As you can well imagine | In 003 Mahinarangi, we had the phrase that may VERY WELL be true, in which very well is used emphasize the fact that you're willing to concede or admit that something is true. In the phrase as you can WELL imagine, the word well also serves as an intensifier. It's used to emphasize or strengthen the verb imagine. In this context, it suggests that the speaker STRONGLY BELIEVES the thing being described is particularly easy or likely for the listener to be able to imagine.So, when someone says as you can well imagine, they're basically saying, «I REALLY THINK YOU'LL HAVE NO PROBLEM IMAGINING THIS». It adds a level of confidence in the listener's ability to understand or relate to the situation being described, perhaps based on their own personal experience. You may also here as you can well guess with more or less the same meaning. We also say as you well know when we're sure that the listener already knows something we're about to tell them, but be careful with this one because it can sound a bit snippy.