# Assignment 5 - 2012

 Due date(s): 03 December (by 16:00; no late handins) (PDF) Assignment questions (PDF) Assignment solutions

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Assignment objectives

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.. question::

:math:2.5\,\text{m}^3 of wastewater solution with :math:0.25\, \text{kg phenol.m}^{-3} is mixed in a batch reactor with 3.0 kg granular activated carbon until equilibrium is reached. Use the following values determined in the lab, calculate the final equilibrium values of phenol extracted and percent recovery.

===================== ====================== :math:C_\text{A} :math:C_\text{A,S} ===================== ====================== 0.004 0.026 0.0087 0.053 0.019 0.075 0.027 0.082 0.094 0.123 0.195 0.129 ===================== ======================

#. Plot the isotherm. #. Determine the isotherm type. #. Calculate the isotherm parameters. #. Calculate the steady-state conditions in the batch reactor for :math:C_\text{A} in :math:\text{g.cm}^{-3} and for :math:C_\text{A,S} in grams solute per gram of activated carbon. #. Calculate the percentage amount of phenol that is recovered by the adsorbent.

.. question::

The aim is to recover ethylene glycol from water using furfural as solvent (the ternary diagram for furfural, ethylene glycol and water at the unit's operating temperature is provided <http://learnche.mcmaster.ca/wiki_4M3/images/1/1a/2012-4M3-Ternary-diagram-question-2-assignment-5.pdf>_).

#. Calculate the equilibrium compositions leaving a single mixer-settler unit operated at:

* the recycled solvent stream: :math:105\,\text{kg.hr}^{-1} with a composition of 84% furfural, and unrecovered ethylene glycol at 5%, with the rest being water. * the feed stream contains 42% ethylene glycol and 58% water at a rate of :math:200\,\text{kg.hr}^{-1}.

#. Calculate the flow rates of the extract and raffinate streams.

#. What is the distribution (partition) coefficient, :math:D_\text{A}, for A = ethylene glycol (see course notes for definition)?

#. What is the distribution (partition) coefficient, :math:D_\text{C}, for C = water, using this same definition?

#. What is the separation factor for :math:i=\text{ethylene glycol} from :math:j=\text{water} in the 1=extract and 2=raffinate streams? Also show the relationship between the separation factor and the previous two distribution coefficients.

#. What will happen to the separation factor when operating at a lower feed flow rate; show a construction on your diagram to demonstrate it.

.. question::

Consider a system for which you have been given the ternary diagram <http://learnche.mcmaster.ca/wiki_4M3/images/2/2c/2012-4M3-Ternary-diagram-question-3-assignment-5.pdf>_. :math:A = solute, :math:S = solvent, :math:C = carrier. The feed, :math:F, enters at 112 kg/hr with composition of 25 wt% solute and 75 wt% carrier, shown as point :math:F.

#. Calculate the flow and composition of the extract and raffinate from (*covered in class*):

#. 1st co-current stage, using a pure solvent flow of 50 kg/hr. #. 2nd co-current stage, which is few with an a fresh solvent flow of 50 kg/hr.

#. For the overall 2-stage system, find the (*covered in class*):

#. overall recovery, defined using the mass flows of :math:\displaystyle \frac{\text{Feed} - R_2}{\text{Feed}} #. overall concentration [kg/kg] of combined extract streams, :math:E_1 and :math:E_2 combined concentration.

#. *New*: The objective now is to have a counter-current system so the raffinate leaving in the :math:N^\text{th} stage, :math:R_N has :math:y_{R_N} = 0.025.

#. What is the *maximum allowable solvent flow* to achieve :math:y_{R_N} = 0.025? #. Explain whether it's possible to achieve a final extract stream of concentration :math:y_{E_1} = 0.20. #. Show the construction on the ternary diagram for the number of equilibrium stages to achieve :math:y_{R_N} = 0.025, given a solvent flow of 27.5 kg/hr (**this number was updated**) #. Plot, on the same axes, the concentrations in the extract and raffinate streams from each stage. #. Calculate the distribution (partition) coefficient for the solute in each stage, :math:D_{\text{A},i} = \displaystyle \frac{y_{\text{E}_i,\text{A}}}{x_{\text{R}_i,\text{A}}}

Submit the single ternary diagram for part (1 and 2), and another ternary diagram for part (3).

Be sure to make a copy of your filled in diagrams, because you might not be able to pick up your graded assignment 5 before the final exam.

.. question::

#. What is the dew point temperature of an air stream containing 15% humidity at 70 :math:^\circ\text{C}? #. What is the amount of water carried in this stream? #. This stream is cooled adiabatically; what is the adiabatic saturation temperature? #. What is the amount of moisture held now per kilogram of dry air? #. *From a previous year's 4M3 assignment*: Read the definition for relative humidity from The Weather Network <http://www.theweathernetwork.com/index.php?product=glossary&pagecontent=relativehumidity>_. Prove that it agrees with our definition in the class.

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