Igenlode Wordsmith

Non-consummation is certainly a valid reason for annulment in the present day.
See https://www.gov.uk/how-to-annul-marriage.

in the late Middle Ages, you could annul a marriage for non-consummation if one of the parties wished to enter a religious order - https://academic.oup.com/book/32828/chapter-abstract/275143750?redirectedFrom=fulltext

There may also be differences depending on which church someone belonged to. eg. Catholics and Protestents may have had different rules from each other in some periods.