Nearly, almost, approximately, well-nigh are comparable when they mean within a little of being, becoming, reaching, or sufficing.
Their differences in meaning are often imperceptible. However, nearly is suitable when mere proximity is implied.
Almost is more explicit when the emphasis is on a falling short or a deficiency.
Approximately is an appropriate choice when the difference is of no practical importance and a reasonable approach to accuracy is implied.
Well-nigh often equals virtually.