of the parameters of the flow simulator the goal of this modification is not to give a physical interpretation of the error induced by upscaling but rather to minimize the consequences thereof by means of certain parameters controllable via the flow simulator in particular upscaling generates a change in the numerical productivity index ipn of the wells the productivity index being a function of the permeabilities ipn 2 ue89e ue89e u03c0 ue89e ue89e h ue89e k x ue89e ue89e k y u03bc ue89e ue89e ln ue89e ue89e r 0 rwe s 36 in order to correct the modification of the numerical productivity index it is possible in certain cases to artificially introduce a factor referred to as skin factor whose value is determined by calibration in a more general context the calibration simulation results are therefore functions of calibration parameters c and s which the reservoir engineer considers necessary to calibrate after carrying out the reference simulation it is possible to carry out the calibration parameters identification by minimizing the objective function as follows j 2 ue89e ue89e c s 1 2 ue89e ue89e d ref d ue89e ue89e c s t ue89e ue89e c d 1 ue89e ue89e d ref d ue89e ue89e c s 38 parameters c opt and s opt resulting from this optimization are.