Dynamics of spatial heterogeneity in a landfill with interacting phase densities

a stochastic analysis

Research output: Contribution to journalArticle

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 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”inthis (largetime) asymptotic limit. The other major implication of incorporation of stochasticity in the land- fill 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.
Original languageEnglish
Pages (from-to)350-358
JournalApplied Mathematical Modelling
Volume41
Early online date31 Aug 2016
DOIs
Publication statusPublished - 1 Jan 2017

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Spatial Heterogeneity
Stochastic Analysis
Land fill
Statistics
Fluctuations
Thermodynamic Equilibrium
Stochasticity
Asymptotic Limit
Prediction
Balance Equations
Deterministic Model
Reaction-diffusion
Stochastic models
Interaction
Modeling
Rendering
Stochastic Model
Time-varying
Continuum
Initial conditions

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

  • stochastic differential equations
  • waste management
  • modelling

Cite this

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title = "Dynamics of spatial heterogeneity in a landfill with interacting phase densities: a stochastic analysis",
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 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”inthis (largetime) asymptotic limit. The other major implication of incorporation of stochasticity in the land- fill 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.",
keywords = "stochastic differential equations, waste management, modelling",
author = "Chattopadhyay, {Amit K.} and Dey, {Prasanta K.} and Ghosh, {Sadhan K.}",
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TY - JOUR

T1 - Dynamics of spatial heterogeneity in a landfill with interacting phase densities

T2 - a stochastic analysis

AU - Chattopadhyay, Amit K.

AU - Dey, Prasanta K.

AU - Ghosh, Sadhan K.

N1 - © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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”inthis (largetime) asymptotic limit. The other major implication of incorporation of stochasticity in the land- fill 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.

AB - 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”inthis (largetime) asymptotic limit. The other major implication of incorporation of stochasticity in the land- fill 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.

KW - stochastic differential equations

KW - waste management

KW - modelling

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DO - 10.1016/j.apm.2016.08.026

M3 - Article

VL - 41

SP - 350

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JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

ER -