## 3 Results and Discussion  
This paper proposed a CFD tube reactor model integrated with HTL kinetics to simulate the HTL process together with convective heat transfer. Figure 3 shows the effect of temperature (Figure 3a) and residence time distribution (Figure 3b) on the biocrude oil yield, the amount of which increased with the increasing temperature, while the amount of the aqueous fraction decreased. This was due to the fact that part of the organic fraction dissolved in water was converted into a gaseous product. As the residence time increased, the amount of gas in the HTL process also increased. At a temperature of 670 K, a yield of approximately 38% biocrude oil was obtained, which corresponded to about 3.8 min of residence time of the slurry suspension in the reactor. Figure 4a,b show the dynamic nature of the changes in concentration of the individual products formed in the HTL process at 600 K and 400 K. At the higher temperature, a much higher degree of sludge over-reactivity and the amount of gas formed can be seen. At 400 K, for a time of 40 min, it had a yield of 27% of biocrude oil, while at 600 K the yield was 34%. At the lower temperature, however, there was a delay in the nature of the resulting phenomena associated with the thermal decomposition of the raw material; thus, the temperature significantly affected the decomposition reactions of the organic matter. The dynamics of change in the solid, liquid, and gas fractions significantly reflected the rate of change in the composition of the reactants involved in the HTL process. It is worth noting that the distributions of temperature and biocrude oil in the HTL reactor were promoted by the convective heat transfer effect, respectively, implying that temperature is a key factor affecting the HTL conversion rate of biomass. Figure 3: Effects of temperature (**a**) and residence time distribution (**b**) on product yield, %. \begin{table}
\begin{tabular}{c c} \hline
**Boundary Conditions** & **Value** \\ \hline Inlet & Inlet volume fraction \(\alpha\): 30\% concentration of \\ sewage sludge \\ \hline Outlet & Outlet boundary conditions: zero-gradient pressure, 160–240 bar \\ \hline Walls & Slip boundary condition: the walls are treated as fixed, \\  & impermeable boundaries. \\ \hline Sludge parameters: & \\ Density & 998.23–1183.4 kg/m\({}^{3}\) \\ Viscosity & 0.12–0.23 Pa\(\cdot\)S \\ Sludge flocs size & 0.008–0.027 mm \\ \hline Flow rate & 1–16 kg/h \\ \hline \end{tabular}
\end{table} 
Table 3: Boundary conditions for sewage sludge liquefaction. Figure 5a shows the effect of the slurry flow rate in the axial direction on the reactor temperature. As the flow rate increased, the temperature of the slurry in the flow decreased, which was related to both the heat transfer coefficient and the residence time of the slurry. Figure 5b shows the convective heat transfer coefficient and discharge temperature of the suspended sludge in a tube reactor. It can be observed that the convective heat transfer coefficient of the sewage sludge slurry increased from 550 to 667 W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) with the increase of the flow rate from 0 to 52 mL/min, while the temperature decreased from 670 to 423 K. In this situation, the conversion rate of the biosolids, assisted by the convective heat transfer coefficient of the slurry by increasing the flow rate in a simple tube reactor, resulted in a lower biomass conversion rate, which is why it is important to ensure a constant temperature throughout the reactor. Contour plots of the slurry flow velocity, temperature, gas mass fraction, and biocrude oil are shown in Figure 6a. Figure 6a illustrates that laminar flow leads to the highest slurry velocity in the center of the tubular reactor, potentially causing clogging, caused by clumping of solid particles. This non-uniform flow likely arises from fluctuations in the reactor volume and pressure drop.