1. Method of exploiting an underground deposit of hydrocarbons containing organosulfur compounds, characterized in that: i. an amount of hydrogen sulfide (H 2 S) is determined, produced by a phenomenon of aquathermolysis induced by a thermal process such as injection of steam into said deposit, using the following steps: describing the hydrocarbons by means of a compositional representation using H 2 S and four fractions: saturated compounds, aromatics, resins and asphaltenes; constructing a kinetic model on the basis of said compositional representation, starting from an elementary model obtained by mass balance for the element sulfur distributed within said fractions; constructing a thermodynamic model on the basis of said compositional representation; determining the amount of hydrogen sulfide (H 2 S) produced, by performing a compositional reservoir simulation by means of a compositional and reactive thermal simulator, said simulator employing said kinetic model and said thermodynamic model; ii. the exploitation conditions of said deposit are determined as a function of said amount of hydrogen sulfide; iii. said hydrocarbons are produced by applying said exploitation conditions.