Underground miners work in dangerous conditions, threatened by tunnel collapse, fires, and explosions. In 2006, three major coal mining accidents occurred, either from explosions or fire, and 19 miners died. As a result, Congress passed the Mine Improvement and New Emergency Response Act of 2006, more commonly known as the MINER Act. That law tasked the National Institute for Occupational Safety and Health (NIOSH) with researching and testing refuge alternatives in mines in the event of another disaster.

One of the main charges investigated by NIOSH’s Office of Mine Safety and Health Research was investigating the practicality, survivability, and cost of refuge alternatives, basically a secure area where miners can flee in the event of life-threatening accidents. The researchers found that built-in-place (BIP) and portable refuge alternatives were practical in most underground coal mines as a refuge of last resort, with BIP refuges a better option.

According to NIOSH, there are about 30 BIP refuge areas in U.S. underground coal mines, all of them located away from the face of the mine. As the name suggests, they are set in place, while mobile refuges can be installed closer to the working face of a mine.

Still, the dimensions of BIP refuges vary as do the number of people they can hold. They must be equipped with survival needs, including food, sanitation, and most importantly, a stable source of fresh air. BIP refuges commonly use a borehole to supply fresh air, although there compressed air or cryogenic systems are also used underground.

Federal regulations require BIP refuges to provide a breathable air supply of 12.5 cubic feet per minute (cfm) or more per person in order to maintain oxygen concentrations between 18.5 percent and 23 percent. Carbon dioxide levels must be maintained below a 1 percent limit.

“These refuges have no specific dimensions, they are usually different sizes,” said Lincan Yan, a research scientist with NIOSH and the Centers for Disease Control. “But this number that is given by regulation about air flow, is it valid?”

Yan and his colleagues at NIOSH sought to validate those numbers. They reported their findings in the paper “Mathematical Modeling for Carbon Dioxide level Within Confined Spaces,” published in the June 2023 edition of ASME’s Journal of Risk and Uncertainty in Engineering Systems.

The task was complicated by a great number of variables involved, including the size of the refuge and the unknown number of people taking shelter.

“There are too many combinations,” Yan said. There’s no practical way to have this kind of physical testing. One solution is to build a model.”

When people breathe, they exhale carbon dioxide, and if a number of people are in a confined space the gas can build up quickly and create a safety hazard. “One other problem is heat and humidity,” he said. “When people stay inside of the refuge, heat and humidity will build up.”

Yan and his team began studying the problem in 2014 and devised two mathematical models to confirm the oxygen and carbon dioxide requirements. The oxygen content is mainly determined by the flow of fresh air into the refuge, the carbon dioxide concentration depends on a number of factors, including the rate of fresh air flow, the size of the refuge, the number of people within it, and the amount of the gas exiting through an exhaust pipe.

The team first produced a simplified model followed by a differential model. The results were tested and validated using a test lab in a converted 20-foot-long, 8-foot by 8-foot shipping container. To simulate human breathing, the researchers burned propane at the rate necessary to mimic the rate of human oxygen consumption.

Flow rates were based on an assumed number of occupants, and the propane rate on the oxygen needs of the assumed number of people. The first test looked at the percentage of carbon dioxide by volume with 40 people and two rates of fresh air flow, the first at 100 cfm and the second at the higher rate of 500 cfm.

The results showed the differential model predictions were closer to the physical test results. For the lower rate of flow, test data and model predictions show the carbon dioxide level reached a steady level in about an hour. That jumped to 15 minutes using the higher rate of flow.

Similar results were confirmed in a second test assuming 48 people in a refuge. Using a 600-cfm flow rate, the models and the data show the percentage of carbon dioxide would reach a steady level within a half hour. For fresh air flow rates higher than 2.5 cfm per person, the percentage of carbon dioxide stabilized below 1 percent.

The models and testing confirmed that 12.5 cfm of supplied air will sustain various numbers of people in a refuge for 96 hours as mandated by federal regulations. It could also help mine owners and manufacturers in the design of refuges.

“For any confined space carbon dioxide mitigation is always a problem,” Yan said. “Based on the research in this paper, we provide a potential solution…without conducting physical testing.”

John Kosowatz is a senior editor at ASME.org.