Dynamics of Spatial Heterogeneity in Landfill - A Stochastic Analysis

TL;DR

This paper models the complex, stochastic, and spatially heterogeneous dynamics of landfills using a reaction-diffusion approach, revealing that realistic steady states are achieved faster than previously predicted by deterministic models.

Contribution

It integrates data-based and equation-based modeling approaches to analyze stochastic fluctuations in landfill dynamics, providing a more realistic prediction of equilibrium times.

Findings

Steady state properties are minimally affected by biochemical fluctuations near stability.

Landfill equilibrium is reached in 20-30 years, shorter than previous estimates.

The model highlights the importance of stochastic effects in landfill evolution.

Abstract

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density. In a marked departure from previous predictions, our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure relates to plant production times of approximately 20-30 years instead of the previous (incorrect) deterministic model predictions of 50 years and above.