Trying to create a future earth which has been thoroughly abused by the excesses of modern capitalism. Extreme weather, rising sea levels, massive droughts, that sort of stuff. My question is: could fracking, on a large enough scale over a long enough period of time, plausibly affect the movement of the tectonic plates? Would it be possible for them to noticeably shift in a span of 100 to 200 years?
Tectonic plate shift takes place at the level of the astenosphere, which is at least 80 km down. Hydraulic fracturing takes place at depths one order of magnitude shallower, and the deepest bore ever drilled was no more than 13 km in depth.
Therefore, fracking cannot reach the astenosphere, and given the viscoelastic properties of the Gutenberg discontinuity, neither could any hypothethical "fracture creep".
So, no, you can't influence continental drift using hydraulic fracturing.
Actually, even if the astenosphere could be reached with frackers (there would be no reason to do so, as kerogenic strata cannot possibly be found beyond Archaean depth), the whole operation might probably not work anyway, because evidence from the Kola Superdeep Borehole and other drilling operations seem to indicate that the rock at a depth beyond several kilometers may be already "fracked".
Almost certainly not. (a) Plate boundaries tend not to be where natural gas is found -- that's normally in older, stable formations and (b) in any event plates are really big, really heavy objects and getting plates to do anything new in a century or two is likely to be really hard and (c) we can't influence them anyway with anything we now have.
It seem plausible that injecting large amounts of water along a fault line might lubricate it enough to release the pent-up stress, but once that stress is released, adding more won't move the plates faster.
Think of the plates as really big, really slow beasts that plod along at their own pace (2-5 centimeters/year, typically) without paying much attention to their neighbors. When they rub up against one another going in opposite directions they just keep moving along and their hides stick and slip and stick and slip, but the beasts don't even notice that -- its too trivial to reach their attention.
In a fault like the San Andreas the plates are moving about 4 cm/year and normally the two sides of the fault are stuck together. As the plates move, the rock along the fault gets more and more bent and stretched and every once in a while the stress builds up so that a small segment of the fault slips on the order of meters to relieve the stress. Bang: Earthquake!
Then, a while later (decades, typically) another segment slips and so forth until eventually LA is just west of Berkeley. We might be able to affect when a segment slips, but the amount it slips will never be more than enough to release the built-up stress -- and the plates will take no notice of our foolish meddling.
It would not.
Fracking just does not work so deep us to cause significant shifts in the tectonic plates. Fracking depth, in most extreme cases, goes down to about 4 kms. It is more like scratching off a layer of skin to draw blood.
The tectonic plates's movements are a different scale entirely.