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1.2 Model Development <br /> ' 1 21 Equation Fonnulation <br /> ' Borden and Bedient(1986)present the theoretical basis for the development of BIOPLU_ME 11 A <br /> summary of their discussion is presented in this section for completeness Borden and Bedient(1986) <br /> simulate the growth of microorganisms and removal of hydrocarbon and oxygen using a modification of the <br /> Monod function where <br /> ' dH k H O <br /> - -M • (1} <br /> dt t KT Ko + O <br /> do <br /> dt Mt • k • F (Kh HH } (KO - 0 } (2) <br /> Ciffd t - Mt• k•Y (K H H) (K O O) + Ke• Ye OC - b•Mt (3) <br /> h } O + <br /> where <br /> H = hydrocarbon concentration <br /> O= oxygen concentration <br /> ' Mt=total microbial concentration <br /> k= maximum hydrocarbon utilization rate per unit mass microorganism <br /> Y= microbial yield coefficient(g cellslg hydrocarbon) <br /> K,= hydrocarbon half saturation constant <br /> Ko= oxygen half saturation constant <br /> K,= first order decay rate of natural organic carbon <br /> OC = natural organic carbon concentration <br /> b= microbial decay rate <br /> F= ratio of oxygen to hydrocarbon consumed <br /> ' Equations (1) and (2) for oxygen and hydrocarbon removal were combined with the advection- <br /> dispersion equation (Bear, 1979)for a solute undergoing linear instantaneous adsorption and the following <br /> equations were obtained <br /> ' aH - '(DVH - vH) - Mt• k H O (q) <br /> TF Rh Rh (Kt, + H) (Ko - O) <br /> 1 <br /> 1-4 <br />