4.3.2. Sealing the Gas

We drew the gas concentration distribution map in the goaf when the time was 0, 0.5, 2, 4, and 6 days, as shown in Figure 11a–e. Due to the existence of gas separation walls, the goaf is like a closed box, which is weakly affected by the air in roadways. Therefore, the gas accumulates continuously in the goaf instead of leaking into the workface. In addition to forming a low gas area near the air inlet, the gas concentration in most areas increases with time. It in dicates that the gas is sealed by the separation walls at two ends of the goaf instead of leaking into the workface, which ensures the safety and stability of the working face.

**Figure 11.** Concentration distribution in gas sealing process: (**a**) *t* = 0 day; (**b**) *t* = 0.5 day; (**c**) *t* = 2 days; (**d**) *t* = 4 days; (**e**) *t* = 6 days.

#### 4.3.3. Replacing the Gas

We drew the gas concentration distribution map in the goaf when the time was 0, 0.125, 0.5, 1, and 3 days, as shown in Figure 12a–e. In the process of gas replacement by the foamed concrete, the gas is expelled into the air-return roadway from the outlet in a short time. Then the goaf become dense by filling with foamed concrete, so there is no new gas accumulation and the gas began to stabilize at a low level from the third day.

**Figure 12.** Concentration distribution in gas replacement process: (**a**) *t* = 0 day; (**b**) *t* = 0.125 day; (**c**) *t* = 0.5 day; (**d**) *t* = 1 day; (**e**) *t* = 3 days.

In this case, the gas in the workface will increase in a short time and the proper ventilation in roadways is necessary to carry out to remove the temporary high concentration gas near the outlet, after which the workface can be safely mined without any hidden danger of gas leakage.

#### 4.3.4. Gas isolation Mechanism

Sealing and replacing are two very different methods of gas isolation. The former prevents the gas from leaking to workface by plugging the gas inlet and outlet using the foamed concrete. The latter firstly evacuates the existing gas, and then replaces the gas position with foamed concrete so as to fundamentally prevent gas leakage. The distribution curves of gas concentration along the workface boundary at different application modes is shown in Figure 13. The figure shows that when sealing the gas, since there is little influence of the air in roadway, only about 25 m range of the workface around the air inlet has the phenomenon of concentration reduction, and the gas concentration in the remaining part of workface exceeds the initial concentration and increases with time. However, when replacing the gas, the gas concentration of the workface boundary rapidly reduces to 0 near the inlet. The gas concentration along this boundary is lower than the initial concentration and decreases with the increase of time, until the entire boundary (except the outlet) remains at a very low level.

**Figure 13.** Concentration distribution along the workface.

## **5. Discussion and Conclusions**

The mix proportions have a significant effect on the properties of foamed concrete, and the foam content is the most important factor. Based on the orthogonal experiment results, the optimum mix proportions were obtained, and a new type of foamed concrete was produced, which has low dry density, low gas permeability, and certain strength.

This new concrete material can be used to isolate the goaf gas in two forms: sealing the gas and replacing the gas. According to the convection-diffusion model of gas, the multi-field physic coupled simulation software COMSOL Multiphysics was utilized to conduct the numerical simulation. The simulation results indicated that when the foamed concrete is used to build air separation walls at both ends of goaf to seal the gas, the gas concentration in most of mined-out area increases with time except for a low gas area near the air inlet. When the foamed concrete is used to replace the gas in the goaf void, the gas can be expelled from the outlet in a short time, and then the gas concentration in the goaf is stable at a low level.

In view of its good gas isolation properties and the effective application modes, it is suitable and feasible to use this new type of foamed concrete as gas isolation material in the coal mine goaf, which can provide a reference for similar engineering.

**Author Contributions:** Conceptualization, L.H.; Formal analysis, C.X.; Investigation, M.T.; Methodology, Y.W.; Software, Y.J.; Writing—original draft, C.X.; Writing—review and editing, L.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (grant number 51574223). **Conflicts of Interest:** The authors declare that they have no conflict of interest.
