## 2 Materials and Methods
### Apparatus and Methodology
#### 2.2.3 Permeability Measurement  
The transient pulse decay method appears to be one of the most applied experimental methods to determine low permeability. The principle of this method is as follows. First, the system is kept at a constant gas pressure. Then, a transient pulse is applied at the upstream end of the rock sample, which causes a pressure difference between the two ends of the rock. The attenuation relation of pressure difference with time is shown in Formula (2), and the permeability can calculated through Formula (3) [33]:  
\[\frac{\Delta P(t)}{\Delta P_{i}}\ =\ \exp(-\alpha t) \tag{2}\]  
Figure 3: Scanning electron microscopy images of the cube samples before the reaction: **(a)** surface before polishing, **(b)** surface after polishing.  
\[k\ =\ \frac{-\alpha\cdot\mu\cdot L}{Ap_{m}\Big{(}\frac{1}{V_{u}}\ +\ \frac{1}{V_{d}} \Big{)}} \tag{3}\]  
where \(t\) (s) is the time, \(\Delta P(t)\) (atm) is the current pressure difference at time t, \(\Delta P_{i}\) (atm) is the initial differential pressure, \(\alpha\) is the exponential decay coefficient, \(k\) (\(\mu\)m\({}^{2}\)) is the permeability of the sample, \(\mu\) (cp) is the dynamic viscosity of the gas, \(L\) (cm) is the length of the sample, \(A\) (cm\({}^{2}\)) is the cross-sectional area of the sample, \(p_{m}\) (atm) is the equilibrium pressure, \(V_{u}\) (cm\({}^{3}\)) is the volume of pipeline of the upstream and \(V_{d}\) (cm\({}^{3}\)) is the volume of pipeline of the downstream.  
A device was developed for the measurement of permeability in this study, and its schematic diagram is shown in Figure 4. The experimental system consisted of a high-pressure nitrogen cylinder, a pore pump, a confining pump, core holder chamber, a vacuum pump, dates acquisition system, some pressure sensors, the differential pressure sensor and other essential components which were connected by high-pressure sealing pipes. The differential pressure curve, \(\Delta p(t)\), was recorded by the differential pressure sensors during the test. The permeability test steps are described as follows:  
1. The sample was wrapped in a heat shrink tube and placed vertically into the core holder. The confining pressure pump was used to deliver the ultrapure water into the pressure chamber of the core holder where a confining pressure of 1 MPa was applied.
2. In order to remove the air of the lines of the pore system, the vacuum pump was applied to vacuum the system for 6 h. After that, the pore pump was set at 0.2 MPa to maintain a constant sample pore pressure.
3. The temperature of the whole system was stabilized at the level of 30 \({}^{\circ}\)C using a water bath. After the whole system had stabilized (where the temperature, the pore pressure and confining pressure were stable), a pressure pulse (20 kPa) was applied. The pressure decay curve was recorded constantly by the differential pressure gauge. The permeability could be calculated through the formulas (2) and (3).
4. The permeability of the sample under the different confining pressures could be obtained by repeating steps (2)-(3) and changing the confining pressure in step (1). In this study, the permeabilities of the cylinder specimens were measured under the confining pressures of 1 MPa, 3 MPa, 5 MPa and 7 MPa.  
Figure 4: Schematic diagram of the permeability measurement system.