A catalytic membrane composite that includes porous supported catalyst particles durably enmeshed in a porous fibrillated polymer membrane is provided. The porous fibrillated polymer membrane may be manipulated to take the form of a tube, disc, or diced tape and used in multiphase reaction systems. The supported catalyst particles are composed of at least one finely divided metal catalyst dispersed on a porous support substrate. High catalytic activity is gained by the effective fine dispersion of the finely divided metal catalyst such that the metal catalyst covers the support substrate and/or is interspersed in the pores of the support substrate. In some embodiments, the catalytic membrane composite may be introduced to a stirred tank autoclave reactor system, a continuous flow reactor system, or a Parr Shaker reaction system and used to effect the catalytic reaction.