Please explain/justify all of your answers

Assignment 2

Please explain/justify all of your answers

Hand-written answers only.

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Assignment 2 on concentration polarization

The rejection, recovery and concentration polarization properties of reverse osmosis membranes are characterized in stainless steel high-pressure test chambers of the type illustrated schematically below.

Prior to characterization, the membranes are soaked in water/alcohol solution for several days, operated overnight in situ using a distilled water feed at 50 Bar, and thereafter a further 3 hours operation at 110 Bar.

Characterization data for a polyamide RO membrane desalinating NaCl feed solutions of concentration 6000 ppm are tabulated below for three feed rates.

(a) Describe in a few paragraphs (with the aid of sketches if necessary) the purposes of the pre-treatments of membranes.(5 marks)

(b) Assume that the feed and permeate on either side of a reverse osmosis membrane of very small thickness membrane behave as ideal dilute solutions and that their concentrations can be maintained uniform throughout by vigorous stirring in the test chamber. Show that the flux of water through membrane is given by;

waterumembranewatermembraneP-where P is the applied pressure difference, the osmotic pressure difference and umembranewater is the mobility of water in the membrane.(7 marks)

(c) Use your answer to part (b) and the tabulated characterization data to estimate average values for and umembranewatermembrane for the indicated feed rates.

Explain in a few paragraphs (with the aid of sketches if necessary), the terms concentration polarization and salt rejection as well as possible origins of variations in the average estimates for .

What is a more common term given to umembranewatermembrane ?.

(7 marks)

(d) Detailed analyses of drifts and diffusions of solute and water through the chamber yield the relationship;

RObserved1-RObserved=watervmembranesoluteExp-watervsolutepolarbetween the water flux, water, and the observable salt rejection coefficient, i.e. RObserved.

Describe in a paragraph (with the aid of sketches if necessary), the origins and significances of the parameters;

vmembranesoluteDmembranesolutemembrane and vsolutepolarDsolutepolarpolarin the relationship, where Dmembranesolute and Dsolutepolar denote respectively, the diffusion constant of the solute in the membrane of thickness membrane and that of the solute in the concentration polarization layer of thickness polar.

Explain why vsolutepolar is referred to as the mass transfer coefficient. (7 marks)

(e) Estimate values for the parameters;

vmembranesolute and vsolutepolarfrom the tabulated characterization data for the indicated feed rates.(7 marks)

(f) Explain in a few paragraphs (with the aid of sketches if necessary) origins of variations in the estimates from part (e) at the indicated feed rates, noting that Dsolutepolar is the known average diffusion constant for salts in solution, i.e. in the feed, polarization and filtrate solutions. (7 marks)

(g) Detailed analyses of drifts and diffusions of solute and water through the membrane also yield the expression;

RTrue11+1-RObservedRObservedExp-watervsolutepolaras an estimate of the true rejection coefficient in terms of the observed rejection coefficient, RObserved. Estimate the true rejection coefficients using this expression and the parameter estimates from (e) for the feed rates in the tabulated data.(4 marks)

(h) Plot the ratio, RTrueRObserved, as a function of the water flux, water, for all of the tabulated feed rates.(4 marks)