What is the quick and effective repair methods for damaged dry gas seal housing without removing the casing and send it back to the factory /workshop ?
I am not aware of any repair method for this damage. Review the seal drawing and determine the effect of the damage. I assume an o-ring crosses this damaged area. What will leak across that o-ring? There is a chance that slight leakage will not be a problem. Often o-rings are redundant.
A single o-ring leak would allow process gas to go directly to the lube oil tank? That seems like some poor design decisions were made. We would normally have a separation seal with air or nitrogen directing any leakage to a vent at an elevated location. I could make more useful comments if you posted the seal cross-sectional drawing with a note where the housing damage is located.