"Logical partition" doesn't sound right for Windows. You probably mean "Logical drive."
Windows has "primary partitions" and "extended partitions."
A primary partition that has the operating system on it is an "active partition."
Windows permits up to 4 primary partitions on a "basic disk."
An extended partition can be subdivided into "logical drives." There can be an "unlimited" number of logical drives on an extended partition (until you run out of drive letters).
See http://www.theeldergeek.com/hard_drives_01.htm
As I understand your description, the system has a single hard drive that has both a primary partition (C:) and an extended partition. The extended partition contains one logical drive (D:).
Putting aside the issue of saving the data that is now in the D: drive, when you delete the D:
logical drive, you just create "free space" within the extended partition (which doesn't have a name). You then have to delete the extended partition in order to create "unallocated space" into which you can then expand the C: partition.