The authors examined the methods hitherto employed for the solution of cylindrical reactor equation in which the radial distributions are taken into account, and here they propose several new numerical methods for it.
These methods can be applied:
When the inner- or outer-catalyst- type heat exchanging reactor is employed;
When there exists non-uniformity in the flow velocity and effective thermal conductivity at the cross section of the reactor; and when the temperature of the cooling or heating path is varied.
1st Method: Previously reported.
8)2nd Method: Simultaneous first order differential equations on
Ti (l) and
Ci (l), i=0, 1, 2, …n, which are defined by the equations (6) and (7), are solved.
3rd Method:
T and
c are expanded into such equations as (10) and (11) and the simultaneous first order ordinary differential equations, containing the expansion coefficient as a function of
l are solved.
4th Method: When the activation energy is small,
VQ is assumed to be expressed by equation (12) in a small division. Analytical solution, satisfying the boundary condition for r and the distribution at the section
l=
lo is used for determining the distribution at
l=
lo+Δ
l.
5th Method:
T and
c are expanded into functional series which satisfy the boundary conditions for r. Simultaneous equations containing the expansion factor which are functions of
l are derived and solved. In this case
VQ is assumed to be expressed by equation (23) in a small division. The last method serves its purpose comparatively better than the rest.
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