For simplicity, let's pretend these are well designed nanobots that don't outright kill their host by blood clots or accidentally ripping holes in capillaries. So let's pretend these great scientists already killed a bunch of small
woodland laboratory creatures and got those little issues figured out relatively early on. We'll assume these nanobots are the size of red blood cells (as you mentioned), deform the same way, can squeeze through capillaries and such one at a time just like normal red blood cells (or they avoid situations like that on their own, etc).
So, let's start with...
Replace (Some) of The Red Blood Cells!
Since we don't want to cause edema or high blood pressure, we will screen out some red blood cells and just replace those with our nanobots. It turns out that in this method there is an existing known condition caused by losing too many red blood cells: anemia. The normal count of red blood cells is noted as 4.7 to 6.1 million cells per microliter for men and a similar 4.2 to 5.4 for women.
That's a range of 1.4 million cells per micro-liter for men, so if we get someone on the "high but normal" RBC count level and replace their blood cells so they are down to the "low but normal" RBC count, that gives us 1.4 million cells per micro-liter; with 5 liters of blood in the human body (5 million micro-liters), that gives us a cool 7 trillion nanobots for starters.
Given these numbers there would normally be 31.5 trillion red blood cells in a human male body who that on the "high" side of the count, so that sounds nice to me. So our nanobots would exist in about a 4.5:1 ratio with red blood cells, or just under 20%.
Current total: 7,000,000,000,000 nanobots (some may experience some mild side-effects, ask your doctor of nanobots are right for you)
Replace (Some) of The Blood
People give a liter of blood all the time, which is 20% of their total blood volume (give or take). So why can't we just take that blood and replace it all with nanobots?
Well, blood isn't all cells - a lot of it is water. So just filling someone 1/5th full of what would probably be like a really fine powder...that'd probably screw up the blood pretty bad. Blood is already pretty tightly packed with cells, so I don't think we can dissolve that much powder into the remaining 4 liters without effecting key properties of the liquid.
But fear not, intrepid scientists - we'll pump people with as many bots as we can!
It turns out that when you separate blood, only about 40% of it is a combination of white blood cells, platelets, red blood cells, etc - with 60% being plasma. So why not take out a liter of blood, filter out all the plasma for mixing, add back in a liquid mixture of about the right viscosity as the blood cells, and pump that back into our
frightened willing test subjects?
Well, since we already have the figure for red blood cells and it seems that white blood cells are puny by comparison, let's go with that previous number of up about 6 million red blood cells per micro-liter of blood.
If we filter out a liter of blood, that would give us room for 6 trillion bots! ...wait, that's almost the same figure we got earlier. What gives? Oh, right - giving blood is expected to cause mild (short-term) anemia! And we were figuring taking subjects who already had a high amount of red blood cells, so suddenly this makes sense.
So we've still got the same figure: 6-7 trillion nanobots (if we tell you we are giving your extra blood cells to sick children, will that make you
stop screaming feel better?) We're still at 20% or less of the blood in nanobots...we have to go higher!
Replace ALL THE BLOOD!
Come on, what kind of scientists are we, anyhow? We know from our calculations that we easily can shove around 37 trillion nanobots into people by removing all their red blood cells, so why don't we just do that?
"Oh, but won't the subjects die?" What are you, a communist? Let's face facts here - we have high technology, nanobots that are as small as red blood cells. Why can't our nanobots do the job of red blood cells, but do the job even better? Think outside the box, here! 100% nanobots!
And why do all nanobots need to be the same? We'll make 4-5 trillion nanobots to do no job related to being a red blood cells, so they can do whatever. The other 33-34 trillion nanobots will do everything a red blood cell does, plus it'll probably do other cool stuff. We aren't banging rocks together here! As we figure out how to make nanobots do stuff even better than red blood cells (maybe using moon dust), we'll be able to shift the proportion of nanobots in favor of non-blood cell activities...like lasers, or something.
Everybody gets 37,000,000,000,000 nanobots! whether they like it or not
Early on, after we've worked our number up this high without
publicly acknowledged any deaths, we start jacking up the counts to replace all blood cells with nanobots, and we can probably start allowing for thicker blood because our ThriveBots™ deal with any side-effects from high blood pressure, so I'd say we can start getting our count up over 40 trillion in the blood alone, no problems (none we allow to be reported, anyway). Maybe even up to 50 trillion, but it's going to get pretty hard to go beyond that.
Say, skin cells are awfully sparse...how many layers of skin do you need, really, when you could have a few layers of EpiThrive™ - the superior human skin alternative! Guaranteed to not give you any cancer that is presently known to man! We'll have a few more trillion ThriveBots™ packed into you in no time!
Final Nanobot Count
3-5,000,000,000,000 nanobots for early, squeamish subjects - minimal side-effects, nanobots can't do red blood cell work
6-7,000,000,000,000 nanobots with still minimal side-effects, but will cause anemia in all but high red blood count subjects
37,000,000,000,000 nanobots, for those who've transcended their childish need for human red blood cells (may cause a change in skin tone, if we don't up-sell them to colored plasma additives)
40 trillion and beyond, for real champions who understand that Maximum OverThrive Technology™ is the true future of whatever it is we are calling human-technology hybrids now adays
Minor side-effects may include: grumpiness and irritability, feeling tired, fatigue especially after exercise, headaches, problems with thinking and concentration, desire to eat ice cream, desire to eat non-food items (organic and inorganic), blue colors to the whites of the eyes, light-headedness, pale skin, shortness of breath, heart murmur, rapid heart beat, low blood pressure, vitamin deficiencies, double vision, sudden and severe unexplained pain, a desire to be part of something greater, a strengthening dedication to The Collective, sudden instant death, restless legs (and arms), memory loss, vivid hallucinations, heart attack, stroke, loss of impulse control, decreased emotion or flat affect, and an increased awareness of the vileness of the common unimproved animal.
Take nanobots only as directed, your mileage may vary. Please report all unexpected symptoms or side-effects to your personal ThriveBot™ representative immediately, before inconveniencing others or your doctor with things they are not capable of understanding.