  Multistep catalytic reactions use two different catalysts for the $A\to B$
and the subsequent $B\to C$ reaction, respectively. Often the employed
catalysts are chemically incompatible, such as acid-base systems, which
prohibits simple mixing in one solution. In this work, we study the efficiency
of reactors where the incompatible catalytic sites are immobilized on fibrous
membranes. We compare a lattice Boltzmann based solver for the
advection-diffusion-reaction equation, a random walk particle tracking method
and a simple theoretical model to investigate the reaction efficiency as a
function of two dimensionless control parameters: the P\'eclet and the
Damk\"ohler number. We find that, while the efficiency decreases with higher
flow speed (due to the reduced reaction time), the total production
nevertheless increases due to the higher mass flux in most cases. Our results
further show that, even at high flow speeds, spatial proximity of the two
catalysts increases reaction efficiency, which supports recent experimental
efforts to locate both catalysts on a single fiber in a side-by-side geometry.
