# 5.8: Untitled Page 106

## Chapter 5



m



m

H2O 1 1

H2O 4

4

MW

MW

H O

H O

Water:

2

2

(9)

 ( y

) M

 ( y

) M

 0

H2O 2

2

H2O 3

3

Here we have identified the mass flow rates of the wet solid streams according to

m

  Q ,

m

  Q

(10)

1

1

1

4

4

4

Figure 5.8c. Wet solids entering the dryer

A little thought (see Problem 5‐33) will indicate that a mass balance for the solid material leads to

Solid material:

1

  

  m

1

  

  m

(11)

H

2O 1

1

H

2O 4

4

and this result can be used in Eq. 9 to obtain



  

H O 4

H O 1 

Water:

2

2

( y

) M

 ( y

) M  

m (12)

H2O 2

2

H2O 3

3

1

 1  

  MW

H

 

2O 4

H

2O 

A molar balance for the air will allow us to eliminate M

 from this result

3

and the calculation of M

 easily follows (see Problem 5‐34).

2  Two‐Phase Systems & Equilibrium Stages

193

5.6 Continuous Equilibrium Stage Processes

In Sec. 5.5 we considered systems that consisted of a single contacting process in which equilibrium conditions were assumed to exist at the exit streams.

Knowing when the condition of equilibrium is a reasonable approximation requires a detailed study of the heat and mass transfer processes that are taking place. These details will be studied in subsequent courses where it will be shown that the condition of equilibrium is a reasonable approximation for many mass transfer processes. Our first example of an equilibrium stage was the batch liquid‐liquid extraction process illustrated in Figure 5‐4. In that case one could repeat the extraction process to obtain an arbitrarily small value of the concentration of species A as indicated by Eq. 5‐45. In this section we wish to illustrate how this same type of multi‐stage extraction process can be achieved for a steady‐state process. In Figure 5‐9 we have illustrated an arrangement of mixer‐settlers that can be used to reduce the concentration of species A in the organic stream to an arbitrarily small value. Rather than working with the details illustrated in this figure, we will represent the mixer‐settler unit as a Figure 5‐9. Multi‐stage extraction process

single box so that our counter‐current extraction process takes the form illustrated in Figure 5‐10. Here we note that the nomenclature used to identify Figure 5‐10. Schematic representation of a multi‐stage extraction process the incoming and outgoing streams is different than that used in Figure 5‐6 for a single liquid‐liquid extraction unit. In this case the number of the unit is used to identify the outgoing streams, and this simplification is necessary for an efficient treatment of a system containing N units. 194