CE20186 – Mass Transfer Charlie Lower

Department of Chemical Engineering 1

Abstract  This experiment monitors how mixing conditions affect the mass transfer of oxygen in a reaction vessel by observing the rate of change of dissolved oxygen concentration in water and calculating the liquid-phase mass transfer coefficients for a curved pitched impeller and a pitched impeller under three different agitation speeds and two flow rates. Consequently, it is found that the greatest liquid-phase mass transfer coefficient is achieved is 0.0362 s-1 using a curved pitched impeller with a speed of 739 rpm and an air flow rate of 10 L min-1. 1 Introduction Dissolved oxygen (DO) is a valuable component in biochemical engineering as it allows the operation and efficiency of various biochemical processes to be determined. One example of this is found in the aerobic fermentation process of particular microorganisms such as yeast. It is essential that the desired amount of oxygen is transferred from one phase to another otherwise this could result in denaturing of the cells present in the system and hence a waste of feedstock for a given process. It is therefore imperative to closely monitor and control the amount of DO is a system in order to achieve a desirable product yield. The primary factors governing the rate at which oxygen dissolves into a system include; the concentration of DO already present in the process fluid, the speed and characteristics of the impeller for an agitated system and in some cases the process fluid temperature. Careful control of these parameters is necessary for the successful operation of a system. In some processes, the process fluid can transform from low-viscous Newtonian characteristics to a rheological complex viscous non-Newtonian fluid [1]. This means that correct choice of stirrer is essential. Impellers have different designs mainly to accommodate different fluid viscosities. This experiment features the gas-liquid mass transfer of oxygen in water for two stirrers (curved pitched and pitched impeller) under three different agitation velocities. The aim of this experiment is to investigate how mixing conditions affect the mass transfer of oxygen. In order to achieve this, the rate of change of dissolved oxygen concentration in water is investigated and the liquid-phase mass transfer coefficients are calculated and compared. 2 Theory Mass transfer sees the transition of mass, in this case mass of oxygen, travelling form a region of high concentration to low concentration. This is more commonly known as diffusion. Fick’s law expresses the relationship that relates diffusion to concentration of a substance;

𝐽 = −𝐷!!"!"

[2] The dissolution rate of oxygen in water, which is driven by a concentration gradient between maximum DO saturation (at constant temperature, pressure and salinity of water) and bulk DO concentration is defined as;

!"

!"= (𝑘!𝑎)(𝐶! − 𝐶) [3]

Let 𝐶∗ denote the dimensionless DO concentration i.e. DO percentage and 𝐶! is the initial DO concentration. Integrating equation (2.2) with these parameters gives;

ln 100 − 𝐶∗ = (−𝑘!𝑎)𝑡 ∴ ln 100 − 𝐷𝑂% = (−𝑘!𝑎)𝑡

Hence by plotting ln 100 − 𝐷𝑂% as a function of time, the gradient of the slope is equal to −𝑘!𝑎.

(2.1)

(2.2)

(2.3) (2.4)

CE20186 – Mass Transfer Charlie Lower

Department of Chemical Engineering 2

3 Method The apparatus used featured A 30 L glass vessel filled with 22 L of water equipped with a variable speed agitator. The rig comprised of a rotameter and a control valve that was directly linked to a nitrogen gas cylinder and an air stream inlet. The DO meter and its probe were linked directly and submerged in the water of the vessel. First, the DO meter was calibrated at 0% and 100% DO. This was achieved by exposing the probe in air until the calibration point was reached. After checking that the curved pitched impeller was securely fixed to the agitator device, the water in the vessel was purged with nitrogen until the saturation of DO was below 30%. This was achieved by shutting off the air supply completely and fully opening the nitrogen supply. Quicker purging was achieved by increasing the nitrogen flow rate and agitation speed. To measure the agitation speed, an infrared tachometer was held in line with the white indicator tape attached to the shaft of the impeller. The nitrogen supply was then shut off whilst turning on the air supply at a flow rate of 5 L min-1. The DO saturation was then recorded every 30 seconds with a stopwatch generally between saturation of 30-80% at a set agitation speed. The timing began when the DO saturation reached 30% i.e. at t=0, DO=30%. This procedure was repeated for three different agitation speeds and again for an air flow rate of 10 L min-1; ensuring the water in the vessel was purged with nitrogen between each run. Almost identical procedure was carried out for the pitched impeller however further calibration was not necessary. Note that it was extremely difficult to achieve the same agitation speeds for each impeller, as the control valve for the agitator motor was not greatly sensitive. 4 Results

Figure 4.1 Plot of ln(100-DO%) as a function of time for three agitation speeds at a flow rate of 5 L min-1 using a curved pitched impeller. Linear trend lines displayed.

Figure 4.2 Plot of ln(100-DO%) as a function of time for three agitation speeds at a flow rate of 10 L min-1 using a curved pitched impeller. Linear trend lines displayed.

0

1

2

3

4

0 20 40 60 80 100 120 140

ln(1

00-D

O%

) [-]

Time [s]

528 rpm

660 rpm

739 rpm

0

1

2

3

4

0 20 40 60 80 100 120

ln(1

00-D

O%

) [-]

Time [s]

528 rpm

660 rpm

739 rpm

CE20186 – Mass Transfer Charlie Lower

Department of Chemical Engineering 3

Figure 4.3 Plot of ln(100-DO%) as a function of time for three agitation speeds at a flow rate of 5 L min-1 using a pitched impeller. Linear trend lines displayed.

Figure 4.4 Plot of ln(100-DO%) as a function of time for three agitation speeds at a flow rate of 10 L min-1 using a pitched impeller. Linear trend lines displayed.

Figure 4.5 Plot of kLa as a function of agitation speed for both 5 and 10 L min-1 flow rates and both curved pitched and pitched impellers. Linear trend lines displayed. Table 4.1 Calculated values of 𝑘!𝑎 with corresponding volumetric flow rates and agitation speeds for both impeller designs.

Impeller Design Volumetric flow rate [L min-1]

Agitation speed [rpm]

𝑘!𝑎 [s-1]

Curved 5 528 0.0086 5 660 0.0018 5 739 0.0268 10 528 0.0129 10 660 0.0246 10 739 0.0362

0

1

2

3

4

5

0 20 40 60 80 100 120

ln(1

00-D

O%

) [-]

Time [s]

538 rpm

661 rpm

749 rpm

0

1

2

3

4

5

0 20 40 60 80

ln(1

00-D

O%

) [-]

Time [s]

538 rpm

661 rpm

749 rpm

0

0.01

0.02

0.03

0.04

500 550 600 650 700 750

k La

[m-1

]

Agitation Speed [rpm]

curved 5 L/min curved 10 L/min pitched 5 L/min pitched 10 L/min

CE20186 – Mass Transfer Charlie Lower

Department of Chemical Engineering 4

Pitched 5 538 0.0113 5 661 0.0171 5 749 0.0227 10 538 0.0157 10 661 0.0246 10 749 0.0324

5 Calculations In order to calculate ln(100-DO%), the observed experimental value for the dissolved oxygen saturation is subtracted and the natural logarithm of the answer is taken. For example, a DO value of 30%;

𝑙𝑛 100 − 30 = 𝑙𝑛  (70) = 4.2485 This value is then plotted against the corresponding time value. In this case, t=0 as DO=30% is the initial value. From the ln(100-DO%) versus time plots, the gradient is found by plotting a linear trend line. The equation of the linear trend line is in the form of y=mx+c where m is the gradient, x is time, c is the ln(100-DO%) intercept and y is ln(100-DO%). The gradient is the relevant part of the equation as this is equal to (−𝑘!𝑎). The gradient of the linear trend line for 528 rpm from figure 4.1 is y= -0.0086x + 4.2625. Hence;

−𝑘!𝑎 = −0.0086  𝑠!! ∴  𝑘!𝑎 = 0.0086  𝑠!!

6 Discussion Figures 4.1-4.4 show the same trends in the sense that all four plots express a linear increase in dissolved oxygen intake as time progresses. All four of these plots also show that as the agitation speed of each impeller is increased, the liquid-phase mass transfer coefficient increases. This is noticeable as the gradients of each impeller speed slope increase with impeller speed. This relationship is expected as the increased impeller speed allows greater agitation within the vessel. This is supported by Doran (2011) who states, “Under typical operating conditions, increasing the stirrer speed improves the value of 𝑘!𝑎”. [2] Figure 4.5 displays very significant results. One being that higher values of 𝑘!𝑎 are in fact achieved at the higher air flow rate. Furthermore, higher 𝑘!𝑎 values are achieved in this experiment using the curved pitch impeller. This may not seem feasible at first analysis, however it is not necessarily correct to use an impeller with more blades to achieve greater gas dispersion. This finding is supported by Doran (2011) who states, “increasing the number of impellers on the stirrer shaft does not necessarily improve 𝑘!𝑎 even though the power consumption is increased”. [2] There are various mechanisms that are related to the bubble flow rate and size influencing the uptake of dissolved oxygen. Examples such as temperature, sparger flow rate and design, however most importantly bubble size. It is very difficult to engineer a sparger that allows for accurate manipulation of bubble size so it is therefore necessary to agitate the reaction vessel with stirred impellers to alter the size off bubbles. This is supported by Doran (2011) who states, “The efficiency of gas-liquid mass transfer depends to a large extent on the characteristics of bubbles in the liquid medium. Bubble behaviour strongly affects the value of 𝑘!𝑎” [2] and “The most important property of air bubbles is their size. For a given volume of gas, more interfacial area is provided if the gas is dispersed into many small bubbles rather

CE20186 – Mass Transfer Charlie Lower

Department of Chemical Engineering 5

than a few large ones; therefore a major goal in bioreactor design is a high level of gas dispersion.” [2] This suggests that as the agitator speed is increased, the bubble size decreases allowing greater uptake of dissolved oxygen. Table 4.1 supports the results discussed previously as it shows how the higher 𝑘!𝑎 values are obtained at higher agitation speeds and higher air flow rates. However, there is not a great variation in 𝑘!𝑎 values between the two impeller designs. With any real working system, there are inevitable factors of error present that are not accounted for in an ideal system. This experiment features errors within the devices and methods used to record data. The rotameter used to measure the volumetric flow rate featured increments of 1 L min-1which poses potential error of ±0.5 L min-1. The infrared tachometer recorded the speed at which the shaft was rotating to 0.1 rpm suggesting possible error of ±0.05 rpm. The stopwatch used to observe the dissolved oxygen percentage every 30 seconds presents possible human error of approximately ±1.5 seconds. Another error lies within the vessel being exposed to the surrounding atmosphere. This means that the surface of the water is in contact with oxygen molecules present in the air which could inevitably alter the true value of the DO% supposedly coming from the air flow inlet. This error is difficult to quantify although calibration attempts to combat this. Furthermore the errors in this experiment do not posses great significance in regard to the accuracy of the data obtained, the focus is based on the impeller design and speed and also the air flow rate. 7 Conclusion This experiment aimed to investigate how mixing conditions affect the mass transfer of oxygen in a reaction vessel. After observing the rate of change of dissolved oxygen concentration in water and calculating the liquid-phase mass transfer coefficients, it is found that the greatest 𝑘!𝑎 value for this experiment is achieved with an air flow rate of 10 L min-1 and an agitation speed of 739 rpm using the curved pitch impeller. Therefore suggesting that the curved pitch impeller offers greater efficiency for the uptake of dissolved oxygen. Nomenclature 𝐽 Diffusion flux [mol m-2 s-1] 𝑥 Length [m] 𝐷𝑂% Dissolved oxygen percentage [-] 𝑡 Time [s] 𝐶 Concentration of DO [mol m-3] 𝐷! Diffusion coefficient [m2 s-1] 𝐶∗ Dimensionless DO concentration [-] 𝜇 Dynamic viscosity [Pa s] 𝐶! Initial DO concentration [mol m-3] 𝜌 Liquid density [kg m-3] 𝑘! Liquid-phase mass transfer coeff. [m s-1] 𝐷 Impeller diameter [m] 𝑎 Interfacial surface area [m-1] 𝑁 Agitation speed [rpm] 𝐶! Saturated DO concentration [mol m-3] References [1] Cabaret, F., Fradette L., and Tanguy, P.A., Gas-liquid mass transfer in unbaffled dual impeller mixers. Chemical Engineering Science, 2008. 63(6): p. 1636-1647. [2] Doran, P.M (2011). Bioprocess Engineering Principles. London: Academic Press p. 191, 202, 204. [3] Micheal H. Kim, F Joe Kragl, Oxygen mass transfer coefficient (kLa') consideration for scale-up fermentation systems at the biotechnology laboratory. 2011 p. 10.