Moment analysis for compounds undergoing sequential chain reactions with first-order decay

摘要

Temporal and spatial moment analysis of one-dimensional equations governing fate and transport of parent compounds along with their transformation products is useful for parameter estimation of model parameters, and for understanding the average attributes of contaminant behavior. The objective of this paper is to present analytical expressions for the lower order moments of members in a sequential chain reaction, where members undergo first-order decay to produce the next member in the chain. Specifically, moments up to second order are discussed for the first two members. For the case of purely advective transport (Peclet number tending to infinity), temporal moment expressions are provided for more members of the chain. The sensitivity of temporal moments is examined with respect to Peclet number and transformation rates. Spatial moments are derived by two methods—one using Fourier transforms and another using moment generating differential equations. The behavior of lower order moments for the first few members of a chain can be elucidated from their mathematical expressions. However, expressions for higher order moments tend to be very complicated especially for members further down the chain.