If after a proceeding has begun a survey has been made and a proceeding to establish a drainage project has been dismissed or the drainage project has not been established, and if all or a part of the former survey is used by the engineer for a drainage proceeding in the same area, the amount saved in the subsequent proceedings must be paid to the proper parties according to this section. If the parties who paid the expense of the former survey make a petition, the drainage authority shall:
(1) determine the amount of benefit that was derived by the subsequent proceedings from the former survey;
(2) order the amount of the benefit to be paid to the proper parties; and
(3) charge the amount paid as a cost of the subsequent drainage proceeding.