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&quot;Vacuum Gas Oil (VGO) as a byproduct of crude oil vacuum distillation is sent to a hydro-cracking unit for upgrading. The flow rate of VGO is...

"Vacuum Gas Oil (VGO) as a byproduct of crude oil vacuum distillation is sent to a hydro-cracking unit for upgrading. The flow rate of VGO is 30000 bbl/day. The flow rate of hydrogen rich gas (make-up hydrogen and recycled hydrogen) is 4000 scf/bbl of VGO. Considering the following conditions, design the hydro-cracking unit (diameter and height of the reactor).
- Operating temperature 350-400 C
- Operating pressure 10-14 MPa
- Catalysts are spherical in shape, diameter = 3 mm, bed voidage = 0.40
- Nitrogen and sulfur are completely converted to H2S and NH3
- Liquid hourly space velocity (LHSV) = 1 h-1
- Maximum allowable pressure drop = 20 kPa/m of the catalyst bed
- Length to diameter ratio of the catalyst bed should not be larger than 1.5 m
- Operational pressure drop should be kept much lower than maximum value for safe and continuous operation, take between 10 – 20% of maximum pressure drop.

Feed conditions at 400 C and 12 MPa:
Liquid phase:
Density: 720 kg/m3
Viscosity:1.778 x 10-5 Pa.s
Gas phase:
Density: 12.68 kg/m3
Viscosity: 0.000134 Pa.s

Assume 1 meter spacing between the beds for redistribution and heat transfer.
Also assume 1.5 m on top and the bottom of the reactor.

Ergun equation:

ε = voidage μ = fluid viscosity A = cross sectional area of the reactor
ρf = liquid density dp = Particle diameter Q = flow rate
1 bbl = 0.15898 m3 1 scf = 0.0283 m3
"

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