污泥干燥模型选择及Weibull分布模型求解与分析

为了研究污泥薄层干燥的动力学模型、明确薄层干燥模型选取原则、分析模型参数影响因素及在干燥中应用，该研究搭建了污泥干燥试验台，对不同干燥温度（50、75、100、125 ℃）、不同风速（0.5、1.0、1.5、2.0 m/s）与不同污泥厚度（5、10、15、20 mm）的污泥进行干燥试验，利用Weibull分布模型对其干燥动力学曲线进行模拟并分析，建立了风温、风速和污泥厚度与模型参数的定量关系。从原模型与改进模型、因变量与自变量转换、多参数模型及初始条件等4个角度分析，选择Lewis、Page、Two-term exponential和Weibull分布模型进行拟合分析，发现污泥的热风干燥过程服从 Weibull 分布模型（R2=0.994～0.997），是典型的降速干燥过程，降速阶段存在第一、第二降速段，模型的尺度参数（α）和形状参数（β）均与热风温度、风速和污泥厚度有关；第二降速段扩散系数大于第一降速段扩散系数，第一降速段活化能变化范围为12.91～17.12kJ/mol，第二降速段活化能变化范围9.56～15.05 kJ/mol。研究结果可为污泥干燥工艺参数优化及干燥设备研制提供参考。

Selection of sludge drying model and the solution and analysis of Weibull distribution model

Sludge contains a lot of water, organic pollutants, and toxic substances after sewage treatment. The proportion of sludge recycling has reached 85% in developed countries, such as Europe and the United States, of which about 60% has been used to improve the soil or crop fertilizers, but less than 10% in China. Among them, the moisture content of sludge can be reduced to realize the recycling and harmless treatment of sludge for land resource utilization. Thermal drying can be utilized to change the chemical structure by heating, and further remove the vicinal and bound water in the sludge. Then, the lower water content of sludge can be obtained to meet the requirements of the agricultural resource utilization of the sludge. The drying kinetic models of sludge were mainly derived from agricultural thin-layer drying. It is unclear on the physical significance of fitting the various parameters in the traditional empirical or semi-empirical drying models. It is a high demand to effectively combine sludge drying and heat-mass transfer during drying. This study aims to establish and then select the dynamic model for the thin-layer drying of sludge, in order to determine the influencing factors of parameters and application. The drying experiments were also carried out at temperatures (50, 75, 100, and 125℃), wind speeds (0.5, 1.0, 1.5, and 2.0 m/s), and the sludge thicknesses (5, 10, 15 and 20 mm). A Thin-layer drying model was proposed for the selection. The drying dynamic curve was simulated using Weibull distribution model. The quantitative relationship was established between the wind temperature, wind speed, thickness, and model parameters. The result demonstrated that the simple model was selected in the thin layer drying model. The original and modified model should not be selected concurrently, in order to avoid the selection of the model that transformed the dependent variable and the parameter, together with the model failing to meet the requirements of the initial conditions. The Weibull distribution model better described hot-air drying. The moisture ratio vs. drying time profile of the model showed a high correlation coefficient (R2=0.994-0.997), and low root mean squared error (RMSE=0.014 4-0.020 6) and chi-squared (χ2=3.22×10-4-5.57×10-4), indicating the typical decelerating drying. There were the first and second decelerating stages. The scale parameters (α) and shape parameters (β) of the model were related to the hot air temperature, wind speed, and thickness. The α value decreased from 145.915 4 to 69.654 3, and the β value increased from 1.269 3 to 1.325 1, when the temperature rose from 50 to 125 °C. Once the sludge thickness rose from 5 to 20 mm, the α value increased from 85.459 9 to 145.996 4, and the β value increased from 1.062 2 to 1.263 4. The α value decreased from 112.352 8 to 68.679 4, and β value decreased from 1.369 2 to 1.336 0, when the wind speed risen from 0.5 to 2.0 m/s. The moisture diffusion coefficient Deff of the sludge during drying showed that the diffusion coefficient of the second deceleration section was greater than that of the first one. The drying activation energy was calculated, according to the Alenius formula. The activation energy of the first deceleration section varied from 12.91 to 17.12 kJ/mol, whereas, the second deceleration section activation energy was changed from 9.56 to 15.05 kJ/mol. The finding can provide a valuable reference for the parameter optimization and equipment design of sludge drying.