For intact cores (Fig. 5.7, top left columns), scCO2 migrated more or less uniformly but with higher saturations within layers containing larger pores (because of the stronger capillary entry pressure in the smaller pores) along the bedding planes. For core‐parallel fractures, the mated fracture (Frac Ia) contributed to somewhat localized distribution of scCO2. However, the scCO2 was still well dispersed throughout the core, possibly because the void space within the fracture was highly disconnected and did not result in an efficient fast path for the scCO2.
In contrast, for core‐parallel fractures with large shear displacement (Frac Ib and Frac Id are shown in Fig. 5.7), almost all the scCO2 migrated through the fracture, and little scCO2 infiltrated into the rock matrix. Also, because of the large aperture of the fracture (~0.54 mm), the vertically oriented fracture in Frac Id exhibited preferential pooling of lighter scCO2 in water along the top edge of the fracture by the buoyancy effect.
For a core‐perpendicular fracture, the migration behavior of scCO2 was initially similar to the intact core, exhibiting a wide distribution of the fluid across the core with preferential flow along the bedding planes. However, the fracture (aperture ~0.26 mm) served as a trap and accumulated scCO2 before the second half of the core was infiltrated.
5.4. DISCUSSION
In this section, we will examine the experimentally observed behavior of Young's modulus and related attenuation during scCO2 injection.
5.4.1. Gassmann Model Interpretation of Young's Modulus Behavior
Detailed dynamic poroelastic modeling of the experimental results is beyond the scope of this chapter. However, we can gain some insights into the observed behavior of fractured samples using a simple, isotropic, quasi‐static model (i.e., isotropic Gassmann model).
Figure 5.6 Shear modulus and related attenuations determined from SHRB tests during scCO2 injection experiments on Carbon Tan sandstone cores: (a) Carbon Tan #1 elastic moduli; (b) Carbon Tan #2 elastic moduli; (c) Carbon Tan #1 attenuations; (d) Carbon Tan #2 attenuations.
In the following, we consider only small stress and displacement perturbations caused by seismic waves. For the porous, intact matrix of the sandstone samples, we assume the following constitutive equations for an isotropic homogeneous poroelastic medium (e.g., Pride et al., 2002):
Figure 5.7 X‐ray CT images of scCO2 invasion into intact and fractured sandstone cores. Brighter colors indicate higher CO2 saturation. Average apertures determined from CT images are indicated for open, sheared fractures. (Note that at the top of the Frac IIb images, unintended shifts of the experimental setup between an initial calibration scan and subsequent scans during the scCO2 injection experiment resulted in false images of scCO2 along the bottom edge of the core, which disappear in the subsequent images.)
In 5.3 and 5.4, repeated indices indicate summation, and, i ≡ ∂/∂x i . u i is the local average solid frame displacement vector. w i ≡ φ (U i ‐ u i ) is the relative fluid volume displacement vector defined via u i , local average fluid displacement vector in the pore space U i , and porosity φ . δ ij indicates an identity tensor. τ ij is the total stress tensor, and p f is the fluid pressure (positive sign for compression). G is the solid frame shear modulus, and K U is the undrained bulk modulus. C and M are the Biot's coupling and fluid storage moduli, respectively. Note that these parameters are related via C = αM, K U = K D +α 2 M, K D =(1‐αB) K U , where α is the Biot‐Willis coefficient, B is the Skempton coefficient, and K D is the drained bulk modulus. For the fracture part, assuming a plane, permeable, and compliant fracture, the boundary conditions for the fracture‐normal displacement, stress, and pressure can be stated as (Nakagawa & Schoenberg, 2007)
The superscripts “+” and “–” indicate the opposing surfaces of the fracture, and subscript “n” indicates the direction perpendicular (normal) to the fracture plane. The effect of fluid flow parallel to the fracture is neglected. The thickness of the fracture h is assumed to be very small compared wih the diameter of the sample. Also note that the effective stress coefficient of the open, permeable fracture α F can be assumed to be 1. η D and η M are the specific drained normal fracture compliance and the specific fracture storage compliance. For an open fracture, η M can be computed via η M = h/M F ~ h/K f , where M F is the storage modulus of the material within the fracture, and K f is the bulk modulus of the fluid contained in the fracture (the fracture porosity