Temperature can exert an effect on biological reactions in two ways: by influencing the rates of enzymatically catalyzed reactions and by affecting the rate of diffusion of substrate to the cells. The importance of both has not always been recognized and this has led to some confusion in the quantification of temperature effects. For example, temperature effects observed in the laboratory are often more pronounced than those observed in the field. This is due in part to the fact that full-scale reactors are apt to be diffusion controlled. Consequently, the temperature coefficients given below are provided simply to give an idea of the importance of temperature to various microbial processes. For system design, actual temperature effects should always be measured in prototype systems that simulate the anticipated mixing regime.
There are three techniques commonly used to quantify the effects of temperature on biochemical operations. The oldest is that of Arrhenius/ who first applied it in 1889 to quantify the effects of temperature on the enzymatic hydrolysis of sugar. It is:
where k is the temperature dependent rate coefficient, A is a constant, u is the temperature coefficient, R is the gas constant, and T is the absolute temperature. The value of u may be obtained by plotting In k versus 1/T and determining the slope. For normal SI units, the units of u are kJ/mole and a positive value means that k increases as the temperature is increased.
Although microorganisms have been found in extreme environments that can grow at temperatures approaching either the freezing point or the boiling point of water, most microorganisms exhibit a relatively narrow temperature range over which they can function. Within that range, most reaction rate coefficients increase as the temperature is increased, but then eventually decrease as the heat begins to inactivate cellular enzymes. The Arrhenius equation, as well as the others to be discussed below, are only applicable over the range where the coefficient increases with increasing temperature. Microorganisms are grouped into three categories depending on that temperature range. Of chief concern in biochemical operations are mesophilic organisms, which grow well over the range of 10-35°C. The two other groups, psy-chrophilic and thermophilic, have ranges on either side and find use under special conditions. Unless otherwise specified, all parameter values given in this book will be for mesophilic microorganisms.
If a rate coefficient is known at one temperature, it may be calculated at another through rearrangement of the Arrhenius equation:
Because the mesophilic temperature range is small when T is expressed in K. the term (R-T, T.) does not vary appreciably and may be considered to be constant. Consequently, a more commonly used expression is:v'
for the normal mesophilic temperature range. Note that when Eq. 3.93 is used, the temperature may be expressed in °C because only the temperature difference enters into the equation. In that case the units of C are °C '. The value of C may be determined by plotting ln(k) versus T, giving a slope equal to C.
Finally, a third equation has found considerable use in the environmental engineering literature:""
Actually, Eqs. 3.93 and 3.95 are the same since:
Thus, the coefficient 0 may also be estimated by plotting ln(k) versus T, giving a slope equal to ln(9). 0 is dimensionless.
The temperature coefficients for the three equations may be interconverted by:
in which the temperature is expressed in °C or K.
Biomass Growth and Substrate Utilization. It will be recalled from Eqs. 3.35 and 3.43 that biomass growth and substrate utilization are proportional to each other, with the yield being the proportionality coefficient. It will also be recalled from Figure 2.4 that temperature can influence the value of the yield. This suggests that temperature can influence growth and substrate utilization in quantitatively different ways. Nevertheless, because of the uncertainty associated with the impact of temperature on Y, most engineers assume it to be independent of temperature, thereby allowing the same temperature coefficient to be used for both growth and substrate utilization.
Two parameters are required to characterize biomass growth, (1 and Ks. The first is clearly a rate coefficient, and as such, its value increases with increasing temperature. The second describes how substrate concentration influences the specific growth rate, and thus the impact of temperature on it is less clear, with it increasing under some circumstances and decreasing under others. Consequently, there is no consensus about its relationship to temperature, and each situation must be experimentally determined.
Most studies of the impact of temperature have been done on the aerobic growth of heterotrophs. Two studies178" have reviewed the literature, and have reported values of u for ji ranging from 21.3 to 167.4 kJ/mole. The average value for the larger data base17 (18 values) was 59.8 kJ/mole, which converts to C and 0 values of 0.090 °C 1 and 1.094, respectively. Very few studies reporting the effects of temperature on Ks were cited, and there was no consensus among them as to whether it increased or decreased with increasing temperature.
Very few studies have been done to quantify the effects of temperature on microbial growth under anoxic conditions, van Haandel et al.i:' recommend that a 0 value of 1.20 (C = 0.182 °C, 1 u = 121 kJ/mole) be used for q. This value is near the upper range for the aerobic values reported above, which suggests that it may be high. Until more data are available, it may be prudent to adopt a value more consistent with aerobic growth and substrate utilization since the two processes are mechanistically similar. No values have been reported for the effect on Ks under anoxic conditions.
Temperature is a critical consideration for nitrifying bacteria because their jx values are low even under the best of circumstances. Characklis and Gujern reported four temperature coefficients for |i for nitrification, with an average u value of 71.8 kJ/mole (C = 0.108 °C 8 = 1.114). However, there appears to be little consensus about the relative effects of temperature on the two major genera of nitrifiers. For example, Characklis and Gujer'7 reported an average u of 74.3 kJ/mole (C = 0.111 °C ', 6 = 1.118) for |i of Nitrosomonas and 44.0 kJ/mole (C = 0.066 °C , 6 = 1.068) for Nitrobacter. In contrast, Hall and Murphy47 reported a u value of 62.4 kJ/ mole (C = 0.094 °C 6 = 1.098) for q for Nitrosomonas and 71.1 kJ/mole (C = 0.107 °C 8 = 1.112) for Nitrobacter. Nevertheless, there still seems to be a general consensus that the temperature coefficient for Nitrobacter is smaller than it is for Nitrosomonas. In contrast to heterotrophs, for which temperature appears to have variable effects on Ks, increases in temperature cause the half-saturation coefficient for nitrifiers to increase. The most widely cited data is that of Knowles et al.,w> for which u associated with the Ks for Nitrosomonas was 78.7 kJ/mole (C = 0.118 °C ', 0 = 1.125) and u associated with the Ks for Nitrobacter was 97.3 kJ/mole (C = 0.146 °C ', 6 = 1.157).
Temperature is also known to play an important role in anaerobic operations. Most studies, however, have looked at overall system performance rather than at the impact on each of the groups of microorganisms discussed in Section 3.2.6. For example, Henze and Harremoes^1 combined data from seven studies to estimate the temperature coefficient for methanogenesis and found u to be 66.7 kJ/mole (C = 0.10 °C ', 8 = 1.105) for a temperature range of 10-30°C. The methane production rate was constant from 30-40°C, and decreased for higher temperatures. Characklis and Gujer17 used data from the literature to estimate that the value of u associated with Ks for acetic acid was -132.9 kJ/mole (C = -0.199 °C ', 8 = 0.819), showing that Ks decreases as the temperature is increased for this process.
Maintenance, Endogenous Metabolism, Decay, Lysis, and Death. Most studies have used the traditional decay concept to quantify the impacts of maintenance, etc. on microbial systems, and thus all temperature data are available in terms of the rate coefficient b (Eq. 3.56). However, because b and bL are proportional to each other (Eq. 3.67), the resulting temperature coefficients should also be applicable to b,.
Because the factors contributing to decay of heterotrophs are the same as those contributing to growth, it is logical to expect temperature to have similar effects on b and (1, and that has been observed, with data from three studies giving u values for b equal to 1.1 times the u values for (1 for a given culture."' Thus, from the effects of temperature on (i, reported earlier, a typical u value for b might be expected to be 65.8 kJ/mole (C = 0.120 °C \ 6 = 1.104). Others,2" however, have used much smaller values for the effects of temperature on decay, with a u value of 19.1 kJ/ mole (C = 0.029 °C 6 = 1.029).
In spite of the importance of temperature to nitrification, few studies have systematically studied the effects of temperature on the decay coefficient for nitrifying bacteria. Dold et al.~" used the same u value for autotrophic decay that was used for heterotrophic decay, although no data were presented.
Solubilization of Particulate and High Molecular Weight Organic Matter. As might be anticipated from the discussion in Section 3.5, relatively little work has been done on the effects of temperature on the hydrolysis of particulate substrate. However, because it is an enzymatic step, the hydrolysis coefficient, kh, is likely to rise as the temperature is increased. From comparison of experimental data to simulation results from a complex system model, van Haandel et al.12'1 concluded that a u value of 38.8 kJ/mole (C = 0.058 °C"6 = 1.060) was appropriate for both aerobic and anoxic environments. No information was given for the effect of temperature on Kx, the half-saturation coefficient for hydrolysis.
Other Important Microbial Processes. Insufficient data are available to allow quantification of the effects of temperature on other processes, such as phosphorus release, but it is likely that appropriate temperature coefficients will be developed for them in the future.
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