## 1 Introduction  
Hydrothermal liquefaction (HTL) is a thermochemical method of converting wet biomass into biofuel from sewage sludge at a temperature of 473-673 K under a pressure of 5-20 MPa [1]. As a result of this process, water, organic, gaseous, and solid fractions are produced. The organic fraction is a viscous, black bio-oil with a calorific value of approximately 28-36 MJ/kg, which can be catalytically upgraded by refining to biofuel used in the transport sector. The resulting water fraction contains a significant amount of dissolved organic substances with a high content of nitrogen and phosphorus, which can be used as a fertilizer in agriculture [2; 3]. Most of the works published in the literature over the last few decades regarding the biomass HTL process focus mainly on improving the efficiency of the product obtained from the bio-raw material [4; 5; 6; 7; 8]. Tubular reactors are characterized by a simple structure, low investment and operating costs, easy technical control of the process, and a high degree of mixing with a relatively short residence time of the liquid in the apparatus. Optimization of the process conditions, such as temperature, pressure, biomass concentration, and reaction time, was carried out by [PERSON] and [PERSON] [9; 10], while the influence of the type of raw material on the process was carried out by [PERSON] and [PERSON] [11; 12]. These works, focused on biomass conversion to biocrude oil, were carried out in small-volume reactors until the optimal product composition was obtained. Designing this type of continuous reactor requires detailed knowledge of flow and heat dynamics, including reaction kinetics. For this reason, computational fluid dynamics (CFD) can be used as a tool to model the hydrothermal liquefaction process and identify important process parameters involved in the production of bio-oil on an industrial scale. [PERSON] and [PERSON] [13] developed a two-dimensional CFD model combining an HTL kinetic model of a microalgae suspension in a continuous plug-flow reactor. The influence of the slurry flow rate, inlet temperature, and heat source temperature on product performance is discussed. [PERSON], [PERSON] et al. [14; 15] analyzed the relationship between temperature profiles and the reaction rate of organic components in a tubular reactor using a CFD model. [PERSON] et al. [16] developed a 3D CFD model to simulate the influence of process parameters on suspension flow and solid particle transport, determined by the Prandtl number. However, previous studies mainly focused on predicting the HTL conversion efficiency of microalgae suspension in continuous tubular reactor mode [15; 16; 17]. [PERSON] et al. [18] presented the multiphase modeling and solution method, which combines the RNG turbulence model and establishes a gas-liquid slurry flow model to simulate the transient flow properties, which calculates the volume fraction, gas flow rates, and pressure pulsation at different working conditions. Simulations were carried out to analyze the phase interface structure of long bubbles to explore the flow characteristics and flow pattern in complex multi-inlet pipelines. In turn, the authors of [19] presented a fluid-solid dynamic model and investigated mixed gas-liquid-solid processes in order to investigate the correct operation and dynamic control strategy. With the above goal in mind, the paper first proposed a mixed gas flow mechanics model, that incorporated both liquids and solids using the CFD-DEM coupling modeling method. It used a self-developed user-defined function (UDF) to measure fluid-particle forces with a novel porous model to obtain particle trajectories. In turn, in [20], an invasive image-based technique was used to study the bubble hydrodynamics in a gas-liquid mixer. The main goal of this work was to present new experimental results and provide a new perspective on the research of tanks with a gas-liquid mixer. Recently, few studies have been reported on the HTL process in continuous reactors on a pilot scale in two-phase flow [13; 16].