KLa

KLa

KLa is the volumetric mass transfer coefficient, it consists of two terms “KL” (mass transfer coefficient) and “a” (Interfacial area of two different phases). Area “a” depends on size, shape and no of bubbles that depends on agitation speed and property of fluid these factor also affect K_L. It is difficult to measure “KL” and “a” separately so both the terms are combined as KLa, having unit h^-1.

KLa is used to determine aeration efficiency of bioreactor and quantifying the effect of variable operating parameters on dissolve oxygen.

Three mass transfer situation occurs in bioprocessing: Gas to Liquid, Liquid to Liquid and Liquid to Solid

In fermenter and Bioreactor oxygen transfer from supply air to cell taken place in three stages:

1)      Transfer of oxygen from air bubble to solution/media

2)      Transfer of dissolve oxygen from media solution to cell membrane

3)      Uptake of the dissolve oxygen by the cell

HOW TO DERIVE MASS TRANSFER EQUATION

As per Fick’s low of diffusion

Rate of mass transfer α Transfer area (TA) × Driving force (DF)

                                   = Mass transfer coefficient × TA × DF

The concentration gradient is the driving force for mass transfer of each fluid on either side of the phase boundary.

cA1 = concentration of component A in phase 1,

cA1i = concentration of component A at phase 1 interface,

cA2 = concentration of component A in phase 2,

cA2i = concentration of component A at phase 2 interface,

Rate of mass transfer ‘NA’ for component A in each phase, having interfacial area “a” NA1 = KL1a (cA1 – cA1i)    eq. 1 &  NA2 = KL2a (cA2i – cA2)   eq. 2 In a steady state, NA1 = NA2 = NA Therefore,  NA/KL1a = cA1 – cA1i    eq. 3 & NA/KL2a = cA2i – cA2    eq. 4 At equilibration solute concentration at two phase is given by distribution coefficient m = cA1i / cA2i so cA1i = m / cA2i or cA2i = cA1i / m therefore, NA/KL1a = cA1 – m/cA2i    eq. 5 & NA/KL2a = cA1i/m – cA2    eq. 6 Multiplying eq 4 by ‘m’ and dividing eq 3 by ‘m’ mNA/KL2a = mcA2i – cA2m  eq. 7 NA/mKL1a = cA1/m – cA1i/m     eq. 8 By adding eq. 7 to 5 and eq. 8 to 6 NA (1/KL1A + m/KL2a) = cA1 – cA2m     eq. 9 NA(1/KL2a +  1/mKL1a) = cA1/m – cA2      eq. 10 Bracketed terms for the combined mass transfer coefficient are used to define the overall phase mass transfer coefficient, 1/KL1a = 1/KL1a + m/KL2a 1/KL2a = 1/KL2a + 1/mKL1a Therefore, NA(1/KL1a) = cA1 – cA2m OR NA = KL1a(cA1-cA2m)    eq. 11 NA(1/KL2a) = cA1/m – cA2 OR NA = KL2a(cA1/m-cA2)      eq. 12 At equilibrium, cA2m = *cA1 Phase 1 Conc. Of component A is in equilibrium with phase 2 and cA1/m = *cA2 Phase 2 Conc. Of component A is in equilibrium with phase 1 Suppose, phase  1 = gas phase and phase 2 = liquid phase NA = KGa(cAG – *cAG) NA = KLa(*cAL – cAL) Different methods for KLa determination Generally, electrode sensor used for determination of dissolve oxygen (DO) in fermenter and bioreactor, which gives the data of dissolve oxygen tension (DOT) not the concentration. For determination of dissolve oxygen concentration, we should have the knowledge of oxygen solubility on that media. By multiplying the solubility with the DOT we can get the DO concentration. SULPHITE OXYDATION TECHNIQUE Principle: This technique is based on the oxidation of sodium sulphite to sodium sulphate, no required to measure the dissolve oxygen. When sodium sulphite (reducing agent) meets oxygen in presence of copper or cobalt ions, it oxidized to sodium sulphate. Take sample and add excess amount of iodine to the sample that react with the unoxydized sodium sulphite, carried out back titration of sample using sodium thiosulphate that react with unconsumed iodine. The volume of sodium thiosulphate consumed is directly proportional to dissolve oxygen concentration. Oxidation reaction: O2 + 2Na2SO3 = 2Na2SO4    (equation 1) Sulphite detection: 2Na2SO3 + 2I +2H2O = 2Na2SO4 + 4HI    (equation 2) Back titration for iodine: 4Na2S2O3 + 2I2 = 2Na2S4O6 + 4NaI  (equation 3) Procedure: Fill the fermenter with a 0.5M solution of sodium sulphite having 0.001M Cu+2 ions and aerated and agitated at fixed rates. Take out sample at define time interval and add excess of iodine which react with unoxydised sodium sulphite. Carried out back titration of sample with standard solution of sodium thiosulphate. Plot a graph of volume of sodium thiosulphate consumed Vs time of sample and the slope of this graph give the oxygen transfer rate.             OTR = KLa . c* As per above equation (1,2 and 3) 1mol O2 can oxidized 2mol Na2SO3 and 4mol Na2S2O3 consumed for back titration. Solubility of oxygen in 0.5M sulfite solution is 0.2mM per liter So      KLa = 1/4(mmol thiosulphate used/liter*hour) * 1/0.2Mml-1       OR     KLa = [(Normality of thiosulphate used ) * (ml used ) / (ml of sample) * (minutes in test)]        * [(1000 * 60 ) / (4 * 0.2)]                (unit h-1)     STATIC GASSING OUT METHOD In this technique, first oxygen is removed from the liquid with purging of nitrogen. Now start aeration and agitation at the set parameters so dissolve oxygen increased in deoxygenated liquid. Monitor the DO level using DO sensor and note down the DO level at time interval. DO concentration is determined by multiplying DO level with the oxygen solubility in respective liquid. The increase in dissolve oxygen has been described by equation dCL / dt = KLa (C* - CL)  integration of equation:  ln(C* -  CL) = - KLa . t A plot of ln(C* - CL) Vs time yield a straight line and the slope of this straight line is ­­­­(- KLa) (C* is the equilibrium oxygen concentration while CL is oxygen concentration at that time)  For below mentioned data,  KLa = 0.1292*3600 = 465.12

Time (sec)     DO % C* - CL    ln(C*-CL) 10 44 30.8 3.43 20 45.5 29.3 3.38 30 47.6 27.2 3.30 40 48.4 26.4 3.27 50 50 24.8 3.21 60 52.2 22.6 3.12 70 54.4 20.4 3.02 90 56 18.8 2.93 100 58.2 16.6 2.81 110 60.1 14.7 2.69 120 62.5 12.3 2.51 130 64 10.8 2.38 140 65.1 9.7 2.27 150 66.2 8.6 2.15 160 67.3 7.5 2.01 170 68.3 6.5 1.87 180 69.2 5.6 1.72 190 70.1 4.7 1.55 200 70.9 3.9 1.36 210 71.4 3.4 1.22 220 72 2.8 1.03 230 72.6 2.2 0.79 240 73 1.8 0.59 250 73.9 0.9 -0.11 260 74.2 0.6 -0.51 270 74.6 0.2 -1.61 280 74.8 0 #NUM! DYNAMIC GASSING OUT METHOD This method is based on the respiration rate of the organism which is used for the process. The procedure in this method is stopping the air supply to the fermentation which result in a linear decline in the DO concentration due to respiration of the culture. As shown in figure by stopping the air at point A, DO concentration decline to point B and slope of the line AB is a measure of respiration rate of the culture. Make sure DO level should not decrease below critical oxygen level which affect the respiration rate of organism. At point B aeration is resumed so DO concentration start to increase this increase in DO level depends on the amount of DO consumed by the organism and expressed by equation. dCL / dt = KLa (C* - CL) – XQO2    Where X = concentration of biomass and QO2 = specific respiration rate The slope line of AB gives XQO2  Rearrange above equation CL = -1/ KLa {( dCL/dt ) + XQO2)} + C* A plot of CL Vs  (dCL/dt ) + XQO2  give a straight line and slope of which equal to   -1/ KLa  OXYGEN BALANCE METHOD This method is useful for measuring the KLa at actual fermentation process. In this method, parameters of gas at inlet and outlets are measured and the difference of O2 at flow in and flow out must equal to rate of oxygen transfer from gas to liquid. The procedure involves measuring the following parameters. The volume of broth contained in the vessel VL (dm3), Airflow rate measured at air inlet (Qi) and outlet (Qo) (dm3/min), Pressure measured at air inlet (Pi) and air outlet (Po) (atm), Temperature of the gases at inlet (Ti) and outlet (To) (unit K), Mole fraction of oxygen measured at inlet (Yi) and outlet (Yo). OTR = 7.32 * 105 / VL (QiPiYi/Ti – QoPoYo/To) Where 7.32 * 105 is conversion factor equaling (60min/h, mole/22.4 dm3, 273K/1atm) KLa determined by using the equation OTR = KLa (C* - CL)