Del. Code tit. 7 § 6126
The Secretary may cancel any lease upon which oil, gas, sulphur or other minerals have not been discovered in paying quantities, upon failure of the lessee after 30 days' written notice and demand for performance, to exercise due diligence and care in the prosecution of the prospecting of development or work in accordance with the terms of the lease. After discovery of oil, gas, sulphur or other minerals in paying quantities on lands subject to any lease, such lease may be forfeited and cancelled only by appropriate judicial proceedings upon failure of the lessee after 90 days' written notice and demand for performance, to comply with any of the provisions of the lease or of laws or regulations applicable thereto and in force at the date of the invitation for bids in pursuance of which the lease was awarded; provided, however, that in the event of any such cancellation, the lessee shall have the right to retain under such lease any and all drilling or producing wells as to which no default exists, together with a parcel of land surrounding each such well and such rights-of-way through the leased lands as may be reasonably necessary to enable such lessee to drill and operate such retained well or wells. In the event of the cancellation of any lease, the lessee shall have a reasonable time within which to remove all property, equipment and facilities owned or used by the lessee in connection with operations under the lease.
7 Del. C. § 6126