B737-700 Captain reported an accumulation of ice on the fan blades of both engines required the use of unfamiliar de-icing procedures. Shortly after takeoff the crew noticed engine vibrations that stopped after leaving icing conditions.

Narrative

First flight of the day on an aircraft that had just landed. First Officer (FO) informed me there was ice accumulation on the engine fan blades on both engines; but #2 Engine had significantly more than #1. I looked myself and there was ice on front and back of fan blades with icicles on front of #2 Engine fan blades. Coordinated with local contract ground operations to use ground air to deice engine fan blades. Process was very slow and ground crew and flight crew had never used the procedure before. I inspected the progress multiple times and spun each engine fan blade and checked they were clear front and back. We discussed that we would do an engine run up on the runway to check for any abnormal engine indications prior to take-off. It began snowing; and we performed two-step deicing. We took the runway; performed engine run up in accordance with deice/anti-ice card; noted normal indications and began the take-off roll. Around 100 kts; I felt a vibration from the #2 Engine Thrust Lever and noted the Vibration Gauge indicated 2.1. Vibration trended down after liftoff and was even with # 1 Engine; approximately 0.5 Units. Encountered moderate rime icing around 3000 ft. At 5000 ft. we performed a gradual power increase from (climb) CLB-2; to CLB-1; to full climb thrust. When we selected CLB-1 vibration increased from 0.5 to 0.9. When we selected full climb thrust; Engine Vibration Gauge increased to approximately 4.2 Units with Flashing White Box around the Secondary Engine Indications; and Vibration felt in # 2 Thrust Lever. Called for engine high vibration checklist; but prior to starting the checklist the engine vibration had returned to normal after 20-30 seconds of exceeding 4.0 Units. The return to normal indications coincided with climbing out of the icing conditions. We reviewed the engine high vibration checklist for familiarity in case the condition returned; but the remainder of the flight was normal and we did not need to use engine anti-ice again.