  Percolation theory and the associated conductance networks have provided deep
insights into the flow and transport properties of a vast number of
heterogeneous materials and media. In practically all cases, however, the
conductance of the networks' bonds remains constant throughout the entire
process. There are, however, many important problems in which the conductance
of the bonds evolves over time and does not remain constant. Examples include
clogging, dissolution and precipitation, catalytic processes in porous
materials, as well as the deformation of a porous medium by applying an
external pressure or stress to it that reduces the size of its pores. We
introduce two percolation models to study the evolution of the conductivity of
such networks. The two models are related to natural and industrial processes
involving clogging, precipitation, and dissolution processes in porous media
and materials. The effective conductivity of the models is shown to follow
known power laws near the percolation threshold, despite radically different
behavior both away from and even close to the percolation threshold. The
behavior of the networks close to the percolation threshold is described by
critical exponents, yielding bounds for traditional percolation exponents. We
show that one of the two models belongs to the traditional universality class
of percolation conductivity, while the second model yields non-universal
scaling exponents.
