To answer this question let's get introduced to the production of hydrogen through steam reforming. This is the standard process used for the production of industrial hydrogen. It involves reacting water and methane at high temperature (1100 oC), pressure (25 bar), in the presence of a metal catalyst (Nickel).
H2O + CH4 → CO + 3 H2
ΔH = +206 kJ
This forms synthesis gas: Carbon Monoxide and Hydrogen gas. The next step is to burn the Carbon Monoxide with water at 400 oC in the presence of a catalyst to get back more Hydrogen.
CO + H2O → CO2 + H2
ΔH = -41 kJ
The energy produced in the second stage can be recovered by preheating the first stage. For for a total enthalpy change of 165 kJ we get out 4 moles of Hydrogen, or 41.25 kJ/mol. This is rather better than electrolysis, which burns low entropy electricity at 286 kJ/mol to make Hydrogen. Coal can also be used in steam reforming, at 45 kJ/mol (but also twice more CO2 production). The Hydrogen and Carbon Dioxide can then be separated by a variety of means. I am going to assume that this is energy neutral, because the mixture should still be suitable for hydrogenation.
Ideal Energy Input
Real-world electrolysis is about 75 % efficient. If we assume reforming has the same efficiency, then the actual energy requirements for hydrogen production through methane production, rounded up, 30 MJ/kg.
Methane has a heating value of 55.7 MJ/kg, so for upgrading bitumen, we'll need about 0.54 kg of methane for every kilogram of methane we convert to hydrogen. This works out to 35 % of the methane from our input stream being diverted to power the process.
I showed in my last post that about 0.3 mcf/bbl of natural gas was needed for tar sand separation and a maximum of 0.45 mcf/bbl used for upgrading bitumen to synthetic crude. If we could replace the 35 % of the upgrading energy with heat from nuclear, we could replace 60 % of the overall natural gas consumption with nuclear power (combined sand-separation and upgrading). The remaining 40 % of energy input would need to come from natural gas. If we drop the upgrading consumption down to 0.3 mcf/bbl, then the ratio rises to 67.5:32.5 so the natural gas reduction is almost proportional.
It's looking progressively worse for the deployment of nuclear steam power for tar sands development. I still need to look at the thermochemical processes that nuclear plants are capable of running for the production of hydrogen from thermal (rather than electrical) energy. Electrolysis is a loser, as always. The only other possible option is to create mobile nuclear steam plants for in-situ production, as Engineer-Poet stated. However, these probably wouldn't be able to make full use of cogenerated electricity, which is part of the whole economic argument.
One thing that is worth nothing is that the study numbers don't match Syncrude's actual natural gas consumption of 1.35 mcf/bbl. Syncrude isn't doing much in-situ production to my knowledge, so I don't know where most of this inefficiency is coming from. If it's all from the extraction and separation process, nuclear might look a little better.