# Assignment 1 - 2014

 Due date(s): 17 September 2014 (at class) (PDF) Assignment questions (PDF) Solutions - thanks Kushlani

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Assignment objectives

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.. |micron| replace:: :math:\mu \text{m}

Separation Processes can be viewed from a number of perspectives: what is the mechanism being used to separate? what phases are being separated from each other; and separating agents are being added to the system?

Let's take a look at these, as well as get into details about the first topic covered so far: sedimentation.

#. Identify the mechanism (principle of separation) by which the components are being separated in the following instances. For example, when concentrating orange juice in an evaporator, we are exploiting the difference in *volatility* between water, and the complex aqueous compounds that make up the juice.

*Unit operations to consider*:

* Ion exchange * Brewing coffee in hot water (focus on the brewing step, not the separation of coffee grounds from the brew) * Flash drum * Hemodialysis * Venturi scrubber

#. Also identify the separating agent in each case, and state whether it is an MSA or ESA.

* Crystallization uses * Adsorption: * Steeping (brewing) tea exploits the different solubilities of the materials. The solvent, water, is the MSA. * MEA CO2

Give actual example(s) of where the following mechanism (principle of separation) could be used to split components from a given feed stream. State the name of a unit operation that exploits this mechanism to cause the separation. *For example*, the first answer could be "a sequence of sieves".

* Difference in particle sizes * Difference in molecule sizes (not particle size) * Difference in liquid densities * Difference in particle's surface charge * Difference in relative solubility * Difference in relative volatility

* Density differences are used during centrifugation. For example a wastewater stream with solids and liquids could be separated into an outlet stream of water and another of solids/cake in a centrifuge.

* Particle size differences are used during size exclusion chromatography. A mixture of proteins and excipients can be separated into a purified protein stream and a mostly excipient stream.

* Solubility differences could be used in a supercritical fluid extractor, using liquid carbon dioxide. The coffee bean feed is separated into a stream containing decaffinated beans, and the supercritical stream contains the dissolved caffeine, which is then recovered and separated further.

* Mobility differences are exploited in gel electrophoresis. A feed of mixed proteins is separated into purer protein outlet streams.

* Particle's surface charge differences are used in electrostatic precipitation. For example an air-dust feed stream can be cleaned to an air stream and a concentrated dust stream.

* Phase changes are used in many separating units, e.g. freeze-drying (lyophilisation). e.g. foods can be separated into dried food and a water stream.

* Magnetism is used in a magnetic separator to isolate iron-bearing material from the gangue.

Describe what the following separators do (be a bit more adventurous than just using Wikipedia in your research)

* mechanical deboner * flotation cell * pressure swing adsorption * fluidized bed

List five ways you can think of to separate dust from a fluid stream. The methods must be physically possible. Use sketches in your answers.

#. Spherical particles of ion-exchange resin of 100 |micron| diameter and density of :math:\rho = 1200\,\text{kg.m}^{-3} are settling in an glycerol solution (:math:\rho = 1100\,\text{kg.m}^{-3} and :math:\mu = 0.05 Pa.s) under gravity.

What is the terminal settling velocity?

#. We have however a complete distribution of particle sizes: the smallest particle size is 50 |micron| and the largest is 140 |micron|. In general, should we plan our design for the separation unit based on the larger size or smaller size particles?

#. Assume Stokes' law applies, then:

.. math::

\begin{array}{rl} v_\text{TSV} &= \displaystyle \frac{\left(\rho_p - \rho_f \right)g D_p^2}{18 \mu_f} \\ &= \displaystyle \frac{\left(1030 - 0.83 \right)(9.81)(400 \times 10^{-6})^2}{(18)(2.38 \times 10^{-5})} \\ &= 3.78~\text{m.s}^{-1} \end{array}

Checking the Reynolds number: :math:\text{Re} = \displaystyle \frac{\rho_f v_\text{TSV} D_p}{\mu_f}= \frac{(0.83)(3.78)(400 \times 10^{-6})}{2.38 \times 10^{-5}} = 52.6, which exceeds 1. So we use the updated drag coefficient estimate :math:C_D = \frac{24}{52.6}\left(1 + 0.15 \times 52.6^{0.687} \right) = 1.5.

Then the update estimate of the terminal velocity is:

.. math::

\begin{array}{rl} v_\text{TSV} &= \sqrt{\displaystyle \frac{4\left(\rho_p - \rho_f \right)g D_p}{3 C_D \rho_f}} \\ &= \sqrt{\displaystyle \frac{4\left(1030 - 0.83 \right)(9.81)(400 \times 10^{-6})}{(3)(1.5)(0.83)}} \\ &= 2.1~\text{m.s}^{-1} \end{array}

which results in a Reynolds number of :math:\displaystyle \frac{(0.83)(2.1)(400 \times 10^{-6})}{2.38 \times 10^{-5}} = 29.

One final iteration to fine-tune the estimate:

:math:C_D = \frac{24}{29}\left(1 + 0.15 \times 29^{0.687} \right) = 2.1 and :math:v_\text{TSV}=\sqrt{\displaystyle \frac{4\left(1030 - 0.83 \right)(9.81)(400 \times 10^{-6})}{(3)(2.1)(0.83)}} = 1.75~\text{m.s}^{-1}, which has a Reynolds number of 24.4.

In this flowsheet for converting sugar cane to raw sugar from King's textbook, *Separation Processes*, identify 2 separation unit operations.

For each unit operation, describe:

(a) the principle being exploited to create the separation (b) the ESA and/or MSA being added.

Also, watch the video on the sugar process again <http://www.youtube.com/watch?v=ZBOou6cahtw>_ [1] to visualize the size of these units.

.. image:: ../figures/examples/sugar-flowsheet/King-Separation-Processes-Sugar-flowsheet.png :align: center :scale: 90% :width: 750px

Figure credit: King, Separation Processes, 2nd edition, McGraw Hill, p. 3.

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