Sealing efficiency analysis for shallow-layer caprocks in CO₂ geological storage

Abstract

The CO₂ migrated from deeper to shallower layers may change its phase state from supercritical state to gaseous state (called phase transition). This phase transition makes both viscosity and density of CO₂ experience a sharp variation, which may induce the CO₂ further penetration into shallow layers. This is a critical and dangerous situation for the security of CO₂ geological storage. However, the assessment of caprock sealing efficiency with a fully coupled multi-physical model is still missing on this phase transition effect. This study extends our previous fully coupled multi-physical model to include this phase transition effect. The dramatic changes of CO₂ viscosity and density are incorporated into the model. The impacts of temperature and pressure on caprock sealing efficiency (expressed by CO₂ penetration depth) are then numerically investigated for a caprock layer at the depth of 800 m. The changes of CO₂ physical properties with gas partial pressure and formation temperature in the phase transition zone are explored. It is observed that phase transition revises the linear relationship of CO₂ penetration depth and time square root as well as penetration depth. The real physical properties of CO₂ in the phase transition zone are critical to the safety of CO₂ sequestration. Pressure and temperature have different impact mechanisms on the security of CO₂ geological storage.

Appendices

Appendix 1: Gas exchange between fracture and matrix

The source term of gas adsorption from the matrix to the fracture is expressed as

$${Q_m}={\rho _{\text{c}}}{\rho _{{\text{ga}}}}\frac{{{\text{d}}{m_{\text{b}}}}}{{{\text{d}}t}},$$

(25)

where $\frac{{{\text{d}}{m_{\text{b}}}}}{{{\text{d}}t}}$ represents the exchange rate of gas content between fractures and matrix, which is decided by the pressure balance. To describe this dynamic diffusion process, a diffusion time $\tau$ is introduced to simply measure the gas exchange rate

$$\frac{{{\text{d}}{m_{\text{b}}}}}{{{\text{d}}t}}=\frac{1}{\tau }\left[ {{m_{\text{b}}} - {m_{\text{e}}}(p)} \right],$$

(26)

where ${m_{\text{e}}}(p)$ is the equilibrium gas content with fracture pressure p. The diffusion time of a shale matrix block is generally expressed by

$$\tau =\frac{1}{{aD}},$$

(27)

where D (m²/s) is the diffusion coefficient of gas and a (m⁻²) is a shape factor. For isotropic matrix, the shape factor is

$$a={\pi ^2}\left( {\frac{1}{{L_{x}^{2}}}+\frac{1}{{L_{y}^{2}}}} \right),$$

(28)

where $L_{x}^{{}}$ and $L_{y}^{{}}$ are the fracture spacing in x-direction and y-direction, respectively. This diffusion in shale involves multi-scale flow mechanism (including adsorption, diffusion, slippage, and viscous flow) and makes the flow substantially deviate from Darcy flow.

Appendix 2: Capillary pressure model

The normalized saturation $s_{{\text{w}}}^{*}$ of wetting phase is (see Brooks and Corey model)

$$s_{{\text{w}}}^{*}={\left( {\frac{{{p_{\text{e}}}}}{{{p_{\text{c}}}}}} \right)^\lambda },$$

(29)

$${s_{\text{w}}}=s_{{\text{w}}}^{*}(1 - {s_{{\text{rw}}}})+{s_{{\text{rw}}}},$$

(30)

where ${p_{\text{c}}}={p_{{\text{nw}}}} - {p_{\text{w}}}$ presents the difference between water pressure ${p_{\text{w}}}$ and gas pressure ${p_{{\text{nw}}}}$. The initial entry capillary pressure decides the occurrence of CO₂ displacement of brine water. This pressure varies in a large range of 0.1–48.3 MPa (Tonnet et al. 2011). $\lambda$ is the pore size distribution index. ${s_{{\text{rw}}}}$ and ${s_{{\text{rnw}}}}$ are the irreducible saturations of wetting and non-wetting phases, respectively. ${p_{\text{e}}}$ is the entry capillary pressure. Therefore, the compressibility with respect to capillary pressure is

$${c_{\text{s}}}=\frac{{\partial {s_{\text{w}}}}}{{\partial {p_{\text{c}}}}}=\frac{{\partial {s_{\text{w}}}}}{{\partial s_{{\text{w}}}^{*}}} \cdot \frac{{\partial s_{{\text{w}}}^{*}}}{{\partial {p_{\text{c}}}}}=(1 - {s_{{\text{rnw}}}} - {s_{{\text{rw}}}}) \times \left[ { - \frac{\lambda }{{{p_{\text{e}}}}}{{(s_{{\text{w}}}^{*})}^{1+\frac{1}{\lambda }}}} \right].$$

(31)