I'm following up on my (top) posting with a detail I didn't fully realize and didn't report: Use soft water for the salting-out process!!! Some years ago I posted on a failure of salting out, and I've since had one more such failure. The problem, I'm convinced, was that in both cases I had used too much hard water.
Soap is the sodium (or potassium) salt of fatty acids (plus a minority of other stuff, perhaps), and is completely soluble in water. But hard water contains calcium and magnesium salts (and possibly iron and others), the "soaps" of which are insoluble in water. Bummer. Using too much hard water turns your batch of salt into a batch of "bathtub ring"!
To prevent this, use either soft water (from a water softener that uses "water softener salt") or just use distilled water (from a dehumidifier). I do the latter because I don't have a water softener, and I'd throw away the condensate from the dehumidifier anyway.
Using distilled water, I am now able to salt out a batch of soap repeatedly, washing away water-soluble impurities each time, and reducing the odor. This is not a 100% effective procedure. The soap from the nasty oil I have been working with still has an odor and a distinct (though not necessarily unpleasant) yellow color.
In my latest go-around, I've done one final salting out, which left a medium-amber-colored brine (as opposed to dark amber or black), and now I'm doing one final brine "rinse" of the batch, and that will be it. I can still smell the bad odor in this soap (derived directly from the nasty oil it was made from) and I rather doubt it will be suitable for the bath.
Bottom line: Salting out is a very useful technique in some instances, especially for correcting an "oops" in which you used too much lye, but will not take a really foul soap and turn it into a lovely, clean-smelling white soap! Start with "clean" oil and fat to get clean soap. Use salting out as a "tool" along the way.
Now, to respond to some questions above (which I saw today for the first time):
Q: Do you always make soap in this manner or were you just trying to find a procedure for salting out, as you called it?
A: I certainly don't ever plan ahead on using salting out in my soapmaking, but I do make soap from my waste cooking oil, and salting out is a way of removing the dark color from such soap, should it happen that refining the oil before soapmaking didn't do the trick.
Q: So, what is the purpose of salting out the soap? Is it so your can remove impurities from used oil to soap with it?
A: Succinctly, salting out allows you to separate the soap from water-soluble impurities, such as odors or colors. I consider it a means of save an otherwise failed batch. I consider it much more important to refine the oil before soapmaking. (I refine the oil by running it through a fine strainer, then boiling it up with water and letting it cool to 40F or so, possibly multiple times, and discarding the water.)
Q: Would this method work with rancid oils or DOS afflicted soaps? Or am I way off track with the purpose of salting out soap?
A: Please avoid acronyms like "DOS" - "Dreaded orange spots". (It took me a while even to learn what it means, from
www.natural-soapmaking.net/DOS.html). Salting out would probably correct the spots, but it would probably work only moderately well for removing the odors of rancidity. However, I simply don't understand how soap can go rancid and SMELL unless it is very significantly overfatted with unsaturated oils. Soap is a salt, and hence is of very low volatility. I would think that only the free fatty acids could give rise to an odor. In any event, this was not MY purpose for salting out. I see it as a means for eliminating excess lye if you muck up the recipe, or excess color if you're working (as I do) with waste oil.
