A falling film absorber is designing for transferring oxygen into a process stre

Question

A falling film absorber is designing for transferring oxygen into a process stream. In total, we will be treating Q 80 L/min of an aqueous solution whose density and viscosity is taken to be those of water at 20 °C, 1 atm. The following figure shows the configuration of the falling film oxygenator. Liquid is distributed to falling down into a set of n-4 parallel plates, where oxygen horizontally flows between the plates. With reference to the model of the sequence of absorbers in series, it should be apparent that a key parameter is the length of the liquid film L-50 cm, in each unit. And the width of the solid plates is W30 cm. The performance of the system, as measured by the total length of required absorption surface (- 2nL), will depend on this effective length in a complex way. Suppose we require that the absorption rate f. The diffusivity is 2 x 10-5 cm/s Liquid distributors Liquad sint Gas fnow between plae Solid plates Write the velocity profile inside the penetration film and use it to determine the thickness of the film. What is the Reynolds number? a) b) Write the pertinent mass transfer equation that can be used to describe the mass transfer of the oxygen inside a single falling film oxygenator. Be sure to specify the appropriate boundary conditions c) Calculate the local evaporative flux at the surface y 0, and the total rate at which moles are evaporated over a length L and width w of a surface Write the equation of the rate of oxygen that enters the falling film oxygenator, and based on the units being designed, calculate the absorption rate f d)

Explanation / Answer

Answer

Volume flowrate in each film= L/min = 10 L/min

Density of the liquid at 20 °C= 0.99819 g/cm3 (for ease of calculation let us consider it

1 g/cm3)

Hence, volume flowrate in each film Q= 10 L/min = 10 dm3/min = 10 *103 cm3/min

= 1*104 cm3/min = cm3/sec.

Q= 166.66 cm3/sec

For momentum balance in Z direction that has normal in x direction as shown in above figure, we introduce the shear force that represents shear force in z direction.

Hence shear force at x=x is

and shear force at x=x+?x is

The Z momentum balance is al follows

Or,

Or,

Now substituting Newton’s law of viscosity for calculation of shear force we get,

To get the velocity profile we need to integrate the above equation.

Consider the boundary conditions: at , and , (approximating no slip condition) and .

Hence, we get

Average velocity can be determined as

Or,

Or,

As we get Q=166.67 cm3/sec, W=30 cm, g/cm3, g/cm –sec, we get

cm

Hence, film thickness is 0.055 cm.

Average velocity is

101 cm/sec

Reynolds number, = 378750

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