According to Google Maps, the distance from Bangkok to U-Tapao is upward of 170 kilometres by road, as shown in the screenshot below. The direct distance, as pointed out in a statement by Eva Air (in the quote below, in bold) is about 140 kilometres.
There are plans for U-tapao Rayong-Pattaya Airport to become Bangkok's third airport. According to The Blue Swan Daily:
The Royal Thai Navy, operator of Utapao Rayong-Pattaya International airport, recently unsealed tender bids for the USD9 billion redevelopment of the facility under the Thai Government’s Eastern Economic Corridor (EEC) scheme.
Its summary of the article lists:
Utapao will ultimately take its place as a ‘Bangkok’ airport, but one dedicated to tourists as it serves nearby Pattaya.
It's not completely unprecedented for flights to Bangkok to head to U-Tapao. In 2008, when both of Bangkok's main airports were closed, some airlines chose to direct their flight there. From web.archive.org's capture of the Eva Air website (emphasis is mine):
Suvarnabhumi Airport in Bangkok is still closed, so EVA Air changes flight schedule to Bangkok and Europe. EVA Air temporarily take Utapao Airport for the operation for flights to and from and via Bangkok.
Utapao is located approximately 140 kilometres and south from Bangkok. However, facilities at Utapao are very basic and the airport is heavily congested, we apologise in advance for the inconvenience, but ask for your understanding that the airport at Utapao is originally designed for military purpose.
It wasn't just Eva Air that decided to move it's flights, it has, for some time, been Thailand's main airport. From Wikipedia:
With the temporary closure of Suvarnabhumi Airport and Don Mueang Airport in late November 2008 because they had been occupied by anti-government protestors, U-Tapao became for a time Thailand's main supplementary international gateway. Many airlines arranged special flights to and from U-Tapao to ferry international passengers stranded by the closure of the Suvarnabhumi Airport.
As you can imagine, this caused quite a few problems (from the same Wikipedia link):
As many as 100,000 passengers were stranded in Thailand until early December. Although its runway can accommodate large aircraft, U-Tapao's terminals are not designed to handle more than a few flights a day. Travellers were subject to many hardships, and as the security was not up-to-date, some US-bound flights were diverted to Japan and their passengers required to go through a supplementary security check before continuing.