Notwithstanding any provisions in sections 57-910 to 57-910.12 to the contrary, any person who owns an oil or gas interest within the unit area in a tract which is not subject to an oil and gas lease or similar contract shall be deemed, for purposes of this section, an owner obligated to pay costs of unit operations to the extent of seven-eighths of such interest and shall be deemed a royalty owner to the extent of one-eighth of such interest free from such costs.