Mathematical model development and simulation of in situ stabilization in lead-contaminated soils

Abstract

Stabilization and remediation of lead-contaminated soils has received considerable attention recently. Amending Pb-contaminated soils with phosphate as an in situ remediation option has been proposed as an alternative to other remediation options, such as soil removal. Research shows that hydroxyapatite (HA) [Ca₅(PO₄)₃OH] can reduce the bioavailability of Pb efficiently and thus is considered as an ideal phosphate source for formation of lead pyromorphite. Environmental models are increasingly being relied upon to help identify the limiting factors in such kind of in situ remediation.

In this work, the contaminated aggregates remediation model has been developed and simulated to describe the effects of initial contaminant concentration, diffusion coefficient, and aggregate diameter on the time of remediation which is defined as the time required to reduce the aqueous phase lead concentration to <1 ppb. Results of simulation demonstrate that the aggregate size plays a significant role in remediation. The compartments-in-series model has been used to describe the dynamics of in situ stabilization in a soil bed. Results show that for a shallow bed a single, well-mixed, one compartment model gives approximately the same remediation time as the three compartments-in-series model.

Introduction

Lead (Pb) is a heavy metal and is potentially toxic to humans. Numerous cases of Pb-contaminated soil and waste have been reported due to its extensive use and widespread distribution in the environment. Among these, soil removal is often the preferred method for Pb-contaminated materials in residential areas. Options for excavated materials include solidification, vitrification, washing, leaching and particle size separation [1]. The methods have a significant drawback given that the volume of material that requires treatment or removal can be quite large. Furthermore, those methods are costly, disruptive and not sustainable.

Recently, the idea of amending Pb-contaminated soils with phosphorus as an in situ remediation option has been proposed. It has been recognized for some time that lead phosphates and in particular pyromorphite (P), are one of the most stable forms of Pb in the environment [2]. Lead reacts with soluble P to form various pyromorphite minerals that are very insoluble in water. Research shows that pyromorphite is a natural weathering product in Pb-contaminated soils [3]. Suggestions of using P for immobilization of Pb in aqueous solutions and in soils soon followed [4], [5], [6]. The transport and reaction processes affecting the fate of lead contaminants during the stabilization of Pb with P amendments are fairly complex and intertwined. The knowledge of the rates of these processes is meager due to insufficient laboratory and field data. Therefore, it is highly desirable to evolve simplistic approaches, e.g. models, that can account for the mechanisms and represent the treatment scheme.

The majority of available transport models take into account the convection-dispersion flux by resorting to the classical convection-dispersion equations [7]. The analytical solutions for convective-dispersive transport in packed beds have been presented [8], [9], [10]. These and many other models consider the system to be homogeneous and isotropic [11], [12]. The biomodal flow of contaminants has been explained by partitioning the porous media into two compartments, namely, mobile and immobile [13], [14]. Little attention has been focused on the effect of aggregate characteristics in the bed.

The void in a porous medium typically is composed of a mobile phase in the relatively large pores, i.e. the macrovoids, and an immobile phase entrapped in the relatively small pores, which are called microvoids. Dispersion and convection dominate the transport in the macrovoids, whereas the transport in the immobile phase is driven by diffusion. The transport of solute through the aggregated medium has been simulated by Rao et al. [15], [16] and Roberts et al. [17]. Pellet [18] and Satterfield et al. [19] have investigated the importance of diffusivity of solute and its adsorption in the aggregates for describing the dynamics of fixed beds. Thus pore diffusion needs to be considered in modeling the remediation of contaminants in soil aggregates.

The exact mechanisms responsible for the stabilization of Pb by Ca₅(PO₄)₃OH (hydroxyapatite (HA)) are not clear, but available knowledge is necessary to understand the behavior of Pb in phosphate rich environments. The mechanism of reaction of Pb in soil with apatite has been studied recently [19], [20], [21], [22]. Ma et al. proposed that dissolved Pb was removed from solution mainly through HA dissolution and Pb₅(PO₄)₃OH (pyromorphite) precipitation. Ma et al. further suggested that such a dissolution-precipitation process was the primary mechanism in the immobilization of Pb in the presence of apatite minerals and resulted in the formation of a carbonate fluoropyromorphite-type phase [23]. Three types of reactions may control Pb immobilization by HA: surface adsorption, cation substitution or precipitation. Experimental results show that hydroxypyromorphite was formed in the presence of HA at all pH values tested (pH=3–7), which strongly supports the hypothesis of HA dissolution and hydroxypyromorphite formation. They also found that the removal of Pb from solution was not related to original surface area of calcium phosphate solids but rather to the total concentration of dissolved P. Thus, the effectiveness of HA or other P-containing minerals in reducing aqueous Pb was proportional to their solubilities. Results show that the immobilization process was rapid. Aqueous P concentration is the key factor in determining the effectiveness of Pb immobilization by apatite. As a result, pH also plays a role since it affects the solubility of apatite and Pb, Table 1.

Research shows that the pH and particle size are two important factors that affect the effectiveness of the remediation process. Ganguly et al. [24] developed a model to simulate the leaching of metal from environmental soils by coupling reversible and irreversible chemical kinetics with a radial intraparticle diffusion model. Simulation results evidently show that the rate and extent of lead leaching are pH-dependent and at lower pH, there is a faster release of Pb. The simulation was conducted under three pH values (pH=1–3). The Pb desorption occurs only at pH 1 near the particle surface, and the desorption front moves slowly into the particle pores at pH 1. At pH 3, Pb diffusion into the bulk solution is slow and retarded by adsorption of Pb ions. For the conditions and time frames considered in these simulations, diffusion, desorption, and the irreversible reaction processes each play an important role on lead removal in the pH range of 1–3. Particle size determines whether the diffusion effects are important or not. According to their research, the extent to which diffusion affects the remediation process is related inversely to the value of D_m/R², where D_m is the metal pore diffusion coefficient and R the particle radius. For larger particles, diffusion effects are more important.

Although, some models dealing with the fate and transport of contaminants in soil are available, none attempts to describe the combined effects of diffusion, adsorption and reaction for the Pb-contaminated soil system. The principal objectives of this work are to develop mathematical models which can be used to examine the fate of contaminants in the aggregate and continuous phase in the soil bed. The results obtained from the simulation of the models will be useful for identifying the most suitable treatment scheme for in situ stabilization. In the presentation which follows the remediation option considered is in situ stabilization.