**4. Results and discussion**

A calibration curve was established using a freshly prepared stock solution of sodium hydroxide of various concentrations. For reaction samples, at time zero, the conductivity values were measured before the reaction was initiated to get the initial concentration of the solutions and then measured at each time interval in batch. Similarly, the samples from the exit of the flow reactors are measured to obtain the amount of sodium hydroxide reacted with ethyl acetate solution and were then correlated by the equation obtained by the slope of the calibration chart (**Figure 5**).

**Figure 4.** *Reaction scheme of saponification reaction.*

*Process Intensification in the Customized Flow Reactors DOI: http://dx.doi.org/10.5772/intechopen.101703*

**Figure 5.** *Calibration chart of standard concentration of NaOH and its conductivity values.*

#### **4.1 RTD studies**

The experiments were performed as per the procedure [22] for reactor type 1 and 2. A constant flow rate of 15.8 mL/min was set for all the tracer studies. The pulse input injection was done by the construction of a T-joint and an injection port, where a 10 mL tracer was used for every injection. For step input studies the input to the pump was transferred from inline water flow into the beaker containing the tracer solution. As we proceeded with the characterization of the flow reactors, the pulse method of injection was found to generate inaccurate and inconsistent data. So, final quantification experiments were conducted only with step inputs. Apart from sodium hydroxide, Rhodamine B was also used for the detection of flow patterns and presented data (**Table 1**).

The C, F, and E curves were drawn for each of the reactors set up. **Figures 6**–**8** represents curves for the tubular reactor of type 1. We observed an *F*(*t*) of 3.5 minutes was 0.12, 5.5 minutes was 0.35, which means 12% and 35% of the molecules spent less the 3.5 and 5.5 minutes respectively in the reactor. Also, we could derive 80% of the molecules spend 13 minutes or less in the reactor and around 20% of the molecules spend longer than 13 min in the reactor. We find that around 54% of the material leaving the reactor spends between 3.5 and 5.5 minutes. The long-time portion in this is between 21 and 36 minutes, which accounts for 3% of the material being spent in the reactor.


**Table 1.**

*Experimental residence time distribution parameters for reactor type 1 and 2.*

**Figure 6.** *F-curve, change in concentration (C/C0) with respect to time.*

**Figure 7.** *C-curve, tracer concentration with respect to time.*

**Figure 8.**

*E-curve, tracer concentration with respect to time.*

Similarly, the C, F, and E curves were developed for the packed bed reactor (type 2). **Figures 9**–**11** represent curves for the type 2 reactor setup. Here we observed an *F* (*t*) of 4 minutes was 0.21, 6 minutes was 0.35, which means 21% and 35% of the molecules spent less the 4 and 6 minutes respectively in the reactor. Also, we could derive 81% of the molecules spend 10 minutes or less in the reactor and around 20% of the molecules spend longer than 14 min in the reactor. We find that around 42% of the *Process Intensification in the Customized Flow Reactors DOI: http://dx.doi.org/10.5772/intechopen.101703*

**Figure 9.** *F-curve, change in concentration (C/C0) with respect to time.*

**Figure 10.** *C-curve, tracer concentration with respect to time.*

**Figure 11.** *E-curve, tracer concentration with respect to time.*

material leaving the reactor spends between 4 to 6 minutes. The long-time portion in this is between 18 and 24 minutes, which accounts for 5.5% of the material being spent in the reactor. So, the type 1 reactor behavior is better in comparison with type 2 reactor concerning the performance and behavior close to the ideality. The performance curves for type 3 reactor are similar to the type 1 reactor, as both are tubular flow reactors. Additional experiments for type 2 reactor were performed under gravity and against gravity conditions to compare the behavior of the two methods. The trend clearly shows the deviation is quite large with gravity conditions due to

by-passing, and channeling effects. To improve the performance, one could use running the packed columns against gravity with an add-on sintered plate at the top of the reactor which could change the dynamics and distributions of flow across the packed bed.

The mean residence time for type 1 and 2 reactors were found to be 9.05 and 11.28 minutes, where the average residence time was around 1.26 and 3.05 minutes respectively. This indicates there is a dispersion all along the fluid path and across boundaries.

The variance (*σ*2) is an indication of the "spread" of the distribution; the greater the value, the higher the distribution across the path for the reactor. In our case, it was around 124,890 and 244,385 s<sup>2</sup> , which clearly states that spread is almost twice in a packed bed reactor in comparison with the tubular reactor. The skewness factor measures the extent that a distribution is skewed in one direction or another about the mean. In general, all the three parameters mentioned above are essential to characterize the distribution and are enough to understand. A skewness factor(S) of around 7.70E+07 and 1.37E+08 sec3 was found for type 1 and type 2 reactors respectively.

The dispersion numbers were also estimated a trial and error basis. First assume a small dispersion, say σ<sup>2</sup> /tm <sup>2</sup> is equal to 2D/uL and equate to get the appropriate dispersion. In our case, we found 0.00068 and 0.0122 for type 1 and type 2 reactors respectively, which clearly states a smaller dispersion in the case of type 1 and reasonable large dispersion in type 2 reactor from ideal plug flow behavior. Since the dispersion number varies along the length of the reactor and the mean residence time is higher than that of the theoretical residence time, the reactors are classified as closed systems. The changes in the packing materials used in the packed column had a significant effect on the flow pattern. To further simplify the plug flow behavior, the ratio of the length of the reactor and their effective diameters revealed to be higher than 50 for all the systems.

The Peclet number (Pe) was estimated and found to be 1470 and 81 for type 1 and type 2 reactors. The behavior of reactor type 1 is more or like the plug flow and reactor type 2 is behaving far from ideal conditions.

The Reynolds number (Re) is dimensionless describes the ratio of inertial to viscous forces. The regime for flow through a packed bed may be identified by the packed bed Re. The type 1 reactor falls under the transitional region and type 2 reactor falls under the laminar region.

Bodenstein number (B0) was estimated and found to be 1452 and 81 for type 1 and type 2 reactor respectively. It could be concluded that both the reactors have varying degrees of back mixing, however, the variation in the flow velocity could be used to control or adjust B0 for the desired condition.

Similarly, the Damköhler number (Da) was estimated to realize the mass transfer rates using the standard equation available in the literature [19]. A 0.163 and 1.57 were found for type 1 and 2 reactors, which signifies diffusion occurs much faster than the reaction, thus diffusion reaches equilibrium well before the reaction is at equilibrium for type 1 reactor and diffusion-limited system for type 2 reactor.

#### **4.2 Estimation of kinetic parameters**

Kinetic experiments were carried out both in batch and flow reactors type 1 and type 2 with defined procedures. The batch experiments were conducted first with concentrations of 0.02 N of ethyl acetate and sodium hydroxide, volumes of 100 mL each. Experiments were performed at three different temperatures such as 26.5, 33 and 44°C respectively. An estimated quantity of ethyl acetate was charged to the reactor and the desired temperature was set through the circulator. An agitation of around 300 RPM was set using the overhead motor connected to the reactor. Once the temperature is stable, the calculated volume of freshly prepared sodium hydroxide solution was dosed into the reactor at one shot, simultaneously the stopwatch was started. A change in the conductivity was noted over time. As the reaction progresses, the conductivity value will decrease, like sodium hydroxide being used in the reaction to form sodium acetate in the solution. The decrease in the concentration of sodium hydroxide was measured against conductance. The C0, Ct, and C<sup>∞</sup> are the specific conductance of reaction mixtures at time zero, t, and infinity. Since the reaction follows second order kinetics, a plot of (C0 Ct)/(Ct C∞) versus time (**Figure 12**) was drawn to estimate rate constant (k) using the reliable method suggested in the literature [23]. Reaction conversion (X) was estimated using second-order kinetics, X = (1 CA/CA0) at every time interval, and reported. The reaction conversion was of the order 68% (42 min), 67% (40 min) and 78% (203 min) for temperatures 26.5, 33 and 44°C. A plot of ln k versus T (**Figure 13**) and ln k/T versus 1/T was plotted (**Figure 14**) to estimate various thermodynamic parameters such as activation energy, activation enthalpy, activation entropy, and Gibbs free energy of activation. The k values (**Table 2**) for temperatures 26.5, 33 and 44°C were in the order of 0.14, 0.215, and 0.305 Lmol<sup>1</sup> s <sup>1</sup> respectively.

A plot of ln k versus 1/T was plotted (**Figure 13** and **Table 3**) to estimate activation energy, the slope of the curve is 4118.5 and intercept of 11.837 to yield activation energy of 34.24 kJ/mol and Arrhenius constant of 8.05 <sup>10</sup><sup>6</sup> min<sup>1</sup> using the formula

**Figure 12.** *Graphical determination of reaction rate constant.*

**Figure 13.** *Arrhenius plot of activation energy.*

**Figure 14.**

*Graphical evaluation of thermodynamic properties.*


#### **Table 2.**

*Thermodynamic parameters of saponification reaction.*


#### **Table 3.**

*Effect of temperature on saponification reaction under batch conditions.*

*k* = *Ae*�*Ea*/*RT*, where *k* = rate constant at temperature *T*, *Ea* = activation energy, *R* = universal gas constant and *A* = Arrhenius constant. The other thermodynamic parameters were estimated using the Eyring-Polanyi Equation [23], through plotting ln k/T versus 1/T (**Figure 14**). The slope of the curve was �14.918 and the intercept was 0.0434, from the slope the activation enthalpy was estimated as �124.02 kJ/mol, activation entropy of 197.18 JK�<sup>1</sup> mol�<sup>1</sup> and Gibbs free energy of activation was 65.24 kJ/mol (**Table 2**). The results of the rate constant and activation energy for saponification reaction are in good agreement and comparable with the literature [22, 24–27, 29]. There could be reasonable errors associated with the sensitivity of conductivity probe and methods of estimation reported by various authors reported in the literature [22].

*Process Intensification in the Customized Flow Reactors DOI: http://dx.doi.org/10.5772/intechopen.101703*

Saponification experiments were conducted in the tubular reactor (type 1) of diameter 1.58 and 3.175 mm with a total reactor volume of 33.5 mL and varying flow rates from 6.7 and 13.4 mL/min respectively. Experiments were performed at two different temperatures such as 26.5 and 44°C. The concentrations of 0.02 N of ethyl acetate and sodium hydroxide solutions were used with varying residence time from 2.5, 5, and 10 min respectively. Once the temperature is stable in the thermostat, two pumps A & B were switched on to initiate the flow of sodium hydroxide solution and ethyl acetate solution into the tubular reactor, which was pre-calibrated for known residence time. Samples were collected regularly at the exit of the tube to measure the conductivity. Estimation of reaction conversion(X) was obtained using the standard irreversible bimolecular second-order equation, X = (1 � (CA/CA0)), and rate constants were estimated using equation XA/(1 � XA)=kCA0 t individually and averaged across experiments. The conversions are in the order of 68–76.6% for experiments at 26.5 and 44°C respectively (**Figure 15**). The k values for temperatures 26.5 and 44°C were in the order of 0.347 and 0.419 Lmol�<sup>1</sup> s �<sup>1</sup> respectively.

Further saponification experiments were conducted in a packed bed reactor (type 2) of diameter and length of the reactor as 24 and 240 mm respectively. The total volume of the reactor is around 105 mL with packing and 56 mL as an available volume for the reaction. The experiments were conducted under gravity and against gravity flow to check the performance of the reactor.

The flow rates for gravity flow experiments were in the range of 6.7, 7.8, and 8.4 mL/min respectively. Experiments were performed at two different temperatures such as 26.5 and 44°C. The concentrations of 0.02 N of ethyl acetate and sodium hydroxide solutions were used with varying residence time from 6.66, 7.17, and 8.35 min respectively. Once the temperature is stable in the thermostat, two pumps A & B were switched on to initiate the flow of sodium hydroxide solution and ethyl acetate solution into the reactor, which was pre-calibrated for known residence time. Samples were collected regularly at the exit of the tube to measure the conductivity. Estimation of reaction conversion (X) was obtained using a standard irreversible bimolecular second-order equation, X = (1 � (CA/CA0)), and rate constants were estimated using equation XA/(1 � XA)=kCA0 t individually and averaged across experiments. The conversions are in the order of 56–63% for experiments at 26.5 and 44°C respectively (**Figure 16**). The k values for temperatures 26.5 and 44°C were in the order of 0.167 and 0.171 Lmol�<sup>1</sup> s �<sup>1</sup> respectively.

Similar experiments were conducted in a packed bed reactor (type 2) against gravity flow through feeding the streams from the bottom of the reactor to minimize the channeling effect in the packed bed reactor.

**Figure 15.** *A plot of reaction conversion verses residence time in tubular reactor (type-1).*

**Figure 16.** *A plot of reaction conversion verses residence time in packed bed reactor (type 2) under gravity flow.*

The flow rates for gravity flow experiments were in the range of 6.8, 7.8, and 8.4 mL/min respectively. Experiments were performed at two different temperatures such as 26.5 and 44°C. The concentrations of 0.02 N of ethyl acetate and sodium hydroxide solutions were used with varying residence time from 6.66, 7.17, and 8.235 min respectively. Once the temperature is stable in the thermostat, two pumps A & B were switched on to initiate the flow of sodium hydroxide solution and ethyl acetate solution from the bottom of the reactor, which was pre-calibrated for known residence time. Samples were collected regularly at the exit of the tube to measure the conductivity. Estimation of reaction conversion (X) was obtained using a standard irreversible bimolecular second-order equation, X = (1 � (CA/CA0)), and rate constants were estimated using equation XA/(1 � XA)=kCA0 t individually and averaged across experiments. The conversions are in the order of 63.7–73.3% for experiments at 26.5 and 44°C respectively (**Figure 17**). The k values for temperatures 26.5 and 44°C were in the order of 0.22 and 0.288 Lmol�<sup>1</sup> sec�<sup>1</sup> respectively.

A new set of experiments was conducted in tubular bed reactor (type 1) submerged in Sonicator bath with sonication frequency (40 Hz) and performed experiments under the following conditions to check the effect of sonication on reaction kinetics under identical conditions.

The flow rates were in the range of 3.35, 6.7, and 13.4 mL/min respectively. Experiments were performed at two different temperatures such as 26.5 and 44°C. The concentrations of 0.02 N of ethyl acetate and sodium hydroxide solutions were used with varying residence time from 2.5, 5, and 10 min respectively. Once the temperature is stable, two pumps A & B were switched on to initiate the flow of sodium hydroxide solution and ethyl acetate solution to the reactor, which was precalibrated for known residence time. Samples were collected regularly at the exit of the tube to measure the conductivity. Estimation of reaction conversion(X) was obtained using a standard irreversible bimolecular second-order equation,

*Process Intensification in the Customized Flow Reactors DOI: http://dx.doi.org/10.5772/intechopen.101703*

**Figure 18.**

*A plot of reaction conversion verses residence time in tubular reactor (type-2) under sonication bath.*

X = (1 � (CA/CA0)), and rate constants were estimated using equation XA/(1 � XA)=k CA0 t individually and averaged across experiments. The conversions are in the order of 59–72.3% for experiments at 26.5 and 44°C respectively (**Figure 18**). The k values for temperatures 26.5 and 44°C were in the order of 0.30 and 0.374 Lmol�<sup>1</sup> s �1 respectively.
