A fixed-bed reactor or a catalyst particle can be considered as a porous media network, which is characterized by the pellet size, void fraction, and connectivity of the network. In a fixed-bed reactor, the percolation threshold was calculated to be 0.13 - 0.17, while the porosity of a fixed bed is similar to 0.38; therefore, there is no percolation problem and a fixed bed can be modeled as a continuum medium. In multiphase flow, the connectivity of the network is much reduced due to the attachment of liquid film on the particles and an analogy was made between a trickle bed and a Bethe tree. It shows from this work that radial velocity profile estimation in a fixed bed could be obtained from transforming the bed space into a tube of a certain equivalent diameter, and the trickling to pulsing flow transition could be explained from its analogy to a Bethe tree. Electrical capacity tomography was employed to measure the dynamic liquid holdup in pulsing flow. Two types of packing have been identified from their different flooding behavior, and a quadralobe extrude was specifically designed to obtain the high flooding velocity. When the catalyst was internally wetted, the reaction rate was found to decrease linearly with the catalyst wetting fraction, nevertheless, and no percolation threshold was encountered, and this strange result was explained from the egg shell-type distribution of Pd beneath the support surface of only 0.4 mm.