Someone was asking for mass-flow numbers earlier on.
RR's Web site gives an intake mass-flow for the RB211-535E4B (I picked an engine arbitrarily) of 1,177lb/sec or 533.87kg/sec.
Based on the figure of 0.3 milligrams per m3 given for Stranraer, at an air density of 1.2kg/m3 at sea level (obviously we're not interested in sea level, but at least it's wrong in a known way - the ash measurement is a sea-level one and I guess RR's figures are test-stand measurements, so it's consistent) that would be 444m3 of air a second and 0.133g of ash a second - 478g of ash per engine-hour.
(Although, the -535 is a very high bypass turbofan, so perhaps we need the core mass flow...)
One can simply divide by the by-pass ratio of 4.3.
But there is the issue, under which conditions is the mass flow rate 1177 lb/s? We probably should consider a density figure at pressure and temperature corresponding to a typical cloud level. You can take standard atmosphere data etc.
However there is another estimate, based upon speed and diameter. Take the fan diameter, 74.1 in. Calculate the area. Divide my the by-pass ratio. If I do that, assume a speed of 180 m/s, for 0.3 g/m3, I end up with actually a very similar figure, 126 g/hour (assuming no algebraic error...) Of course one would hope crossing an ash zone would take less than an hour.
(From peter_we)
Thats a pretty high level.
BTW, indeed the new threshold figure of 2 g/m3 comes across as not very conservative. I would have expected them to pick a figure more like 0.5?