*3.7.1 Effect of porosity on cave pressure drop*

For a given porosity of the cave and airflow in the production drifts, the pressure difference across the cave was calculated and then plotted against the airflow quantity flowing through the cave, as shown in **Figure 18**. For example, five

### **Figure 16.**

*Static pressure distribution under undercut ventilation (left) and without undercut ventilation (right) using a discrete model.*

*Block Cave Mine Ventilation: Research Findings DOI: http://dx.doi.org/10.5772/intechopen.104856*

**Figure 17.** *Comparison of drift resistance with and without the undercut ventilation (nu—no undercut).*


### **Table 3.**

*Comparison of pressure drop equation for model with undercut ventilation.*


### **Table 4.**

*Comparison of pressure drop equation for model without undercut ventilation.*

different air quantities were simulated for a bulk cave porosity of 35%. Therefore, for six different bulk cave porosities, a total of 30 simulations were performed to develop the pressure-quantity (P-Q) characteristic curves for a mature panel cave mine. **Figure 18** shows the variation of the airflow resistance value with respect to the bulk cave porosity.

### **3.8 Finding 8: relationship between airflow and radon concentration**

As per the Mine Safety and Health Administration (MSHA) regulations, personnel shall not be exposed to air-containing concentrations of radon daughters exceeding 1.0 WL. No person shall be permitted to receive exposure over 4 WLM (Working Level Months) in any calendar year. 30 CFR 57.5005 suggests dilution with uncontaminated air to mitigate radon exposure. Therefore, we studied the effect of airflow on radon concentration [20, 21]. The airflow through the production drifts is increased, and radon concentration at the outlets of the drifts is measured after 8 minutes. **Figure 19** show radon concentrations with airflow at the outlets of the first, second, and third drifts.

**Figure 18.** *P-Q characteristic curves for a mature cave under different porosity conditions.*

**Figure 19.**

*Effect of increasing airflow on working level at the outlet of the (a) first drift; (b) second drift; (c) third drift.*

McPherson (1993) stated that if an airway is supplied with uncontaminated air and the rate of radon emanation remains constant, then the exit working level of radon daughter is proportional to the residence time ð Þ **tr** raised to the power of 1.8 Eq. (1).

$$\mathcal{W}L \propto (t\_r)^{1.8} \tag{1}$$

The results show that the radon concentration decreases with increased airflow, and an empirical relationship is developed for each drift. Due to the difference in the number of radon sources, the relationship varies for the three drifts. Therefore, based on the drift's configuration, the empirical relationship between the working level and airflow might be different, unlike in Eq. (1).

### *3.8.1 Comparison of discrete and continuum model*

The airway characteristics are analyzed with the help of a discrete and continuum model [19, 22]. Both models show that radon growth through the production drift is non-linear; however, the continuum model does not replicate the significant variation in radon concentration with time compared to the discrete model [23]. Basically, the continuum model indicates that, beyond a specific time, consistent

*Block Cave Mine Ventilation: Research Findings DOI: http://dx.doi.org/10.5772/intechopen.104856*

**Figure 20.**

*Comparison of the discrete and continuum models for predicting radon levels at the outlet of the second drift with time.*

airflow keeps the concentration constant with respect to time. This is further verified in **Figure 20**, which compares the radon concentration at the outlet of the second production drift for both models.

The discrete model demonstrates that the concentration increases with time, unlike the continuum model, which shows that after about 5 hours, the radon concentration is almost steady. In addition, we replicated the study on the effects of airflow using the continuum model. The empirical relationships developed are compared with the discrete model in **Table 5**, and both models suggest that different relationships are required for the drifts based on their configuration.

### **3.9 Finding 9: characteristics of model with no undercut ventilation**

This section considers the fully developed panel cave without the undercut ventilation (second stage). This is usually after the whole panel is developed, and the undercut level no longer exists. No flow is assigned to the undercut inlet duct and outlet to represent this condition, but all other conditions presented in the previous section are used. **Figure 21** shows the velocity contours through the drifts without the undercut ventilation. Unlike in **Figure 10** (with undercut ventilation), the velocity magnitude through the three drifts is more uniform. However, based on the number of pressure loss sources (drawbells), the magnitude of velocity through the first (seven shock loss sources) and third (six shock loss sources) drifts are pretty similar.

**Figures 22** and **23** show the concentration through the production and undercut drifts, respectively, after 9 hours. The concentration through the production drift (**Figure 22**) is significantly lower than in the first stage with undercut ventilation (**Figure 12**).

This suggests that the undercut ventilation increases radon concentration in the production drift by transporting radon generated within the cave into the drifts.


**Table 5.**

*Empirical relationships—Effect of airflow on radon concentration for the first stage of a fully developed cave.*

**Figure 21.**

*The magnitude of velocity through production drift without undercut ventilation.*

**Figure 22.** *Radon concentration in the production drift without the undercut ventilation.*

### **Figure 23.**

*Radon concentration through the production drift is limited to 0.2 WL.*

Even though the airflow is almost uniform through the production drifts, the locations of the maximum concentration vary inside the drawbells—**Figure 22**. To investigate this, **Figure 23** shows a localized image of the concentration with a 0.2 WL limit. The drawbells are oriented in two directions (340 and 560) to the flow based on the flow direction. The shock loss is greater with the 56° orientations; hence the airflow is less efficient in this region, as indicated in **Figure 23**.

Therefore, due to shock losses, the orientations of the drawbells affect the efficiency of the airflow in mitigating radon exposure. Since there is no notable

### **Figure 24.**

*Radon concentration in a section of the cave without the undercut ventilation.*

airflow inside the cave, **Figure 24** shows that the concentration inside the cave increases significantly. In this case, the maximum concentration is about 20 WL, though mine personnel is not usually exposed to the higher levels in these regions. This agrees with previous studies that the working level in abandoned mines or caves can be as high as 81 WL [24]. Therefore, without undercut ventilation, radon accumulates significantly within the cave.

*Without undercut ventilation, negative pressure on top of the cave might have a negative impact on the radon concentration in the production drift.*

We studied the effect of maintaining a negative pressure on top of the cave without undercut ventilation. **Figure 25a** shows radon concentrations before imposing the negative pressure condition, and **Figure 25b** shows the concentrations after imposing the condition.

The effectively imposed negative pressure condition reduces radon concentration in the drawbell; however, radon concentration increases toward the end of the production drifts. This is due to significant air loss through the porous drawbells to satisfy the condition imposed. Therefore, the magnitude of air flowing through the drifts decreases, and the radon concentration increases. Although in most cases, the cave is not as porous as the discrete model (47%), this scenario is possible for a very porous cave or drifts with one or two hang-ups close to the drift's inlet. Hence, without the undercut ventilation, maintaining a negative pressure on top of the cave might have a negative impact on the radon concentration in the production drift. Therefore, mitigation measures should be appropriately investigated before implementation because the system might respond differently based on the mine condition. In addition, since there is no more undercut level, one can consider increasing the airflow through the drifts instead of imposing a negative pressure condition on top of the cave.

### **3.10 Finding 10: ventilation shutdown causes variation in radon concentration at the production drifts**

In most underground mines with radon sources, the ventilation is continuous to ensure radon concentration is within the permissible levels. However, certain situations such as maintenance or mechanical malfunction could lead to the shutdown of the ventilation system. This study investigates the effects of shutting down the ventilation system for a period of time using the discrete model without the undercut ventilation. **Figure 26a** shows the radon concentration contours for the model after about 1 hour without ventilation.

The result shows significantly higher radon levels due to the pressure drop in the production drifts after the ventilation is shut down. It is observed that locations

**Figure 25.**

*(a) Radon concentration before imposing negative pressure; (b) radon concentration after imposing negative pressure condition.*

**Figure 26.**

*(a) Radon concentration contours after 1 hour of ventilation shutdown; (b) pressure distribution after 1 hour of ventilation shutdown.*

*Block Cave Mine Ventilation: Research Findings DOI: http://dx.doi.org/10.5772/intechopen.104856*

with a high radon concentration level vary based on the pressure distribution shown in **Figure 26b**. There is a significant pressure drop at the inlet for the first and second drift as the airflow stops. Therefore, radon concentration increases suddenly toward both inlets due to the pressure difference. However, for the third drift, the trend is different. The third drift develops the maximum pressure due to the distance between the inlet and the first source of pressure loss (drawbell). Hence, after shutting down the ventilation of a mine, the pressure around the inlet of the third drift is still high enough to keep radon concentration low. Therefore, in the event of a ventilation shutdown, there might be a considerable variation in radon concentration through the drifts.
