A comprehensive mathematical model is developed to simulate gas-liquid reactor in which both, reactants as well as products enter or leave the reactor in gas phase while the reactions take place in liquid phase. A case of first-order reaction (isothermal) was investigated in detail using the dynamic model and numerical bifurcation tools. Strong coupling between reaction kinetics and product removal rate was found to lead to complex dynamic (including over-flow/dry-up or oscillatory) behaviour. Key parameters controlling operability and dynamic characteristics were identified. Operability maps of the reactor/separator are presented. The model and results discussed will be useful for design and operation of industrial reactor/separators.