This equation shows that YCOD for aerobic growth is not a constant, as often assumed (26) with YCOD ^ 0.50-0.67, but it depends also on the type of C source, because this determines 1 /YGX (equations 3a and 3b). Also, to decrease the YCOD leading to lower surplus-sludge production, one must, according to equations 11b and 11c:

Yda = 36.50/25.03 = l.46 C-mol acetate/mol methanol

• Decrease ( — DGCAT), by, for example, using anaerobic metabolism producing CH4

• Increase 1 / YGX by increasing temperature or decreasing the growth rate according to equation 1

These predicted phenomena are well known and applied in waste-treatment processes.

Relation between Heat Production and Gibbs Energy Dissipation. According to equation 9d, the heat production (1 / Yqx) is related to Gibbs energy need (1/YGX) by the enthalpy and Gibbs energy of the catabolic reaction (DGCAT and DHcat). Table 6 shows some examples of growth systems to illustrate the relation between heat production and dissipated Gibbs energy for growth (29). From Table 6 we can conclude the following rules of thumb:

• For aerobic (or denitrifying) growth systems on organic substrate, the Gibbs energy dissipation and heat production are nearly equal. The entropy contribution in the catabolic reaction is minimal (see glucose and acetate aerobic growth).

• For anaerobic growth, heat production and Gibbs energy dissipation can be substantially different, due to entropic effects.

Obviously, if in the catabolic reaction there is a net decrease of molecules or a consumption of gaseous molecules, then there is a strong negative entropy contribution (see H2/CO2 aerobic and anaerobic) and there is a much higher heat production than Gibbs energy dissipation. If, however, in the catabolic reaction there is a net production of the amount of molecules and/or production of gaseous molecules (e.g., the glucose/ethanol fermentation or the methane production from acetate), then there is a very large positive entropy contribution, leading to a much lower heat production than the Gibbs energy dissipation. The entropic effect can even be so large that there is a calculated heat uptake during growth (e.g., methanation of acetate). This is obviously endothermic growth. So, contrary to a common belief, growth of microorganisms is not necessarily related to heat production; there can be heat uptake as well. Experimental proof is, however, still lacking.

Maximal Product Yields in Anaerobic Metabolism. In many microbial processes the valuable product (e.g., eth-anol or lactic acid) is related to catabolism. The relevant stoichiometric coefficient is then the yield of the electron acceptor couple to electron donor YDA.

Equation 9e shows how this coefficient is determined by various factors and it appears that YDA is maximized.

• For high Gibbs energy dissipation 1/YGX. This means that high catabolic product yields are achieved for poor carbon sources, low growth rate, and high temperature, because 1/YGX is then maximized.

• For catabolic reactions with low DGCAT. This is understandable, because then the growth yield is minimized, which leads directly to higher product yield.

• For highly reduced electron donors (yD high) and highly oxidized products (yA low). It is then even possible to achieve C yields larger than 1. An excellent example is the anaerobic production of acetate from methanol, where YDA ^ 1.4 C-mol acetate/C-mol methanol (Example 4).

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