Modeling Tools for Environmental Engineers and Scientists

Table 8.4 Bioregeneration Model Equations Generated by ithink ®C(t) = C(t – dt) + (Noname 1) * dtINIT C = Co INFLOWS: dcdt = r1 + amkdV*(Cs–C)G(t) = G(t – dt) + Noname 3) * dtINIT G = G0 INFLOWS: dGdt = Mu*XX(t) = X(t – dt) + (Noname 2) * dtINIT X = Xo INFLOWS: dxdt = (Mu–b)*XModel Parameters:amkdV = 12.6; b = .002 Co = 350; V = 1 qo = 4;G0 = 10; kf = .0585; n = 4.65; Ki = 200; Ks = 150;m = 20; Xo = 200; Y = .6 MuMax = .175;Regen = 100*(qo–q)/qo;q = qo–(V*((C–Co)+∆G/Y))/1000;Mu = MuMax*C/(Ks+C+(C^2)/Ki);r1 = –Mu*X/YCs = ((q/m)/kf)^n;∆G = G–G0In this example, ithink ® ’s built-in feature for conducting sensitivity studiesis demonstrated. By selecting any one of the model parameters at a timeand assigning a range of values to it and selecting the SensiRun option,ithink ® will run the model repeatedly for each of the values in the range andproduce the results for comparison. For example, the sensitivity of the OBRprocess to initial biomass concentration, X o , is examined in this case, and theresults are shown in Figure 8.32. These model results are comparable to thosepresented by Goeddertz et al. (1988) who validated their model with experimentallymeasured data.8.10 MODELING EXAMPLE: PIPE FLOW ANALYSISIn this example, an analysis of sewer flow is illustrated. It is a commonproblem in environmental systems and has often been solved using graphicalmethods or tabulated data. Even though the governing equations are relativelysimple and algebraic, their solution is cumbersome due to power termsand a trigonometric term. The following equations (in SI units) are wellknown in sewer flow analysis:Velocity = 1 n 3(Hydraulic radius) 2 2(slope) 1 AreaHydraulic radius = Wetted perimeter© 2002 by CRC Press LLC