**4. Results and discussions**

*<sup>u</sup> u Nu* = (18)

*<sup>p</sup> p Np* = (19)

*<sup>T</sup> T NT* = (20)

¯ are the nodal values of the

(22)

(23)

(21)

Where N is the corresponding shape function and *u*¯, *p*¯ and *t*

ab

g

temperature, T is the fluid temperature and *μ* is the fluid viscosity.

**3. Fracture network generation**

directions.

vation equations can be written as follow [29, 30]:

580 Effective and Sustainable Hydraulic Fracturing

corresponding state variable. By applying the Galerkin's method and replacing the weighting functions by the corresponding variables' shape functions, the discretized form of the conser‐

> 2 <sup>1</sup> ( )( ) 0 3 *<sup>m</sup> <sup>G</sup> K uG u p T* + Ñ Ñ× + ×Ñ - Ñ - Ñ =

> > *u p pT* m

Ñ× + - Ñ - = gg g

<sup>2</sup> () 0 *<sup>T</sup> Tv T c T* +Ñ -Ñ =

a

2 <sup>2</sup> ( ) <sup>0</sup> *<sup>k</sup>*

where, K is the bulk modulus of elasticity, G is the shear modulus, *γ*1 and *γ*<sup>2</sup> are the thermal expansion coefficient of the fluid and solid respectively; k is the permeability Tm is the matrix

Simulation of naturally fractured reservoirs offers significant challenges due to the lack of a methodology that can utilize field data. To date several methods have been proposed in the literature to characterize naturally fractured reservoirs. In this study a hybrid tectonostochastic simulation is proposed to characterize a naturally fractured reservoir [31]. A finite element based model is used to simulate the tectonic event of folding and unfolding of a geological structure. A nested neuro-stochastic technique is used to develop the interrelationship between different sources of data (seismic attributes, borehole images, core description, well logs etc.) and at the same time the sequential Gaussian approach is utilised to analyze field data along with fracture probability data. This approach has the ability to overcome commonly experienced discontinuity of the data in both horizontal and vertical

 g

 g The proposed methodology is used to generate the discrete fracture map of the Soultz geothermal reservoir at the depth of 3650 m. the statistical parameters used to generate the discrete fracture map is shown in Table 1.


**Table 1.** Statistical data used for the discrete fracture network generation. After [32]

The discrete fracture map, the corresponding mesh generated for the reservoir domain and the permeability tensors for each triangular element (a sample region which is cut by a fracture of length<50m) are shown in Fig. 5 (a), (b) and (c) respectively.

Also the reservoir properties used for the stimulation purpose are shown in Table 2. The reservoir is pressurized by injecting fluid through the injection well (GPK2). The pressurization was carried out over a period of 52 weeks. During the pressurization, the change in fracture width for each individual natural fracture and the resulting permeability tensor were calcu‐ lated. Following stimulation of the reservoir, a flow test was carried out over a period of 14 years. During the flow test, changes in fracture apertures due to thermo-poro-elastic stresses and the consequent changes in permeability were determined. Also estimated were the thermal drawdown, produced fluid temperature and production rate of the Soultz EGS.

Results of shear dilation are presented as average percentage increase in fracture aperture (see Fig. 6). From Fig. 6, it can be seen that there exists three distinct aperture histories: 0-40 weeks, 40-50 weeks and 50 weeks and above. Until about 40 weeks, a slow but linear increase in occurrence of dilation events due to induced fluid pressure of 51.7 MPa (bottom hole) and reaches a value of about 18% (average increase in aperture). Following this time, the rate of occurrence of dilation events increases sharply until about 50 weeks, thus reaching 60% increase in average fracture aperture. After which, no significant dilation events can be observed (a plateau of events is reached). When compared with previous study [29], in which shear dilation events are estimated based on a semi-empirical model (Willis-Richards et al,

**Figure 5.** a) discrete fracture network at the depth of 3650 m (b) the corresponding discretization for the fractures longer than 50 m and (c) permeability tensor for a sample fracture (<50m).

1996), it can be seen that the time required to overcome the threshold stress is 40 weeks which is about 12 weeks longer than the previous studies. Also the time requires for an increase in the average fracture aperture of 58 % is about 8 weeks longer than that predicted by the previous study. During the flow test, changes in fracture apertures due to thermo-poro-elastic stresses and the consequent changes in permeability were determined. Also estimated were the thermal drawdown, produced fluid temperature and production rate of the Soultz EGS.

The locations of the dilation events during the stimulation period are shown in Fig. 7. As shown in this figure, after 40 weeks of stimulation about half of the reservoir is affected by the shear dilation and after 52 weeks of injection shear dilation happened in almost all parts of the reservoir.

Also the reservoir pressure and stress distribution profiles (see Figs. 8 and 9) show that after 40 weeks of stimulation the injected fluid pressure affected almost all of the fractures and that after 52 weeks of injection the pressure is established in all part of the reservoir domain. Similarly the x- and y component of the effective stress decreased significantly over the entire reservoir domain towards the end of the stimulation period.

After the stimulation period a numerical experiment is carried out to assess the produced matrix temperature for 14 years of cold fluid circulation. Because of the low fluid and rock matrix contact area at the early stage of production, the heat transfer and the resulting thermal drawdown is very low (see Fig 10 a). With the pass of time the fluid sweeps over a large part of the reservoir which increases thermal drawdown. At the end of the 14 years of production the average matrix temperature drops from 200 to 150°C which is quite low (drop of 500 C) compared to previous studies (drop of 80o C over the production period of 14 years as in [29]) under the same reservoir conditions. Also in Fig. 10 (bottom) the Log10 RMS fluid velocity profile after 1 year, 10 years and 14 years of production are presented. From the results it can be observed that during the early production period (1 year) high pore pressure is primarily

built up around the injection well and the flow of fluid is primarily through major interconnected flow paths. With the progress of time the injection pressure advances towards the

**Rock Properties**

**Fracture properties**

**Stress data**

**Fluid properties**

**Other reservoir data**

**Table 2.** Stress and reservoir data for strike-slip stress regime at Soutlz geothermal reservoir.

Young's modulus (GPa) 40 Poisson's ratio 0.25 Density (kg/m3) 2700

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583

A New Approach to Hydraulic Stimulation of Geothermal Reservoirs by Roughness Induced Fracture Opening

Fracture basic friction angle (deg) 40 Shear dilation angle (Deg) 2.8 90% closure stress (MPa) 20 In situ mean permeability (m2) 9.0 x 10-17

Fractal Dimension, D 1.2 Fracture density (m2/m3) 0.12 Smallest fracture radius (m) 15 Largest fracture radius (m) 250 Fracture Permeability 0.3x10-15

Maximum horizontal stress (MPa) 78.9 Minimum horizontal stress (MPa) 53.3

Hydrostatic fluid pressure (MPa) 34.5 Injector pressure, stimulation (MPa) 51.7 Injector pressure, production (MPa) 44.8 Producer pressure, stimulation (MPa) N/A Producer pressure, production (MPa) 31.0

Density (kg/m3) 1000 Viscosity (Pa s) 3 x 10-4

Well radius (m) 0.1 Number of injection wells 1 Number of production wells 2 Reservoir depth (m) 3650


1996), it can be seen that the time required to overcome the threshold stress is 40 weeks which is about 12 weeks longer than the previous studies. Also the time requires for an increase in the average fracture aperture of 58 % is about 8 weeks longer than that predicted by the previous study. During the flow test, changes in fracture apertures due to thermo-poro-elastic stresses and the consequent changes in permeability were determined. Also estimated were the thermal drawdown, produced fluid temperature and production rate of the Soultz EGS.

**Figure 5.** a) discrete fracture network at the depth of 3650 m (b) the corresponding discretization for the fractures

(a) (b) (c)

The locations of the dilation events during the stimulation period are shown in Fig. 7. As shown in this figure, after 40 weeks of stimulation about half of the reservoir is affected by the shear dilation and after 52 weeks of injection shear dilation happened in almost all parts of the

Also the reservoir pressure and stress distribution profiles (see Figs. 8 and 9) show that after 40 weeks of stimulation the injected fluid pressure affected almost all of the fractures and that after 52 weeks of injection the pressure is established in all part of the reservoir domain. Similarly the x- and y component of the effective stress decreased significantly over the entire

After the stimulation period a numerical experiment is carried out to assess the produced matrix temperature for 14 years of cold fluid circulation. Because of the low fluid and rock matrix contact area at the early stage of production, the heat transfer and the resulting thermal drawdown is very low (see Fig 10 a). With the pass of time the fluid sweeps over a large part of the reservoir which increases thermal drawdown. At the end of the 14 years of production the average matrix temperature drops from 200 to 150°C which is quite low (drop of 500

under the same reservoir conditions. Also in Fig. 10 (bottom) the Log10 RMS fluid velocity profile after 1 year, 10 years and 14 years of production are presented. From the results it can be observed that during the early production period (1 year) high pore pressure is primarily

C over the production period of 14 years as in [29])

C)

reservoir domain towards the end of the stimulation period.

longer than 50 m and (c) permeability tensor for a sample fracture (<50m).

582 Effective and Sustainable Hydraulic Fracturing

compared to previous studies (drop of 80o

reservoir.

**Table 2.** Stress and reservoir data for strike-slip stress regime at Soutlz geothermal reservoir.

built up around the injection well and the flow of fluid is primarily through major interconnected flow paths. With the progress of time the injection pressure advances towards the

**Figure 6.** Comparison of Average aperture increase between the current approach and the previous study.

**Figure 7.** Location of the dilation events marked by the dots after (a) 1 week (b) 40 weeks and (c) 52 weeks of stimula‐ tion with σH = 78.9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

geothermal reservoir during different stages of production are shown in Fig. 11. These results show that by the end of 14 years of production the effective stresses throughout the reservoir are significantly reduced, thus allowing most fractures to open and conduct fluid. The reduction in the effective stresses is caused by the cold circulating fluid as well as thermal

**Figure 9.** x (top) and y (bottom) components of effective stress after: (a) 1 week, (b) 40 weeks and (c) 52 weeks of

stimulation for σH = 78. 9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

(a) (b) (c)

**Figure 8.** Pore pressure distribution of the fractured reservoir at different stimulation stages: after (a) 1 week, (b) 40 weeks and (c) 52 weeks for a strike slip stress regime with σH = 78.9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

A New Approach to Hydraulic Stimulation of Geothermal Reservoirs by Roughness Induced Fracture Opening

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585

drawdown.

production well. After 14 years of production, the fluid sweeps through a significant part of the reservoir. Also the x- and y components of effective stress distribution of the Soultz

A New Approach to Hydraulic Stimulation of Geothermal Reservoirs by Roughness Induced Fracture Opening http://dx.doi.org/10.5772/56447 585

**Figure 8.** Pore pressure distribution of the fractured reservoir at different stimulation stages: after (a) 1 week, (b) 40 weeks and (c) 52 weeks for a strike slip stress regime with σH = 78.9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

**Figure 9.** x (top) and y (bottom) components of effective stress after: (a) 1 week, (b) 40 weeks and (c) 52 weeks of stimulation for σH = 78. 9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

geothermal reservoir during different stages of production are shown in Fig. 11. These results show that by the end of 14 years of production the effective stresses throughout the reservoir are significantly reduced, thus allowing most fractures to open and conduct fluid. The reduction in the effective stresses is caused by the cold circulating fluid as well as thermal drawdown.

production well. After 14 years of production, the fluid sweeps through a significant part of the reservoir. Also the x- and y components of effective stress distribution of the Soultz

**Figure 7.** Location of the dilation events marked by the dots after (a) 1 week (b) 40 weeks and (c) 52 weeks of stimula‐

tion with σH = 78.9 MPa and σh = 53.3 MPa, Pinj = 51.7 MPa.

584 Effective and Sustainable Hydraulic Fracturing

**Figure 6.** Comparison of Average aperture increase between the current approach and the previous study.

**5. Conclusions**

**Author details**

**References**

5374-5378.

11(3): p. 143-150.

additional permeability enhancement.

Nima Gholizadeh Doonechaly1

\*Address all correspondence to: sheik.rahman@unsw.edu.au

troleum Science and Technology, 2013. 31(7): p. 727-737.

Geomechanics Abstracts, 1980. 17(1): p. 25-33.

In this paper, a roughness induced shear displacement model in a poro-thermoelastic envi‐ ronment combined with an advanced computational technique is used to study the effects of induced fluid pressure and thermal stresses (cooling effect) on reservoir permeability and consequent increase in hot water production. It has been shown that surface roughness induced shear displacement provides a more realistic prediction of residual fracture aperture. These results agree well with the experience of existing EGS trials around the world. An average increase in aperture due to fluid induced shear dilation has been found to be lower and time required to obtain a maximum stimulated volume is greater. Results of this study are in consistent with that of previous studies: for every geothermal system there exists an optimum injection schedule (injection pressure and duration). Any further increases in stimulation effort, i.e. stimulation time for a given stimulation pressure, does not provide

A New Approach to Hydraulic Stimulation of Geothermal Reservoirs by Roughness Induced Fracture Opening

http://dx.doi.org/10.5772/56447

587

, Sheik S. Rahman1\* and Andrei Kotousov2

1 School of Petroleum Engineering, University of New South Wales, Sydney, Australia

2 School of Mechanical Engineering, the University of Adelaide, South Australia, Australia

[1] Roshan, H. and S.S. Rahman, Effects of Ion Advection and Thermal Convection on Pore Pressure Changes in High Permeable Chemically Active Shale Formations. Pe‐

[2] Lockner, D.A., J.B. Walsh, and J.D. Byerlee, Changes in seismic velocity and attenua‐ tion during deformation of granite. Journal of Geophysical Research, 1977. 82(33): p.

[3] Hast, N., Limits of stress measurements in the Earth's crust. Rock mechanics, 1979.

[4] Solberg, P., D. Lockner, and J.D. Byerlee, Hydraulic fracturing in granite under geo‐ thermal conditions. International Journal of Rock Mechanics and Mining Sciences &

**Figure 10.** Reservoir temperature profile (top) and Log10RMS fluid velocity profile (bottom) after (a) 1 year (b) 10 years and (c) 14 years of production with σH = 78.9 MPa and σh = 53.3 MPa, Pinj=44.8 MPa and Pprod=31 MPa.

**Figure 11.** x (top) and y (bottom) component of effective stress after (a) 1 year (b) 10 years and (c) 14 years of produc‐ tion with σH = 78.9 MPa and σh = 53.3 MPa, Pinj=44.8 MPa and Pprod=31 MPa.
