S.D. Codified Laws § 5-7-52
All leases issued under these provisions shall be for a primary term of three years and as long thereafter as any mineral or minerals in paying quantities be produced or mined from the lands, subject to the continued payment of annual rentals.
If the lessee fails to discover and produce minerals in paying quantities during the primary term of the lease, the lessee may continue the lease in full force and effect for an additional or secondary term of two years and as long thereafter as any mineral or minerals in paying quantities be produced or mined from the leased land, by paying each year in advance two times the rental provided in the primary term.
However, if the lessee fails to discover and produce minerals in paying quantities during the secondary term of the lease, the lessee of record or the record owner of an approved assignment may continue the lease, as to the portion held by him, in full force and effect for an additional or tertiary term of five years and so long thereafter as any mineral or minerals in paying quantities be produced or mined from the leased land, by paying each year in advance not less than three dollars per acre per year as rental.
If the lessee fails to discover and produce minerals in paying quantities during the tertiary term of the lease, the lessee of record or the record owner of an approved assignment may continue the lease, as to the portion held by him, in full force and effect for an additional or quaternary term of five years and so long thereafter as any mineral or minerals in paying quantities be produced or mined from the leased land, by paying each year in advance of the lease anniversary date not less than ten dollars per acre per year as rental, plus a sum as advance royalty computed as follows:
For the eleventh year, not less than ten dollars per acre per year;
For the twelfth year, not less than twenty dollars per acre per year;
For the thirteenth year, not less than thirty dollars per acre per year;
For the fourteenth year, not less than forty dollars per acre per year; and
For the fifteenth year, not less than fifty dollars per acre per year.
However, upon the commencing of the production of minerals in paying quantities, the principal sum so paid as advance royalty for the lease year in which the mineral is produced and the advance royalty paid for the two previous years shall be credited against the royalty payable to the lessor.
SDCL 5-7-52