Risk-minimizing operating policies for granular-bed anaerobic reactors treating poultry slaughterhouse wastewater: A Bayesian causal framework

Abstract

Optimizing organic loading rate (OLR) and hydraulic retention time (HRT) in granular-bed anaerobic reactors treating poultry slaughterhouse wastewater requires an explicit understanding of the causal relationships between operational decisions and chemical oxygen demand (COD) removal. A Bayesian causal framework was developed to estimate dose–response functions, quantify uncertainty, and derive risk-minimizing operating policies across three reactor configurations (SGBR, DEGBR, and EGSB). Hierarchical Bayesian additive spline models, informed by an explicit causal structure represented as a directed acyclic graph, were applied to 59 observations spanning OLRs of 0.7–38.9 g COD L -1 d -1 and HRTs of 0.6–4.5 days. The results reveal structurally stable dose–response relationships across start-up, steady-state, and high-load operating phases. Pareto-optimal policies at OLRs of 7.5–9 g COD L -1 d -1 and HRTs of 2.6–3.2 days achieved mean COD removals exceeding 95.7%, with less than an 8.6% probability of falling below 90%. Causal effects were highly transportable across reactor configurations, with prediction errors below 3%, enabling robust generalization of operating guidelines. Compared with conventional kinetic models, the Bayesian causal model improved predictive performance by [13] , [14] , [15] , [16] , [17] , [18] , [19] expected log predictive density (ELPD) units while providing decision-relevant uncertainty quantification. This study demonstrates how explicit causal reasoning combined with Bayesian inference can convert correlational reactor data into actionable and uncertainty-aware operating policies.