Detecting leaks in gas-filled pressure vessels using acoustic resonances

We demonstrate that a leak from a large, unthermostatted pressure vessel into ambient air can be detected an order of magnitude more effectively by measuring the time dependence of the ratio p/f(2) than by measuring the ratio p/T. Here f is the resonance frequency of an acoustic mode of the gas inside the pressure vessel, p is the pressure of the gas, and T is the kelvin temperature measured at one point in the gas. In general, the resonance frequencies are determined by a mode-dependent, weighted average of the square of the speed-of-sound throughout the volume of the gas. However, the weighting usually has a weak dependence on likely temperature gradients in the gas inside a large pressure vessel. Using the ratio p/f(2), we measured a gas leak (dM/dt)/M ≈ - 1.3 × 10(-5) h(-1) = - 0.11 yr(-1) from a 300-liter pressure vessel filled with argon at 450 kPa that was exposed to sunshine-driven temperature and pressure fluctuations as large as (dT/dt)/T ≈ (dp/dt)/p ≈ 5 × 10(-2) h(-1) using a 24-hour data record. This leak could not be detected in a 72-hour record of p/T. (Here M is the mass of the gas in the vessel and t is the time.).