Question

A continuous sterilizer with a steam injector and a flash cooler will be employed to sterilize growth medium continuously with a flow rate of 2 m/hr. The time for heating and cooling is negligible with this type of sterilizer. The typical bacterial count of the medium is 5X10m, the desired probability of failure is 0.001. The bacterial spores in the medium can be characterized by an Arrhemus coefficient (a) of 4.707x10" hr and an activation energy (Ed) of 2.834x10 J/mol. The sterilizer will be constructed using pipe with inner diameter of 0.1 m. Saturated steam at temperature of 400 K is used for the sterilization process. Calculate the length of the pipe to be used in the sterilizer..

Answer 1

Sdni Given, Bacterial count - sxion 3 Glow rate = 2 milne (time is anegligible) no = 6x109) (2) - 10x = 1000 Da In ano - In 10 = 23.025 I Temp of holding nection will be con Dould = Ka Tendal = 23-025 را کالر Ka= kdo exp (-Ed/RT) - (1) < do= 2.70781039 hr 1 (Arhenin ca) Ed= 2.634x10s J/mol

Above attatched images are my handwritten solution to find the length of the pipe used in sterilzer.

First find $\triangledown$ using

u] =Δ.

now since temperature at the holding section is constant $\triangledown=$ $\triangledown _{hold}$

Using
Vhold = kd.hold
find $\lambda _{hold}$

where,

1-Ed kd = kdo.e.pl CAPRT

Ed, R, T, Kd0 is all given in the question.

now,

Length of the pipe= (Velocity of the pipe). $\lambda _{hold}$

Velocity=flowrate/area

Hence find length of the pipe.

(here to find length of the pipe I've assumed flow to be plug flow. If flow is not plug flow then axial dispersion is considered, where we use Peclet number(uavL/D) where D is axial dispersion cofficient which depends on structure of reactor, operating conditions and properties of fluid, if we can assume D then trial and error method should be done with values plotted from a graph of nt/n0 vs kdL/uav  as shown below: )

Peclet number KIL av