Accelerated Blast is a mod that increases the fire rate of Shotguns by 15% and Script error: The function "Proc" does not exist. damage by 15% per rank for a maximum of 60% at rank 3 for both values.
Can be paired with Shotgun Spazz and Frail Momentum to provide a 240% increase in fire rate.
Stacks with Flechette and Breach Loader for a maximum of 210% Script error: The function "Proc" does not exist. damage.
There are only 3 shotguns that deal primarily Puncture damage; the Hek, Vaykor Hek, and Corinth. All other shotguns, including the Sweeper for Sentinels, deal less than 20% of their base damage as Puncture.
The Phage deals no physical damage whatsoever, so it only benefits from the increase in fire rate.
Trivia
Prior to Update 12.4 (2014-03-05), at base level the mod was increasing Script error: The function "Proc" does not exist. damage by 22% rather than 15% and adding the Puncture damage based on the weapon's total base damage, causing unusually large boosts in Puncture damage as a result. These bugs have since been fixed.
The mod picture is misleading, as it implies that it adds punch through in order to puncture the Shield Lancer's shield, when in reality it increases the puncture damage type. while also, the shotgun featured in the image is a Sobek. which deals mostly Script error: The function "Proc" does not exist. damage.