In the present study, we developed a multi-component one-dimensional mathematical model for simulation and optimisation of a commercial catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2, operating in a churn-turbulent regime. DME productivity and CO conversion were optimised by tuning operating conditions, such as superficial gas velocity, catalyst concentration, catalyst mass over molar gas flow rate (W/F), syngas composition, pressure and temperature. Reactor modelling was accomplished utilising mass balance, global kinetic models and heterogeneous hydrodynamics. In the heterogeneous flow regime, gas was distributed into two bubble phases: small and large. Simulation results were validated using data obtained from a pilot plant. The developed model is also applicable for the design of large-scale slurry reactors.