**2.3 Solubility trapping**

Solubility trapping is the dissolution of CO2 in the formation fluid to achieve CO2 storage. After injection, CO2 is dissolved in the fluid formation until reaching saturation, due to the interaction of CO2, groundwater, and hydrocarbons. The density difference between the fluid formation and CO2 causes the CO2 to migrate upward to contact more water formation that is not saturated. Meanwhile, CO2 dissolved in the groundwater will slightly increase its density. Both of these phenomena increase the exchange of CO2 and groundwater and accelerate solubility trapping. The solubility of CO2 depends on the temperature, pressure, and saturation of the formation water [22].

## **2.4 Mineral trapping**

Mineral trapping is a long-term trapping mechanism that involves contact and reaction with stratigraphic minerals and organic substances after CO2 injection to form a stable mineral phase, resulting in long-term storage of CO2. For example, the forming of carbonate minerals reduces the porosity and permeability of the rock and enhances the stability and integrity of the reservoir over time. The reaction rate of formation minerals with CO2 depends on temperature, pressure, pH, and the concentration of other substances. It is noted that the forming of carbonate mineralization is a very slow process, as the reaction rates are usually very low, and therefore mineral trapping will only become important on geological time scales [23].

## **3. Stress response**

The geomechanical issues in the GCS process are all driven by changes in the formation of pressure and ground stress. Therefore, it is important to first clarify the characteristics of the stress response in the formation for investigating the geomechanical issues.

### **3.1 Effective stress and stress path**

### *3.1.1 Effective stress*

The mechanical response of the rock is the result of the combination of pore pressure and in-situ stress. Terzaghi (1996) proposed the effective stress principle for describing the mechanical response of porous media. Effective stress is defined as the stress applied on the porous medium or the total stress minus the product of the pore pressure (fluid pressure) and the effective stress coefficient. In one-dimensional conditions it can be expressed as follows [24, 25]:

$$
\sigma' = \sigma - a\mathbb{P}\_p \tag{1}
$$

where *σ*<sup>0</sup> is the effective stress; *σ* is the total stress; *α* is the effective stress coefficient; *Pp* is the pore pressure.

The three-dimensional condition is expressed as:

$$
\sigma'\_{\vec{\eta}} = \sigma\_{\vec{\eta}} - aP\_p \delta\_{\vec{\eta}} \tag{2}
$$

where *σ*<sup>0</sup> *ij* is the index notation of the effective stress tensor; *σij* is the index notation of the total stress tensor; *δij* is Kronecker's delta, when*i* ¼ *j*, *δij* ¼ 1; *i* 6¼ *j*, *δij* ¼ 0.

The effective stress coefficient, also called the Biot coefficient, can be calculated by the following equation.

*Geomechanics of Geological Carbon Sequestration DOI: http://dx.doi.org/10.5772/intechopen.105412*

$$a = 1 - \frac{K\_{dry}}{K\_m} \tag{3}$$

where *Kdry* is the bulk modulus of the dry porous rock; *Km* is the bulk modulus of the matrix mineral in the rock. In Terzaghi's effective stress law *α* =1.

#### *3.1.2 Stress path*

The stress path, also known as the "stress history in the plane of maximum obliquity" is a common concept in geotechnics and rock mechanics. It refers to the trajectory of the stress path and stress history in the stress plane of stress space of a point in the core under the action of external forces, and is generally divided into effective stress path (ESP) and total stress path (TSP).

To understand the stress paths, consider a typical triaxial stress experiment in a core (**Figure 4a**). At any time, the stress state in the core can be represented by a Mohr circle (**Figure 4b**). It should be noted that during the triaxial experiments, the pore pressure can be neglected so that the total stress is equal to the effective stress. In triaxial compression tests, the maximum principal stress (*σ*1) is applied along the axis of the cylindrical rock specimen, and the minimum principal stresses (*σ*<sup>2</sup> and *σ*3) are applied on the lateral surface of the specimen. It is necessary to supplement the Mohr-Coulomb theory. Shear damage occurs at that point when the shear stress is equal to the shear strength of the material in any plane. The shear stress (shear strength) on the damaged plane depends on the normal stress on the shear plane and the properties of the rock and is a function of the normal stress on the shear plane [27–29].

The coordinates on the Mohr circle when considering the effective normal and shear stresses in the plane at an angle of 45o to the principal plane are calculated by [30–32]:

$$\text{The effective normal stress } p' = \frac{\sigma\_1' + \sigma\_3'}{2} \tag{4}$$

$$\text{The effective shear stress } q' = \frac{\sigma\_1' - \sigma\_3'}{2} \tag{5}$$

where *σ*<sup>0</sup> <sup>1</sup> is the effective maximum principal stress; *σ*<sup>0</sup> <sup>3</sup> is the effective minimum principal stress.

#### **Figure 4.**

*(a) Triaxial stress experiment schematic; (b) laboratory stress path schematic; (c) schematic of total stress circle and effective stress circle (reproduced from [26]).*

Connecting the points corresponding to coordinates *p*<sup>0</sup> and *q*<sup>0</sup> on each Mohr circle, as shown in line AB, is the stress path. In the formation conditions, the in-situ stress generally refers to the total stress. The pore pressure separates the effective stress circle from the total stress circle, as shown in **Figure 4c**, but they have the same diameter. In GCS engineering, shear failure, fault activation, and caprock failure can be determined by plotting the effective stress Mohr circle and effective stress path at a point in the formation [32].

#### *3.1.3 Stress path coefficient*

Effective stress is the key parameter for determining whether or not damage will occur in the rock. The injection of CO2 will lead to an increase in the pore pressure. According to Eq. (1), the effective stress decreases, and the response to the Mohr circle is shifted to the left, as shown in **Figure 5**. Assuming constant total stress, the Mohr circle simply translates to the left until it intersects the failure envelope, resulting in shear damage. However, the increase in pore pressure leads to the expansion of the formation, which further leads to the change in total stress. The ratio of the variation of the total stress and the variation of the pore pressure is the stress path coefficient [33].

$$\gamma\_v = \frac{\Delta \sigma\_v}{\Delta p\_p}, \gamma\_h = \frac{\Delta \sigma\_h}{\Delta p\_p} \tag{6}$$

where *γ<sup>v</sup>* is the vertical stress path coefficient; *γ<sup>h</sup>* is the horizontal stress path coefficient; Δ*σ<sup>v</sup>* is the vertical stress variation value; Δ*σ<sup>h</sup>* is the horizontal stress variation value; Δ*pp* is the pore pressure variation value.

#### **3.2 Effective stress variation law**

During field construction, once fluid injection begins, the reservoir stress will change with the rapid propagation of fluid pressure in the injection zone, causing the

**Figure 5.** *Trend of Mohr circle with increasing pore pressure at constant total stress.*

change in the reservoir stress field. In this case, the calculation of the effective stress requires consideration of the stress path coefficients. In a formation with a wide lateral distribution, the horizontal stress path coefficient can be calculated as [33, 34]:

$$\gamma\_h = \frac{\Delta \sigma\_h}{\Delta p\_p} = a \frac{1 - 2\mu}{1 - \mu} \tag{7}$$

where *μ* is the Poisson's ratio.

The horizontal stress path coefficient is less than 1 because is less than 1. However, the vertical total stress can be considered to remain constant since the vertical formation expansion is not constrained, that is, the vertical stress path coefficient is equal to 0. It means that the horizontal total stress will change, while the vertical total stress remains constant. At this time the maximum and minimum effective stress change differently, Mohr's circle will not only move but also the diameter will change, as shown in **Figure 6**.
