Page 183 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.4 Pressure Drop in Reactors 155

where P = pressure, Ib/ft2
volume of void
+ = porosity =
total bed volume
l-+,= volume of polid
total bed volume
g, = 32.174 lb, . ft/s2. lb,(conversion factor)
= 4.17 X lo8 lb, *ft/h2 lbf
(recall that for the metric system g, = 1.0)
Dp = diameter of particle in the bed, ft
p = viscosity of gas passing through the bed, lb,/ft h

z = length down the packed bed of pipe, ft
u = superficial velocity = volumetric flow f cross-sectional
area of pipe, ft/h
p = gas density, Ib/ft3
G = pu = superficial mass velocity, (g/cm2. s) or (lb,/ft2 h)
8

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In calculating the pressure drop using the Ergun equation, the only
parameter that varies with pressure on the right-hand side of Equation (4-22)
is the gas density, p. We are now going to calculate the pressure drop through
the bed.
Because the reactor is operated at steady state, the mass flow rate at any
point down the reactor, riz (kg/s), is equal to the entering mass flow rate, rizo
(i.e., equation of continuity),

mo = m

POVO = PV
Recalling Equation (3-41), we have

(3-41)

(4-23)

Combhing Equations (4-22) and (4-23) gives