ABSTRACT There are two experiment carried out for Tubular Plug Flow Reactor which are pulse input in tubular flow reactor and step change input in a tubular flow reactor .The purposes of Tubular Plug Flow Reactor are to examine the effect of a pulse input in a tubular flow reactor , the step change input in a tubular flow reactor are to examine the effect of a step change input in a tubular flow reactor and to construct a residence time distribution (RTD) .For the pulse input experiment ,the flow rate was set up to 700 ml/min then let the salt solution flow for one minute and take reading of conductivity interval 30 seconds until reading are almost constant and stable at low values. After that for step change input again flow rate was set at 700 ml/min and recorded conductivity at intervals of 30 seconds until reading also almost constant. The observation throughout the experiment are for pulse input the mean residence time is 1.5045 minute, while the peak is at around 1 minute. This should indicate positive skewness. This is consistent with the value of cubic s which is positive. The variance is 5.0942, and this is rightfully so. The high value indicates that the data is distributed widely, and is deviated far from normal distribution while for step change experiment the mean residence time does not signal anything significant. The graph is also positively skewed and this is rightfully shown by the graph. The variance is 1.8848, which is lower than that of pulse input. This is seen from the fact that 62.5% of the whole experiment operates at constant reading. This experiment is a success. It is found that be it through step change or pulse change, the time taken for the reactor to experience complete change of material is the same. Both graph exhibits positive skewness, and has rather marginally different value of variance.
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1.0 INTRODUCTION A plug flow reactor (PFR) consists in a long, straight pipe in which the reactive fluid transits at steady state (no accumulation). The main assumptions of this model are that the fluid is completely mixed in any cross section at any point, but it experiences no axial mixing, i.e. contiguous cross-sections cannot exchange mass with each other (1). Plug flow reactors, also known as tubular reactors, consist of a cylindrical pipe with openings on each end for reactants and products to flow through (2).
FIGURE 1.0 Reactants are continually consumed as they flow down the length of the reactor. Plugs of reactants are continuously fed into the reactor. As the plug flows down the reactor the reaction takes place, resulting in an axial concentration gradient. Products and unreacted reactants flow out of the reactor continuously. The flow can be laminar and greatly deviate from ideal plugflow behaviour, or turbulent, as with gases. There is a technique which is called as stimulus - response technique. The technique is applied by injecting a pulse of tracer at the inlet. However, it does not disperse and appear as pulse at the outlet. The concentration of tracer versus time at the exit should be followed in order to obtain the degree of dispersion that would occur in the real reactor. Faulty operation caused by malfunction of chemical reactors can be effectively diagnosed by Residence Time Distribution (RTD) analysis. RTD shall be used to characterize existing (i.e. real) reactors and then use it to predict exit conversions and concentrations when reactions occur in these reactors (3). Firstly, the non-reactive or inert tracer will be injected at the inlet. The concentration of the tracer is changed according to a known function and the response is found by measuring the concentration of the tracer at the outlet. The hydrodynamics condition and the physical characteristic of the fluid should not be altered by the selected tracer. The quantity E(t) is called the residence-time distribution function. It is the function that describes in a quantitative manner how much time different fluid elements have spent in the reactor. The
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quantity E(t) dt is the fraction of fluid exiting the reactor that has spent between time t and t + dt inside the reactor (4).
FIGURE 1.1
2.0 OBJECTIVE The two objectives for this experiment are:
To examine the effect of a pulse input and step change input in a tubular flow reactor.
To construct a residence time distribution (RTD) function for the tubular flow reactor.
3.0 THEORY Let consider the chemical reaction as 𝑎𝐴 + 𝑏𝐵 → 𝑐𝐶 + 𝑑𝐷 Residence time, τ is the average amount of time that a particle spends in a particular system. The τ is a representation of how long it will takes for the concentration to significantly change in the sediment. 𝜏 =
𝑉𝑇𝐹𝑅 𝑣0
Where 𝑉𝑇𝐹𝑅 is the reactor volume and 𝑣0 is the total feed flow rate. In this experiment, the pump was adjusted until the flow rate become constant. The flow rate for each experiment is variable but the reactor volume remain constant for every experiment.
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Conversion is a way of determining how far has the reaction is done, or how many moles of products are formed for every mole of A has consumed. Conversion 𝑋𝐴 is the number of moles of A that have reacted per mole of A fed to the system. 𝑋𝐴 =
moles of A reacted moles of A fed
A reaction rate constant, 𝑘 quantifies the rate of a chemical reaction. The reaction rate is often found to have the form 𝛽
−𝑟𝐴 = 𝑘𝐶𝐴𝛼 𝐶𝐵
Where CA and CB are the concentration of the species A and B respectively, each has the powers and , while 𝑘 is the reaction rate constant. The power of and are the partial reaction orders. In this experiment, we can calculate the reaction rate constant, 𝑘 by the following formula. 𝑘=
𝑣0
𝑋 ( ) 𝑉𝐶𝑆𝑇𝑅 1 − 𝑋
Where, 𝑘 is the reaction rate constant, 𝑣0 the total inlet flow rate of solutions, 𝑉𝑇𝐹𝑅 is the reactor volume, 𝐶𝐴 0 is the inlet concentration of reactant NaOH in the reactor, and 𝑋 is the percentage of conversion. From definition, rate of reaction is defined as the rate of disappearance of reactant or rate of formation of product. Rate of reaction of each species corresponds respectively to their stoichiometric coefficient. −𝑟𝐴 −𝑟𝐵 𝑟𝐶 𝑟𝐷 = = = 𝑎 𝑏 𝑐 𝑑 The negative sign indicates reactants while the positive sign indicates products. A usual equation for rate of reaction is 𝛽
−𝑟𝐴 = 𝑘𝐶𝐴𝛼 𝐶𝐵
Where CA and CB are the concentration of the species A and B respectively, each raised to the powers and , while kA is the reaction rate constant. The exponents and are the partial reaction orders. The overall order of reaction is given by the following: 𝑛=𝛼 + 𝛽 4
Tubular flow reactors are one type of flow reactors. It has continuous inflow and outflow of materials. In the tubular reactor, the feed enters at the one end of a cylindrical tube and the product stream leaves at the other end. The lack stirring in the long tube prevent the fluid from mixing completely in the tube. Assumptions that was made was there is no mixing in axial direction, complete mixing in radial direction and an uniform velocity profile across the radius.
4.0 APPARATUS AND MATERIAL
APPARATUS
1. Burette 2. Dropper 3. Conical flask 4. Measuring cylinder
MATERIALS
1. Hydrochloric acid (HCI) 2. Sodium Hydroxide (NaOH)
FIGURE 4.0 SOLTEQ (BP101-B)
3. Ethyl Acetate
5.0 PROCEDURES 5.1 General Start-Up Procedures 1. All valves were initially closed except valves 7. 2. Solution was prepared for the experiment. 3. The power for the control panel was turned on. 4. Water jacket B4 and pre-heater B5 were filled with clean water. 5. Stirrer motor was switched on and the speed of motor was set about 200 rpm. 6. Valve V2 and V10 were opened. Switch on the pump P1 and P1 was adjusted to flowrate of 700 mL/min at flow meter F1-01. Valve 10 was closed and pump P1 was switched off.
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7. Valve V6 and V12 were opened. Switch on the pump P2 and P2 was adjusted to flowrate of 700 mL/min at flow meter F1-02. Valve 12 is closed and pump P2 is switched off. 8. The unit was ready for experiment. 5.2 EXPERIMENT 1: Pulse Input In A Tubular Flow Reactor 1. The general start-up procedures were performed. 2. Valve V9 was opened and pump P1 was switched on. 3. Pump P1 flow controller was adjusted to give a constant flow rate of de-ionized water into the reactor R1 at approximately 700 ml/min at FI-01. 4. Let the de-ionized water to continue flowing through the reactor until the inlet (QI-01) and outlet (QI-02) conductivity values were stable at low levels. Both conductivity values was recorded. 5. Valve V9 was closed and pump P1 was switched off. 6. Valve V11 was opened and pump P2 was switched on. The timer was taken simultaneously. 7. Pump P2 flow controller was adjusted to give a constant flow rate of salt solution into the reactor R1 at 700 ml/min at FI-02. 8. Let the salt solution to flow for 1 minute, then reset and restart the timer. This will start the time at the average pulse input. 9. Valve V11 was closed and pump P2 was switched off. Then, valve V9 was quickly opened and pump P1 was switched on. 10. The de-ionized water flow rate was always maintained at 700 ml/min by adjusting P1 flow controller. 11. Both the inlet (QI-01) and outlet (QI-02) conductivity values at regular intervals of 30 seconds were recorded. 12. The conductivity values were continually recorded until all readings were almost constant and approach the stable low level values.
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5.3 EXPERIMENT 2 : Step Change Input In A Tubular Flow Reactor 1. The general start-up procedures was performed. 2. Valve V9 was opened and pump P1 was switched on. 3. Pump P1 was adjusted flow controller to give a constant flow rate of de-ionized water
into the reactor R1 at approximately 700 ml/min at FI-01. 4. Let the de-ionized water to continue flowing through the reactor until the inlet (QI-01)
and outlet (QI-02) conductivity values were stable at low levels. Both of the conductivity values were recorded. 5. Valve V9 is closed and pump P1 was switched off. 6.
Valve V11 was opened and pump P2 was switched on. The timer was start simultaneously.
7.
Both of the inlet (QI-01) and outlet (QI-02) conductivity values were recorded at regular intervals of 30 seconds.
8. The conductivity values were continually recorded until all readings were almost
constant. 5.4 General Shut-Down Procedures 1. Pump P1, P2 and P3 were switched off. Valves V1 and V2 were closed. 2. The heater also switched off. 3. The cooling water was kept circulating through the reactor while the stirrer motor was running to allow the water jacket to cool down to room temperature. 4. If the equipment is not going to be used for long period of time, all liquid from the unit are drained by opening valves V1 to V16. The feed tanks were rinsed with clean water. 5. The power for the control panel was turned off.
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6.0 RESULT AND CALCULATION
Conversion 0% 25% 50% 75% 100%
TABLE 6.0 Data Obtained For Conductivity Solution Mixtures Concentration Conductivity, 0.1 M 0.1 M of NaOH (M) H2 O 𝜿 (mS/cm) NaOH Na(Ac) 100 mL 75 mL 50 mL 25 mL -
25 Ml 50 mL 75 mL 100 mL
100 mL 100 mL 100 mL 100 mL 100 mL
0.0500 0.0375 0.0250 0.0125 0.0000
11.45 7.52 5.83 1.95 0.1195
Conductivity vs Conversion 14
Conductivity(mS/cm)
12 10 8 6 4
y = -0.1129x + 11.02 R² = 0.9832
2 0 0 -2
20
40
60
80
100
120
Conversion(%)
FIGURE 6.0 Graph Of Conductivity Versus Conversion
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Calculation : TABLE 6.1 Calculated Value From The Conductivity
𝑥
TOTAL
𝑛 [ ∑𝑥
𝑥2
𝜅
𝜅2
𝑥𝜅
0
11.95
0
0
131.1025
0.25
7.52
0.0625
1.88
56.5504
0.5
5.83
0.25
2.915
33.9889
0.75
1.95
0.5675
1.4625
3.8025
1.00
0.1195
1
0.1195
0.0143
2.5
26.8695
1.875
6.377
225.4586
∑𝑥
∑𝑦 𝑎0 ] [𝑎 ] = [ ] 1 2 ∑𝑥 ∑ 𝑥𝑦 𝑎0 𝑛 [𝑎 ] = [ ∑𝑥 1 =[
∑ 𝑥 −1 ∑ 𝑦 ] [ ] ∑ 𝑥𝑦 ∑ 𝑥2 𝑛 ∑𝑥
=[
∑ 𝑥 −1 ∑ 𝜅 ] [ ] ∑ 𝑥𝜅 ∑ 𝑥2
5 2.5 -1 26.8695 ] [ ] 2.5 1.575 6.377
11.0201 =[ ] −11.2927 𝜅 = 11.0201 − 11.2927𝑥 𝑅=
𝑛 ∑ 𝑥𝑦 − ∑ 𝑥 ∑ 𝑦 √(𝑛 ∑ 𝑥 2 − (∑ 𝑥)2 (𝑛 ∑ 𝑦 2 − (∑ 𝑦)2 )
=
5(6.377) − (2.5)(26.8695) √9.375 − 6.75)(1127.293 − 721.9700) −35.2888
= | 35.5898 | = 0.9915
Therefore, since R2 = 0.9832, the calibration curve is still reliable as it suffers only 1.6843% deviation from perfect unity. From the table above also, conversion and concentration are related by equation C = −0.0125𝑥 + 0.062
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EXPERIMENT 1 : Pulse Input In A Tubular Flow Reactor Flow Rate = 700 mL/min Input Type = Step change TABLE 6.2 Data Obtained for the Conductivity
Conductivity, 𝜿 (mS/cm) Time(min) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Inlet
Outlet
0.2 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.4 0.5 0.4 0.2 0.0 0.0 0.0 0.0 0.0 0.0
Outlet Conversion, 𝒙 0.9759 0.9404 0.9316 0.9404 0.9581 0.9759 0.9759 0.9759 0.9759 0.9759 0.9759
Outlet Concentration, C (M) 0.050301 0.050745 0.050855 0.050745 0.050524 0.050301 0.050301 0.050301 0.050301 0.050301 0.050301
FIGURE 6.1 Graph Of Outlet Conductivity Versus Time
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FIGURE 6.2 Graph Of Concentration Against Time
∞
∫ 𝐶(𝑡)𝑑𝑡 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 0
𝐴 = (𝑡𝑛−1 − 𝑡𝑛 ) [
𝑓(𝑡𝑛−1 ) + 𝑓(𝑡𝑛 ) ] 2
Sample calculation, for time between 0 to 0.5 minutes, 𝐴 = (0.5 − 0.00) (
0.050301 + 0.050745 mol ∙ min ) = 0.252615 2 m3
Time interval (minute) 0.00-0.50 0.50-1.00 1.00-1.50 1.50-2.00 2.00-2.50 2.50 – 3.00 Total area
𝐦𝐨𝐥∙𝐦𝐢𝐧
Area (
𝐦𝟑
)
0.025262 0.025400 0.025400 0.025317 0.025206 0.025151 0.151736
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Total Area, 4
∫ 𝐶(𝑡)𝑑𝑡 = 0.151736 0
mol ∙ min m3
Next is the calculation of E(t) or residence time distribution function. The following is the formula to calculate 𝐸(𝑡) =
𝐶(𝑡) ∞ ∫0 𝐶(𝑡)𝑑𝑡
(min−1 )
Sample calculation, 0.050301 mol⁄m3 mol At 𝑡 = 0.00, C = 0.050301 = 0.331504 min−1 ⁄m3 . 𝐸(𝑡) = mol ∙ min 0.151736 ⁄m3
Time(min) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Concentration (M) 0.050301 0.050745 0.050855 0.050745 0.050524 0.050301 0.050301 0.050301 0.050301 0.050301 0.050301
E(t) (min-1) 0.331504 0.334431 0.335156 0.334431 0.332974 0.331504 0.331504 0.331504 0.331504 0.331504 0.331504
FIGURE 6.3 Residence Time Distribution (RTD) Function For Plug Flow Reactor 12
Next we calculate the mean residence time by computing the area under the graph, and multiplying it with 𝑡. This is mathematically shown as: ∞
𝑡𝑚 =
∫0 𝑡𝐸(𝑡) 𝑑𝑡 ∞
∫0 𝐸(𝑡) 𝑑𝑡
∞
= ∫ 𝑡𝐸(𝑡) 𝑑𝑡 0
∞
From the expression above, ∫0 𝐸(𝑡) 𝑑𝑡 is expected to be equal to 1. 𝑡𝐸(𝑡) is dimensionless. Integrating it with respect to 𝑑𝑡 gives a value of time. This is the mean residence time. Sample calculation, for time interval between 0.0 – 0.5 minutes, 0.331504 + 0.334431
𝐴 = (0.5 − 0.00) (
2
) = 0.166484
Time interval (minute) 0.00-0.50 0.50-1.00 1.00-1.50 1.50-2.00 2.00-2.50 2.50 – 3.00 Total
Area 0.166484 0.167397 0.167397 0.166851 0.166120 0.165752 1.000001
As expected, ∞
∫ 𝐸(𝑡)𝑑𝑡 = 1.000001 min−1 0
𝒕 0 0.5 1.0 1.5 2.0 2.5 3.0
𝑬(𝒕) 0.331504 0.334431 0.335156 0.334431 0.332974 0.331504 0.331504
𝐂(𝒕) 0.050301 0.050745 0.050855 0.050745 0.050524 0.050301 0.050301 ℎ
𝑡𝑚 = ∫0 𝑓(𝑥)𝑑𝑥 =
0.5 3
𝒕𝑬(𝒕) 0 0.167215 0.335156 0.501647 0.665948 0.82876 0.994512
(𝒕 − 𝒕𝒎 ) -1.504535 -1.004535 -0.504535 -0.004535 0.495465 0.995465 1.495465
(𝒕 − 𝒕𝒎 )𝟐 𝑬(𝒕) 0.750401 0.337471 0.085316 0.000007 0.081740 0.328504 0.741381
(𝒕 − 𝒕𝒎 )𝟑 𝑬(𝒕) -1.129004 -0.339002 -0.043045 -0.00000003119
0.040499 0.327014 1.108709
(0 + 4(0.167216) + 2(0.355156) + 4(0.501647) +
2(0.665948) + 4(0.828760) + 0.994512) = 1.504535 minutes ∞
Second moment, variance, 𝜎 2 = ∫0 (𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡. By polynomial regression, the data in the sixth column needed to find the second moment could be related with 𝑡 using function 𝑓(𝑡) = 0.3313𝑡 2 − 0.9974𝑡 + 0.7515, with value of 𝑅 2 = 1.00. Thus,
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∞ 2
5
)2
𝜎 = ∫ (𝑡 − 𝑡𝑚 𝐸(𝑡) 𝑑𝑡 = ∫ 0.3313𝑡 2 − 0.9974𝑡 + 0.7515 𝑑𝑡 = 5.0942 0
0 1
∞
Third moment, skewness, 𝑠 3 = 𝜎1.5 ∫0 (𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡. By polynomial regression, the data in the seventh column needed to find the skewness could be related with 𝑡 using function 𝑓(𝑡) = 0.3307𝑡 3 − 1.4926𝑡 2 + 2.2475𝑡 − 1.1295, with value of 𝑅 2 = 1.00. Thus, ∞ 1 𝑠 = 1.5 ∫ (𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡 𝜎 0 5 1 = ∫ 0.3307𝑡 3 − 1.4926𝑡 2 + 2.2475𝑡 − 1.1295 𝑑𝑡 0.74791.5 0 = 1.0373 3
Result of calculations 𝑡𝑚 = 1.504535 minute 𝜎 2 = 0.7479 𝑠 3 = 0.017741
EXPERIMENT 2 : Step Change Input In A Tubular Flow Reactor
TABLE 6.3 Data Obtained for the Conductivity
Conductivity (mS/cm) Time(min) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Inlet
Outlet
0.0 3.6 3.7 3.7 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.9 3.9
0.0 0.0 0.0 0.2 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Outlet conversion 0.975861 0.975861 0.975861 0.958150 0.949295 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440 0.940440
Outlet concentration (M) 0.050302 0.050302 0.050302 0.050523 0.050634 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745 0.050745
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Outlet conductivity vs time 0.45
Outlet conductivity(mS/cm)
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05
0
1
2
3
4
5
6
7
8
9
Time(min)
FIGURE 6.4 Graph of outlet conductivity versus time
FIGURE 6.5 Concentration versus time
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Stepwise notation of the concentration would be, 𝐶0 (𝑡) {
0 for t < 0 (𝐶0 ) for t ≥ 0
Because we assume inlet concentration to be constant from the point where inlet conductivity stays constant, we take 𝐶0 = 0.0545. Conductivities, 𝜅 (mS/cm) Inlet Outlet 0 0 3.6 0 3.7 0 3.7 0.2 3.8 0.3 3.8 0.4 3.8 0.4
Time (min)
0 0.5 1.0 1.5 2.0 2.5 3.0
𝐶(𝑡) ∙ 𝑡
Outlet concentration, 𝐶(𝑡) (M) 0.050302 0.050302 0.050302 0.050523 0.050634 0.050745 0.050745
0 0.025151 0.050302 0.075785 0.101268 0.126863 0.152235 0.531604
𝐸(𝑡) 𝐶(𝑡) ∙ 𝑡 = ∑ 𝐶(𝑡) ∙ 𝑡 0 0.047212 0.094623 0.142559 0.190495 0.238642 0.286369 0.999999
Next the moments are calculated. 𝒕 0 0.5 1.0 1.5 2.0 2.5 3.0
𝐂(𝒕) 0.050302 0.050302 0.050302 0.050523 0.050634 0.050745 0.050745
(𝒕 − 𝒕𝒎 ) 0 0 -0.8574 0.047212 0.023606 -0.3574 0.094623 0.094623 0.1426 0.142559 0.2138385 0.6426 0.190495 0.38099 1.1426 0.238642 0.596605 1.6426 0.286369 0.859107 2.1426 𝑬(𝒕)
𝒕𝑬(𝒕)
(𝒕 − 𝒕𝒎 )𝟐 𝑬(𝒕) 0 0.006030613 0.001924136 0.058867566 0.248697844 0.643888275 1.314644122
(𝒕 − 𝒕𝒎 )𝟑 𝑬(𝒕) 0 -0.002155341 0.000274382 0.037828298 0.284162157 1.057650881 2.816756497
ℎ
𝑡𝑚 = ∫0 𝑡𝐸(𝑡)𝑑𝑡. By polynomial regression, 𝑡𝐸(𝑡) can be related to 𝑡 by equation 𝑓(𝑡) = 0.0959𝑡 2 − 0.0014𝑡 + 0.0002. Thus, 3
𝑡𝑚 = ∫0 0.0959𝑡 2 − 0.0014𝑡 + 0.0002 𝑑𝑡 = 0.8574 minutes ∞
Second moment, variance, 𝜎 2 = ∫0 (𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡. By polynomial regression, the data in the sixth column needed to find the second moment could be related with 𝑡 using function 𝑓(𝑡) = 0.0956𝑡 3 − 0.164𝑡 2 + 0.0703𝑡 , with value of 𝑅 2 = 1.00. Thus, ∞
3
𝜎 2 = ∫ (𝑡 − 𝑡𝑚 )2 𝐸(𝑡) 𝑑𝑡 = ∫ 0.0956𝑡 3 − 0.164𝑡 2 + 0.0703𝑡 𝑑𝑡 = 0.7763 0
0 1
∞
Third moment, skewness, 𝑠 3 = 𝜎1.5 ∫0 (𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡. By polynomial regression, the data in the seventh column needed to find the skewness could be related with 𝑡 using function 𝑓(𝑡) = 0.0953𝑡 4 − 0.2447𝑡 3 + 0.2088𝑡 2 − 0.0592𝑡, with value of 𝑅 2 = 1.00. Thus,
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∞ 1 (𝑡 − 𝑡𝑚 )3 𝐸(𝑡) 𝑑𝑡 ∫ 𝜎 1.5 0 3 1 = ∫ 0.0953𝑡 4 − 0.2447𝑡 3 + 0.2088𝑡 2 − 0.0592𝑡 𝑑𝑡 0.77631.5 0 = 1.8848
𝑠3 =
7.0 DISCUSSIONS The numerical methods adopted in evaluating the result obtained are Simpson’s Rules of Numerical Integration, and linear and polynomial regressions. The reason why linear and polynomial regressions are used because in evaluating the moments, the variables and its relations are ascended in degree, from 𝑛 = 1 to 𝑛 = 3 for pulse change, and 𝑛 = 4 for step change. Accuracy is also much higher when regression is utilized to come with the relationship between the variables, and hence integrations ensuing are also much accurate. Also, while the instruction requires us to only plot a curve of conductivity vs time, a graph of concentration vs time is still plotted nonetheless. This is because: 1. To show how each quantities are brought to their units. 2. To utilize the calibration curve. Experiment 1 : Pulse Input In A Tubular Flow Reactor In essence this experiment works in the following ways: 1. A tubular reactor is passed through with deionized water until it is homogenously filled with it. This is indicated by low conductivity values at both ends. 2. Salt solution is then passed through for one minute. 3. Deionized water is then passed through again, and the outlet concentration of the salt solution with respect to every point of time is recorded and plotted. A few observation and conclusion can be made. 1. The graph is shaped like bell. a. This indicates that as water is passed through the reactor, salt solution is gradually pushed out. b. From zeroth to first minute we see gradual increase of salt concentration, indicating that the amount of salt pushed out is increasing.
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c. Eventually the concentration decreases as the tubular flow reactor has water as its resident. The concentration perpetually decreases until eventually the concentration goes to roughly zero. 2. Analyzing the E(t) curve, if we are to take any two point in time, say from 𝑡 = 1 to 𝑡 = 2.5, Calculating the area under the graph by numerical integration, 𝐴=
3ℎ 1.5 (𝑓1 + 3𝑓2 + 3𝑓3 + 𝑓4 ) = (𝐸1 + 3𝐸1.5 + 3𝐸2 + 𝐸2.5 ) 8 8
= 0.1875(2.668875) = 0.5004 a. This means that 50.04% of the salt leaving the reactor spends time in the reactor between 1 to 2.5 minutes. That is the meaning of E(t). b. E(t), according to Fogler, is the fraction of material leaving the reactor that has resided in the reactor between any two point in time. (Fogler, 2008). 3. In its totality, we find that from zeroth minute to third minute, the area under the graph is equal to 1. a. Thus, all salt spent only three minutes in the reactor before they leave. b. That is why the experiment is required to run until the reading of conductivity stays constant at low value, to show that all salt has left the reactor. 4. The mean residence time is 1.5045 minute, while the peak is at around 1 minute. This should indicate positive skewness. This is consistent with the value of cubic s which is positive. The variance is 5.0942, and this is rightfully so. The high value indicates that the data is distributed widely, and is deviated far from normal distribution.
Experiment 2: Step Change Input In A Tubular Flow Reactor In essence, the experiment is done to see the time taken for salt solution to replace deionized water in the tubular reactor. Several observations are made. 1. It takes three minutes of the reactor to be filled with salt solution. a. This is deduced from the fact that the graph started to stay horizontal from t = 3 minutes. b. This brings a significant meaning because with both experiments run at flow rate 700 ml/min, both experiment took 3 minutes for complete discharge of salt solution (in pulse input experiment) and water (in step input experiment).
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2. There is slight fluctuation between 2.6 minutes to 2.75 minutes. This may be due to clogging/accumulation of salt that causes slight jump in reading. 3. The mean residence time does not signal anything significant. The graph is also positively skewed and this is rightfully shown by the graph. The variance is 1.8848, which is lower than that of pulse input. This may be due to the fact that narrower distribution is observed in this experiment. This is seen from the fact that 62.5% of the whole experiment operates at constant reading.
8.0 CONCLUSION This experiment is a success. It is found that be it through step change or pulse change, the time taken for the reactor to experience complete change of material is the same. Both graph exhibits positive skewness, and has rather marginally different value of variance. The theories are also proven to be true, where E(t) is dependent on time, and that residence time is also affected by concentration.
9.0 RECOMMENDATIONS Below are some recommendations that can help to get better and accurate results for the experiment. 1.
Make sure to open and close the right valve according to the procedure.
2.
The readings should be taken twice or thrice to and average is calculated to obtain more accurate and precise data.
3.
Make sure the equipment is in good condition and throughout the experiment, make sure there are no leakages happen.
4.
Perform the general start-up procedures correctly and make sure to also perform the general shut-down procedures before ending the experiment.
5.
Always run the experiment after fully understand the unit and procedures.
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10.0 REFERENCES
1.
Foglers. (n.d.). Retrieved from http://www.umich.edu/~essen/html/byconcept/chapter13.pdf
2.
Gurmen, F. &. (n.d.). Distribution of Residence Times for Chemical Reactors. Retrieved from http://www.umich.edu/~elements/fogler&gurmen/html/course/lectures/thirteen/index .htm#top3
3.
Stenstrom, M. (n.d.). Fundamentals of Chemical Reactor Theory. Retrieved from http://www.seas.ucla.edu/stenstro/Reactor.pdf
4.
Visual Encyclopedia of Chemical Engineering. (n.d.). Retrieved from http://encyclopedia.che.engin.umich.edu/Pages/Reactors/PFR/PFR.html
11.0 APPENDICES -see next page-
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