Empirical correlations to estimate agglomerate size and deposition during injection of a polyelectrolyte-modified Fe0 nanoparticle at high particle concentration in saturated sand

Controlled emplacement of polyelectrolyte-modified nanoscale zerovalent iron (NZVI) particles at high particle concentration (1–10 g/L) is needed for effective in situ subsurface remediation using NZVI. Deep bed filtration theory cannot be used to estimate the transport and deposition of concentrated polyelectrolyte-modified NZVI dispersions (> 0.03 g/L) because particles agglomerate during transport which violates a fundamental assumption of the theory. Here we develop two empirical correlations for estimating the deposition and transport of concentrated polyelectrolyte-modified NZVI dispersions in saturated porous media when NZVI agglomeration in porous media is assumed to reach steady state quickly. The first correlation determines the apparent stable agglomerate size formed during NZVI transport in porous media for a fixed hydrogeochemical condition. The second correlation estimates the attachment efficiency (sticking coefficient) of the stable agglomerates. Both correlations are described using dimensionless numbers derived from parameters affecting deposition and agglomeration in porous media. The exponents for the dimensionless numbers are determined from statistical analysis of breakthrough data for polyelectrolyte-modified NZVI dispersions collected in laboratory scale column experiments for a range of ionic strength (1, 10, and 50 mM Na+ and 0.25, 1, and 1.25 mM Ca2+), approach velocity (0.8 to 55 × 10−4 m/s), average collector sizes (d50 = 99 μm, 300 μm, and 880 μm), and polyelectrolyte surface modifier properties. Attachment efficiency depended on approach velocity and was inversely related to collector size, which is contrary to that predicted from classic filtration models. High ionic strength, the presence of divalent cations, lower extended adsorbed polyelectrolyte layer thickness, decreased approach velocity, and a larger collector size promoted NZVI agglomeration and deposition and thus limited its mobility in porous media. These effects are captured quantitatively in the two correlations developed. The application and limitations of using the correlations for preliminary design of in situ NZVI emplacement strategies is discussed.