Application of fractal flocculation and vertical transport model to aquatic sol-sediment systems

In estuarine and coastal environments, flocculation occurs between particles of different fractal dimensions and of different densities. Questions remain concerning the level of detail required to model particle flocculation and settling in these heterogeneous systems. This paper compares the goodness of fit between two flocculation models, using measured time series particle size distribution data collected from clay, colloidal silica, emulsified crude oil, clay-crude oil, and silica-crude oil systems. The coalesced sphere (CS) flocculation model includes the effects of heterogeneous particle size and density; the modified coalesced fractal sphere (mCFS) model adds effects due to heterogeneous fractal dimension. Goodness of fit was quantified using values of a minimized objective function, the mean of the sum of the square of the relative residuals (MSSRR). For nearly all tested experimental conditions, MSSRR values varied less than 5% between the CS and mCFS flocculation models. Additionally, collision efficiency values for single-particle-type (alpha(HOMOO)) and dual-particle-type (alpha(HETT)) systems were obtained through parameter regression using the CS and mCFS models. Using the mCFS model, estimated fractal dimension (D) values obtained for clay and clay-oil systems were between 2.6 and 3.0, lower than that postulated by the CS model but higher than that estimated experimentally by the particle concentration technique. The Stokes settling velocity of a clay aggregate of a given mass is reduced with decreased fractal dimension. This results in clay-oil flocculation occurring faster than floc sedimentation in the studied hydrodynamic range. Thus, the mCFS model provides insights to the fate of spilled oil in inland and coastal waters.