Load up your KJ with charcoal and start a small fire with some small wood chunks mixed in. I can hold a low and slow smoking temp in my KJ for a loong time. I would say at least 16-20 hours on a load. And I would still venture to guess it could go for longer on one lone (I've never tested how long it would go).
For me after cooking butts for briskets for 10-12 hours, I still have plenty of lump left.
Like jonboy said, fire and temperature management on a kamado is much easier than a stick burner.
Also, are you soaking your wood chunks? If so, don't soak them, put them in dry.
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