A space-and-time dependent model was developed for a reactor. The model, which combines heat transfer and chemical reaction, was intended to identify kinetic parameters under non-isothermal conditions for lowintermediate moisture foodstuff. In particular, the model was used to evaluate the effect of high temperature heat treatments (100-140 °C) on anthocyanins degradation in blackberry juice - quartz sand system at low water activity (aw 0.34). The coupled transport equations were solved using Comsol® calculation code. Kinetic and thermal parameters were identified with a nonlinear regression method. The relevance of this approach was assessed by comparison between the kinetic parameters estimated as described before (heterogeneous assumption) and the parameters identified by considering a homogeneous temperature distribution inside the reactor. The results showed no significant difference between the anthocyanins degradation reaction rate constant (k120°C) for the heterogeneous (3.29±0.05×10-3 s-1) and the homogeneous (3.5±0.3×10-3 s-1) assumption. And a slight difference was found between the activation energies (Ea) for the heterogeneous (95±5 kJ mol-1) and the homogeneous (108±7 kJ mol-1) identification. Therefore, the use of the developed model allowed a slight improvement in the identification of the kinetic parameters. However, the assumption of a heterogeneous distribution of temperature inside the reactor is valid for the identification of kinetic parameters with high orders of magnitude.