This is a common problem in most Galaxy phones,
#Make sure the replacement battery is original and not a knock-off
# Try not to run many apps at the same time
# The phone (or the battery) could not be faulty, the Galaxy Grand is supposed to operate for 3-4 hours with a Li-Ion 2100 mAh battery
# Consider buying an external power bank (battery) [http://www.amazon.com/gp/product/B00MWBSRZA?keywords=Power%20bank&qid=1445289579&ref_=sr_1_3&sr=8-3|This] power bank should last with you for a good 15-20 hours before needing to be recharged.