Your batteries are Ni-MH (Nickel-metal hydride). I looked up some discharge curves on the internet and they run out of power at about 1.1 volts. Another way of expressing that last sentence is as the battery is discharged at a constant current the voltage will slowly go down until it gets down to about 1.1 volts and then drop rapidly.  If you have 10 of those in series when they are fully charged they will put out about 14 volts but will drop to about 12.5 volts in about 2 to 4 hours of detector use. Then the voltage will stay fairly constant until the detector has been on for 14 to 17 hours. At 18 to 20 hours the voltage will be down to about 11 volts.  About 20 minutes later the battery voltage will be so low the unit will not work.  The math says 10 of those batteries (1900mAh to 2000mAh) should run your detector (100mA) for 19 to 20 hours.  I would need 3 sets of those for a 10 day trip.