Okay, so here is where it gets mildly fuzzy for me. Bear with me. If I had eight gallons of my filtered tap water (pH 6.6, bicarb 138, Ca 34, Cl 21, SO4 27)
You've got some magnesium and/or sodium you are not telling me about so I'm putting in 13 mg/L magnesium and 15.25 mg/L magnesium
...and added some sort of acid to it until the pH was 5.5 and then added only pale malt (which should keep the pH in the same area code), that would be the same as diluting to remove the bicarb?
Not exactly the same, of course. If you add phosphoric acid it would take 32 mL of 10% acid and you would have 21.6 ppm alkalinity left out of the original 113. IOW your alkalinity would have been reduced 81% and your bicarbonate would be at 27 mg/L. You would not have saturated WRT apatite and no calcium would precipitate.
If you used sulfuric acid your alkalinity would be a wee bit lower at 19.8.
While acid gets rid of the bicarbonate (or the lions's share of it) it obviously does not reduce chloride or sulfate or calcium (unless you saturate WRT apatite) and it replaces all the bicarbonate removed with sulfate or phosphates. With RO all ions get diluted by an equal factor and no acid anion(s) is/are added.
If so, how do I know how much bicarb is left after all of that?
For starters you should be thinking in terms of alkalinity: not bicarbonate, not residual alkalinity. For acidification to pH 5.5 starting from 6.6 all but about 20% of alkalinity is removed. How do you know that? Well you have to do some pretty hairy calculations but I am trying to come up with some curves that include all those for you. Equipped with that set of curves you will use a curve for target pH and follow it to starting pH and read off the percentage of alkalinity not converted.
Also, if I were to do that for a beer that was say, 10-12 SRM, I assume the addition of darker malts would lower the pH into a zone that was too low.
When I say it is like RO water what I mean is that if you plan your brew as if the alkalinity were 0 as opposed to 112 you won't be far off. That's what I'd do. I'd just use 3% sauermalz and go unless I wanted some extra chloride and sulfate.
I guess I'm having a hard time determining how the addition of acid reduces the bicarb level and by how much.
How is easy:
HCO3- + HA --> CO2 + H2O + A-
How much is a little harder. That's why I hope to be able to offer curves. There are some out there but they were a first run and are in error. Corrected ones are in the works.
This angle interested me because, if I'm understanding correctly, this would be a way for me to use my filtered tap water without lugging RO or distilled water around. Maybe you could explain it as it might apply to making a soft beer like a Czech Pils.
Czech pils would be one case where you would not want to take this approach as the best Boh. Pils is made with the lowest mineral content water possible consistent with having enough calcium to keep the yeast happy and chloride to give it a bit of body.
Lower the pH of the water to 5.5, add the pale malts and water to the mash, check the pH, further adjust with lactic acid if necessary, etc.?
That is how you would do it.
Also, what does this do to my calcium, chloride and sulfate level and what if I wanted to raise calcium because I'm only at 34ppm to begin with?
Your calcium, chloride and sulfate levels are unchanged as you have not diluted them (except by the volume of the added acid). With respect to the calcium: you should not try to raise it above 112 mg/L as the solution would be saturated at that point and it would probably just precipitate out.
Hmm, I apologize in advance for the confusion.
The questions are well put and reasonable ones. To summarize:
You add acid to a chosen mash pH.
You look on a curve to see if your alkalinity reduction is acceptable
You look on another curve to see how much extra calcium you can tolerate.