The exchange process worked on numbers: a private for a private, a sergeant for a sergeant, a major for a major, etc. A larger number of junior personnel could be exchanged for a more senior person. It didn't operate on a unit for unit exchange.
The Confederate's decision to declare regiments surrendered at Vicksburg, Port Hudson, and Arkansas Post exchanged had serious ramifications over the remainder of the war. Under the surrender cartels, the surrendered officers and men were paroled and permitted to return to their homes until they were exchanged for an equivalent number of Federal Army prisoners. There has been reasonable conjecture that that Federal Army expected that while the men were on parole numbers of them would stay home and simply disappear. Problems arose when the Confederates refused to deliver and exchange black soldiers from the U.S. Colored Troops (USCT) and their white officers. It was alleged that some of them were hanged, and some of the black enlisted men were sold into or returned to slavery, all of which was a violation of the law of land warfare and was intolerable to the Federal Army. As Lieutenant General Grant would later write to General Lee in 1864, "…the Government is bound to secure to all persons received into her armies the rights due to soldiers." In the fall of 1863 the Confederates declared the surrendered officers and men from Vicksburg, Port Hudson, and Arkansas Post exchanged with no equivalent release of Federal Army prisoners. Federal General-in-Chief Henry W. Halleck countered by directing that no further Confederate prisoners be exchanged until USCT troops were properly treated by the Confederates under the laws of war. He also significantly tightened the restrictions under which Confederate prisoners of war were being held. When some of the troops from regiments declared exchanged were subsequently captured by the Federal Army at Chattanooga and during the Atlanta Campaign, they could have been shot out-of-hand by the Federal Army for violating their parole oath and returning to combat without proper exchange, an act which effectively placed them outside the laws of war. With exchanges significantly curtailed, prisoner of war populations increased on both sides, with resulting allegations that prisoners were being mistreated, allegations which were particularly true with regard to the Confederacy's handling of its Federal prisoners.
Among the Confederate units involved were the 1st, 23rd, 40th and 42nd Alabama Infantry, the 34th, 36th, 39th, 41st, 43rd, 52nd, and 56th Georgia Infantry, the 4th 37th, 40th, 43rd, and 46th Mississippi infantry, the 18th, 26th, 32nd, 46th, 49th, and 53rd Tennessee Infantry, and the 6th, 10th and 15th Texas Cavalry Consolidated. But, the Confederate high command were honorable men who scrupulously followed the laws of war.
Regards,
Don Dixon