Continuous Stirred Tank Reactors - Research Paper Example

Division of Chemical and Petroleum Engineering CONTINUOUS STIRRED TANK REACTORS Effect of Residence Time on Conversion Report Written by “I hereby declare that this report is my own work and effort and that is has not been submitted anywhere for any award. Where other sources of information have been used they have been acknowledged” _______________________ Signature Name Contents ABSTRACT 3 SUMMARY 3 OBJECTIVES 3 INTRODUCTION 4 EXPERIMENTAL THEORY 4 EXPERIMENTAL EQUIPMENT AND APPARATUS 6 EXPERIMENTAL PROCEDURE 7 EXPERIMENTAL RESULTS 9 DATA ANALYSIS AND CALCULATIONS 15 CONCLUSIONS 17 NOMENCLATURA 18 REFERENCE 19 ABSTRACT The goal for this research was the study of continuous stirred tanks in series. We have studied CSTR in series configuration to estimate the conversion of reactant in a cascade of three continuous stirred tanks. In addition, we have studied the effect of flowrate on the conversion of reactant in one tank. Conversion of reactant is then estimated by graphical/numerical integration for both the experimental results and theoretical data. We have implemented two experiments and we have compared their results with numerical simulations. We have confirmed the variations of salt concentration with time in each tank and we compared with results expected from theoretical equations. SUMMARY In chemical industry it is common practice to use a number of tanks connected in series equipped with agitators. These systems are frequently used to know the time required to reduce the concentration of off-quality material in the system below a certain acceptable limit. In this research we have studied continuous stirred tanks connected in series, and we evaluated experimentally the variation in concentration in the series configuration. We have confirmed the exponential decay of the concentration initial varying with time within the first tank. In addition, we have proved the characteristic profile for subsequent tanks connected in series: Initially starts to grow and then begin to decay exponentially with time. On the other hand, we have studied the conversion of reactants as a function of flowrate. In order to calculate conversion factors, we have implemented the Simpson’s rule to integrate numerically the area under the curves experimentally. Thus, we have confirmed the predicted concentration as a function with time in the continuous stirred tanks. OBJECTIVES 1. To simulate the conversion of reactant in a cascade of three continuous stirred tanks. 2. To determine the effect of flowrate (i.e. residence time) on the conversion of reactant in one tank in a cascade of continuous stirred tanks. INTRODUCTION Nowadays, chemical industry has processes that involve the mix of reactants to a cascade of several continuous reactors in series, i.e. CSTR. In thanks-in-series reactor configuration the effluent of one reactor is entering a second one and so on [1]. The rate of reaction in each tank is affected by the concentration of the reactants at any specific time. For the manufacture of organic chemicals and pharmaceutical products the liquid phase reactions are carried out on small to medium scale. For example, in order to produce ethanol is necessary to get a reaction between sodium hydroxide and ethyl acetate [2]. In order to simply the model, in this research, we assume that there is no chemical reaction. The residence time behavior of a dissolved salt through a cascade of three continuous stirred tanks is examined at different flowrates for a constant starting concentration of salt. EXPERIMENTAL THEORY In this experiment, the following assumptions were made: a) salt concentration is proportional to solution conductivity (units: Siemens∙m-1) for dilute solution and does not vary very much with temperature. b) complete mixing takes place in each tank instantaneously. c) zero concentration corresponds to the concentration of the raw water supply, about 800 microSiemens∙cm-1 Tank 1: Water enters the tank with flowrate, Q and salt concentration C0 at zero time. The salt concentration C0 starts to decrease with time because it is diluted by influent water. Taking an incremental mass balance for the salt when the concentration changes by in time , we have the mass balance equation [3]. Mathematically, Rearranging we get: Equivalently, we have Where, the mean residence time is defined as, Rearranging, Eq. gives us: Integrating for time between 0 and t; and concentration between C0 and C1 gives: Rearrange to give: i.e. decreases exponentially with time. Tank 2: By similar differential mass balance and integration, we get: i.e. grows linearly with time, from up to t= and then starts to decrees exponentially with time. Tank 3: Similarly, the time dependent concentration in tank 3 is given by: i.e. C3 grows parabolically with time from t=0 up to to t= then starts to decrees exponentially with time. We release that the concentration in an tank connected in series can be written as: where at , . The maximum concentration occurs at , . [4] Standardized conductivity We pay attention that the standardized value of the conductivity in each tank was calculated from, Conductivity(t) – Conductivity of tap water(t=0) Reactant conversion The reactant conversions were calculated using the numerical method called, Simpson’s rule for experimental data. EXPERIMENTAL EQUIPMENT AND APPARATUS 1. Three equal sized Perspex tanks with provision for overflow from tank 1 to tank 2 then to tank 3, and for the overflow from drain. Each tank measures 152mm by 254mm deep with the overflow weirs being placed 228mm from the base. The tanks are stirred by propellers driven by the same drive motor. A rotameter controls the feed to tank 1. 2. A portable conductivity meter is available to measure the conductivity of the solution in each tank. It has four scales, which can be adjusted to give a reading in the desired range. For dilute solutions, conductivity is approximately proportional to salt concentration. The units on the meter must be checked. EXPERIMENTAL PROCEDURE Experiment 1 1. Fill the tanks with cold water directly from the tap initially, and then through the rotameter unit all tanks are full and flowing freely down the cascade. Stop the water flow and remove half of the water from the first tank. Place 50g of sodium chloride in a 500ml beaker, add some cold water and stir with a glass rod to dissolve the salt. Pour the solution into the first tank and start the stirrers to mix completely. 2. Start the water flow at 1.0 litre per min into the first tank using the rotameter (range 0.2 to 3.4 L/min). The water levels in each tank will automatically adjust until the flow in and out of each tank is the same. 3. The test starts when the water starts to overflow from tank 1 to tank 2. Start the clock at this point and take conductivity readings in each tank at various time intervals, e.g. every 1 or 2 minutes, so that graphs of conductivity in each tank can be drawn as a function of time. The solution conductivity is measured by dipping the probe into the tank and allowing a few seconds before taking a reading. It is not necessary to wash the probe between readings. Also it is not necessary to sample all tanks at exactly the same time provided that the correct time is recorded for each reading. 4. Take a sample of tap water in a clean beaker and measure the conductivity. (Typically the conductivity of the tap water about 700 to 800 microSiemens cm-1). Obtain standardised values of the conductivity in each tank by deducting the conductivity of tap water from the values measured in step 3. For example, when the salt solution is added to tank 1 in step 1 and the tank is filled with water to the weir from the rotameter, the conductivity should be about 2000 microSiemens cm-1. 5. Deducting the conductivity of tap water (e.g. 800 mS∙cm-1) from this value gives the standardized value of the initial concentration: C0=(2000-800)=1200 mS∙cm-1 Experiment 2 Repeat the procedure in experiment 1 at water flowrates of 0.5 L/min and 2 L/min respectively, but measure the time dependent conductivity in tank 1 only. EXPERIMENTAL RESULTS Experiment 1 Flowrate = 1.0 L/min Measured C0 = 18.24 Tap water conductivity = 0.69 Standardised C0 = 17.55 Time (s) Tank 1 Measured conductivity (micro-Siemens/cm)   Tank 2 Measured conductivity (micro-Siemens/cm)   Tank 3 Measured conductivity (micro-Siemens/cm) Tank 1 Standardised conductivity (micro-Siemens/cm)   Tank 2 Standardised conductivity (micro-Siemens/cm)   Tank 3 Standardised conductivity (micro-Siemens/cm) 0 18.24 0.69 0.69 17.55 0 0 60 15.72 3.38 1.04 15.03 2.69 0.35 120 13.19 5.13 1.69 12.5 4.44 1 180 11.22 6.21 2.35 10.53 5.52 1.66 240 9.46 6.9 3.01 8.77 6.21 2.32 300 7.99 7.1 3.66 7.3 6.41 2.97 360 6.71 7.1 4.26 6.02 6.41 3.57 420 5.73 6.92 4.72 5.04 6.23 4.03 480 4.85 6.62 5.05 4.16 5.93 4.36 540 4.15 6.27 5.29 3.46 5.58 4.6 600 3.57 5.81 5.39 2.88 5.12 4.7 660 3.09 5.41 5.42 2.4 4.72 4.73 720 2.69 4.92 5.37 2 4.23 4.68 780 2.36 4.55 5.25 1.67 3.86 4.56 840 2.06 4.19 5.11 1.37 3.5 4.42 900 1.82 3.8 4.9 1.13 3.11 4.21 960 1.64 3.45 4.68 0.95 2.76 3.99 1020 1.45 3.13 4.43 0.76 2.44 3.74 1080 1.3 2.84 4.17 0.61 2.15 3.48 1140 1.17 2.56 3.91 0.48 1.87 3.22 1200 1.08 2.27 3.62 0.39 1.58 2.93 1260 1 2.1 3.4 0.31 1.41 2.71 1320 0.93 1.88 3.1 0.24 1.19 2.41 1380 0.89 1.66 2.91 0.2 0.97 2.22 1440 0.81 1.56 2.75 0.12 0.87 2.06 1500 0.76 1.45 2.53 0.07 0.76 1.84 1560 0.73 1.32 2.34 0.04 0.63 1.65 1620 0.69 1.22 2.14 0 0.53 1.45 Experiment 2 Measured C0 = 15.15 Tap water conductivity = 0.69 Standardised C0 = 14.46, 17.55,14.98 Time (s) Flowrate = 0.5 L/min Measured conductivity (micro-Siemens/cm)   Flowrate = 1.0 L/min Measured conductivity (micro-Siemens/cm)   Flowrate = 2.0 L/min Measured conductivity (micro-Siemens/cm) Flowrate = 0.5 L/min Standardised conductivity (micro-Siemens/cm)   Flowrate = 1.0 L/min Standardised conductivity (micro-Siemens/cm)   Flowrate = 2.0 L/min Standardised conductivity (micro-Siemens/cm) 0 15.15 18.24 15.67 14.46 17.55 14.98  120 13.24 13.19  13.82 12.55 12.50 13.13  240 11.42  9.46 11.8 10.73 8.77 11.11  360 9.87  6.71 9.95 9.18 6.02 9.26  480 8.56  4.85 8.37 7.87 4.16 7.68  600 7.4  3.57 7.12 6.71 2.88 6.43  720 6.44  2.69 6.03 5.75 2.00 5.34  840 5.62  2.06 5.16 4.93 1.37 4.47  960 4.88  1.64 4.38 4.19 0.95 3.69  1080 4.26  1.3 3.73 3.57 0.61 3.04  1200 3.71  1.08 3.21 3.02 0.39 2.52  1320 3.22  0.93 2.78 2.53 0.24 2.09  1440 2.84  0.81 2.42 2.15 0.12 1.73  1560 2.5  0.73 2.11 1.81 0.04 1.42  1680 2.21   1.85 1.52   1.16  1800 1.97   1.61 1.28   0.92  1920 1.75   1.44 1.06   0.75  2040 1.6   1.31 0.91   0.62  2160 1.42   1.17 0.73   0.48  2280 1.3   1.05 0.61   0.36  2400 1.2   0.98 0.51   0.29  2520 1.1   0.91 0.41   0.22  2640 1.03   0.86 0.34   0.17  2760 0.97   0.76 0.28   0.07  2880 0.9   0.72 0.21   0.03  3000 0.86   0.69 0.17   0.00  3120 0.82     0.13      3240 0.79     0.10     Experiment 1 The figure 1 shows standardized conductivity vs time for each tank. The solid-red line shows tank 1 standardized conductivity vs time. The solid-blue line shows tank 2 standardized conductivity vs time. Whereas, the solid-green line shows tank 3 standardized conductivity vs time. The three standardized conductivity curves show the expected conductivity profiles with the expected mean residence time, . The theoretical values of conductivity for each tank were calculated from the equations vi, vii,viii as is shown in the table below. For each tank, we show the theoretical and experimental conductivities in the figure 2, figure 3 and figure 4. For both the experimental and theoretical curves were calculated the area under the graph for each tank up to t=5τ. We have used the Sumpson’s rule as our numerical integration method [5]. The results were the following, Area under the curve in figure 2 (tank 1) is given as: Theoretically Experimentally Area under the curve in figure 3 (tank 2) is given as: Theoretically Experimenetally Area under the curve in the figure 4 (tank 3) is given as: Theoretically Experimentally With and . We take tank Experiment 2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. For tank 1 only, we have measured the standardised conductivity vs time. The profile for the standardised conductivity is as expected. The profile is affected by the flowrate. 11. Once again, for experimental curves were calculated the area under the graph for tank 1 up to t=5τ. We have used the Sumpson’s rule as our numerical integration method [5]. The results were the following, Area under the curve in figure 5 (solid-red line) with flowrate = 0.5 L/min is given as: Experimentally 12. Area under the curve in figure 5 (solid-green line) with flowrate = 1.0 L/min is given as: 13. Experimentally Area under the curve in figure 5 (solid-blue line) with flowrate = 2.0 L/min is given as: 14. Experimentally DATA ANALYSIS AND CALCULATIONS In order to study the effect of residence time on conversion we have used a chemical process that involves the addition of reactants to a cascade of several continuous reactors in series i.e. CSTR. Thus from the experimental data obtained for experiment 1 (see Experiment 1). As we expected, we got three shapes in agreement with theory, i.e. we get the standardized conductivity vs time that obeys the equations for tank 1, tank 2 and tank 3 respectively [6]. 15. The theoretical values of conductivity for each tank is in excellent agreement with theoretical predictions, with standardised conductivity and Figure 1 illustrates how standardized conductivities of the 3 tanks vary with time. The standardized conductivity for tank 1 decreases exponentially with time from a high conductivity value. The standardized conductivity for tank 2 grows linearly with time from t=0 up to and then starts to decreases exponentially with time. Similar shape goes for conductivity of tank 3 which grows parabolically with time from t=0 up to to t= then starts to decreases exponentially with time. The exponential decay of the standardized conductivity is characterized by mean residence time that depends in volumetric flowrate and volume of tank. In order to estimate the conversion of reactant in a cascade of three continuous stirred tanks, we have measured/calculated the conductivity for theses three reactors in cascade. We have calculated the area under the graph for each tank, in order to do so, we have implemented the numerical integration method Simpson’s rule using MATLAB. Both the experimental and theoretical area under the graph for each tank up to t=5τ. As we know, the area represents reactant conversion and should be approximately the same for all tanks. Because, theoretically it is equal to affected by a numerical factor when we integrated over a finite range, for example: Tank 1, area under the curve over Tank 2, area under the curve over Tank 3, area under the curve over We concluded that when the upper limit tends to infinity, we have the area under the curve equal to . The experimental reactant conversion is within an acceptable error 5.85%, 2.00% and 1.50% for tank 1, tank2 and tank 3, respectively. Finally, in experiment 2, we have studied both the reactant conversion and standardized profile as a function of flowrate. We confirm the expected conductivity profile as a function of flowrate, however when the flowrate is equal to 2 L/min it seems that the conductivity is overestimated. CONCLUSIONS After all experiment has been done we have find some points that make our conclusions. The conductivity of chemical solutions for tank 1, it decreases exponentially with time from a high conductivity value. The conductivity of chemical solutions for tank 2, it grows linearly with time from t=0 up to and then starts to decreases exponentially with time. The conductivity of chemical solutions for tank 3, it grows parabolically with time from t=0 up to to t= then starts to decreases exponentially with time. The theoretical values of conductivity for each tank is in excellent agreement with theoretical predictions, with standardised conductivity and the mean residence time in each tank agrees with theoretical predictions and depends on geometry (volume) and flowrate: , The experimental reactant conversion is within an acceptable error 5.85%, 2.00% and 1.50% for tank 1, tank2 and tank 3, respectively. For tank 1, area under the curve over is give as For tank 2, area under the curve over is given as For tank 3, area under the curve over is given as We concluded that when the upper limit tends to infinity, we have the area under the curve equal to . The area under the curves represents reactant conversion and should be approximately the same for all tanks. However reactant conversion is underestimated due to discrete experimental data. Finally, we confirm the expected conductivity profile as a function of flowrate, however when the flowrate is equal to 2 L/min it seems that the conductivity is overestimated. NOMENCLATURA Q = volumetric flowrate m3∙s-1 V = volume of tank m3 C = solution conductivity Siemens m-1 C0 = initial salt concentration in tank 1 Siemens m-1 C1 = conductivity in tank 1 at time t Siemens m-1 C2 = conductivity in tank 2 at time t Siemens m-1 C3 = conductivity in tank 3 at time t Siemens m-1 t = the time after start up s τ = mean residence time in each tank s REFERENCE 1. 2. [1] Carberry J. J., 1976 "Chemical & Catalytic Reaction Engineering", p.92, McGraw-Hill. 1976 [2] Denbigh K.G. and Turner J.C.R., 1984 “Chemical Reactor Theory: An Introduction”. p.1. CUP Archive, 1984. [3] Holland F.A. and Brag R. 1995, "Fluid Flow for Chemical and Process Engineers", p.164, 2nd Edition, Butterworth-Heinemann. [4] Holland F.A. and Chapman F.S., 1966, "Liquid Mixing and Processing in Stirred Tanks", p.109. Reinhold Pub. Corp. 1966. 3. [5] Trambouze P. and Euzen J.P. 2004 “Chemical Reactors: From Design to Operation”, p.123. Editions OPHRUS, 2004. [6] Ulrich, G.D. 1993 “A guide to chemical engineering reactor design and kinetics”, p.1 Ilustrated 1993. Read More