Multiphase Numerical CFD Simulation of the Hydrothermal Liquefaction Process (HTL) of Sewage Sludge in a Tubular Reactor

Abstract

This article presents multiphase numerical computational fluid dynamics (CFD) for simulating hydrothermal liquefaction of sewage sludge in a continuous plug-flow reactor. The discrete particle method (DPM) was used to analyze the solid particles’ interaction in liquid–solid high shear flows to investigate coupling computational fluid dynamics (CFD). Increasing solid particles’ interactions were observed with the increasing liquid velocity. The study examined the influence of parameters such as flow rate, temperature, and residence time on the efficiency of bio-oil production. An increase in temperature from 500 to 800 K caused an increase in the amount of biocrude oil produced from 12.4 to 32.9% within 60 min. In turn, an increase in the flow rate of the suspension from 10 to 60 mL/min caused a decrease in the amount of biocrude oil produced from 38.9 to 12.9%. This study offers insights into optimizing the flow channel of tubular reactors to enhance the HTL conversion efficiency of sewage sludge into biocrude oil. A parametric study was performed to investigate the effect of the slurry flow rate, temperature, and the external heat transfer coefficient on the biocrude oil production performance. The simulation data will be used in the future to design and scale up a large-scale HTL reactor.

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 Labanpour and Patel [9,10], while the influence of the type of raw material on the process was carried out by Chen and Ruiz [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. Ranganathan and Savithri [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. Xiao, Chen 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. Joshi 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].

G. Zheng 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]. In addition, there is a big gap between the local structure flow of the liquid–solid–gas three-phase interaction, transient motion characteristics, velocity, and pressure field distribution of slurry sewage sludge flow characteristic parameters. The actual situation and the numerical simulation aspects of segment slug flow need to be further studied. Therefore, it is necessary to carry out a numerical simulation study of slurry biomass flow and different aspects, especially in situations to avoid clogging. The related multiphase flow modeling and solution methods also need to be further explored [21,22,23,24]. The behavior of solid particles of varying sizes within an accelerated toroidal volume filled with fluid has been analyzed using computational fluid dynamics–discrete-phase model (CFD-DPM) simulations by Elaswad and Brazhenko [25,26] and Wu and Nandakumar [27]. During the flow of sewage sludge suspension, a critical factor is its heat uptake behavior under external heating. The hydrothermal liquefaction (HTL) process operates at temperatures exceeding 350 K, inducing rheological variability in the sewage sludge suspension. This variability significantly influences the flow field, consequently impacting the efficiency and composition of the resultant bio-oil. Notably, simulations can incorporate the temperature-dependent rheokinetics of the suspension, which plays a crucial role in the reactor’s heat transfer convection.

This article presents a multiphase CFD simulation of the HTL process in a three-dimensional reactor. The influence of individual process parameters on the course of the reaction was determined. The simulation was conducted using ANSYS FLUENT software version 15.0, offering versatility in adjusting various parameters, such as temperature, pressure, residence time, flow rate of feedstock, as well as properties of operational units. This process simulation was applied to multiple feedstocks and reaction conditions, and the results were compared with published experimental data [16,22]. In this study, an integrated CFD model with HTL process kinetics was proposed to simulate the effects of slurry flow rate, temperature, residence time, and convective heat transfer on the biocrude oil yield of the resulting product in a pilot-scale tubular reactor. The obtained results can be practically used to optimize the structure and determine intensive mixing zones in the HTL process.

2. Materials and Methods

The three-dimensional Lagrangian–Eulerian multiphase transient model was used to simulate the flow pattern of three-phase gas–liquid–solid flow. The present numerical study includes the continuity and momentum conservation equations, which were applied for each phase.

The governing equations of continuity (1) and momentum (2) balance for the liquid phase can be written as follows:

$$\nabla \cdot \left(\rho u\right)=0$$

(1)

$$\rho \frac{\mathsf{\partial }u}{\mathsf{\partial }t}+\rho \left(u\cdot \nabla \right)u=\nabla \cdot \left[-pI+\mu (\nabla u+{\left(\nabla u\right)}^T)\right]$$

(2)

where: $\rho$, $\mu$, and $u$ are the density (kg/m³), viscosity (m²·s⁻¹), and fluid velocity (m/s), respectively, $p$ is the pressure (Pa), and $I$ is the unit vector of the phase.

The energy conservation equation is calculated from Formula (3):

$$\rho C_p\left(\frac{\mathsf{\partial }T}{\mathsf{\partial }t}+\left(u\cdot \nabla \right)T\right)+\nabla \cdot \left(-k\nabla T\right)=Ua\left(T_{ext}-T\right)$$

(3)

The gas phase is described by the continuity equation and the volume-averaged Navier–Stokes equations, where the gas phase density is calculated using the Peng–Robinson equation of state. The gas particle drag is calculated using the Beetstra correlation. The calculation of gas phase mass fraction is determined by Equation (4):

$$\frac{\mathsf{\partial }({\epsilon }_q{\rho }_q{w}_q)}{\mathsf{\partial }t}+\nabla \cdot \left({\epsilon }_q{q}_g{u}_q{w}_q\right)=-\nabla \cdot \left({\epsilon }_q{\rho }_q{q}_m\right)+S_m$$

(4)

where: ${\epsilon }_q$ is the gas holdup, $\rho$ is the density (kg/m³), $u$ is the velocity (m/s), $w_q$ is the liquid mass fraction, and $S_m$ is the source term for gas particle mass transfer.

The gas phase thermal energy balance is represented by Equation (5) below:

$$c_{p,g}\left[\frac{\mathsf{\partial }({\epsilon }_q{\rho }_q{T}_q)}{\mathsf{\partial }t}+\nabla \cdot \left({\epsilon }_q{q}_g{u}_q{T}_q\right)=-\nabla \cdot \left({\epsilon }_q{q}_T\right)+Q_p\right]$$

(5)

where: $T_q$ is the temperature (K), $c_{p,g}$ is the specific heat of the gas (J/mol·K), and $q_T$ and $Q_p$ are the source terms for the interphase with the particle.

The basic transport reaction for concentration of species is written as follows:

$$\frac{\mathsf{\partial }}{\mathsf{\partial }t}\left(\rho {\omega }_i\right)+\nabla \cdot \left(\rho {\omega }_{i}u\right)=-\nabla \cdot J_i+R_i$$

(6)

where: ${\omega }_i$ is the mass fraction of the k-th component in the phase i, $J_i$ is the diffusive flux of the k-th component (kg/m²s), and $R_i$ is the production of i as a result of a chemical reaction.

In this study, the average mixture diffusion model was used, which was selected for the diffusive stream and was calculated as follows:

$$J_i=-\left(\rho D_i^m\nabla {\omega }_i+\rho {\omega }_i{D}_i^m\frac{\nabla M_n}{M_n}\right)$$

(7)

where: ${\omega }_i$ is the mass fraction of the k-th component in the phase i, $J_i$ is the diffusive flux of the k-th component (kg/m²s), $R_i$ is the production of i as a result of a chemical reaction, and $D_i^m$ is the multi-component diffusion coefficient.

The solid phase is represented by particles, which are regarded as the discrete phase, where the Lagrange method is employed to describe particle motion control.

The momentum balance equation is as follows:

$$\frac{\mathsf{\partial }{u}_p}{\mathsf{\partial }t}=-\frac{\nabla p}{{\rho }_p}+F_D\left(u_f-u_p\right)+\frac{\left({\rho }_p-{\rho }_f\right)}{{\rho }_p}g-\frac{\nabla \cdot \stackrel{=}{\tau }}{{\rho }_p}$$

(8)

where: $u_p$ is the particle velocity (m/s), ${\rho }_p$ is the particle density (kg/m³), $\stackrel{=}{\tau }$ is the solid tensor caused by the particle interaction, $F_D\left(u_f-u_p\right)$ is the particle acceleration caused by resistance, and $\frac{\nabla p}{{\rho }_p}$ is the acceleration of particles due to the pressure gradient. This equation assumes that with particle collision below 10%, takes the value of an expression $\frac{\left({\rho }_p-{\rho }_f\right)}{{\rho }_p}g-\frac{\nabla \cdot \stackrel{=}{\tau }}{{\rho }_p}$ appropriate for discrete-phase model, which is suitable for diluted conditions.

Here, ${\epsilon }_q$ is the gas holdup, $\rho$ is the density (kg/m³), $u$ is the velocity (m/s), $w_q$ is the liquid mass fraction, and $S_m$ is the source term for gas particle mass transfer.

In the coupling calculation, CFD-DPM, the program of the discrete-phase model includes the analysis of the fluid and particle governing equations. Initially, the void fraction is determined based on the particle positions and the geometry of the finite-volume grid elements. Following this, the particle momentum equation is solved. Under dense conditions, the discrete-phase model is solved by refining the user-defined functions (UDFs).

A crucial aspect of this process is the source term resulting from the interaction between the fluid and the particles. This source term is computed and stored in the user-defined memory to minimize additional computational loops, as the user-defined source function is called by the solver at the cell level. Subsequently, the fluid’s governing equation is solved, and the collision dynamics are calculated. After updating the fluid region, the simulation proceeds to the next time step.

2.1. Kinetics

A kinetics model to calculate biocrude oil in the HTL process from sewage sludge based on reaction pathways was taken from [24], as presented in Figure 1. The individual abbreviations mean, respectively: BC—biocrude oil, AQ—aqueous phase, and SD—component content in sewage sludge. This model incorporates the biochemical content of protein, carbohydrates and lipids, thereby predicting the yields of biocrude oil, gas and aqueous phase. Reaction pathways are typically modeled by ordinary differential equations that are often assumed to follow Arrhenius kinetics, which have been implemented by user-defined functions (UDFs) written in C language. Arrhenius parameters for the reaction pathways are presented in

Table 1. Arrhenius parameters for the reaction rate constants for HTL of sludge.

Pathway	k, 350 °C (s−1)	Log (A, s−1)	Ea (kJ·mol−1)
SD-BC	1.1 × 10−2	3.0 ± 0.8	60 ± 8
SD-AQ	1.2 × 10−2	3.6 ± 1.0	66 ± 11
SD-GAS	1.0 × 10−2	5.9 ± 0.3	94 ± 3
BC-AQ	1.5 × 10−5	6.0 ± 1.9	129 ± 27
AQ-VT	1.9 × 10−3	4.8 ± 0.6	90 ± 7
AQ-GAS	5.4 × 10−4	5.9 ± 0.8	110 ± 11

.

2.2. Geometric and Mesh of HTL Reactor

A 3D geometry model of the tube reactor is presented in Figure 2. The reactor’s geometric details and the physicochemical properties of the slurry are presented in

Table 2. HTL reactor dimensions for sewage sludge liquefaction.

Reactor Dimensions
Inner diameter, m	0.008
Outer diameter, m	0.014
Horizontal distance between pipes, m	0.04
Vertical distance between pipes, m	0.04
Length of one pipe, m	0.5
Length of the entire reactor, m	8
Reactor volume, dm3	0.4

. The analyses employed the hexahedral mesh elements embedded thin mesher, where the geometry was mesher in the ICEM code.

To achieve a balance between accuracy, convergence and computational cost, a suitable numerical grid was employed with various mesh refinement levels. The impact of the computational mesh independence test on the simulation results was performed for range of 0.9–1.8 million mesh elements. For 1.46 million elements, computational independence was achieved. The initial wall boundary y+ spacing remained the same for each grid refinement level. In the simulations, y+ values were within the following range: 44 < y+ ≤ 198. Typically, a y+ value should be less than 300 to remain in the logarithmic layer. Good mesh quality was controlled as skewness > 0.7. The mesh size was refined near the geometry faces to improve the calculation accuracy in regions of higher process intensity.

2.3. Boundary Conditions and Numerical Simulation Parameters

The HTL process of sewage sludge was carried out at a temperature of 350–430 °C and a pressure of 160–240 bar. The boundary conditions for sewage sludge liquefaction are presented in

Table 3. Boundary conditions for sewage sludge liquefaction.

Boundary Conditions	Value
Inlet	Inlet volume fraction α: 30% concentration of sewage sludge
Outlet	Outlet boundary conditions: zero-gradient pressure, 160–240 bar
Walls	Slip boundary condition: the walls are treated as fixed, impermeable boundaries.
Sludge parameters:
Density	998.23–1183.4 kg/m3
Viscosity	0.12–0.23 Pa·S
Sludge flocs size	0.008–0.027 mm
Flow rate	1–16 kg/h

. Nonlinear differential equations with distributed parameters were solved by the ANSYS FLUENT solver, based on the finite-volume method (FVM). The coupled velocity–pressure equation was solved using the SIMPLEC algorithm. The Peclet number of the sewage sludge suspension in the flow ranged from 56 to 952. A second-order differential scheme was used to approximate the convective heat transfer “second-order upwind scheme”. The lateral walls were modeled using the slip velocity boundary condition. The central difference scheme was used to approximate diffusion terms in the momentum, energy, and composition conservation equations. The CFD-DPM model was applied to study the solid particles’ movement and their tendency to interact with each other in contact surfaces. Thus, the particle injection region supplements an exact numerical solution of species concentration distribution and particle diffusion. The convergence criteria for conservation of momentum, heat, and mass were set to a value of 10⁻⁶.

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 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·m⁻²·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. Pressure fluctuations in the system depend mainly on the reactor volume, solid particle size distribution, as well as the kinematic viscosity and flow rate of the reactor slurry. Therefore, pressure drops can be significantly used to indicate the degree of reactor clogging. An overall high ash content increases the probability of flow clogging in a tubular reactor (>24.1%). Additionally, the possibility of clogging increases with the increasing kinematic viscosity (>8.6 mm²/s) and solid particles’ diameter. Therefore, the ash content has a significant impact on the possibility of reactor clogging. Potentially, this problem can be solved by increasing the heating efficiency of the reactor, allowing rapid liquefaction of the feedstock, reducing the ash content of the feedstock, or increasing the tube diameter. Figure 6b shows the temperature distribution of the reactor, where it can be seen that this temperature gradient was mainly due to heat transfer from the reactor wall to the slurry mixture, which had a temperature of about 300 K at the reactor inlet. For the most part, the sludge suspension behaved according to the thermodynamic properties of subcritical water. In Figure 6c, using contours plot of the gas mass fraction in the external view of the reactor and its cross-section, it can be seen that the fluid velocity was lower at the reactor wall and the reactor wall was warmer, which accumulated more gas. In Figure 6c, the biocrude oil concentration is presented, which was irregularly distributed in the middle of the tubular reactor due to hydrodynamic conditions related to mass and heat exchange in the mass flow. Trajectories of the solid particles were significantly affected by the ash flow and the solid particle size, and thus the trajectories of particles were streamlined.

Figure 7 shows the effects of time and temperature (a) and of time and the sludge flow rate (b) on biocrude yield. As the time of the conducted reaction and the temperature increased, the biocrude oil yield increased, with the increase in temperature playing a much greater role than the time of the HTL process. The hydrolysis and dissolution stage of the solids proceeded rapidly, reaching completion after 7 min at 330 °C, 43.2% of the solids were dissolved. At temperatures above 500 K over 3 min, 58.3% solids’ conversion was achieved. At a predicted temperature of 300 °C, the gas yield increased from 6.6 wt.% to 20.2 wt.% as the reaction time increased from 1 to 60 min. Temperature played a more significant role in obtaining a higher gas yield during the process time. For a given reaction time of 1 min, the gas yield increased from 6.6 wt.% to 65.0 wt.% when the temperature increased from 300 °C to 600 °C. Therefore, the highest temperature increase (600 °C and 60 min) and highest gas yield (66.9 wt.%) were obtained. Figure 7b shows the effects of flow rate and temperature on the biocrude oil yield produced. As the flow rate increased, the yield of biocrude oil decreased because the residence time of the slurry in the reactor decreased. There are two opposite inhibiting processes at play here: temperature and flow rate, with flow rate having a much greater role in the decreased yield of biocrude oil produced.

Figure 8 shows the effects of temperature and time on biocrude yield in the plug-flow tube HTL reactor. It shows that as the time increased from 15 to 60 min, the amount of biocrude oil in the reactor increased from 23% to 42% at a constant flow rate of 6 kg/h. As the reaction progressed, the amount of gaseous phase also increased, and the liquid phase showed an increasing trend up to about 52 min and a decreasing trend after 52 min. The yield of biocrude oil also increased with the increasing temperature, which is a key factor affecting the rate of biomass conversion in the tubular reactor. In the temperature range of 150 °C to 250 °C, depolymerization reactions took place. For the 250–350 °C temperature range, decomposition reactions predominated, where the decomposition reaction time could be similar to the depolymerization reaction time but could be longer for more complex organic compounds.

4. Conclusions

This article presented a 3D multi-physics CFD model of the hydrothermal liquefaction of sewage sludge in a tubular reactor with flow, heat, and mass transfer characteristics, as well as a chemical reaction. Simulating biocrude oil production in the continuous tubular reactor, the temperature and residence time of the process had the greatest impact on the biocrude oil’s efficient production. The effect of the slurry flow rate, temperature, residence time distribution, and external heat transfer coefficient on the HTL products’ yield was investigated. It is worth noting that the residence time and temperature affected the efficiency of slurry conversion to biocrude oil, which may be important in future reactor design. Future efforts will focus on optimizing the process for minimal energy consumption based on the type of raw material feed. Additionally, various aspects will be addressed to scale up the design for industrial applications