Real Tubular Reactors in Laminar Flow Quak Foo Lee Department of Chemical and Biological Engineering The University of British Columbia

Isothermal Laminar Flows with Negligible Diffusion In laminar flow reactors, there will be a pronounced velocity gradient across the tube, with zero velocity at the wall and high velocities near the centerline. Molecules near the center will follow high-velocity streamlines and will undergo relatively little reaction. Those near the tube wall will be on low-velocity streamlines, will remain in the system for long times, and will react to near completion.

Isothermal Laminar Flows with Negligible Diffusion In the absence of diffusion, each streamline through a laminar flow reactor can be treated as if it were a piston flow reactor. The system as a whole can be regarded as a large number of piston flow reactors in parallel. Concentrations along the streamlines are

Convective Diffusion of Mass For chemical reactions to occur, molecules must come into contact; and the mechanism for this contact is molecular motion. (This is also the mechanism for diffusion.) With unmixed feed, mixing occurs inside the reactor under reacting conditions. Diffusion is a slow process, and the actual rate of reaction will typically be limited by the diffusion rate rather than by the intrinsic kinetics that would prevail if the reactants were premixed. Thus diffusion is important in unmixed feed reactors unless the reaction is very low.

Convective Diffusion of Mass For chemical reactions to occur, molecules must come into contact. The mechanism for this contact is molecular motion. This is also the mechanism for diffusion. There are some reactor design problems where diffusion need not be explicitly considered.

Convective Diffusion of Mass With unmixed feed, mixing occurs inside the reactor under reacting conditions. Diffusion is a slow process, and the actual rate of reaction will typically be limited by the diffusion rate rather than by the intrinsic kinetics that would prevail if the reactants were premixed.

Convective Diffusion of Mass With premixed reactants, molecular diffusion has already brought the reacting molecules in close proximity. In an isothermal batch reactor, various portions of the reacting mass will all react at the same rate and will thus have the same composition at any time. No concentration gradients develop, and molecular diffusion is unimportant during the reaction step of the process even though it was important during the premixing step. In a flow process, whether isothermal or not, different portions of the fluid will have different compositions.

1-D Velocity Profiles with Diffusion Molecular diffusion is important. For reactions in circular tubes with 1-D velocity profiles (convective diffusion equation): Determine the significant of molecular diffusion Determine the importance of diffusion in the radial direction compared to that in the axial direction. Normally (R/L) 2 < Typically (R/L) 2 < Negligible compared to radial direction.

Boundary Conditions

Temperature Profiles in Laminar Flow Thermal diffusivity R/L is small. Therefore this term is dropped out. If the overall reaction is exothermic, will be positive so that T will be an increasing function of z *.

Boundary Conditions Initial condition Constant wall temperature Adiabatic operation Radial symmetry