You shouldn't slurp files unless you actually need all of the file in memory at the same time. Your normal action should be to process the file a record at a line.

I'd do something like this:

my %fh; # store handles of new log files

open OLDLOG, $path_to_old_log or die $!;

while (<OLDLOG>) {
  my $proc = extract_process_id_from_old_log_record($_);

  unless (exists $fh{$proc}) {
    open $fh{$proc}, '>', "$proc.log" or die $!;
  }

  print $fh{$proc} $_;
}
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Update: Reread the first line. It made no sense, so I fixed it.