The catalytic hydrogenation of 2-butyne-1,4-diol to cis-2-butene-1,4-diol and butane-1,4-diol was carried out in a circular capillary operating in co-current down-flow mode in order to mimic the behaviour of a monolith channel. The selected model reaction was performed over a 4 wt.% palladium/alumina catalyst using 30% (v/v) isopropanol/water solvent. Liquid and gas superficial velocities were varied over a wide range (0.0098 < VSG < 0.0356 m s−1 and 0.0074 < VSL < 0.1485 m s−1) in order to study the effect of gas bubble and liquid slug lengths on the observed reaction rate and selectivity towards cis-2-butene-1,4-diol. At constant VSG, upon increasing VSL the reaction rate was sensitive to liquid slug length (LS) and flow pattern such that the maximum reaction rate occurred at LS/D = 1.2. While at constant VSL, upon increasing VSG the reaction rate was influenced by both gas (LG) and liquid slug lengths, decreasing from 0.0012 mol l−1 min−1 to reach a steady value. Varying the liquid slug length caused the selectivity to increase from 20 to 88%, whilst varying the gas slug length had a smaller effect, whereupon the selectivity slightly decreased from 95 to 83.6%. A model was developed to predict the concentration profiles of reactants and products incorporating a Langmuir–Hinshelwood model of the kinetics and correlations for estimating mass transfer coefficients from the literature.