A packing ring set for a rod, comprising: a first ring comprising a plurality of segments (311 1-3) formed by tangential cuts along a first ring segment interface between each of the plurality of segments wherein each of the plurality of segments (311 1-3) is slidably movable along the first ring segment interface, the first ring having a first ring inner diameter and a first ring outer diameter, wherein the first ring has a first axial thickness; a second ring having an outer surface comprising a plurality of segments (351 1-3) formed by tangential cuts along a second ring interface between each of the plurality of segments wherein each of the plurality of segments is slidably movable along the second ring segment interface, the second ring comprising: a first portion having a first portion inner diameter, and a first portion outer diameter, wherein the first potion has a second axial thickness; a second portion having a second portion inner diameter equal to the first ring outer diameter, and a second portion outer diameter equal to the first portion outer diameter, the second portion having a third axial thickness and being configured such that the first portion and second portion together form a shelf sized to accommodate the first ring; a groove formed on the outer surface of the second ring; and an elastic member disposed in the groove providing a compressive force on the second ring and the first ring, wherein when the first ring is on the shelf the first axial thickness equals the second axial thickness and the second axial thickness equals the third axial thickness. a first ring comprising a plurality of segments (311 1-3) formed by tangential cuts along a first ring segment interface between each of the plurality of segments wherein each of the plurality of segments (311 1-3) is slidably movable along the first ring segment interface, the first ring having a first ring inner diameter and a first ring outer diameter, wherein the first ring has a first axial thickness; a second ring having an outer surface comprising a plurality of segments (351 1-3) formed by tangential cuts along a second ring interface between each of the plurality of segments wherein each of the plurality of segments is slidably movable along the second ring segment interface, the second ring comprising: a first portion having a first portion inner diameter, and a first portion outer diameter, wherein the first potion has a second axial thickness; a second portion having a second portion inner diameter equal to the first ring outer diameter, and a second portion outer diameter equal to the first portion outer diameter, the second portion having a third axial thickness and being configured such that the first portion and second portion together form a shelf sized to accommodate the first ring; a groove formed on the outer surface of the second ring; and a first portion having a first portion inner diameter, and a first portion outer diameter, wherein the first potion has a second axial thickness; a second portion having a second portion inner diameter equal to the first ring outer diameter, and a second portion outer diameter equal to the first portion outer diameter, the second portion having a third axial thickness and being configured such that the first portion and second portion together form a shelf sized to accommodate the first ring; a groove formed on the outer surface of the second ring; and an elastic member disposed in the groove providing a compressive force on the second ring and the first ring, wherein when the first ring is on the shelf the first axial thickness equals the second axial thickness and the second axial thickness equals the third axial thickness.