A natural gas wellhead is located 400 m from an instrument control room. The control room is a potential ignition hazard in the event of a leak of natural gas (essentially pure methane). Studies have shown that a suitable safety margin is imposed if the downwind gas concentration is determined using one-half the LFL. For methane this represents a concentration of 2.5 vol. %.

a. What is the minimum release rate of methane (in kg/s) that will result in a concentration at the control room equal to half the LFL? Be sure to state your assumptions clearly. Assume a temperature of 298 K and an ambient pressure of 1 atm.

b. If the methane pressure in the wellhead is at 10 atm pressure, what hole size (in cm) will produce the release rate of part a?

c. If the largest pipe size in the wellhead is 4 cm (internal diameter), comment on the likelihood of an ignition hazard from the control room.