I have asked myself the very same question in the past.
This is the best answer I can come up with. I hope it is close to being right.
I figure the flood happened around 2500 BC.
At 2500 BC, there were 8 people, and I figure 3 fertile couples.
These 3 couples had 16 sons according to the Bible. They probably had 15-20 daughters.
The total population by 2460 BC was probably at least 40. This would include the 'original 8' plus 30 children, plus the young children of the original 8's older children. By 2460, there were probably 4 generations co-existing on Earth.
With my assumptions, Earth's population increased by a factor of 5 in just 40 years (8 x 5 = 40).
Now the issue is: Is it reasonable to assume that couples average 10 children (5 sons, 5 daughters)?
I believe so. The Bible is loaded with examples of families with 10 or more children. For example, Jacob had 12 sons. Moreover, before 1940, many families in the US had about 10 children.
Anyway, let's say the population increases by a factor of 5 every 40 years, this is how the population can skyrocket:
2500 BC population of 8
2460 BC 40
2420 BC 200
2380 BC 1,000
2340 BC 5,000
2300 BC 25,000
2260 BC 125,000
2220 BC 625,000
2180 BC 3,125,000 (around Abraham's time)
2140 BC 15,625,000
2100 BC 78,125,000
2060 BC 312,500,000
These calculations don't factor in extremely long lifespans enjoyed by some people just after the flood. There could have been 10 - 15 generations co-existing when Shem was alive. This could have further increased population.
These calculations also don't factor in 'short' generations in which 20 year old women give birth to children, who in turn give birth when they are 20....
The point of the above calculations is to show how in 300 years, you can easily go from 8 people to hundreds of thousands.
On the other hand, when I read of Abraham's travels, I am often struck by how in one sense, it was still a small world. The world was so small that even powerful leaders knew he existed and had a beautiful wife. It was so small he and Lot could explore relatively uninhabited - fertile - areas in the Middle East.
Therefore, in one sense Abraham's world may have had small spreadout populations, but on the other hand Abraham's world may have had empires with thousands of troops.
When I read history, I am often struck how nations can change greatly over 100 or so years. 140 years ago, the US only had about 33 million people. An Indian fellow once told me that 100 years ago, India only had about 200 million people, and that because of that India was a far different place.