Some projects are part of national projects and have important roll in economic growth. Financing of these projects wants so much money and has so much risk. Gas and oil projects want so much money and have important effect on economic growth. In Iran, we use from some contracts for finance of oil and gas contracts such as buyback contracts. In this paper we extract optimal extraction and modeling utility functions in buyback contracts. In this paper we introduce all of financing method and every contract in Iran. Buy back contracts have so much benefits for owner oil or gas country and country which invest in foreign country, which we model these benefits in Iran and for south pars field. South pars field is the biggest gas source of Iran which Iran uses from some buyback contracts for extraction from this big source because usage from this source can causes we accrue to economic growth