I have a ticket Istanbul-Beijing-Istanbul (13 days in BJ)

and a SEPARATE ticket (different rates, different airline WITHIN the BJ dates, BJ-Seoul-BJ (where I would connect back to Istanbul). I will spend fewer than 144 hours in BJ before heading to Seoul. Sounds complicated, but altogether it is IST-PEK-SEL-PEK-IST, with the 2nd PEK a 2 hour change of plane connection.
Would this qualify for the visa 144 hour exemption? What would I need to do to make it qualify, since I will be spending only 5 days in BJ?