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PROCEEDINGS, Fourtieth Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 26-28, 2015
SGP-TR-204
1
Thermo-Hydro-Mechanical modeling of EGS using COMSOL Multiphysics
Danijela Šijačić and Peter A. Fokker
TNO, Princetonlaan 6, 3584CB Utrecht, The Netherlands
[email protected] and [email protected]
Keywords: EGS, Induced seismicity, Finite element modeling, Full coupling, Thermal effect.
ABSTRACT
We investigated the occurrence of induced seismicity during operations of EGS (Enhanced Geothermal Systems) with a focus on the
thermal effects. To this end we employed a finite element model with a full coupling of mechanics, flow and temperature. It became
clear that the thermal effects play a crucial role in the development of injectivity, and thus should be taken into account in the
operational design. The thermal effects are not limited to the time of injection but persist during shutin. Especially boundaries with large
permeability contrasts are important as they generate large temperature gradients which slowly level due to thermal diffusion.
Furthermore, our work focused on the incorporation of seismicity. We derived a seismicity model starting from basic physical processes
and we developed a fully coupled thermo-hydro-mechanical model for seismicity from the fundamental physics. The seismic model
includes frictional weakening and healing, inspired by current rate-and-state-friction models. With our model the estimated seismicity is
realistic and that the events of larger magnitudes are included. A quantitative comparison with field test results is still beyond the reach
of our simplified model.
1. INTRODUCTION
The operation of Enhanced Geothermal Systems (EGS) is intended to stimulate the permeability of a network of natural fractures
(Tester, Anderson et al. 2006). High pressures and low temperatures of the injected water cause the fractures to deform and to open, thus
providing additional injectivity.
The effective modeling of EGS requires the coupling of geomechanics, fluid flow and thermal processes. Understanding of the complete
system with these coupled processes is vital, not just for reservoir stimulation targeted at enhancing reservoir performance, but also for
the understanding, prediction and prevention of induced seismicity (Davis and Frohlich 1993). The injection of cold water and
extraction of hot water and steam leads to alterations in in-situ stresses and strains in the reservoir, which can result in fracture initiation,
opening, and activation of faults and joints leading to induced seismicity. Indeed, many EGS sites (like Soultz and Geysers) have shown
significant seismicity upon injection and production. It is generally understood that poromechanical and thermomechanical processes
cause a fracture opening and slip and that induced seismicity is also related to water flow and enhanced permeability. However, thermal
effects tend to be neglected in models for reservoir stimulation (Wassing et al. 2014), although there is strong evidence that they can
play an important role (Gunnarsson 2011).
In this work we investigated the coupling of all processes, and especially the influence of temperature changes on the full system. Our
coupled model was built on basic physical laws and from that physical standpoint we aimed to say something about induced seismicity.
The platform which we used to build coupled model is COMSOL Multiphysics. Full coupling of flow, heat transfer and mechanics
(Figure 1) was implemented using three COMSOL built in modules: Darcy’s Law, Solid Mechanics and Heat Transfer in Porous
Media.
The induced seismicity is directly proportional to the seismic moment which depends on failing area, shear displacement and shear
modulus, and can be calculated using COMSOL. This way, geomechanical coupled modeling can be related to seismic hazard
assessment which leads to understanding, predicting and preventing undesired seismicity.
2. THE MODEL
2.1 Geometry
We started by building a simple 2D model representing a cross-section of a (quarter) of an injection well and a squared area around it
(see Figure 1). The area around the well represents the rock matrix. A plane or a zone that was fractured and had different properties
from the surrounding rock is depicted as a domain F in Figure 1 (Fractured zone).
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Figure 1: The model: Well (1/4) and a surrounding area of 100x100m, with the Fracture Zone (domain F).
We also investigated a 3D model with horizontal 2D cross section as in Figure 2, consisting of a rock mass (block) of 100x100x100 m3.
It contained a fracture zone with a dip of 60° in an impermeable matrix of granites. The fracture zone had a thickness of 20 m and initial
permeability of 500 mD. Via a vertical injection well, located at the bottom of the matrix block, cold water (20°C) was injected into the
fracture zone at constant injection rate (see Figure 2).
Figure 2: Injection of cold water into the fractured zone of the warm matrix.
2.2 Coupled Processes
The injection of cold water and the extraction of hot water and steam perturbs the in situ stress in the reservoir. Poroelasticity describes
the influence of pore pressure on stress and strain. In turn, the changes in stress and strain change permeability and porosity, which
influences fluid flow. Heat-convecting fluid flow (cold water injected in hot rock) influences the temperature distribution, which in turn
influences the fluid viscosity (and density), altering again the flow itself. The temperature change will also create thermal stresses,
affecting the geomechanics. In the geomechanical model we used Mohr-Coulomb failure and associated shear dilation for fault
reactivation.
We used the following COMSOL Multiphysics and coupled processes:
• Flow in the porous medium is described by Darcy’s law and the continuum equation. Permeability of the fracture zone
behaves according to the cubic law. Porosity changes due to volumetric strain and viscosity change due to temperature.
F
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• Mechanics: Intact parts of rock matrix are described by a Linear Elastic Model, while deformation of fracture zone is
described by the Mohr-Coulomb Model. Poro- and thermo- elastic stresses are taken into account.
• Heat Transfer is described by the heat equation (with diffusion and conduction term) where the Darcy velocity field and the
pore pressure are leading the heat flow (convection).
3. RESULTS
3.1 Model Implementation
A number of sensitivity tests were performed on the 2D model to identify the influence of the incorporation of thermal effects.
Incorporating thermal effect, however, was far from trivial. The abrupt change in permeability between the fracture zone and its
surroundings resulted in large temperature gradients at the interface (Figure 3), leading to numerical instabilities. To numerically
stabilize the calculations we had to add crosswind diffusion to the heat transfer process and we had to use boundary layer elements in
the mesh at the internal boundaries. Still, the highly nonlinear effects and the very different time scales on which temperature effects
interact with flow and mechanics caused numerical instabilities and solutions which were diverging soon after failure. We report the
effects as observable as long as code stability lasted.
Table 1: Base case input parameters
Pressure increase rate 1000 Pa / s Maximum in-situ stress 16 MPa
Friction angle 0.4 rad Minimum in-situ stress 12 MPa
Injection time 63 hr Duration of Shutin 542 hr
Figure 3: Temperature profile calculated with the fine mesh and mesh boundary layers.
3.2 Thermal Effects
In this paper we mainly focus on investigating the influence of temperature and heat transfer on stress distribution displacements and
flow properties.
Figure 4 compares the Von Mises stresses for the base case simulations with and without incorporation of thermal effects. The von
Mises stress is a measure for the anisotropy of the stress. The Von Mises stress is up to 3 times higher for the system where temperature
effect are included compared when they are neglected. The highest stress is distributed at the fracture zone walls; that is also the region
where failure is occurring.
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Figure 4: Von Mises stress for the system where thermal effects are ignored (left) and incorporated (right)
The stresses induced by the water injection lead to deformation. With temperature effects included (Figure 5), the cooling of fracture
zone reduces the normal stresses considerably; the sustained large shear stresses cause plastic failure in a large regions, with much
larger deformations than without. The effect of the cooling is in this case larger than the effect of the poro-elastic reduction of the
effective stresses, which also tend to promote failure.
Figure 5: Total displacement without (left) and with (right) thermal effects included.
The final effect of temperature is not established in a straightforward manner. Figure 6 presents the development of the permeability in a
point close to the injection point. After 55 hours of injection, the incorporation of coupling of the temperature effects has increased the
permeability of the system more than 3 times as compared to a system where temperature is neglected. In the startup phase of the test,
however, the permeability behaves differently: in the fully coupled system the permeability first decreases with 20%, then stabilizes for
some time before eventually increasing more rapidly than in the case of the system where temperature is neglected. The dynamics of
pressure and temperature distributions during the injection phase cause a non-trivial behavior that can only be understood through
modeling. The cooling effects in the well proximity are substantial and should not be ignored.
Figure 6: Permeability curves for fully coupled system and system where temperature effects are neglected.
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It has been noticed in field tests that after injection of water is stopped, induced seismicity does not vanish immediately. In some cases,
the level of seismicity even increased after shutin, until all pressures had relaxed (Dorbath and Cuenot et al. 2009) . Therefore we
modelled a case where injection of water was stopped at t= 300000 s with the goal to investigate the effects of continued temperature
diffusion. Figure 7 shows the actual injection scheme and the evolution of the well pressure and the pressure in the formation close to
the well. The cooling process reduces pressures substantially and the effect of pressure redistribution is continued long after shutin.
Figure 7: Well pressure and the applied injection scheme (left) and resulting pressures in fracture zone at 1 m from the well.
Figure 8 visualizes the Von Mises stresses for the systems without and with thermal effects. The effect is even larger than for the case
with continuous injection. This may be related to the ongoing thermal diffusion, causing the cooling to enter the matrix deeper. Figure 9
shows that indeed the temperature is distinctly different from the profile with continued injection (Figure 3), with the large gradients
now smoothed by the diffusion.
Figure 8: Von Mises stress after 83 hours of injection, and 542 hours after shutin; for the system without (left) and with (right)
thermal effects.
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Figure 9: Temperature profile after shutin.
3.3 Relation to EGS in Iceland
A good example of the effect of temperature is the operation of the Hellisheidi Power Plant, SW-Iceland (Gunnarsson 2011).
Reinjection was scheduled in this field to maintain the reservoir pressures. The formation temperature at the originally planned
reinjection zone turned out to be very hot: more than 300°C. The new wells were drilled into an active fault and injection tests resulted
in swarms of small earthquakes. The temperature of the reinjected water was varied between 20°C and 120°C. Surprisingly, the
injectivity of the wells in the new reinjection zone was much higher for colder water than for warmer water, although the viscosity of te
cold water is 5 times larger than of hot water. This effect was observed in a number of wells, and the injectivity ratio between injection
with cold and with hot water varied between 3 and 6.
Our 2D models with the wide fault zones and the very limited incorporation of local geology of course can not be expected to yield
quantitatively matching results. Our aim here is to test whether the effect of the temperature-dependent flow properties can be overruled
by thermo-mechanical effects. Figure 10 shows relative permeability change during injection of warm water (left side) and cold water
(right). One can see that due to the cooling, shrinking of matrix occurs and permeability increase is higher when the injected water is
colder. In Figure 11 we can see that the temperature-dependent enhancement of flow is substantially diminished by the geomechanical
response of the fracture.
Figure 10: Permeability distribution for the injection of warm water (left) and cold water (right).
This modeling does not predict higher injectivity of cold water than of warm water, however, the thermoelastic stress does increase
permeability. If tensile opening occurs – which was not modeled in our approach – increased injectivity of cold water will be the result.
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Figure 11: Injectivity rate for the injection of warm water (red) and cold water (blue).
Figure 12: Injectivity rate for the injection of warm water (red) and cold water (blue) scaled with the viscosity of water at
T=120°C and T=20°C, respectively.
4. INDUCED SEISMICITY
To understand processes and parameters that influence seismicity during operation of EGS we connect fully coupled physical model
with the theory of induced seismicity. The seismic moments (M0) and moment magnitudes (Mw) were calculated from the shear
displacement and failing area. Shear failure was described by a Mohr-Coulomb failure envelope between effective normal stress ‘n
and shear stress , with the cohesion c and the friction angle as parameters:
tan'
nc (1)
The initial friction angles were given spatially varying values. We start with the inhomogeneous distribution of the angle of internal
friction as shown in Figure 13 with a random distribution of friction angle in the range from 23deg° to 29deg°.
Slip weakening was implemented as a decrease of the friction angle (up to 3 deg°) in the area where Mohr-Coulomb failure has started.
With such slip weakening, which is realistic in view of the geological reality and fault rupture models (McClure and Horne 2011),
seismic events of larger magnitudes can be expected. After a seismic event, healing could be enabled by letting the friction angle
increase to its original value. The concept of healing was inspired by current dynamic seismicity models, such as those using a rate-and-
state description for fault friction (Marone 1998).
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The seismic moments M0 and the moment magnitudes Mw were calculated from the shear displacement in every failing grid block (Aki
1966, Hanks and Kanamori 1979). They are given by:
07.6log 03
2
0
MM
AdGM
w
(2)
in which G is the shear modulus, d the displacement and A the fracture area that is failing. To arrive at interpretable moment magnitudes
of events, all simultaneous seismic moments of different grid blocks were summed. Since from 2D cross-section models we are missing
third dimension to determine failing area, we have estimated it to be in the order of 10 meters. Sensitivity analysis is done for H= 10, 20
and 30 m. Presented results are for 30 meters.
Figure 13: Random distribution of friction angle at initial stage.
Figure 14: Weakening of the failing area close to well (left) and its recovering (right) at the times 3000s and 5000s respectively.
Considering the seismic properties, we are interested in moment magnitudes, and the number of events with the certain magnitudes. For
that reason we look at the frequency-magnitude correlation. One example of induced seismicity from the injection of cold water (of
20°C) is presented in Figure 15 where evolution of moment magnitudes is depicted. In Figure 16 the frequency-magnitude distribution
is presented. Gutenberg and Richter (1944) modeled the magnitude distribution as log𝑁 = 𝑎 − 𝑏 wM , where N is the number of
seismic events having a magnitude larger than wM , and 𝑎 and 𝑏 are constants. In that empirical relation for seismicity occurrence, 𝑏-
value represents the cumulative number of seismic events at each location within the reservoir with the local magnitude evaluated from
its seismic moment. Common range for a b-value is from 0.5 to 2, where 1 (or close to 1) is being the most frequent value. Higher
values (such as 2.5 for example) are indicating a very high proportion of small earthquakes to large ones and are typical for swarms
which are often associated with volcanic activity.
As the main focus of this work was the influence of temperature and the full coupling of all hydro-mechanical and thermal processes,
we have investigated the consequences of neglecting thermal effects. In Figure 17 the evolution of moment magnitudes and the
frequency-magnitude correlation (from Figure 15 and 16) are compered for simulations from the fully coupled model (case 1) and for
the model where thermal effects are neglected (case NT – no thermal). Omitting the thermal stress leads to the prediction of fewer
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triggered seismic events during the stimulation period and to a reduction of about 20% of the largest expected magnitude. In both cases
the b-value remains at the high side, around 2.
Figure 15: Moment magnitudes of events as they evolve in time (left), close up of the events during the injection period (right).
Temperature of injected water is 20°C.
Figure 16: Frequency-magnitude correlations.
Figure 17: Moment magnitudes evolution (left) and frequency-magnitude correlations (right) for the fully coupled THM model
– (case 1 – in blue color) and for the reduced model where thermal effects are neglected (case NT – in green color).
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5. CONCLUSION
We implemented a finite element modeling approach for the simulation of EGS operations with a full coupling of mechanics, flow and
temperature. In particular the influence of temperature was tested. From our calculations it became clear that the thermal effects play a
crucial role in the development of injectivity, and thus should be taken into account in the operational design. The thermal effects are
not limited to the time of injection but persist during shutin. Especially boundaries with large permeability contrasts are important as
they generate large temperature gradients which slowly level due to thermal diffusion. Neglecting the thermal effects is not justified,
since they do change the physics of the system. The von Mises stress is more than three times higher for the system where thermal
effects are included, and so is the permeability enhancement. Also, stress effects are localized at the fracture walls for the fully coupled
system.
Furthermore, our work focused on the incorporation of seismicity. We derived a seismicity model starting from basic physical processes
and we developed a fully coupled thermo-hydro-mechanical model for seismicity from the fundamental physics. The seismic model
includes frictional weakening and healing. Those processes ensure that the estimated seismicity is realistic and that the events of larger
magnitudes are included. The fully coupled model triggered more seismicity during the stimulation period and the largest seismic event
had larger magnitude compared to that of the model where thermal effects were neglected. A next step would be to calibrate the model
and the resulting seismicity using real parameters for, e.g., the Soultz geothermal field. Further sensitivity analysis on parameters like
injection rates, in-situ stress regime, fracture strength and frictional weakening will allow to evaluate the trends of their impact on
seismic moment and moment magnitudes.
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