I found an interesting letter in the New York Times, August 16, 1863, in which it states that Colonel Duff, Grant's chief of Artillery estimated that from May 1, 1863, to July 4, 1863, the Army of the Tennessee fired 18,889 solid shot, 72,314 shell, 47,897 case, and 2,723 rounds of canister. It further broke the expenditure of ammunition down by battle:
Port Gibson: 3,900
Pursuit from Port Gibson: 82
Raymond: 620
Jackson: 476
Champion Hill: 3,422
Big Black River: 1,297
May 19 at Vicksburg: 9,598
May 22 at Vicksburg: 10,754
Remainder of the Siege: 111,614