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 1atm).
• 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 calcu- lated 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 uncon- trolled 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.
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Assignment 2
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 1m 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. (List atleast 3 options)
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 kgms−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 func- tional. 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 ?
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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 1m 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 1ms−1. Taking the calculated value of the flux from Question 3.c to be constant along the length (50m) 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)
The end 🙂
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Assignment 2
Table 1: Question 1 Values
(a) EHMT Groups
Group Percentage deviation [%] 1 0.300 2 0.600 3 0.900 4 1.200 5 1.500 6 1.800 7 2.100 8 2.400 9 2.700 10 3.000 11 3.300 12 3.600 13 3.900 14 4.200 15 4.500 16 4.800 17 5.100 18 5.400 19 5.700 20 6.000 21 6.300 22 6.600 23 6.900 24 7.200 25 7.500 26 7.800 27 8.100 28 8.400 29 8.700 30 9.000 31 9.300 32 9.600 33 9.900 34 10.200 35 10.500 36 10.800 37 11.100 38 11.400 39 11.700 40 12.000
(b) SPDO Groups
Group Percentage deviation [%] 1 12.300 2 12.600 3 12.900 4 13.200 5 13.500 6 13.800 7 14.100 8 14.400 9 14.700 10 15.000 11 15.300 12 15.600 13 15.900 14 16.200 15 16.500
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Table 2: Question 2 Values
(a) EHMT Groups
Liquid 1 Liquid 2 Group A B C A B C 1 5.030 2221.537 7.423 5.272 2309.402 7.959 2 5.087 2227.431 7.077 6.739 2259.264 6.878 3 5.361 2218.885 7.049 6.159 2348.939 6.222 4 5.401 2262.177 7.004 6.100 2237.791 6.516 5 6.439 2362.527 6.131 5.290 2337.355 6.817 6 5.886 2302.712 6.460 6.706 2236.702 7.190 7 6.691 2373.295 6.234 6.244 2273.697 6.524 8 5.780 2396.097 7.980 5.702 2325.124 7.206 9 6.675 2265.331 6.141 6.026 2356.045 7.422 10 6.497 2243.923 6.120 5.804 2216.225 6.443 11 6.168 2303.645 7.323 5.152 2385.877 6.235 12 5.321 2270.601 6.688 5.480 2355.143 6.593 13 6.058 2371.895 6.257 5.247 2297.358 6.638 14 5.925 2252.004 7.274 5.368 2287.172 6.848 15 5.759 2368.744 7.493 5.480 2289.357 7.016 16 5.186 2316.560 7.611 5.835 2261.270 6.171 17 5.518 2343.881 6.538 5.099 2301.702 6.525 18 5.672 2268.705 6.868 6.805 2302.154 7.602 19 5.750 2201.855 6.804 6.890 2363.526 6.058 20 5.293 2238.489 7.216 5.982 2358.966 7.858 21 5.634 2301.478 7.540 5.979 2328.864 7.461 22 5.562 2204.848 7.882 5.675 2275.722 6.977 23 6.640 2310.008 6.263 6.800 2362.316 7.157 24 5.684 2255.237 6.511 5.738 2306.565 6.475 25 6.744 2339.248 6.757 5.222 2270.145 6.918 26 5.536 2376.271 7.987 6.561 2387.800 7.926 27 6.551 2204.936 6.682 5.779 2375.189 7.094 28 6.218 2268.241 7.799 5.483 2310.031 7.042 29 5.036 2284.281 6.475 5.808 2324.495 6.463 30 6.403 2216.002 6.440 5.193 2317.409 6.978 31 5.032 2215.871 7.982 5.264 2241.548 7.248 32 6.368 2214.475 7.902 6.884 2260.249 7.358 33 6.756 2380.068 7.276 6.912 2294.185 6.791 34 5.864 2393.862 7.008 6.150 2246.098 6.735 35 6.263 2278.261 6.716 5.120 2368.862 7.976 36 6.172 2262.717 7.537 5.470 2238.953 6.075 37 5.455 2310.663 7.569 5.706 2245.184 7.770 38 6.569 2358.410 6.058 6.642 2234.142 7.827 39 5.575 2359.663 6.105 5.031 2245.533 7.592 40 6.849 2372.652 6.647 5.086 2287.140 6.197 41 5.597 2359.592 7.599 5.338 2262.220 6.524 42 6.073 2201.275 7.260 6.298 2384.676 6.671 43 5.667 2383.980 7.966 6.463 2286.041 7.359 44 5.475 2203.592 6.316 6.295 2236.963 6.273 45 6.090 2205.883 7.233 5.902 2380.976 7.442
(b) SPDO Groups
Liquid 1 Liquid 2
A B C A B C
5.607 2228.587 7.082 5.787 2387.934 6.708 6.215 2234.284 6.833 6.204 2200.052 7.021 5.558 2325.169 7.034 5.048 2287.761 7.389 6.599 2205.903 7.772 5.775 2202.234 7.191 6.592 2294.466 6.299 5.113 2246.903 7.012 6.908 2335.689 6.869 6.379 2341.397 7.553 5.889 2222.958 6.118 6.041 2338.833 7.370 5.914 2247.213 6.762 5.152 2253.024 6.639 6.200 2257.816 7.445 5.813 2265.315 7.664 6.685 2234.551 6.190 5.860 2218.647 7.322 5.062 2264.741 7.334 6.319 2208.320 7.174 5.375 2360.222 6.593 5.437 2351.856 6.038 6.887 2259.927 7.197 5.162 2264.975 7.674 6.896 2355.125 6.304 5.935 2304.364 6.228 5.906 2310.554 6.873 6.457 2390.378 7.681
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