PlugFlow

Plug flow is a model of flow through a tubular reactor in which the fluid elements moving along the reactor length remain unmixed with elements ahead or behind them; the concentration and temperature are uniform across any cross-section, so each differential element behaves like a plug that travels down the axis. It is the classic idealization behind the plug flow reactor (PFR) concept, used to predict how concentrations change along the reactor length.

Key characteristics include laminar flow in long, narrow tubes, a high Peclet number indicating convection dominates axial transport, and negligible axial dispersion or back-mixing. Rapid transverse mixing establishes a uniform composition across the cross-section, while mixing between different axial sections is minimal.

Mathematically, for a single reaction A -> products in a PFR, the molar flow rate F_A changes with volume V as dF_A/dV = r_A, where r_A is the rate of consumption of A per unit volume. With F_A = C_A v (v is the superficial velocity) and uniform cross-section, the design equation is integrated to obtain outlet concentrations given inlet conditions, the rate law, and the temperature profile. Temperature may be controlled externally or coupled via an energy balance.

Limitations of the plug flow assumption include the reality of axial dispersion, nonuniform cross-sectional mixing, and heat transfer limitations that create temperature gradients. Real systems may deviate from ideal plug flow, especially for fast reactions, highly viscous mixtures, or short residence times, where diffusion and diffusion-related dispersion become significant.

Applications often contrast plug flow reactors with continuous-stirred tank reactors (CSTR). PFRs are used where high conversion per unit reactor volume is desirable, such as in tubular reactors, petrochemical processes, pharmaceutical manufacturing, and flow chemistry setups that require well-defined residence times.