## 4 Discussion
An evidence for the predominant effect of HDM and the first reactor \(\Delta\)T on the conversion is the nonlinear regression developed by the use of these two variables and processing the data in Table S2. The nonlinear regression is shown as Equation (5). \[ \begin{split}\text{Conversion}=-3.081\text{HDM}-0.0381\text{AT}( \text{R1})+271.76-\frac{3298.3469}{\text{HDM}}-\frac{1628.92}{\Delta\text{T}( \text{R1})}+\\ 0.017781\text{HDM}^{2}\end{split}  \tag{5}\]  
where,  
Conversion = net vacuum residue conversion, wt.%;  
HDM = HDM extent, %;  
\(\Delta\)T(R1) = the first reactor \(\Delta\)T, %. Equation (5) was developed for the following range of variation of HDM, between 39.4 and 97.9%, and the first reactor \(\Delta\)T, between 49 and 91 \({}^{\circ}\)C. It predicts conversion with an average absolute deviation of 1.36 wt.%; maximum absolute deviation of 4.3 wt.%, and a bias of 0.00 wt.%. By simulating different cases of HDM enhancement while keeping \(\Delta\)T(R1) constant and \(\Delta\)T(R1) increase while keeping HDM constant, one can see that Equation (5) quantifies a stronger influence of \(\Delta\)T(R1) on conversion than the HDM extent. From the data generated in this study, it is difficult to segregate the effect of HDM from that of \(\Delta\)T(R1) because both variables are statistically meaningfully related, as shown in Tables 3 and 4. Figure 14: Relation between HDM, and HDAs (C\({}_{5}\)) for the commercial ebullated bed vacuum residue hydrocracking. However, the effect of \(\Delta\)T(R1) on sediment formation, as observed from the data in Tables 3 and 4, is stronger than that of the HDM, which is in line with the statement made above, that \(\Delta\)T(R1) more strongly affects conversion enhancement than the HDM. A calculation of metal removal extent occurring in the first reactor indicates 50% for the cascade model versus about 70% for the parallel mode when the fresh catalyst addition in the first reactor is about 70% (Figure 15). Therefore, one may suggest that the greater metal removal extent in the first reactor is crucial for the sediment control, allowing operation at a higher reactor temperature and consequently registering a higher conversion level. Therefore, the conversion augmentation during processing the Urals and Siberian Light vacuum residues should be mainly ascribed to the higher catalyst activity and the higher metal removal in the first reactor during implementation of the parallel mode of fresh catalyst addition. The data in Figure 11 indicates that higher activity of the catalyst in the first reactor is a result of a higher addition rate in this reactor 60-70% versus 30-40% in the second reactor. Another regression equation for conversion prediction from data on LHSV and reaction temperature was developed using the data in Table S3. It is shown as Equation (6). \[\text{Conversion}=-113.3653\text{LHSV}+1.079446\text{WABT}-365.0 \tag{6}\]  
where,  
LHSV = liquid hourly space velocity, h\({}^{-1}\);  
WABT = weight average bed temperature, \({}^{\circ}\)C.  
Equation (6) was developed for the following range of variation of LHSV, between 0.10 and 0.24 h\({}^{-1}\), and WABT, between 411 and 431 \({}^{\circ}\)C. It predicts conversion with an average absolute deviation of 1.21 wt.%; maximum absolute deviation of 4.7 wt.%, and a bias of \(-0.039\). Equation (6) reflects the impact of process variables such as reaction time and reaction temperature on vacuum residue conversion, while Equation (5) allows to quantify the effect of HDM and \(\Delta\)T(R1) on conversion. As a whole, this study has shown that the separate addition of fresh catalyst in both reactors with a higher percent added in the first reactor contributes to HDM enhancement, metal removal in the first reactor, and \(\Delta\)T(R1). This, in turn, has a retardation effect on the sediment formation rate that allows the reaction temperature to increase and the conversion rate to raise. Figure 15: Calculated metal removal extent in the first ebullating bed reactor.