmed by Figure S5 in Supporting Infor-

mationS1. This figure demonstrates a consistent rise in transient permeability enhancement corresponding to

higher slip velocities, and the rate of increase is primarily controlled by the dilation factor (Ψ) and critical slip

distance (Dc).

Figure4 illustrates that the transient permeability enhancement is evidently not controlled by the slip displace-

ment change, in line with previous results on permeable in-situ faults (Cappa, Guglielmi, & De Barros,2022).

Figure 3. Transient evolution of normalized aperture change (measured and calculated), permeability change and slip velocity during fracture slip in the fluid

injection experiments. Results of experiments performed at a pressurization rate of (a and b) 0.0004, (c and d) 0.002, and (e and f) 0.01MPa/s. The aperture change is

normalized with respect to the maximum value in each experiment. Ψ, Dc and root mean square error (RMSE) represent the dilation factor, critical slip distance and

RMSE, respectively. The correlation coefficients (CC) between transient permeability change and slip velocity in the three experiments are all close to unity, suggesting

the dominant control of slip velocity on the transient permeability change.

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In particular, the transient permeability enhancement in the first ∼0.24mm

slip displacement is larger at higher pressurization rates. However, the tran-

sient permeability enhancement in the case at 0.002MPa/s starts to exceed

that of the case at 0.01MPa/s at ∼0.6mm slip displacement before drop-

ping lower at ∼0.9mm, followed by the increasing divergence of the tran-

sient permeability enhancement in the two cases. The evolution of transient

permeability enhancement with slip displacement change shows a similar

trend to slip velocity in the three cases (Figure S2 in Supporting Informa-

tion S1), reconfirming that the rate of increase of transient permeability

change with slip displacement is dictated by slip velocity. Since transient

permeability enhancement is mainly regulated by slip velocity, its fluctu-

ations likely stem from variations in slip velocity, which can be linked to

diverse asperity strengths and sizes (Goebel etal.,2012; Xu etal.,2023; Ye

& Ghassemi,2020). Particularly, the central roughness profile of the fracture

surface is characterized by larger-sized waviness and smaller-sized uneven-

ness (Li etal.,2019; Zou etal.,2015; Text S5 and Figure S6 in Support-

ing Information S1). As we observed an increase in slip displacement up

to 1.34mm within our experimental scope, the primary influencer of fric-

tional resistance alteration is the unevenness of asperities, characterized by

an average wavelength of ∼1.36mm (Text S5 and Figure S6 in Supporting

InformationS1). Previous studies suggest that the frictional resistance can

change over a slip displacement of less than half the wavelength of uneven-

ness (approximately ∼0.68mm in our case) due to surface wear effects (Li

etal.,2015). In our experiments, indications of surface wear are apparent

(Figure S7 in Supporting InformationS1). This implies that a slip displacement of approximately ∼0.68mm

or beyond would be sufficient to initiate diverse fluctuations in frictional resistance, depending on sizes and

strengths of unevenness of asperities. Consequently, these fluctuations would impact both slip velocity and

transient permeability. Given the uncertainties involved in determining the average half wavelength of asperity

unevenness, the close proximity of 0.68mm to the observed slip displacement of ∼0.6mm exhibiting a signif-

icant fluctuation further supports this interpretation. That is, our results demonstrate that increasing the fluid

pressurization rate can enhance transient permeability in our experimental case, suggesting that fluid pressuri-

zation rate can promote the transient permeability enhancement by causing faster slip velocity, with concurrent

modulations of surface asperities as the slip displacement increases.

4. Discussion

This study has demonstrated that increasing the rate of fluid pressurization can enhance the transient permeability

increase, with fluctuations modulated by surface asperities, during fracture slip in triaxial shear-flow experiments

with direct fluid injection to the fracture. Our results were obtained on a natural rough fracture without initial

filling material in granite under a pre-stressed state. It is important to note that our experiments represent a case

where the fracture has a high initial permeability and a slight velocity-strengthening frictional behavior favoring

aseismic slip during the fluid injection. The presented results support the hypothesis that the fluid pressurization

rate and fracture surface asperities have a significant influence on the transient permeability evolution in a single

deformable natural fracture and confirm that the slip velocity dependency of transient fracture permeability

previously observed in the laboratory (Fang etal.,2017) and in situ (Cappa, Guglielmi, & De Barros,2022) is a

key process for fluid transport in fractures and faults. Nevertheless, it is important to highlight that our findings

are particularly relevant to shallow aseismic slip and the accompanying changes in transient permeability, even

though they might not comprehensively encompass the entire steady-state range. These results could also offer

valuable insights into the understanding of permeability evolution associated with tremors occurring at greater

depths due to slow slip events (cf., Guglielmi etal.,2015).

The excellent agreement between the experimental data and the numerical solutions highlights that the velocity

dependency of transient fracture permeability is a dominant process during injection. Although we obtained

a good fit to data with the velocity-dependent aperture model, other mechanisms may also influence the frac-

ture's hydromechanical responses. In our experiments, the clogging and unclogging of fluid pathways associated

Figure 4. Transient permeability change (k/k0) against slip displacement

change during fracture slip in the fluid injection experiments. A higher fluid

pressurization rate tends to promote the transient permeability enhancement

at smaller slip displacement changes, while this trend is influenced by fracture

surface asperities when the slip displacement change exceeds the average half

wavelength of asperity unevenness (∼0.68mm in this study).

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with flux-driven particle mobilization (Candela etal.,2014) may only have a minimal impact on the transient

permeability changes. Indeed, we observed that the root mean square asperity height and peak-to-trough distance

decrease by only 0.74 and 0.68mm, respectively, after the experiments (Table S2 in Supporting InformationS1).

Given that the average grain size of the granite is approximately 2mm (Li etal.,2020), we infer that the fracture

surface primarily underwent surface wear (Figure S7 in Supporting InformationS1), rather than significant grain

detachments. This observation also guarantees that the results of the three consecutive fluid injection experiments

on the same natural rough fracture can be reasonably used for comparison to explore the effects of pressuriza-

tion rate and surface asperities, which is also supported by the negligible reduction of JRC from 12.5 before the

experiments to 12.4 after the experiments (see Table S2 in Supporting InformationS1 and the notes below). The

insignificant surface damage after the experiments could be due to the low effective normal stress (σ′n) relative to

the uniaxial compressive strength of the host rock (i.e., σ′n<0.1 UCS, Table S1 in Supporting InformationS1),

which prevents the occurrence of severe asperity breakages (cf., Ji etal.,2021; Li etal.,2022; Oh etal.,2016).

Therefore, due to the trivial surface damage and the small amount of small-sized wear particles produced, it is

likely that flux-driven particle mobilization did not exert a substantial effect on the transient permeability changes

in our experiments. In addition, as opposed to injection-induced slow slip in our experiments, fast stick-slip events

may further complicate the transient permeability evolution in the laboratory scale (Almakari etal.,2020; Rutter

& Mecklenburgh,2018). Similarly, in-situ fluid injection experiments on slowly slipping faults also demonstrated

that the permeability evolution can be affected by slip modes (i.e., aseismic and seismic) (Cappa, Guglielmi, &

De Barros,2022; Cappa, Guglielmi, Nussbaum, etal.,2022; Guglielmi etal.,2015).

However, when the fracture slip occurs at higher effective pressures (cf., Goebel etal.,2012,2017,2023; Ji,

Wang, etal.,2022; Ji, Hofmann, Rutter, etal.,2022; Ye & Ghassemi,2018,2020), the presence of wear parti-

cles and any associated colloidal seal are anticipated to have a notable impact on the transient fracture perme-

ability evolution during fluid injection, in addition to the velocity-dependent process (e.g., Cappa, Guglielmi,

& De Barros, 2022). Specifically, the combination of pore throat expansion through shear dilation (cf., Im

etal.,2018) and fluid pressure migration during injection (e.g., Ji etal.,2020; Passelègue etal.,2018) is likely

to favor the flux-driven unclogging of the fracture, potentially leading to further transient permeability enhance-

ment. Meanwhile, the transition from slow slip to stick-slip failure of fractures could be promoted by elevating

effective pressures (e.g., Dieterich,1978; Scuderi etal.,2016) and reducing the friction rate parameter (e.g., Fang

etal.,2017), possibly causing complex transient permeability evolution arising from the cycling between near-

zero slip velocity during the stick period and abrupt velocity jump during the dynamic slip period (cf., Almakari

etal.,2020; Morad etal.,2022). Additionally, elevating both normal stress and shear stress have the tendency to

decrease fracture permeability due to the obstruction of fluid pathways by the produced abrasive particles (Rutter

& Mecklenburgh,2018). Moreover, the ratio of shear stress to shear strength could impact the slip velocity during

injection-induced slip (Passelègue etal.,2018), potentially promoting aperture changes facilitated by velocity

augmentation. Nonetheless, the interaction between the flux-driven particle mobilization and the intricate perme-

ability evolution resulting from complex slip modes remains uncertain. Consequently, there is a need to explore

the transient evolution of permeability during fluid injection at elevated effective pressures and diverse shear

stress levels in fractures with different roughnesses and exhibiting a range of frictional properties and slip modes.

In terms of scales, laboratory fractures in this study represents a fracture of zero or low effective fracture tough-

ness and cohesion, which discounts the crack propagation-induced permeability change (Abe & Horne,2023;

Abe etal.,2021; Ye & Ghassemi,2019), which are clearly idealizations of the complexity of natural fracture

networks. Thus, at the reservoir-scale fracture network, the transient permeability change of individual fractures

can be complicated by fracture surface topography and infilling, fracture interactions and connectivity, stress

state, rock type, as well as the decoupling of fracture slip and opening in the case of initially low-permeability

fractures (Cappa, Guglielmi, Nussbaum, etal.,2022; Rutter & Hackston,2017). Clearly, fracture permeability

during fluid injection is a fast-evolving property significantly affected by different processes that are difficult to

compare across scales. To further bridge the scale gap, our results obtained from lab-scale single fracture experi-

ments with the centimeter scale need to be extended for mine- and reservoir- scale injection experiments, in which

increasing pressure gradients can also alter the flow-through area of a heterogeneous fracture/fault.

Beyond improving the fundamental understanding of the process of fracture permeability enhancement controlled

by pressurization rate and surface asperities, the mechanism observed in this lab-scale experiment can be useful

for implementing permeability enhancement and seismicity mitigation in the reservoir scale. The transient perme-

ability increases in the pressurized zone upon local slip may accelerate fluid flow in mainly the fault-parallel

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direction and the rapid transfer of high pressure at distance from the fluid source. Moreover, as shown in previ-

ous studies, high-rate fluid pressurization could enhance the seismic hazard (e.g., Goebel & Shirzaei,2020; Ji,

Wang, etal.,2022; Ji & Wu,2020; Passelègue etal.,2018; Rudnicki & Zhan,2020; Wang etal.,2020). Thus,

the competition between pressurization and frictional processes in fracture/fault stability is a dominant factor in

the trade-off between increasing reservoir permeability and the mitigative impact of slowing or ceasing injection

on seismic hazard.

5. Conclusions

Our fluid injection experiments on a pre-stressed natural fracture with high initial permeability have demon-

strated that injecting fluid into fractures with a slightly velocity-strengthening frictional behavior leads to slow

slipping and a significant transient increase in permeability. The permeability can reach up to approximately

41 times its initial value when the maximum slip velocity of 0.085mm/s is achieved through high-rate fluid

injection. We have identified that the change in hydraulic aperture due to slip velocity is the primary factor

driving the temporary evolution of fracture permeability, and this effect is modulated by fluid pressurization

rate and fracture surface asperities. These findings highlight the potential to engineer permeability evolution

for subsurface geoenergy applications by controlling the fluid pressurization rate specifically on slowly slipping

fractures.

Notation

JRC joint roughness coefficient

RMS root mean square

RMSE root mean square error

UCS uniaxial compressive strength

A area of the elliptical fracture

b hydraulic aperture

b0 initial hydraulic aperture

𝐴𝐴𝐴𝐴

evo

modeled aperture at the nth velocity step

𝐴𝐴𝐴𝐴

slip

slip-dependent aperture at the nth velocity step

d slip displacement change

Dc critical slip distance

k fracture permeability

k0 initial fracture permeability

kn transient fracture permeability at the nth velocity step

p fluid pressure

v slip velocity

v0 background slip velocity

Δb transient change of hydraulic aperture

ΔVf additional injected fluid volume caused by fracture slip

Δε dilation parameter

μ friction coefficient

σn normal stress

σ′n effective normal stress

τp peak shear strength

Ψ dilation factor

Data Availability Statement

This manuscript is accompanied by Supporting InformationS1. The experimental data generated in this study

are available at https://figshare.com/s/2fa49f5a2240aff4785e, and the Python code for the numerical inversion is

freely available via https://github.com/Ranger-boop/Inversion_of_aperture_changes_accompanying_injection-in-

duced_fracture_slip.

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Acknowledgments

We would like to thank Thomas H. W.

Goebel and an anonymous reviewer for

many valuable comments and suggestions

that helped to improve the original

manuscript. This work is financially

supported by the Helmholtz Association’s

Initiative and Networking Fund for the

Helmholtz Young Investigator Group

ARES (contract VH-NG-1516). This

material is based on a part of the PhD

work of the first author, and thus the first

author acknowledges the PhD Research

Scholarship from Nanyang Technologi-

cal University (NTU), Singapore. Open

Access funding enabled and organized by

Projekt DEAL.

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