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In this paper the Petersen and composition matrices that modellers are now familiar with are used as a basis to construct interfacing models between subsystems considered in wastewater treatment. Starting from continuity considerations and a set of transformation reactions between components used in the two models of the subsystems to be interfaced, a set of linear algebraic equations needs to be solved. The theoretical development is illustrated using a simplified integrated model of an activated sludge system coupled to an anaerobic digester. Continuity-guaranteed interfacing of subsystems will facilitate optimization studies of the within-the-fence process units of a wastewater treatment plant or of the integrated urban wastewater system.

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In waste materials, proximate analysis measuring the total concentration of carbohydrate, protein, and lipid contents from solid wastes is challenging, as a result of the heterogeneous and solid nature of wastes. This paper presents a new procedure that was developed to estimate such complex chemical composition of the waste using conventional practical measurements, such as chemical oxygen demand (COD) and total organic carbon. The procedure is based on mass balance of macronutrient elements (carbon, hydrogen, nitrogen, oxygen, and phosphorus [CHNOP]) (i.e., elemental continuity), in addition to the balance of COD and charge intensity that are applied in mathematical modeling of biological processes. Knowing the composition of such a complex substrate is crucial to study solid waste anaerobic degradation. The procedure was formulated to generate the detailed input required for the International Water Association (London, United Kingdom) Anaerobic Digestion Model number 1 (IWA‐ADM1). The complex particulate composition estimated by the procedure was validated with several types of food wastes and animal manures. To make proximate analysis feasible for validation, the wastes were classified into 19 types to allow accurate extraction and proximate analysis. The estimated carbohydrates, proteins, lipids, and inerts concentrations were highly correlated to the proximate analysis; correlation coefficients were 0.94, 0.88, 0.99, and 0.96, respectively. For most of the wastes, carbohydrate was the highest fraction and was estimated accurately by the procedure over an extended range with high linearity. For wastes that are rich in protein and fiber, the procedure was even more consistent compared with the proximate analysis. The new procedure can be used for waste characterization in solid waste treatment design and optimization.