D.C fan and Battery?

And don't use a car battery as doing a deep discharge will ruin it after a short time - it is designed to deliver lots of amps for a short time for starting the engine without being mostly discharged. You need a deep discharge battery as are used in mobility scooters, wheelchairs, power backup and solar storage systems. Costs about twice what an auto battery of the same amp hours costs.

Your fan draws 70/12=5.83A. In 8 hours it will draw 5.83x8=46.47 AH. That's enough to drain a good-size car battery.

THAT is a mighty BIG fan, like the electric fans used in cars. Ohm's law says P=IE, Power in watts (P) equals voltage (E) in volts times current in amperes (I). Solving for amps means 70 watts divided by 12 volts (actually a typical lead-acid battery is 13.2 volts at full charge in an open circuit), which equates to approximately 6 amps. For it to run for 8 hours, means you need 48 ampere-hours of battery capacity, which is MORE than a typical car battery can deliver. A car battery is designed to deliver huge current in short bursts (the starter motor). RV batteries (deep cycle) are the opposite, low drain over a long time. Exchange the roles (short term versus long term drain and charge) will destroy the battery in short order. It will essentially "wear out" the battery very rapidly. A typical car battery will start a car reliably every day for several years but will fail in a few months if the voltage (charge) is allowed to go below about 8 volts (90% discharge). Use a deep cycle battery if possible. Or use a 2nd battery in parallel to divide the load. Dividing the load will prolong the life of the batteries.

From calculation is 46.67AH, but it needs at least 50AH 12V battery.

At 12 Volts, your 70 Watt fan will draw about 6 Amps. To run it for 8 hours, you need to deliver 48 Ah (Amp-hours) of energy, plus a margin. Get a 60 Ah battery, at least.