Modeling Tools for Environmental Engineers and Scientists

where V (t) is the volume remaining in the tank at any time; Q in(t) is the volumetricinflow at any time; Q des is the desired, constant flow out of the tank;and C (t) and C in(t) are the instantaneous BOD concentrations in the tank andthe influent, respectively.In this example, the Extend dynamic simulation package is chosen tomodel the system. The model segment in which the above two equations forthe equalization tank are implemented is shown in Figure 8.14. This segmentreceives three inputs (RawQIn, QdesignIn, and RawBODIn) and producestwo outputs (VolOut and BODOut). Block 1 inside the segment receives twoinputs—Input1 (=RawQin) and Input2 (=QdesignIn)—and executes the equation(entered by the modeler into its dialog box) to produce the result asResult1 = Input1 – Input2. (Note that this result is the right-hand side of theODE describing the MB equation for water.) This result is fed to Block 2,which performs the numerical integration of its input, to produce its output,Result2, which, in this case, is the volume V (t) remaining in the tank at anytime, t. The modeler can set the initial value for this integrator in the dialogbox and choose the preferred numerical model from Euler Forward, EulerBackward, or Trapezoidal.Blocks 3, 4, and 5 are assembled in a similar manner to solve the two MBequations. It has to be noted that the inputs and outputs are not necessarilyflows of material. They are flows of information or values that the Blocks canoperate upon, following the equations and settings embedded in them.The entire plant is modeled with graphic icons representing each process,as shown in Figure 8.15. The icons mimic the “unit operations” concept inthat each process receives one or more inputs and produces one or more outputs,functioning as subroutines or submodels. All the model parameters andgoverning equations are fully embedded within each icon, for example, doubleclicking on the equalization tank icon will reveal the submodel shown inFigure 8.14 Equalization tank model in Extend .© 2002 by CRC Press LLC