Method executed by a computer for determining the quantity and/or the quality of the hydrocarbons present in a sedimentary basin, said hydrocarbons having been generated by maturing of the organic material of a mother rock of said basin, said sedimentary basin having undergone a plurality of geological events defining a sequence of states of said basin, by means of a numerical basin simulation executed on computer, on the basis of values representing the artificial maturing of an immature sample representing said mother rock and a sequence of artificial maturing temperatures, the method comprising at least the following steps: A. physical parameters relating to said basin are measured by means of sensors, said measurements comprising at least measurements of petrophysical properties of said basin, measurements representing the thermicity of said basin for said states, measurements of the advance of the maturing of said organic material of said basin; B. by means of said numerical basin simulation, a basin model is determined for each of said states as a function at least of said measurements of said petrophysical properties and at least one historical record of the temperatures of said basin for said states is determined; C. values of kinetic parameters of a reaction rate law representing the evolution of the maturing of said organic material for each of said states are determined, minimizing simultaneously: i. a difference between values predicted by said reaction rate law applied with said historical record of temperatures of said basin determined for said states, and said measurements of the advance of the maturing of said organic material, and ii. a difference between values predicted by said reaction rate law applied according to said sequence of temperatures for said artificial maturing and said values representing said artificial maturing; D. said quantity and/or said quality of said hydrocarbons is/are determined from said kinetic parameters of said updated reaction rate law and said historical record of temperatures for said states. A. physical parameters relating to said basin are measured by means of sensors, said measurements comprising at least measurements of petrophysical properties of said basin, measurements representing the thermicity of said basin for said states, measurements of the advance of the maturing of said organic material of said basin; B. by means of said numerical basin simulation, a basin model is determined for each of said states as a function at least of said measurements of said petrophysical properties and at least one historical record of the temperatures of said basin for said states is determined; C. values of kinetic parameters of a reaction rate law representing the evolution of the maturing of said organic material for each of said states are determined, minimizing simultaneously: i. a difference between values predicted by said reaction rate law applied with said historical record of temperatures of said basin determined for said states, and said measurements of the advance of the maturing of said organic material, and ii. a difference between values predicted by said reaction rate law applied according to said sequence of temperatures for said artificial maturing and said values representing said artificial maturing; i. a difference between values predicted by said reaction rate law applied with said historical record of temperatures of said basin determined for said states, and said measurements of the advance of the maturing of said organic material, and ii. a difference between values predicted by said reaction rate law applied according to said sequence of temperatures for said artificial maturing and said values representing said artificial maturing; D. said quantity and/or said quality of said hydrocarbons is/are determined from said kinetic parameters of said updated reaction rate law and said historical record of temperatures for said states.