# Investigation of Properties Alternation during Super-Critical CO\({}_{2}\) Injection in Shale
## 3 Results and Discussion  
### Mechanical Property Deformation  
The mechanical properties alteration during the variable Sc-CO\({}_{2}\) injection times is crucial for the formation of the evaluation process. Since that, we applied a most advanced equipment, the nano-indenter, to measure the Young's modulus of the samples, which are the main mechanical properties for the rock. Nanoindentation test is considered as a unique technique whereby a sharp indenter tip is used to touch the smooth surface of the sample with a certain mode, then the penetration depth will be recorded along with the applied load [20]. Figure 3a illustrates the typical curve of the indentation test. Generally, the curve consists of three stages, which are the initial loading stage, medium-term holding stage, and following the unloading stage. For the initial loading stage, since the penetration depth get increased with the applied load increases it can be regarded as the association of elastic and plastic deformation; whereas at the unloading stage, it was assumed that the elastic deformation is the only recoverable parameter, which was applied to conduct the following calculation procedure of the rock mechanical properties. Figure 3b identified the standard unloading process of the nano-indentation test. In our test, the peak force that we applied is 6000 uN. The loading time, holding time and unloading time will be 5 s, 5 s, 5 s, respectively. Figure 4 presents the effect of the Sc-CO\({}_{2}\) injection time on the samples' Young's modulus value. It can be observed that the Young's modulus tends to decrease gradually with the injection time increasing. The original sample from the two different depths, 9848 ft and 9850 ft, had the highest Young's modulus of 75.91 GPa and 68.37 GPa, respectively. When the samples were flooded in the Sc-CO\({}_{2}\) for 10 days, 20 days, 30 days and 40 days, for the first sample, the Young's modulus value reduced 2.54% to 73.98 GPa, 10.082% to 68.26 GPa, 14.379% to 65.00 GPa, and 15.446% to 64.03 GPa, respectively. While for the second sample, the [PERSON]'s modulus value reduced 2.42% to 68.37 GPa, 10.274% to 61.35 GPa, 13.693% to 59.00 GPa, and 14.429% to 58.50 GPa, respectively. This may be caused by the Sc-CO\({}_{2}\) adsorption behavior. As the samples adsorb more and more Sc-CO\({}_{2}\) through the pore throat, the pore will get swelled, which contributes to the rock strength decrease. With the Sc-CO\({}_{2}\) flooding time increase, the decline in the strength of the two core samples slacks off, which is mainly due to the ultra-low permeability of the Middle Bakken sample. By the curves interpreting, after 30 days of Sc-CO\({}_{2}\) adsorption, both curves were observed to reach a stable status. Some researchers obtained the relationship between the [PERSON]'s modulus (E) and the adsorption time for the Sc-CO\({}_{2}\) injection to the sample with variable lithological character [16; 23]. Based on the previous research, we fitted the data for the two samples with a Boltzmann sigmoid relationship  
Figure 3: Schematic illustration of the nano-indentation test. (**a**) Typical indentation load-displacement curve, Reproduced with permission from [20; 21], Elsevier, 2019; (**b**) unloading process, Reproduced with permission from [22], Cambridge University Press, 2019.  
between the [PERSON]'s modulus (E in GPa) and the Sc-CO\({}_{2}\) injection time (t in days) by the curving fitting tool of OriginPro:  
\[E=65.0457+11.1906/\left(1+e^{\frac{t-16.0421}{4.3314}}\right)\ \text{(Sample Depth : 9848 ft)} \tag{1}\]  
\[E=57.9459+10.8331/\left(1+e^{\frac{t-17.7967}{5.2977}}\right)\ \text{(Sample Depth : 9850 ft)} \tag{2}\]  
The R-squares are 0.9934 for the sample at depth of 9848 ft and 0.9968 for the sample at depth of 9850 ft, which shows the models and the experimental data are fitting very well.