The charcoal adsorbs toxins, and the bloodstream passes through the mouth every 20 minutes (so the OP experts say), so you would think that IF#2 would do a better job than oil, no? Then you could swallow it, and it would adsorb toxins from the gastrointestinal tract...
But that only lasts for a few hours (or overnite). The best option (especially for consistency & efficacy) is taking it internally. Charcoal/bentonite aDsorb (aDsorb is a kind of 'electric' "pulling to itself", where aBsorb is like a sponge, and has to be touching the toxin).
So a poultice over the liver draws toxins from the liver and from the blood that's passing through the liver...but it can't pull toxins/poisons from the intestinal tract & colon...and that's where the majority of them are. Why let the poisons get INTO the bloodstream to overwhelm the already overburdened organs of elimination, eh? That just makes no sense at all.
Remember :::wink wink::: the very first order of business for healing is stop doing/ingesting what's making you sick, and start doing what will make you better. So, if you're still taking the Effexor, weaning off it is your first order of business (this drug plays MAJOR havoc with your liver - it's insidious). And also, using charcoal WILL lower the blood level of most pharmaceuticals...so no matter how you use it (if the Effexor is still at play), you can expect to experience some level of withdrawal symptoms.
Btw, whether you're still on it or not, I've been meaning to get you this: http://www.petitiononline.com/effexor/
Be sure to click on the 'view current signatures' link at the bottom and read through a few pages of the 20k+ notes & signatures.