Screened in patio with outdoor kitchen

I’m screening in my 20’ x 15’ patio with a kitchen including a grill. It has a 10’ ceiling fan. Should I consider a vent fan like the link below or will smaller fans while leaving the door open be sufficient to clear smoke?

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https://www.homedepot.com/pep/VEVOR-12-in-Shutter-Exhaust-Fan-High-Speed-1000-CFM-Aluminum-Wall-Mount-Attic-Fan-Wall-Fan-with-Ventilation-and-Cooling-BYCSPQSDJAC12DLJSV1/326145231