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Continuous flow synthesis of catalysts with custom made reactor with flow and temperature studies

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Continuous flow synthesis of catalysts with custom made reactor with flow and temperature studies

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Content 1 Continuous flow synthesis of catalysts with custom made reactor with flow and temperature studies By Kiran Vishveshvar Viswanath University of Southern California August 2019 A Thesis presented to the University of Southern California in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering 2 Acknowledgements I would sincerely like to thank my supervisors Dr. Noah Malmstadt and Dr. Richard Brutchey for providing me the opportunity to work in their projects and helping me learn a lot in the last couple of years. I would like to thank Dr. Noah Malmstadt for providing me with direction and answers to my endless stream of questions which helped me to complete my thesis at the graduate level. I am also very thankful for Lu Wang, who is pursuing her PhD at University of Southern California for her assistance in the completion of my project. I am forever grateful to my parents for working tirelessly towards making my graduate school dream a reality by supporting me in every step of the way. Finally, I want to thank my friends and colleagues at the University of Southern California for helping me enjoy my graduate school life and for helping me stay strong mentally and physically over the last 2 years by providing undying support. 3 Authors declaration I hereby declare that I am the sole author of my thesis and I authorize University of Southern California to reproduce this thesis by photocopying or by any other means, in part or as a whole, if requested by anyone for the sake of research or scholarly purposes. 4 Abstract At this day and age where the world is moving towards more efficiency, we are trying to find ways to make every process continuous from a batch process. Applying these criteria on the synthesis of catalysts requires the use of a reactor which allows continuous flow and constant monitoring. This is hence carried out in 2 steps, the first step conducting the reactions and the second one was to check for consistency of the thermodynamic aspect of the reactor. Custom made glass reactors were used to compare results from both batch and continuous flow. These reactors were used for the synthesis of catalyst nanoparticles like MoC, WC and tested in terms of XRD and mass throughput flowing out. The second part wherein the temperature in the sand bath was measured and an analysis of the reactor was made in terms of temperature distribution with respect to height of the reactor and width of the reactor and simultaneously carrying out these in numerical simulations too. Methods to improve the heating system in the reactor was carried out by reducing any chance of heat loss from the reactor by designing an appropriate lid for the reactor sand bath. To analyze this in terms of flow rate, a flow rate counter was used which allowed the fluid to flow through and real time data was collected to check for consistency with the flow meter reading. Methods to improve the reactor in the future has been discussed in brief to analyze the scope of this sand bath. 5 Contents Acknowledgements ....................................................................................................................................... 2 Authors declaration ...................................................................................................................................... 3 Abstract ......................................................................................................................................................... 4 Table of Figures ............................................................................................................................................. 6 Chapter 1 Introduction ................................................................................................................................. 7 Chapter 2 Theory .......................................................................................................................................... 9 2.1:Why is flow synthesis better than batch? ................................................................................. 9 2.2 Measurement of Flow data ..................................................................................................... 11 2.3Temperature distribution ......................................................................................................... 12 2.4 Chemistry of Nanoparticle synthesis ....................................................................................... 14 Chapter 3 Experimental Apparatus ............................................................................................................. 16 3.1 Synthesis of MoC 1-x nanoparticles in a tubular reactor ........................................................... 16 3.2: Synthesis of WC and COP Nanoparticles ................................................................................ 21 3.3 Synthesis of NiP nanoparticles ................................................................................................ 22 3.4 Flow Testing using the Fluigent Flow Apparatus ..................................................................... 23 3.5 Temperature testing of the Sand bath .................................................................................... 24 Chapter 4 Results and Discussions .............................................................................................................. 27 4.1 Synthesis of MoC1-x nanoparticles ......................................................................................... 27 4.2 Tungsten Carbide reaction ...................................................................................................... 32 4.3 Flow Testing ............................................................................................................................. 33 4.4 Temperature distribution of the reactor ................................................................................ 36 4.5 Use of Temperature experiment data ..................................................................................... 42 4.6 Comparison of the Results from the Theoretical Model and the Experimental results ......... 46 Chapter 5 Conclusions ................................................................................................................................ 49 References .................................................................................................................................................. 50 6 Table of Figures 1. Figure 1 …..….9 2. Figure 2 ...….10 3. Figure 3 …….10 4. Figure 4 …….11 5. Figure 5 …….12 6. Figure 6 …….13 7. Figure 7 …….14 8. Figure 8(a) …….16 9. Figure 8(b) ….…17 10. Figure 9 …….18 11. Figure 10 …….19 12. Figure 11 …….20 13. Figure 12 …….21 14. Figure 13 …….23 15. Figure 14 …….24 16. Figure 15 …….25 17. Figure 16 …….25 18. Figure 17 …….27 19. Figure 18 …….28 20. Figure 19 …….29 21. Figure 20 …….30 22. Figure 21 …….30 23. Figure 22 …….31 24. Figure 23 …….32 25. Figure 24 …….33 26. Figure 25 …….34 27. Figure 26 …….36 28. Figure 27 …….42 29. Figure 28 …….43 30. Figure 29 ..44,45 31. Figure 30 ..45,46 32. Figure 31 …….47 7 Chapter 1 Introduction The rate of advancement in technology has greatly affected us to a stage where we are dependent on electrical energy more than any other source. As coal, petroleum and natural gas are used at the current rate we need to find other sources of fuel for example biomass whose synthesis are greatly affected by catalysts for pyrolysis of biomass 1 . The current roadblock with biofuels is the lack of economic conversion technologies. Heterogeneous catalysis offers immense potential in helping to make lignocellulosic biofuels a commercial reality 2 . Their excellent catalytic properties due to their ability to match the ability of metal counterparts for hydrogenation reactions 3 , like in the case of molybdenum carbide nanoparticles which showed more activity compared to their metal counterparts during benzene hydrogenation reactions 3 . Syngas which is actively used for the synthesis of ammonia have been manufactured using high surface area catalysts like Molybdenum and tungsten carbide nanoparticles. Generally, nanoparticle-sized transition metals have a better surface to volume ratio that allows better use of these materials as catalysts. Another Important reason is the abundance of these nanoparticle transition metal oxides over the noble(precious) metals, these metals can be synthesized from raw materials which are available in plenty. This reduces the cost of the catalyst which plays a major role in any manufacturing process 4 .These reasons clearly indicate that moving towards the synthesis of transition metal catalysts like MoC and WC over noble metals is a wiser choice. Furthermore, the activity of the metal carbide catalysts increases with a reduction in the coordination number on the carbon atom whereas reducing the stability of the compound 5 . Studies regarding the flow of liquid through the tubes have been done over a long time. Experimental and mathematical studies to test the laminar compressible flow 6 , flow of gas 7 , flow through cylindrical capillaries 8 . Flow monitoring studies for Nanoparticle synthesis is an important aspect for throughput analysis of product. For the synthesis of nanoparticles in the transition metal, high temperature is required. Monitoring the flow allows us to find discrepancies in flow that arises due to improper heating that arises in the tubes and thereby solidifying of the product which changes the throughput of the process. In the synthesis of transition metal nanoparticles, solvents and used for the sole purpose of improving mixing and reduce axial distribution. The flow of liquid through micro and nano scale synthesis channels results in different flow regimes as mentioned by Gunther et al., 9 . Micromachined flow sensors are also used for flow monitoring 10 . Flow monitoring for harsh environment has been mentioned using the concept of Micro-electro-mechanical systems(MEMS) which are used for harsh environments in the range of up to 500℃. 11 In the oil and gas industry where catalyst are used for conversion into fuels, piezoelectric sensors 12 have been put to use. These thermal sensors are more suited for extreme conditions because of faster response time. Semiconductor sensors have also been put into use for high temperature sensing especially the ones made with SiC where they talk about why this sensor is highly applicable for elevated temperature measurements 13 . 8 Temperature studies in the reactor have been studied to analyze the convective and conductive temperature distribution in it. Temperature distribution in a cylindrical reactor is a common problem that arises when you model a cylindrical reactor. This is done by the use of partial differential equations 14 and by solving these using common mathematical solutions given by particular and complementary solutions. 15 9 Chapter 2 Theory Stage 1 Synthesis of transition metal nanoparticles in flow. Transition metals form the majority of the elements in the periodic table and their true potential wasn’t understood until the last few decades. Batch processes were used for the synthesis of nanoparticles which proved to not be feasible since after every run the reactor had to be cleaned. Continuous processes were the next big thing in the synthesis of Nanoparticles. 2.1: Why is flow synthesis better than batch? Flow synthesis is characterized by 5 different components 1. Syringe pump 2. Tubular connections 3. Reactor setup 4. Product container 5. Product Monitoring As shown in the paper published by Roberts et al., 16 synthesis of NiP nanoparticles have been characterized by the use of these five things as can be seen by the picture below. Figure 1: Synthesis of NiP nanoparticles through a continuous flow process (Roberts, E. J. et al. High- Throughput Continuous Flow Synthesis of Nickel Nanoparticles for the Catalytic Hydrodeoxygenation of Guaiacol. ACS Sustain. Chem. Eng. 5, 632 –639 (2017).) The precursor is sent with the help of a pressure driven setup through the one-way valve. The precursor moves into the reactor and after a residence time inside the reactor, flows out as a product which is collected in a product cylinder. The product is then taken for testing and weight is monitored real time with the analytical balance. Another paper published by Cole et al. 17 shows the clear distinction between the batch and the flow 10 Figure 2: Basic distinction between a batch process and flow in continuous flow 17 . As can be seen in the figure above, Flow production has clear advantages over batch in the way that it simultaneously allows the reaction to happen in the reactor, allows the product to be extracted and then formation of the Nanocrystals at the end of the reaction. The graph shown above between collected product amount vs time allows us to infer 2 things: 1. The flow process being continuous allows us to make products at a steady rate thereby the plot is linear. 2. The batch processes on the other hand has a more temporary approach wherein the collected product amount at every step is higher than that of flow but cleanup and setting up of the reactor seems to be more time consuming. This is shown by the step shaped graph denoted by batch processes. To further clarify this point, Cole et al. 17 , has shown that over the last decade the amount of publication in flow has been increasing based out of a Survey conducted in November of 2017. The following graph clearly shows this point. Figure 3: Graph showing the percentage of publications in the last decade with the term’ continuous ‘in it 17 . 11 2.2 Measurement of Flow data The reactions that take place in flow for the synthesis of catalysts are at an elevated temperature and the whole system is also under pressure. Literature review shows that MEMS sensors are the most apt form of the flow measurement under such conditions. Figure 4: A sample flowchart of the use of flow sensors in various industry where the environment is harsh 11 . As seen in the above pictorial representation by Vivekanathan et al. 11 , the use of sensors in harsh environment has been shown in a broad sense of mind. We are looking at flow sensors, in the corrosion department as the precursors required for the synthesis have high viscosity and they are corrosive. Advances have been made in the flow sensor 18 in terms of 1. Sensitivity 2. Response time 3. Cost effectiveness 4. Power consumption The flow meter used in this experiment is manufactured by Fluigent, FRP. It worked on the following principle 12 Figure 5: A screenshot of the principle behind the sensor used in the Fluigent apparatus( Source: https://www.fluigent.com/product/microfluidic-components/frp-flow-rate-platform/) The sensor used in this system is called a thermal flow sensor, which works on the concept of forced convection. As explained by Vivekanathan et al. 11 , the heat exchange between the liquid and the surroundings is what triggers the sensor to sense the flow of liquid. The two temperature sensors were placed on either side of the heater and any change in temperature due to the flow of liquid gives us the desired result in flow. The flow sensors work on the principle that the temperature signal is converted to a voltage reading which is then sent to the PC to give us real time data for liquid and gases when they flow through the system. 2.3 Temperature distribution 2.3.1 Numerical method The numerical method uses the concept of a heat balance for the system which is the starting point. The heat balance is of the form of a complex differential equation due to the fact that the sand bath is a cylindrical reactor shown as follows. 13 Fig 6: A diagram showing the different axes and the boundary considerations involved in the mathematical process. For the cylindrical reactor, as shown by Ilyas et al., 19 numerical computations must be done on the reactor setup and the solution for the differential equation is given using various concepts like the use of Bessel functions, y"(x) + (d − 1) ∗ 1 𝑥 y′ (x) − (ν − 𝜇 𝑥 2 )y(x) = 0 If we try to model these equations with respect to the problem in hand, the variables simply transform to y(x) being the heat distribution that is the model that is developed using theory, i.e., the dependent variable. The independent variable(x) is the distance along the axial or the radial directions. All the other terms are constants that appear in the differential equation that can be obtained with comparison as shown in section 4.4. Bessel functions are derived when we try to solve partial differential equation using the solution of separation of variables 15 14 Figure 7: Shows the graph for Bessel function of the first and second kind I0, K0 15 The eigenvalues are a set of values related to a particular set of equations to which the equations have solutions for their unknown variables. These are sometimes known as characteristic roots . So the eigenvalues can be any real number which is shown in the paper by Kaitlyn et al., 15 . 2.4 Chemistry of Nanoparticle synthesis Synthesis of nanoparticles involves simple steps where a precursor of the nanoparticle is selected followed by the solvent and using suitable surfactants so that the catalyst is prevented from aggregation. This involves careful selection of these 3 things: 1. Selection of a precursor 2. Selection of a solvent 3. Selection of surfactants For the synthesis of transition metal nanoparticles, use of high boiling point solvents and surfactants are required due to high reaction temperatures. The precursors selected in this case are metal carbonyls which are complex coordinate compounds of the transition state metals. These carbonyls are reduced at high temperatures in the range of around 350˚C and this requires the use of high boiling point solvents and surfactants. As seen by Mourdikoudis et al. 21 , use of oleylamine as a surfactant and coordinating solvent is highly recommended due to the following reasons 1. Because the compound has a long hydrocarbon chain which allows polar capping of the groups, this prevents the compound from aggregating. This allows the growth of the nanoparticle by selective adsorption 21 . 2. Oleylamine also acts as an electron donor at high temperatures thereby becoming a reducing agent. It also has a high boiling point (around 350˚C). The precursors used for the reactions tend to have a really high viscosity which meant the use of solvents which allowed free flowing of the precursors through narrow tubes at high temperatures. Octadecene (ODE), due to the high boiling point at around 315˚C which allows its use as a suitable solvent. 15 As shown in the works of Mourdikoudis et al. 21 , the use of these solvents enable the formation of complexes with the precursor when the metal is magnetic and then reduced at high temperatures due to the thermal reduction of the hexacarbonyls to carbides. Here the molybdenum hexacarbonyl (molybdenum being paramagnetic) forms a complex with the Oleylamine which reduces in the presence of solvents like ODE to form corresponding metal carbides. 16 Chapter 3 Experimental Apparatus 3.1 Synthesis of MoC 1-x nanoparticles in a tubular reactor The nanoparticles were synthesized in a custom-made glass reactor wound up in a helix shaped tube made at the glass shop here at the USC. The reactor was designed for previous projects in the lab and no further changes were made to the reactor. The reactor was placed in a Glas Col heating mantle of size 4L purchased online from HiTechtrader.com. Temperature was measured with the help of J-Type Thermocouple connected to a temperature controller manufactured by J-Kem. The glass reactor, with a volume of 35mL, is placed in the heating mantle which is filled with a coarse sand and this helps secure the heat required to run the reaction. The whole reactor system is kept pressurized by maintaining a back-pressure setup through the use of N2 tanks. The N2 outlet is connected to the system through a glass bottle which allows the entry of N2 into the setup. Visual confirmation of the back-pressure system is found out by connecting the one end of the tube to a vial filled with water. A pressure regulator was connected at the end which had different ratings ranging from 20psig to 40psig. This allowed us to maintain the desired pressure in the setup. When the pressure exceeded the rated value, bubbles are spotted in the vial and the N2 supply to the setup can be switched off. The reactor setup can be shown as follows: 17 Figure 8: a) A picture of reactor system( In Page 16) b) A picture of the syringe and the pressure regulator used for the pushing the precursors through into the reactor Preparation of the MoC 1-x was done by mixing molybdenum hexacarbonyl with oleylamine and octadecene. Various concentrations of the Molybdenum precursor were used. The reaction conditions for the first set of runs are: Concentration of the MoC 1-x : 78mM Rate of flow : 12 ml/hr. Quantity of the precursor: 40 mL Temperature of the reactor: 320 deg C Pressure was setup : 25psig Residence time : 30 minutes The initial syringe pump was manufactured by Harvard Apparatus Model 11 which couldn’t operate at the current pressure. The pump didn’t have enough power to push the liquid forward and the throughput was not uniform. There were numerous cases were the reactor used to be clogged due to uneven pumping of the liquid by the syringe pump. The pump was run for about 2 hours and the products started to come out of the reactor at the half hour mark. The product was collected in a collection cylinder located at the end of the setup. The product was placed in a weighing balance so that real time measurements of the weight of the product was measured with respect to time. This allowed us to monitor the rate of flow out with respect to the mass of the product coming out. 18 Figure 9: A picture of the Harvard 11 syringe pump The reaction conditions for the second set of runs: Rate of Flow : 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor:320 deg C Pressure : 40 psig Residence time : 36 minutes The syringe pump model no 22 was used this time. This pump proved to be more powerful than the pump used initially and hence we could operate the system at a higher pressure of 40psig backpressure. This allowed the reactants a better environment to react and this time the output was more uniform and organized. The pump was run for about 3 hours and the products started to come out at the half hour mark. The product was collected at the end of the setup in a bottle which was placed inside a weighing balance and this allowed us to monitor the weight of the product with respect to time, thereby giving us a better picture for the mass flow rate of the product out. 19 Figure 10: A picture of the Harvard Apparatus 22 pump. Before we talk further about the reactions. We have to look at what happened for the previous sets of runs. As we could see, synthesis of MoC 1-x involved the use of high temperature and relatively higher pressures. This made the flow of the products from the reactor a little uneven. This prompted another question. What is the flow pattern or the flow rate of the product coming out of the reactor? To answer this question, we used a flow counter device manufactured by Fluigent flow measurement apparatus. This device has a screw on holes which allowed the tubing we had to be placed at the inlet and outlet. The device works on the principle wherein a microheater provides a minimal temperature rise to the liquid medium flowing through. The temperature sensors placed on the either side of the heater monitor the change in the temperature and this heat spread is directly related to the flow rate. The device could be connected to a PC through a USB port and a Fluigent measurement software gives us real time data for flow. This device gave us a brief idea for how the fluid flows in the reactor and how uniform the slugs of the liquid are. 20 The third set of runs in the MoC 1-x were run with the help of the Fluigent device. Syringe pump 15 model 22 was the same instrument used for these sets of runs also. The concentration of the precursor was also changed. The reaction conditions are as follows: Concentration of the precursor: 88mM Rate of Flow : 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor:320 deg C Pressure : 40 psig Residence time : 25.5 minutes The syringe pump model no 22 was used this time. The model 22 pump which was used looks to be working in a similar way to the previous runs and the liquid moves forward even with a 40-psig backpressure at the same flow rate as shown on the syringe pump. With similar conditions, the reaction seemed to be working good inside the reactor and the product was coming out at the end of the reactor at a consistent flow rate. The pump was run for about 3 hours and the products Figure 11. Picture of the Fluigent flow measuring apparatus 21 started to come out at the 25-minute mark. The product was collected at the end of the setup in a bottle which was placed inside a weighing balance and this allowed us to monitor the weight of the product with respect to time, thereby giving us a better picture for the mass flow rate of the product out. The main difference lay in the implementation of the Fluigent droplet counter at the product end of the setup before they eventually fall into the container placed to collect the MoC1-X nanoparticles. The data from the Fluigent apparatus was saved in a notepad file which was then incorporated into the system to find out the amount of gas and liquid evolved in the process. Figure 12: The reactor after a run of the MoC1-x clogged with residue 3.2: Synthesis of WC and COP Nanoparticles Synthesis of Tungsten Carbide Nanoparticles Concentration of the precursor: 78mM Rate of Flow : 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor: 320 deg C Pressure : 40 psig Residence time : 21.7 minutes The syringe pump manufactured by Harvard Apparatus model no 22 was used this time. The model 22 pump which was used looks to be working in a similar way to the previous runs and the liquid 22 moves forward even with a 40 psig backpressure at the same flow rate as shown on the syringe pump. With similar conditions, the reaction seemed to be working good inside the reactor and the product was coming out at the end of the reactor at a consistent flow rate. The pump was run for about 3 hours and the products started to come out at the 22-minute mark. The product was collected at the end of the setup in a bottle which was placed inside a weighing balance and this allowed us to monitor the weight of the product with respect to time, thereby giving us a better picture for the mass flow rate of the product out. The main difference lay in the implementation of the Fluigent droplet counter at the product end of the setup before they eventually fall into the container placed to collect the WC nanoparticles. The data from the Fluigent apparatus was saved in a notepad file which was then incorporated into the system to find out the amount of gas and liquid evolved in the process. Synthesis of Cobalt Phosphide Nanoparticles Rate of Flow : 4 ml/hr Quantity of Precursor: 30 mL Temperature of the reactor: 350 deg C Pressure : 40 psig Residence time : 12 minutes The syringe pump manufactured by Harvard Apparatus model no 22 was used this time. The syringe pump used was again put under test because the reaction conditions were different from before. The reactants were filled in a syringe and the pump was started. Initially the pump couldn’t push the liquid forward because of some gaps in connections in the setup and there was loss of pressure. Once that issue was identified and sorted, the reaction was run and a residence time of about 13 minutes was observed. The pump ran for a total of almost 3 hours and the product was collected in a jar placed at the outlet of the setup. A volume of about 25 mL of the product was collected. Similar flow rate testing was employed in this reaction setup also. Fluigent apparatus was used and the software gave us a way to test the flow conditions of the product flowing out. 3.3 Synthesis of NiP nanoparticles This was a new reaction that was run in flow to further supplement the idea of transforming batch processes into flow. The following reaction conditions were employed. Rate of Flow : 4 ml/hr Quantity of Precursor: 30 mL Temperature of the reactor: 350 deg C Pressure : 20 psig 23 Residence time : 30-40 minutes Reactants were loaded onto the syringe and the syringe pump used was the Harvard Apparatus 22 pump. Various runs were conducted on the NiP reaction of different flow rates. Starting off with 6ml/hr and 40psig, the reaction was started, and the precursors were pumped into the reactor. The reactor was clogged because the conditions weren’t suitable for the reaction to take place. We switched to a lower flowrate and lower pressure of 4ml/hr and 20 psig and this supplemented us to proceed with the reaction and better results were observed. The tubes were made sure that they were heated up to around 70 deg C so that the reactants don’t solidify at any point during flow. Fluigent flow measurement apparatus was used to measure the flow rate of the product that came out of the reactor setup. The pump was run for about 3 hours and the first product came out around 40 minutes since the start of the reaction. Figure 13: A picture of the reactor after a run of the NiP synthesis. 3.4 Flow Testing using the Fluigent Flow Apparatus The flow apparatus was manufactured by Fluigent Microfluidics, who specialize in manufacture of flow, pressure and variety of sensors in the microfluidic platform. This device is unidirectional with an arrow mentioned for the direction of the flow. The device comes with a communications hub which allows us to communicate with a PC using an USB. There is a software that could be installed in the PC which can be used to measure real time flow data. The machine works on the principle of the whether the flow is a liquid or gas and senses the change in material with inbuilt sensors. The flow is measured with peaks that denote the presence of liquid and dips that let us know that the flow is gaseous. 24 Figure 14: Sample data that was used to test the measurability of the system. As seen the figure above the peaks denote the flow of water and the peaks maximize based on the size of the droplet as it flows through the setup. The dips denote the flow of gas through the system. For my studies of flow, a syringe filled with water having an orange dye was used and another syringe that was empty. These were then loaded onto the syringe pumps which then allows us to observe the flow patterns at the constant flow rate. 3.5 Temperature testing of the Sand bath During the NiP reactions discussed before, there were huge differences in results of the flow that arose due to a variety of factors. The major one included the clogging of the tubes due to irregular heating inside the sand bath which made a huge lingering doubt. What is the temperature distribution in the sand bath which contained the reactor? The answer to this question can only be provided if a detailed testing of the reactor was undertaken. This was done in 3 different procedures. Procedure 1 included the use of Mathematical models which made the use of concepts from complex mathematical solutions of partial differential equations. The Sand bath was modelled in terms of a cylindrical reactor having a heat source surrounding it. The cylinder was modelled with the use of heat equations in cylindrical coordinates. 25 Figure 15: Cylindrical coordinate geometry ( Picture taken from: https://medium.com/@lucidlearning314/heat-conduction-equation-in-cylindrical- coordinates-3e26402ee1f8) As shown in the figure above, cylindrical coordinate geometry was used to model the cylindrical heating mantle. The mantle can be depicted as follows: The cylindrical sand bath has a diameter of 34 cm and a height of 25 cm with a heating jacket around it. The heating jacket has coils inside of it which are covered by an insulating fabric that allows us to assume that the heat loss through the sides of the mantle were negligible and all the heat generated Figure 16: A graphic representation of the sand bath used for the synthesis of various nanoparticles 26 were kept inside the mantle. To reinforce this concept, this insulator was wrapped with insulating wool wrapped in aluminum foil around the middle of the heating mantle. A hot plate, manufactured by Corning Inc., was used to maintain a uniform heat distribution at the base of the heating mantle. The top of the heating mantle was left open to the atmosphere and covered with insulating aluminum foil. This allowed us to maintain a uniform heat distribution in the sand bath and perform mathematical calculations related to the temperature distributions. Procedure 2 was to measure the heat distribution of the system experimentally. Experimental studies were carried out by filling the reactor with sand till the brim and the temperature measurements were taken at different points in the system. The temperature was measured both radially and axially by the use of T-type and J-type thermocouples. The J-Type thermocouple was used as the reference thermocouple which controlled the temperature in the sand bath. This thermocouple was connected to the temperature controller manufactured by J-Kem which heated the sand bath through a 15 Amp power supply. Another T-Type thermocouple was connected to the sand bath and this was used as the measurement thermocouple. This was connected to a smaller J- Kem temperature controller. This controller was used as a temperature measurement device as this was not related to the temperature controller of the heating mantle by any way. Data was recorded in Excel by manually moving the thermocouple that measures the temperature both axially and radially which was used to compare with the data that was obtained theoretically. 27 Chapter 4 Results and Discussions 4.1 Synthesis of MoC 1-x nanoparticles The first stage included the MoC 1-x nanoparticle synthesis. As discussed in the procedure section the first set of runs that we conducted, we used the following reaction conditions: Concentration of the MoC 1-x : 78mM Rate of flow : 12 ml/hr Quantity of the precursor: 40 mL Temperature of the reactor: 320 deg C Pressure was setup : 25psig Residence time : 30 minutes Figure 17: XRD data from the MoC1-x reaction About 25 mL of the product was collected and analyzed via X-Ray diffraction. The XRD 22 data can be interpreted and the 2𝜽 peaks at 36.6 degrees and 42.2 degrees indicates the presence of the Molybdenum Carbide NPs - 𝜶 -MoC 1-x in the product. The weight of the product with respect to the time was measured in real time by connecting the weighing balance to the computer. The values were recorded in a MATLAB code which communicated with the weigh balance. The weight was recorded every second and a graph between the mass of the product and the time measured were plotted as follows: 28 Figure 18: Mass of the product collected vs time for the first set of reactions As seen from the figure above, the graph in blue, which denotes the first runs for the NP synthesis is almost linear with slight variations which suggests that the flow of the product coming out is uniform. The equations derived from the graphs is an indicator of the initial weight of the bottle when inside the weight balance. The y-intercept values shown gives us how the bottle weighed initially and kept increasing at a steady rate. The graph shown above marked in orange, denotes the second set of runs for the NP synthesis shows us that the variations in the mass of the product with time was not a linear plot. This was due to irregular slugs that arose in the product side of the reactor setup due to differential heating. The product looked to solidify at the end of the tubes which was attributed to the heat not enough to let the fluid flow. This was solved by covering the tubes with a heat tape which was controlled with a temperature controller and this wrapped with aluminum foil to sustain the heat within the tube. The graphs are a clear indicator that further studies are required to ensure a constant product throughput. Further runs of the reaction was established for the same. 29 Figure 19: XRD data for the synthesis of MoC1-x NPs for the above runs About 23 mL of the product was collected to test the product in XRD. The peaks were not as sharp as the previous runs indicating poor crystalline structure 22 of the product. But the peaks at the corresponding angles indicate the presence of MoC1-x nanoparticles. Second set of runs Rate of Flow: 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor: 320 deg C Pressure: 40 psig Residence time: 36 minutes The graphs plotted below show the mass flow rate of the product coming out of the reactor setup for the second set of runs and the y-intercept of the slope equation gives us the initial weight of the product collection container. As can be seen the blue graph shows us that this run has a straight slope which shows that the product that flowed out in this reaction gives us a good and steady output flowrate. But the run after that denoted by the orange bar shows us that the output flowrate is not perfect and various discrepancies at the beginning of the reactor setup was due to clogging which arose because of an error in the connections between the tubes. This was sorted out as soon as the problem was identified, and the flow rate was consistent throughout after that. 30 Figure 20: Graph indicating the Mass of the product collected vs the time The third set of runs: The third set of runs produced about 33 mL of the product and the reaction conditions were as follows: Rate of Flow : 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor: 320 deg C Pressure : 40 psig Residence time : 25.5 minutes Figure 21: XRD Pattern for the third set of runs. The XRD pattern shows a similar trend of the peaks showed us that the product obtained in this set of runs were the best in composition that was required as the peaks are pretty sharp indicating the 31 structure of the crystal to be really good and the flow rate was monitored with a flow measurement device. Figure 22: The graph indicates mass of the product collected vs the time for the third set of runs. The graph between the mass flow of the product that came out with respect to the time was plotted for this case and the y-intercept gives the weight of the bottle that was kept inside the weighing balance initially. As can be seen in the orange plot, the weight of the bottle was a little inconsistent at the beginning due to issues with solidifying of the product at the end of the product line. This was sorted by tightly sealing every section of the tube with a heat tape and aluminum foil. This helped the flow become more consistent hence the graph becomes pretty linear which implies that the throughput was uniform in the end of the process. The blue graph denotes the next run in this set of reactions run and the weight of the bottle was given by the y-intercept. This run gives us a good throughput because the mass of the product changed in a consistent way with time. This was due to proper heating of every section of the tube and this gave us a good product composition. 32 4.2 Tungsten Carbide reaction The reaction conditions for this reaction are as follows: Rate of Flow : 12 ml/hr Quantity of Precursor: 40 mL Temperature of the reactor: 320 deg C Pressure : 40 psig Residence time : 21.7 minutes Figure 23: The mass of the product collected (Tungsten Carbide Nanocrystals) vs the time taken to collect it. About 26 mL of the product was collected in this reaction. The weighing balance was tared before the start of the reaction hence the value was really close to 0. The mass of the product collected vs the time gave us a picture of the throughput or the product flow rate. Since the product did not solidify at the end of the product line, the results looked really consistent and a linear graph was obtained over the entire time range. 33 4.3 Flow Testing For this section of the testing, the Fluigent apparatus was used which allowed unidirectional flow through the sensor situated inside the apparatus. The testing was done with the use of orange dyed water and air was used in the other syringe. Data obtained from this was plotted in a scatter plot and the inferences were noted: Figure 24: The figure indicates the difference between the liquid and gas droplets that arose during the testing phase of the Fluigent apparatus As can be seen in this graph shown above, the full scale % value is maximum in liquid droplets and the values get closer to zero when there are air droplets in between 2 liquid droplets. It shows that the liquid is quite consistent with the flow initially and then slows down in between and then becomes consistent again. Shown below is a screenshot of the flow meter giving us values when the reaction was running giving us real time data related to the device. The panel on the left gives us details for saving the files. Pressing the log button allows us to save the data in the PC which could be transferred to a MATLAB file which analyzes the data giving us the flowrate in terms of volume. We can use this to calculate the residence time and compare it with the theoretical flow rate. -400 -200 0 200 400 600 800 1000 1200 1400 0 20 40 60 80 100 120 Full Scale % Time(s) Full Scale % vs time 34 Figure 25: A screenshot gives us an idea of the peaks and the dips which indicate the flow of liquid and gas respectively Calculations were done in MATLAB using the data measured using the Fluigent apparatus. The data stored in a notepad file was exported to the MATLAB workspace and then the following steps were applied: 1. The volume of liquid was measured with the time gap between the two drops. With the flowrate that we are pumping the liquid in, the volume of each liquid droplet was calculated as follows: 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 = 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆 𝒈𝒂𝒑𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝑭𝒖𝒍𝒍 𝑺𝒄𝒂𝒍𝒆 % 𝑽𝒂𝒍𝒖𝒆𝒔 𝑻𝒊𝒎𝒆 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒕𝒉𝒆 𝒗 𝒂𝒍𝒖𝒆𝒔 2. The volume of gas was measured similarly with the time gap between the two drops. With the flowrate that we are pumping the liquid in, the volume of each liquid droplet was calculated as follows: 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒔 = 𝑫𝒊𝒇𝒇𝒆𝒓 𝒆 𝒏𝒄𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆 𝒈𝒂𝒑𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝑭𝒖𝒍𝒍 𝑺𝒄𝒂𝒍𝒆 % 𝑽𝒂𝒍𝒖𝒆𝒔 𝑻𝒊𝒎𝒆 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆𝒔 3. This gives us the volume of the liquid droplet that passed through the sensor in that time frame. This value was measured at room temperature, so to calculate the value at a higher temperature 35 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 = 𝑽𝒐𝒍𝒖𝒎𝒆 ∗ 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒂𝒕 𝒊 𝒏𝒊𝒕𝒊𝒂𝒍 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 𝒇𝒐𝒓 𝒍𝒊𝒒𝒖𝒊𝒅 The ratio on the right-hand side denotes the elevated mass for the liquid with the numerator denoting the mass at the elevated temperature (320˚C) and the denominator denoting the mass at starting temperature (60˚C). 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒈𝒂𝒔 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 = 𝑽𝒐𝒍𝒖𝒎𝒆 ∗ 𝑬𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 (𝑲 ) 𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 (𝑲 ) The numerical values for the ratios are that the elevated temperatures are 320˚C and Initial temperature is measured at 60˚C. 4. This volume was then used to calculate the flowrate of the liquid flowing out 𝑭𝒍𝒐𝒘 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒈𝒂𝒔 𝒂𝒕 𝒊𝒏𝒊𝒕𝒂𝒍 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 = 𝑭𝒍𝒐𝒘𝒓𝒂𝒕𝒆 𝒂𝒕 𝒓𝒐𝒐𝒎 𝒕𝒆𝒎𝒑𝒆𝒓 𝒂 𝒕𝒖𝒓𝒆 ∗ 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝑮𝒂𝒔 The Volume of the liquid and the gas denoted here are calculated from Steps 1 and 2. 5. The flow rate of the liquid initially is given by the values on the syringe pump and the flow rates at elevated temperatures are calculated: 𝑭𝒍𝒐𝒘 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 = 𝑭𝒍𝒐𝒘𝒓𝒂𝒕𝒆 𝒂𝒕 𝒓𝒐𝒐𝒎 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 ∗ 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒊𝒏𝒊𝒕𝒂𝒍 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 6. Flow rate of the gas at elevated temperature is calculated based on the ratio of the elevated volumes of the liquid and the gas: 𝑭𝒍𝒐𝒘 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒈𝒂𝒔 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕 𝒆 𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 = 𝑭𝒍𝒐𝒘𝒓𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒊𝒒𝒖𝒊𝒅 ∗ 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝑮𝒂𝒔 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 7. The total flow rate is given by the sum of the results from Step 5 and 6 which is the flow rates of the liquid and the gas at elevated temperatures. 𝑻𝒐𝒕𝒂𝒍 𝑭𝒍𝒐𝒘 𝒓𝒂𝒕𝒆 = 𝑭𝒍𝒐𝒘𝒓𝒂𝒕𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 + 𝑭𝒍𝒐𝒘𝒓𝒂𝒕𝒆 𝒐𝒇 𝒕 𝒉𝒆 𝒈𝒂𝒔 𝒂𝒕 𝒆𝒍𝒆𝒗𝒂𝒕𝒆𝒅 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆𝒔 This residence time was then calculated using: 𝑹𝒆𝒔𝒊𝒅𝒆𝒏𝒄𝒆 𝑻𝒊𝒎𝒆 = 𝑽𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒓𝒆𝒂𝒄𝒕𝒐𝒓 𝑻𝒐𝒕𝒂𝒍 𝑭𝒍𝒐𝒘 𝒓𝒂𝒕𝒆 36 4.4 Temperature distribution of the reactor Procedure 1: Use of Mathematical Model Figure 26: A representation of the heating mantle filled with Sand. The dimensions of the Heating mantle are as follows: Diameter of the heating mantle: 34cm Height of the heating mantle: 25 cm Assumptions: 1. Since the heating mantle is covered by a coil that heats up the device, the heat is generated from the outside and moves inside radially. So, variation in radial direction is considered whereas variation along the angular direction is same as the heating is uniform all around. 2. The variation of the heat along the axial direction is also considered. As the top of the reactor is open this variation becomes crucial too. 3. The heat flux from the heating coils surrounding the heating mantle is a constant. 4. Steady state has been reached before measurement of readings. 5. Heat loss through the walls of the mantle are negligible because of the use of the hot plate for the base and the aluminum foils for the side. 6. Power loss due to the length of the cable are negligible. For the heat conduction we start from the basic temperature conduction equations: 𝛁 𝑻 + 𝒒 = 𝝆𝑪𝒑 ∆𝑻 ……………….1 Heating Mantle filled with Sand 37 The term on the right-hand side of the equation can be assumed to be 0 because ∆𝑻 is negligible because the values have reached steady state. So, equation 1 becomes 𝛁 𝑻 + 𝒒 = 𝟎 ………………….2 The first term is the variation of temperature in different directions in cylindrical coordinates: 𝛁 𝑻 = 𝟏 𝒓 𝝏 𝝏𝒓 (𝒌𝒓 𝝏𝑻 𝝏𝒓 ) + 𝟏 𝒓 𝟐 𝝏 𝝏 ∅ (𝒌 𝝏𝑻 𝝏 ∅ ) + 𝝏 𝝏𝒛 (𝒌 𝝏𝑻 𝝏𝒛 ) ……………………3 The heat generation term can be calculated using the electrical energy being converted to heat energy. The power of the J-Kem electrical setup allows the temperature to reach the set value at around 2.5 hours which was measured. Q= Power of the electrical system*t= VIt=15amp*120 Volts*(150*60) = 16200KJ is the energy being given to the heating coil to heat the system to the set temperature. So, we need to solve the differential equation : 𝟏 𝒓 𝝏 𝝏𝒓 (𝒌𝒓 𝝏𝑻 𝝏𝒓 ) + 𝟏 𝒓 𝟐 𝝏 𝝏 ∅ (𝒌 𝝏𝑻 𝝏 ∅ ) + 𝝏 𝝏𝒛 (𝒌 𝝏𝑻 𝝏𝒛 ) = −𝟏𝟔𝟐𝟎𝟎𝑲𝑱 ……………….4 The solution to this equation can be divided into two different solutions. The first one is the complimentary solution which is given by putting the right-hand side to 0. The Total solution T(r,z)= Complimentary solution+ Particular Solution So, the equation becomes: 𝟏 𝒓 𝝏 𝝏𝒓 (𝒌𝒓 𝝏𝑻 𝝏𝒓 ) + 𝟏 𝒓 𝟐 𝝏 𝝏 ∅ (𝒌 𝝏𝑻 𝝏 ∅ ) + 𝝏 𝝏𝒛 (𝒌 𝝏𝑻 𝝏𝒛 ) = 𝟎 …………….5 Now putting the assumptions to use, the second term goes to zero as we have assumed that heat variation is only along the radial and axial directions. This leads us to the differential equation to this way: 𝟏 𝒓 𝝏 𝝏𝒓 (𝒌𝒓 𝝏𝑻 𝝏𝒓 ) + 𝝏 𝝏𝒛 (𝒌 𝝏𝑻 𝝏𝒛 ) = 𝟎 ……………………6 This is a partial differential equation in 2 variables which is given by: 𝟏 𝒓 𝝏 𝝏𝒓 (𝒓 𝝏𝑻 𝝏𝒓 ) + ( 𝝏 𝟐 𝑻 𝝏 𝒛 𝟐 ) = 𝟎 ….……………….7 We can use separation of variables to solve this equation which can be explained by assuming the Solution to be T(r,z)=F(r)G(z) where F(r) can be the variation in the radial direction alone and G(z) is the variation in the axial direction alone. Thus, the partial differential equation gets to a normal differentiation format: 38 𝑮 (𝒛 ) 𝒅 𝟐 𝑭 𝒅 𝒓 𝟐 + 𝑮 (𝒛 ) 𝒓 𝒅𝑭 𝒅𝒓 = 𝑭 (𝒓 )( 𝒅 𝟐 𝑮 𝒅 𝒛 𝟐 ) = 𝜶 𝟐 …………………………….8 α here denotes the eigenvalues for this equation. Dividing the equation 8 with F(r)*G(z) gives us 𝑭 " 𝑭 + 𝟏 𝑭 ∗𝒓 𝒅𝑭 𝒅𝒓 = 𝜶 𝟐 …………………………………9 and 𝟏 𝑮 ( 𝒅 𝟐 𝑮 𝒅 𝒛 𝟐 ) = 𝜶 𝟐 …………………………….10 Equation 9 can be solved easily as it is a normal differential equation whose solution is given by: 𝑭 " 𝑭 + 𝟏 𝒓 ( 𝑭 ′ 𝑭 ) = 𝜶 𝟐 ……………….……………11 Now 𝜶 𝟐 could have 3 choices 𝜶 𝟐 = { > 𝟎 < 𝟎 = 𝟎 Case 1 : 𝜶 𝟐 > 𝟎 This is given by 𝑭 " + 𝟏 𝒓 (𝑭 ′) − 𝜶 𝟐 𝑭 = 𝟎 ……………………………12 The solution to this is given by y"(x) + (d − 1) ∗ 1 𝑥 y′ (x) − (ν − 𝜇 𝑥 2 )y(x) = 0 Comparing it gives us: d=2, ν = α 2 , μ = 0 The solution is given by F(r)= C 1K 0(r α)+C 2I 0(r α) which is a modified Bessel equation We must apply the boundary conditions to this system of equations: BC’s for the radial direction: @r=R, −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 "; @r=0, −𝒌 𝒅𝑭 𝒅𝒓 = 𝟎 𝒒 " = 𝒒 𝑨 where A= 2*π*r*L=2 π *34*25=0.534m 2 𝒒 " = 𝟏𝟖𝟎𝟎 𝟎 . 𝟓𝟑𝟒 = 𝟑𝟑𝟕𝟎 . 𝟕𝟖 𝑾 /𝒎 𝟐 As shown by Hamdam et al., k for coarse dry sand is 0.25 W/mK Thus −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 " becomes 𝒅𝑭 𝒅𝒓 = 𝟏𝟑𝟒𝟖𝟑 . 𝟏𝟒𝟔 K/m So differential of the Bessel equation gives: 𝒅𝑭 𝒅𝒓 = 𝑪 𝟏 𝑲 −𝟏 (𝒓𝜶 ) + 𝑪 𝟐 𝑰 −𝟏 (𝒓𝜶 ) ……………………………14 39 Applying both boundary conditions gives us the value that C 1=C 2=0. This gives us a trivial solution. Case 2: 𝜶 𝟐 < 𝟎 This is given by 𝑭 " + 𝟏 𝒓 (𝑭 ′) + 𝜶 𝟐 𝑭 = 𝟎 The solution to this is given by y"(x) + (d − 1) ∗ 1 𝑥 y′ (x) − (ν − 𝜇 𝑥 2 )y(x) = 0 Comparing it gives us: d=2, ν = −α 2 , μ = 0 The solution is given by F(r)= C 1K 0(r𝒊 α)+C 2I 0(r iα) which is a modified Bessel equation. The imaginary term arises because of the presence of a negative sign on the 𝛎 term. We must apply the boundary conditions to this system of equations: BC’s for the radial direction: @r=R, −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 "; @r=0, −𝒌 𝒅𝑭 𝒅𝒓 = 𝟎 𝒒 " = 𝒒 𝑨 where A= 2*π*r*L=2 π *34*25=0.534m 2 𝒒 " = 𝟏 . 𝟖𝟎𝟎 𝟎 . 𝟓𝟑𝟒 = 𝟑 . 𝟑𝟕𝟎 𝑾 /𝒎 𝟐 As shown by Hamdam et al., k for coarse dry sand is 0.25 W/mK Thus −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 " becomes 𝒅𝑭 𝒅𝒓 = 𝟏𝟑 . 𝟒𝟖𝟑 K/m So differential of the Bessel equation gives: 𝒅𝑭 𝒅𝒓 = 𝑪 𝟑 𝑲 −𝟏 (𝒓𝒊𝜶 ) + 𝑪 𝟒 𝑰 −𝟏 (𝒓𝒊𝜶 ) …………………………….14 Applying both boundary conditions gives us the value that C 3=C 4=0. This gives us a trivial solution Case 3: 𝜶 𝟐 = 𝟎 This is given by 𝑭 " + 𝟏 𝒓 (𝑭 ′) = 𝟎 This is an ordinary differential equation and the solution is given by: 𝑭 " 𝑭 ′ = − 𝟏 𝒓 Integrating both sides gives us 𝑭 ′ = 𝑪 𝟓 𝒍𝒏 (𝒓 ) Further integration gives, 𝑭 (𝒓 ) = −𝑪 𝟓 (𝒓𝒍𝒏 (𝒓 ) − 𝒓 ) + 𝑪 𝟔 40 We must apply the boundary conditions to this system of equations: BC’s for the radial direction: @r=R, −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 "; @r=0, −𝒌 𝒅𝑭 𝒅𝒓 = 𝟎 𝒒 " = 𝒒 𝑨 where A= 2*π*r*L=2 π *34*25=0.534m 2 𝒒 " = 𝟏 . 𝟖𝟎𝟎 𝟎 . 𝟓𝟑𝟒 = 𝟑 . 𝟑𝟕𝟎 𝑾 /𝒎 𝟐 As shown by Hamdam et al. 23 , k for coarse dry sand is 0.25 W/mK Thus −𝒌 𝒅𝑭 𝒅𝒓 = −𝒒 " becomes 𝒅𝑭 𝒅𝒓 = 𝟏𝟑 . 𝟒𝟖𝟑 K/m Applying the first boundary condition gives: @r=17cms, 𝒅𝑭 𝒅𝒓 = −𝑪 𝟓 (𝒍𝒏 (𝒓 ))=13.483/ln(0.17) C 5 = 7.609 K @r=0, 𝒅𝑭 𝒅𝒓 = 𝟎 ; T=Tmin; C 6 = Tmin Thus 𝑭 (𝒓 ) = 𝑻 𝒎𝒊𝒏 𝟕 . 𝟔𝟎𝟗𝒓 (𝒍𝒏 (𝒓 ) − 𝟏 ) The value of (ln(r)-1) <<1 because the value of ln(r) is very close to 0 we can safely assume the results changes to the following: 𝑭 (𝒓 ) = 𝑻 𝒎𝒊𝒏 + 𝟕 . 𝟔𝟎𝟗𝟒𝟐𝒓 The second part of Equation 8 is determined in a similar way 𝑮 "/𝑮 = 𝛽 𝟐 for 𝛽 2 = { > 0 < 0 = 0 For 𝛽 2 > 0 𝑮 " − 𝜶𝜷 𝟐 𝑮 = 𝟎 …………………………………………15 Solution is given by : 𝑮 (𝒛 ) = 𝑪 𝟕 𝒆 𝜷𝒛 + 𝑪 𝟖 𝒆 −𝜷𝒛 …………………………………………16 Boundary conditions for the axial direction includes: @z=0, G(z)=h*A*(Ts-Ta) h can be calculated from modified equations such as in the case of natural convection across a hot surface. h= 𝑪 ∗ ( 𝑻𝒔 −𝑻𝒂 𝒅 ) 𝒌 = 𝟏 . 𝟑𝟐 ∗ ( 𝟓𝟓𝟑 −𝟐𝟗𝟖 𝟎 .𝟏𝟕 ) 𝟎 .𝟐𝟓 = 8.214 W/m 2 ˚C 41 @z=0, G(z) = 8.2114*0.0907*(593-298) = 294.03 ˚C = 567.03 K @z=L, −𝒌 𝒅𝑮 𝒅𝒛 = −𝒒 "( because of the use of the hot plate) 𝒒 " = 𝒒 𝑨 where A= π*r 2 = π*17*17= 0.0907m 2 𝒒 " = 𝟏 . 𝟖𝟎𝟎 𝟎 . 𝟎𝟗𝟎𝟕 = 𝟏𝟗 . 𝟖𝟒𝟓𝟔𝟒𝟒 𝑾 /𝒎 𝟐 Substituting the value of k and q”. −𝟎 . 𝟐𝟓 𝒅𝑮 𝒅𝒛 = −𝟏𝟗 . 𝟖𝟒𝟓𝟔𝟒𝟒 𝒅𝑮 𝒅𝒛 = 𝟕𝟗 . 𝟑𝟖𝟐𝟓𝟕 𝑲 /𝒎 Substituting the BCs in the solution gives us 2 equations: Equation 1: 𝑪 𝟕 + 𝑪 𝟖 = 𝟓𝟔𝟕 . 𝟎𝟑𝑲 Equation 2: 𝑪 𝟕 𝒆 𝟎 .𝟐𝟓𝜷 + 𝑪 𝟖 𝒆 −𝟎 .𝟐𝟓𝜷 = 𝟕𝟗 . 𝟑𝟖𝟐𝟓𝟕 𝑲 /𝒎 Solving : 𝑪 𝟕 = 𝟓𝟔𝟕 . 𝟎𝟑 − 𝑪 𝟖 ; 𝑪 𝟖 = 𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 −𝟓𝟔𝟕 .𝟎𝟑 𝒆 −𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) Thus 𝐶 7 = 𝟓𝟔𝟕 .𝟎𝟑 𝒆 𝟎 .𝟐𝟓 𝛽 −𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) Case 2 for 𝛽 2 < 0 and Case 3 for β=0, we get trivial solutions, hence we can safely say that 𝑮 (𝒛 ) = 𝟓𝟔𝟕 . 𝟎𝟑 𝒆 𝟎 .𝟐𝟓 𝛽 − 𝟕𝟗 . 𝟑𝟖𝟐𝟓𝟕 (𝒆 𝟎 .𝟐𝟓 𝛽 − 𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 𝟎 .𝟐𝟓𝜷𝒛 + 𝟕𝟗 . 𝟑 𝟖𝟐𝟓𝟕 − 𝟓𝟔𝟕 . 𝟎𝟑 𝒆 −𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 − 𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 −𝟎 .𝟐𝟓𝜷𝒛 − 𝑻 𝒎𝒊𝒏 Thus, the complementary solution for the equation is : T(r,z)=F(r)G(z) =(𝑻 𝒎𝒊𝒏 + 𝟕 . 𝟔𝟎𝟗𝒓 )( 𝟓𝟔𝟕 .𝟎𝟑 𝒆 𝟎 .𝟐𝟓 𝛽 −𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 𝟎 .𝟐𝟓𝜷𝒛 + 𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 −𝟓𝟔𝟕 .𝟎𝟑 𝒆 −𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 −𝟎 .𝟐𝟓𝜷𝒛 − 𝑻 𝒎𝒊𝒏 ) Where Tmin is the Temperature of the sand bath at the center of it. α,β are eigenvalues given by 1,2,3…… Substituting in the original equation to find out the particular solution: Since there is no constant term arising in complimentary solution, it is safe to say that the particular solution is: 42 T(r,z)={ 𝑻 𝒎𝒊𝒏 − 𝟕𝟔𝟎𝟗 . 𝟒𝟐𝒓 )( 𝟓𝟔𝟕 .𝟎𝟑 𝒆 𝟎 .𝟐𝟓 𝛽 −𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 𝟎 .𝟐𝟓𝜷𝒛 + 𝟕𝟗 .𝟑𝟖𝟐𝟓𝟕 −𝟓𝟔𝟕 .𝟎𝟑 𝒆 −𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 −𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 −𝟎 .𝟐𝟓𝜷𝒛 −𝑻 𝒎𝒊𝒏 ) where the temperature is measured in Kelvin. 4.5 Use of Temperature experiment data The data for temperature was measured in the following steps: Case 1: The temperature of the sand bath was set to 320℃ Temperature of the hot plate: 120℃ The inferences from the graphs below: 1. The hot plate placed at the bottom serves the purpose of providing the same temperature distribution at base of the heating mantle. It was observed earlier that the temperature in the middle was the only section where the temperature was the set point value. 2. The value of temperatures was all measured once they reached steady state and every time the thermocouple moved, due to the friction between the thermocouple and sand cause a slight increase in temperature which reduced to these values once steady state was achieved. 3. Having an aluminum foil on the top improves the temperature distribution slightly but such variations in temperature is the reason for the irregular product throughput. A graph can be plotted with between the height of the reactor to the temperature distribution along the height. Figure 27 : A plot of the temperature distribution at 320 ℃ 280 290 300 310 320 330 340 0 5 10 15 20 25 30 Temperature height of the reactor Temperature distribution at 320deg C Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil Linear (Temperature In the reactor with the lid) 43 The graph plotted shows us that the temperature of the sand bath varies a lot initially without the presence of the aluminum foil which are the two points of entry and exit for the reactants. Care must be taken for the reactants when they proceed through this region which might cause discrepancies in the flow patterns in the product line. Temperature of the Sand bath was set to 350℃ For this case, a new idea was brought into place which was to change the temperature of the hot plate at the bottom of the heating mantle. This allowed us to maintain a more uniform temperature throughout but the variations in temperature from the top to the middle of the reactor is still high. This can be attributed to the air pocket available between the aluminum foil and the sand bed. This gap cannot be avoided in the current reactor setup since the tubes are made of glass and are fragile. Increasing the temperature of the hot plate had a significant change as the value was closer to the set point which meant that 70% of the reactor was above the set point which still meant that the reactant could solidify at the entry or the exit point which meant that the throughput would not be uniform. The value in red indicated that the temperature was maximum at that exact point. Figure 28 : A graph denoting the temperature distribution at 350℃ for the four cases The graph plotted with these set of values are really close to each other thus these overlap except for the initial stages of the height of the sand bath. This meant that the same issue arose in both the 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 Temperature( degC) Height(cm) Temperature distribution vs height at 350 deg C Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil Temperature In the reactor with the aluminium lid Temperature in the reactor without the aluminium foil Linear (Temperature In the reactor with the lid) 44 temperatures. The linear plotted for the range of values is really close to 350 ℃ which meant that the sand bath is still useful, but care should be taken when the liquid flows through the initial stages of the sand bath. Variation of Temperature with respect to the radius of the reactor. For this set of values, 3 different height were chosen. The reactor could be divided into three equal parts. The first part of the reactor being in the first 8 cms of the reactor. The height that the thermocouple which measured the value of the temperature at different points on the radius of the sand bath. Holes were pored in the aluminum foil at different points along the radius of the cylinder. The distance between the holes were 1cm apart which meant that there were 17 holes from the center. Graphs plotted for the different heights with and without the aluminum lid are as follows: 280 300 320 0 2 4 6 8 10 12 14 16 18 Temperature height of the reactor Temperature distribution at 320deg C at 5cms Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil Linear (Temperature In the reactor with the lid) 310 315 320 325 330 0 2 4 6 8 10 12 14 16 18 Temperature height of the reactor Temperature distribution at 320deg C at 13 cms Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil 45 Figure 29: (Top to bottom) The graphs for the temperature distribution along the radial direction at 5 cm, 13 cm and 21 cm. Variation of the temperature with respect to radius of the reactor at 350 deg C 310 315 320 325 330 0 2 4 6 8 10 12 14 16 18 Temperature height of the reactor Temperature distribution at 320deg C 21 cms Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil Linear (Temperature In the reactor with the lid) 315 320 325 330 335 340 345 350 0 5 10 15 20 Temperature distribution Radius of the reactor Radial temperature distribution at 5cm Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil 320.1 353 354 355 356 357 358 359 360 361 0 5 10 15 20 Temperature distribution Radius of the reactor Radial temperature distribution at 13 cm Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil 46 Figure 30: (From top to bottom): The data were plotted in Excel and the temperature distribution radially was carried out. 4.6 Comparison of the Results from the Theoretical Model and the Experimental results • Theoretical predictions were aligned with the experimental results, but the heating mantle proved to be ineffective in the way that the variations in temperature were really high along both the radius and the axial directions. The variation along the radial and axial direction can be seen through the graphs from the experimental values. 1. The variation along the radial direction can be seen as a linear relationship between the temperature measured along the Y-axis and the radial distance measured along the X-axis. These variations can be seen to change linearly with the graph intercepting at the minimum temperature possible which is at the center of the mantle. 2. The variation along the axial direction can be seen as an exponential relationship between the temperature measured along the Y-axis and the axial height measured along the X-axis. The values increase exponentially initially and then saturate at the maximum values attained which show that the temperature is maximum along the center of the heating mantle • Graphs plotted with experiments showed a linear relationship of temperature with radial distance and this is similar to the theoretical model developed which showed that the 𝑭 (𝒓 ) = 𝑻 𝒎𝒊𝒏 + 𝟕𝟔𝟎𝟗 . 𝟒𝟐 𝒓 ; 0<r<0.17 This relationship of the radius with temperature is linear too with the intercept on the y-axis being the T-minimum at the center of the heating mantle which is similar to the value attained from the experimental results 345 346 347 348 349 350 351 0 5 10 15 20 Temperature distribution Radius of the reactor Radial temperature distribution at 21 cm Temperature In the reactor with the lid Temperature in the reactor without the aluminium foil 47 • Graphs plotted with experiments showed an exponential relationship for variation along the axial direction which is similar to the axial variation model developed which showed that 𝑮 (𝒛 ) = 𝟕𝟗 . 𝟑𝟖𝟐𝟓𝟕 − 𝟓𝟔𝟕 . 𝟎 𝟑 𝒆 𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 − 𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 𝟎 .𝟐𝟓𝜷𝒛 + 𝟕𝟗 . 𝟑𝟖𝟐𝟓𝟕 − 𝟓𝟔𝟕 . 𝟎𝟑 𝒆 −𝟎 .𝟐𝟓 𝛽 (𝒆 𝟎 .𝟐𝟓 𝛽 − 𝒆 −𝟎 .𝟐𝟓 𝛽 ) 𝒆 −𝟎 .𝟐𝟓𝜷𝒛 − 𝑻𝒎𝒊𝒏 The variation along the axial direction comes as an exponential relationship with distance which is similar compared to the graphs that were obtained from the experimental results. The results from the experimental and theoretical results can be depicted as follows: Fig 31: (top) Comparison of the theoretical and experimental results at 320˚C (bottom) Comparison of the theoretical and experimental results at 350˚C 0 100 200 300 400 500 0 0.05 0.1 0.15 0.2 0.25 0.3 Temperature(˚C) Height(m) Comparison of the theoretical and experimental results at 320 ˚C Theoretical results Experimental results 0 100 200 300 400 500 0 0.05 0.1 0.15 0.2 0.25 0.3 Temperature(˚ C) Height(m) Comparison of the theoretical and experimental results at 350 ˚ C Theoretical results Experimental results 48 On comparison of the results obtained from experimental results, the plots seem to be similar to the values that we got at lower heights but as the height increases, the values tend to deviate from the original behavior. The following reasons could be the answer to the discrepancies: 1. Non-uniform heating of the mantle could result in a stark difference in the temperature variation along the height. The mantle as it is kept in an environment where the surrounding temperature is very low compared to the surface temperature, heat transfer rates increases due to natural convection. 2. The values obtained through calculations at low heights can be seen as similar to the experimental values with minimum arising around 280˚C for the temperature set at 320 ˚C and a minimum arising around 300˚C for the temperature set at 350˚C A solution to avoid the use of a heating mantle would be to incorporate furnaces in its place so that uniform heating can be ensured. 49 Chapter 5 Conclusions Stage 1: The first step was the synthesis of catalyst nanocrystals namely Molybdenum Carbide, Tungsten Carbide, Cobalt Phosphide, Nickel phosphide which yielded results that can be classified as: 1. The XRD patterns for the MoC 1-x reactions were really good for a couple of runs with the 2𝜽 values measuring at 36.6 degrees, 42.2 degrees which implied the presence of the MoC nanoparticles 2. Mass of the product was measured with the respect to time and graphs were plotted. The graphs suggested that there could be clogging in the reactions that ran be it MoC, WC, CoP or NiP in at least one of the runs. The reason for something like this to happen was due to the fact that there was uneven heating in the tubes and also uneven heating in the reactor side. This was sorted by completely sealing the tubes with aluminum foil and heat tape. This maintained the tubes at around 80 ℃. 3. Flow rate of the product was analyzed too with the help of Fluigent Apparatus which used the concept of thermal flow sensor, based on the idea of a small difference in temperature which were converted to electrical signals. Stage 2: The second step was the testing of the Fluigent apparatus and this was done with water, food coloring and air and the different flow patterns were observed. The only drawback of the Fluigent apparatus was because of its low tolerance to high temperatures (>80 ℃ ). This could be solved by fabricating sensors with the help of SiC, GaAs and many more methods like the use of Polymers and ceramics too as mentioned by Vivekananthan et al., 11 . Stage 3: The heating mantle that sustains or heats up the reactor was modelled both mathematically and experimentally. Mathematically, the heating mantle filled with sand was modelled as a cylindrical reactor made of sand with variations in the axial and radial directions. The differential equations were solved with the use of Bessel equations and figuring out the particular and complementary solutions. 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Abstract (if available)

Abstract At this day and age where the world is moving towards more efficiency, we are trying to find ways to make every process continuous from a batch process. Applying these criteria on the synthesis of catalysts requires the use of a reactor which allows continuous flow and constant monitoring. This is hence carried out in 2 steps, the first step conducting the reactions and the second one was to check for consistency of the thermodynamic aspect of the reactor. Custom made glass reactors were used to compare results from both batch and continuous flow. These reactors were used for the synthesis of catalyst nanoparticles like MoC, WC and tested in terms of XRD and mass throughput flowing out. ❧ The second part wherein the temperature in the sand bath was measured and an analysis of the reactor was made in terms of temperature distribution with respect to height of the reactor and width of the reactor and simultaneously carrying out these in numerical simulations too. Methods to improve the heating system in the reactor was carried out by reducing any chance of heat loss from the reactor by designing an appropriate lid for the reactor sand bath. To analyze this in terms of flow rate, a flow rate counter was used which allowed the fluid to flow through and real time data was collected to check for consistency with the flow meter reading. Methods to improve the reactor in the future has been discussed in brief to analyze the scope of this sand bath.

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Asset Metadata

Creator Viswanath, Kiran Vishveshvar (author)

Core Title Continuous flow synthesis of catalysts with custom made reactor with flow and temperature studies

School Viterbi School of Engineering

Degree Master of Science

Degree Program Chemical Engineering

Publication Date 06/17/2019

Defense Date 03/29/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag batch chemistry,catalyst synthesis,chemical reaction engineering,flow chemistry,heat transfer,OAI-PMH Harvest,residence time distributions,thermodynamics,X-ray diffraction

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Malmstadt, Noah (committee chair), Brutchey, Richard (committee member), Shing, Katherine (committee member)

Creator Email kiranviv@usc.edu,vkiranv95@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-175117

Unique identifier UC11662698

Identifier etd-ViswanathK-7489.pdf (filename),usctheses-c89-175117 (legacy record id)

Legacy Identifier etd-ViswanathK-7489.pdf

Dmrecord 175117

Document Type Thesis

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Rights Viswanath, Kiran Vishveshvar

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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