Table 3.

Fitted parameters for fouling models according to the modified Hermia’s models for cross-flow filtration, unified model of flux decline, and statistical model analysis for the studied membranes. S-W: Shapiro–Wilks test; K-S: Kolmogorov–Smirnov test; RMSE: root mean square error.

Fouling Model			Membrane Pore Size
			0.14 µm	0.2 µm	0.8 µm
Hermia’s models adapted for cross-flow microfiltration [34]	Complete pore blocking	Kc	32.535	26.001	95.9345
		R2	95.2028	96.3153	91.6064
		RMSE	0.0049	0.0017	0.0038
		S-W test (p-value)	7.83 × 10−10	0.2746	4.3 × 10−6
		K-S test (p-value)	0.000657	0.6340	0.0846100
	Standard pore blocking	Ki	0.656384	0.73382	0,67193
		R2	67.13958	55.6330	89.655
		RMSE	0.0042	0.0013	0.0028
		S-W test (p-value)	1.43 × 10−3	0.0157	2.89 × 10−9
		K-S test (p-value)	0.022328	0.4564	0.006085
	Intermediate pore blocking	Ks	36.9425	47.5505	129.562
		R2	95.2028	97.8559	90.5891
		RMSE	0.0035	0.0008	0.0023
		S-W test (p-value)	9.49 × 10−10	0.0003	5.95 × 10−9
		K-S test (p-value)	0.000516	0.2808	0.037512
	Cake formation	Kg	5,800,344	8,642,697	11,030,594
		R2	88.53165	97.5383	82.30814
		RMSE	0.0031	0.0013	0.0015
		S-W test (p-value)	2.89 × 10−8	3.76 × 10−6	3.74 × 10−11
		K-S test (p-value)	0.004099	0.33078	0.0104003
Unified model for flux decline Yee et al. [35]		K1	0.000292	0.00054	4.55 × 10−4
		b1	−10.9087	−10.734	−10,9964
		K2	0.0000811	0.00013	1.291 × 10−5
		b2	−11.7368	−11.3531	−12.1731
		K3	5.05 × 10−5	4.7 × 10−5	1.115× 10−5
		b3	−11.9331	−12.0056	−12.3943
		R2	90.594	97.35	80.576
		RMSE	3.3 × 10−3	0.5 × 10−3	1.6 × 10−2
		S-W test (p-value)	5.86 × 10−10	0.61	1.13 × 10−6
		K-S test (p-value)	9.41 × 10−5	0.7652	0.04760