Why is "fridge" spelt with a 'd' but "refrigeration" spelt without one?

Solution 1:

Most sources suggest that the term was an alteration of frig, probably because of the influence of the famous brand 'Frigidaire' whose sound matches with the second syllable of 'refrigerator'

Fridge: also frig:

• Colloq. abbrev. of refrigerator.

• The proprietary name Frigidaire may also have contributed to the currency of the shortened form frig. Cf. also frigerator in D.A. (quots. 1886, 1909).

Early usage examples:

• 1926 E. F. Spanner Broken Trident xvi. 181 Best part of our stuff here is chilled, and with no 'frig plant working, the mercury will climb like a rocket.

• 1935 C. Brooks Frame-Up xix. 243 Do you mean that you keep a dead body in a fridge waiting for the right moment to bring her out?

• 1939 M. Dickens One Pair of Hands xii. 198 Your frig is out of order and the trifle hasn't got cold.

• 1946 News Chron. 25 Feb. 3/7 (heading) A Communal ‘Frig.’ with 300 Lockers.

• 1955 G. Greene Quiet American 90 We haven't a frig—we send out for ice. 1960

Fridge (n.) :

• shortened and altered form of refrigerator, 1926, an unusual way of word-formation in English; perhaps influenced by Frigidaire (1919) , name of a popular early brand of self-contained automatically operated iceless refrigerator (Frigidaire Corporation, Detroit, Michigan, U.S.), a name suggesting Latin frigidarium "a cooling room in a bath." Frigerator as a colloquial shortening is attested by 1886. (Etymonline)

From Grammarphobia:

• We can’t tell from the published examples in the OED (or some earlier ones in Google Books) who originated the “frig” and “fridge” spellings. But we can speculate about why “fridge” has become the dominant spelling.

• First of all, the natural pronunciation of “fridge” matches the way the second syllable sounds in “refrigerator.”

• Although “frig” is pronounced the same way as “fridge” when it means a refrigerator, the natural pronunciation of “frig” would be like that of the naughty verb we mentioned above.

• Our guess is that English speakers generally prefer the “fridge” spelling because they instinctively pronounce it the way the letters f-r-i-g sound in “refrigerator.”

1922 Frigidaire "iceless" refrigerator newspaper ad.

Edit:

The term frigid, though related to 'cold', does not appear to have influenced 'fridge' spelling:

• 1620s, "intensely cold," from Latin frigidus "cold, chill, cool," figuratively "indifferent," also "flat, dull, trivial," The meaning "wanting in sexual heat" is attested from 1650s, originally of males.