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The MBR Book: Principles and Applications of Membrane

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42 <strong>The</strong> <strong>MBR</strong> <strong>Book</strong><br />

<strong>of</strong> <strong>MBR</strong>s operating under thermophilic conditions, though this mode appears to <strong>of</strong>fer<br />

some promise for treatment <strong>of</strong> heavy COD loads <strong>and</strong>/or recalcitrant organic matter<br />

(Section 5.4.4).<br />

2.2.4 Process design <strong>and</strong> operation fundamentals<br />

Monod kinetics can be used to design biological systems for a limiting substrate<br />

(S kg/m 3 ), usually organic carbon provided as BOD or COD. Using known biokinetic<br />

constants (Appendix B) the system kinetics <strong>and</strong> system mass balance can be used to<br />

define the rate <strong>of</strong> substrate degradation, biomass growth <strong>and</strong> sludge production.<br />

A full description <strong>of</strong> Monod kinetics for process design can be found in Metcalf <strong>and</strong><br />

Eddy (2003).<br />

2.2.4.1 Substrate degradation<br />

<strong>The</strong> rate biokinetics determine the loading rate (the rate at which organic matter is<br />

introduced into the reactor, kg BOD/m 3 ), as determined by Monod kinetics. Accordingly,<br />

the rate <strong>of</strong> reaction is first order with respect to a limiting substrate up to a maximum<br />

specific growth rate, after which growth is unaffected by any increase in substrate<br />

concentration:<br />

mmS<br />

m �<br />

K � S<br />

(2.2)<br />

where � is the growth rate (/h), <strong>and</strong> � m is the maximum specific growth rate (/h), S is<br />

the limiting substrate concentration (g/m 3 ) <strong>and</strong> K s is the saturation coefficient (g/m 3 ). It<br />

follows that there is a maximum specific substrate utilisation rate which is defined as:<br />

k<br />

s<br />

�<br />

Y<br />

mm (2.3)<br />

Where Y is the biomass yield (i.e. the mass <strong>of</strong> cells formed per mass <strong>of</strong> substrate consumed)<br />

(g Volatile suspended solids (VSS)/g BOD). Y can be controlled by manipulating<br />

environmental factors such as temperature <strong>and</strong> pH, but such changes are<br />

detrimental to biodegradation in the reactor (Eckenfelder <strong>and</strong> Grau, 1998). Substituting<br />

terms defined by Monod kinetics into a mass balance expression for the system <strong>and</strong><br />

rearranging produces an expression in terms <strong>of</strong> effluent dissolved substrate S e in g/m 3 :<br />

( )<br />

( )<br />

Ks 1�<br />

keux<br />

S �<br />

u Yk �k�1 x e<br />

(2.4)<br />

where � x is the SRT or sludge age (/day) <strong>and</strong> k e term is the death rate constant. SRT<br />

is an important design parameter used for suspended growth systems. One <strong>of</strong> the<br />

advantages <strong>of</strong> an <strong>MBR</strong> system is that all <strong>of</strong> the solids are retained by the membrane

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