I would like to stay in Beijing for less than 72 hours. I will arrived to Beijing from Hong Kong

and leave this city in flight to Taipei. In this case, it possible to get the 72 hour free transit in Beijing Airport? In addition, if I travel from Taipei to Beijing doing a transfer in Hong Kong, it possible to get this visa or it necessary to buy two independent flights (One from Taipei to Hong Kong and an other one from Hong Kong to Beijing? I have a passport from Spain.