**3. Thermal fracturing in the reservoir below isothermal fracture pressure**

Thermal effects of CO2 injection is expected to affect the magnitude of displacements, pressure, stresses, and the possibility of shear and tensile failure in the reservoir and caprock. Injecting fluid with temperature lower than reservoir rock temperature will cause reduction of stresses in the injection layer and once the temperature front has reached a relatively large area around the wellbore, this reduction in stresses will result in negative volumetric strains that can propagate to the surface. Therefore the surface displacement for the thermal model would be smaller than that of isothermal model [6].

One of the most important effects of injecting a fluid with a lower than reservoir temperature is the reduction of fracture pressure. Cooling of the formation rock during injection of cold CO2 through thermal conduction and convection lowers the total stresses in the reservoir and possibly caprock layer. This results in reduction of fracture pressure and the pressure differ‐ ential available for injection, and therefore injectivity. In the case of injection at fracturing conditions, the fracture propagation pressure will decrease and, if the same injection rate is used, this will accelerate fracture propagation.

In order to examine thermal effects of injection on the possibility of reaching tensile failure in the reservoir, the variation of total stress and pressure needs to be studied. In order to do that, the coupled geomechanical, flow and thermal simulation has been carried out with two different injection temperatures. The injection of CO2 for these models is through a single vertical well with constant rate of 3.4E4 m3/day such that the bottomhole pressure will remain below fracture pressure for the isothermal model during 30 years of injection. It should be noted that fracturing was not allowed in these models. Thermal model in this study refers to injection temperature (30 C) being lower than the reservoir temperature (60 C),while in the isothermal model, it is equal to reservoir's temperature. Figure 3 shows the modeling results for pressure, and total minimum stress for well block in the reservoir during 30 years of injection for the thermal and isothermal model. As it is seen in Figure 3, the total stress falls below the bottomhole pressure (fracture pressure) for the thermal model in the reservoir at quite early injection times which means that minimum effective stress will reduce beyond zero. Therefore, although CO2 is injected below the original fracture pressure, fracture would initiate in the reservoir for the thermal case. Since fracturing is not allowed in these models, the stress magnitudes after the onset of fracturing are not valid. If propagation was allowed, minimum total stress would reduce to slightly below bottomhole pressure such that the effective stress on the fracture wall would remain close to zero.

in the model both as a function of pressure or effective minimum stress. The actual fracture

**Figure 3.** Pressure, minimum stress, and stress level for the thermal and isothermal model for the well block in the

0 5 10 15 20 25 30

Pressure (Isothermal)

Pressure (Thermal)

Minimum Stress (Isothermal)

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Minimum stress (Thermal)

**Time(yr)**

Figure 4 shows the bottomhole pressure and fracture length for the reservoir's top layer for the thermal and isothermal model. As expected, since the bottomhole pressure remains below the fracture pressure for the isothermal model, there is no fracture initiation in the reservoir for the isothermal model. However since minimum effective stress reduces beyond zero in the thermal model (thermoelastic effects), fracture initiates and propagates through reservoir to a half length of 250 m. The bottomhole pressure in the thermal model is now significantly different. For the thermal model, it increases to fracture initiation pressure (equal to the thermally reduced minimum total stress) and then remains almost constant for the injection period. However for the isothermal model, the pressure history is the same as in Fig. 4.

Figure 5 shows the fracture length, pressure and temperature profile for the well block in the reservoir's top and bottom layer. The results show that under thermal conditions, fracture propagates to a larger extent in the lower reservoir layers than the top ones. As seen in the Figure, the pressures in the reservoir's top and bottom layers are very close. However, the temperature in the bottom of the reservoir is significantly lower than in the top. This results in higher reduction of minimum total stress and lower fracture pressure for the reservoir's bottom layer. This effect can also be clearly seen in Figure 6 which shows the permeability multiplier, temperature and pressure profile in fracture plane near the wellbore (zoomed to 300 m) across reservoir layers. As seen the temperature reduction and permeability multipliers

geometry can be calculated by the coupled model.

**Pressure,Minimum stress(kPa)**

reservoir's top layer

are higher in the bottom layer.

In order to study the thermal effects of injection on the propagation of the induced fracture, for the next set of model cases we allowed fracture propagation in all layers. To model the potential fracture propagation, a transmissibility multiplier technique is incorporated in the model, which essentially accounts for the fluid flow transmissibility through the fracture by a transmissibility multiplier function, specified as a table. The multiplier is calculated from an estimated fracture opening of a 2-D Griffith crack [15] based on the mechanical properties of the injection zone and an estimate of the fracture height [5]. This function can be incorporated

**3. Thermal fracturing in the reservoir below isothermal fracture pressure**

Thermal effects of CO2 injection is expected to affect the magnitude of displacements, pressure, stresses, and the possibility of shear and tensile failure in the reservoir and caprock. Injecting fluid with temperature lower than reservoir rock temperature will cause reduction of stresses in the injection layer and once the temperature front has reached a relatively large area around the wellbore, this reduction in stresses will result in negative volumetric strains that can propagate to the surface. Therefore the surface displacement for the thermal model would be

One of the most important effects of injecting a fluid with a lower than reservoir temperature is the reduction of fracture pressure. Cooling of the formation rock during injection of cold CO2 through thermal conduction and convection lowers the total stresses in the reservoir and possibly caprock layer. This results in reduction of fracture pressure and the pressure differ‐ ential available for injection, and therefore injectivity. In the case of injection at fracturing conditions, the fracture propagation pressure will decrease and, if the same injection rate is

In order to examine thermal effects of injection on the possibility of reaching tensile failure in the reservoir, the variation of total stress and pressure needs to be studied. In order to do that, the coupled geomechanical, flow and thermal simulation has been carried out with two different injection temperatures. The injection of CO2 for these models is through a single vertical well with constant rate of 3.4E4 m3/day such that the bottomhole pressure will remain below fracture pressure for the isothermal model during 30 years of injection. It should be noted that fracturing was not allowed in these models. Thermal model in this study refers to injection temperature (30 C) being lower than the reservoir temperature (60 C),while in the isothermal model, it is equal to reservoir's temperature. Figure 3 shows the modeling results for pressure, and total minimum stress for well block in the reservoir during 30 years of injection for the thermal and isothermal model. As it is seen in Figure 3, the total stress falls below the bottomhole pressure (fracture pressure) for the thermal model in the reservoir at quite early injection times which means that minimum effective stress will reduce beyond zero. Therefore, although CO2 is injected below the original fracture pressure, fracture would initiate in the reservoir for the thermal case. Since fracturing is not allowed in these models, the stress magnitudes after the onset of fracturing are not valid. If propagation was allowed, minimum total stress would reduce to slightly below bottomhole pressure such that the effective stress

In order to study the thermal effects of injection on the propagation of the induced fracture, for the next set of model cases we allowed fracture propagation in all layers. To model the potential fracture propagation, a transmissibility multiplier technique is incorporated in the model, which essentially accounts for the fluid flow transmissibility through the fracture by a transmissibility multiplier function, specified as a table. The multiplier is calculated from an estimated fracture opening of a 2-D Griffith crack [15] based on the mechanical properties of the injection zone and an estimate of the fracture height [5]. This function can be incorporated

smaller than that of isothermal model [6].

950 Effective and Sustainable Hydraulic Fracturing

used, this will accelerate fracture propagation.

on the fracture wall would remain close to zero.

**Figure 3.** Pressure, minimum stress, and stress level for the thermal and isothermal model for the well block in the reservoir's top layer

in the model both as a function of pressure or effective minimum stress. The actual fracture geometry can be calculated by the coupled model.

Figure 4 shows the bottomhole pressure and fracture length for the reservoir's top layer for the thermal and isothermal model. As expected, since the bottomhole pressure remains below the fracture pressure for the isothermal model, there is no fracture initiation in the reservoir for the isothermal model. However since minimum effective stress reduces beyond zero in the thermal model (thermoelastic effects), fracture initiates and propagates through reservoir to a half length of 250 m. The bottomhole pressure in the thermal model is now significantly different. For the thermal model, it increases to fracture initiation pressure (equal to the thermally reduced minimum total stress) and then remains almost constant for the injection period. However for the isothermal model, the pressure history is the same as in Fig. 4.

Figure 5 shows the fracture length, pressure and temperature profile for the well block in the reservoir's top and bottom layer. The results show that under thermal conditions, fracture propagates to a larger extent in the lower reservoir layers than the top ones. As seen in the Figure, the pressures in the reservoir's top and bottom layers are very close. However, the temperature in the bottom of the reservoir is significantly lower than in the top. This results in higher reduction of minimum total stress and lower fracture pressure for the reservoir's bottom layer. This effect can also be clearly seen in Figure 6 which shows the permeability multiplier, temperature and pressure profile in fracture plane near the wellbore (zoomed to 300 m) across reservoir layers. As seen the temperature reduction and permeability multipliers are higher in the bottom layer.

**Figure 4.** Bottomhole pressure and fracture length for the reservoir's top layer for the thermal and isothermal model

are significantly larger than in the reservoir, tensile fracturing in the caprock is of low likeli‐ hood. However given the large initial deviatoric stress in the caprock, the chance of reaching shear failure due to thermally induced stresses is high. In order to evaluate the possibility of reaching shear failure, we have used the Mohr-Coloumb criteria and studied the variation of "Stress level", lσ in the caprock during injection. Stress level is defined as the ratio of deviatoric

**Figure 6.** Permeability multiplier(top), Temperature(middle), Pressure distribution (bottom) after 30 years of injection

**Bottomhole** **Fracture Length(m)**

**pressure(kPa)**

max min max min ( ) <sup>1</sup>

is the maximum principal stress, σmin'

stress (all stresses are effective). The deviatoric stress at failure is a function of cohesion c and

*cCos Sin Sin* js

When the stress level is less than 1, the shear stress has not exceeded the shear strength of the rock and when it is larger than 1, the shear strength of the rock has been reached in a plane which is aligned in the direction found from the Mohr stress circle. The nominal rock cohesion for the caprock (Beekmantown Dolomite) is 9000 kPa [17]. Linear elastic constitutive model was used to describe the mechanical behavior of the formation rock. In order to examine the thermal effects on the stress state in the caprock, the variation of total stress, pressure and stress

j

 j

¢ ¢¢ - = = £ ¢ ¢¢ - (1)

<sup>+</sup> ¢ ¢ <sup>=</sup> - (2)

)f is the

30

35

40

45

**Temperature(C)**

50

55

60

953

is the minimum principal

is the deviatoric stress at the current condition, (σdev'

**Figure 6: Fracture length and pressure profile (left), fracture length and temperature profile (right)** 

0 5 10 15 20 25 30

Thermal Effects on Shear Fracturing and Injectivity During CO2 Storage

Fracture length‐Reservoir'stop Fracture Length‐Reservoir's bottom Temperature‐Reservoir'stop Temperature‐Reservoir's bottom

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**Time(year)**

()( )

 ss

<sup>3</sup> 2 2 ( ) (1 ) *dev f*

 ss

*dev f f*

stress at the current condition to the deviatoric stress at failure condition:

*dev*

s

s

s

*l* s

**for the reservoir's top and bottom layer** 

0 5 10 15 20 25 30

Fracture Length‐Reservoir'stop Fracture Length‐Reservoir's Bottom Pressure‐Reservoir'stop Pressure‐Reservoir's bottom

**Time(year)**

Where, lσ is the stress level, σdev'

friction angle ϕ and is defined as:

deviatoric stress at failure, σmax'

for the reservoir layers

**Fracture Length(m)**

level needs to be studied.

**Figure 5.** Fracture length and pressure profile (left), fracture length and temperature profile (right) for the reservoir's top and bottom layer

#### **4. Thermally induced shear failure in the caprock**

The thermally induced reduction of minimum stress in the caprock could lead to tensile or shear failure of the formation rock which could cause tensile fracture propagation through these layers or hydraulic communication through shear fractures. If there is no stress contrast between the caprock and reservoir, reaching tensile failure in the caprock is possible for injection above fracture pressure [16]. In this study, since the horizontal stresses in the caprock

**Figure 6: Fracture length and pressure profile (left), fracture length and temperature profile (right) for the reservoir's top and bottom layer Figure 6.** Permeability multiplier(top), Temperature(middle), Pressure distribution (bottom) after 30 years of injection for the reservoir layers

are significantly larger than in the reservoir, tensile fracturing in the caprock is of low likeli‐ hood. However given the large initial deviatoric stress in the caprock, the chance of reaching shear failure due to thermally induced stresses is high. In order to evaluate the possibility of reaching shear failure, we have used the Mohr-Coloumb criteria and studied the variation of "Stress level", lσ in the caprock during injection. Stress level is defined as the ratio of deviatoric stress at the current condition to the deviatoric stress at failure condition:

$$d\_{\sigma} = \frac{\sigma\_{d\sigma}^{\prime}}{\left(\sigma\_{d\sigma}^{\prime}\right)\_{f}} = \frac{\left(\sigma\_{\max}^{\prime} - \sigma\_{\min}^{\prime}\right)}{\left(\sigma\_{\max}^{\prime} - \sigma\_{\min}^{\prime}\right)\_{f}} \le 1 \tag{1}$$

Where, lσ is the stress level, σdev' is the deviatoric stress at the current condition, (σdev' )f is the deviatoric stress at failure, σmax' is the maximum principal stress, σmin' is the minimum principal stress (all stresses are effective). The deviatoric stress at failure is a function of cohesion c and friction angle ϕ and is defined as:

**Fracture Length(m)**

0 5 10 15 20 25 30

Fracture length-Reservoir's top Fracture Length-Reservoir's bottom Temperature-Reservoir's top Temperature-Reservoir's bottom

0

50

100

150

**Fracture length(m)**

200

250

300

**Time(year)**

**Temperature(C)**

0 5 10 15 20 25 30

Pressure(Isothermal)

Fracture Length(Isothermal)

Fracture Length(Thermal)

Pressure(Thermal)

**Time(year)**

**Figure 4.** Bottomhole pressure and fracture length for the reservoir's top layer for the thermal and isothermal model

**Fracture Length(m)**

**Figure 5.** Fracture length and pressure profile (left), fracture length and temperature profile (right) for the reservoir's

The thermally induced reduction of minimum stress in the caprock could lead to tensile or shear failure of the formation rock which could cause tensile fracture propagation through these layers or hydraulic communication through shear fractures. If there is no stress contrast between the caprock and reservoir, reaching tensile failure in the caprock is possible for injection above fracture pressure [16]. In this study, since the horizontal stresses in the caprock

top and bottom layer

25000

27000

29000

31000

**Pressure(kPa)**

33000

35000

952 Effective and Sustainable Hydraulic Fracturing

**Bottomhole pressure(kPa)**

0 5 10 15 20 25 30

Fracture Length-Reservoir's top Fracture Length-Reservoir's Bottom Pressure-Reservoir's top Pressure-Reservoir's bottom

**4. Thermally induced shear failure in the caprock**

**Time(year)**

$$(\sigma'\_{dev})\_f = \frac{2c\mathcal{C}os\rho + 2\sigma'\_3 Sim\rho}{(1 - Sim\rho)}\tag{2}$$

When the stress level is less than 1, the shear stress has not exceeded the shear strength of the rock and when it is larger than 1, the shear strength of the rock has been reached in a plane which is aligned in the direction found from the Mohr stress circle. The nominal rock cohesion for the caprock (Beekmantown Dolomite) is 9000 kPa [17]. Linear elastic constitutive model was used to describe the mechanical behavior of the formation rock. In order to examine the thermal effects on the stress state in the caprock, the variation of total stress, pressure and stress level needs to be studied.

Figure 7 shows the pressure, stress and stress level evolution for the well block in the caprock for the thermal and isothermal model. In the isothermal model, due to the low permeability of caprock, pressure increase in caprock is negligible compared to the reservoir, and stress level remains low. However as seen in Figure 8 (which shows the stress, pressure and temperature variation of the well block in the caprock during the first 10 years of injection), the first caprock layer is quickly pressurized, and later its temperature also decreases due to heat transfer. Stress level is rapidly increasing with time due to thermally induced decrease of total stresses. Therefore the chance of failing the rock in shear for the caprock is higher for the thermal model compared to isothermal model.

35

0 2 4 6 8 10

**Figure 8.** Minimum total stress, pressure and temperature variation for the well block in the caprock during the first

This paper studies thermo-elastic and poro-elastic response of the reservoir and caprock to increasing of pressure and reduction of temperature after CO2 injection and the resulting consequences for the possibility of reaching tensile or shear failure both for the injection below

When injecting a fluid below isothermal fracture pressure with a temperature below reservoir temperature, the fracture pressure will decrease and minimum effective stress in the reservoir

Our results show that the reduction of the minimum effective stress due to thermal effects is larger for the lower reservoir layers. Therefore in case of dynamic fracture propagation, fracture growth would be larger for the lower reservoir layers due to larger cooling for these

Thermal effects of injection with cold CO2 may also create the possibility of shear failure in the

may reduce below zero for the fracturing to initiate and propagate in the reservoir.

Pressure(Isothermal) Pressure(Thermal) Minimum stress(Isothermal) Minimum Stress(Thermal) Temperature(Thermal) Temperature(Isothermal)

**Time(yr)**

24000

10 years of CO2 injection

**5. Conclusions**

layers.

caprock.

and above reservoir's fracture pressure.

29000

34000

39000

**Pressure,Minimum stress(kPa)**

44000

49000

40

45

50

**Temperature(C)**

55

60

65

70

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Thermal Effects on Shear Fracturing and Injectivity During CO2 Storage

**Figure 7.** pressure, minimum total stress, and stress level for the thermal and isothermal model for the well block in the immediate caprock layer

The changes inthe stress level correspondto themovement oftheMohr circle withtime. Shortly after injection (0.1 days), the stress circle moves to the right due to the slight growth of total stresses. This is a poroelastic effect which is a result of early time-increase of the block pres‐ sure in the caprock. This can be clearly seen in Figure 8. However, as soon as the block temper‐ ature is lowered due to thermal diffusion (conduction), thermoelasticity dominates and total minimum stress reduces (Figure 8) and stress circle moves to the left toward the failure cone.

The mechanism shown here is somewhat exaggerated because of the upstream numerical treatment of the fracture transmissibility between the blocks, but the relative comparison is valid. Accurate modeling would require very fine vertical grid at the reservoir-caprock interface or the development of more sophisticated numerical technique. These aspects are being currently studied.

**Figure 8.** Minimum total stress, pressure and temperature variation for the well block in the caprock during the first 10 years of CO2 injection
