Time-Varying Hydraulic Transport and Demographic Trends: Calibrated Modeling of Inflow to a Metropolitan Wastewater Treatment Plant by 2040 (La Chira, Lima, Peru)
Abstract
Long-term influent flow projection governs the sizing of wastewater treatment plants (WWTPs), yet conventional practice estimates future flows using per capita generation rates and coefficients assumed to remain constant over time, neglecting the fact that, in urbanizing catchments, the fraction of generated wastewater that reaches the treatment plant increases as the sewer network expands and densifies. This study develops and validates an explicit-structure model that separates demographic wastewater generation from hydraulic conveyance, disaggregates the service area into fully contributing and partially contributing sectors, and introduces a time-dependent transport coefficient, k(t). Applied to the La Chira WWTP (Lima, Peru; approximately 2.6 million inhabitants), the model was evaluated through leave-one-year-out cross-validation against both a static transport model and an aggregated formulation. The proposed formulation consistently outperformed the alternatives in out-of-sample prediction (Nash–Sutcliffe efficiency of 0.965 and mean absolute percentage error of 1.88%, compared with 0.825 and 0.799 for the benchmark models), providing falsifiable evidence of the value of spatial disaggregation and time-varying transport representation. The transport coefficient increases from 0.491 in 2017 to 0.813 in 2040 under the linear reference specification, with a logistic alternative—statistically indistinguishable in calibration—bounding the projection from below; a formal Shapley decomposition attributes 44% of the projected flow increase to this coefficient. The observed flow rate in 2025 (7.341 m3 s−1) provides an external validation point, predicted with a relative error of 0.7%. Mean influent flow is projected to reach 10.12 m3 s−1 by 2040 (95% CI: 8.55–11.69), representing a 61% increase above the design average flow and approaching the design peak capacity (11.3 m3 s−1), with an exceedance probability of the annual mean of approximately 5%. These results indicate a progressive approach to hydraulic saturation within the planning horizon. The proposed framework is robust to alternative per capita generation assumptions, mechanistically grounded, interpretable, and transferable to sanitation systems characterized by evolving coverage and network connectivity.