CSTR

A continuous stirred-tank reactor (CSTR) is a well-mixed chemical reactor designed to operate with a continuous flow of reactants into and products out of the vessel. In a CSTR, the contents are assumed to be perfectly mixed, so the reactor interior has uniform concentration and temperature at any given time. The volume is often kept constant, with feed and effluent flows balancing.

Material balances for a CSTR describe the time evolution of species concentrations. For a species A in a reaction A → products with rate rA (positive for consumption of A per unit volume), the balance is dCA/dt = (F/V)(CA,in − CA) − rA, where F is the volumetric flow rate into and out of the reactor and V is the reactor volume. For systems with multiple reactions or species, a set of coupled differential equations governs all concentrations and their production rates ri.

An energy balance accompanies the material balances. For a liquid-phase reactor, ρCp dT/dt = FρCp (Tin − T) + (−ΔH) rA V − Q̇, where ρ is density, Cp is heat capacity, ΔH is the reaction enthalpy (negative for exothermic reactions), and Q̇ represents net heat transfer to or from the reactor (positive for heat removal).

Key design parameter is the space time τ = V/F, the average time a fluid element spends in the reactor. Steady-state operation sets dCA/dt = 0 and dT/dt = 0, yielding constant concentrations and temperature. CSTRs are common in chemical production, polymerization, fermentation, and wastewater treatment, but the ideal mixing assumption may limit accuracy for systems with strong gradients or fast kinetics.