Here goes; I was flying my Beech Sierra out of Ketchikan intending to go nonstop to Jefferson County International in WA State My home airport I was in VMC but at 9,000 feet and an overcast layer was a few thousand feet below. As I passed over Bella Bella, I noticed that the right tank was indicating that only some of the reserve fuel was left in that tank even though I had been switching the selector on the hour and I was about 2 hours and 30 minutes into the flight. I told my passenger that I was concerned about this, made sure the selector was on the left tank and waited the situation out. About 30 miles south of Bella Bella and over 6,500 foot peaks under the overcast, the engine stopped running. ATC vectored me west to get over lower terrain and we began to discuss the choices of landing sites. After about 15 or 20 seconds, the engine started back up again, but only for a couple of seconds and it continued to cycle like this for 10 or 15 minutes. It would quit for 3 to 4 seconds and then surge to life for about two, sort of like riding a bucking bronco. Amazingly at the end of the 15 minutes or so I was still at 7,000 feet and that was encouraging. All of a sudden the engine began to run normally and, except for the SAR helicopter crew, the amublances, fire trucks etc on the runway, the end of the flight was uneventful. ATC thought I had ice impaction in the air intake, but I was quite certain I had either dragged debris from the empty tank or air because of the fuel selector valve. They suggested I go lower, but I declined, thinking as far away as I was from a suitable field altitude was gold. Once the engine began to run steadily I climbed back to 9,000 for the added comfort of space between me and the ground. I found a mechanic at Port Hardy who was willing to work on my problem and within a week I got him a repair kit for the fuel selector valve and he was able to fix the problem. Turns out, the last guy who worked on the valve (and this was within the last year) must have incorrectly placed a small ballbearing that provides a detent and also seals off the inards so that you only select one tank at a time. The ball bearing was found in the gascolator and once it was put back the valve worked fine. I believe the scenario that caused the entire event was as follows: I must have been in a slight skid the first half of the flight causing the fuel to feed out of the right tank no matter what position the selector was in. I had essentially only a BOTH selection and the acceleration of the skid caused that tank to empty. When all the usable fuel was burned out of the right tank, the engine driven fuel pump still busily sucked at whatever it could get - in this case air. After awhile, gravity feed from the left tank (perhaps lower nose position and a skid in the other direction may have facilitated this) filled up the selector and the engine ran for a moment but the engine driven fuel pump fired up at the same time and sucked more air when that gravity fed fuel was emptied. I suspect that after 15 minutes for whatever reason I had the a/c in enough of a skid the other direction to accelerate fuel from the left tank and the engine began to run normally. I did not figure all this out during the flight and had not developed the skid theory. Thus any changes in fuel acceleration from right to left were purely serendipitous.
If anyone has questions, feel free to ask. Incidentally I flew to Prince Rupert last week and I spent some sleepless nights worrying about that leg from Prince Rupert to Port Hardy. I had been thinking that going back was the best thing - like getting back on the horse (getting tired of this analogy?) and I was really surprised to find how much anxiety I went through before and during this flight.