Method for developing a hydrocarbon reservoir by injecting a gas in the form of foam

A method for exploiting hydrocarbons in a reservoir, by injection of an aqueous solution containing a gas form into at least one injection well and of a flow simulator, based on a displacement model of the gas form, the displacement model being expressed as a function of a mobility reduction function of the gas, the function being expressed as a function of a mobility reduction factor of the gas and at least one interpolation function of the mobility reduction factor, the interpolation function being a function of at least one parameter relative to at least one characteristic of the foam and of at least two constants, the at least one parameter of the interpolation function corresponding to an injection rate of the gas, from at least one sample of the formation and from a gridded representation representative of the reservoir, comprising steps of:

• A—determining the displacement model by determining the mobility reduction factor of the gas and the constants of the interpolation function of the displacement model, from at least pressure drop measurements performed while injecting into the at least one sample the gas in non-foaming form and the gas foam for values of the injection rate of the gas;
• B—determining for each cell of the gridded representation traversed by the at least one injection well, a productivity index IP corrected for shear thinning effects of the gas foam in each cell according to a formula:
• IP=α·IP0
• where IP0 is a productivity index determined with an assumption that the aqueous solution containing the gas in foam which is a Newtonian fluid, and α is a correction factor that is a function of at least one characteristic of the aqueous solution containing the gas in the gas foam;
• and
• C—determining from the displacement model, the flow simulator, the gridded representation and the productivity indices determined for each cell of the gridded representation traversed by the injection well, a development scheme for the reservoir;
• and
• D—exploiting the hydrocarbons.