A mathematical model of phytoremediation for petroleum-contaminated soil: model development

We present a simple model for root length density that combines the generally accepted spatial (exponential decrease with depth) and temporal (sinusoidal) variability of root length. Parameters in this model for root length density can be determined from assumed or measured information regarding the annual biomass turnover, maximum standing biomass, and maximum depth of root penetration. The root length density model, coupled with information regarding the average root lifespan, gives specific root growth and senescence functions that are the forcing functions for the phytoremediation model. We present a screening level mathematical model for phytoremediation that accounts for the growth and senescence of roots in the system. This is an important factor for recalcitrant, immobile compounds found in weathered crude oil contaminated soils. The phytoremediation model is based on variable volume compartments that have individual first-order degradation rate constants; as the roots move through the soil, the soil cycles through the rhizosphere zone, decaying root zone and bulk soil zone. Thus, although the oil is immobile, as the roots penetrate through the soil the oil is brought into contact with the rhizosphere.