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Dynamic Modeling of a Batch Sludge Settling Column by Partial Differential Non Linear Equations with a Moving Interface

机译：具有移动接口的部分差分非线性方程的批量污泥沉降柱的动态建模

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The further goal of the model presented in this paper is to propose a digital tool to predict the behaviour of a main equipment of the water resource recovery facilities, the secondary settling tank. Most of the time, models of this liquid/solid two-phase system are based on a dynamic solid phase mass balance and a settling velocity constitutive expression stemming from the Kynch’assumption. The model presented here is based on both dynamic mass and dynamic momentum balance equations and on an explicit representation of the sludge blanket depth. Therefore, it is able to be used in a wider range of operating conditions than existing models in the literature. It includes effective solid stress appearing when the solid particles concentration is above a given threshold and a moving interface above which there is no solid particles: the sludge blanket. A study of the main physical phenomena into a batch sludge sedimentation column (hydrodynamics of two-phase suspensions) is usually carried out before a faithful representation of continuous sedimentation within a continuous settling tank is deduced. The batch settler is divided into three zones (clarification, thickening and compression). A one dimensional implicit hybrid partial differential non linear equations (Hybrid NL-PDE’s) state space representation is proposed based on the different dynamics in each of the three zones as well as the constitutive equations and the boundary conditions. Some simulations are given and compared with sludge blanket height measurements in a batch settling column.
机译：本文呈现的模型的进一步目标是提出一种数字工具，以预测水资源回收设施，二级沉降罐的主要设备的行为。大多数时间，该液体/固体两相系统的模型基于动态固相质量平衡和源于kynch'assuplation的稳定速度组成型表达。这里呈现的模型是基于动态质量和动态动量平衡方程，并在污泥毯深度的明确表示。因此，它能够在比文献中的现有模型更广泛的操作条件中使用。当固体颗粒浓度高于给定阈值的当固体颗粒浓度高于给定的阈值和上述移动界面时，它包括有效的固体应力：污泥毯。将主要物理现象进入批量污泥沉降柱（两相悬浮液的流体动力学），通常在推导出连续沉降内的连续沉降的忠实代表之前进行。批量定居者分为三个区域（澄清，增厚和压缩）。基于三个区域中的每一个以及组成方程和边界条件，基于三个区域中的不同动态提出了一维隐式混合偏差非线性方程（混合NL-PDE的）状态空间表示。给出了一些模拟并与批量沉降柱中的污泥毯高度测量进行了比较。

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