BASE='-np 4 my_app --help'
The quoting here iis good and will make sure all space separated variables are combined as one string into the variable.
The quoting here is not good, because this too will combine the contents of the $BASE
variable as one string and pass the one string as one parameter to mpiexec. If you remove the double-quotes, the substitution will make sure all space separated content in $BASE
will be treated as separate arguments.
Just remove the double quotes and it should work.