Assignment 4 - 2014
| Due date(s): | 11 November 2014 |
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Assignment questions |
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Solutions |
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Assignment objectives
=========
- Objectives**: This assignment is to gain some experience with the membrane calculations.
.. question::
:grading: 28 = 5 + 2 + 12 + 2 + 3 + 2 + 2
.. The retentate stream leaves at 5.25 wt% dissolved solids.
A reverse osmosis plant treats :math:`120,000\,\text{m}^3` of seawater per 8 hours, at 20°C and 3.5 wt% solids (assume it to be NaCl). The molar mass of NaCl is 58.4 g/mol and is 18.02 g/mol for water. The aim is to obtain :math:`35,000\,\text{m}^3` of drinking water within an 8 hour period, with only 500 ppm (0.05 wt%) dissolved solids in it.
The feed pressure is 140 atm entering and leaving at 4 atm in the permeate. The total area of the spiral wound membranes is :math:`180,000\,\text{m}^2`. The plant only operates 8 hours per day, in the evenings, when electricity is cheapest. Storage tanks are used to hold the water produced during the 8 hours, so that it is available 24 hours per day to the town.
From lab experiments at the supplier, the permeance of water through a single membrane module was found to be :math:`5.5 \times 10^{-5}\,\text{kg.s}^{-1}\text{.m}^{-2}\text{.atm}^{-1}`. The permeance of salt through the membrane was :math:`21 \times 10^{-8}\,\text{m.s}^{-1}`.
#. Give a few bullet points that describe how the membrane's permeance with respect to water is calculated. Your description must take the given units into account. **[5]**
#. Is that water permeance value applicable to all :math:`180,000\,\text{m}^2` of membrane area? Explain. **[2]**
#. Calculate the actual flow rate of drinking water leaving the plant. **[12]**
#. Will the drinking water flow meet the demand required? If the demand cannot be met, name one thing that can be improved or changed to meet demand. **[2]**
#. Is this flux close to typical LMH values experienced on reverse osmosis applications? Explain why. **[3]**
#. What is the rejection coefficient for this system? **[2]**
#. What is the cut value? **[2]**
.. question:: :grading: 20
An asymmetric ultrafiltration membrane is used with the aim of separating dyes from a liquid stream and to achieve a more concentrated dye-water mixture. The feed waste stream arrives at a flow rate of 2.2\ :math:`\text{~m}^{3}\text{.hour}^{-1}` with concentration of 1.2 :math:`\text{kg}\text{.m}^{-3}`. The membrane's operating characteristic was calculated from various experiments:
.. math::
J_v = 0.04 \ln \left(\frac{15}{C}\right)
where the bulk concentration :math:`C` has units of :math:`\text{kg}\text{.m}^{-3}` and flux is measured in :math:`\text{m}^{3}\text{.hour}^{-1}\text{.m}^{-2}`.
If two membrane modules, each of area 25 :math:`\text{m}^2`, are simply placed in series, give reasonable estimates of:
#. the dye concentration from the first membrane module? #. the permeate flow rate from the first membrane module? #. the dye concentration from the final membrane module? #. the permeate flow rate from the final membrane module? #. Then explain whether the above answers seem reasonable.
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