Mathematical modelling for the shell and tube reactor

Suitable models for the individual tubes in a multituubular reactor have been presented in the literature. However, basing the overall design on this, with perhaps a simple scaling factor for number of tubes, provides no mechanism for describing the way in which interaction between tubes arises. It also ignores issues associated with the mechanical design of the equipment and the impact it has on the coolant hydrodynamics. The coolant flow distribution depends on the area but must also satisfy the pressure distribution on the shell-side. A suitable model for multitubular reactors can be developed using a two dimensional array of cells. They are made up of a group of tubes which are assumed to have the same environmental conditions. The shell and tube-side equations must be solved simultaneously. The system of partial differential equations describing the tube-side is conveniently solved using the method of lines with the radial coordinates being discretized using orthogonal collocation and the resulting system of ordinary differential equations in the axial distance being integrated using a suitable algorithm such as Range-Kutta-Merson. The equations for the coolant flow distribution constitute a system of non-linear algebraic equations. The most convenient method is to solve the system of equations using Newton-Raphson with a step length restriction together with the Levenberg-Marquard and Continuation Method. The algorithm used in this work, as well as the global solution procedure, has been tested over a range of conditions and design parameters. It seems to be both realiable and robust for all conditions used and it is practically independent of the initial values used for the parallel flow velocity.