A derivation of a multiple-porosity model for the flow of a single phase, slightly compressible fluid in a multiscale, naturally fractured reservoir is presented by means of recursive use of homagnetization theory. We obtain a model which generalizes the double-porosity model of Arbogast et al. (1990) to a flow system with an arbitrary finite number of scales.

We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involving $C^{1,1}$ data. We show that these conditions are stronger than those in literature obtained by means of second-order Clarke subdifferential.