# Assignment 5 - 2014

 Due date(s): 03 December 2014 [no late hand-ins or late day credits can be used for this one - solutions will be posted on the 3rd] (PDF) Assignment questions (PDF) Solutions

# Assignment objectives

Objectives: We have been doing non-stop examples and problems in class. This assignment gives you a chance now to try some more problems related to liquid-liquid extraction, adsorption and drying; without my help and guidance.

All these questions are from prior exams and tests.

Question 1

The isotherm for benzene, at 25°C, on an activated carbon adsorbent is given as:

$C_\text{A,S} = 32 C_\text{A}^{0.428}$

where $$C_\text{A,S}$$ is in units of mg benzene per gram of carbon, and $$C_\text{A}$$ is in units of mg benzene per litre of water-based solution.

You want to create your own adsorber packed bed from a piece of piping that has diameter of 24.5 cm.

The activated carbon supplier has given you the following specification sheet (and the isotherm information above):

• activated carbon mean diameter = 2 mm
• activated carbon size distribution range 0.4 mm to 3.8 mm
• activated carbon bulk density = 410 g/L
• activated carbon particle density = 520 g/L
• cost of activated carbon is \$5.50 per kilogram.

You would like a breakthrough time of 4 hours when treating a feed stream containing 2.8 g of benzene per litre. You have to treat 30 L per minute of waste water.

1. What type of adsorption isotherm is this? [1]

2. How long should your packed bed be? Be clear with any simplifying assumptions you make. [14]

Use the rule of thumb that if you cannot perform a lab experiment to calculate the MTZ, that your MTZ is 4ft, and assuming a symmetric wavefront, that the $$\text{LUB} = 2 \times \text{MTZ}$$.

3. What will be the cost of the adsorbent you need to purchase? [3]

Question 2

A filter cake from a plate-and-frame press is to be dried by circulating warm, dry air over the solids. See this photo for a visual idea of what the material looks like. Trays are loaded with the solid, which is 3 cm high and an area of 2.0 $$\text{m}^2$$ per tray. Each tray contains 80 kg of wet filter cake, and the filtration press step leaves the solids with approximately 30 wt% moisture on a dry basis.

Air at 1 atmosphere, 70°C, and a relative humidity of 10% is used, at an approximate velocity of $$4.2 \text{m.s}^{-1}$$, in a direction that flows parallel to the solids.

1. Estimate the mass of water that would be evaporated from the cake after 4 hours. Be clear on all assumptions you make as you proceed. [12]
2. What is the moisture content of the cake after 4 hours, expressed on a dry basis? [2]
3. Name one method we can implement to reduce the drying time. [1]

Question 3

$$140\,\text{kg.hr}^{-1}$$ of a 40% acetone-in-water mixture are to be separated using trichloroethane as solvent.

1. Draw a flow diagram that illustrates the cross-current streams, having only 2 cross-current stages.

2. Draw a general flow diagram that illustrates the counter-current system, with two stages on one end, and two stages on the other end, and a general "Nth" stage in the middle.

3. If $$80\,\text{kg.hr}^{-1}$$ of pure solvent is fed into the first cross-current stage and $$60\,\text{kg.hr}^{-1}$$ into the second cross-current stage, what will be the acetone purity leaving in the raffinate from stage 1 and stage 2? Show all constructions and calculations on the ternary diagram (download the PDF to get a copy of this diagram). Make sure all lines are clearly visible. Hint: you should achieve an acetone concentration in the raffinate of about 11%. [8]

4. What is the overall acetone recovery from such a 2-stage cross-current system? [3]

5. Now use a clean copy of the drawing (i.e. your assignment submission should have two ternary diagrams). In this second diagram start the construction for the counter-current system. The objective is to achieve the same (or better) raffinate concentration in terms of acetone as the cross-current system, but using $$40\,\text{kg.hr}^{-1}$$ of pure solvent.

With a few basic lines on the drawing you should be able to find the values for these cross-current system:

1. the expected raffinate flow rate;
2. the expected extract flow rate;
3. the expected extract composition.
6. Now locate the operating point, $$P$$, and use this to calculate the number of stages required. Submit your ternary diagram showing these calculations.

7. Assume that the last stage is at the point you selected in part 5 of this problem (i.e. that it was at that desired 11% level for acetone). Calculate the recovery of acetone for the counter-current system.

8. Now compare and contrast the following parameters for the two configurations:

• the extract concentration (for the cross-current system this is the blended concentrations of $$E_1$$ and $$E_2$$)
• the extract flow rate
• the recovery
• the solvent use compared
• for extra credit: the capital and operating costs compared between the two systems.

Question 4

A fourth practice question for the exams (no credit for the assignment) appears in the PDF download for this assignment.