Oxygen Mass Balance and Modeling in Sewers

This set of coupled differential equations can—as also expressed for the activated sludge model concept—be formulated in terms of a matrix. This matrix includes the relationships between the relevant components, processes, expressions, process rates and coefficients (Table 5.3). The mass balances shown in Equations (5.6) to (5.9) can be identified as columns in the matrix. 

Methods for determination of kinetic and stoichiometric parameters and components relevant for the conceptual model shown in Table 5.3 will be dealt with in Chapter 7. These symbols are given in Appendix A. 

FIGURE 5.8. Main processes involved in the DO mass balance in a sewer network (Matos and de Sousa, 1996). 

The DO mass balance in a sewer can be established at different levels. Basically, it is either expressed by the conceptual model, i.e., Equation (5.9) that is the same as column number 5 in the matrix, Table 5.3, or simply stated as follows (Parkhurst and Pomeroy, 1972 Jensen and Hvitved-Jacobsen, 1991 Matos and de Sousa, 1991, 1996)  

Different levels of description of the rate expressions, rw and tp can be selected when using a simple mass balance as expressed in Equation (5.10). Matos and de Sousa (1996) propose a temperature-dependent, however, DO nondependent value for rw  

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