However, for Case 1, there are still differences in details, in particular the pressure response caused by creep is very different. Before the first rarefaction wave returns, the maximum pressure decreases a little and rapidly from 0.23 to 1.56 s due to the joint action of the pipe hydraulic resistance and the pipe–wall VE of a stress release with a retarded strain increase, and then there is no slight pressure increase due to the line packing effect like in Case 2, as can be seen in Figures 22(a), 23(a) and 24(a). As can be seen in Table 4, compared to the numerical results for Case 2, the maximum pressure relative errors at T1 predicted by the elastic models are smaller as the initial velocity decreases for Case 1 in Figure 18, and the pressure peak relative errors increase with time for these three models; the maximum pressure relative errors at T1 by the SF-VE, the CB-UF-VE and the MIAB-UF-VE change a little, the predictions are much more accurate than those by the three elastic models. For Case 1, the pressure peak relative errors by the SF-VE increase as the transient evolves, whereas the pressure peak relative errors by the CB-UF-VE and the MIAB-UF-VE are very small and the maximum errors are 0.06 and 0.04%, respectively. Except that the SF-VE can accurately predict the pressure phase in the first period, its pressure phase prediction error is large and gradually increases with time, whereas the CB-UF-VE and the MIAB-UF-VE can accurately predict the pressure phase in the whole transient process. On the whole, the at T1 shown in Table 5 indicate that the prediction by the CB-UF-VE is the most accurate, followed by the MIAB-UF-VE and worse by the SF-VE.

Table 5

at T1 by the three viscoelastic models for Cases 1–3

Case no. .	at T1 by the three viscoelastic models (–) .
	SF-VE (%) .	CB-UF-VE (%) .	MIAB-UF-VE (%) .
1	9.2	2.5	2.6
2	4.7	2.8	2.3
3	5.7	4.6	3.6

Case no. .	at T1 by the three viscoelastic models (–) .
	SF-VE (%) .	CB-UF-VE (%) .	MIAB-UF-VE (%) .
1	9.2	2.5	2.6
2	4.7	2.8	2.3
3	5.7	4.6	3.6

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