Page 137 - Fluid Catalytic Cracking Handbook

112 Fluid Catalytic Cracking Handbook

... . (Second Order Conversion)
r v
Dynamic Activity =
(Coke Yield, Wt% of Feed)
Where;

(MAT Conversion, Vol%)
Second Order Conversion =
(100 - MAT Conversion, Vol%)

For example, a catalyst with a MAT number of 70 vol% and a 3.0
wt% coke yield will have a dynamic activity of 0.78. However, another
catalyst with a MAT conversion of 68 vol% and 2.5 wt% coke yield
will have a dynamic activity of 0.85. This could indicate that in a
commercial unit the 68 MAT catalyst could outperform the 70 MAT
catalyst, due to its higher dynamic activity. Some catalyst vendors have
begun reporting dynamic activity data as part of their E-cat inspec-
tion reports. The reported dynamic activity data can vary significantly
from one test to another, mainly due to the differences in feedstock
quality between MAT and actual commercial application. In addition,
the coke yield, as calculated by the MAT procedure, is not very
accurate and small changes in this calculation can affect the dynamic
activity appreciably.
The most widely accepted model to predict E-cat activity is based
on a first-order decay type [7]:

A - A X c~ (S+K)t , A 0 X S v n _, e-<K+S)fv
A A xe
(t) - (0) c i i^ ^ '
o 4" IV
At steady state, the above equation reduces to:

A X S
A
x e
A A - A x c - (S+K)t I ° x f'1 - p-tK+S)')
(t) ~~ (0) c , v ^ '
O + IS.
Where:
A (t) = Catalyst microactivity at anytime
A 0 = Catalyst microactivity at starting time
t - Time after changing catalyst or makeup rate
S = Daily fractional replacement rate = addition rate/inventory
K = Deactivation constant = ln(A t - A 0)/-t