A membrane system is used to filter waste products from the bloodstream (see Fig

Question

A membrane system is used to filter waste products from the bloodstream (see Figure). The blood can be thought of as being comprised of "waste" and "all other blood constituents." The membrane can extract 30.0 mg/min of pure waste (stream W) without removing any blood. The unfiltered entering bloodstream (stream U) contains 0.17% waste, and the mass flow rate of the entering bloodstream is 25 g/min. After exiting the membrane, the blood is split into two streams: one (stream R) is recycled to join with the unfiltered blood stream before entering the membrane and one (stream F) leaves the system as filtered blood. The recycle mass flow rate (stream R) is known to be twice that of the filtered mass flow rate (stream F). Calculate the mass flow rate and the wt% of waste in streams A, B, F, and R.

Explanation / Answer

Example: A membrane system is used to filter waster products from the blood stream.

     

The membrane can extract 30 mg/min of waste , without removing any blood. The waste concentration in the entering blood is 0.17 wgt %, and the flow rate of blood is 25 g/min. A recyle stream is used to help control the concentration of the waste before it enters the membrane.

If the recycle rate is twice that of the filtered blood rate, what is the composition at A?

If the composition at A is to be 0.1 % waste, what must be the recycle rate, assuming streams U, W and F remain the same?

We first label the individual streams U, F, W, A, B, and R as shown on the sketch. U=unfiltered blood, A=input stream to filter (A=U stream + R stream), B = output stream from filter, F=filtered blood, W = pure waste, R=recycle stream.

We can draw several “systems.” We will choose the membrane plus recycle stream as the first system.

    

We start with the rate equation

                     

For steady state and no gen/con in the system, the above reduces to . We construct the mass balance table:

Note that the Recycle Stream is inside the system and does not enter into the mass in and out terms.

                     =   

Species    Stream U            Stream W         Stream F

                    (g/min)               (g/min)              (g/min)

Blood     0.9983(25)    =           0            +         ?

Waste     0.0017(25)    =       0.030        +         ?

               __________           ______              _____

Total            25.0         =       0.030        +         ?

From the above, we conclude that for stream F the filtered blood flow rate is 24.9575 g/min, the waste flow rate is 0.0125 g/min or 12.5 mg/min and the total flow rate is 24.9700 g/min. The filtered blood contains 0.05 % waste (0.125/24.97x100%)

To evaluate stream A we can consider the junction of streams U, R and A as a system:

      

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