The Reactor Design Project Engineering Essay

The Reactor Design Project Engineering EssayThe fuddle objective was to optimise three different adiabatic ammonium hydroxide nuclear nuclear nuclear nuclear nuclear nuclear reactor configurations with respect to reactor performance in ready to produce 800 tonnes of ammonium hydroxide per day, or the molar equivalent of 0.5447 kmol s-1 of ammonia water water. The optimizations in reactor performance problematic primarily, minimizing the particle accelerator passel and indorsementarily, maximizing the throttle valve lifespan, as well as ensuring the final direct chassiss were stable. Due to the absence of a cost function, the reactor could NOT be optimized with respect to cost minimization.Three different reactor types were considered, namely a private plug-flow reactor, a dual inter deliver alter reactor and a dual cold-shot temperature reduction reactor. Temperature, blackjack and subdivision of ammonia in the nutrition stream were ground to prolong the greatest onus on the resultant particle accelerator garishness. Using MATLAB, it was found that the negligible mints were 9.61 m3, 3.94 m3 and 4.78 m3 for a virtuoso form plug-flow, an interstage chill system configuration and a cold shot cooling reactor configuration respectively. The interstage cooling reactor supported for a 59% decrement in total atom smasher volume when modified from the ace stage purport, solo necessary an addition in approach execute temperature of 115K and 2 redundant kindle exchangers. The cold shot cooling method individuallyowed for a 50.2% come down in reactor volume from the iodin stage introduction, requiring a 75K increase in feed temperature.1. Introduction1.1. BackgroundAmmonia entailment ( withal cognize as the Haber deal) is one of the most widely applied chemical substance processes in the world in 2009, the total worldwide production of ammonia exceeded 133,000 metric tonnes 1, this is routine only to the worldwi de production of sulphuric acid. about of the ammonia produced is employ in the manufacture of fertilisers ( such as ammonium nit account), ammonia is to a fault utilise in the manufacture of nitrogen-based polymers such as nylon. another(prenominal) noteworthy use of ammonia is as the starting reagent for the manufacture of nitrogen-based explosives such as nitroglycerin.The response which gene gaits ammonia is exothermic and equilibrium circumscribedN2 + H2 is in equilibrium with NH3 HR (298K, 1atm) = -46.11 kJmol-1 Eqn. 1In the early 20th century, Fritz Haber discovered that in order to obtain a hearty yield of ammonia, the chemical reply requisite both full(prenominal) extorts and low temperatures (in accordance with the van t Hoff-Le Chatelier principle). It was known that the position at which N2 decomposed in the chemical reaction was very slow (N2 is thermodynamically much stable than NH3) in that locationfore a very efficient throttle was required in order to facilitate ammonia formation. Nowadays, the gas used in most industrial ammonia reactors is usually a holey form of enriched iron. accelerators ar expensive, plainly they present a good handle off reactors ar able to produce sufficient touchstones of product at lower, more manageable temperatures and rams.1.2. Design objectiveThe boilers suit objective was to convention a continuous located bed plug-flow process to run regulateways the companys perfunctory ammonia production demand of 800 tonnes per day (exclusive of any ammonia in the feed). The primary soma objective was to try to minimize the gas volume the process required in order to meet the production requirement. The design in like manner had to be considered safe to figure out and had to ope station at conditions that were considered to maximise the lifespan of the throttle valve these cardinal were considered as imprimaturary objectives. The preliminary design of the reactor considered a adept-sta ge adiabatic bed with a bed cross- discussion sectioned ara of 2.0 m2. The final designs involved deuce different two-stage systems one implementing interstage cooling and the other implementing cold-shot cooling.Reactor performance and sensitivity were analysed by observing the make of altering specific in operation(p) and design variables. The cost function for the process was not known, then it is important to note that the reactor could not be optimized with respect to cost, however the design could be enforced such that the reactor performance was greatly improved. For example, minimizing the required particle accelerator volume (and thereof minimizing the reactor volume) will reduce the construction cost of the reactor. However this may shine at the expense of great operating and maintenance be and, in the case of two-stage systems, may result in additional construction costs (interstage cooling requires heat exchanger(s) to be built). The investigating will only allow qualitative suggestions to be made as to which specific design aspects tot up to the generation and/or reduction of costs.1.3 SafetyThe reactor operating conditions should be stable such that small disturbances will not lead to caloric runaway (which has important implications for safety). Other than that, there ar no blown-up risks involved with operating the ammonia reactor, provided that good process control is implemented by the operator.2. Kinetic theory and types of reactor configurations2.1. The kinetics of ammonia entailment and its implications on reactor designAmmonia synthesis involves a single exothermic, reversible reaction between nitrogen and hydrogen. For reversible reactions, the renewing analogous to thermodynamic equilibrium at the chosen operating conditions cannot be surpassed. Since the reaction is exothermic, the activation muscularity (which is only temperature dependent) of the backwards reaction is great than that of the prior reaction. Th erefore an increase in temperature causes a rise in the put of the reverse reaction which is greater than the rise in the roll of the forrader reaction then change magnitude the maximum attainable reincarnation but decreasing the required gas volume. On the other hand, operating at a lower temperature increases the maximum attainable conversion, whilst reducing the total reaction rate and increasing the required gas volume. With regard to blackmail, the effect is the polar increasing the embrace causes a greater rise in the rate of the advancing reaction compared the backward reaction and vice versa.Designing a reactor producing ammonia thereof requires a compromise between belongings temperatures sufficiently extravagantly such that reaction rate remains strong whilst obtaining a respectable conversion of ammonia. Similarly, the pressure should be great abounding so as to maintain a significant reaction rate, but not so high as to cause the reactor to deviant from safe operation.In order to minimize gas volume (and meet the primary objective), it is desirable to interlace at the maximum send on rate of reaction at each cross-section crossways the reactor thus maximizing the average forward rate crosswise the reactor, this allows the desired boundary to be met with the negligible catalyst originate part and hence with the minimum catalyst volume. In order for this to turn over, each cross-section in the reactor must be work outd at the unique pressure and temperature required to light upon maximum rate for a particular finale, i.e. the reactor moves on the venue of maximum reaction judge. This is unfeasible in this investigation since there is no temperature or pressure control implemented across the reactor (the reactor is adiabatic and WSHAFT=0) and even so, maintaining specific pressures and temperatures at each power point along the reactor is practically unfeasible in itself as each point in the reactor would require its o wn heat exchanger and pressure control system.Therefore for exothermic reversible reactions (without heat removal), the temperature increases along the distance of the reactor and the rate vs intent profile will always have a characteristic maximum because the temperature along the reactor increases due to the heat released by the reaction, causing the net production rate to increase up to a certain extent in the lead the reverse reaction starts to cash in ones chips significant. As the rate of the backwards reaction tends to increase further and temperature rises, the overall reaction rate will eventually reach zero at equilibrium.2.2. Brief description of the Plug-Flow Reactor (PFR)A plug-flow reactor is characterized by smooth-spoken flowing through one end of the reactor and out the other, whilst unanimous the assumptions of plug-flow. The assumptions stateFluid properties and flow rate remain constant across any cross-section of the reactor.The flow is orderly, with no element overtaking or flux with liquid ahead or behind, (i.e. the residence time is the same for all fluid elements).The above assumptions tend to hold true where there is turbulent flow (Re 105), ensuring good radial mixing, and if the ratio of reactor duration to diameter of the reactor is large (ratio 50), where lateral mixing may be neglected 2. frame of reference 1 An illustration of a plug-flow reactor 32.3. Brief description of Interstage CoolingInterstage cooling, also known as intercooling, is a multiple reactor design suitable for exothermic reversible reactions. wake exchangers are used to cool the yield of each reactor before being passed on to the next reactor, allowing for a greater possible conversion to be succeedd in each successive reactor. This process can be replicated for an indefinite number of reactors until the reactor temperature is too low for reactions to occur or until the decrease in catalyst volume is not worth the additional cost of construction a nd complexity of operation. This project considers only the case where two reactors are used. double 2 An illustration of a dual reactor interstage cooling system42.4. Brief description of Cold-shot CoolingCold-shot cooling reactor designs are similar to that of interstage cooling, but allow for elimination of the intermediate heat exchangers by injecting cold feed directly into the government issues of each reactor. This addition cools down the vent-hole stream of the reactor and also has the effect of decreasing the fundamental law and conversion of the flow into the subsequent reactor (corresponding to the path from point b to c in invention 3 below). manakin 3 An illustration of a dual reactor cold-shot cooling system 5The flow plat of two cold-shot reactors illust pass judgment the lack of heat exchangers as compared to interstage cooling, as well as the splitting of the sign feed stream by the splitting fraction alpha, , which is the fraction of the fresh feed used as the coolant. The extent of reaction remains constant after mixing (which can be be by a cumulation balance).3. Mathematical forge Derivations of derivative instrument equations only the assumptions of plug-flow mentioned above were applied in the construction of the equations below the reactor was also assumed to operate at steady state (there is no mass hold up due to the catalyst). All other assumptions are mentioned in the derivations. It should be noted that rNH3 is specialised as (rNH3 generated rNH3 consumed) and is measured per unit of catalyst volume hence the equations specify the volume of catalyst VC and not the reactor volume VR.3.1. Change in catalyst volume with respect to the extent of reactionMass balance on ammonia Eqn. 2The extent of reaction can be defined asEqn. 3 comparabilitys 2 and 3 were have to obtain the following equationSince , the equation above was rearranged to give the initial catalyst volume gradientEqn. 43.3. Change in temperature with respect to the extent of reactionFigure 4 An illustration of the cross section of a plug-flow reactorAn energy balance across an infinitesimally small cross section of the catalyst bed gaveShaft work (W), changes in kinetic energy and changes in potential energy were neglectedThe equation above was dual-lane by the cross-section(a) plain of the tube, Awhere Q denotes the heat transfer by conduction.In the equation below, the enthalpy change upon mixing was neglected (a completed solution was assumed). It was also assumed that the gases in question were ideal and hence their enthalpy was independent of pressure, the energy balance then took the formEqn. 5is the timeworn heat of formation of compound.i denotes each species present.Recalling that for a tubular reactor, and does not have a negative sign as rproduct is calculated as the main subject)Eqn. 6The heat of reaction was simplified as shown belowEqn. 7Equation 7 was substituted into Equation 6 which was then substituted into Equatio n 5Eqn. 8The kitchen stove rule was used to combine and Since the reactor was assumed to be adiabatic, Q = 0Eqn. 93.4. Change in pressure with respect to the extent of reactionThe ambit rule was used to find using the formula for , bed cross-sectional domain A and since A dl = dVC.Substituting the components of the three terms above, we get the initial pressure against extent gradient formulaEqn. 104. subterfuge theory and strategy4.1. Main assumption objectivesRegardless of the design used, these objectives are overarching and apply to all three reactor types The runner two bullet-points define what is meant by optimizing the reactorMinimizing catalyst volumeOperating temperatures and pressures are limited by safety considerations (preventing thermal runaway), material construction and catalyst debasement conditions. These debasement conditions are undertake by actual limits set by ammonia process operators in industry these are above 823 K and above 300 immobilize 6Inter stage and cold-shot cooling designs are only dual reactor designs.The derivation of the required total extent for all simulations is as followsThe MATLAB cryptology incorporating the required data and was used to solve the differential equations described earlier in the mathematical model for the spill temperature, pressure and catalyst volume all the assumptions applied in the mathematical model were thus applied in the coding, unit consistency was also retained in the architectural planming.4.2. Single stage simulation strategyIt is clear that a plug-flow reactor can take advantage of concentration profiles present in the reactor in order to minimize the total catalyst volume. lift the desired extent, adiabatic plug-flow reactors (running exothermic reversible reactions) operate ideally manyplace between the equilibrium barrier, where the rate of the forward and backwards reaction are equal, and the best line, which is a curve connecting the maximas of all the different r ate curves, also known as the locale of maximum rank.Figure 5 A graph displaying the variation of forward rate with extent It is opted to run the reactor under conditions such that the entre rate is exactly equal to the wall plug rate where the reactor exits at the desired extent of 0.5447. The rin = throw out condition limits the maximum average rate by a small amount but provides a greater amount of kinetic stability in the event of a disturbance a small increase in the inlet temperature may push the reaction closer to equilibrium whilst a small decrease in the inlet temperature will decrease the government issue rate slightly but still allow the reactor to operate in a region of higher(prenominal) rates. The locus of rin = rout is found between the optimum line and the equilibrium line.As shown in Figure 5, this condition also means that the region of maximum reaction rate is taken advantage of i.e. the rate in the reactor is always greater than or equal to the inlet rate. Therefore, although the temperature increases along the reactor, the forward rate is unploughed as high as possible.As the extent of reaction increases across the reactor for a fixed set of inlet conditions, it is expected for the surface area of catalyst to increase if more product is generated, more catalyst is required to facilitate this generation. There is a limit in the MATLAB coding such that the catalyst volume decreases whilst the reaction extent continues to increase the autograph is such that results after this point are treated as wild and are not used, thus the code finds the inlet conditions needed to achieve the maximum possible extent for an adiabatic reactor.To apply the simulation strategy, a MATLAB computer programme was created to find the inlet conditions which satisfy the rin = rout condition for a desired final extent (0.5447 in this case). A separate program was also created to vary operating and design conditions individually and examine their effect on the catalyst volume. Graphs of the locus of maximum reaction rate, locus of rin = rout rates and the equilibrium curve were constructed using the desired inlet conditions resolved from the single stage simulation.4.3. Interstage cooling simulation strategyThe overall reaction follows the adiabatic operating curve (it may not necessarily be a straight line due to the pressure drop across the reactor). It was desirable for the reaction to end at the same point as in the single stage simulation (with the same final extent) where the rate at the outlet of the entropy base reactor lies on the rin = rout line for the desired extent. It was also desirable for the rate at the exit of the starting line reactor to be equal to the rate at the entrance of the second reactor so that the reactor can continue onwards from the same rate in the second reactor (and maintain the average forward reaction rate).For this code, there was no condition that the rate at the inlet of the offset printing reactor must equal the rate at the outlet of the number 1 reactor (and likewise for the second reactor) since it was unfeasible to make the rates equivalent at all the inlets and outlets. Instead it was specified that rate1 OUT= rate2 IN and that rate2 OUT = rate OPTIMIZED SINGLE STAGE OUT.The extent in the premier reactor (and therefore in the second reactor) had to be specified for each set of results. If the extent was too high, the outlet of the starting time reactor would be very near equilibrium whilst if it was set too low the outlet of the first reactor would be reached before the maximum rate had been obtained therefore a degree of overshoot other(prenominal) the maximum reaction rate was desirable the program ensured that there was a degree of overshoot past the maximum reaction rate in both reactors before substantiative a result.The locus of maximum reaction rates (from the single stage optimization) was used to determine the feed temperature for which the rate is a maximum at the start this temperature was roughly 790K (located graphically). Above this temperature, the region of maximum reaction rates was not utilised at all and the maximum extent achievable (using the gradient of the operating line) at equilibrium was roughly 0.28. This specified the minimum extent of reaction in reactor 1. If the feed temperature were too low, the first reactor would perform similar to a single PFR, defeating the purpose of having two reactors. Thus a moderate extent range of 0.3 0.4 was chosen for the first reactor as it was unworkable to put an excessive production core on either reactor.In order to apply this strategy, a program was used to specify the inlet conditions to the second reactor the program go along the operating curve using the initial conditions obtained in the single stage reactor up to the desired extent in the first reactor. This gave the inlet rate to the second reactor as well as the flow rate, temperature and composition of this stream. Following this, the rate1 OUT = rate2 IN condition was used to acquire the inlet and outlet temperatures and pressures of the first reactor and its volume. Lastly, the inlet conditions to the second reactor and the remaining extent were used to calculate the volume of the second reactor. The combined volumes and degrees of cooling between the reactors were compared for the chosen range of extents.4.4. Cold-shot cooling simulation strategyFigure 6 A graph displaying the variation of extent with temperature for a cold-shot systemThe rate identity rin=rout used to optimize the single PFR was used in the cold-shot cooling reactor design. With reference to Figure 6, optimization was achieved by ensuring that the reaction travel from points abcd , with the following rate identities ra = rb and re = rd. The second reactor would operate along the path that the optimum single PFR would operate on (e d).By adhering to the above conditions, there were three variables left to define, n amely alpha (), initial feed temperature Tini and the interstage extent 1. Fixing alpha and Tini would automatically define 1 and outlet temperature of the first reactor as the rates at points a and b must be the same. This optimized the first reactor for the given inlet conditions. By constructing enthalpy and mass balances on the mixing point of the outlet from the first reactor with the cold stream, the inlet temperature into the second reactor was determined, thereby finding outlet conditions of the second reactor, should it achieve the required extent of 0.5447 kmol s-1. Finally, in order to ensure that total optimization had occurred for the specified alpha and temperature, the difference in rates at points e and d was confirmed to be as close to zero as possible. some(prenominal) iterations would be required to home in on the best inlet temperature for a given extent.The temperature of the feed used for cooling, Tf, was 298K significantly lower than the temperature of the f luid exiting the reactor. This imposed an upper limit on the split fraction , beyond which the feed temperature into the second reactor would be too low for reactions to operate at an acceptable rate catalyst volume would need to be larger to counter this effect, meaning optimization would not achieved.Therefore, by change for 50 equal intervals from 0.01 to 0.5, and finding the 50 corresponding Tini pass judgments that well-provided the above stated rate identities gave the optimum reactor for each value of . The best cold-shot reactor specification was easily deduced from the setup which had the smallest overall catalyst volume.Results and Discussion5.1. Single Plug-flow Reactor5.1.1. Varying the ammonia composition in the feedFigure 7 A graph displaying the effect of ammonia feed mol % change on catalyst volumeThe composition of ammonia in the feed was changed while keeping the molar feed rate constant. (Change ratio 4% decrease in NH3 = 1% increase in N2 + 3% increase in H2, etc).Figure 7 shows that decreasing the ammonia fraction from the original 8 mol % (while increasing the reactant mol %) lead to a significant drop in catalyst volume required. The greater concentration of reactants favoured the forward reaction, increasing the rate of formation of ammonia, conduct to a smaller catalyst volume. When the ammonia fraction was too high (0.16), the initial concentration of reactants was insufficient to achieve the required extent. Also, as the partial(p) pressure of ammonia increase in the reactor, a greater equalizer of the catalysts active sites became blocked and the forward rate decreased, increasing the required catalyst volume 7.It was decided to keep the mol % of ammonia in the feed at 8% in subsequent simulations although the lowest mol % of ammonia in the feed produces the minimum catalyst volume, it is impractical for this to occur since ammonia is normally recycled in industrial reactors 8.5.1.2. Varying the reactor cross-sectional areaFi gure 8 A graph displaying the effect of cross-sectional area on catalyst volumeFigure 8 shows that increasing the cross-sectional area reduced the catalyst volume, but this reduction was more significant only at the smaller area determine. Increasing the area increased the number of catalyst pellets available at the reactor cross-section therefore a greater reaction rate was initially facilitated as the volume increased. However, the inlet flow was fixed, and beyond a certain area, the flow into the reactor did not utilise the additional pellet area at the cross section and thus the catalyst volume was less affected. The cross sectional area for the remainder of the investigation was kept at 2m2 because the increase in cross-sectional area above 2m2 does not justify the relatively minimal reduction in catalyst volume.5.1.3. revolution of catalyst voidageTable 1 Displays catalyst volumes for different values of catalyst voidageVoidage0.70.60.50.40.3Vc at = 0.54466 (m3)23.464223.48 7723.539923.672824.1043Voidage is the ratio of the catalyst volume to the reactor volume. A larger voidage means a higher catalyst pellet density, thereby allowing a smaller catalyst volume. However, increases in voidage past 0.4 did not contribute to any further significant decrease in catalyst volume. For the purpose of subsequent simulations, the voidage was kept to the original 0.4.5.1.4. Variation of catalyst diameterTable 2 Displays catalyst volumes for different values of catalyst diameterCatalyst Diameter0.0110.0090.0070.0050.003Vc at = 0.54466 (m3)23.588123.620923.672823.767523.9954It is seen from the data that vary catalyst diameter had a negligible effect on the catalyst volume, suggesting that although the surface area of each catalyst pellet increased, the number of catalyst pellets decreased, and thus the overall catalyst area did not change significantly. It was decided to stick to the original catalyst diameter provided.5.1.5. Varying temperature and pressureFigure 8 A graph displaying the effect of inlet temperature on catalyst volume for different isobarsAs the temperature was increased, a decrease in the catalyst volume was observed. At lower pressures, the gradient of the graph (the change in VC with inlet T) was much higher and therefore inlet temperature was more efficient at reducing the catalyst volume at lower pressures. This has some implications with respect to cost if the inlet temperature is increased, there is an electricity cost associated with operating the reactor at this higher inlet temperature, but there is also a saving due to the reduction in catalyst volume.Figure 9 A graph displaying the effect of inlet pressure on catalyst volume for different isothermsAs inlet pressure was increased, the catalyst volume decreased. As discussed in the theory, the increase in pressure favoured the forward reaction, thereby increasing the reaction rate per unit volume of catalyst. However, the metropolis costs spent on reactor materia ls able to withstand the high pressures have to be taken into consideration in addition to the greater maintenance cost of the catalyst bed (since a higher pressure reduces the longevity of a catalyst).5.1.6. Results of single stage simulationTable 3 Displays the specifications and feed conditions the optimized single PFRFeed CompositionCrosssectional area(m2)Catalyst Diameter(m)VoidageExtentTemperature(K)Pressure(Bar)N2H2NH3InOutInOut0.230.690.0820.00070.40.5447624.2796.0300298.6It can be observed that the pressure drop throughout the reaction was rather insignificant compared to the total pressure in the reactor. The optimization values from the single stage plug-flow reactor were substantive for designing dual reactors that utilized interstage or cold-shot cooling as the second reactors were designed to follow the reaction path taken by the single stage PFR.The optimum single stage pressure of 300 bar was also the optimum pressure used for the subsequent simulations the maximum operating pressure tolerable is 300 bar according to the catalyst degradation conditions specified in the simulation objectives.5.2. Interstage CoolingFigure 10 A graph displaying the extents of reaction for different temperatures. The interstage path for 1 values of 0.3, 0.34 (optimum), and 0.4 are displayed along with the locus of maximum reaction rates, the equilibrium curve and the locus of rin = rout.Results were obtained for 10 extents between 0.3 and 0.4 these are displayed in the appendix. From the graph above, it can be seen that for all three extents 0.3, 0.34, 0.4, the reaction in the first reactor moved past the locus of maximum rates and the locus of rIN = rOUT and then approached the equilibrium curve, thereby maximizing conversion. The outlet stream was then cooled to a point along the path taken by the volume minimizing single PFR. The graph thus shows that performance optimization occurred in the interstage cooling design as catalyst volumes in both reactors were mi nimized.The range of chosen extents for the first reactor, 0.3 0.4 kmol s-1, also proved to be robust, providing well performing reactors with small catalyst volumes (where all reactors had a combined catalyst volume less than half(prenominal) of that of the single stage reactor). Volume reached a minimum of 3.94 m3 when the extent was fixed at 0.34 kmol s-1 with an inlet feed temperature of 737.1K.5.3. Cold-shot CoolingTable 4 Conditions and results for the optimum cold-shot systemExtent AchievedTemperature (K)Catalyst volume (m3) first2nd1st2ndInOutInOutVr1Vr20.29580.2489699795.769717.172796.4071.5233.254(Vc 1 Vc 2 = 1st 2nd Catalyst volume respectively)Figure 11 Catalyst volume minimizing temperatures at specific alpha valuesDuring simulation of the cold-shot cooling reactor design, it was deduced that the range of was restricted from 0.01 to 0.38, beyond which the bulk of the reaction would occur in one of the two reactors, making the other redundant. Optimally, should be someplace between the limits of the range for = 0.19 and feed temperature at 699K, a minimum overall volume of 4.78 m3 was achieved. It is seen from the graph above that as deviates from 0.19 and tends towards 0, the first reactor behaves more like a single PFR. The same happens to the second reactor as tends towards the upper limit.Increasing the initial feed temperature causes to increase in order for optimization to occur, while a decrease would bring about the confrontation effect. This is because a larger fraction would be required to cool the output from the first reactor to achieve optimization should the reactor operate at a higher temperature. The contrary is true with a larger , the initial feed temperature cannot be too low as excessive cooling of the second fraction would occur.6. ConclusionIt can be concluded that the investigation w