Analysis of the Significant Level of Sludge Rheological Models With Different Moisture Contents
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摘要: 典型的非牛顿流体流变模型有7种,为给出相对最优模型,结合污泥对流变模型进行显著性水平分析. 采用旋转黏度计在20℃时对含水率为93.99%~98.72%的污泥进行流变实验,分析其流变特性,并对这7种流变模型进行拟合和白噪声检验,验证其有效性. 结果表明:在低剪切速率0~150s-1时,含水率对污泥黏度的影响更大. 其中含水率为96.31%~98.72%的污泥表观黏度在0.5Pa·s以下,适合于远距离运输,而含水率93.99%~95.52%的污泥表观黏度偏大,不适合于远距离运输. 含水率为93.99%~95.52%时,两参数模型中,Power-law模型的显著性水平较高,优于其他两参数流变模型;含水率为93.99%~98.72%时,三参数模型中,流变模型Sisko优于H-B模型,四参数模型中,流变模型Carreau优于Cross模型.Abstract: There are seven typical non-Newtonian rheological models. Significant level of these models was analyzed by combining with sludge in order to establish the relative optimal model. The rheological experiments of sludge with moisture content in the range of 93.99%-98.72% were carried out at 20℃ by using a rotating viscosity meter, and sludge rheological characteristics were analyzed. The seven rheological models were fitted with the experimental results and white noise test was carried out to verify the effectiveness. Results display that the moisture content has bigger effect on the viscosity of sludge at the low shear rate of 0-150s-1. The apparent viscosity is below 0.5Pa·s when the sludge is in the range of moisture contents of 96.31%-98.72%, which is suitable for long-distance transportation. While the sludge in the range of moisture contents of 96.31%-98.72% is not suitable for long-distance transportation as it has higher apparent viscosity. The significance level of Power-law model is better than the other two parameter models when the moisture contents are among 93.99%-95.52%. When the moisture contents are among 93.99%-98.72%, the Sisko one is better than the H-B among the three parameter models, the Carreau model is better than the Cross among the four parameter models.
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Key words:
- rheological models /
- rheological property /
- significant level /
- residual /
- white noise test /
- AIC/SBC criteria
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图 1 HAAKE Viscotester-550型旋转黏度计与转子结构
Figure 1. Rheological experimental platform of HAAKE Viscotester-550 rotary viscometer and rotor structure
图 4 Power-law模型的残差序列的自相关与偏自相关函数
Figure 4. Autocorrelation function(ACF) and partial autocorrelation function (PACF)of residual Sequence in Power-law model
表 1 7种非牛顿流体模型及其数学表达式
Table 1. Seven non-Newtonian fluid models and their mathematical equations
流变模型 模型表达式 Power-law τ=kγn Bingham τ=τ0+μpγ Casson τ0.5= + γ0.5 H-B τ=τ0+kγn Sisko μ=μ∞+kγn-1 Cross = Carreau = 
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表 2 20℃时Matlab对不同含水率下污泥流变模型的拟合
Table 2. Fitting of the rheological models of the sludge with different water contents at 20℃ by Matlab
模型 含水率/% 流变参数 R2 Power-law k n 98.72 0.0199 0.8032 0.8803 97.90 0.5663 0.3920 0.9792 97.37 0.5390 0.4609 0.9196 96.31 1.4650 0.4256 0.9849 95.52 11.7000 0.2478 0.9891 93.99 24.3300 0.2678 0.9767 Bingham τ0 μp 98.72 0.2887 0.0055 0.9028 97.90 2.2356 0.0102 0.9639 97.37 2.6910 0.0159 0.9441 96.31 6.4850 0.0336 0.9752 95.52 28.2200 0.0662 0.9378 93.99 62.9400 0.1635 0.9214 Casson τ0 μ∞ 98.72 0.0681 0.0043 0.8913 97.90 1.3972 0.0042 0.9841 97.37 1.5090 0.0075 0.9425 96.31 3.8350 0.0149 0.9916 95.52 21.2410 0.0182 0.9825 93.99 46.1700 0.0483 0.9644 H-B τ0 k n 98.72 0.4670 0.0009 1.3066 0.9114 97.90 1.1542 0.1605 0.5703 0.9846 97.37 2.4070 0.0322 0.8865 0.9454 96.31 3.6350 0.3675 0.6249 0.9922 95.52 12.9500 4.0150 0.3807 0.9933 93.99 14.9300 15.2500 0.3248 0.9778 Sisko k μ∞ n 98.72 0.3329 0.0042 0.0871 0.9588 97.90 0.5411 0.0068 0.2786 0.9957 97.37 1.3510 0.0085 0.2191 0.9957 96.31 1.9270 0.0089 0.3771 0.9909 95.52 13.1500 0.0492 0.1208 0.9993 93.99 37.2800 0.1046 0.1244 0.9990 Cross μ0 μ∞ λ m 98.72 0.1718 0.0058 0.2756 1.1070 0.9594 97.90 0.2005 0.0123 0.0501 1.2889 0.9961 97.37 0.9529 0.0138 0.3382 0.9638 0.9964 96.31 0.7860 0.0385 0.0768 1.1890 0.9974 95.52 5.3630 0.0822 0.1410 1.1090 0.9990 93.99 11.9500 0.1755 0.1585 1.0716 0.9995 Carreau μ0 μ∞ λ n 98.72 0.1490 0.0043 0.3637 0.0549 0.9587 97.90 0.1777 0.0097 0.0707 0.0060 0.9976 97.37 0.5138 0.0119 0.2317 0.1304 0.9962 96.31 0.6388 0.0326 0.0951 0.0263 0.9983 95.52 3.7100 0.0655 0.1362 0.0251 0.9994 93.99 7.9150 0.1396 0.1453 0.0552 0.9998
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表 3 Power-law模型残差序列的白噪声检验
Table 3. White noise test of Power-law model residual series
延迟阶数 指标 延迟阶数 指标 Q-Stat Prob Q-Stat Prob 1 2.33 0.13 13 7.55 0.87 2 3.94 0.14 14 8.93 0.84 3 4.96 0.17 15 9.55 0.86 4 5.93 0.21 16 10.22 0.89 5 6.59 0.25 17 10.25 0.90 6 6.97 0.32 18 10.81 0.89 7 7.25 0.40 19 11.69 0.90 8 7.37 0.50 20 12.07 0.89 9 7.38 0.60 21 12.83 0.91 10 7.40 0.69 22 13.89 0.90 11 7.47 0.76 23 14.85 0.90 12 7.53 0.82 24 15.72 0.89
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表 4 含水率93.99%下不同流变模型的AIC与SBC值
Table 4. AIC and SBC values of different rheological models with the moisture content of 93.99%
模型 参数个数 AIC SBC Power-law 125.37 137.40 Bingham 2 193.35 205.38 Casson 149.83 161.86 Sisko 3 -214.54 -208.52 H-B 123.77 131.80 Cross 4 -429.13 -421.42 Carreau -472.13 -478.13
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