Sterling Michael C, Bonner James S, Ernest Andrew N S, Page Cheryl A, Autenrieth Robin L
Environmental and Water Resources Division, Civil Engineering Department, Texas A&M University, College Station, TX 77843-3136, USA.
Water Res. 2005 May;39(9):1818-30. doi: 10.1016/j.watres.2005.02.007. Epub 2005 Mar 31.
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.
在河口和沿海环境中，不同分形维数和不同密度的颗粒之间会发生絮凝。关于在这些非均质系统中对颗粒絮凝和沉降进行建模所需的详细程度，仍然存在问题。本文使用从粘土、胶体二氧化硅、乳化原油、粘土 - 原油和二氧化硅 - 原油系统收集的实测时间序列粒度分布数据，比较了两种絮凝模型的拟合优度。聚结球体（CS）絮凝模型包括了颗粒大小和密度不均一的影响；改进的聚结合分形球体（mCFS）模型增加了由于分形维数不均一所产生的影响。拟合优度通过最小化目标函数的值进行量化，即相对残差平方和的均值（MSSRR）。对于几乎所有测试的实验条件，CS和mCFS絮凝模型之间的MSSRR值变化小于5%。此外，通过使用CS和mCFS模型进行参数回归，获得了单颗粒类型（alpha(HOMOO)）和双颗粒类型（alpha(HETT)）系统的碰撞效率值。使用mCFS模型，粘土和粘土 - 油系统获得的估计分形维数（D）值在2.6至3.0之间，低于CS模型假设的值，但高于通过颗粒浓度技术实验估计的值。给定质量的粘土聚集体的斯托克斯沉降速度随着分形维数的降低而减小。这导致在研究的水动力范围内，粘土 - 油絮凝比絮凝物沉降发生得更快。因此，mCFS模型为内陆和沿海水域溢油的归宿提供了见解。
