WOW... 15TB of files.. heck.. streuth.. blimey.. Unbelievable.
Since you are on Sierra.. I would get OFF Time Machine as soon as possible.. it is simply unreliable.
You can still run TM but restrict it to the boot drive..
Get another much more efficient backup software like Carbon Copy Cloner to do all your other disks.. plus you can include the boot drive as well. But making a bootable clone of the boot drive to a USB makes better sense.
The padding required with Automatic backup can be extremely large..
Open console and type backup in the search.
You might have to go backwards and forwards a bit to get the exact messages.
I am having the same issue.. This is only testing for me.. as I have now abandoned Time Machine as a bad joke. But I wanted to test it on a USB drive plugged into Asus high end router.. and it was running fine for about a week.. early this morning it failed.. after a reboot (and firmware update and holding your tongue on the right side of your mouth while drinking a glass of water).. I was able to manually run a backup.
Check the amount of space that is required.. it can be huge.. 10x the amount of space needed for the actual files.
The next automated backup failed.
(error was not a capacity issue but it is simply difficult to get reliable backups with Sierra to network drives).
If you wish to keep trying with TM..
Sierra cannot tolerate Anti-Virus software.. Apple do have a document that says to make sure it is not scanning network drives.. but we have found just having it active makes the backup fail. Same for any added security software and adware (which I am sure would only be accidently installed).
In your synology check the log messages. You might also find some interesting details there.
My Asus is tossing up some interesting info.
Dec 16 08:19:19 Timemachine: User select disk start TimeMachine
Dec 16 08:19:19 afpd[18736]: Couldn't open extension maping file /usr/etc/extmap.conf
Dec 16 08:19:19 afpd[18736]: Couldn't load extension -> type/creator mappings file "/usr/etc/extmap.conf"
Dec 16 08:19:19 cnid_metad[18740]: Couldn't open extension maping file /usr/etc/extmap.conf
Dec 16 08:19:19 cnid_metad[18740]: Couldn't load extension -> type/creator mappings file "/usr/etc/extmap.conf"
Dec 16 08:19:19 cnid_metad[18740]: CNID Server listening on localhost:4700
Dec 16 08:19:19 afpd[18736]: WARNING: signature string RT-AC3200-82F0.local is very long !
Dec 16 08:19:19 afpd[18736]: Netatalk AFP/TCP listening on 192.168.2.254:548
Dec 16 08:19:19 Timemachine: daemon is started
Dec 16 08:21:45 afpd[1148]: AFP3.3 Login by admin
Dec 16 08:21:46 cnid_dbd[1786]: Couldn't open extension maping file /usr/etc/extmap.conf
Dec 16 08:21:46 cnid_dbd[1786]: Couldn't load extension -> type/creator mappings file "/usr/etc/extmap.conf"
Dec 16 08:21:52 kernel: thfsplus: keylen 810 too large
Dec 16 08:21:52 kernel: thfsplus: keylen 810 too large
Dec 16 08:24:48 kernel: thfsplus: keylen 28535 too large
Dec 16 08:24:52 kernel: thfsplus: keylen 28535 too large
Dec 16 08:24:54 kernel: thfsplus: keylen 28535 too large
Dec 16 08:24:54 kernel: thfsplus: keylen 28535 too large
Dec 16 08:27:17 kernel: thfsplus: keylen 810 too large
Dec 16 08:27:17 kernel: thfsplus: keylen 810 too large
Dec 16 08:28:15 kernel: thfsplus: keylen 28535 too large
Dec 16 08:28:30 kernel: thfsplus: keylen 810 too large
Dec 16 08:28:30 kernel: thfsplus: keylen 810 too large
Dec 16 08:28:55 kernel: thfsplus: keylen 810 too large
Dec 16 08:28:55 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:07 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:07 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:26 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:26 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:57 kernel: thfsplus: keylen 810 too large
Dec 16 08:29:57 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:07 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:07 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:15 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:15 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:24 kernel: thfsplus: keylen 810 too large
Dec 16 08:30:24 kernel: thfsplus: keylen 810 too large
Dec 16 08:31:49 afpd[1148]: AFP logout by admin
Dec 16 08:31:49 afpd[1148]: AFP statistics: 1214553.16 KB read, 825252.60 KB written (successful manual backup)
Dec 16 08:31:49 afpd[1148]: done
Dec 16 08:53:23 rc_service: httpd 510:notify_rc restart_rstats;restart_conntrack;restart_leds;restart_cstats
Dec 16 08:53:24 syslog: module nf_conntrack_proto_gre not found in modules.dep
Dec 16 08:53:24 syslog: module nf_nat_proto_gre not found in modules.dep
Dec 16 08:53:24 syslog: module nf_conntrack_pptp not found in modules.dep
Dec 16 08:53:24 syslog: module nf_nat_pptp not found in modules.dep
Dec 16 09:00:45 disk_monitor: Got SIGALRM...
Dec 16 09:15:38 afpd[1618]: dsi_init_buffer: OOM
Dec 16 09:15:38 afpd[1619]: dsi_init_buffer: OOM
Dec 16 09:15:38 afpd[1620]: dsi_init_buffer: OOM
Dec 16 09:15:38 afpd[1621]: dsi_init_buffer: OOM (Failed automatic backup)
I used to run TM backups to a Synology NAS.. as well and that was very reliable.. so I am not blaming the Synology.. It is just one day TM does a hissy fit and refuses to work or wipes out its backup Autonomously.
You do not want to have TM delete your 15TB of backup any time soon and it can do it in a moment without warning.