The invention relates to a method for recovery of hydrocarbons in a geological reservoir by injection of a low-salinity aqueous solution. A representative model of the evolution of the flow parameters as a function of the aqueous solution salinity is calibrated by use of laboratory measurements performed on a rock sample from the reservoir for at least two salinity values. Then, by use of a flow simulator including the calibrated model, the injection of aqueous solutions into the sample is simulated, with and without capillary effects, for at least the two salinity values with a microscopic residual oil saturation being determined for each salinity value. Then, from the flow simulator including the calibrated model and the microscopic residual oil saturation values, a reservoir development scheme is determined with hydrocarbons of the reservoir being exploited according to the development scheme.