# Assignment 4 - 2014

 Due date(s): 11 November 2014 (PDF) Assignment questions (PDF) Solutions

# Assignment objectives

Objectives: This assignment is to gain some experience with the membrane calculations.

Question 1 [28 = 5 + 2 + 12 + 2 + 3 + 2 + 2]

A reverse osmosis plant treats $$120,000\,\text{m}^3$$ 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 $$35,000\,\text{m}^3$$ 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 $$180,000\,\text{m}^2$$. 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 $$5.5 \times 10^{-5}\,\text{kg.s}^{-1}\text{.m}^{-2}\text{.atm}^{-1}$$. The permeance of salt through the membrane was $$21 \times 10^{-8}\,\text{m.s}^{-1}$$.

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]
2. Is that water permeance value applicable to all $$180,000\,\text{m}^2$$ of membrane area? Explain. [2]
3. Calculate the actual flow rate of drinking water leaving the plant. [12]
4. 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]
5. Is this flux close to typical LMH values experienced on reverse osmosis applications? Explain why. [3]
6. What is the rejection coefficient for this system? [2]
7. What is the cut value? [2]

Question 2 [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$$\text{~m}^{3}\text{.hour}^{-1}$$ with concentration of 1.2 $$\text{kg}\text{.m}^{-3}$$. The membrane's operating characteristic was calculated from various experiments:

$J_v = 0.04 \ln \left(\frac{15}{C}\right)$

where the bulk concentration $$C$$ has units of $$\text{kg}\text{.m}^{-3}$$ and flux is measured in $$\text{m}^{3}\text{.hour}^{-1}\text{.m}^{-2}$$.

If two membrane modules, each of area 25 $$\text{m}^2$$, are simply placed in series, give reasonable estimates of:

1. the dye concentration from the first membrane module?
2. the permeate flow rate from the first membrane module?
3. the dye concentration from the final membrane module?
4. the permeate flow rate from the final membrane module?
5. Then explain whether the above answers seem reasonable.