You want to be careful with long-running PHP processes as, for one PHP is not very memory efficient (as an example an array of just 100 ints in PHP can consume as much as 15KB of memory). This is normally fine for 99% of the use cases since most people are just using PHP for websites and those processes run for fractions of a second so memory is sacrificed for speed. However, for a long-running process (especially if you have a lot of them) this may not be your best solution.
You also want to be very careful calling exec/shell_exec like functions in PHP as they are internally implemented as streams (i.e. they can cause blocking in the parent process as it normally has to wait on the stream to return data).
One option to background the task is to use fork. However, I strongly suggest using a proper job manager like gearman (see php extensions also), or queue, like amqp or zmq, to handle these tasks more cleanly. Which one is more suitable for your use case, I'll let you decide.