# 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

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Assignment objectives

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• 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::

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

.. math::

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

where :math:C_\text{A,S} is in units of mg benzene per gram of carbon, and :math: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.

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

#. 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 :math:\text{LUB} = 2 \times \text{MTZ}.

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

.. question::

.. inspired from example 18.7, Seader, Henly and Roper, p 753.

A filter cake from a plate-and-frame press is to be dried by circulating warm, dry air over the solids. See this photo <http://www.flickr.com/photos/cdeimages/6322211031>_ 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 :math:\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 :math:4.2 \text{m.s}^{-1}, in a direction that flows parallel to the solids.

#. 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]**

#. What is the moisture content of the cake after 4 hours, expressed on a dry basis? **[2]**

#. Name one method we can implement to reduce the drying time. **[1]**

.. question::

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

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

#. 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.

#. If :math:80\,\text{kg.hr}^{-1} of pure solvent is fed into the first cross-current stage and :math: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]**

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

#. 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 :math: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:

a) the expected raffinate flow rate; b) the expected extract flow rate; c) the expected extract composition.

#. Now locate the operating point, :math:P, and use this to calculate the number of stages required. Submit your ternary diagram showing these calculations.

#. 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.

#. 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 :math:E_1 and :math: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::

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

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