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A simple method to leverage fermentation heat transfer data.
Tracking the heat removal data from fermentation processes is a powerful aid in specifying scale-up characteristics such as cooling requirements. These same data can help define the metabolic activity of the cells in the fermenter. By reversing metabolic heat equations and defining the heat characteristics of the fermenter, the oxygen uptake rate can be determined from the fermenter heat removal data. This offers a simple, inexpensive method to determine the metabolic state of the fermentation. When the heat input and removal for a fermentation process have been properly investigated, the oxygen uptake rate determined from the metabolic heat equation will closely follow the values measured with external devices such as a mass spectrometer.
Gaining an understanding of a fermentation process can take many forms, such as investigating biomass increase, substrate use, metabolite production, and oxygen use. Of these metabolic indicators, one of the most common is the analysis of oxygen use. The oxygen uptake rate (OUR) can be measured through multiple methods. These techniques include a dynamic OUR determination method and a steady-state OUR method based on an overall oxygen balance. The dynamic OUR determination uses a dissolved oxygen probe that is located in the fermenter. The airflow is temporarily stopped during the fermentation and the rate of dissolved oxygen (DO) decline is used to determine the use of oxygen by the cells. This method requires accurate determination of the mass transfer coefficient and assurance that the system is not in the regime of DO dependent oxygen transfer. This method can be further confounded by factors such as slow DO probe response and localized oxygen conditions near the probe.
The steady-state method for determining OUR uses a material balance to calculate the amount of oxygen that is consumed by the fermentation. Essentially, the amount of oxygen entering the system is subtracted from the amount of oxygen leaving the system, and that difference is the oxygen uptake. This method requires very accurate gas flow measurement, a nitrogen balance to correct for flow differentials, and analytical equipment, such as a mass spectrometer. When all of the components are working properly, this method is quite accurate in describing the OUR of the entire system. Another method to determine OUR relies on a correlation between the fermentation heat transfer rate and oxygen uptake rate based on theoretical and empirical data. This method is very practical and can provide a quick answer because it uses equipment that is generally in place for a fermenter.
Heat balances often used in chemical engineering to break down very complex systems into manageable pieces. The underlying principle is that the heat inputs and outputs can be summed for a system to determine the flow of heat. In the case of fermentation, the heat balance represents a biological system that is in steady state. This means that the net heat difference when the inputs and outputs are added together is zero. Heat is generated and lost in fermentation systems. If the heat generation exceeds the heat loss, then the fermentation will require cooling to maintain steady-state conditions or steady temperature for the heat balance.
Sources of heat for fermentations include feeds, air in-flow, agitation, recirculation pumps, and the metabolic activity of the cells, which is the largest heat generation component. Sources of cooling for fermentations may include water evaporation, environment, and broth temperature increases. Each of these heat balance components is described in the following sections.
The heat input from the feeds can alternately be a heat loss depending on the conditions of the feed itself. If the feed is hotter than the fermentation broth temperature, then it will act as a heat input. If the feed is cooler than the fermentation broth, then it will act as a heat loss. The use of certain chemical additions, such as sulfuric acid for pH control, can also add reaction heat, but these generally represent a small portion of heat from feed inputs, and are routinely ignored. The operating conditions of the particular process in use will dictate the actual role that the feeds play with regard to the heat balance. The heat from the temperature difference between the feed and fermentation broth is calculated though the use of Equation 1:
RHs heat from substrate (W)
Qs = flow of substrate (m3/s)
ρs = density of substrate (kg/m3)
Cρs = heat capacity of substrate (J/kg/°K)
ΔT = temperature difference between broth and feed (°K)
The heat input from air is very similar to that of the feed additions. Again, as in the case of the feeds, this may not be the case for smaller scale fermentations, and needs to be dealt with as such. The heat input from airflow can be calculated from Equation 2:
RHA = heat from air (W)
QA = flow of air (m3/s)
ρA = density of air (kg/m3)
CρA = heat capacity of air (J/kg/°K)
ΔT = temperature difference between broth and air (°K)
The heat from the recirculation pumps that are used to force coolant through the jacket or coils is usually ignored, because it does not contribute much to the overall heat balance. This is another aspect of the system that should be investigated, depending on the particular fermenter layout.
The heat from the metabolic activity of the cells is the largest heat input component, especially when dealing with fast growing bacteria such as E. coli. As the cells respire, they release heat, in the same manner as a person working up a sweat while running on a treadmill. If the oxygen uptake rate is known, the amount of heat from the respiration of the cells can be determined using Equation 3:
RHM = heat from metabolism (W)
OUR = oxygen uptake rate (mmol/kg/hr)
G = weight of fermentation broth (kg)
The factor, 430, represents the amount of heat that is released per mmol of oxygen that the cells consume.1,2 This empirical factor may vary slightly from cell line to cell line, but as seen in previous work, there does not appear to be much variation, and this number can be adjusted as needed to meet the cellular requirements of the fermentation based on experimental data.1
The heat from the agitator can be calculated from theoretical models, which use the power number, the speed, and physical characteristics of the stirrer blade.2 The primary challenge with using the theoretical models is that there are many assumptions that have to be made about the agitation of the fermenter, especially when dealing with multiple impellers and a gassed system. It is simpler to determine the power draw of the agitator from direct electrical measurement. When measuring the power draw directly, the value will need to be multiplied by the efficiency of the motor to determine how much power is transferred to the fermentation broth. All of the power that is transferred to the fermentation broth is dissipated as heat. If the power draw for an agitator is 100 KW and the motor's efficiency is 0.9, then 90 KW of heat will be added to the heat balance of the fermenter.
The heat loss that results from the evaporation of water is caused by the airflow entering the fermenter. The airflow is generally not saturated with water, but becomes saturated as it passes through the fermentation broth. Heat is needed for this evaporation to occur, and this is counted as a loss to the system. At this point, it is important that the moisture condition of the air entering the fermenter is known. This can be determined by directly measuring the humidity of the air, or by tracing back the air supply to the point where the specific conditions of the air stream is known. The conditions of the air at either of those points can be used to identify the absolute moisture of the air using a psychrometric chart. The temperature of the air exiting the fermenter is assumed to be at the same temperature as the broth, which allows for the absolute humidity of the saturated exit air to be determined. The rate of water evaporation is determined by subtracting the water entering the system in the air from the water leaving the fermenter in the exit air. The mass flow rate is used to determine the heat needed to evaporate the water. This is calculated using Equation 4:
RHev = heat of evaporation (W)
Cv = heat of evaporation (2.27 x 106 J/kg)
ΔH2O = water evaporation (kg/s)
The heat loss of the vessel greatly depends on the particulars of the vessel in question. The construction materials, tank geometry, wall thickness, insulation use, and environmental conditions play roles in this determination. The heat loss is generally only about 1–2% of the total heat balance, so this portion of the loss is ignored.
The heat loss caused by the increase of the broth temperature is another portion of the heat balance that rarely comes into play. Most fermentations are held at a steady state, meaning that the temperature is maintained at a specified set point. If the fermentation was not held at steady state, the effect of the varied temperature would have to be incorporated into the heat balance.
The heat loss resulting from the cooling of a fermenter is the largest component of the negative portion of the heat balance for most of the fermentation. Initially, when the fermenter has been inoculated, the losses to the environment, evaporation, etc., outweigh the heat inputs, and the fermenter will have to be heated. Once the cells start to grow, the heating will have to be switched to cooling. There are two primary methods that are used to cool a fermenter: coils, and jackets. At most fermentation scales used in good manufacturing practices facilities, jackets are the sole cooling methodology used. At large scale (greater than 20,000 L), both may be used in combination to maintain the steady-state temperature of the fermenter. The heat removal by jackets and coils can be described by Equation 5:
RHC = heat flow due to cooling water (W)
LMTD = log mean temperature difference (°K)
A = cooling surface area (m2)
U = overall heat transfer coefficient (W/m2 – °K)
Tout = outlet cooling water temperature (°K)
Tin = inlet cooling water temperature (°K)
Tf = fermenter broth temperature (°K)
The overall heat transfer coefficient is determined through the summation of resistances to heat transfer. The overall resistance is the inverse of the overall heat transfer coefficient.3
U = overall heat transfer coefficient (W/m2 – °K)
h1 = heat transfer coefficient of broth (W/m2 – °K)
df = thickness of fouling layer (m)
kf = heat conductivity of fouling layer (W/m – °K)
dw = wall thickness of cooling coil or wall (m)
kw = heat conductivity of cooling coil or wall (W/m – °K)
h2 = heat transfer coefficient of cooling water (W/m2 – °K)
Equation 6 can be better visualized if the concept of electrical resistance is brought to mind. The electrical resistance of a circuit can be determined by adding each of the ohm ratings for individual resistors in series to determine the total resistance. The individual resistances to heat transfer also follow that same concept. Equation 6 represents the resistance to heat transfer for the fermentation broth, the fouling layer on the wall of the coil or jacket, the coil, or jacket material, and the cooling water itself. When the overall heat transfer coefficient is determined experimentally, it is usually lumped together with the surface area available for heat transfer to create a term known as UA. The major challenge with using UA for these calculations is that as the fermenter continues to be used, the fouling layers will build up and change the UA values. The UA values also change as the fermenter fills during the run. It is instead much easier to measure the amount of heat removed by the jacket or coils using a heat balance on the coolant. If the flow rate and the temperature in and out for the coolant can be measured, Equation 1 can be again used to determine the amount of heat removed from the fermenter into the coolant stream in this case. The ability to measure the flow rate of the coolant and temperature as it enters and exits the jacket or coil is required for this calculation. The heat removal determined from this calculation would look similar to Figure 1.
Figure 1. Raw heat removal data from the fermentation
Initially, there is a negative value for heat removal because the fermenter is being heated. The heating is necessary because the heat losses outweigh the heat inputs to the fermenter.
Now that the basic heat balance around a fermenter has been described, the value of those data can now be better understood. The goal is to use the heat data to calculate the oxygen uptake rate. This can be done by solving the heat balance for all parts except the metabolic heat input. The equation
Equation 8 can be further simplified using information that can be gained from the starting conditions of the fermentation. If agitation, aeration, and environmental conditions do not change, the effect of these components on the heat balance can be summed together into a variable RS (= RHev – RHS – RHA). This is equivalent to the amount of heating that is needed to keep the fermenter at the temperature set-point as seen in Figure 1. The totalized value acts as a cooling function, which results in a positive component as seen in Equation 9.
If variable agitation and aeration were used, the effective cooling at multiple conditions would be needed. It would be best to develop a plot of the RS values so they can be fit to an equation that can accommodate the differing values of RS at the varied agitation and aeration conditions. The simplified metabolic heat equation (Equation 9) can then be solved using Equation 3, therefore, the only remaining value is the OUR.
OUR = oxygen uptake rate (mmol/kg/hr)
RS = summed initial heat loss (W)
RHC = heat removal through cooling system (W)
G = weight of fermentation broth (kg)
A practical example of Equation 10 can be developed from the data given in Figure 1. The first aspect to note is that the fermentation in the example uses fixed agitation and aeration. This implies that the heat loss seen at the beginning of the run will remain essentially constant throughout the remaining fermentation. If agitation or aeration were changed, a new value for the heat loss would have to be determined, as indicated earlier. Because the described system for this example does not vary agitation or aeration, but uses oxygen supplementation to maintain dissolved oxygen, the heat removal data can be shifted by the initial heat input data, which are shown in Figure 2. This new data can then be used in Equation 10 to calculate the OUR from the heat removal data. This is shown in Figure 3, where the triangle symbol represents the calculated OUR value based on heat transfer data. The solid line represents the actual OUR measurement data by a mass spectrometer with steady-state method.
Figure 2. The balanced heat removal data for the fermentation
As shown in the comparative OUR plot (Figure 3), the values calculated from the heat removal information follow the data gathered using a mass spectrometer. They may not exactly match, but they are close enough from a comparative standpoint. The heat-generated OUR data allow a researcher to understand the metabolic state of a process, and show what the peak OUR values are likely to be. The data can be further defined using more exacting flow measurements and coolant flow control. For the above example, much of the noise that enters the heat removal data pool stems from the flow fluctuations that result from the pulses of coolant into the recirculating fluid in the jacket or coils of the fermenter. The secondary value of such heat removal OUR data lay with the corroboration of other OUR calculation methodologies. If a mass spectrometer is normally used to calculate OUR values, the data can be verified by the heat removal for the fermenter. The heat removal information adds an important data set for scale-up purposes.
Figure 3. The oxygen uptake rate (OUR) calculated from the heat removal data as compared to the measured OUR
Mark Berge is a scientist, Swapnil Bhargava is a senior scientist, Radu Georgescu is an associate scientist, and Xiaoming (Jerry) Yang is scientific director, all at Amgen, Inc., Thousand Oaks, CA, 805.313.6362, firstname.lastname@example.org
1. Cooney CL, Wang DIC, Mateles RI. Measurement of heat evolution and correlation with oxygen consumption during microbial growth. Biotechnol Bioeng. 2000 Mar 20;67(6):691–703.
2. Bailey J, Ollis D. Biochemical engineering fundamentals. New York: McGraw-Hill; 1986.
3. Lydersen B, D'elia N, Nelson K. Bioprocess engineering: systems, equipment, and facilities. Hoboken, NJ: John Wiley & Sons Inc.; 1994.