The gas-phase cracking of a Salina light gas-oil reaction

A typical cost
of the catalyst is
$1 million

gas-oil (g) products (g) + coke (s)
A B

is to be carried out in a straight-through transport reactor containing a catalyst that decays as a result of coking. The reaction is carried out at 750°F.

The entering concentration of A is 0.2 kmol/m ³ . The catalyst particles are assumed to move with the mean gas velocity (U _g =U _s = 7.5 m/s). The rate law is

with K _A = 3 m ³ /kmol and K _B = 0.01 m ³ /kmol. The maximum value of the term K _B C _B is small (0.002), so it can be neglected with respect to the other terms (e.g., 1). Using this fact and the bulk density,_b , the rate law becomes

with k = 8 s ^-1 . At 750°F, the catalyst activity for light gas-oil over a synthetic catalyst for short contact times (i.e., less than 100 s) is

with A ´= 7.6 s ^-1/2 . As a first approximation, neglect volume change with reaction, pressure drop, and temperature variations.

Determine the conversion as a function of distance down the reactor. The reactor length is 6 m.

Solution

For a catalyst particle traveling with a velocity of U, the time that the catalyst particle has been in the reactor when it reaches a height is just

(CDE10-4.4)

and

(CDE10-4.5)

where

Stoichiometry. Gas-phase reaction with= 0, T = T ₀ , and P = P ₀.

Combining yields

(CDE10-4.6)

POLYMATH Solution. In using POLYMATH to obtain a solution, it is usually easiest to write the mole balance, rate law, and stoichiometry separately rather than combining them into a single equation. Therefore, starting with the mole balance

(CDE10-4.7)

we substitute for -r _A and a using Equations (CDE10-4.2) and (CDE10-4.5). The POLYMATH program and solution are shown in Table CDE10-4.1 and Figure CDE10-4.1 respectively.

Table CDE10-4.1
POLYMATH Program Coking in a Straight-Through Transport Reactor

Figure CDE10-4.1
Conversion and Activity Profiles