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The continuous stirred-tank reactor (CSTR) model is used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. The mathematical model works for all fluids: liquids, gases, and slurries.

Operating a stirred-tank reactor with continuous-flow reactants and products (CSTR) has some advantages over batch operation.

The reactor can operate 24 hours a day for weeks at a times. The CSTR is an easily constructed, versatile and cheap reactor, which allows simple catalyst charging and replacement.

Its well-mixed nature permits straightforward control over the temperature and pH of the reaction and the supply or removal of gases (Harriott, 2003).

By using a continuous agitated-tank reactor in or der to obatain a particular output, the Continuous Stirred-Tank Reactor (CSTR) model is used to measure the key unit operation variables. The mathematical model works for all fluids: liquids, gases, and slurries. Morevoer, operating a stirred-tank reactor with continuous-flow reactants and products (CSTR) carries some advantages over batch operation. It is to be noted that the reactor can continuously operate for the full span of 24 hours a day for weeks without stopping.

The CSTR is an easily constructed, all-purpose, and cheap reactor. The CSTR allows simple catalyst charging and replacement. Its well-mixed nature allows uncomplicated control of the reaction and the provision or elimination of gases over the temperature and pH (Harriott, 2003). Figure AAA shows the schematic diagram of CSTR.

Reactant were continuous pumped in at an inlet port, usually at a constant rate. The reactor was vigorously stirred to ensure good mixing. The reactant solution pumped in pushed out an equal volume of the solution.In Figure AAA is displayed diagram of CSTR with a sequence.

In an inlet port, 1regularly at a constant rate the reactants were continuously propelled. Good mixing was prioritized so the reactor was vigorously stirred. As a result, the reactant solution that was driven in shoved out an equal volume of the solution With CSTR, under normal operating conditions the overall volumetric flow rate of feed streams equals to the flow rate of effluent stream, Q. In order to maintain sufficient oxidant, the oil/water ratio were set at 1:1 (v/v) with in the vessel.

The volumetric flow rates of organic stream and aqueous H2O2 are the same and should be equal to 0.5Q. The total sulfur concentration in the feed stream is CAO. Since the reactor is perfectly mixed, within the volume V the concentration of OSCs is uniform and equal to the exit concentration, CA.

It allows that the reaction rate is also uniform through the reactor and is a function of CA, r(CA). The material balance equation can be written as:(5.1)The overall volumetric flow rate of feed streams with CSTR (which was observed under normal order of operation) equals to the flow rate of effluent torrent, Q. In the vessel, to maintain adequate oxidant, the ration of oil/water was set at 1:1 (v/v).

The volumetric flow rates of organic stream and aqueous H2O2 are the same and are required to be equal to 0.5Q. The total sulfur concentration in the feed stream is CAO. As the reactor is flawlessly mixed, in consequence, the volume V the concentration of OSCs is uniformed and is equivalent to the exit concentration, CA.

It results in the observation that the reaction rate is also coherent through the reactor and is a function of CA, r(CA). Henceforth, the material balance equation can be written as: The item on the left-hand side of Equation 5.1 is the accumulation rate of OSCs in the reactor. The first two items on the right-hand side of Equation 5.

1 are the mass flow rate of OSCs entering and leaving the reactor, respectively. The difference between them is the new mass flow rate into the reactor. The last item on the right-hand side of Equation 5.1 is the disappearing rate of OSCs due to the oxidation reaction in the system.

The accumulation rate of OSCs in the reactor, on the left-hand side of Equation 5.1, is the accumulation rate of OSCs in the reactor. Similarly, the first two items on the right-hand side of Equation 5.1 present the mass flow rate of OSCs which are respectively going into and flowing out of the reactor.

The difference found between these items is the new mass flow rate into the reactor. The last item on the right-hand side of Equation 5.1 is the disappearing rate of OSCs which takes place owing to the oxidation reaction in the system. Since design is often based on the steady-state operation for which accumulation rate is zero, the Equation 5.

1 becomesDue to the observation that the design in generally based keeping in view the steady state of an operation, for which the rate of accumulation becomes zero, the Equation, as such, reads(5.2)As discussed in chapter, the pseudo-first-order kinetics for oxidation of OSCs has been established in a batch process. Therefore, r(CA) = -kCA, substituting into Equation 5.2 gives(5.

3)As has already been discussed in the Chapter, here, in a batch process, the pseudo-first-order kinetics for oxidation of OSCs has been instituted. Henceforth, r(CA) = -kCA, substituting into Equation 5.2 reads Equation 5.3 can be rearranged to obtain the fractional conversion, fs(5.

4)Equation 5.3 (as shown) may be reorganized in order to obtain the fractional conversion, fs: For CSTR, the mean residence time and space time are equal, and t= V/Q. Therefore, Equation 5.4 becomes(5.

5)The mean residence time and space time come to be at par with each other for CSTR, and t= V/Q. Therefore, Equation 5.4 reads: Equation 5.5 indicate that with known value of rate constant, K, and a chosen space time, t, we would be able to predict the oxidation conversion of OSCs, fs and evaluate the performance of the continuous modified UAOD system.

In Equation 5.5, it is shown that with known value of rate constant, K, and a chosen space time, t, it would be proficient to predict the oxidation conversion of OSCs, fs and calculate the performance of the continuous modified UAOD system.Just as the reaction time, t, is the natural performance measure for a batch reactor, so are the space-time and space velocity the proper performance measures of flow reactors. These terms are defined as follows by equation 5.

6 and 5.7.In correspondence to the reaction time, t, which is the natural performance quantify for a batch reactor, the space-time and space velocity are the proper performance measures of flow reactors. In Equation 5.

6 and 5.7, define these terms.Space-time: Time required to process one reactor volume of feed measured at specified conditions.(5.

6)Space-time is the time required to process one reactor volume of feed deliberated at particularly worked out conditions.Space-velocity: Number of reactor volumes of feed at specified conditions which can be treated in unit time.(5.7)Space-velocity is the number of reactor volumes of feed at particularly worked out conditions which can be operated in unit time.

Now we may arbitrarily select the temperature, pressure, and state at which we choose to measure the volume of material being fed to the reactor. Certainly, then, the value for space-velocity or space-time depends on the condition selected. If they are of the stream entering the reactor, the reaction between s and ? and the other pertinent variables is shown by equation 5.8(5.

8) The temperature, pressure, and state at which it is selected to measure the volume of material (being fed to the reactor) may now be arbitrarily chosen. Without doubt, then, the value for space-velocity or space-time relies on the conditions chosen. If these are of the stream flowing into the reactor, the reaction between s and ? and the other pertinent variables is shown in Equation 5.8 Thus, a space-time of 10.

5 min means that every 10.5 minutes one reactor volume (1,000 ml) of feed at specified conditions is being treated by the reactor. Henceforth, a space-time of 10.5 min denotes that each 10.

5 minutes one reactor volume (1,000 ml) of feed on specified conditions is being handled by the reactor. Can you write a paragraph of the following information: (PLEASE: (1) Modified UAOD process, (2) batch type continuous flow reactor is always one ward (is noun)Thus it is the observation by the above discussion of the processes that (1) Modified UAOD process, and (2) batch type continuous flow reactor are always one ward.The oil company request me to have daily production of 20,000 gallon per day with ultra-low sulfur diesel (15 ppm) from Valley oil with initial sulfur concentration 8,100 ppm. In order to lower the total sulfur content of Valley to less than 15 ppm, for each single organic sulfur compounds need to be reach more than 99% oxidized and sulfone can be removed by solvent extraction or alumina adsorption.

It was requested by the oil company to have daily production of 20,000 gallon per day with ultra-low sulfur diesel (15 ppm) from Valley oil with initial sulfur concentration 8,100 ppm. As such, in order to lower the total sulfur content of Valley to less than 15 ppm, for each single organic operation, sulfur compounds need to attain more than 99% oxidized; and sulfur can be removed by solvent extraction or alumina adsorption. In chapter 4, the GC-SCD analysis of Valley oil through modified UAOD process shows that 46DMDBT is one of the most abundant sulfur species in original Valley oil and has sulfur concentration approximately 88 ppm. Therefore 46DMDBT were chosen for reactor design.

The oxidation of 46DMDBT in Valley oil under modified UAOD conditions follows pseudo-first-order kinetic with apparent rate constant of 0.0239 min-1 at 70oC.In chapter 4, the GC-SCD the analysis of Valley oil by modified UAOD process manifests that 46DMDBT is one of the richest sulfur species in original Valley oil and has approximately 88 ppm sulfur absorption. Consequently, 46DMDBT was crafted for reactor design.

The oxidation of 46DMDBT in Valley oil under modified UAOD conditions follows pseudo-first-order kinetic with obvious rate constant of 0.0239 min-1 at 70oC. In order to achieve over 99.9% oxidation of 46DMDBT in Valley oil, the size of batch type continuous flow reactor can be obtained from Equation 5.

4 as, than I can use Equation 5.9 to find out the suitable reactor size.(5.9)In order to obtain over 99.

9% oxidation of 46DMDBT in Valley oil, the size of batch type continuous flow reactor can be acquired from Equation 5.4 and, subsequently, Equation 5.9 can be used to uncover the suitable reactor size. Where:Q = 20,000 gallon/day = 476 barrel/day = 0.

05 m3/minCAO = 8,100 ppm, CA = 15 ppmK (46DMDBT)= 0.0239 min-1Therefore, the volume of the batch type continuous flow reactor is From previous section, the treatment rate of Valley oil for batch type continuous flow system is 1 kg / 3.3 hours, known as 2.4 gallon per day, reached 99.

8% sulfur removal in 3.3 hours. However, this result is still insufficiency for practical application. In this study, the treatment capacity of Valley oil has been scaled up ten times with 10 kg, and working volume of reactor has been increase to two liter instead of one liter, although the feed rate of has increase to 160 ml / min instead 95.

2 ml /min. The operation conditions of both studies were shows as Table XXX.The treatment rate of Valley oil for batch type continuous flow system, in the previous section, is 1 kg / 3.3 hours (known as 2.

4 gallon per day), reached 99.8% sulfur removal in 3.3 hours. However, this outcome is still inadequate for the practical application.

In the present study, the treatment capacity of Valley oil has been scaled up ten times with 10 kg; similarly, the working volume of the reactor has been increased to 2 liters instead of 1 liter. This is to be noted that the feed rate of has increased to 160 ml / min instead of 95.2 ml /min. Table XXX manifests the operation conditions of both studies.

ParametersSmall Scale CSTRLarge Scale CSTRValley oil1 kg10 kgSulfur concentration8,100 ppm8,100 ppmHydrogen Peroxide (30%)100 g1000 gRTIL25 g250 gAcid Catalyst (40% TFA)35 g350 gTemperature50oC +/- 5oC50oC +/- 5oCWorking volume of reactor1 L2 LFeed rate95.2 ml/min152 ml/minSpace time10.5 min13.2 minTable YYY shows the result for desulfurization efficiency for large scale treatment, Moreover, results indicate that the desulfurization efficiency was reached 88% in very short time (10 min) and this result is very much similar compare to small scale treatment, this also tell us that increase the treatment volume does not affect much on desulfurization efficiency.

The final sulfur reduction of 10 kg/3.3 hours treatment rate was reached at 99.7% in 3.3 hours, but it did not reach 15 ppm.

Therefore, by reaction for another 30 minutes, the desulfurization can 99.8% with 13 ppm as the final sulfur concentration that is acceptable.In Table YYY are displayed the result for desulfurization efficiency for large scale treatment. Moreover, the results indicate that the desulfurization efficiency was attained up to 88% in a very short period of time (10 min); and this result is very much similar as compared to the small scale treatment.

This observation also indicates that increase in the treatment volume does not highly affect desulfurization efficiency. The final sulfur reduction of 10 kg/3.3 hours treatment rate was reached at 99.7% in 3.

3 hours, but it did not reach 15 ppm. Therefore, by reaction for another 30 minutes, the desulfurization can be 99.8% with 13 ppm as the eventual sulfur concentration which can be acceptable. Time(min)Small scaleDesulfurization(%)Large scaleDesulfurization(%)Conc.

(ppm)Conc. (ppm)08,10008,10001091488.798787.82077990.

480190.13064292.168491.64056493.

062492.36031496.136695.58022797.

226596.61408498.910198.82001599.

82299.72301399.8sSeveral studies indicated that in presence of an excess of H2O2, the oxidation of organic sulfur compounds follows pseudo first order kinetics in carboxylic acid/ H2O2 and polyoxornetalate/ H2O2 systems (Te, et al. 2001; Otsuki, et al.

2000; Collins, et al. 1997). Since H2O2 was present in excess under UAOD condition, the reaction data should be fitted to a first-order rate equation. A plot of ln(Ct /C0) versus reaction time showes as Figure XCV.

The fitting curve displayed a linear relationship that confirmed the pseudo-first-order reaction kinetics.Several studies in the available literature inform us that in the presence of an excess of H2O2, the oxidation of organic sulfur compounds follow pseudo first order kinetics in carboxylic acid/ H2O2 and polyoxornetalate/ H2O2 systems (Te, et al. 2001; Otsuki, et al. 2000; Collins, et al.

1997). As H2O2 was at hand in excess under UAOD condition, it is needed for the reaction data to be adjusted to a first-order rate equation. A plot of ln (Ct /C0) versus reaction time is shown in Figure XCV. The fitting curve displays a linear relationship which substantiates the pseudo-first-order reaction kinetics.

Figure XCVThe apparent rate constant for oxidation of Valley oil was determined to be 0.0197 min-1. Compare to the oxidation reaction rate of T (0.0196 min-1), 2MT (0.

0199 min-1), 2ET (0.0224 min-1), BT (0.0276 min-1), 2MBT (0.0223 min-1), DBT (0.

0228-1) and 46DMDBT (0.0231 min-1), it is relatively much lower than these OSCs in batch scale. It is because a complex system as diesel fuels, there exits competitive oxidation among organic sulfur compounds and other unsaturated constituents such as olefinic compounds. Furthermore, the continuous desulfurization unit can not reach as perfect operation conditions as batch scale.

This result is very important and can be applied to evaluate the performance of modified UAOD process on diesel fuels as well as to enhance the capacity of continuous desulfurization unit.As the diesel fuels are complex systems, there exits competitive oxidation among organic sulfur compounds and other unsaturated constituents, such as olefinic compounds. Furthermore, the continuous desulfurization unit cannot reach up to as ideal operation conditions as batch scale. This result is a very important step in the process and can be applied to calculate both the performance of modified UAOD process on diesel fuels and to improve the capacity of continuous desulfurization unit.

For the quality and quantity purpose and performance, multiple reactors can be scaled up to connect in either series of parallel. In this study, the high sulfur reduction of Valley oil (99.8%) was successfully demonstrated by a single batch type continuous flow reactor at treatment rate of 3.03 kg / hour.

Therefore, quantity purpose and performance, two or more reactors can be connected in parallel to reach high desulfurization efficiency (99.8%) with higher treatment rate which reaches the basic requirement of commercial scale.With the purpose and performance of the qualitative and quantitative paradigm, multiple reactors can be scaled up to connect in either series or parallel structure. In the present study, the high sulfur reduction of Valley oil (99.

8%) was successfully displayed by a single batch type continuous flow reactor at treatment rate of 3.03 kg / hour. Hence, for the quantity and performance purpose, two or more reactors can be connected in parallel to reach high desulfurization efficiency (99.8%) with higher treatment rate which also reaches up to the basic requirement of commercial scale.

Moreover, diesel has a density of 0.827 g/ml, as compared to water with density close to 1 g/ml. The treatment rate at small scale (0.303 kg/hr) is approximately 0.

06 bpd, and the treatment rate at large scale (3.03 kg/hr) is approximately 0.6 bpd. The batch type continuous flow system has demonstrated the feasibility of large scale operation even in a relatively small installation with low capital investment and maintenance cost.

In addition to the above, as compared to water density close to 1 g/ml, diesel has a density of 0.827 g/ml. treatment rate at small scale (0.303 kg/hr) is approximately 0.

06 bpd, and the treatment rate at large scale (3.03 kg/hr) is approximately 0.6 bpd. Consequently, the batch type continuous flow system has demonstrated the practicability of large scale operation even in a relatively small installation with low capital investment and maintenance cost.

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