1

A review on fluid-injection induced seismicity with emphasis on

Hydraulic Fracturing

(DRAFT)

Konstantinos Leptokaropoulos, Monika Staszek, Szymon Cielesta

Contents

SECTION I: Mechanisms of Induced Seismicity in Injection Sites (Geothermal,

Wastewater Disposal, Hydro-Fracturing)

1.1 Introduction

1.2 Basics of Poroelasticity Theory

1.3 Mechanisms of Induced Seismicity in Injection Sites:

1.3.1 Pore Pressure

1.3.2 Thermal Effects

1.3.3 Volume Change

1.3.4 Chemical Effects

1.4 Combined Effects and Case Studies

SECTION II: Characteristics of Seismicity Related to Hydro-Fracturing: A Review and

Case Studies

2.1 Summary of Major Findings

2.2 Basic Concepts

2.2.1 Introduction on Hydro-Fracturing

2.2.2 Reported Cases and comparison to other Induced Seismicity Types

2.2.3 Fracking related seismicity mechanisms

2.3 Case Studies

2.3.1 Preese Hall, Lancashire (UK)

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2.3.2 Horn River Basin, British Columbia (Canada)

2.3.3 Geothermal fields & associated induced seismicity: The Geysers (US)

2.4 Conclusions

SUPPLEMENTARY MATERIAL

GLOSSARY – and a Brief Review on Poroelasticity Terms and Approaches

APPENDIX A – Formulation of Poroelasticity (references)

APPENDIX B – Solved Problems of Poroelasticity and Applications

ACKNOWLEDGEMENTS

REFERENCES

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SECTION I: Mechanisms of Induced Seismicity in Injection Sites

(Geothermal, Wastewater Disposal, Hydro-Fracturing)

1.1 Introduction

It is repeatedly acknowledged that long-term injection of wastewater into disposal

wells can induce small-to-moderate earthquakes, primarily because of weakening of

preexisting faults by increase of pore pressure (Ellsworth, 2013, and references therein).

Well-documented examples of seismic activity induced by fluid injection are dated back

in the 1960’s (see Nicholson and Wesson (1990) and Davies et al. (2013) for review) and

include earthquakes triggered by wastewater disposal, secondary oil recovery, solution

mining for salt, fluid stimulation to enhance geothermal energy extraction and during the

last decades, hydraulic fracturing for shale gas exploitation.

The increasing needs for ores and energy along with the recent requirement for

better usage and exploitation of the deep underground have resulted to enhancement of

the triggered and induced seismicity in urbanized and industrialized areas all over the

globe. Considerable seismic activity seems to appear and increase in areas, which were

up to day characterized by low or even no seismicity and negligible hazard levels. One of

the most discussed examples is the seismicity burst that have taken place in the central

and eastern continental United States after 2010, which has been a subject of several

researches (e.g. Ellsworth, 2013). The recent seismic episodes associated to hydro-

fracturing in Canada, USA and UK, have contributed to an increasing public reaction

against shale gas exploitation, appending seismic risk to the list of fracking-connected

environmental impacts. These raising concerns are verified by the large number of

published studies on induced seismicity, which are considerably increased during the last

years (e.g. a focus section on injection induced seismicity, published in Seismological

Research Letters, July/ August 2015).

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The comprehensive understanding of these processes are of paramount

importance in order adjust technological activities properly, controlling seismicity

occurrence and mitigating seismic hazard. In addition to seismic risk, production issues

are also incorporated. For example, Enayatpour et al., 2013 showed that for the case of gas

production presented in their work, production enhancement due to thermal cracks

declines from 150% to 20% in the first 5 years of operation, remaining at 20% thereafter.

Fluid production from the low permeability formations depends on the connectivity of

natural and induced fractures. Majer and Peterson (2007), among others, suggest that if

geothermal sites are to provide a significant increase in energy in the United States (the

US Department of Energy goal is 40,000MW by 2040), injection must play a larger role in

the overall strategy.

One may therefore find numerous recent review studies and technical reports on

seismicity in geothermal fields and other fluid injection sites (see Majer et al., 2007; Evans

et al., 2012; Ghassemi, 2012; Majer et al., 2012; Ellsworth, 2013; Committee on Induced

Seismicity Potential in Energy Technologies, 2013; Zang et al., 2014; Gaucher et al., 2015).

In addition, several recent researches have been accomplished since the last 5 years: Some

of the mostly recent researches investigate seismicity induced by fluid driven processes

connected to fluid injection sites (Aochi et al., 2013; Elsworth, 2013; Kim, 2013; van der

Elst et al., 2013; Gan and Elsworth, 2014; McGarr, 2014; McClure and Horne, 2014; Verdon,

2014), production of geothermal energy (Barth et al., 2012; Catalli et al., 2013, 2016; Dinske

and Shapiro, 2012; Elsworth and Douglas, 2013; Häge et al., 2013; Plenkers et al., 2012;

Martínez-Garzón et al., 2013, 2014; Izadi and Elsworth, 2014, 2015; Terakawa, 2014;

Trugman et al., 2014; Albaric et al., 2014; Lenglinié et al., 2014) and gas field exploitation

(conventional/ unconventional) or storage and wastewater injection (Dost et al., 2012,

2013; Cesca et al. 2013; Kraaijpoel and Dost, 2013; Lei et al, 2013; Keranen et al., 2014;

Rutqvist et al., 2014; Friberg et al., 2014; Turcotte et al., 2014; Norris et al., 2014, 2015;

Skoumal et al., 2014, 2015; Priolo et al., 2015; Roche and van der Baan, 2015; Yeck et al.,

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2015; Atkinson et al., 2015, 2016). There also several notable cases where the origin of

seismicity, in particular of magnitudes capable to induce considerable hazard, is not clear

and the potential involvement of human activities cannot be ignored (Dahm et al., 2013;

Keranen et al., 2013; LLenos and Michael, 2013; Oprsal and Eysner, 2014; Gasparini et al.,

submitted manuscript).

Concerning the methodologies and the scientific background accompanying

injection induced seismicity studies, there is a wide variety of models and techniques

applied and tested in order to obtain results of significant scientific, societal and economic

interest. In addition to seismic hazard assessment implementations (e.g. Convertito et al.,

2012; Atkinson et al., 2015b), induced seismicity catalogs constitute a very rich source of

high quality and accuracy data in order to verify the efficiency of both routine and

recently proposed methodologies and algorithms. Innovative methods have been recently

applied in spatial-temporal-energy scales which bridge the gap between laboratory

experiments and tectonic events. Some examples of the mostly recent scientific techniques

developed and tested concern, among others, calculation of absolute/relative focal

coordinates and relocalization of events focii, moment tensor inversion, source

parameters determination and analysis, stress field variations, time series analyses,

magnitude distribution and related issues, pore pressure and thermal variations effects,

combined thermal-hydarulic-mechanical-chemical effects on seismicity and on material

properties and various mechanical, numerical and stochastic models (see reference

below).

There are some specific features characterizing seismic events occurring in such

sites which discriminate those events from natural seismicity. First of all, it is important

to emphasize that most injection wells do not cause felt earthquakes. Rubistein and

Mahani (2015) state that among the approximately 35000 active wastewater disposal

wells, 80000 active enhanced oil-recovery wells, and tens of thousands of hydraulically

fractured wells every year in the United States, only a few dozen of these are known to be

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associated with induced felt earthquakes. Especially concerning hydrofracking there is

only a handful of cases worldwide (mostly in British Columbia and Alberta, Canada)

where seismicity above M~2.0 has been recorded (Davies et al., 2013). A combination of

several factors is necessary for fluid injection to induce considerable seismic energy

release (e.g. existence and properties of faults, state of stresses, the presence of fluid

pathways from the injection point to faults etc). More injection wells may be inducing

earthquakes (mostly microseismicity), but current studies are limited to the largest

earthquakes and those with the best seismological and industrial data available. It is likely

that too small to detect induced earthquakes are occurring in other sites, yet monitoring

is insufficient. In some sense, all hydraulic fracturing induces earthquakes, although

typically well below detection level: When production engineers hydraulically fracture,

they are intentionally cracking the rock, causing microearthquakes that are typically

smaller than M=0.0 (Davies et al., 2013; Rubistein and Mahani, 2015).

The most important feature of seismicity (either induced or triggered) is its direct

correspondence with technological-production processes, (i.e. injection or production

volumes/ rates/ pressures). As a result, the deep understanding of the mechanisms

involved to the seismogenesis processes should be employed for adjusting injection/

production parameters in order to control seismic activity. In such way seismic hazard

may be mitigated and maintained below acceptable thresholds. Note also that the

magnitude of the events does not solely depend on the injection-induced stress changes,

but should additionally be more related to the tectonic load and the size of the faulting

area, meaning that larger events could only occur on features that exhibit sufficient

dimensions to accommodate such a large rupture area (Rutqvist et al., 2016). Therefore,

supplementary data such as geological, hydrological, geomechanical, tectonic, records

and reports of past and historical seismicity should be taking into consideration as well,

together with the seismicity data and production process, for a robust seismic hazard

evaluation.

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Triggering is a generally delayed process since aftershocks and reservoir induced

earthquakes may occur with delay times from hours up to 10–20 yr (Parsons 2002),

depending on a variety of factors such as distance from the injection, rock properties, in

situ stresses etc. It is however, more often that seismicity onset takes place soon after the

initiation of fluid injection (at timescales up to a few weeks). Evans et al. (2012) review 41

European case histories related to fluid injection in geothermal fields, where in most cases

seismicity starts to be detected some hours after the initiation of operations. Nearly

immediate seismic response to the injection was also noticed in several stimulation wells

in The Geysers (e.g. Martinez-Garzon et al., 2014; Garcia et al., 2012; 2016). An analysis of

seismicity induced by wastewater injection in the great onshore Val d’Agri oil field, Italy,

in 2006, was performed by Improta et al. (2015). The researchers found that seismicity,

started 3 hours after the injection initiated, strictly correlates with injection operations and

temporal variations of elastic and anisotropic parameters. Over the following 7.5 years,

seismicity rate correlated with short-term increases in injection pressure. It was suggested

that seismicity was induced by rapid communication of pore pressure perturbations

along a high-permeability fault zone favorably oriented with respect to the local

extensional stress field. However, there are cases where induced earthquake occurrence

exhibit a time lag of ~20 years (e.g. at the Cogdell oil field in Texas - Davis and Pennington,

1989, or at the oilfields near Prague, the first event occurred 17 years after injection

commenced - Keranen et al., 2013).

A simple relation connecting the distance of the distance of the propagating front

to the time elapsed since the initiation of injection was proposed by Shapiro et al. (1997;

2003), taking into account the scalar hydraulic diffusivity in a homogeneous isotropic

medium. Their approach is connected to the notion of “triggering front” they introduced

in the same studies as well. Van der Elst et al. (2013) suggested that a long delay before

seismic activation implies that faults may be moving toward a critical state for years

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before they eventually fail. How long the delay will be depends on the time required for

pressure to reach the critical threshold at the fault (Keranen et al., 2013; Walsh and Zoback,

2015). This time depends in turn of a plethora of additional parameters such as injection

rate, distance and stress state of the nearby faults, rock mass permeability and reservoir

volume. A similar mechanism is probably responsible for the delayed seismic response in

cases of surface reservoir impoundment (e.g. Simpson et al., 1988; Mekkawi et al., 2004).

Note that a proportion of the delayed seismic response is also due to thermal effects which

are generally much slower processes than fluid and pore pressure transmission, as will

be discussed later on. Seismicity may occur at distances more than 10km from the injection

point and at depths remarkably greater than the injection (Rubinstein and Mahani, 2015).

Recent reports have argued that seismicity may be induced at 20 km or more from the

injection point (Keranen et al., 2014). Mulargia Bizzarri (2014) state that the injection of

pressurized fluids in the subsoil may trigger destructive earthquakes on active faults at

distances over a few tens of kilometers and therefore, should be effected with great care

to avoid anthropogenic seismic Hazard. Seismicity may also insist for a period of time

following the termination of stimulation. Dieterich et al. (2015) showed that both the time

needed for excess pore pressure diffusion and rate-state properties of the faults (Richards-

Dinger and Dieterich, 2012) are responsible for the persistent of seismic activity after shut-

in. The authors conclude that once this delayed nucleation process resulting from rate-

state friction is underway, it is largely self-driven and relatively insensitive to the

subsequent stressing history.

An alternative mechanism that may lead to triggering relative to large destructive

earthquakes, deals with pore pressure waves propagation, proposed by Mulargia &

Bizzarri (2014). The authors found that small fluid overpressures trigger nearby tectonic

faults and pore pressure wave propagates with such a delay that no matter how fast one

reacts to the onset of minor precursory seismicity, it will be too late. In fact, the fluid

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pressure pulse propagates independently of what is done at the source, even after the

whole process has been shut off. Fluid-Pressure waves appear therefore, to play a major

role in earthquake triggering, being capable to account for aftershock delay without any

further assumption (Mulargia and Bizzarri, 2015). Another alternative to the

poroelasticity theory, the Non-Critical Precursory Accelerating Seismicity Theory (N-C

PAST) was proposed and applied in both tectonic and induced seismicity regimes by

Mignan et al., (2007) and Migan, (2008; 2012; 2016). This theory, although needs further

testing, seems to be in satisfactory agreement with the two descriptive laws of induced

seismicity, i.e. the linear relationship between injected fluid volume and cumulative event

number and the parabolic induced seismicity spatial envelope radius.

The consideration of pure shear (double couple) component is usually proven

insufficient for describing focal mechanisms of events occur in fluid injection sites.

Earthquakes associated with geothermal areas typically involve significant volumetric

changes (e.g. Foulger and Long, 1984; Miller et al., 1998; Ross et al., 1996; 1999). The

industrial processes of hydraulic fracturing commonly involves both tensile and shear

failure (Ellsworth, 2013). Interpretation of well constrained micro-seismic events indicate

rock failure in shear, and shear slippage on newly formed or pre-existing fracture planes

(Pearson, 1981) as well as tensile fracture initiation (Julian et al. 2010). Both of these failure

modes can be related to injection induced pore pressure increases in a critically stressed

rock and/or fractures (Ghassemi and Tao, 2016), as will be discussed later on. Rocks fail

in tension when the pore pressure exceeds the sum of the least principal stress, and the

tensile strength of the rock, forming an opening-mode fracture that propagates in the

plane normal to the least principal stress.

Julian et al., 2010 studied an injection experiment that took place in 2005 at the Coso

geothermal field in eastern California. As very frequently evident in such areas, seismicity

exhibited a swarm-like activity with similar non‐double‐couple mechanisms involving

volumetric changes (increases). Implosive mechanisms were completely absent during

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the injection phase, probably due to either increased fluid pressure or tensile stresses

caused by thermal contraction. Moreover, the fault plane was found far from the nodal

curve of the focal mechanism, bisecting the dilatational field. This fact may imply that

hydraulically drivel tensile crack dominates the failure process (Julian et al., 1998), the

existence of heterogeneous stress field and possibly, the induction of thermal stresses by

introduction of cold fluid. In addition Johnson (2014a,b), studied source mechanisms for

twenty seismic events in The Geysers enhanced geothermal field area around Prati-32

injection well. They found evidence indicating the existence of a significant opening mode

together with shear faulting and interpreted the seismic events using a source model of a

shearing fracture with wing-cracks, which could explain the substantial volumetric

component.

1.2 Basics of Poroelasticity Theory

The available literature suggests that in several cases the poroelastic effects are the

dominant mechanism related with induced and triggered seismic activity and for that

reason a more detailed description of poroelasticity is presented here. It is well established

by both experimental observations and theoretical studies that the mechanical behavior

of elastic solids strongly depend on whether they are saturated with water or they are

primarily dry. Poroelasticity theory was originally developed by Terzhaghi (1923, 1925)

for one dimensional cases and was further generalized by Biot (1941), still being

extensively studied and improved (see also at Glossary). Poroelasticity is capable to

explain a variety of cases of induced seismicity and related phenomena, over time periods

from hours to years, but yet, no satisfactory, generalized solutions have been proposed.

As stated in Ghassemi and Tao (2016) the fundamental mechanisms in reservoir seismicity

are still not adequately understood and several key questions remain unresolved in the

analysis of micro-seismicity, namely the variation of seismic activity with injection rate,

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delayed microseismicity, the relation of the stimulated zone to the injected volume and

the injection rate, the connectivity of the fractures hosting micro-seismic events and the

resulting reservoir permeability. A possible reason for the limited understanding of these

processes is that other phenomena such as thermic effects, chemical reactions, visco-

elastic behavior of material etc, may play an important role on mechanical response of the

rock matrix and consequently, on the induced seismicity in deep reservoirs. These

complex phenomena have only recently been thoroughly modelled, studied and

combined with each other (e.g. The coupled model by Taron et al. (2009) incorporates

features unique to fractured reservoirs involving the undrained pressure response in a

dual-porosity medium and with chemo-mechanical effects on deformation and on

transport). For example, it is shown that injection-induced pressure changes (if pressure

is above a certain threshold) results in an immediate response of microseismic activity,

first along major permeable fractures connected to the well, and later in the fractured

rockmass between major fractures. Thermal effects involve mainly cooling contraction of

the reservoir rock, which results in stress changes that can strongly contribute to

stimulation and microseismic activity, especially in geothermal fields where high

temperature differences between the injected fluid and the reservoir environment are

evident.

Stimulation processes may result to changes in various reservoir properties, such

as Young modulus, fracture porosity, opening of cracks and flow transmissivity along

fractures, permeability etc (e.g. Rutqvist et al., 2016 and references therein). Martinez-

Garzon et al. (2014) found that stress tensor orientation changes may be related to

increased pore pressure and the corresponding changes in poroelastic stresses at reservoir

depth. These changes result in turn to seismically release of strain energy. Inversely, the

locations and temporal variation of the induced earthquakes are routinely used as

indicators to characterize patterns of permeability in reservoirs (Majer and Peterson,

2007). However, this is a rather complex issue, since under different circumstances

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earthquakes can be more closely associated with either relatively low or relatively high

permeability.

Two mechanisms play a key role in the interaction between the interstitial fluid

and the porous rock, leading to apparent time-dependent rock properties (Detournay &

Cheng, 1993): An increase of pore pressure induces a dilation of the rock and compression

of the rock causes a rise of pore pressure (if the fluid is prevented from escaping the pore

network). Therefore, fluid extraction or injection induces stress changes in fluid saturated

rock formations and conversely, applied loads to an aquifer (by infrastructures,

atmospheric pressure, earth and ocean tides, tectonic activity, water reservoir level

changes, etc) produce water-level changes in wells. The theory of poroelasticity has been

proposed to investigate the time-dependent coupling between the deformation of the

elastic solid skeleton and fluid flow within the skeleton, i.e. the coupling between changes

in stress and variations of fluid pressure (Wang, 2000; Verruijt, 2013, see Glossary as well).

Poroelasticity may be recalled to interpret a variety of phenomena associated with

induced seismicity such as the initially unexpected connection between a causal event and

its subsequent effect and the time delay between water reservoir impoundment and

initiation of seismic activity. The time periods that poroelastic phenomena are evident

range from hours to several years. The principal assumptions in poroelasticity theory as

stated by Zoback (2007) are:

o There is an interconnected pore system uniformly saturated with fluid.

o The total volume of the pore system is small compared to the volume of

the rock as a whole.

o Pressure in pores, total stress acting on the rock externally and stresses

acting on individual grains are considered in terms of statistically

averaged uniform values.

Following this concept, an increase of fluid pressure causes the medium to expand

just as an increase of temperature causes a similar expansion. The magnitude of the solid-

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to-fluid coupling (i.e. a change in applied stress produces a change in fluid pressure or

fluid mass) depends on the compressibility of the framework of the porous material, the

compressibility of the pores, solid grains and pore fluid, and the porosity of the medium

(Wang, 2000). It is to be expected that the compressibility of the porous medium is

considerably larger than the compressibilities of the two constituents (i.e. fluid and solid

particles), because the main mechanism of soil deformation is not so much the

compression of the fluid or the particles, but rather the deformation due to a

rearrangement of the particles, including sliding and rolling of these particles over each

other (Verruijt, 2013).

One manifestation of poroelasticity is that the stiffness of a fluid saturated rock will

depend on the rate at which external force is applied. When force is applied quickly, the

pore pressure in the rock’s pores increases because the pore fluid is carrying some of the

applied stress and the rock behaves in an undrained matter. In other words, if stress is

applied faster than fluid pressure can drain away (e.g. coseismic stresses are connected to

such undrained conditions, Cocco and Rice, 2002), the fluid carries some of the stress and

the rock is relatively stiff. However when an external force is applied slowly, any increase

in fluid pressure associated with compression of the pores has time to drain away such

that the rock’s stiffness is the same as if no fluid was present. Therefore there is a trade-

off among loading rate, permeability of the rock and viscosity of the pore fluid (Zoback,

2007).

Besides long-term changes in permeability associated with chemical reactions and

pore redistribution, the dynamical response of saturated porous media to rapid stress

transients (dynamic stresses) can also significantly affect the effective permeability of

saturated porous media because of poroelastic effects. Maurice Biot developed the first

theoretical model of the propagation of acoustic waves in saturated porous media in the

mid-1950s. Biot found two independent solutions to the propagation of acoustic waves in

porous media that he referred to as waves of the first and second kind (see Huber et al.

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(2015) for an application concerning the dynamic response of fluid saturated media). As

mentioned earlier, Mullargia and Bizzari (2015) presented a mechanism of pressure wave

propagation which is capable to account for delayed aftershock activity without any

further assumption. However, in the quasi-static approach which is most commonly

applied in several cases, elastic wave propagation and pressure gradients are considered

to be second order phenomena and are usually neglected.

1.3 Mechanisms of Induced Seismicity in Injection Sites:

The most prominent mechanisms of Induced Seismicity on fluid injection sites and

their characteristics are presented here. The combined effect of those mechanisms is also

described and demonstrated by case studies.

1.3.1 Pore Pressure

An increase of pore fluid pressure can decrease static friction and thereby facilitate

seismic slip on favourably oriented planes, when deviatoric stress field is present. In such

cases, the seismicity is driven by the local stress field, but triggered on an existing fracture

by the pore-pressure increase. At higher pressures, tensile microseismicity can also be

induced by the increasing of pore pressure which enhances crack opening and new

fractures in the rock mass (Majer et al., 2007). Pore pressure in the rock matrix tends to

gradually increase in response to injection into the fracture, but the increase is not

monotonic and episodes of pore pressure rise and drop are observed as well. This is

because the pore pressure responds to three driving mechanisms: Fracture opening and

poroelastic deformation of the rock matrix, pressure diffusion, and cooling of the

fluid/matrix (Ghassemi & Tao, 2016), as will be discussed below.

1.3.2 Thermal Effects

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Heat transport and conductive temperature changes have a significant effect on the

rockmass stress state and should be therefore considered as well. Temperature changes

are mainly driven by advection and conduction (radiation can be discarded in this case).

Advective heat flow is coupled to mass transfer of fluids and, thus, dominant in rock

fractures that serve as a heat exchanger. On the other hand, conductive heat flow

governed by Fourier's law is the ruling mechanism in an impermeable rock matrix

(Gaucher et al., 2015). Thermal shock occurs when a material’s temperature is changed

over a short period of time such that constituent parts of the material deform by different

amounts (Enayatpour et al., 2013).

Temperature is incorporated in thermoelasticity theory in analogous way in which

pore pressure is involved in poroelasticity. Similarly heat conduction corresponds to fluid

flow and entropy corresponds to fluid mass. Constant temperature (isothermal) and

insulated (adiabatic) boundary conditions correspond to constant pore pressure (drained)

and no-flow (undrained) boundary conditions, respectively, in the poroelastic case. Both

Isentropic and adiabatic conditions are equivalent to undrained conditions in

poroelasticity (Wang, 2000). Concerning the thermo-elastic coupling, temperature

changes produce considerable thermal stresses, but, inversely, stress changes do not

significantly alter the temperature field for most of known materials.

When cool water flows into hot rock voids, thermally induced fractures are opened

in the rock matrix, because of the high temperature difference, potentially accompanied

by water flashing to steam (Perkins and Gonzalez, 1985). For relatively small temperature

differences between the injection water and the rock matrix induced thermal stresses are

relatively small and develop very slowly, localized in the central region of the fracture

where most of the cooling occurs. In high temperature contrast, however, the cooling-

induced fracture opening is increased (Ghassemi & Tao, 2016). Fracture faces contract by

cooling and tend to lose their frictional resistance, becoming more prone to stress release

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by seismic slip (Majer and Peterson, 2007). Cooling could also make the rock mass more

brittle, especially when injecting near the brittle-ductile rock transition, progressively

extending the stimulation zone downwards, to the originally ductile layers (Rutqvist et

al., 2016).

1.3.3 Volume Change

As fluid is produced from (or injected into) an underground resource, the reservoir

rock may compact or be stressed. These volume changes cause a perturbation in local

stress conditions, which are already close to the failure state (geothermal systems are

typically located within faulted regions under high states of stress). This situation can lead

to seismic slip within or around the reservoir. A similar phenomenon occurs where solid

material is removed underground, such as in mines, leading to “rockbursts,” as the

surrounding rock adjusts to the newly created void space (Majer et al., 2007).

1.3.4 Chemical Effects

Chemical effects and their coupling to thermal-hydraulic-mechanical processes are

a very complex issue. Fluids that are injected into a reservoir are typically far from

geochemical and thermal equilibrium with minerals in the host rock. As minerals

precipitate from the injected fluid and dissolve from the rock, changes are incurred in the

porosity and permeability of the fracture system (Taron and Elsworth, 2009). In addition,

geochemical alteration of fracture surfaces, may result to variation of friction coefficient,

leading to microseismicity. However, Pennington et al. (1986) made the hypothesis that if

seismic barriers evolve and asperities form (resulting in increased friction), larger events

may become more common. In general, small progress has been achieved so far in

modelling geochemical processes coupled to the thermo-hydro-mechanical processes in

fractured reservoirs (Jing et al., 2002; Bächler and Kohl 2005). This is probably due to the

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small impact that these processes are believed to have to induced seismicity, at least on a

short time scale, but also to the complexity of the topic (Gaucher et al., 2015).

1.4 Combined Effects and Case Studies

There are several recent studies that attempt to combine the influence of the

aforementioned factors, since it has been accepted that a coupled effects provide a more

comprehensive approach. The coupled thermo-poroelastic effects have impact on

reservoir in situ stress state and fracture zone evolution, such that consideration of

injected volume alone is not adequate for understanding the spatio-temporal distribution

of injection related seismic activity. Abundant microseismicity is likely to be triggered in

association to thermal contraction in the vicinity of the well where cool water is injected.

When the rock matrix permeability is low (Delaney, 1982) and fluid flows mainly within

deformable fractures or a fault, coupling between temperature, pore pressure, and stress

may result in delayed rock matrix and/or natural fracture failure, potentially producing

delayed seismicity (Ghassemi & Tao, 2016). If the heat is transferred dominantly by

conduction, thermal fracturing induced seismic activity exhibits no preferential direction

or orientation. In contrast, if pore fluid advection phenomena also facilitate heat transport,

anisotropy on the microseismicity distribution around the well may occur caused by

preferential orientation of conductive fractures (Martinez-Garzon et al., 2014).

As injection rate increases, the pressure builds up in the fractures causing them to

open more rapidly (and ultimately to propagate) with potential for induced seismicity at

early times. Compressing the surrounding rock and increasing its pore pressure can cause

slippage on other favorably oriented fractures (e.g, Safari and Ghassemi, 2015). On the

other hand, a faster injection rate increases the cooling effect on the rock matrix stress and

pore pressure compared to a slower injection case. Due to the fact that the pressure

responses are immediate, whereas the thermal effects are generally much slower, the

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microseismic activity (number of events and energy release) generally responds quickly

to pressure changes induced by changes in injection rate. In many rock types (e.g. granitic

rocks), fluid diffusivity is an order of magnitude higher than thermal diffusivity so that

thermal stress effects tend to develop later than pore pressure effects. This means that the

rate of microseismic activity around an injection well can be controlled by regulating the

injection rate (Rutqvist et al., 2016). Seismic events during peak injections tend to occur at

greater distances from the injection well, preferentially trending parallel to the maximum

horizontal stress direction. On the other hand, at lower injection rates the seismicity tends

to align in different directions suggesting the presence of a local fault. Furthermore,

increases in fluid injection rates also coincide with a decrease in b values (Martinez-

Garzon et al., 2014), which may subsequently increase after injection ceases (Goebel et al.,

2016). Martinez-Garzon et al. (2014) also suggested that regardless of the injection stage,

most of the induced seismicity results from thermal fracturing of the reservoir rock.

However, during peak injection intervals, the increase in pore pressure may likewise be

responsible for the induced seismicity.

The complete effect on seismicity is a result of combined Thermal-Hydrologic-

Mechanical-chemical (THMC) forces operate upon temporally dynamic and spatially

variable fluid transport properties, such as permeability, porosity, and fracture

interconnectivity (e.g. Taron and Elsworth, 2009; Taron et al., 2009). Fluid injection at

pressures intermediate between the minimum principal stress and the Coulomb stress

will induce shear failure within enhanced geothermal reservoirs (Hubbert and Rubey,

1959; Majer et al., 2007) and may trigger seismicity (Grasso and Wittlinger, 1990). Induced

seismicity results from fluid injection and is expected to migrate within the reservoir with

time as driven by the various interactions of thermal, hydraulic, mechanical and chemical

(THMC) processes, which also migrate through the reservoir on different length-scales

and time-scales (Walsh, 1965; Taron and Elsworth, 2009). Note that changes in pressure

19

and temperature induce displacements that consequently lead to a new change in

pressure distribution. The coupled effects control the development of permeability, heat-

transfer area, and thereby thermal output of the reservoir, together with the evolution of

induced seismicity (Izadi and Elsworth, 2013). Majer et al. (2007) reviewed the potential

mechanisms of induced seismicity in geothermal environments: Pore pressure increase

(effective stress reduction), temperature decrease (thermoelastic strain), change of fluid

volume due to fluid withdrawal/ injection, and chemical alteration of fracture surfaces.

The extent to which these subsurface phenomena are active within any specific situation

is influenced by a number of local and regional geologic conditions that can include the

orientation and magnitude of the deviatoric stress field in relation to fault geometry, the

extent of faults and fractures, the rock mechanical properties, hydrologic factors and

natural (background) seismic activity. Majer et al. (2007) suggest that since a variety of

factors are needed to come all together at the right time and place for producing a large

energy release, a significant earthquake occurrence should not be a common

phenomenon. This statement has been verified by the observed seismicity cases up to date

in geothermal systems and fluid injection sites worldwide (Elsworth, 2013; Davies et al.,

2013).

Izadi and Elsworth (2013) showed that the rate of propagation of the

hydrodynamic front is approximately twice as rapid as the thermal front. Therefore, the

very short-term response (days to months - figure 1.1 by Izadi and Elsworth, 2013) is

controlled by fluid pressure and effective stress effects relative to the initiation of

stimulation. At later time (month to years), thermal effects specifically, or chemical effects

possibly, may contribute to the seismicity when the seismicity front lags behind the

hydrodynamic front due to small changes in pressure. According to these mechanisms,

the authors associated the large early-time events with the fluid front and the lower

seismic magnitude later-time events with the transit of the thermal/chemical front. For

20

later time (over 1 year), thermal drawdown and potentially chemical influences

principally trigger the seismicity, but result in a reduction in both the number of events

and their magnitude, with respect to the size of the disturbance and the volume of the

area being affected (Majer and Peterson, 2007; Izadi and Elsworth, 2013). During the shut-

in period the rates of moment release typically drop, however, acceleration of moment

release rates may be observed as well at larger distances from the injection location (Grob

et al., 2016).

Figure 1.1. It is shown that the rate of propagation of the hydrodynamic front is

approximately twice as rapid as the thermal front. This illustrates that most of the seismic

activity is triggered by hydraulic effects at early times (days to month) relative to the

initiation of stimulation. At later time (month to years), thermal effects specifically, or

chemical effects possibly, may contribute to the seismicity when the seismicity front lags

behind the hydrodynamic front due to small changes in pressure. By following the

propagation of both fluid pressure and thermal fronts through the reservoir with time,

we associate large early-time events with the fluid front and the lower seismic magnitude

later-time events with the transit of the thermal/chemical front (Izadi and Elsworth, 2013).

21

Enayatpour et al. (2013) showed that injection of cold fracturing fluid into reservoir

rock, induces thermal fractures perpendicular to hydraulic fracture. Figure 1.2 shows the

thermal cracks of depth d perpendicular to hydraulic fracture in a horizontal wellbore in

a tight formation. Hydraulic fractures tend to grow normal to the minimum horizontal

stress, Shmin. As the cold fluid is injected into the fractures, the transient heat diffusion

causes the heat to be transferred into the hydraulic fracture as it is colder. This heat

transfer, cools down the zone neighboring the fracture and the rock shrinks parallel to

hydraulic fracture length. Since the reservoir rock is confined, thermal stresses are created

in rock, leading to thermal cracks. Here we are looking at the physics behind this

phenomenon and come up with a formulation of a model to obtain the depth d along x-

axis, distance b, and width t of thermal cracks.

Figure 1.2. Thermal fractures created perpendicular to the hydraulic fracture

direction (Enayatpour et al., 2013). It is demonstrated that the thermal cracks have to open

against the maximum in-situ horizontal stress SHmax, perpendicular to the hydraulic

fracture. As we see from numerical simulations, these thermal cracks do not extend far

from hydraulic fracture face, hence, we can assume these cracks as straight fractures. This

observation can justify that as the thermal cracks open, they do not interfere with heat

transfer in x-direction.

22

Izadi and Elsworth (2014) attempted to understand the mechanisms of seismic

triggering due to fluid and thermal effects for the proposed stimulation of the Newberry

enhanced geothermal site, Oregon, USA. In doing so, they applied the Taron et al., (2009)

THMC numerical simulation method that couples the multiphase, multi-component, non-

isothermal thermodynamics, reactive transport, and chemical precipitation/dissolution

phenomena with the stress/deformation analyses. They correlated the evolution of

seismicity with the transit of the hydrodynamic, thermal and chemical fronts within a

short-term (~21 days) stimulation, to determine associations of events with the various

causal mechanisms. They found that the largest event occurs at the location (outward

from injection) where the stress drop is highest and on the largest fracture, while the

number of seismic events decays with time and distance from the injection point at each

reservoir. They associated large early-time events with the fluid front and later lower

seismic magnitude events with the transit of the thermal (and chemical) front. Large

events at early-time (days to month) occur due to the fluid front. Over longer periods of

time (month to years) smaller seismic magnitude formed as a result of thermal (-chemical)

front within reservoir.

All deformations resulting from thermal, pore pressure, and flow are mechanical

deformations and result in fracture aperture variations. For relatively higher permeability

rocks and higher cooling rates, a zone of tensile stress develops for some time which can

produce tensile microseismicity. Ghassemi and Tao (2016) demonstrated by numerical

modeling that the lower the matrix permeability, the stronger the stress shadow and its

stress effects on pore pressure, and the stronger the thermal effect on stress. This

phenomenon is more conspicuous for the case of 80 K injection cooling (Figure 3). Note

that pore pressure tends to rise in the beginning in response to fracture (element) opening

at the injection well. But then, cooling dominates and causes a substantial reduction in

pore pressure before leak-off prevails and the pore pressure begins to increase (at about

23

24 days). The initial peak in pore pressure can be explained by matrix compression

associated with natural fracture opening in response to injection cooling. This peak is not

observed for the isothermal injection case (no cooling) as the fracture opening is minimal

in that case.

Figure 3. Induced pore pressure history in the rock matrix (Ghassemi and Tao, 2016). The

peak of pore pressure change propagates into the rock with time but its intensity is

reduced with distance. The lower the matrix permeability, the stronger the coupling

effects on pore pressure.

24

SECTION II: Characteristics of Seismicity Related to Hydro-Fracturing: A

Review and Case Studies

2.1 Summary of Major Findings

Horizontal hydraulic fracturing has been routinely used for shale gas exploitation

since the early 2000’s, especially in the United States and Canada. More than 1 million

wells have been created for Hydraulic Fracturing operations. Amongst them only 6 cases

have been currently connected with M>2.0 and even fewer reported for which events were

felt at the surface. In general, the energy release of fracking associated seismicity is much

less than the other kinds of Induced Seismicity (e.g. mining, reservoir impoundment).

Intensity at the surface is also likely to be smaller due to the greater depths (>2000m) at

which shale gas is extracted compared with other technologies.

Two classes of events related to hydro-fracturing operations can be identified.

Seismicity directly associated with fracking, generally implies large but highly localized

stresses, therefore fresh fractures occur on small volumes of the bulk rock and

consequently, the size of the events is also small. Literature distinguishes one more class

of events, the so called ‘fault reactivation events’. Those events are larger and they are

considered to be caused by fluid transmission and pore pressure changes which reduce

the effective normal stress leading to sheer failure. The energy released by those events is

several orders of magnitude greater than the induced microseismicity energy. Fault

25

reactivation events seem to have differences from fracking events in terms of spatio-

temporal-size distribution and source mechanism.

Studies performed up to days demonstrate variable and in some cases

contradictory results. However there are some characteristics for which most of the

researches agree, or provide similar findings. Note that this report considers only

hydraulic fracturing operation and no further injection of wastewater (which is not

permitted in EU).

1) Event Detection (Network)

Regional/ National networks can only detect the strongest events, since the closest

stations are essentially located tens or hundreds of kilometers from the fracking sites.

Local, surface networks may detect much more events. However, the majority of fracking

induced events have typically M<0.5 or even lower, which roughly corresponds to the

detection level of the network (signal to noise ratio). Therefore, recording and location

analysis of microseismicity requires specialized seismic sensing equipment and

processing algorithms. Microseismicity can only be sufficiently analyzed by either

downhole geophones (in one or more boreholes) or massive surface arrays (hundreds or

thousands of instruments), such that the signal to noise ratio is enhance by stacking

techniques (e.g. Grechka, 2010; Gei et al., 2011). In any case the evaluation of a network

performance is a very important for sufficiently recording of local seismic activity

(Mahani et al., 2016).

2) Locations

As discussed in (1) the detection of microseismicity by regional/ local networks is

problematic. The location of those events is even harder. Absolute locations are hard to

be obtained with acceptable vertical and horizontal errors. Relative locations and

distances from the monitoring well/ stations are constrained with better accuracy, also in

26

combination with waveform data elaboration. A routinely applied relative relocation

technique is the one by Waldhauser and Ellsworth (2000) which uses differential travel

times of P and S waves to refine the initial earthquake hypocentral location. On the

contrary, surface and downhole arrays provide very accurate locations, yet the data are

usually not available by the operators. Template event cross-correlation signal detection

techniques can also be applied to detect smaller magnitude events by local networks (e.g.

Holland, 2013; Friberg et al., 2014).

3) Waveforms

Signals of hydro-fracking events usually demonstrate remarkable similarity.

Waveforms can be easily compared with each other by superimposing the signals from

different events (recorded in certain stations and components) after normalizing them on

their maximum amplitude. Waveform similarity, especially among the largest events (for

which data is more robust) indicate they all sources are tightly localized and the seismic

energy was radiated through identical travel paths (e.g. Green et al., 2012; Friberg et al.,

2014). Waveforms are usually utilized for relative and absolute location, moment tensor

inversion and magnitude determination among clusters of events with similar recordings.

4) Source Mechanisms

Most of seismic activity comprises low magnitude Mode-1 (Tensile) failures. These

events usually demonstrate significant CLVD and ISO components. On the other hand,

triggered (fault reactivation) events are larger, caused by fluid transmission and pore

pressure changes. The energy they released is several orders of magnitude greater than

the induced microseismicity energy and their focal mechanisms are highly DC. Hybrid

events, with combined characteristics (both sheer and tensile mechanisms) are also

present.

5) Magnitudes

27

Hydraulic fracturing usually causes events with magnitudes much lower than the

detection ability of surface regional, even local networks (M<0.5 or even lower). This fact

may be connected with the water volumes used for fracking which are usually

significantly lower than those injected during waste water disposal or geothermal

applications. Fracking events are considered to be directly associated with crack opening

due to the high pressure water injection. However there may be stronger events (with

M>1.0 up to 4.6) which are believed to be connected with reactivation of optimally for

failure oriented fault segments. According to Warpinski et al. (2012), deeper sources

demonstrate higher magnitudes.

6) b-values

Fracking events usually demonstrate a b-value~2.0, whereas fault reactivation events

have a lower b-value~1.0 (e.g. Maxwell et al., 2009; Downie et al., 2010; Kratz et al., 2012).

The changes of the b-values in time and among specific clusters (detected by spatio-

temporal, size and focal mechanism criteria) are considered to be a useful tool for

discrimination between fracking and fault reactivation events. However, an accurate and

robust determination of b-value (and its uncertainties) requires relatively large datasets

and wide magnitude range, which are not always available in several cases of fracking

induced seismicity.

7) Geomechanical Features

Pore pressure perturbations due to fluid injection result to change of the normal

stress on faults causing failure. The magnitudes of the events depend on area of fault and

amount of slip. Potential mechanisms for the transmission of a pore fluid pressure pulse

or fluid into a fault to cause reactivation are the direct injection into the fault, fluid flow

through the stimulated or existing hydraulic fractures and/or through permeable strata

and along bedding planes. The hydraulic fractures typically propagate parallel to the

28

maximum stress direction in the reservoir. Contrarily, in areas of low stress differences,

the hydraulic fracture pattern can be quite complex, as there is no preferential direction

for the fracture to grow. Evidence also show that the fracture propagation is much more

oriented on the horizontal than the vertical direction across the well (Warpinski, 2013).

Unmapped faults are very often evident and microseismicity is routinely used to map the

progress of fractures and identify fault structures. In some cases subseismic faults may

exist and only become apparent when illuminated with microseismicity (e.g. Maxwell,

2013).

8) Seismicity Clustering (spatial – temporal – size – associated with fracking

processes)

Events epicenters are usually located close to the injection well-head and the depth

at which fracking has taken place. Both field observations and geomechanical simulations

(Rutqvist et al., 2013; 2015) confirm that the fault activation (shear failure) occurred

simultaneously with the hydraulic fracturing (tensile failure), starting near the well and

propagating away from the well in repeated microseismic events. The events are mostly

concentrated in the close vicinity of the injection stages, much closer than the 5km radius

boundary (usually some hundred meters) proposed by Davis and Frohlich (1993). The

maximum magnitude events occur from one to several hours after the initiation of

injection, whereas smaller size events occurs immediately. Even where faults are

intersected by the treatment wells, there is often a time lag of several hours between the

start of pumping and fault reactivation. The delay between pumping and the reactivation

of some faults may in part be because the fault into which fluid is injected has inherent

storage capacity and transmissibility characteristics, or due to the time period required

for the transmission of fluid pressure by pressure diffusion and due to poroelasticity (i.e.

coupling of stress in the solid skeleton of the rock to the in-situ fluids - stress changes can

29

affect the fluid pressure in a natural fracture without fluid flow, Lacazette and Geiser,

2013).

9) Risk Mitigation

Hydraulic fracturing is generally considered to be of lower risk than disposal wells

for inducing large earthquakes, because the injections are short-term and add smaller

amounts of fluid into the subsurface compared to most disposal wells (CRS report, Folger

and Tiemann, 2015). However, the larger events may cause damage to the well casing and

therefore slow down the production and potentially, cause undesirable environmental

impacts. Many researchers have proposed traffic light systems, adjusted to the conditions

and the potential (e.g. maximum magnitude estimates) of the fracking site. Generally, the

nucleation and magnitudes of the events are partially controlled by the fluid injection

volumes and rates. In addition, fluid flow back usually leads to the inverse effect,

reducing the pressure at the perforation depth and consequently lead to decrease of

seismic activity.

2.2 Basic Concepts

2.2.1 Introduction on Hydro-Fracturing

Shale is the rock equivalent of mud, just as sandstone is the rock equivalent of sand.

Shale formations are usually found at depths between 2-6 km and they may exhibit

horizontal extend over 1000km. Their permeability is characterized as low to very low

(grain size 4µm) and their porosity is typically 2-20%. The so called “Black Shales” are the

main hydrocarbon source which are formed under anoxic conditions (Turcotte et al.,

2014).

Hydro fracturing is a common technique applied for shale gas exploitation. The

EPA (Enviromental Protection Agency of Ireland) defines “fracking” as “the process of

directing pressurized fluids containing any combination of water, proppant, and any added

30

chemicals to penetrate tight formations, such as shale or coal formations, that subsequently

require high rate, extended flowback to expel fracture fluids and solids during completions”.

Fracking was pioneered in 1947. While this experiment failed to produce a significant

production increase, it did mark the beginning of hydraulic fracturing. Since that time,

this completion technique has been used in over 1.2 million wells. Modern day fracking

did not begin until the late 1990s when it became commercially viable. This originated

when George P. Mitchell created a new technique (“slickwater”, i.e. low viscosity fluid

with proppant injected at high pressure), which utilized hydraulic fracturing, and

combined it with horizontal drilling (Hefner, 2014).

The ability of fluids to flow through rock is controlled by a property called

permeability, itself a function of porosity. The pore space in rocks is made up of a diverse

range of voids in the solid rock matrix and includes cracks induced by stresses. The

aim of fracking is to massively improve permeability by creating (or reopening) a locally

dense network of open and connected – i.e. hydraulically conductive – fractures (Healy,

2012).

A recognized complicating factor in many shale gas formations is that of elastic

anisotropy. Many rocks, including common hydrocarbon reservoir sandstones can be

considered as elastically isotropic – i.e. their elastic properties, such as Young’s modulus

and Poisson’s ratio, do not vary with direction, as their constituent clay minerals are platy

in form and are then compacted into aligned parallel layers. This gives an important and

measurable directionality to their elastic and mechanical response. The precise physical

nature of the control exerted by lithology anisotropy on rock fracture is poorly

understood; although the effects are well known/documented. Many anisotropic rocks

such as shale fail much more easily/frequently along/parallel to their fabric than across it

and the orientation of any cross-cutting fractures is different to those orientations

predicted for an isotropic rock in the same stress field. These observations have

31

potentially important implications for the connectivity, and therefore permeability, of any

fracking induced fracture array in anisotropic shales. The exact details of the created

fracture network are critical to the effective extraction of shale gas, but also for the

ultimate fate of the injected fracking fluid (e.g. Harper, 2011). A better mechanical

understanding of rock fracture in anisotropic rocks will help improve the predictive

capabilities of geomechanical models, which also need to be tested under controlled

conditions (Healy, 2012).

The nucleation and propagation of hydraulic rock fractures are chiefly

controlled by the local in situ stress field, the strength of the rock (stress level needed to

induce failure), and the pore fluid pressure. Temperature, elastic properties, pore water

chemistry and the loading rate also have secondary influence. It is important to

recognize that the fracking process of pumping large volumes of water into a borehole

at a certain depth cannot control the type of fractures that are created or reactivated

(Healy, 2012). The array of fractures created and/or reactivated or reopened depends on

a complex interplay of the in situ stress, the physical properties of the local rock volume

and any pre-existing fractures, and the pore fluid pressure (Phillips, 1972). This

could have implications for the risk of ground water contamination by fracking

operations, as the fracture network generated by the fracking fluid could be complex and

difficult to predict in detail.

In brief, the technique involves pumping a water-rich fluid into a borehole until

the fluid pressure at depth causes the rock to fracture. The pumped fluid contains small

particles known as proppant (often quartz-rich sand) which serve to prop open the

fractures. After the fracking job, the pressure in the ell is dropped and the water

containing released natural gas flows back to the well head at the surface. The

boreholes themselves are often deviated away from the vertical, into subhorizontal

orientations, to ensure better and more efficient coverage of the targeted shale gas

32

reservoir. The fracking fluid also contains small amounts (typically < 2% in total by

volume, or even less) of chemical additives such as acid to help initiate fractures, corrosion

and scale inhibitors to protect the borehole lining and gelling agents to alter the fluid

viscosity (e.g. British Geological Survey).

Commonly, the “plug-and-perf” stimulation technique is employed in wells with

cemented liners. Plug-and-perf includes pumping down a bridge plug on wireline with

perforating guns to a given horizontal location near the toe of the well. The plug is set,

and the zone is perforated. The tools are then removed from the well, and the fracture

stimulation treatment is pumped in. The set plug or ball-activated plug then diverts

fracture fluids through the perforations into the formation. The stage is completed, the

next plug and perforations are initiated, and the process is repeated moving back to the

heel of the well (http://www.undeerc.org/).

The recent large-scale increase in unconventional oil and gas production may

result in considerable environmental. Injecting large volumes of fluid into the subsurface

is not without risk, and recent reports in the media and, to a much lesser extent, in the

scientific literature have highlighted the potential for the following (Healy, 2012; Turcotte

et al., 2014):

need of large volumes of water

contamination of ground water, and possibly even drinking water, with

natural gas and other chemicals

emissions of volatile components, such as CO2 or methane, into the

atmosphere

the leakage of contaminated drilling waste fluid from storage ponds

induced seismicity

2.2.2 Reported cases and comparison with other Induced Seismicity Types

33

There is a variation of the strongest events magnitude related to different kinds of

anthropogenic activities (updated from Davies et al., 2013): mining (5.6), oil and gas field

depletion (7.3), water injection for secondary oil recovery (5.1), reservoir impoundment

(7.9 – potentially), waste disposal (5.3), academic research boreholes investigating induced

seismicity and stress (3.1), solution mining (5.2), geothermal operations (4.6) and

hydraulic fracturing for recovery of gas and oil from low-permeability sedimentary rocks

(4.6, updated, 2015).

Though fluid disposal and hydraulic fracturing both have the potential to trigger

earthquakes, it has become clear that the potential for induced seismicity is higher for

fluid (usually saltwater) disposal than for hydraulic fracturing. For instance, saltwater

disposal involves very long injection times (years to decades) and very large injection

volumes (often thousands to tens of thousands of m3 per day). This leads to much more

extensive pressure perturbations than hydraulic fracturing operations, in which 1000 m3

might be injected over an ∼2 hr period (Walters et al., 2015).

The most important hydraulic fracturing cases, with the highest magnitudes (until

January of 2016) are the following (Cases in bold will be described in detail in Part III):

Horn River Basin, British Columbia (Etsho and Kiwigana, Canada), 2009-2011,

Mmax=3.8

Eola Field, Oklahoma (US) 2011, Mmax=2.8. In south-central Oklahoma, hydraulic

fracturing injections between January 16, 2011, and January 22, 2011, induced a

series of 116 earthquakes of M=0.6 to M=2.8 (Holland, 2011; 2013). 50 events

occurred within 24 hours of the first activity and were coincident with the location

of the fracking. 43 of them were large enough to be located (M=1.0–2.8), which from

the character of the seismic recordings indicate that they were shallow and

generated significant surface wave energy.

34

Preese Hall, Lancashire (UK), 2011, Mmax=2.3.

Harrison County, Ohio (US), 2013, Mmax=2.2. Approximately 480 events were

identified, with ten of them recorded by regional network having moment

magnitudes MW=1.7-2.2. There were no felt reports for any of these events (Friberg

et al., 2014).

Poland Township, Ohio (US), 2014, Mmax=3.0. Hydraulic fracturing operations

affected a previously unmapped fault in the Precambrian crystalline rocks lying

below the sedimentary rocks that were being hydraulically fractured. 77 events

with M>1.0 were identified. Various lines of evidence suggested that the fault

responsible for the small earthquake was triggered by hydraulic fracturing

operations (Skoumal et al., 2015).

Montney, British Columbia (Canada), 2013-2016, Mmax=4.6 (August 17th 2015)

Fox Creek, Alberta (Canada), 2015, Mmax=4.4

2.2.3 Fracking related seismicity mechanisms

Anthropogenic seismicity (or ‘Stimulated’ according to Mc Garr and Simpson,

1997), is divided into Triggered and Induced seismicity. Triggered Seismicity is caused by

transient phenomena, concerning the nucleation of a small region of the rupture area,

whereas the entire rupture is controlled by the background stress. It Regards large events

(M>5.5) on nearby active tectonic faults (critically pre-stressed faults, independently close

to instability), at a distance up to a few tens of kilometers. On the other hand, in induced

seismicity the nucleation process is entirely (e.g. in terms of rupture size, stress changes

and energy released) controlled by its causative origin and would not occur otherwise.

Unfavorable conditions for high amount slip are evident since there could be potentially

large stresses, yet highly localized. Most of the induced earthquakes demonstrate small

magnitudes (typically M<3.0) and they are located in the vicinity of the activities

35

themselves, whereas triggered seismicity is connected with activation of optimally

oriented for failure, pre-existing fault systems and may result to much higher energy

release.

The largest events associated with hydraulic fracturing are triggered events, which

occur on the faults located in the vicinity of injection well. The rock model used for

description of rock seismic response to hydraulic fracturing is the poroelastic model. The

model is based on three principal assumptions: (1) the rock consists of the skeleton and

interconnected pore system uniformly saturated with fluid, (2) total volume of the pore

system is small in comparison with the volume of the rock as a whole, (3) the forces

considered are: pore pressure, total stress acting on the rock externally and stresses acting

on individual grains. Basing on this model we can imagine that pumping fluid into the

well causes an increase of pore pressure and fluid migration through the permeable rock.

The migration range depends on injection pressure, injection time and fracture system in

the rock. Preexisting natural fracture system in the rock facilitates fluid diffusion and

increases its speed, range or both.

Physically, the role of pore pressure in fault reactivation was firstly described by

Terzaghi law (1923), and later generalized by Biot in three dimensions (e.g. 1941).

According to this concept the effective stress is a difference between total stress acting on

the rock externally and pore fluid pressure (equation 1).

𝜎𝑖𝑗 = 𝑆𝑖𝑗 − 𝛿𝑖𝑗𝑃𝑝 (1)

σij – effective stress

Sij – total stress acting on the rock externally

Pp – pore pressure

δij – Kronecker delta

36

An increase of pore pressure leads to the decrease of effective normal stress on the

fault. This decreases fault strength (shear stress > static friction) and shear failure occurs.

Kronecker delta in the equation (1) means that pore pressure influences only normal

components of stress tensor. Shear components remain unchanged.

The concept of pore pressure increase and shear failure can be visually presented

on the Mohr diagram (Fig. 1). The increase of pore pressure shifts the circle towards 0 and

closer to the failure envelope. If the circle crosses the envelope the shear failure occurs.

Therefore, the increase of pore pressure increases also the probability of failure

occurrence. This situation can be observed during hydraulic fracturing (pore pressure

increase due to fluid injection). On the other hand decrease of pore pressure is associated

with reservoir depletion (Mohr circle shifted towards high values on x axis, Figure by

Altmann, 2010). What is important is that even very small increase of pore pressure, such

as 0.1 MPa, can lead to fault reactivation (e.g. Mulargia & Bizzarri, 2014).

Fig. 1 (from Altmann, 2010). Mohr diagram, illustrating the effect of pore pressure change on the effective state of stress.

σmax and σmin are equally influenced by the pore pressure, therefore the diameter of the Mohr circle is does not

change. The dashed Mohr circle describes an initial state of stress, the red Mohr circle the effective state of stress after

fluid injection, the blue Mohr circle the effective state of stress after depletion. During injection of fluid the Mohr circle

37

shifts towards the failure envelope, thus failure becomes more likely. During fluid depletion, failure becomes more

unlikely, (Altmann, 2010).

There are some features characteristic for the seismicity caused by fault

reactivation mentioned in the literature:

Anomalously large magnitudes,

Clustering at specific distances from well.

increase in the magnitude of the microearthquakes with time,

sharp reduction in b-value (calculated for a moving subset of events over the time

that pumping took place),

significant increase in the normalized seismic energy emitted (Wessels et al., 2011),

Time lag between start of pumping and fault reactivation (several hours or days).

o ca 10h – Preese Hall,

o ca 80min – Western Canada,

o several hours – Horn River.

The delay between pumping and the reactivation of some faults may in part be

because the fault into which fluid is injected has inherent storage and transmissibility

characteristics, or due to the time required for the transmission of fluid pressure by

pressure diffusion and due to poroelasticity. Note that Pressurization takes place across a

limited volume of rock, (typically only a few hundred meters in any direction) and over

a limited timescale, (typically only a few hours). Moreover pressure dissipates into the

surrounding geology as more fractures are created, limiting the pressure that can build

up. Pressure in the well is supposed to be a key determinant of induced seismicity,

affected by the volume of injected fluid (Larger volumes generate higher pressures) and

the volume of flowback fluid. Approximately 25-75% (commonly close to 50%) of the

hydraulic fracturing fluid used flows back after stimulation. Larger flowback volumes

38

reduce the pressure. Properties of faults (dimensions, pre-stress status) and shale

(strength) also affect the characteristics of seismic activity.

Warpinski et al., (2012) derived some contradictory results concerning the

correlation to technological processes. Although there are sparse data and uncertainties

in the cases they investigated, they concluded that there is enough information to support

a lack of correlation between magnitude and either the rate or volume of injection. The

largest magnitudes occurred at relatively modest rates and volumes – more related to

location than to the treatment parameters. However, it is important to emphasize that

these results are obtained for specific US shale plays where the maximum magnitudes

were <0.9.

2.3 Case Studies

2.3.1 Preese Hall, Lancashire, UK

Fig. 2. The location of the Preese Hall Well

Lancashire is a low natural seismicity area (even for the UK standards). No seismic

events with M>0 were recorded for one year and three months before March 30, 2011

(Eisner et al., 2012). In the spring of 2011, the first UK multi-stage fracking of a shale rock

39

took place (by Cuadrilla) at Preese Hall, Lancashire (Fig. 2), in a 1000m section of the

Namurian Bowland Shale (Wilson et al., 2015). The treatment operations started on the 26th

of March, whereas the Stage 2 (main) fracture treatment was conducted on March 31th.

The sequence of events was as follows (see also Table 1):

• On 31st of March 11 events with ML<1.5 were recorded

• On 1st of April an ML=2.3 event occurred at 3.6km depth

• No further events of analogous size were detected – fracking recommenced on

April 8th. From the 5th of April to 26th of May (when Stage 3 treatments took place),

only three events with ML≤1.2 occurred.

• On 27th of May an ML=1.5 occurred and the operations were suspended

• A total of 52 events were detected between 31/3 and 02/08 2011 (According to

Eisner et al., 2011, the completeness magnitude, Mc, of the catalog is considered

equal to 0.4, and the b-value was found equal to 0.79±0.21, surprisingly lower than

expected for a fracking case)

• Only 2 weak events (ML<0) occurred after 27th of May (July 30th, and August 2nd)

• Waveforms of the recorded events were similar to those from the 2 strongest events

Although six fracturing stages were planned at Preese Hall, Cuadrilla only

completed five before ceasing its operations. Seismicity was only induced following

hydraulic fracturing stages where larger volumes of fluid were injected and/or where

there was little or no flowback of fluids (de Pater and Baisch 2011).

In two of the hydraulic fracture treatments, in zones 2 and 4, the largest

earthquakes occurred approximately ten hours after the start of injection, while the well

was shut-in under high pressure (Fig. 3). These events were preceded by smaller events,

which started immediately after injection. Reported events of April 1, 2011 and May 27,

40

2011 show great similarity on the regional stations that recorded them, limiting the

relative distance between the two events to less than 120 meters (Eisner et al., 2012).

Table 1. Connection between seismicity characteristics and fluid flow during and between stages.

Fig. 3. Overview of injection volume and seismicity of all treatment stages in well PH1. More small events were

recorded in May because the monitoring system was improved with local stations, Vinj- injection volume, Vfb- flowback

volume, de Pater and Baisch 2011

The causative fault has not actually been identified, and more generally that there

is only a limited understanding of the fault systems in the basin. The fault may be at a

distance of up to a few hundred meters from the well-bore, but that fluid was able to flow

into the fault through bedding planes in the reservoir that opened during stimulation as

a result of the high pressures (Green et al., 2012)

41

A summary of Findings from Baisch and Voros, 2011; Harper 2011; GMI, 2011; de

Pater and Pellicier, 2011; de Pater and Basch, 2011; Green and Styles, 2012 concludes that

the Bowland Shale consists of impermeable, hard rock where the stresses are anisotropic.

In-situ stress regime is strike-slip, implying a large SHmax-Shmin. This stress difference

obtained from minifrac pressure declines and image log break-outs is some 25-30MPa ≠

2-4 MPa in US shale plays. Based on the seismic observations an MLmax=3 is estimated as a

worst case scenario (de Pater and Baisch, 2011). An event of this size is not expected to

provoke significant hazard. These studies concluded that seismicity depends on three

factors concerning a fault which should be critically stressed, transmissible so that it

accepts large quantities of fluid and brittle enough to fail seismically. All factors are

considered very unlikely, classifying Preese Hall Stage 2 event, as a ‘worst case scenario’.

(a crude probability estimate by de Pater and Baisch, 2011 is ~0.01%)

Concerning the risk mitigation strategy, A Traffic Light System was proposed by

de Pater and Baisch, (2011):

o Magnitude smaller than ML=0: regular operation

o Magnitude between ML=0 and ML=1.7: continue monitoring after the treatment until

the seismicity rate falls below one event per day, for at least 2 days.

o Magnitude > ML=1.7: stop pumping and bleed off the well, while continuing

monitoring.

The maximum post-injection magnitude increase has been estimated to be 0.9

magnitude units (Q-con, 2011). ML=1.7 is selected as the threshold in order to prevent the

occurrence of an ML,max =2.6 (Other studies suggest ML,max =3.0). Green & Styles (2012)

propose different magnitude thresholds, considering MLmax=1.7 as undesirably high.

Based on this limit, no action would have been taken before the ML=2.3 event on 1 April

2011. A lower limit of MLmax=0.5 is recommended instead.

42

Summarizing the Lancashire Fracking Episode:

• Similar waveforms, location and mechanism indicate a highly repeatable source

(events originated from the same fault)

• Rapid decay of seismicity

• The events are located close to the point of injection and the timing clearly

corresponds to the treatment schedule (fluid flow)

• The injected volume and flow-back timing are an important controlling factor in

the level of seismicity

2.3.2 Horn River Basin, British Columbia, Canada

The Horn River Basin is an unconventional shale play targeting dry gas from mid-

Devonian aged, over-pressured shales of the Muskwa, Otter Park and Evie Formations.

Situated in the northeast corner of the province, the Horn River Basin is confined to the

west by the Bovie Lake Fault Zone and to the east and south by the time equivalent

Devonian Carbonate Barrier Complex (www.nrcan.gc.ca/). Currently, British Columbia

and Western Alberta are in the center of scientific concern concerning fracking-induced

seismicity due to the ongoing operations and the intense recent seismic activity, also

characterized by the highest magnitudes recorded for that type (Atkinson et al., 2015,

2016; Farahbod et al., 2015; Mahani et al., 2016; Schultz et al., 2015; Wang et al., 2015,

20167)

Between April 2009 and July 2011, 31 seismic events were recorded and located by

Natural Resources Canada (NRCan) in the Etsho area of the Horn River Basin in northeast

British Columbia (Fig. 4). Seven more events were recorded near the Tattoo area between

December 8 and 13, 2011 (BC Oil and Gas Commission, 2012).

43

Fig. 4. Location of Etsho, Tattoo and Kiwigana areas in the Horn River Basin. Red triangles show NRCan reported

epicentres, Bovie and Trout Lake Fault zones noted. Liard Basin to west of Bovie Fault. Blue star indicates location of

Kiwigana seismograph array (BC Oil and Gas Commission, 2012).

The observed events ranged in magnitude between ML=2.2-3.8 as recorded by

NRCan. Two NRCan seismograph stations, part of the Canadian National Seismograph

Network (CNSN), were at this time operational in northeast British Columbia. The Bull

Mountain station near Hudson’s Hope (from January 1998) and the Fort Nelson (from

1999). The CNSN is designed to monitor moderate to strong magnitude earthquakes that

pose a risk to public safety and not to detect low magnitude induced seismicity. Therefore

the uncertainty of epicentral locations was 5 to 10km, whereas the uncertainty in

earthquake focal depths was even larger.

Hydraulic fracturing operations in the Etsho area have been ongoing from

February 2007 to late July 2011. During this period, 14 different drilling pads were used

to drill over 90 wells with more than 1,600 hydraulic fracturing stage completion

operations.

44

Additionally, a 20-seismograph dense array was deployed by an operator in the

Etsho area; operated from June 16 to Aug. 15, 2011. A second one was deployed at

Kiwigana, 40 kilometres to the southwest of the Etsho area. This 151-station seismograph

array operated from Oct. 25, 2011 to Jan. 27, 2012.

Twenty-seven of the recorded Etsho events lie within a 10 km radius circle

(Fig. 5, Fig. 6). Within this same circle are seven multi-lateral drilling pads. Five of these

pads were conducting hydraulic fracturing operations when events occurred. At Tattoo

all seven of the recorded events can be encompassed within a 10 km radius circle that

encloses two multi-well shale gas drilling pads. One pad at Tattoo had ongoing hydraulic

fracturing operations when the seismicity occurred (BC Oil and Gas Commission - August

2012).

A number of events, ranging from magnitude ML=-0.8 to 3.0 were recorded by the

Etsho dense array during hydraulic fracturing. Of these, 216 are interpreted to be related

to fault movement (197 events, of ML=1.0 – 2.0 and 19 events of ML=2.0-3.0). Operator

provided b-value analysis indicated that magnitudes from ML=0.5 to 1.0 indicate the

transition from fracture driven seismicity to seismicity driven by fault movement. For the

dense array’s operational date range, June 23 to August 14, 2011, the two northeast B.C.

stations in the CNSN recorded four events (ML=2.5 to 3.1) (BC Oil and Gas Commission,

2012).

The horizontal and vertical locations of several events at Etsho detected by NRCan

were relocated by the Operator using data obtained from the dense array. The results of

this work placed event hypocentres within 200 m vertically and horizontally of hydraulic

fracturing stages. True vertical depths (TVD) of hydraulic fracturing completions at the

Etsho d-1-D pad range from approximately 2,650 to 2,889 meters. Of the 69 magnitude

ML=1.5 to 3.0 seismic events recorded by the dense array and linked to this pad, all fall

45

within the targeted, shale formations. 66 of these events occurred between 2,800 and 2,870

meters.

Fig. 5. Tattoo area NRCan event epicentres and Multi-

well Pads, shown within “20km buffer”, 10km radius

red circle (BC Oil and Gas Commission, 2012).

Fig. 6. shows the horizontal wellbores for the d-1-D

drilling pad, volumes injected at each hydraulic fracturing

stage and the magnitude >1.0ML events occurring from

June 23 to August 14, 2011(BC Oil and Gas Commission,

2012).

At Kiwigana, numerous micro-seismicity events, ranging from ML=-1.7 to 0.5, were

detected between October 25, 2011 and January 27, 2012 by the deployed operator dense

array. These micro-seismicity events resulted from tensile failure and shear movement

during the normal process of hydraulic fracturing to develop the reservoir. An additional

18 events ranging from ML=1.0 to 1.86 were detected and were interpreted to be the result

of triggering caused by injection and transmission of fluid along pre-existing fault

structures (BC Oil and Gas Commission, 2012).

46

Hydraulic fracturing operation timing was compared to seismicity occurrence

times. At Etsho and Tattoo, all 38 NRCan reported events occurred either during a

hydraulic fracturing stage or sometime after one stage ended and another began. No

events were recorded before hydraulic fracturing operations began or after the last

hydraulic fracturing operations ended.

Analysis of Time Lapse from start of hydraulic Fracking to associated seismic event

was performed. On average, stage start time to stop time was 5 ½ hours. Eight events

occurred during stage operations. Seventeen events occurred within 17 ½ hours and all

events occurred within 24 hours after stage start times. Fault mapping at Etsho shows

abundant faulting. Interpretations vary but it appears most of this faulting (including the

larger, regional faults in this grouping) is deep seated and concentrated in a north-south

trending fault fairway centered at Etsho.

NOTE: The investigation was completed by the Commission’s geological and engineering staff

within the Resource Development department, and they benefited from consultation with NRCan,

the University of British Columbia and the Alberta Geological Survey. Data was obtained from

numerous sources including open source information as well as proprietary data acquired by oil

and gas companies working near the area of the investigation. There is no direct information about

the creator of this analysis. For more detailed information the reader may refer to

https://www.bcogc.ca/. Available data is provided by BC Oil and Gas Commission and includes:

Summary catalog of 38 events recorded by NRCan,

Cross-section of Horn River Basin (Muskwa, Otter Park, Evie) formation shale gas targets,

Pad Hydraulic Fracturing Statistics for Etsho,

Correlations of Event Times to Horn River Pad Operations,

Time Lapse from Start of Hydraulic Fracturing to Associated Seismic Event,

Frac Fluid Placed versus Average Magnitude,

Pump Rate versus Average Magnitude,

47

Breakdown Pressure versus Average Magnitude for d-1-D pad,

Air Summary,

Quarterly Oil and Gas Water Use Summary,

Water Use for Oil and Gas Activity Annual Report,

Pipeline Performance Summary,

Horn River Shale Reservoir Parameters,

Structure Map of Top Muskwa Formation,

Isopach Map of Muskwa Otter Park Formations,

Temperature Map of Muskwa Otter Park Formations,

Public Safety Report

2.3.3 The Geysers Case Study

Introduction – History:

‘The Geysers’ case study concerns seismicity associated with geothermal fields in

California. This case is included in this report because the mechanism of inducing

seismicity in such areas is similar to that in hydraulic fracturing regions. Moreover, the

Geysers (the largest producing geothermal field in the world) is a very well monitored

and studied area since the last decades. MEQ monitoring has been applied as a general

indicator of fluid paths and general response to injection at The Geysers for almost 30

years (Majer & Peterson, 2007 and references therein), showing a strong spatial and

temporal correlation between MEQs activity and both water injection and steam

extraction. Stark (1992) showed that plumes of MEQs are clustered around many injection

wells, and the seismic activity around each injection well correlates with its injection rate.

Ross et al. (1999) suggested that the sources might be explained by combinations of tensile

cracks and shear movements accompanied by fluid flow. In any case, it is likely that

48

thermo-elastic responses, induced by rapid cooling, play a major role in inducing MEQs

at The Geysers.

The modeling and results by Rutqvist et al. (2015) also indicates that MEQ and

shear reactivation of pre-existing fractures are caused by the combined effects of injection-

induced cooling and pressure changes, with the cooling being more important for

triggering seismicity near the injection well and around the zone of cool liquid water. On

the other hand, injection-induced changes in steam pressure are the dominant cause of

seismicity farther away from the injection well. Note that these are very small changes in

steam pressure, and the model simulations of pressure evolution, corroborated with

pressure monitoring, indicate that reservoir pressure changes on the order of 1 MPa are

sufficient to trigger a significant number of small events. This supports the notion that

rock mass within The Geysers geothermal field is near critically stressed for shear failure,

and that small perturbations in the stress field could induce seismicity.

Garcia et al. (2016) published a recent study on two previously abandoned wells,

Prati State 31 (PS-31) and Prati 32(P-32), which have been reopened and deepened to be

used as an injection and production doublet to stimulate the High Temperature Reservoir.

They found that a seismicity cluster began to develop almost immediately after P-32 water

injection was initiated, and their data analysis indicated among others a deeper

permeability stimulation and an increased seismicity associated with an injection rate

increase, followed by a significant decrease in event frequency.

Rutqvist et al. (2016) modeling indicates that the microseismic events in The

Northwest Geysers EGS Demonstration Project system are related to shear reactivation of

pre-existing fractures, triggered by the combined effects of injection-induced cooling

around the injection well and rapid but small changes in steam pressure as far as a

kilometer from the injection well. It is also notable that larger events may occur at some

distance from the injection well and are associated with larger features such as minor

49

faults. Yet, the authors acknowledge that substantial uncertainties still remain regarding

the exact mechanisms of induced seismicity, in particular related to the role of thermal

effects.

(Check this part – not published work!!)

Mossop and Segall (2006) ???? performed a comprehensive correlation study based on

induced seismicity and operational data from 1976 to 1998 and they distinguished 3 types

of seismicity (Better set reference Majer et al., 2007):

a) shallow, production-induced seismicity that has a long time lag on the order of

1 year, (caused by poroelastic stresses, The observations are consistent with a

contracting reservoir, which as it shrinks, induces stresses and strains in the

surrounding crust). However these results suggest that shallow earthquakes are

production induced, in contrast with results of Rutledge et al., 2002.

b) deep, injection-induced seismicity with short time lag of less than 2 months. For

deep induced MEQs occurring after the 1980s, there seems to be a consensus that

these are correlated to local injection rates with some time lag (e.g. Parotidis et al.,

2004).

c) deep, production-induced, seismicity with short time lag of less than 2 months

that appears to diminish in the late 1980s.

Seismicity associated with geothermal fields

Generally, the local magnitude of events related to geothermal fields exploitation

does not exceed 2, however, there were quite several exceptional cases. The largest

magnitude event ( ML 4.6) was observed in 1982 at The Geysers geothermal field. Similarly

as in the case of hydraulic fracturing, gradual migration of seismicity is observed as the

fluid diffuses though the rock skeleton.

50

Fig. 7. Observed maximum magnitude of seismic events in geothermal operations (squares), wastewater disposal wells

(triangles), hydraulic fracturing (circles), and fluid injection in the KTB scientific well (stars) as functions of volume of

injected fluid (McGarr, 2014).

McGarr (2014) derived a relation which expresses the theoretical maximum

magnitude to be proportional to the total injected volume of the fluid (Fig. 7 from McGarr,

2014). On the plot we can see also that the largest magnitude events are observed during

wastewater injections. The magnitudes of events associated with hydraulic fracturing are

quite small in comparison with other injection-related activities.

It is important to mention that character of seismicity differs depending on the

distance from the injection well. Events which occur in the vicinity of the injection well,

where the pore pressure is high, have low stress drops and mainly tensile character. The

b-value in this region is relatively high. On the other hand, far from the injection well,

where pore pressure is low, events have high stress drops and mainly shear character.

Additionally, events with big magnitudes are more probable to occur far from the well

51

(lower b-value), on the peripheries of seismic cloud and during the post shut-in phase

(Zang et al., 2014).

The other thing that matters is the type of rock into which injection is carried on -

seismic cloud is narrower in weak (sedimentary) rocks compared to hard rocks

(crystalline), which are naturally fractured. What is more, in crystalline rocks the Kaiser

effect is observed, which means that seismicity is absent until the stress level of previous

stimulations is exceeded.

The Geysers geothermal field

The example of seismicity induced in geothermal field, which will be described

below, comes from The Geysers field in California. It is the biggest producing geothermal

field in the world with ca 300 producing wells and ca 60 injection wells. The production

takes place from 1960s and the maximum production was reached in 1987. From that time

the reservoir is permanently stimulated by water injections to enhance the production and

prevent reservoir depletion.

The reservoir is vapour-dominated and is located in metamorphic rocks. The

temperature of steam is 240°C at 2 km depth, but exceeds 350°C in the northwestern part

of The Geysers at depths below ca 2.75 km (so called high-temperature zone). What is

important is that at The Geysers there are no classical water injections with the use of high

pressures at the injection wells. Here, relatively cool surface water falls freely into the

injection well resulting in significant volume reduction as the reservoir steam condenses.

This causes negative gauge pressure at the wellhead, in contrast to active surface

pumping commonly performed for reservoir stimulation with injection at elevated

wellhead pressures (Martinez-Garzon et al., 2014). The injection has seasonal tendency

and peak injection rates are observed during winter months.

52

At The Geysers, the pore pressure at reservoir depth is subhydrostatic. The height

of the water column filled inside the well remains mostly within the reservoir limits, (<1

km from the bottom of the well). However, the increase in the injection rate closely

correlates with migration of IS suggesting that pore pressure changes may also influence

seismic activity. In addition, the spatial extent of the seismic cloud suggests that seismicity

is induced by pore pressure changes at larger distance to the well (Martinez-Garzon et al.,

2014).

Fig. 9. Analysis of seismicity cluster in NW Geysers (Majer & Peterson, 2007)

Seismic activity in this region is very intense: it is about 4000 events/year with

magnitudes 1.0-4.5. The largest event occurred in 1982 and its magnitude was 4.6. Figure

53

3 presents seismic activity at The Geysers throughout the years of production. We can see

that: (1) the number of events with magnitudes between 1.5 and 3.0 is in the order of

hundreds per year, but with the magnitudes 3.0-4.0 is less than 30/year. Events with

magnitudes > 4.0 are marked with green crosses, (2) maximum production was in 1980

and from that moment the amount of injected water is growing in order to stimulate the

reservoir (Fig. 8 from Majer & Peterson, 2007).

Analysis of seismicity cluster in NW Geysers (Martinez-Garzon et al., 2014)

Observations:

Clear correlation between monthly seismicity rates and injection rates in two

wells

During injection:

o Decrease of b-value,

o Increase in relative amount of strike-slip and thrust events,

o Increase in average distance from injection well (pulsation of seismic

cloud).

An important part of the analysis is identification of physical processes leading to

inducing of seismic events. . Martinez-Garzon et al. (2014) agreed that two effects are

responsible for it: thermoelastic and poroelastic effects. Thermoelastic effect dominates in

the proximity of the well regardless of the injection stage. The value of estimated

thermally induced stress magnitude is ca -26 MPa and it is a result of strong thermal

contraction at the wellbore wall. The effect attenuates rapidly with distance. On the other

hand the poroelastic effect, which is connected with pore pressure diffusion, dominates

at some distance from the well and during peak fluid injections. Estimated pore pressure

difference of about 1 MPa between peak injection and pre/post injection periods has been

observed (capable of inducing seismicity). Both these effects can induce seismicity,

54

because in both cases the failure envelope is more likely to be crossed (Mohr diagrams).

However, at hydraulic fracturing sites the thermoelastic effect is very unlikely to be

observed but poroelastic effect works in the same way.

To summarize, thermal stresses are responsible for the long-term seismic moment

release and seismic activity, whereas poroelastic stresses seem to affect the characteristics

of seismicity at greater depths, (i.e., higher pore fluid pressure), as well as at greater

distances from the well. The large discrepancy in seismic moment release and seismic

activity for Prati-9 and Prati-29 wells may be explained by differences in thermal stresses

resulting from different water and/or host rock temperatures at both wells as well as

increasing pore pressure and poroelastic effects that tend to dominate at greater depths.

The influence of poroelastic effects on seismic moment release is unclear, however, on

long term they do seem to affect the source characteristics of seismicity (Kwiatek et al.,

2015).

2.4 Conclusions

Seismicity connected with hydraulic fracturing has not yet been satisfactory

studied and large amount of the associated data are not available for elaboration. After

hundreds of thousands of fracturing operations, only few examples of felt seismicity have

been documented. It is generally accepted that the combination of favorable conditions to

exist at the same time for generating such events is highly unlikely. Therefore, the

likelihood of inducing damaging of even felt (at surface) seismicity by hydraulic

fracturing is extremely small but cannot be ruled out. Since fracking is extensively applied

for less than 10 years, more studies need to be carried out for investigating and

quantifying the potential hazard. Some additional findings of the researches

accomplished up to date are summarized below:

55

1. Microseismicity can be used to monitor fracture propagation during hydraulic

fracturing of shales.

2. Events triggered by hydraulic fracturing can be used to delineate preexisting

faults.

3. The strongest events associated with hydraulic fracturing are triggered events

occurring on preexisting faults. In the case of fluid injection in geothermal energy

production the biggest magnitude events occur on the peripheries of seismic cloud

and during post injection phase (results of modeling).

4. The largest magnitude recorded is M=4.6 (up to January 2016)

5. Sufficient geological reconnaissance should be carried out before commencing

hydraulic fracturing operations (e.g. identification of faults and their age) in order

to predict and prevent potential dangers connected with seismicity.

6. The probability of a damaging earthquake is very low, however it cannot be ruled

out. Even though the effects at the surface may be negligible, the well may suffer

significant damage with potential production and environments impacts.

56

SUPPLEMENTARY MATERIAL

GLOSSARY – and a Brief Review on Poroelasticity Terms and Approaches

Terminology (also https://cogcc.state.co.us/COGIS_Help/glossary.htm)

Leak-off:

The magnitude of pressure exerted on a formation that causes fluid to be forced

into the formation. The fluid may be flowing into the pore spaces of the rock or into cracks

opened and propagated into the formation by the fluid pressure. This term is normally

associated with a test to determine the strength of the rock, commonly called a pressure

integrity test (PIT) or a leak-off test (LOT). During the test, a real-time plot of injected fluid

versus fluid pressure is plotted. The initial stable portion of this plot for most wellbores

is a straight line, within the limits of the measurements. The leak-off is the point of

permanent deflection from that straight portion. The well designer must then either adjust

plans for the well to this leak-off pressure, or if the design is sufficiently conservative,

proceed as planned.

Shut-in pressure

Shut-in is the implementation of a production cap set lower than the available

output of a specific site. This may be part of an attempt to constrict the oil supply or a

necessary precaution when crews are evacuated ahead of a natural disaster.

The surface force per unit area exerted at the top of a wellbore when it is closed at

either the “Christmas tree” (figure below) or the blowout preventer stack. The pressure

may be from the formation or an external and intentional source. The SIP may be zero,

indicating that any open formations are effectively balanced by the hydrostatic column of

fluid in the well. If the pressure is zero, the well is considered to be dead, and can normally

be opened safely to the atmosphere.

57

Triggering Front (Shapiro et al., 1997, 2000, 2003)

The permeability-related features of the hydraulically-induced seismicity can be

identified in a very natural way from the notion of triggering fronts. To recall this notion

let us approximate a real configuration of a fluid injection in a borehole by a point source

of pore pressure perturbation in an infinite, heterogeneous, anisotropic, poroelastic, fluid

saturated medium. The time evolution of the pore pressure at the injection point is

assumed to be a step function. It is natural to assume that the probability of the triggering

of microseismic events is an increasing function of the power of the pore pressure

perturbation. Thus, at a given time to it is probable that events will occur at distances

which are smaller or equal to the size of the relaxation zone of the pore pressure. The

events are characterized by a significantly lower occurrence probability for larger

distances. The spatial surface which separates these two spatial domains is called the

'triggering front'. Because the size of the relaxation zone is to some extent a heuristic

parameter, we introduce a more formal quantity which is directly proportional to this

size. The triggering front at the time t0 is the front of the zero phase at the time to of a

harmonic diffusion wave of pore pressure relaxation radiated with zero phase at the time

0 at the injection source with the frequency 2π/t0.

58

Basic Poroelastic Parameters and Definitions)

o Total stress, σij (tensor): Total force in the xj direction per unit area whose

normal is in the xi direction (a positive normal stress implies tension).

o Pore pressure, p (scalar): In a material element, it is the pressure in a

hypothetical reservoir which is in equilibrium with this element, i.e. no fluid

exchange takes place between reservoir and the material element.

Alternatively, pore pressure at depth, is defined as a scalar hydraulic

potential acting within an interconnected pore space at depth – with

reference to earth’s surface (Zoback, 2007). Conceptually, the upper bound

for pore pressure is the overburden stress, Sv. Because of the negligibly small

tensile rock strength, pore pressure will always be less than the least

principal stress, S3.

The respective conjugate quantities for stress and pore pressure are strain

and variation of fluid content.

o Variation of Fluid Content, ζ: Variation of fluid volume per volume of the

porous medium. A positive ζ corresponds to a gain of fluid by the porous

solid whereas a negative ζ indicates fluid withdrawal from the solid

material.

Consolidation:

o The simultaneous deformation of the porous material and the flow of the

pore fluid is the subject of the theory of consolidation, often denoted as

poroelasticity.

o According to Karl von Terzaghi "consolidation is any process which involves

decrease in water content of a saturated soil without replacement of water by air."

o The progressive settlement of a soil under surface surcharge (Terzaghi,

1923; Biot, 1935, 1941).

59

o Alternatively, Consolidation is a volume change in saturated soils caused

by the expulsion of pore water from loading (Verruijt, 2013).

Effective Stress:

o Effective Stress: The difference between externally applied stresses acting

on a rock matrix and internal pore pressure.

o Concept of Effective normal stress: Difference between total normal stress

and pore pressure (Terzaghi, 1943). Because the pore pressure acts equally

on all three normal stresses, and not at all on the shear stresses, the

difference of maximum and minimum principal stress, known as

differential stress, is constant; only the mean effective stress, known as sum

of maximum and minimum principal stress divided by two, changes by the

amount of pore pressure. This behavior is illustrated by means of a Mohr

diagram (Mohr radius is the same, the circle’s center is shifted towards left

or right when pore pressure increases or decreases, respectively). This

stands in the uncoupled case (see Coupled and Uncoupled Approaches below).

Due to the coupling between P and σh, the effective minimum horizontal

stress increases less than the effective vertical stress. This leads to an

increase in differential stress and an enlargement of the Mohr circle.

(Altman, 2010)

Assumptions and Approaches (Consolidation problems):

o Coupled/ Uncoupled approach: The coupling between changes in stress and

changes in fluid pressure forms the subject of poroelasticity. Two basic

phenomena underlie poroelastic behavior: 1) Solid-to-fluid coupling occurs

when a change in applied stress produces a change in fluid pressure or fluid

mass. According to Roeloffs (1988) there are three types of poroelastic

approximations defined as:

60

Coupled: The elastic stresses influence pore pressure and vice versa.

Uncoupled: The elastic stresses and pore pressure are independent.

Decoupled: The elastic stresses influence pore pressure but not vice

versa.

2) In addition, Wang (2000) refers to Fluid-to-solid coupling, which occurs

when a change in fluid pressure or fluid mass produces a change in the volume

of the porous material. Applied stress changes in fluid-saturated porous

materials typically produce significant changes in pore pressure, and this

direction of coupling is significant (therefore a coupled approach should

usually be considered). Negligible solid-to-fluid coupling occurs for a highly

compressible fluid such as air. An example of solid-to-fluid coupling is the

response of water levels in a well to the passage of nearby trains (Wang, 2000).

Yet, there are some classes of cases which can be treated sufficiently (at least as

a first approximation) by an uncoupled analysis (Detournay & Cheng, 1993;

Verruijt, 2013). However, applied stress changes in fluid-saturated porous

materials typically produce significant changes in pore pressure, and this

direction of coupling is significant.

Some uncoupling conditions (Verruijt, 2013; Detournay and Cheng,

1993; Wang, 2000):

- Constant isotropic normal stress

- Horizontally confined deformations

- Highly compressive fluid

- Irrotational deformations

o Isotropic/ Anisotropic medium: A material is isotropic when no material

frame is preferred to formulate its constitutive equations. As a consequence

energy functions can depend only on the scalar invariants of the involved

tensors (Coussy, 2004). The origin of anisotropy may be twofold. In the first

61

place it may be due to the anisotropy of both the matrix and the porous

geometry. In the second place it may also be due to an anisotropic pre-loading,

as for instance gravity, which has induced a prestressed anisotropic reference

state with regard to the original stress-free state. Two main kinds of linear

anisotropy are presented by Coussy (2004), namely orthotropy and transverse

isotropy. Elastic anisotropy is generally not very important in geomechanics,

although, shear wave velocity anisotropy can be related to principal stress

directions or structural features. On the other hand, anisotropic rock strength,

due, for example, to the presence of weak bedding planes, has a major effect

on wellbore stability.

o Quasi-static Approach: Solid Consolidation problems (quasi-static) and Wave

propagation (dynamic). The couplings are assumed to occur instantaneously

in the quasi-static approximation in which elastic wave propagation is ignored.

According to the quasi-static governing equations, the response of the elastic

medium is instantaneous. In quasi static limit (low frequency) fluid pressure

may be taken as uniform throughout a porous rock sample. This means that

elastic wave propagation and pressure gradients that might be associated with

fluid flow are disregarded (Wang, 2000; Zoback, 2007). However, for the full

poroelastic governing equations, containing second order partial derivatives in

time, the response propagates with the elastic wave speed of the medium

(Pride 2005). Elastic anisotropy can have considerable effects on seismic wave

velocities, and is especially important with respect to shear wave propagation.

An isotropic material is defined fully by two constants, whereas a material with

cubic symmetry is fully described by three constants, and a material

characterized by transverse isotropy (such as a finely layered sandstone or

shale layer) is characterized by five constants, and so on (Zoback, 2007).

62

o Linear/ Non-linear elastic solids: A linearly elastic material is the one in which

stress and strain are linearly proportional and deformation is reversible. The

linear quasi-static theory of poroelasticity is established by the formulation of

Rice & Cleary (1976). The non-linear behavior is generally associated with the

closing/opening of crack-like pores, but in very porous and weak rocks, it is

caused by progressive pore collapse (Detournay & Cheng, 1993). Coussy (2004)

provides solutions for some non-linear problems. The assumption of linear

elastic behavior of the porous medium may be the weakest part of the theory.

The approximations introduced in the behavior of the fluid and the particles

usually are very accurate compared to the approximations made by assuming

linear elastic soil behavior. Real soils often exhibit non-linear behavior, for

instance by a difference in stiffness in loading and unloading, and plastic

deformations if the stresses exceed a certain level. (Verruijt, 2013)

o Drainage conditions: Three cases are often considered: fully drained, partially

drained, fully undrained. The drained (excess pore pressure is completely

dissipated – constant pore pressure) and undrained (no fluid flow – constant

fluid mass per unit volume, but pore pressure is altered) conditions are the

limiting cases of the slow and fast loading respectively. Relatively slow loading

leaves the pore pressure unchanged in the control volume because fluid flow

has adequate time to equilibrate with an external boundary. In contrast, little

fluid amount flows into or out of the control volume if the loading is rapid

(Singh et al., 2013).

Undrained conditions: Δu≠0, Δσ≠Δσ’; appropriate when

permeability is low and rate of loading is high/ short term behavior

has to be assessed.

63

Drained conditions: Δu=0, Δσ=Δσ’; appropriate when permeability is

high, rate of loading is low/ short term behavior is not of interest for

the problem considered.

o Compressible/ Incompressible Fluid and Particles: The compressibility refers

to the two constituents: fluid and solid particles, because the main mechanism

of soil deformation is not so much the compression of the fluid or the particles,

but rather the deformation due to a rearrangement of the particles, including

sliding and rolling of particles over each other. Rice & Cleary (1976) showed

that the governing equations are not significantly more complicated when

arbitrary compressibilities are assigned to the fluid and solid constituents. The

same formulation could have been used to obtain the more general dislocation

solution with such full compressibility.

o Geometry - Loading: Axisymmetric, Planar, Circular, Linear etc. E.g.

Concentrated line force, suddenly introduced edge dislocation, suddenly

pressurized cylindrical and spherical cavities, plane strain consolidation,

axially-symmetric consolidation etc (see case studies, examples below in ‘Problems

and Applications’ Section).

o Analytical/ Numerical Solutions & Methods, Poroelastic Medium modeling

as a Finite Layer/ Half-Space.

– (e.g. Detournay and Cheng, 1993; Philips, 2005; Verruijt, 2013 – see

Problems/ Application Section for details)

o Other phenomena and properties: Thermoporoelasticity, Poroplasticity,

Poroviscoelasticity (Coussy, 2004), etc. For example the Theory of linear

coupled thermoelasticity (e.g. Carlson, 1972).

64

APPENDIX A – Formulation of Poroelasticity (references)

Biot’s 1941 poroelastic theory for an isotropic fluid filled porous medium are

constrained in just two linear constitutive equations for an isotropic applied stress field,

σ. Biot’s equations of the linear poroelasticity theory are derived from:

Equations of linear elasticity for the solid matrix,

Navier–Stokes equations for the viscous fluid, and

Darcy's law for the flow of fluid through the porous matrix.

Rice and Cleary (1976) reformulated Biot’s linear poroelastic constitutive

equations, chosing constitutive parameters that emphasized the drained (constant pore

pressure) and undrained (no flow) limits of long- and short-time behavior, respectively.

Their formulation has been adopted widely for geophysical and seismological problems

(e.g. Cocco and Rice, 2002).

The solid-to-fluid and fluid-to-solid couplings are assumed to occur

instantaneously in the quasistatic approximation in which elastic wave propagation is

ignored. The simplest mathematical description of the two basic forms of coupling

between solid and fluid is a set of linear constitutive equations. The equations relate strain

and fluid-mass changes to stress and fluid-pressure changes. The poroelastic constitutive

equations (equations that describe the deformation of a rock in response to an applied

stress – or vice versa) are generalizations of linear elasticity whereby the fluid pressure

field is incorporated in a fashion entirely analogous to the manner in which the

temperature field is incorporated in thermoelasticity. (Wang, 2000)

In volumetric response of a linear isotropic poroelastic material, many constants

are introduced in this presentation, but only three of these parameters are actually

independent. These basic material constants selected to constitute the reference set are:

the drained bulk modulus K, the undrained bulk modulus Ku, and the Biot coefficient α.

α can be defined as the ratio of the fluid volume gained (or lost) in a material element to

65

the volume change of that element, when the pore pressure is allowed to return to its

initial state.

To construct a well-posed mathematical system for the description of the stress,

pore pressure, flux, and displacement in the medium, additional equations based on mass

and momentum conservation principles need to be introduced. Together with the

constitutive laws, these equations constitute the governing equations of the theory of

poroelasticity (Detournay & Cheng, 1993).

Constitutive Equations + Mass Conservation Principles + Momentum Conservation

Principles (a special case of which is the Darcy’s Law) Governing Equations (reduced

through variable elimination and substitutions to produced systems amenable for

mathematical treatment) Field equations (Equilibrium & Fluid diffusion equations). Initial

and Boundary Conditions should be also considered.

The complete system of the basic field equations comprises:

16 unknowns: 6 stresses, 6 strains, 3 displacements & pore pressure

16 equations: 3 equilibrium equations, 6 compatibility equations, 6

intependent stress-strain relations and the storage equation

An important basic equation of the theory of consolidation is the storage equation.

It admits a simple heuristic interpretation: the compression of the soil consists of the

compression of the pore fluid and the particles plus the amount of fluid expelled from an

element by flow. As the derivation shows, the equation actually expresses conservation

of mass of fluids and solids, together with some notions about the compressibilities.

The system of equations can be simplified considerably by eliminating the stresses

and the strains, finally expressing the equilibrium equations in the displacements. The

complete system of differential equations consists of the storage equation and the

66

equilibrium equations. These are four equations with four variables: p, ux, uy and uz.

(Verruijt, 2013)

Initial/ Boundary conditions:

The most common initial conditions are that the pore pressure p and the three

displacement components ux, uy and uz are given at a certain time, usually at time t = 0. It

is often most convenient to assume that at t = 0 all these quantities are zero. This means

that the pore pressure and the displacements at a later instant of time are all considered

with reference to the initial state.

Because the differential equations are 4 linear equations the boundary conditions

should specify 4 conditions. The most common system is that one boundary condition

refers to the pore pressure (e.g. either the pore pressure or the flow rate normal to the boundary

must be specified) and the other three to the solid material (e.g. either the 3 surface tractions

or the 3 displacement components must be prescribed - or some combination). (Verruijt, 2013)

References (formulation):

Kalpna, 1997: On the 2D plain strain for a harmonic stress applied to an impervious

elastic layer resting on a porous elastic half space. Matrix formulation of Singh and

Garg (1985) for the elastic layer and the procedure of Roeloffs (1988) for the formal

solutions for the porous elastic half space. Combination of the two solutions by

matching the displacements and stresses at the boundary between the layer and the

porous elastic half space and obtain the complete formal solution. (illustrated example

provided).

Pan, 1999: Complete Green’s functions in multi-layered isotropic and poroelastic half-

space.

67

Wang and Kumpel, 2003: Poroelasticity: Efficient modeling of strongly coupled, slow

deformation processes in multilayered half-space. Analytical Solutions for some

special cases i.e. Transient Green’s functions for the homogeneous whole space, Steady

state Green’s functions for the homogeneous half-space. Numerical Solutions for a

multilayered half-space i.e. Laplace-Hankel transform in poroelasticity, Fundamental

poroelastic solutions, The extended Haskell’s propagator algorithm. Application and

test to a field (Appendices with Poroelastic Layer Matrix, Haskell Propagator

Algorithm and Orthonormalized Propagator Algorithm)

Soltanzadeh et al., 2009: Poroelastic Modeling of Production and Injection-Induced

Stress Changes in a Pinnacle Reef. The work summarizes semi-analytical and closed-

form solutions that can be used to assess the poroelastic stress changes induced within

a porous formation (reservoir) during a pore pressure change. Further, solutions are

presented for the stress discontinuities at the interfaces between reservoirs and the

rocks that surround them.

Hesse and Stadler, 2014: Joint inversion in coupled quasi-static poroelasticity

68

APPENDIX B – Solved Problems of Poroelasticity & Applications (references)

References: Zoback, 20071; Coussy, 20042; Detournay & Chen, 19933; Verruijt, 20134; Singh et al.,

20135; Philips, 20056;Altmann, 20107; Rice & Cleary, 19768.

Measuring Stress Orientation and Magnitude - Stress concentration around a

cylindrical hole and wellbore failure 1

Wellbore Stability 1

Effects of Reservoir Depletion 1

Critically Stressed Faults and Fluid Flow 1

Injection of a Fluid 2

Consolidation of a Soil Layer 2

Drilling of a Borehole 2

Cylinder Problems 3

Borehole Problems 3

Early Time Evolution of Stress near a Permeable Boundary 3

Hydraulic Fracture 3

One dimensional problems 3, 4

- Terzaghi’s problem

- Terzaghi and mixture theory

- Periodic load

- Two-layered soil

- One-dimensional finite elements

Elementary problems 4, (2)

- Mandel’s Problem

- Cryer’s problem

- De Leeuw’s problem

- Spherical source or sink in infinite medium

69

- De Josselin de Jong’s problem

Flow to wells 4

Plain Strain Half Space Problems 4, 5

Plain Strain Layer 4

Plain Strain Finite Elements 4

Axially Symmetric half space problems (axially symmetric consolidation of a

poroelastic half space with a given normal load on the surface) 4

Axially Symmetric Finite Elements 4

Consolidation of a poroelastic half-space with anisotropic permeability 5

The cantilever bracket problem 6

Well placement and subsidence 6

Sudden pressure changes in Porous deformable media 6

Continuous point injection into homogeneous full space 7

Influence of tectonic regime on rock stability during fluid injection/ depletion 7

Borehole breakouts along inclined wellbores 7

Stresses near a pressurized cylindrical cavity 8

Spherical cavity in a porous solid 8

(see also the review study by Singh et al., 2013)

Solutions & Methods

Method of Potentials: Biot’s decomposition, Biot functions, Displacement functions 3

Finite Element Method 3

Boundary Element Method: Direct and Indirect methods 3

Method of Singularities: Modeling Consolidation and Subsidence, Modeling Fracture 3

Numerical inversion of the Laplace transforms pore pressure, isotropic total stress,

vertical total stress, vertical effective stress, horizontal total stress, horizontal effective

stress 4

70

Plain strain poroelasticity - The finite element method for two-dimensional problems

of poroelasticity (Galerkin’s method) 4

Axially Symmetric Finite Elements (Galerkin’s method) 4

Continuous and Discontinuous Galerkin for displacements – Theoretical & Numerical

results for Terzaghi, Mandel’s and Barry & Mercer problems 6

Adaptive Grid Refinement Strategy: Numerical Results for Terzaghi, Mandel’s and

Barry & Mercer problems 6

ADDITIONAL CASE STUDIES (references are not included in the list):

Modeling the medium as a HALF SPACE

This assumption is applicable only to consolidation problems where the thickness of the soil

stratum is much greater than the dimensions of the loaded area.

Paper PROBLEM

Terzaghi, 1923 One dimensional consolidation problem

Biot, 1941 Three dimensional consolidation problem

Biot 1955,

1956a,b

Consider also the effect of anisotropy and wave propagation

in fluid filled media

Rice & Cleary,

1976

Solved a number of problems, including suddenly introduced

edge dislocation, concentrated line force and suddenly

pressurized cylindrical and spherical cavities.

Also reformulated Biot’s linear poroelastic constitutive equations

using more familiar constants

McNamee &

Gibbson,

1960a, b

Solved plain strain & and axially-symmetric consolidation

problems of a semi-infinite clay stratum having incompressible

fluid and solid constituents with isotropic permeability.

71

2 problems of a semi-finite body to the surface of which a

uniform pressure is applied along an infinite strip or over a

circular area.

Schiffman and

Fungaroli,

1965

Extended the previous (displacement function formulation) to

non-axisymmetric problems: Consolidation of a semi-infinite

solid subjected to a uniform tangential load at a pervious and

an impervious surface.

Bell & Nur,

1978

Used two-dimensional half-space models with surface loading

to study the change produced by reservoir-induced pore

pressure and stresses for thrust, normal and strike-slip faults,

assuming that only stresses influence the pore pressure and not

vice-versa

Booker and

Randolph,

1984

Effect of circular and rectangular loading numerically

(consolidation of a poroelastic half-space with cross-anisotropic

deformation and flow properties.

Roeloffs, 1988

Evaluation of stress and pore pressure changes produced by a

steady periodic variation of water level on the surface of a

uniform porous elastic half-space

Yue &

Selvadurai,

1995

Axisymmetric interaction between a rigid, circular flat indenter

and a poroelastic half-space, considering 3 drainage conditions.

Kalpna, 1997

Stresses and pore pressure estimation for an impervious elastic

layer resting on a water-saturated porous elastic half-space

when the upper surface of the layer is acted upon by a normal

stress field varying harmonically in time.

72

Kalpna, 2000

Calculated stresses and pore pressure in a porous elastic half-

space for a time-varying finite reservoir surface load, using

Green’s function approach

Mei et al., 2004

Presented a finite layer procedure for Biot’s consolidation

analysis of layered soil using a cross-anisotropic elastic

constitutive model. Both fluid and solid constituents were

assumed to be incompressible.

Chen, 2005

Steady state response of a multilayered poroelastic half-space

to a point sink. Fluid/ Solid assumed incompressible,

permeability and poroelasticity assumed as transversely

isotropic.

Chen et al,

2005

Axisymmetric consolidation of a semi-finite, transversely

isotropic saturated soil subjected to a uniform circular loading

at ground surface

Singh and

Rani, 2006

Solved two-dimensional plane strain problem of the quasi-

static deformation of a multi-layered poroelastic half-space by

surface loads. Fluid/ Solid assumed compressible with

isotropic permeability

Conte, 2006

Analysis of coupled consolidation in unsaturated soil under

the condition of plane strain as well as axial symmetry due to

strip and circular loads.

Singh et al.,

2007

quasi-static plane strain deformation of a poroelastic half-space

with anisotropic permeability and compressible constituents

by two-dimensional surface loads (analytical solution). Normal

strip problem discussed in detail.

73

Singh et al.,

2009

Problem of consolidation of a poroelastic half-space with

anisotropic permeability by axisymetric surface loads,

assuming compressible fluid and solid constituents.

Ai et al., 2008

Solved Biot’s 3D consolidation problem for a saturated

poroelastic multi-layered soil due to loading at an arbitrary

interface. Incompressible medium and isotropic permeability.

Ai et al., 2010a

Solved the corresponding problem with the previous one for a

circular loading. Incompressible medium and isotropic

permeability.

Ai et al, 2010b

Axisymmetric and non-axisymmetric consolidation of a multi-

layered solid under arbitrary loading. Incompressible medium

and isotropic permeability.

Modeling the poroelastic medium as FINITE LAYER

Paper PROBLEM

Gibson et

al., 1970

Solution for consolidation of a uniform clay layer resting on a

smooth-rigid base subjected to circular or strip loading.

Booker,

1974

Problem of the consolidation of a uniform clay layer subjected to

general normal surface loading, assuming that the lower strip

surface adheres completely to a rigid base. Solutions for the case

of uniformly loaded strip, circle and square were evaluated for a

variety of Poisson’s ratio values. Incompressible medium and

isotropic permeability were assumed.

Booker and

Small, 1987

Consolidation of a layered soil subjected to strip, circular and

rectangular surface loading, or subjected to fluid withdrawal due

to pumping (numerical inversion)

74

Yue et al.,

2004

Analytical investigation of the quasi-static development of excess

pore pressure in a poroelastic seabed layer, of finite thickness,

saturated with a compressible pore fluid and resting on a rough-

rigid impermeable base.

Selvadurai

& Yue, 1994

The axisymmetric contact problem related to the indentation of a

fluid saturated poroelastic layer resting on a rigid impermeable

base due to circular foundation.

Conte, 1998

Consolidation problem involving anisotropic layered soils which

contain incompressible as well as compressible pore fluid caused

by surface loading (numerical procedure).

Chen et al.,

2005b

Axisymmetric consolidation of a transversely isotropic soil layer

resting on a rough impervious base and subjected to a uniform

circular pressure at the surface (semi-analytical solution).

Transversely isotropic medium in each elastic and hydraulic

properties. (However, in numerical computations, only the effect of the

elastic anisotropy was studied)

Chen et al.,

2007

Analytical solution for the consolidation of a soil layer subjected

to vertical point loading. Incompressible medium and isotropic

permeability.

Ai and

Wang, 2008 Axisymmetric consolidation problem of a finite soil

Ai and Wu,

2009

A solution for plane strain consolidation of a soil layer with

anisotropic permeability and incompressible fluid and solid

constituents due to surface loads.

Rani et al.,

2011

Obtained the corresponding axisymmetric solution when the

fluid and solid constituents are compressible.

75

Other solutions for Consolidation Problems

Paper PROBLEM - SOLUTION

Carter, 1986

Close-form solutions for the steady-state distribution of

displacement, pore pressure and stress around a point sink.

Solutions obtained for the long-term settlement caused by

withdrawal of fluid from a point sink at finite depth below the

surface of a homogeneous isotropic porous elastic half-space

with isotropic permeability.

Booker and

Carter, 1987

Solution for the transient effect of pumping fluid from a point

sink embedded in a saturated porous, elastic half space.

Homogeneous and isotropic medium elastic properties,

anisotropic pore fluid, incompressible fluid.

Booker and

Carter, 1987b

Corresponding problem of withdrawal of a compressible pore

fluid from a point sink in an isotropic elastic half-space with

anisotropic permeability.

Tarn and Lu,

1991

Analytical solutions of the long-term consolidation and excess

pore water pressure due to fluid withdrawal from saturated

porous elastic half-space. Both permeability and elastic

properties were considered to be cross-anisotropic

Chau, 1996

Fundamental solutions for the interior fluid point source

and point forces embedded in a poroelastic half-space with

incompressible constituents and isotropic permeability.

Ganbe and

Kurashige,

2000

Fundamental solutions for an elastically isotropic poroelastic

solid having transversely isotropic permeability due to

instantaneous fluid point source and instantaneous point force.

76

Taguchi and

Kurashige,

2002

Fundamental solutions for point forces acting on three

orthogonal directions and an instantaneous fluid point source

in a fluid saturated, porous and infinite solid of transversely

isotropic elasticity and permeability. (too lengthy solutions)

Wang and

Kuumpel, 2003

Numerical scheme to compute poroelastic solutions for excess

pore pressure and displacements in a multilayered half-space

(using mirror-image technique and an extension of Haskell’s

propagator method).

Chen, 2003 Analytical solutions for the steady-state response of a multi-

layered poroelastic half-space subjected to pumping

Chen and

Gallipoli, 2004

Analytical solution for the steady state infiltration from a

buried point source into a heterogeneous cross-anisotropic

unsaturated half-space.

Lu and

Hanyga, 2005

Fundamental solution for a layered porous half-space

subjected to a vertical point force or a point source.

Singh and Rani

(2007)

Formulated the two-dimensional plane strain problem of the

quasi-static deformation of a multi-layered poroelastic half-

space with compressible constituents by internal sources. The

integral expressions for the surface displacement and fluid flux

are obtained for a vertical line force, a horizontal line force and

a fluid injection line source.

ACKNOWLEDGEMENTS: This work was supported within SHEER: "Shale Gas Exploration and Exploitation Induced Risks" project funded from Horizon 2020 – R&I Framework Programme, call H2020-LCE-2014-1 and within statutory activities No3841/E-41/S/2016 of Ministry of Science and Higher Education of Poland.

77

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