Study on Foamed Concrete Used as Gas Isolation Material in the Coal Mine Goaf

: In view of the serious threat of gas accumulation in the coal mine goaf and the limitations of the existing gas sealing materials, the orthogonal experiment was developed to study a new type of foamed concrete for mine gas sealing. Dry density, gas permeability, and compressive strength were studied as the material indicators according to the demands of the gas isolation material in the coal mine goaf, and the experimental results showed that foam content was the most important factor. Meanwhile, the optimum mix was selected according to the inﬂuence of foam content as well as the engineering requirement. Then two application modes of this foamed concrete for goaf gas isolation were put forward, after which the convection-di ﬀ usion model of gas was built by COMSOL Multiphysics (COMSOL Inc., Stockholm, Sweden) to reveal the mechanism of di ﬀ erent application modes using the parameters of the new foamed concrete. Simulation results showed that this foamed concrete used as isolating material for goaf gas could signiﬁcantly decrease the gas concentration in workface, which can provide a reference for similar engineering.


Introduction
In recent years, China has widely used the comprehensive mechanized coal mining method, which has the characteristics of fast advancement speed and long workface. However, this method has a high degree of disturbance to the coal and rock mass, which can make the gas rapidly accumulate in the goaf and pose a serious threat to the safe production in a gas-rich coal mine [1][2][3]. Filling and sealing, as one of the key technologies to control the goaf gas, is a necessity to isolate the gassy areas and achieve permanent barriers between the workface and gas sources [4]. However, the existing inorganic gas-sealing materials are not efficient enough to seal the leaking gas, and the existing organic foam materials have negative impacts on the underground environment. Therefore, it is necessary to develop a low-cost, effective, and environmentally friendly material for roadway filling and sealing, which has the properties of compression, expansion, filling, sealing, and gastight, so as to ensure the safety, reliability, simplicity, and rapidity of coal mine underground work. Due to its low density, low thermal conductivity, low permeability, high expansibility, and high strength, foamed concrete has interested many experts [5,6]. Wang et al. [7] studied the effects of foam content, crumb rubber content, fly ash content, and water/binder ratio on the physical, mechanical, and waterproof properties of a lightweight foamed concrete by the single-factor and orthogonal tests. Ben et al. [8] investigated the mechanical characterization of non-autoclaved foam concrete according to its macro porosity. Khan et al. [9] investigated the effects of cement and recycled glass powder

Design of the Orthogonal Experiment
The four main factors of foamed concrete that can affect its properties were chosen according to the experimental goal: water cement ratio, foam (by volume), water reducing agent (by weight), and sodium silicate solution (by weight) based on 1 kg mass of solid powder. For each component, there were four levels, and thus, in total, 16 concrete series were investigated. According to the early analysis of the single factor influence of foamed concrete, the most suitable proportioning interval is determined, as shown in Table 3.

Specimen Preparation
As shown in Figure 1, the specimen preparation can be summarized as follows: firstly, the foaming agent was diluted with water at a ratio of 1:20 (by volume) and then added to the foaming machine. Secondly, the Portland cement, water-reducing agent, and sodium silicate solution are mixed evenly according to a certain mix proportion to make a cement slurry of certain water cement ratio, and then the foam produced in the first step was added and mixed until a uniform slurry was produced. Thirdly, the specimens were poured into molds and compacted with an external vibrator, demolded after 24 h, and kept in a box at constant temperature (22 ± 2 • C) and humidity (95%) up to the day of testing.

Design of the Orthogonal Experiment
The four main factors of foamed concrete that can affect its properties were chosen according to the experimental goal: water cement ratio, foam (by volume), water reducing agent (by weight), and sodium silicate solution (by weight) based on 1 kg mass of solid powder. For each component, there were four levels, and thus, in total, 16 concrete series were investigated. According to the early analysis of the single factor influence of foamed concrete, the most suitable proportioning interval is determined, as shown in Table 3.

Specimen Preparation
As shown in Figure 1, the specimen preparation can be summarized as follows: firstly, the foaming agent was diluted with water at a ratio of 1:20 (by volume) and then added to the foaming machine. Secondly, the Portland cement, water-reducing agent, and sodium silicate solution are mixed evenly according to a certain mix proportion to make a cement slurry of certain water cement ratio, and then the foam produced in the first step was added and mixed until a uniform slurry was produced. Thirdly, the specimens were poured into molds and compacted with an external vibrator, demolded after 24 h, and kept in a box at constant temperature (22 ± 2 °C) and humidity (95%) up to the day of testing.

Dry Density
In order to save the engineering cost, foamed concrete needs to be of good expansibility, and dry density was chosen as the evaluation index of the expansibility, which is convenient for measurement. The standard cylindrical samples of 50 mm × 100 mm were selected, put into a constant temperature vacuum drying oven (see Figure 2), adjusted to 80 ± 5 • C for 24 h, and then the temperature adjusted to 120 • C until gaining the constant weight M. The diameter and height of the sample were measured, and its volume was calculated V. Then the dry density ρ of the concrete material can be obtained by the formula: where, ρ is the dry density of the sample, kg/m 3 ; M is the mass of the sample after drying, g; V is the volume of the sample, cm 3 .

Dry Density
In order to save the engineering cost, foamed concrete needs to be of good expansibility, and dry density was chosen as the evaluation index of the expansibility, which is convenient for measurement. The standard cylindrical samples of 50 mm × 100 mm were selected, put into a constant temperature vacuum drying oven (see Figure 2), adjusted to 80 ± 5 °C for 24 h, and then the temperature adjusted to 120 °C until gaining the constant weight M. The diameter and height of the sample were measured, and its volume was calculated V. Then the dry density ρ of the concrete material can be obtained by the formula: where, ρ is the dry density of the sample, kg/m 3 ; M is the mass of the sample after drying, g; V is the volume of the sample, cm 3 .

Gas Permeability
The foamed concrete is mainly used to isolate gas in the coal mine goaf, so the gas permeability is used as anther evaluation index, which can be tested by gas permeability measurement system (see Figure 3). First, 50 mm of the samples was cut off in dry density test, a layer of epoxy resin was applied on the outside of samples, and the sample was put into the concrete gas penetration tester, ensuring the airtightness of the device. Then the air pressure was controlled to be about 0.1-0.2 MPa at the inlet in the tester, so that the gas entered into the sample from the lower surface and exited from the upper surface. The air inlet pressure P 1 and air outlet pressure P 2 were recorded under different air supply pressures. Then, the gas permeability of the sample can be easily obtained from the apparent gas permeability , which can be calculated as follows: where, k a is the apparent gas permeability, m 2 ; Q is the gas flow, mL/min; A is the cross section area of the sample, mm 2 ; η is the viscosity of the compressed gas, Pa·s; h is the height of the test piece, mm; P 1 is the inlet pressure, bar; P 2 is the outlet pressure, bar.

Gas Permeability
The foamed concrete is mainly used to isolate gas in the coal mine goaf, so the gas permeability is used as anther evaluation index, which can be tested by gas permeability measurement system (see Figure 3). First, 50 mm of the samples was cut off in dry density test, a layer of epoxy resin was applied on the outside of samples, and the sample was put into the concrete gas penetration tester, ensuring the airtightness of the device. Then the air pressure was controlled to be about 0.1-0.2 MPa at the inlet in the tester, so that the gas entered into the sample from the lower surface and exited from the upper surface. The air inlet pressure P 1 and air outlet pressure P 2 were recorded under different air supply pressures. Then, the gas permeability of the sample can be easily obtained from the apparent gas permeability k a , which can be calculated as follows: where, k a is the apparent gas permeability, m 2 ; Q is the gas flow, mL/min; A is the cross section area of the sample, mm 2 ; η is the viscosity of the compressed gas, Pa·s; h is the height of the test piece, mm; P 1 is the inlet pressure, bar; P 2 is the outlet pressure, bar.

Compressive Strength
Although there is less requirement for the compressive strength of the foamed concrete, the higher the compressive strength, the more stable the whole goaf can be maintained, and the more conducive to the mining of the adjacent workface. Considering the short time filling effect and long time supporting effect, the compressive strength of 3 days and 28 days of the foamed concrete were selected as the other evaluation indexes, which can be tested by universal testing machine CSS-14100 (see Figure 4). Cube samples of 70.7 × 70.7 × 70.7 mm were taken, their dimensions measured, and the contact area A 1 was calculated. Then the sample was placed on the press plate center of the universal testing machine. The testing machine was started and controlled with a displacement loading speed of 0.02 mm/s. When the specimen cracks and reaches the complete failure state, the test is finished and the data as well as the maximum axial pressure F is recorded in the computer. Then the compressive strength σ of the foamed concrete can be obtained by the formula: where, σ is the compressive strength of the sample, MPa; F is the maximum failure load of the sample, N; A 1 is the contact area of the sample, mm 2 .

Compressive Strength
Although there is less requirement for the compressive strength of the foamed concrete, the higher the compressive strength, the more stable the whole goaf can be maintained, and the more conducive to the mining of the adjacent workface. Considering the short time filling effect and long time supporting effect, the compressive strength of 3 days and 28 days of the foamed concrete were selected as the other evaluation indexes, which can be tested by universal testing machine CSS-14100 (see Figure 4). Cube samples of 70.7 × 70.7 × 70.7 mm were taken, their dimensions measured, and the contact area A 1 was calculated. Then the sample was placed on the press plate center of the universal testing machine. The testing machine was started and controlled with a displacement loading speed of 0.02 mm/s. When the specimen cracks and reaches the complete failure state, the test is finished and the data as well as the maximum axial pressure F is recorded in the computer. Then the compressive strength σ of the foamed concrete can be obtained by the formula: where, σ is the compressive strength of the sample, MPa; F is the maximum failure load of the sample, N; A 1 is the contact area of the sample, mm 2 . As a result, the dry density, gas permeability, compressive strength of 3 days and 28 days, which were used as four test indexes according to the demands of the foamed concrete for gas isolation, were obtained by the methods above [17,18].  As a result, the dry density, gas permeability, compressive strength of 3 days and 28 days, which were used as four test indexes according to the demands of the foamed concrete for gas isolation, were obtained by the methods above [17,18].

Test Results and Analysis
Average level is the average value of each factor at the same level. The average level of four indicators (dry density, gas permeability, compressive strength of 3 days and 28 days) under different factors can be seen in Figure 5a-d, and it can be noted that the foam is the main factor influencing the four indexes as mentioned above. The dry density and compressive strength drop and the gas permeability increases as the volume of foam increases. In order to further investigate the mechanism of this phenomenon, a microscope was used to magnify the samples with different foam content for 500 times, as shown in Figure 6.

Test Results and Analysis
Average level is the average value of each factor at the same level. The average level of four indicators (dry density, gas permeability, compressive strength of 3 days and 28 days) under different factors can be seen in Figure 5a-d, and it can be noted that the foam is the main factor influencing the four indexes as mentioned above. The dry density and compressive strength drop and the gas permeability increases as the volume of foam increases. In order to further investigate the mechanism of this phenomenon, a microscope was used to magnify the samples with different foam content for 500 times, as shown in Figure 6.
When the foamed concrete sample is magnified by microscope, it can be seen that when the amount of foam is less, there are fewer pores in the sample, and these pores are small, airtight, and smooth. With the increase of foam content, both the number and the diameter of pores increase significantly. When the amount of foam reaches 2 L, the pores in the samples are denser and larger, and the connected pores are formed, which leads to larger gas permeability of the foamed concrete. At the same time, since the fact that foam helps to produce more pores, the increase of foam content can lead to a decrease in other solid materials in the unit volume, resulting in a decrease in density and strength. As a result, the dry density, gas permeability, compressive strength of 3 days and 28 days, which were used as four test indexes according to the demands of the foamed concrete for gas isolation, were obtained by the methods above [17,18].

Test Results and Analysis
Average level is the average value of each factor at the same level. The average level of four indicators (dry density, gas permeability, compressive strength of 3 days and 28 days) under different factors can be seen in Figure 5a-d, and it can be noted that the foam is the main factor influencing the four indexes as mentioned above. The dry density and compressive strength drop and the gas permeability increases as the volume of foam increases. In order to further investigate the mechanism of this phenomenon, a microscope was used to magnify the samples with different foam content for 500 times, as shown in Figure 6.  When the foamed concrete sample is magnified by microscope, it can be seen that when the amount of foam is less, there are fewer pores in the sample, and these pores are small, airtight, and smooth. With the increase of foam content, both the number and the diameter of pores increase significantly. When the amount of foam reaches 2 L, the pores in the samples are denser and larger, and the connected pores are formed, which leads to larger gas permeability of the foamed concrete. At the same time, since the fact that foam helps to produce more pores, the increase of foam content can lead to a decrease in other solid materials in the unit volume, resulting in a decrease in density and strength.

Effect of Foam Content on Properties of Foamed Concrete
In order to further verify the effect of foam content on the properties of foamed concrete, the samples of 0.5, 1.0, 1.5, and 2.0 L foam based on 1 kg mass of solid powder with a water cement ratio of 0.40 was prepared, and the change rules of gas permeability, dry density, and compressive strength  When the foamed concrete sample is magnified by microscope, it can be seen that when the amount of foam is less, there are fewer pores in the sample, and these pores are small, airtight, and smooth. With the increase of foam content, both the number and the diameter of pores increase significantly. When the amount of foam reaches 2 L, the pores in the samples are denser and larger, and the connected pores are formed, which leads to larger gas permeability of the foamed concrete. At the same time, since the fact that foam helps to produce more pores, the increase of foam content can lead to a decrease in other solid materials in the unit volume, resulting in a decrease in density and strength.

Effect of Foam Content on Properties of Foamed Concrete
In order to further verify the effect of foam content on the properties of foamed concrete, the samples of 0.5, 1.0, 1.5, and 2.0 L foam based on 1 kg mass of solid powder with a water cement ratio of 0.40 was prepared, and the change rules of gas permeability, dry density, and compressive strength

Effect of Foam Content on Properties of Foamed Concrete
In order to further verify the effect of foam content on the properties of foamed concrete, the samples of 0.5, 1.0, 1.5, and 2.0 L foam based on 1 kg mass of solid powder with a water cement ratio of 0.40 was prepared, and the change rules of gas permeability, dry density, and compressive strength were studied. As shown in Figure 7, when other conditions remain unchanged, the dry density and compressive strength decrease with the increase of foam content, and the gas permeability increases with the increase of foam content, which is consistent with the above results.
Energies 2020, 13, x FOR PEER REVIEW 8 of 14 were studied. As shown in Figure 7, when other conditions remain unchanged, the dry density and compressive strength decrease with the increase of foam content, and the gas permeability increases with the increase of foam content, which is consistent with the above results.

Optimum Mix
The comprehensive balance method was used to compare the results of each factor. As the effect of foam content on foamed concrete is far greater than the other three factors, we first determined the foam content. Due to the large consumption of foamed concrete in the coal mine goaf, considering the economy, Level 1 and Level 2 were excluded according to the dry density in Figure 5a. Meanwhile, considering the stability of the foamed concrete after consolidation, it can be seen that the compressive strength of Level 4 is far below the average level according to Figure 5c,d, so the foam content was selected at Level 3.
As can be seen from Figure 5, the water cement ratio is the secondary factor. In order to isolate gas better, Level 4 with highest gas permeability was first eliminated according to Figure 5b. Considering the economy, the water cement ratio should be as large as possible, so Level 3 was selected according to Figure 5a.
The above analysis can preliminarily determine the selection of the 11th mix proportion of 16 concrete series. In the 11th mix proportion, water reducing agent is at Level 1 and sodium silicate solution is at Level 2, which is very economical. According to the research results and the actual engineering requirements, the 11th mix proportion was chosen to be the optimum mix which can be seen in Table 4, as well as its engineering properties.

Optimum Mix
The comprehensive balance method was used to compare the results of each factor. As the effect of foam content on foamed concrete is far greater than the other three factors, we first determined the foam content. Due to the large consumption of foamed concrete in the coal mine goaf, considering the economy, Level 1 and Level 2 were excluded according to the dry density in Figure 5a. Meanwhile, considering the stability of the foamed concrete after consolidation, it can be seen that the compressive strength of Level 4 is far below the average level according to Figure 5c,d, so the foam content was selected at Level 3.
As can be seen from Figure 5, the water cement ratio is the secondary factor. In order to isolate gas better, Level 4 with highest gas permeability was first eliminated according to Figure 5b. Considering the economy, the water cement ratio should be as large as possible, so Level 3 was selected according to Figure 5a.
The above analysis can preliminarily determine the selection of the 11th mix proportion of 16 concrete series. In the 11th mix proportion, water reducing agent is at Level 1 and sodium silicate solution is at Level 2, which is very economical. According to the research results and the actual engineering requirements, the 11th mix proportion was chosen to be the optimum mix which can be seen in Table 4, as well as its engineering properties.

Application Modes
For the gas-rich coal mine, the gas flows into the goaf from the coal wall, the falling coal and the roof, which makes a large number of high concentration gas accumulated in the goaf, causing the gas leakage into the workface. Under normal conditions, the air pressure between the goaf and workface is Energies 2020, 13, 4377 9 of 14 basically balanced, and the gas in the goaf is mainly brought out from the upper corner by the roadway air from the lower corner, as shown in Figure 8. In order to reduce the gas concentration and ensure the safety and stability during the operation of the workface, two ways of isolating gas by using the foamed concrete are put forward: • Sealing the gas, that is separating the goaf gas from the workface air by building the gas separation walls on both lower and upper corners.

•
Replacing the gas, that is using the foamed concrete to replace the gas in the goaf void, after which the void can be filled and there is little space for gas accumulation.

Application Modes
For the gas-rich coal mine, the gas flows into the goaf from the coal wall, the falling coal and the roof, which makes a large number of high concentration gas accumulated in the goaf, causing the gas leakage into the workface. Under normal conditions, the air pressure between the goaf and workface is basically balanced, and the gas in the goaf is mainly brought out from the upper corner by the roadway air from the lower corner, as shown in Figure 8. In order to reduce the gas concentration and ensure the safety and stability during the operation of the workface, two ways of isolating gas by using the foamed concrete are put forward: • Sealing the gas, that is separating the goaf gas from the workface air by building the gas separation walls on both lower and upper corners.

•
Replacing the gas, that is using the foamed concrete to replace the gas in the goaf void, after which the void can be filled and there is little space for gas accumulation.

Establish Mathematical Model
According to the characteristics of gas migration in the large-space goaf under the condition of high-intensity and rapid mining advance, the Brinkman seepage equation and Fick diffusion equation can be coupled to solve the transient process of gas diffusion under the action of air flow, so as to study the mechanism of the two application modes.
The convection and migration process of gas diffusion in goaf includes two physical processes: gas ventilation convection and concentration diffusion [19,20]. The gas diffusion equation conforms to Fick diffusion law, that is where, δt is the instantaneous time proportion coefficient, which is equivalent to porosity; C is the gas concentration, mol/m 3 ; ∇ is the lalpace operator; D is the diffusion coefficient, m 2 /s; v is the average velocity, m/s; R is the source term, mol/(m 3 ·s).

Establish Mathematical Model
According to the characteristics of gas migration in the large-space goaf under the condition of high-intensity and rapid mining advance, the Brinkman seepage equation and Fick diffusion equation can be coupled to solve the transient process of gas diffusion under the action of air flow, so as to study the mechanism of the two application modes.
The convection and migration process of gas diffusion in goaf includes two physical processes: gas ventilation convection and concentration diffusion [19,20]. The gas diffusion equation conforms to Fick diffusion law, that is where, δt is the instantaneous time proportion coefficient, which is equivalent to porosity; C is the gas concentration, mol/m 3 ; ∇ is the lalpace operator; D is the diffusion coefficient, m 2 /s; v is the average velocity, m/s; R is the source term, mol/(m 3 ·s).
Under the condition of fully mechanized coal mining, the goaf caving area is composed of broken caving rock mass, which can be regard as the large porous medium. Its compaction degree is related to the support pressure above the goaf, in which the air flow channel system is relatively complex, and the Brinkman seepage equation is more suitable, that is where, v is the flow velocity of fluid, m/s; k is the permeability, m 2 ; η is the dynamic viscosity coefficient, Pa·s; p is the fluid pressure, Pa; I is the unit vector; F is the fluid resistance. In the calculation model of this paper, the simultaneous equations (Equations (4) and (5)) can solve the transient process of gas diffusion under the action of air flow, which can be calculated by numerical simulation software COMSOL Multiphysics.
COMSOL Multiphysics is a large-scale advanced numerical simulation software developed by the Swedish company COMSOL. Based on the finite element theory, COMSOL Multiphysics is developed to simulate various physical phenomena, which can better simulate the coupling of multiple physical fields and describe physical phenomena by solving various mathematical models [19].

Model Calculation
Referring to the actual size of the comprehensive mechanized coal mining workface, the calculation model of 80 × 195 m was established by COMSOL Multiphysics (in order to simplify the calculation, this paper only studied the goaf area formed by about one week of coal mining without considering the dynamic process). As shown in Figure 9, the width of the roadway is 5.6 m, so the lower 5.6 m part of the left side is treated as the boundary of air inlet, and the upper 5.6 m part of the left side is treated as the boundary of air outlet, and the other boundaries are airtight. Since the air flow in the roadway of workface accounts for the majority, and the air flow penetrating into the goaf only accounts for the minority, the pressure difference between air inlet and outlet is set as 100 Pa. At the same time, the air inlet and outlet are set as the convection boundary, between which is the airtight boundary, and the gas concentration flux was supplied by the other boundaries. There are 1 atm and 3 mol/m 3 initial concentration gas in the goaf, and the other numerical simulation parameters are shown in Table 5.
broken caving rock mass, which can be regard as the large porous medium. Its compaction degree is related to the support pressure above the goaf, in which the air flow channel system is relatively complex, and the Brinkman seepage equation is more suitable, that is η k ·v = ∇·( − pI+η(∇v+(∇ ) ))+F (5) where, v is the flow velocity of fluid, m/s; k is the permeability, m 2 ; η is the dynamic viscosity coefficient, Pa·s; p is the fluid pressure, Pa; I is the unit vector; F is the fluid resistance. In the calculation model of this paper, the simultaneous equations (Equations (4) and (5)) can solve the transient process of gas diffusion under the action of air flow, which can be calculated by numerical simulation software COMSOL Multiphysics.
COMSOL Multiphysics is a large-scale advanced numerical simulation software developed by the Swedish company COMSOL. Based on the finite element theory, COMSOL Multiphysics is developed to simulate various physical phenomena, which can better simulate the coupling of multiple physical fields and describe physical phenomena by solving various mathematical models [19].

Model Calculation
Referring to the actual size of the comprehensive mechanized coal mining workface, the calculation model of 80 × 195 m was established by COMSOL Multiphysics (in order to simplify the calculation, this paper only studied the goaf area formed by about one week of coal mining without considering the dynamic process). As shown in Figure 9, the width of the roadway is 5.6 m, so the lower 5.6 m part of the left side is treated as the boundary of air inlet, and the upper 5.6 m part of the left side is treated as the boundary of air outlet, and the other boundaries are airtight. Since the air flow in the roadway of workface accounts for the majority, and the air flow penetrating into the goaf only accounts for the minority, the pressure difference between air inlet and outlet is set as 100 Pa. At the same time, the air inlet and outlet are set as the convection boundary, between which is the airtight boundary, and the gas concentration flux was supplied by the other boundaries. There are 1 atm and 3 mol/m 3 initial concentration gas in the goaf, and the other numerical simulation parameters are shown in Table 5.    When simulating 'gas sealing', the gas separation walls with equal width of roadways were arranged on both sides of the goaf, the parameters of which were set as the foamed concrete in Table 4, and the remaining parts of the model were unchanged. When simulating 'gas replacement', the foamed concrete was used to block the entire cavity of the goaf and replace the gas in the empty hole, which could completely block the gas source. Since the replacement process was dynamic, the parameters of the whole calculation range were constantly changing. In order to simplify the study, the pressure difference between the air inlet and outlet was increased by five times in consideration of the displacement effect of the gas when the filling material was pumped, after which the parameters of the whole goaf were set as the foamed concrete in Table 4 [21-23].

No Gas Isolation
We drew the gas concentration distribution map in the goaf when the time was 0, 0.5, 1, 3, and 5 days, as shown in Figure 10a-e. The results show that under the condition of 100 Pa air pressure difference, it will take a certain time to start dispersing the gas because of the existence of 1 atm and 3 mol/m 2 initial concentration in the goaf. With the development of time, from the air inlet to the outlet, a fan-shaped concentration reduction area was gradually formed until it became stable about 5 days later, forming an accumulation area in the upper corner and keeping stable at 5-6 mol/m 2 . If measures are not taken to isolate gas, the gas accumulation area near the upper corner will make the gas continuously flow out with the air, causing the hidden danger to the workface.  When simulating 'gas sealing', the gas separation walls with equal width of roadways were arranged on both sides of the goaf, the parameters of which were set as the foamed concrete in Table  4, and the remaining parts of the model were unchanged. When simulating 'gas replacement', the foamed concrete was used to block the entire cavity of the goaf and replace the gas in the empty hole, which could completely block the gas source. Since the replacement process was dynamic, the parameters of the whole calculation range were constantly changing. In order to simplify the study, the pressure difference between the air inlet and outlet was increased by five times in consideration of the displacement effect of the gas when the filling material was pumped, after which the parameters of the whole goaf were set as the foamed concrete in Table 4 [21][22][23].

No Gas Isolation
We drew the gas concentration distribution map in the goaf when the time was 0, 0.5, 1, 3, and 5 d, as shown in Figure 10a-e. The results show that under the condition of 100 Pa air pressure difference, it will take a certain time to start dispersing the gas because of the existence of 1 atm and 3 mol/m 2 initial concentration in the goaf. With the development of time, from the air inlet to the outlet, a fan-shaped concentration reduction area was gradually formed until it became stable about 5 days later, forming an accumulation area in the upper corner and keeping stable at 5-6 mol/m 2 . If measures are not taken to isolate gas, the gas accumulation area near the upper corner will make the gas continuously flow out with the air, causing the hidden danger to the workface.

Sealing the Gas
We drew the gas concentration distribution map in the goaf when the time was 0, 0.5, 2, 4, and 6 d, 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 indicates 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.

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. Energies 2020, 13, x FOR PEER REVIEW 12 of 14

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 d, 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.
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.

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

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.

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 d, 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.
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.

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 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.

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.
Energies 2020, 13, x FOR PEER REVIEW 13 of 14 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.

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.

Conflicts of Interest:
The authors declare that they have no conflicts of interest.

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.