# Multi-Scale Modeling of Plastic Waste Gasification: Opportunities and Challenges

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## Abstract

**:**

_{2}+CO) and energy in the presence of an oxygen-rich gas. Plastic waste gasification is associated with many different complexities due to the multi-scale nature of the process, the feedstock complexity (mixed polyolefins with different contaminations), intricate reaction mechanisms, plastic properties (melting behavior and molecular weight distribution), and complex transport phenomena in a multi-phase flow system. Hence, creating a reliable model calls for an extensive understanding of the phenomena at all scales, and more advanced modeling approaches than those applied today are required. Indeed, modeling of plastic waste gasification (PWG) is still in its infancy today. Our review paper shows that the thermophysical properties are rarely properly defined. Challenges in this regard together with possible methodologies to decently define these properties have been elaborated. The complexities regarding the kinetic modeling of gasification are numerous, compared to, e.g., plastic waste pyrolysis, or coal and biomass gasification, which are elaborated in this work along with the possible solutions to overcome them. Moreover, transport limitations and phase transformations, which affect the apparent kinetics of the process, are not usually considered, while it is demonstrated in this review that they are crucial in the robust prediction of the outcome. Hence, possible approaches in implementing available models to consider these limitations are suggested. Finally, the reactor-scale phenomena of PWG, which are more intricate than the similar processes—due to the presence of molten plastic—are usually simplified to the gas-solid systems, which can result in unreliable modeling frameworks. In this regard, an opportunity lies in the increased computational power that helps improve the model’s precision and allows us to include those complexities within the multi-scale PWG modeling. Using the more accurate modeling methodologies in combination with multi-scale modeling approaches will, in a decade, allow us to perform a rigorous optimization of the PWG process, improve existing and develop new gasifiers, and avoid fouling issues caused by tar.

## 1. Introduction

_{2}emissions, causing another important environmental problem.

_{2}+ CO) or so-called syngas, and is conducted at high temperatures (e.g., 850 °C) and usually at atmospheric pressure. This fact can be understood from the strong increase in the number of publications and citations in the field of plastic waste gasification (PWG) and its modeling (Figure 3). Considering this trend and the extensive efforts that should be made to solve the problem of plastic waste, the goal of this review is to assess the opportunities and challenges of PWG from the viewpoint of multi-scale modeling. To do so, first, the process and its multi-scale modeling perspective in this review should be understood and clarified, which is summarized in Section 2. Afterward, opportunities and challenges in modeling this process on different scales, from molecular to the reactor, are reviewed, which span modeling the: thermophysical properties, reaction kinetics, internal and external transport phenomena together with phase transformations, and multi-phase flow modeling.

## 2. Plastic Waste Gasification: A Promising, but Less Mature Recycling Route

#### 2.1. Opportunities and Challenges of PWG

**Figure 4.**An overview of the plastic gasification process and the reactions taking place (the equations are taken from [20,22,23,24,25]). The separation of the hydrocarbons/partially cracked plastics and char is for the sake of illustration. Otherwise, they are present simultaneously in the reactor.

#### 2.2. Numerical Modeling

**Figure 5.**Simplified schematic of the sequential phenomena happening during the solid plastic pyrolysis and gasification (adapted from [38,51,52]); (

**a**) Comprehensive modeling approach: (1) Porous solid plastic core; (2) Melt front; (3) Liquid layer; (4) Pyrolysis and evaporation (devolatilization) layer; (5) Gasification layer (including char); (6) Bubbles present in the liquid layer as the result of pyrolysis and evaporation; (7) Vortex-pattern flows as the result of Marangoni and convection effects; (8) Diffusive transport phenomena; (9) Possible temperature (or concentration) profile as the result of internal circulations in the liquid phase; (10) Internal radiative and conductive heat transfer; (11) Conductive and convective heat and mass transfer; (12) Radiation and convective heat and mass transfer; (13) Mass diffusion; (14) Heat of melting; (15) Heat of decomposition and evaporation; (16) Heat of gasification; (

**b**) An example of a simplified approach: (1) Solid plastic core; (2) Sharp melt front; (3) Liquid layer; (4) Pyrolysis and evaporation (devolatilization) layer; (5) Gasification layer (including char); (6) Infinite internal heat and mass transfer; (7) Convective heat and mass transfer; (8) Heat of melting; (9) Heat of decomposition and evaporation; (10) Heat of gasification; A detailed description of each part is given throughout this review.

#### 2.3. Multi-Scale Modeling of Plastic Waste Gasification

- The plastic, in the solid phase, is fed into the reactor
- The plastic is melted first and then fed into the reactor to cover the fluidization agent or to be present as liquid droplets. The latter is reported very rarely [66].
- The plastic is melted first but fed as a layer into a falling film reactor [67].

## 3. Thermophysical Properties

#### 3.1. Individual Species

#### 3.1.1. Conventional Methods

#### 3.1.2. Advanced Numerical Methods

#### 3.2. Effective Properties

- Structural effects
- The presence of impurities, or
- Internal motions (in the liquid phase)

#### 3.3. Mixture Properties

## 4. Reaction Kinetics

#### 4.1. Challenges Faced in Gasification and/vs. Pyrolysis

#### 4.1.1. Diverse Micro-Scale Characteristics of Plastics

#### 4.1.2. Coupling of Available Kinetic Models

#### 4.1.3. Presence of Char

#### 4.2. Global vs. Detailed Kinetic Models

#### 4.2.1. Global Kinetic Models

#### 4.2.2. Detailed Kinetic Models

#### Feedstock Description

#### Devolatilization

#### Gasification

#### Challenges and Opportunities

- Coupling

- The mechanistic models are feedstock independent. Hence, they are supposed to perform properly for different compositions and feedstock characteristics. Moreover, the similarities in the polymer segments and reaction families make it less burdensome to introduce new polymer types.
- The presence of different gasification agents with different concentrations can be taken into account in a single model. This may also reflect the synergistic effects as a result of gasification with multiple gasification agents. As it can be seen in the developed detailed kinetic models [137], all the gasification agents are present and based on their concentration, their contribution to the overall gasification process is accounted for.
- To introduce new species, only the initial propagation and decomposition steps should be defined [107]. Hence, reliable modification of the model can be done easily in this approach.

- Size of the Reaction Network

_{1}-C

_{16}, can include 621 species and 27,369 reactions [137], or the automated reaction kinetic network of naphtha steam cracking (which can be considered as a similar process to gasification), can encompass 1947 species and 82,130 reactions [144]. For polymers, the network size can grow exponentially. This can pose two important challenges: on the one hand, generating such a huge network is a cumbersome task; On the other hand, implementing the produced reaction network in higher scale frameworks, e.g., CFD, is unfeasible because of their high computational costs. To overcome these two challenges, some possible solutions are introduced in the next paragraphs.

**Table 2.**Overal comparison of different kinetic modeling approaches with a focus on multi-scale modeling of PWG.

Global Modeling | Mechanistic (Detailed) Modeling | ||
---|---|---|---|

MOM | kMC | ||

Requires detailed feedstock description | No (pre-defined lumps) | Yes | |

Degree of complexity | Low | Medium | High |

Degree of details on the product description | Low | Medium (average properties) [98] | High (full molecular detail) [98] |

Computational cost | Low | Medium | High |

OM of number of species | 50 | 100–1000 [154] (Reduced: 10–100) | 1000–10,000 [154] (Reduced: 10–100) |

OM of number of reactions | 50 | 1000–50,000 [154] (Reduced: 100–1000) | 1000-50,000 [154] (Reduced: 100–1000) |

Common application | CFD/1D Models | 1D Models (Reduced: CFD) | |

Feedstock independent | No | Yes | |

Reliable coupling to other kinetic models | No | Yes | |

Adaptability to new species (and gasification agents) | No | Yes | |

Reliable temperature extrapolation | No | Yes | |

Needs reaction network generator (extra complexity) | No | Yes | |

Ability to consider dynamic char activity | No | Yes |

#### 4.2.3. Validation Challenges

- TGA data include the evaporation rates, which are not equal to the degradation rates. So, if a kinetic model is validated against it, in FB regimes with higher evaporation rates, it is supposed to underestimate the devolatilization rate (if the evaporation and degradation models are not decoupled).
- The reactive environment affects the degradation and the evaporation rate of polymers, as was discussed in Section 4.1.2.
- It can include the internal heat and mass transfer limitations, which are not considered in the kinetic models. For large sample sizes [161], providing the isothermal conditions is not possible, and for samples with weak mass transfer properties, concentration gradients are observed within them [162]. Even if in a kinetic model, the effect of diffusion limits on the kinetic parameters is considered [111], two other problems can be raised: First, this shows the incapability in deriving the pure intrinsic kinetic data; and second, the mixing degree and mass transfer limitations can be different from the conditions in which this kinetic model is derived. Hence, this increases the uncertainty in using this kinetic model in different conditions.
- It is not possible to measure the concentration of reacting species in the liquid phase, or the products right after being produced in the gas phase. Hence, secondary reactions can and will happen.
- The uncertainty related to enough sensitivity of the balance used in the TGA instrument is another challenge [162].
- The effect of radiation on the sample in high temperatures is different for the samples with different absorption properties [162].

## 5. Internal Transport Limitations

#### 5.1. Internal Mass Transfer

#### 5.1.1. Solid Phase

_{2}gasification of char in a TGA instrument. This trend can be changed due to the decrease in char reactivity caused by thermal annealing, which should be assessed via the coupling of a semi-detailed model of char gasification and diffusion models [143].

#### 5.1.2. Liquid Phase

#### Simplifying Assumptions

#### 5.2. Internal Heat Transfer

#### 5.2.1. Solid Phase

#### 5.2.2. Liquid Phase

- A weaker effect of Marangoni convection (and hence weaker internal motions or circulative heat transfer); and
- Monotonically decreasing temperature profile toward the center of the droplet.

## 6. Phase Transformations and Interfacial Transport Phenomena

#### 6.1. Melting

#### 6.1.1. Melting Phenomenon

#### 6.1.2. Melting Models

#### Extrusion Models

#### Enthalpy-Based Models

#### Phase-Field Models

#### Reaction-Type Models

#### 6.1.3. Application in the Multi-Scale Framework

#### 6.2. Evaporation

#### 6.2.1. From 0D to 1D Models

#### 6.2.2. Modeling Complexities for PWG

#### Multiple Components

#### Mass Fraction at the Interface

#### Non-Ideal Behavior

#### Role of Radiation

#### Role of Surface Area

#### 6.2.3. Simplifying Assumptions

- Considering the liquid as a spherical droplet
- The presence of an inert atmosphere
- Negligible diffusion of the gas to the liquid
- Negligible mass diffusion due to temperature and pressure gradients

- The heaviest component that has been implemented in these simulations is C
_{20}. Although the table doesn’t cover all the available studies in this regard, it can demonstrate that in general, not all the components available in the liquid phase of PW during the pyrolysis have been assessed extensively. Hence, one of the main areas to be focused on is the assessment of the cases that, from the components’ point of view, are closer to what is happening in PWG. - The shape of the liquid phase is important in simulations. In each study, either spherical or film shape is assessed. This is while different shapes can be simultaneously present in PWG, e.g., it can be droplet, agglomerate, or the liquid film on the wall. Besides, in all cases in the table, a uniform characteristic length of the liquid phase is considered, while the shapes that are present in the PWG are not perfect spheres or liquid film. This demonstrates the complexity that is faced in PWG due to the shape imperfections.
- Most of the cases consider the ideal gas assumptions and this can be true due to the high temperature and low pressure [172,219]. However, for the liquid phase, due to the presence of multiple components with different properties, this is not necessarily true. Implementing the non-ideal conditions for a large number of components is a challenge itself.
- Many of the studies use the DMC approach. This demonstrates that the simulation of the evaporation in the PWG can also be done in this approach at a logical computational expense and hence, can be coupled to the available detailed kinetic models for the plastic pyrolysis.

#### 6.3. Interfacial Heat and Mass Transfer

#### 6.3.1. Empirical-Based Correlations

#### 6.3.2. Numerical-Based Correlations

- Each of them is derived for a specific range of void fraction and Reynolds and Prandtl numbers
- For the particles with different shapes, the Nusselt correlations have been developed, including the incident angle of the particles [233]
- Depending on the direction of heat flow, the Nusselt correlation is different, due to the different behavior of water properties in the heating and cooling process at supercritical conditions [234]

- The application of the classical empirical correlations for the complex systems is in doubt because it has been shown that for each case, a different correlation (which has been validated against the experimental data) should be developed
- The numerical tools have been advanced enough to be used for developing new correlations for each specific condition of PWG process. This way, it is possible to increase the precision of the interfacial heat and mass transfer models used in this process.

Feedstock | Liquid Shape | Ideality | Spherical Droplet/Uniform Film Thickness | 0D/1D | Internal Heat/Mass Transfer | External Heat/Mass Transfer | Reactive | Radiation | Equilibrium | Approach | Ref |
---|---|---|---|---|---|---|---|---|---|---|---|

H_{2}O, CH_{3}OH, C_{2}H_{5}OH, 1-C_{4}H_{9}OH, n-C_{7}H_{16}, n-C_{10}H_{22} | Droplet | Real fluid (UNIFAC), ideal gas | Yes | 0D | No/No | No/No | No | No | Yes | DMC | [175] |

C_{2}H_{5}OH, n-C_{5}H_{12}, cyclo-C_{5}H_{10}, 1-C_{6}H_{12}, n-C_{7}H_{16}, C_{7}H_{8}, iso-C_{8}H_{18} | Droplet | Real fluid (UNIFAC), Ideal mixture for the gas phase | Yes | 1D | Yes/Yes | Yes/Yes | Yes | Yes | Yes | DMC | [172] |

iso-C_{6}H_{14}, n-C_{7}H_{16}, iso-C_{8}H_{18}, cyclo-C_{9}H_{18}, n-C_{10}H_{22}, ben-C_{10}H_{14}, n-C_{11}H_{24}, n-C_{12}H_{26}, ben-C_{12}H_{18}, n-C_{13}H_{28}, n-C_{14}H_{30}, n-C_{15}H_{32}, n-C_{16}H_{34}, n-C_{17}H_{36}, n-C_{18}H_{38}, n-C_{19}H_{40}, n-C_{20}H_{42}, n-C_{21}H_{44}, n-C_{22}H_{46}, n-C_{30}H_{62} | Droplet | Real fluid, Real gas | Yes | 1D | Yes/Yes | Yes/Yes | No | - | No | DMC | [216] |

n-C_{6}H_{14}, n-C_{7}H_{16,} iso-C_{8}H_{18,} n-C_{10}H_{22} | Film | Ideal fluid, Ideal gas | Yes | 1D | Yes/No | - | No | - | Yes | DMC | [176] |

C_{4}H_{9}OH, C_{7}H_{8,} n-C_{10}H_{22} | Droplet | Non-Ideal fluid (UNIFAC) | Yes | 1D | Yes/Yes | Yes/Yes | No | Yes | Yes | DMC | [219] |

n-C_{7}H_{16}, n-C_{16}H_{34} | Film | Ideal gas | Yes | 1D | Yes/Yes (polynomial expressions) | Yes/Yes | No | - | Yes | DMC | [181] |

C_{10}H_{22}, C_{16}H_{34} | Film | Ideal and Non-Ideal Gas | Yes | 1D /Quasi-Dimensional | Yes/Yes (polynomial expressions) | Yes/Yes | No | - | Yes | DMC | [213] |

C_{7}H_{16}, C_{10}H_{22}, C_{16}H_{34} | Droplet | Ideal Gas | Yes | 1D | Yes/Yes | Yes/Yes | No | - | Yes | DMC | [173] |

n-C_{5}H_{12}, iso-C_{5}H_{12}, C_{7}H_{16}, iso-C_{8}H_{18}, C_{9}H_{20}, C_{10}H_{22}, C_{12}H_{18}, C_{12}H_{26}, C_{16}H_{34}, C_{20}H_{42} | Droplet | Ideal and Non-Ideal Gas | Yes | 1D /Quasi-Dimensional | Yes/Yes (polynomial expressions) | Yes/Yes | No | Yes | Yes | DMC | [209] |

H_{2}O, CH_{3}OH, C_{2}H_{5}OH, C_{3}H_{6}O, C_{4}H_{9}OH, 3-C_{5}H_{10}O, C_{8}H_{18}, C_{10}H_{22}, C_{12}H_{26}, C_{14}H_{30}, C_{16}H_{34} | Droplet | - | 1D | No/No | No (Isothermal)/Yes (Stefan-Maxwell approach) | No | - | - | DMC | [177] | |

Air, H_{2}O | Droplet | Ideal Gas | Yes (Including the number of droplets) | 1D | Yes/Yes | Yes/Yes | No | - | - | DMC | [221] |

C_{7}H_{8}, tr-C_{10}H_{18}, C_{12}H_{26}, iso-C_{16}H_{34} | Droplet | Ideal/Real Gas/Liquid | Yes | 0D | Yes/Yes | Yes/Yes | Yes | No | Yes | DMC | [235] |

n-Paraffin, Iso-Paraffin, Cyclo-Paraffin, Aromatics, Olefin | Droplet | Real Fluid, Ideal Gas (Modified) | Yes | 1D | Yes/No | Yes/Yes | No | No | Yes | DMC | [179] |

C_{2}H_{6}O (DME), C_{7}H_{16} | Droplet | Real Fluid (UNIFAC), Ideal Gas | - | 0D | - | - | No | - | No (LK) | DMC | [217] |

C_{2}H_{5}OH, iso-C_{5}H_{12}, iso-C_{6}H_{14}, iso-C_{7}H_{16}, iso-C_{8}H_{18}, C_{9}H_{20}, C_{10}H_{22}, C_{12}H_{26} | Droplet | Real Fluid (Wilson equation), Ideal Gas | Yes | 1D | Yes/Yes | Yes/Yes | No | No | Yes | DMC | [182] |

C_{7}H_{16}, C_{10}H_{22} | Droplet | Real/Ideal Gas | Yes | 1D | No/No | Yes/Yes | No | No | Yes | DMC | [178] |

iso-C_{5}H_{12}, iso-C_{6}H_{14}, iso-C_{7}H_{16}, C_{7}H_{8}, iso-C_{8}H_{18}, C_{9}H_{20}, C_{10}H_{22}, C_{12}H_{26}, C_{14}H_{30}, C_{16}H_{32}, C_{18}H_{34} | Droplet | Ideal Fluid | Yes | 1D (Implemented in multi-dimensional CFD) | Yes/No | Yes/Yes | No | No | Yes | DMC (Derived from CMC) | [236] |

#### 6.3.3. Determining the Limiting Step

#### 6.4. Momentum Transfer

- The role that it plays in the interaction between the particle/droplet/bubbles and change in the interfacial area and shapes as the result of agglomeration, coalescence, and breakup

- The drag force is the main contributing force in the momentum transfer, which acts against the fluid flow direction to resist the motion of a particle, droplet, or bubble. This force is a function of fluid density, dispersed phase diameter, the slip velocity (difference between the velocity of the continuous and discrete phase), and a drag coefficient.
- The lift force acts perpendicular to the flow direction and is the result of turning of the fluid because of the presence of the discrete phase.
- The virtual mass force is the result of acceleration of the discrete phase, i.e., change of its relative motion compared to the fluid phase. This imposes an extra force as an extra mass or “added mass” in the acceleration force.
- The buoyancy force acts against the gravity force as the result of the difference between the density of the fluid and the discrete phase

#### 6.4.1. Drag Force

**Table 4.**Recently developed Nusselt correlations via numerical methods for the particle-fluid systems (Adopted from Ref. [223]). Reprinted from Chemical Engineering Journal, Vol. 374, Li-Tao Zhu, Yuan-Xing Liu, Zheng-Hong Luo, An enhanced correlation for gas-particle heat and mass transfer in packed and fluidized bed reactors, Pages No. 531–544, Copyright (2019), with permission from Elsevier.

Correlation | Method | Limit | Year | Ref | |||
---|---|---|---|---|---|---|---|

$\mathit{\epsilon}$ | $\mathit{R}\mathit{e}$ | $\mathit{P}\mathit{r}$ | Shape/Conditions | ||||

$Nu=\left(7-10\epsilon +5{\epsilon}^{2}\right)\left(1+0.1R{e}^{0.2}P{r}^{1/3}\right)+\left(1.33-2.19\epsilon +1.15{\epsilon}^{2}\right)R{e}^{0.7}P{r}^{1/3}$ | DNS | 0.4–0.9 | 10–100 | 1.0 | Spherical | 2014 | [255] |

$Nu=\left(-0.46+1.77\epsilon +0.69{\epsilon}^{2}\right)/{\epsilon}^{3}+\left(1.37-2.4\epsilon +1.2{\epsilon}^{2}\right)R{e}^{0.7}P{r}^{1/3}$ | PR-DNS | 0.5–0.9 | 1–100 | 0.7 | Spherical | 2015 | [256] |

$Nu=2.67\left(\pm 1.48\right)+0.53R{e}^{0.77}P{r}^{0.53}$ | PR-DNS | 0.351–0.367 | 9–180 | 0.5–1.0 | Spherical | 2017 | [257] |

$Nu=1.77\left(\pm 1.39\right)+0.29{\epsilon}^{0.81}R{e}^{0.73}P{r}^{0.5}$ | PR-DNS | 0.418–0.526 | 9–180 | 0.5–1.0 | Cylindrical | 2017 | [258] |

$Nu=\left(1.49-0.88\epsilon +0.078{\epsilon}^{2}\right)\left(2.458-0.042R{e}^{1.09}P{r}^{1/3}\right)+\left(1.114-0.62\epsilon -0.08{\epsilon}^{2}\right)R{e}^{0.7}P{r}^{1/3}$ | PR-DNS | 0.65–0.9 | 10–200 | 0.74 | Ellipsoidal | 2017 | [259] |

$Nu=\left(8.35-7.4\epsilon \right)\left(1-0.11R{e}^{0.2}P{r}^{1/3}\right)+\left(3.92-7.67\epsilon +3.96{\epsilon}^{2}\right)R{e}^{0.7}P{r}^{1/3}$ | DNS | 0.877–0.948 | 0–550 | 1 | Cellular porous media | 2018 | [260] |

$Nu=\left(2+0.77\epsilon +0.64{\epsilon}^{2}\right)+\left(0.6+1.1\epsilon \right)R{e}^{0.5}P{r}^{1/3}$ | LBM | 0.5–0.9 | 1–100 | 0.7 | Sphere | 2019 | [261] |

$Nu=\left(3.2846-5.1844\epsilon +3.1741{\epsilon}^{2}\right)\left(1+0.7R{e}^{7.219{e}^{-8}}P{r}^{1.0663}\right)+\left(1.3715-1.3531\epsilon +0.334{\epsilon}^{2}\right)R{e}^{0.5939}P{r}^{0.328}$ | DNS-LBM | 0.6–1.0 | 20–500 | 0.5–1.5 | Sphere | 2019 | [262] |

$Nu=0.3832R{e}^{2/3}P{r}^{1/3}A{r}^{-0.2456}-0.0641R{e}^{1/2}P{r}^{1/3}A{r}^{0.2411}+5.1188A{r}^{0.0452}$ | PR-DNS | - | 10–200 | 3.07 | Spheroid (Ar = 0.5–2.5)/SCW | 2019 | [232] |

$Nu=0.3695R{e}^{2/3}P{r}^{1/3}A{r}^{-0.2761}-0.0387R{e}^{1/2}P{r}^{1/3}A{r}^{-0.6632}+5.2154A{r}^{0.0254}+A{r}^{-0.5561}\left(Ar-1\right)0.153R{e}^{0.6989}{\mathrm{sin}}^{2}\left(\frac{1.1187\theta \pi}{180}\right)$ | PR-DNS | - | 10–200 | 0.744, 3.07 | Spheroid (Ar = 0.5–2.5)/SCW | 2019 | [233] |

$Nu=N{u}_{0}{\left(\frac{{\rho}_{in}}{{\rho}_{p}}\right)}^{-0.718}{\left(\frac{{c}_{{p}_{in}}}{{\overline{c}}_{{p}_{p}}}\right)}^{0.33}{\left(\frac{{\lambda}_{in}}{{\lambda}_{p}}\right)}^{-0.4}$ $N{u}_{0}=2+P{r}^{0.4}\left(0.4R{e}^{1/2}+0.06R{e}^{2/3}\right){\left({\mu}_{in}/{\mu}_{p}\right)}^{0.25}$ | PR-DNS | - | 10–200 | 0.7–380 | Spherical/SCW/Cold particle | 2020 | [234] |

**Figure 13.**Schematic representation of different forces that contribute to the momentum transfer between phases (adapted from [263]). Indices 1 and 2 are related to the primary/fluid phase and the discrete phase, respectively.

#### 6.4.2. Non-Drag Forces

## 7. Multi-Phase Flow Modeling

#### 7.1. Reactor Modeling Approaches

#### 7.1.1. Complex vs. Ideal Models

#### 7.1.2. Engineering Models

#### 7.1.3. 3D Computational Fluid Dynamics

#### Eulerian-Eulerian

#### Eulerian-Langrangian

**Table 5.**Overview of fluidized bed gasification studies using two-phase modeling in engineering approach for different feedstocks.

Feed | Gasification Agent | Time (Reaction/ Space/Residence) (s) | Plant Size (OM-m ^{3}) | Bed Material | Temperature (°C) | Kinetic | Software/Code | Ref |
---|---|---|---|---|---|---|---|---|

Plastic (PVC) | Steam | - | Lab | Alumina | ~900 | - | Inhouse | [299] |

Plastic (Poly Olefin) | Air-Steam | Pyrolysis: 0.02 Mixing: 5.4 | Pilot (0.02 & 0.67) | - | 700–850 | Global | Inhouse | [122] |

Coal, petcoke | Oxygen-Steam | - | Commercial (72) | - | 1100 (Non-isothermal) | Global | Inhouse | [314] |

Coal, limestone, inert material | Air-Steam-Carbon Dioxide | Devolatilization: <10 | Pilot (0.07) | Limestone, Sand | 600–1000 | Global | Inhouse (FORTRAN) | [315] |

Coal | Air-Steam | - | Lab & Pilot (2.6) | Dolomite | 750–950 (Non-isothermal) | Global | Inhouse | [296] |

Coal | Oxygen-Steam | Particle residence: 3600 | - | - | 700–900 (Isothermal) | Global | Inhouse | [295] |

Biomass (Wood) | Air-Steam | - | Pilot (0.57) | - | 900–950 | Global | Inhouse | [297] |

Biomass (Wood powder) | Air-Steam | - | - | - | 700–900 | Global | Inhouse (MATLAB) | [316] |

Biomass (Straw) | Air-Steam | - | - | - | - | Equilibrium | Inhouse (FORTRAN) | [317] |

Biomass (Sawdust) | Air | - | - | Sand | 600–1600 | Global | Inhouse | [318] |

Biomass (Sawdust) | Air-Oxygen-Steam | Reaction: 140–3000 | Pilot (0.06 & 2) | Ofite, Quartz & Silica Sand | 700–900 | Global | Inhouse | [319] |

Biomass (Pine Sawdust, Rice husk) | Air-Steam | - | Lab (0.003) & Pilot (0.2) | - | 665–900 | Global | Inhouse (FORTRAN) | [298] |

Biomass (Beech Wood) | Air-Steam | Gas residence time in the freebord: 2–4 | Pilot (0.02) | Silica Sand | 800–815 | Global | Inhouse | [320] |

^{7}–1 × 10

^{10}) that should be solved in each iteration for each time step.

**Table 6.**Overview of Eulerian-Eulerian simulation studies for different feedstocks and reactor designs that can be used as a guide in the PWG simulations.

Feed | Type | Gasification Agent/Process Gas | Gas Residence/ Space Time (s) | Plant Size (OM-m ^{3}) | Bed Material | Temperature (°C) | Phase | Software/Code | Ref |
---|---|---|---|---|---|---|---|---|---|

Plastic (Waste) | Circulating FB | Air | 1–3 | 0.1 m^{3} | Sand | - | GS | MFIX | [313] |

Plastic (PE) | Conical Spouted Bed | Air-Steam | ~3 | Lab (0.001) Pilot (0.03) | Sand | 800–900 | GS | Fluent + Aspen Plus | [61] |

Molten Plastics (mix PE, PP, and PS) ^{1} | Falling Film | Nitrogen | - | Lab (0.002) | - | 550–650 | GL | OpenFOAM | [169] |

Molten Plastic (PP) ^{1} | Falling Film | Nitrogen | - | Lab (0.00004) | - | 460–500 | GL | Fluent | [311] |

Molten Plastic (PE, PP, PS, mix) ^{1} | Falling Film | Nitrogen | - | Lab (0.002) | - | 550–625 | GL | - | [67] |

MSW, RDF | Plasma (Fixed Bed) | Air-Steam | - | - | - | ~2200 (max) | GS | Inhouse (COMMENT) | [330] |

MSW, Biomass (Coffee husk, Forest residues, Vines pruning) | Bubbling FB | Air-Steam | - | Semi-Industrial (0.8) | Dolomite (Experimentally) | 500–1000 | GS | Fluent | [278] |

MSW | Bubbling FB | Steam | - | Semi-Industrial | - | 850 | GS | - | [331] |

MSW | Bubbling FB | Air | - | Semi-Industrial (0.8) | Dolomite (Experimentally) | 700–900 | GS | Fluent | [332] |

MSW | Bubbling FB | Air-Carbon Dioxide | - | Semi-Industrial (0.8) | Dolomite (Experimentally) | 500–900 | GS | Fluent | [279] |

MSW | Bubbling FB | Air-Steam-Carbon Dioxide | - | Semi-Industrial (0.8) | Dolomite, NiO/MD Catalyst | 700–900 | GS | Fluent | [333] |

MSW | Bubbling FB | Air | - | Semi-Industrial (0.8) | - | 500–700 | GS | Fluent | [280] |

MSW | Bubbling FB | Air | - | Semi-Industrial (0.8) | Dolomite (Experimentally) | ~ 500–700 | GS | Fluent | [224] |

MSW | Plasma/Melting | Air-Steam | - | Pilot (2.7) | - | ~2200 max | GS | Fluent | [225] |

MSW | Plasma/Melting | Air | - | - | - | - | GS | - | [65] |

Biomass & Plastic (Wood, PE) ^{1} | Rotary Kiln | - | - | - | - | - | GS | Fluent | [310] |

Biomass | Circulating FB | Air | - | Pilot (0.2) | - | ~400–1000 | GS | Fluent | [334] |

Biomass (Bagasse, Rice husk, Switchgrass) | Bubbling FB | Nitrogen | - | Lab (0.006) | Sand | 400–600 | GS | Fluent | [335] |

Biomass (Coffee husk) | Bubbling FB | Air | - | Pilot | - | ~600–1400 | GS | Inhouse (COMMENT) | [336] |

Biomass (Forest residues) | Bubbling FB | Air | - | Pilot (1) | Dolomite | ~ 800 | GS | Fluent | [337] |

Biomass (Forest residues, Peach Pits, Ground Coffee) | Plasma | Air-Steam | - | - | - | 1000–2000 | GS | Inhouse (COMMENT) | [338] |

Biomass (Pinewood) | Vortex Reactor | Nitrogen | <1 (order of ms) | Lab (0.0001) | - | 500–600 | GS | Fluent | [339] |

Biomass (Wood) | Bubbling FB | Air | - | Lab (0.0004) | Sand | ~ 900 | GS | Inhouse (FORTRAN) | [340] |

Biomass (Wood) | Bubbling FB | Air | - | Lab-Pilot (0.01) | - | 700–750 | GS | ModifiedK-FIX | [341] |

Biomass (Wood) | Bubbling FB | Air | - | Lab (0.0004) | Sand | 850 | GS | MFIX-based | [342] |

Biomass (Wood) | Bubbling FB | Air | - | Lab-Pilot (0.01) | - | ~400–800 | GS | - | [343] |

Biomass (Wood) | Fixed Bed | Air-Steam | - | Pilot (0.22) | - | ~450–1000 | GS | Fluent | [344] |

Biomass (Wood) | Fixed Bed | Air-Steam | <1 (order of ms) | - | - | ~650–1300 | GS | - | [345] |

Coal | Bubbling FB | Air-Steam | - | Pilot (0.07) | - | ~400 | GS | OpenFOAM | [306] |

Coal | Bubbling FB | Air-Oxygen-Steam | - | Pilot (1) | Silica Sand | ~900 | GS | Fluent | [346] |

Coal | Bubbling FB | Air | - | Lab (0.1) | - | ~600–1000 | GS | Fluent | [347] |

Coal | Bubbling FB | Air-Steam | - | Lab (0.07) | Limestone | 812, 855 | GS | ANSYS | [270] |

Coal | Bubbling FB | Air-Steam | - | Lab (0.07) | Sand | 821, 846, 855 | GS | - | [348] |

Coal | Bubbling FB | Air-Steam | - | Lab (0.07) | - | 812-866 | GS | - | [349] |

Coal | Entrained Flow | Air | - | Commercial (15) | - | ~370–2000 | GS | CFC code PHOENICS (Inhouse) | [350] |

Coal | Fixed Bed | Air-Steam | - | Lab (0.01) | - | ~600–1300 | GS | MFIX | [351] |

Glycerin solutions containing xanthan gum ^{2} | Bubble Column | Air | - | Lab (0.01) | - | 25 | GL | CFX (MUSIG) | [352] |

Glycerol | FB | Steam | - | 0.001 | Sand | 600–750 | GS | Fluent | [353] |

Manure Slurry ^{2} | Anaerobic Digester | - | - | Industrial (791) | - | 35 | GL | Fluent | [354] |

Water | Bubble Column | Air | - | - | - | - | GL | OpenFOAM | [355] |

Water | Bubble Column | Air | - | Lab (0.01) | - | Room | GL | OpenFOAM | [286] |

Water ^{3} | Bubble Column | Air | - | Lab (0.007) Pilot (4) | - | - | GL | OpenFOAM (OpenQBMM) | [356] |

Water | Laboratory Tank | Air | - | Lab (0.02) | - | 22 | GL | OpenFOAM | [274] |

Water ^{3} | Vertical Tube | Air | - | Lab (0.01) | - | - | GL | OpenFOAM (twoWayGPBEFoam) | [357] |

Water ^{4} | Bubble Column | Air | - | Lab (0.07) | - | - | GL | - | [358] |

Water ^{4} | Bubble Column | - | - | - | - | - | GL | - | [359] |

Water ^{4} | Bubble Column | Air | - | Lab (0.007) Pilot (0.27) | - | 30 | GL | CFX | [360] |

^{1}VOF method was used.

^{2}Non-Newtonian fluid.

^{3}Quadrature-Based Method of Moments (QBMM) method was used.

^{4}Population balance model (PBM) was implemented.

^{TM}(an emulsion of 70% bitumen and 30% water) in the presence of oxygen. Then, they assessed two different gasifiers for the oxygen-gasification of pitch-water slurry. In this study, the pitch particles are surrounded by a water layer to form the pitch-water slurry to be pumped at the top of the gasifier. The simulation framework in this study includes models for slurry atomization, water evaporation, pitch pyrolysis, and heterogeneous and homogeneous gasification reactions. A global reaction scheme of 12 reactions is considered for pyrolysis and gasification reactions. Although water evaporation and pitch pyrolysis is considered in the mass evolution of the particle, the effect of water on the hydrodynamic behavior of the particles has not been reported. They also studied the particle residence time and their conversion, which can be an important parameter also in the PWG.

#### 7.2. Multi-Phase Flow Modeling Challenges and Possible Solutions

#### 7.2.1. Irregular Shape

**Table 7.**Overview of Eulerian-Lagrangian simulation studies for different feedstocks and reactor designs that can be used as a guide in the PWG simulations.

Feed | Type | Gasification Agent/Process Gas | SRT (s) | Plant Size (OM-m ^{3}) | Bed Material | Temperature (K) | Lagrangian Approach | Software | Ref |
---|---|---|---|---|---|---|---|---|---|

Plastic (PE, PP, PS, mix) | Entrained Flow | Air | - | Lab (0.005) | - | ~50–1100 | - | Fluent | [29] |

Pitch-water slurry | Entrained Flow | Oxygen | 0–50 | Pilot (0.2)/Industrial (33) | - | ~1500 | - | Fluent | [226] |

- | Conical Spouted Bed | Air | - | Lab (0.001) | ZiO_{2} | 25 | DEM | Fluent | [363] |

Biomass | Bubbling FB | Air-Steam | - | Lab (0.003) | Sand | ~800–900 | DEM | - | [323] |

Biomass | Spouted Bed + DFB | Steam | - | SB Lab (0.01)/DFB Pilot (0.3) | Silica Sand | 820–870 | MP-PIC | OpenFOAM | [364] |

Biomass (Almond prunings) | DFB | Steam | Up to ~100 | Pilot (0.7) | Sand | ~400–900 | MP-PIC | OpenFOAM | [365] |

Biomass (Glucose) | FB | Super Critical Water | - | Lab (0.001) | Quartz Sand | ~500–600 | DEM | Fluent | [366] |

Biomass (Pinewood) | Bubbling FB | Steam-Nitrogen | - | Lab (0.06) | Sand | 820–920 | CGM & DEM | STAR-CGM+12.02 | [367] |

Biomass (Pinewood) | Bubbling FB | Steam-Nitrogen | - | Lab (0.0005) | Sand | 820–920 | DEM | OpenFOAM | [368] |

Biomass (Pine, Beech, Holm oak, Eucalyptus) | Conical Spouted Bed | Steam-Argon | - | Lab (0.01) | Sand | 770–920 | MP-PIC | OpenFOAM | [369] |

Biomass (Pine, Beech, Holm oak, Eucalyptus) | Entrained Flow | Air-Steam | Up to ~2.5 | Lab (0.01) | - | 1000–1400 | - | OpenFOAM | [370] |

Biomass (Raw, Torrefied) | FB | Air-Nitrogen-Steam | - | Lab (0.0001) | Olivine | 750–850 | DEM | OpenFOAM | [371] |

Biomass (Raw, Torrefied) (Forest residues, Spruce) | Entrained Flow | Air-Steam | - | Lab (0.01) | - | 1400 | - | OpenFOAM | [372] |

Biomass (Rice husk) | Entrained Flow | Oxygen-Steam-Carbon Dioxide | - | Lab (0.01) | - | 1400 | - | OpenFOAM | [373] |

Biomass (Rice husk, Cotton stalks, Sugarcane bagasse, Sawdust) | Concentric tube entrained flow | Oxygen | - | Pilot (0.25) | - | ~900–2300 | DPM | Fluent | [374] |

Biomass (Sawdust) | Entrained Flow | Air | Lab (0.015) | - | 800–1000 | DPM | Fluent | [375] | |

Biomass (Sawdust, Cotton trash) | Entrained Flow | Air-Steam | - | Pilot (4) | - | ~800–1100 | - | CFX | [376] |

Biomass (Wood pellet) | FB | Steam | Up to ~36 | Lab (0.02) | Sand | ~600–800 | CGM-DEM | Fluent | [377] |

Biomass (Wood) | Bubbling FB | Steam | - | Lab (0.06) | Sand | 820 | DEM | Inhouse (MFIX-DEM) | [378] |

Biomass (Wood) | FB | Air | Up to ~84 | Lab (0.01) | Charcoal | ~500–700 | DEM | - | [379] |

Coal | Bubbling FB | Air-Steam | Up to ~20 | Lab (0.07) | Sand | ~ 800 | MP-PIC | OpenFOAM | [380] |

Coal | Circulating FB | Air | - | Pilot (0.2) | Sand | ~600–850 | MP-PIC | - | [381] |

Coal | Circulating FB | Carbon Dioxide-Oxygen-Nitrogen | - | Pilot (0.03) | Sand | ~950 (max) | DPM + MP-PIC | Fluent + CPFD Barracuda | [382] |

Coal | Entrained Flow | Oxygen-Steam | - | Industrial | - | 1370–1620 | - | Fluent | [383] |

Coal | Entrained Flow | Air-Steam | - | Lab (0.004) | - | ~200–1850 | - | Fluent | [384] |

Coal | Entrained Flow | Air | - | Pilot (0.26) | - | ~700–1900 | - | CFX + FORTRAN | [385] |

Coal | Two-stage Entrained Flow | Oxygen | - | Industrial (32) | - | ~700–2100 | DPM | Fluent | [386] |

Coal | Updraft gasifier | Air-Steam | - | Industrial (60) | - | ~500 (mean) | DPM | Fluent | [387] |

Water ^{1} | Bubble Column | Air | - | Lab (0.01) | - | - | DEM | OpenFOAM | [388] |

Water ^{1} | Bubble Column | Air | - | Lab (0.01) | - | - | DEM | OpenFOAM | [389] |

^{1}Gas-Liquid system.

#### 7.2.2. Roughness

#### 7.2.3. Polydispersity

#### 7.2.4. Aggregation, Coalescence, and Breakup

_{2}particles, which are cohesive powders. In their DEM framework, they considered adhesive forces in addition to drag, gravitational, and contact (normal and tangential) forces.

#### 7.2.5. Regime Transition

#### 7.2.6. Non-Newtonian Behavior

#### 7.3. Multi-Scale Frameworks and Computational Efficiency

## 8. Conclusions

- It does not require extensive sorting of PW.
- It does not necessarily require a catalyst that could be easily deactivated by impurities present in PW.

- The wide variety of plastic types and elements in PW that result in the necessity of substantial upgrading of the syngas, e.g., removal of HCl, or dealing with the fluctuations in the feedstock composition.
- PWG setups are studied and designed based on the existing knowledge when gasifying coal or biomass, and hence are believed to be not optimal for PW. In particular, the presence of liquid is usually neglected.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Acronyms | |

CFB | Circulating Fluidized Bed |

CGM | Coarse Grain Model |

CMC | Continuous Multi-component |

DAEM | Distributed Activation Energy Model |

DFB | Dual Fluidized Bed reactor |

DPM | Discrete Particle Method/Discrete Phase Method |

DQMOM | Direct Quadrature Method of Moments |

E-E | Eulerian-Eulerian approach |

E-L | Eulerian-Lagrangian approach |

ERN | Equivalent Reactor Network |

FB | Fluidized Bed |

FCMOM | Finite-size Domain Complete Set of Trial Functions Method of Moments |

FTS | Fischer-Tropsch Synthesis |

GL | Gas-Liquid |

GS | Gas-Solid |

KTGF | Kinetic Theory of Granular Flow |

LBM | Lattice-Boltzmann Method |

LK | Langmuir-Knudsen Model |

MD | Molecular Dynamics |

MOM | Method of Moments |

MP-PIC | MultiPhase Particle-in-Cell |

MSW | Municipal Solid Waste |

OM | Order of Magnitude |

PBE | Population Balance Equation |

PR | Particle Resolved |

PW | Plastic Waste |

PWG | Plastic Waste Gasification |

RDF | Refuse-Derived Fuel |

SB | Spouted Bed |

SCW | Super Critical Water |

SRT | Solid Residence Time |

Roman and Greek Letters | |

$A$ | Pre-exponential factor/Surface area |

Ar | Aspect ratio of spheroids |

$Bi$ | Biot number |

${c}_{p}$ | Specific heat capacity |

$Cou$ | Courant number |

$D$ | Diffusivity coefficient |

$Da$ | Damköhler number |

E | Activation energy |

$\overrightarrow{F}$ | Force |

$\overrightarrow{g}$ | Gravity acceleration |

$h$ | Convective heat transfer coefficient |

H | Enthalpy |

$k$ | Reaction kinetic constant |

L | Latent heat/Characteristic length |

$m$ | Mass |

Ma | Dimensionless Marangoni number |

${n}_{l}$ | Number of droplets per mass of liquid |

${n}_{p}$ | Number of particles |

Nu | Nusselt number |

$p$ | Pressure |

${P}_{c}$ | The perimeter of the circle equivalent to the maximum projection area of a particle |

${P}_{mp}$ | Maximum projection perimeter |

Pr | Prandtl number |

Py | Pyrolysis number |

$q$ | Heat |

${Q}_{r}$ | Generated or consumed heat due to reaction |

$r$ | Radius |

R | Production rate/Universal gas constant |

Re | Reynolds number |

$s$ | Solid-liquid interface position |

${S}_{h}$ | Heat transfer between phases |

${S}_{u}$ | Momentum transfer between phases |

${S}_{y}$ | Species transfer between phases |

${S}_{\rho}$ | Net mass transfer rate between phases |

SP | Particle-based mass source term |

Sc | Schmidt number |

$t$ | Time |

T | Temperature |

$u,\overrightarrow{u}$ | Velocity |

V | Volume |

$x$ | Spatial coordinate/Interface position |

${X}_{m}$ | Monomer conversion |

$Y$ | Mass fraction |

$\alpha $ | Volume fraction |

$\epsilon $ | Porosity, void fraction |

$\theta $ | Incident angle |

$\lambda $ | Thermal conductivity |

$\mu $ | Dynamic viscosity |

$\nu $ | Kinematic viscosity |

$\rho $ | Density |

$\sigma $ | Surface tension |

$\stackrel{=}{\tau}$ | Stress-strain tensor |

$\varphi $ | Sphericity parameter |

$\chi $ | Circularity |

$\psi $ | Shape factor/Particle-based species transfer rate between phases |

Sub/Superscripts | |

$0$ | Initial |

$I$ | First |

$II$ | Second |

$B$ | Bulk |

$c$ | Contact |

$cond$ | Conduction |

$conv$ | Convection |

$d$ | Drag |

$eff$ | Effective |

$f$ | Fluid |

$i$ | The i^{th} species |

$l$ | Liquid |

$p$ | Particle/Particle surface |

$pr$ | Pressure gradient |

$rad$ | Radiation |

$reac$ | Reaction |

$s$ | Solid |

$turb$ | Turbulent |

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**Figure 1.**The evolution of the share of treatment methods for the post-consumer (PC) plastic waste in EU member states, Norway, Switzerland, and the United Kingdom (Adapted from Ref. [4]).

**Figure 2.**Thermo-chemical recycling path of the plastic circular economy (adapted from [3]).

**Figure 3.**Increased number of publications and citations related to the PWG and modeling of PWG (extracted from [16]).

**Figure 7.**The initial, and transformation of the, chain-length distribution (molar mass distribution) of a type of Poly(styrene peroxide) (P

_{12}) during the thermal degradation, predicted by a tree-based kinetic Monte Carlo coupled to an artificial intelligence tool. Reprinted (adapted) with permission from [94]. Copyright 2021 American Chemical Society.