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Dynamics of spatial heterogeneity in a landfill with interacting phase densities - a stochastic analysis

机译：具有相密度交互作用的垃圾填埋场空间异质性动态-随机分析

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摘要

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 sub-processes 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, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. 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 is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.
机译：垃圾填埋场代表着一个复杂的，动态变化的结构，该结构可以被外源因素随机扰动。垃圾填埋场的热力学（平衡）和时变（非稳态）特性都受到空间异质性和非线性子过程的影响，这些子过程与相关环境的约束初始条件和边界条件相结合。尽管通过一方面结合空间相关参数（基于数据的方法）和另一方面具有连续动态质量平衡方程式（基于方程的建模）的方法，已经采取了多种方法来对垃圾填埋场统计进行建模，但实际上尚未尝试将这两种方法合并同时还引入了内在的随机性引起的波动，这些波动会影响整个过程。在本文中，我们将通过基于反应扩散的方法，实现一个逼真的三维垃圾填埋场时间演变的极简方案，重点关注四个关键变量（固体质量密度，水解质量密度，产乙酸质量密度）的相互作用和产甲烷的质量密度，它们本身会受到周围环境波动的随机影响，以及各个密度的扩散弛豫。我们的结果表明，接近线性稳定极限时，由随机驱动变量之间的一系列复杂的耦合相互作用引起的大时间稳态特性几乎不受生化生长衰减统计的影响。我们的结果清楚地表明，平衡的垃圾填埋场结构主要由固体和水解质量密度决定，仅使其他变量在此（较大时间）渐近极限上在统计上“无关紧要”。将随机性纳入垃圾填埋场演变动态的另一个主要含义是，工厂的生产时间大大减少，现在大约为20-30年，而不是以前的50年及以上的确定性模型预测。该随机模型的预测与可用的实验观察结果一致。

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