Assignment 2 – Mass Transfer

Overview
• Consider all the mixtures/solutions to be ideal unless otherwise mentioned.
• The ambient conditions are assumed to be at NTP (20 ◦C and 1 atm).
• During grading, least importance will be given to accuracy in the end values. Therefore try to answer using sufficient concepts and equations. Keep your answers short, but don’t miss out the key words.
• This is an educational exercise. Therefore, we tried to keep it as practical as possible.
• A Q&A session will be held online. The time and date will be notified via brightspace.
• You can upload your completed report to the brightspace assignment page. Make sure that the first page of the report contains the course name, group number, student names and student IDs.
In the brightspace assignments page, EHMT student can upload it under their group number, and SPDO students can upload it under their individual name/IDs (it is enough if one person from the group uploads it).
• The file name should be course groupnumber. course = EHMT/SPDO, group number =Group numericvalue. For example, EHMT Group 1
• Bonus marks with be given for the report formatting. You can refer to the pdf attachment provided with the assignment for the type setting requirements.
• Also for setting up meetings, doubts, etc.. you are welcome to e-mail: n.nagalingam@tudelft.nl.

Question 1
Imagine you are a consultant engineer. You have been invited to solve the scaling issues within a boiler in a thermal power plant.

a. At first you decide to trouble shoot the boiler system by checking the pressure within it. Assuming the water is pure, what would be the expected pressure value for a boiler operating at 150 ◦C. (for pressure in bar and temperature in K, the component-specific constants in Antoine equation for water are A=6.20963, B=2354.731, C=7.559, use log10)

b. Since you physically observe scaling over the boilers inner surface, you suspect the presence of some dissolved salts in the boiler feed water. Will the dissolved salts increase/decrease/not-affect the calculated pressure in the above question? Lets say the deviation is as mentioned in table 1, what is the concentration of the salt in wt% ? Upon further inspection you notice a fault in the desalination system due to which there is an uncontrolled amount of salt in the boiler feed water. Therefore, at the desalination tank you decide to add some special home made mineral(in solid state) at the tank’s bottom, which has the ability to combine with the existing salt and precipitate it.

c. If the container is left undisturbed, How long will it take for the special mineral to diffuse to the top layer of the desalination tank ? (lets say the desalination tank is 1 m heigh and the diffusion coefficient of the mineral is 1 × 10−9 m2/s)

d. Lets say you decide to increase the diffusion process by heating up the tank. To do so you use the waste steam from the turbines that could heat up the tank to 80 ◦C. What would be the percentage increase/decrease in the time calculated from the previous question.

e. Can you mention what design parameters can be changed to make the process faster? Also mention the associated dimensionless numbers that can be used to characterise/rationalise the changes made.

Question 2
a. In the new waste heat recovery system, unfortunately, a leak was found in the heat exchanger pipeline that collects the heat from steam and transfers it to desalination tank. You suspect a higher pressure within the exchanger pipeline than it could withstand. Considering the coolant within the pipeline is a mixture of 2 liquids (A and B), calculate the maximum and minimum pressure that you can expect at 80 ◦C. (their component-specific constants are given in table 2)

b. Lets say all of a sudden this mixture becomes a non-ideal mixture. What is the additional coefficient(s) that you should consider for your calculations?. If we consider both of our ingredients to have activity coefficient greater than 1 what will be the newly measured total pressure. Will it be greater or smaller than before? why?

Question 3
All of a sudden you remember that your mass transfer course has taught you an alternate way to purify salt water. Therefore you decide use a membrane as an alternative to extract the fresh water from the desalination talk without the use of your special home made mineral. (only passage of the solvent is allowed in all the below cases)

a. You decide to use a a big compartment containing two containers separated by a membrane. Container A is filled with the salt water (concentration is same as in Question 1.b) and container B is filled with fresh water. How can you make the water(solvent) from container A to permeate to container B via membrane. What is the name of the process ? What is the minimum pressure need for the water purification in the above question ?

b. Since you are a smart engineer, you try to avoid the use of power/electricity to supply this necessary pressure. Therefore, you now do some basic calculation to let the gravity do the work by creating a pressure head. You plan to place one container at a certain height above the other to make the process in the above question happen. What should be the minimum height between the two containers ? Which container should be placed above and which one should be below ? For some reason you decide to drop the plan on leaving things to gravity. Therefore, now have decided to use the help of a pressure pump, with the containers placed at the same height level.

c. For the water purification to happen, you have decided to supply twice the osmotic pressure over the appropriate container. How much and when would you have the maximum solvent flux through the membrane? (let the solvent permeability and membrane thickness be 3.5 × 10−10 kg m s−1 m−2 bar−1 and 2 μ m)

d. While performing the purification process, at one point you notice that the system is no longer functional. Upon inspection, you notice some solid matter blocking the membrane within the container A. What could these solid matter be ? How/why did the appear within the container A ?

e. Using the solution from container A (concentration is same as in Question 1.b), you decide to make this a continuous process. In order to do so you roll the membrane into the shape of a tube with diameter 1 m and pass the salt water (from container A) through it with fresh water on the exterior side of the tube. The flow velocity of the solution is 1 m s−1. Taking the calculated value of the flux from Question 3.c to be constant along the length (50 m) of the tube, can you calculate the final concentration of the solution exiting the tube?

f. (bonus question) In a real case there should be a pressure drop across the tube in order to make the solution flow. Lets say you supply twice the osmotic pressure at the inlet compared to the outlet. Can you expect the reverse osmosis to happen through the length of the tube? If yes/no, then when/why? For this question you don’t need to calculate any numeric values. Just mention and balance the equations. (tip: Hagen–Poiseuille equation)