DOI: 10.3303/CET2188152 
 

 
 

 
 

 

 
 
 

 
 
 

 
 

 
 
 

 
 

 

 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 

Paper Received: 19 June 2021; Revised: 8 August 2021; Accepted: 5 September 2021 
Please cite this article as: Harb R., Rivera-Tinoco R., Zeghondy B., Bouallou C., 2021, Modelling of Physical Method for Tar Elimination from 
Producer Gas at Low Temperature, Chemical Engineering Transactions, 88, 913-918  DOI:10.3303/CET2188152 

CHEMICAL ENGINEERING TRANSACTIONS 

VOL. 88, 2021 

A publication of 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

Copyright © 2021, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-86-0; ISSN 2283-9216 

Modelling of Physical Method for Tar Elimination from 
Producer Gas at Low Temperature 

Rita Harba,b, Rodrigo Rivera-Tinocoa, Barbar Zeghondyb, Chakib Boualloua,* 
a MINES ParisTech, PSL Research University, Center for Energy Efficiency of Systems (CES), 60 Bd St Michel, F-75006 

Paris, France 
b School of Engineering, Holy Spirit University of Kaslik (USEK), Jounieh, Lebanon 

chakib.bouallou@mines-paristech.fr 

Combining a methanation step with biomass gasification requires an intensive tar removal process that reduces 
its content down to 1 mg/Nm3. In this paper, low temperature processes are suggested for treating tar and 
reducing its content to the acceptable limit. However, the gas must be pre-treated prior to the low temperature 
process in order to reduce its temperature, its moisture content and the heavy tar fraction. Two water scrubbers 
are placed prior to the low temperature tar removal process. Benzene and toluene remains in the producer gas 
after the scrubbers. Those two components can be valorised if separated from the producer gas at low 
temperature. The tar removal, at low temperature, induces the water vapour frosting remaining in the producer 
gas. The simultaneous frosting and condensation takes place over a cold plate. Modelling simultaneously the 
multi-component frost growth and condensation requires complex mathematical approach. A parametric study 
is completed to assess the impact of the wall temperature and the producer gas flow rate on the tar removal 
process function of time and plate length. Results showed that a wall temperature of -20 C is required to lead 
to the benzene frost formation for an initial molar fraction of 0.024. After one hour, the thicknesses of benzene 
and ice frost layers reach 1.5 and 2.5 mm, respectively. Therefore, the heat transfer between the gas and the 
cold surface is reduced.  

1. Introduction

Lately, production of methane based on biomass gasification is widely studied as a possible route for replacing 
fossil natural gas. Biomass gasification yields a gaseous product named producer gas that can be converted 
into bio-methane if treated (Anis and Zainal, 2011). Tars among other impurities present in the producer gas 
must be removed in order to successfully convert it into bio-methane. Very few researchers reached the suitable 
tar content for methanation (1 mg/Nm3). Reaching a low tar content is usually achieved by combining two 
cleaning methods. For instance, in GoBiGas project, the polycyclic aromatic hydrocarbons (PAH) and benzene, 
toluene, and xylene (BTX) contents were respectively reduced to 0.1 µg/m3 and 100 µg/m3, by combining a 
scrubbing column with 4 activated carbon (AC) beds (Thunman et al., 2018). However, high operating costs are 
imposed by the treatment section; one of the AC beds should be replaced each 2.5 months and the oil-based 
scrubbing liquid is wasted. Therefore, in this study, reducing the temperature of the producer gas is suggested 
as an effective solution for reducing the tar content and it takes place in two units in series. The first unit targets 
the removal of the heavy tar fraction by scrubbers while the second unit aims at removing the lightest tar 
components by deposition over low temperature surfaces. The removal of the heavy fraction of tars is well 
developed, while more attention should be given to the removal of the lightest tar fraction formed mainly of BTX. 
Many previous studies have handled the tar removal by wet scrubbers using different types of scrubbing 
mediums (Harb et al., 2020 a). Since BTX compounds can be valorised, it is important to keep their content 
unaffected in this stage of tar removal while reducing the producer gas temperature and the heavy tar fraction. 
Therefore, water was selected as the suitable scrubbing medium although it has a removal efficiency lower than 
those of oily materials (Phuphuakrat et al., 2011). In order to enhance the removal efficiency, the producer gas 
flows through two water scrubbers placed in series. The scrubbers reduce the gas temperature from 350 to 
5 C, the molar water fraction from 0.295 to 0.009 and the tar content from 100 g/Nm3wet to 83 g/Nm3wet. Benzene 

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and toluene remain in the producer gas after the scrubbers as seen in the gas composition in Table 1. Benzene 
and water will form a frost layer below 5.5 and 0C, respectively, while toluene will condense as a liquid film. 

Table 1: The composition of the producer gas after the water scrubbers. 

Components H2 CO CO2 CH4 C2H4 N2 H2O C6H6 C7H8 
Mole percentage (%) 38.57 23.09 18.99 8.33 2.20 5.15 0.90 2.44 0.33 

The second unit targets the deposition of tars and water over cold surfaces. Many studies have handled the 
mechanism of frost formation and of condensation but separately. Most of these studies cover the deposition of 
water vapour present in the moist air for domestic or industrial applications, while none of them covers organic 
compounds, such as tar components. Simultaneous heat and mass transfer takes place during frost deposition 
and condensation. The formation of a frost layer limits the heat transfer due to its high thermal resistivity.  
In this study, the simultaneous frosting and condensation phenomenon is considered to take place over a cold 
plate having a constant wall temperature. The multi-phase deposition process is explained in the first part. Then 
the equations governing the heat and mass transfer in the different sub-domains are presented. Finally, a 
parametric study is completed in order to analyse the impact of the gas flow rate and the wall temperature on 
the frosting parameters including the gas temperature, the frost thickness and the frost density.  

2. Mathematical model of tar deposition

The producer gas is cooled by flowing over a cold plate whose temperature is lower than the dew point of the 
condensable components. Frost and liquid film will appear if the wall temperature is lower than the freezing point 
and the condensation point, respectively. Since studies tackling this simultaneous multi-component deposition-
condensation do not exist, each phase is treated hypothetically separately. Therefore, two separate frost layers 
are considered, the first one for benzene and the second one for ice, in addition to a liquid toluene film that fills 
a certain volume from the pores. In this study, the producer gas flows through a duct where the upper plate is 
insulated to avoid the heat transfer between the gas and the environment. The process of frosting and 
condensation happens only on the lower plate of the duct, which is maintained at a constant low temperature. 
Figure 1 describes the physical model of heat and mass transfer between the gas and the condensable 
components. The process is divided into 6 subdomains: the gas, the interface between the ice frost layer and 
the gas, the ice frost layer, the interface between the ice and the benzene frost layers, the benzene frost layer 
and the toluene liquid volume. 

Figure 1: Frosting and condensation process diagram 

Hayashi et al. (1977) work was among the first ones to study the frost growth process and divided it into three 
different periods; the “crystal growth period”, followed by the “frost layer growth period”, and finally the “frost 

layer full growth period”. The crystal growth period corresponds to the first moments of frost formation in the 

form of frost column. It is relatively short in time with respect to the whole frost formation process. To consider 
its impact on the frost growth, appropriate initial conditions, for the frost thickness (𝛿𝑓𝑟,𝑖𝑛𝑡 = 2 × 10−5 𝑚) and
frost density (𝜌𝑓𝑟,𝑖𝑛𝑡 = 25 𝑘𝑔/𝑚3), are considered (Lenic et al., 2009). The frost layer growth period is the most
studied period during which the frost growth takes place in the form of a porous structure formed of a porous 
solid phase containing gaps filled by the producer gas. During this phase, the mass transferred from the gas 
phase to the cold surface is divided into two parts. The first one deposits on the surface of the frost and tends 
to increase the frost thickness, while the second one diffuses through the frost layer and contributes in increasing 

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the frost density (Wang et al., 2012). This continues until the surface temperature of the frost layer reaches the 
melting point of the condensable components, indicating the beginning of the frost layer full growth period. The 
developed mathematical model is formulated using 1D Cartesian coordinate system for the gas side and 2D 
Cartesian coordinate system for the condensate, it is discretized according to the finite volume method and 
implemented using Dymola.  

2.1 Gas stream 

Starting with the producer gas subdomain, the sensible heat transferred from the producer gas to the frost 
surface is calculated according to Eq(1). 

�̇�𝑠𝑒𝑛𝑠𝑖𝑏𝑙𝑒 =  ℎ𝑐,𝑔𝑎𝑠. 𝑆. (𝑇𝑔𝑎𝑠 − 𝑇𝑓𝑟𝑜𝑠𝑡,𝑠) (1) 

The total mass flow rates of benzene, water vapour and toluene, transferred from the producer gas to the frost 
surface, are calculated according to the heat and mass transfer analogy as in Eq(2) where j ∈ {benzene, 
 toluene,  water vapour}. Those mass flow rates will undergo a phase change. Benzene and water vapour are 
subject to frosting while toluene is subject to condensation. 

�̇�𝑠,𝑗 = 𝑘𝑚,𝑗 . 𝑆. 𝜌𝑔𝑎𝑠. (𝑤𝑔𝑎𝑠,𝑗 − 𝑤𝑠,𝑗 ) (2) 

Note that the frost surface is considered at thermodynamic equilibrium. Thus the mass fraction at  the frost 
surface can be linked to the saturation curves developed, in previous work (Harb et al., 2020 b), for each 
component at the surface temperate as follows: 𝑤𝑠,𝑗 = 𝑓(𝑇𝑓𝑟𝑜𝑠𝑡,𝑠 ). 

2.2 Frost surface 

As mentioned previously, the total mass flow rate transfer from the gas to the frost surface (�̇� 𝑠) is splitted into 
two terms. The first term (�̇�𝛿 ) corresponds to the mass flow rate that increases the frost thickness by deposition 
on the surface while the second term (�̇�𝜌) is the mass flow rate that increases the frost density by diffusion 
inside the frost. Eq(3) applies to the benzene and the ice frost layers. 

�̇�𝑠 = �̇�𝛿 + �̇�𝜌 (3) 

The mass flow rate that increases the frost density by diffusion inside the frost can be calculated function of the 
water vapour mass fraction variation along the y-axis at the surface and the effective diffusion coefficient of the 
water vapour in the gas of the frost pores as in Eq(4). Note that the effective diffusion coefficient is equal to the 
diffusion coefficient multiplied by the diffusion resistance factor (Le Gall et al., 1997). 

�̇�𝜌,𝑤𝑎𝑡𝑒𝑟 = −𝐷𝑒𝑓𝑓,𝑤𝑎𝑡𝑒𝑟 . 𝑆. 𝜌𝑔𝑎𝑠. (𝜕𝑤𝑤𝑎𝑡𝑒𝑟 𝜕𝑦⁄ )𝑠 (4) 

Once the diffusing mass flow rate is calculated, the increasing thickness mass flow rate can be deduced from 
Eq(3). Therefore, the variation of the frost layer thickness can be calculated as follows: 

�̇�𝛿 = 𝜌𝑓𝑟𝑜𝑠𝑡 . 𝑆. (𝑑𝛿 𝑑𝑡⁄ ) (5) 

The heat transfer at the frost surface can be expressed by Eq(6). The conductive heat transfer flow rate at the 
surface is calculated function of the temperature variation in the frost when y tends to 𝛿 𝑓𝑟,𝑤𝑎𝑡𝑒𝑟  and the effective 
thermal conductivity of the frost (keff) as in Eq(7). Note that keff is calculated based on the correlation presented 
by Le Gall et al. (1997) based on the thermal conductivities of the solid and gas phase and the frost porosity. 

�̇�𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦,𝑤𝑎𝑡𝑒𝑟,𝑠 = �̇�𝑠𝑒𝑛𝑠𝑖𝑏𝑙𝑒 + �̇�𝛿,𝑤𝑎𝑡𝑒𝑟 𝐿𝑠𝑣,𝑤𝑎𝑡𝑒𝑟 + �̇�𝑠,𝑡𝑜𝑙𝑢𝑒𝑛𝑒 𝐿𝑣𝑎𝑝,𝑡𝑜𝑙𝑢𝑒𝑛𝑒  (6) 

�̇�𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦,𝑤𝑎𝑡𝑒𝑟,𝑠 = −𝑘𝑒𝑓𝑓,𝑤𝑎𝑡𝑒𝑟 . 𝑆. (𝜕𝑇 𝜕𝑦⁄ )𝑠 (7) 

2.3 Interface between the benzene and ice frost layers 

The same equations for the mass fluxes apply to the benzene-ice interface. The difference between them is that 
the mass flux leading to the benzene frost densification is function of the benzene mass fraction variation at the 
interface. The total mass flow rate of benzene transferred from the gas to the benzene frost surface is calculated 
according to Eq(2). The benzene mass flow rate that increases the frost density by diffusion inside the frost can 
be calculated in Eq(8).  

�̇�𝜌,𝑏𝑒𝑛𝑧𝑒𝑛𝑒 = −𝐷𝑒𝑓𝑓,𝑏𝑒𝑛𝑧𝑒𝑛𝑒 . 𝑆. 𝜌𝑔𝑎𝑠 . (𝜕𝑤𝑏𝑒𝑛𝑧𝑒𝑛𝑒 𝜕𝑦⁄ )𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 (8) 

Once the diffusing mass flow rate is calculated, the increasing thickness mass flow rate can be deduced from 
Eq(3). Then the variation of the benzene frost layer thickness (𝑑𝛿 𝑑𝑡⁄ ) can be calculated from Eq(5). 

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The heat balance, at the interface between the two frost layers of benzene and ice, can be expressed by: 

(−𝑘𝑒𝑓𝑓,𝑤𝑎𝑡𝑒𝑟 . 𝑆. (𝜕𝑇 𝜕𝑦⁄ )𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 ) = (−𝑘𝑒𝑓𝑓,𝑏𝑒𝑛𝑧𝑒𝑛𝑒 . 𝑆. (𝜕𝑇 𝜕𝑦⁄ )𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 ) + �̇�𝛿,𝑏𝑒𝑛𝑧𝑒𝑛𝑒 𝐿𝑠𝑣,𝑏𝑒𝑛𝑧𝑒𝑛𝑒 (9) 

2.4 Frost layer 

The mass balance of benzene or water vapour inside the frost layers can be predicted according to Fick’s law 
and it is expressed by: 

𝜕

𝜕𝑥
(−𝐷𝑒𝑓𝑓 . 𝑆. 𝜌𝑔𝑎𝑠.

𝜕𝑤

𝜕𝑥
) +

𝜕

𝜕𝑦
(−𝐷𝑒𝑓𝑓 . 𝑆. 𝜌𝑔𝑎𝑠.

𝜕𝑤

𝜕𝑦
) = −𝛼. 𝑆 (10) 

Note that saturation condition is also considered inside the frost layer. Thus the same analogy discussed in the 
previous section applies also to the mass fraction gradient inside the frost layer. 
The densification of the frost layers can be then calculated: 

𝑑𝜌𝑓𝑟𝑜𝑠𝑡 𝑑𝑡⁄ = 𝛼 (11) 

The energy balance inside the frost layer can then be applied according to Eq(12). The latter links between the 
heat transfer based on Fourier’s law and the latent heat related to the mass densification. 

𝜕

𝜕𝑥
(−𝑘𝑒𝑓𝑓 . 𝑆.

𝜕𝑇

𝜕𝑥
) +

𝜕

𝜕𝑦
(−𝑘𝑒𝑓𝑓 . 𝑆.

𝜕𝑇

𝜕𝑦
) = 𝛼. 𝑆. 𝐿𝑠𝑣 (12) 

2.5 Liquid toluene film 

The volume fraction of the pores that will be filled by the liquid toluene is equal to the ratio of the accumulated 
volume of the condensed toluene to the volume of the frost pores as expressed in Eq(14). 

𝑣𝑡𝑜𝑙𝑢𝑒𝑛𝑒 = (�̇�𝑡𝑜𝑙𝑢𝑒𝑛𝑒,𝑠 𝜌𝑡𝑜𝑙𝑢𝑒𝑛𝑒⁄ ). 𝑡 ((𝛿𝑏𝑒𝑛𝑧𝑒𝑛𝑒,𝑓𝑟 + 𝛿𝑤𝑎𝑡𝑒𝑟,𝑓𝑟 ). 𝑆. )⁄ (14) 

3. Results and discussion

Models handling a simultaneous multi-component frosting and condensation do not exist. Thus the heat and 
mass transfer equations were first validated by comparing the results with different previous available studies 
for the case of water vapour frosting in humid air (Lee et al., 2003) as seen in Figure 2. 

Figure 2: Validation of the frost growth model based on a comparison with Lee et al., (2003) for the variation of 

the frost layer thickness, frost surface temperature and heat fluxes over time  

After validating the model, a parametric study is carried out. Table 2 summarises the different initial operating 
conditions considered for the parametric study. The initial mass fraction of the different condensable 
components is fixed for all the cases. Case 1 considers a low gas velocity (laminar flow), case 2 is similar to 
case 1 with higher velocity (turbulent flow). Case 3 has a low velocity with a higher wall temperature. 

Figure 3 illustrates the variation of the gas temperature function of the plate length and the time, for the different 
inlet conditions shown in Table 2. It can be observed that, in all the cases, the gas temperature is decreasing 
along the plate length while it is increasing as the operating time increases. The lowest gas temperature at the 
end of the plate is reached in case 1, while the highest one is encountered in case 3. In addition, the gas 

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temperature variations in case 1 and case 2 are very close. However, it can be seen that in case 1, the rate of 
increase of the gas temperature, function of time, at the end of the plate, is lower than that of case 2. 

Table 2: Different inlet conditions considered for the parametric study 

Case 𝑻𝒘𝒂𝒍𝒍 (℃) 𝑻𝒈 (℃) 𝒘𝒃𝒆𝒏𝒛𝒆𝒏𝒆  𝒘𝒕𝒐𝒍𝒖𝒆𝒏𝒆  𝒘𝒘𝒂𝒕𝒆𝒓  𝒗𝒈 (𝒎/s) Plate dimensions 𝒘 × 𝒉 × 𝑳 (𝒎𝟑) 
1 -20 5 0.089 0.0142 0.0075 0.6 0.05 × 0.05 × 5 
2 -20 5 0.089 0.0142 0.0075 1 0.05 × 0.05 × 5 
3 -10 5 0.089 0.0142 0.0075 0.6 0.05 × 0.05 × 5 

Figure 3: Variation of the gas temperature function of the plate length and the time for different initial conditions 

Figure 4 presents the variation of the benzene and ice frost thicknesses function of the plate length and the 
time, for the different inlet conditions shown in Table 2. It can be observed that benzene frost thickness is 
increasing along the plate length and with respect to the operating time, in all the cases except case 3. In the 
latter, the difference between the gas temperature and the wall temperature is not high enough to promote the 
mass transfer and consequently thicken the initial benzene frost layer. The deposited weight of benzene is low 
and therefore, it is only leading to density increase. The ice frost thickness is increasing with respect to the 
operating time while it is decreasing along the plate length, in all the cases. Note that, due to the accumulation 
of the total frost thickness function of time, the resistivity of the frost thickness is increasing leading to an increase 
in the gas temperature with time. Even though the initial content of benzene is higher than that of water, the ice 
frost layer is thicker than the benzene frost layer. This is related to the saturation vapour pressure which is 
higher for benzene.  

Figure 4: Variation of the benzene and ice frost thicknesses function of the plate length and the time for different 

initial conditions  

As for the frost density, in both sub-domains, the density is higher at the front end of the plate where the producer 
gas with high tar content enters. The density decreases towards the rear end of the cooling surface. In general, 

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the density is higher near the cold surface and it decreases towards the frost surface. As the frost layer grows, 
the distance between the cold surface and the frost surface increases, leading to an increase in the thermal 
resistance. Therefore, the frost surface and the gas temperatures increase. This general behavior of 
densification is encountered in all the cases but it is less important in case 3 where the temperature difference 
is not high enough to sharply increase the density. Based on the model results, it can be seen that benzene 
frost is denser than the ice frost due to its higher initial mass fraction. After 60 minutes, the benzene frost density 
is equal to 90 and 120 kg/m3 at the beginning of the plate and it decreases to 40 and 50 kg/m3 at the end of the 
plate in case 1 and case 2, respectively. As for the ice frost density, it is equal to 40 and 45 kg/m3 at the beginning 
of the plate and it decreases to 26 and 30 kg/m3 at the end of the plate in case 1 and case 2, respectively. In 
case 3, the benzene and ice frost densities remain constant around 35 and 30 kg/m3, respectively.  

4. Conclusions

The mathematical model of simultaneous frost growth and condensation is developed on Dymola, while the 
properties of the mixtures are extracted from Aspen Properties. The results of the sensitivity study showed that 
a temperature difference of 15C between the wall and the gas inlet is not sufficient to lead to benzene frosting 
nor to reduce its content in the producer gas. Comparing case 1 to case 2, the latter has a higher velocity 
therefore higher turbulence. The gas temperature, after 60 minutes of operation, is reduced to -3.5C in case 1, 
while in case 2 to -1.5C. Consequently, the benzene content is reduced to 0.075 in case 1 and to 0.0784 in 
case 2. The content of toluene was not importantly affected by condensation. Thus a lower temperature is 
required. A future improvement to reduce the remaining content could be placing several plates in series having 
decreasing wall temperatures until reaching the required target.  

Nomenclature

Deff – effective diffusion coefficient, m2/s 
hc – convective heat transfer coefficient, W/(m2·K) 
keff – effective thermal conductivity, W/(m·K) 
km – mass transfer coefficient, m/s 
Lsv – latent heat of sublimation, J/kg 
Lvap – latent heat of evaporation, J/kg 
ṁ  – mass flow rate, kg/s 
Q̇ – heat transfer rate, W
S – gas side heat transfer area, m2 
s – surface 

t – time, s 
T – Temperature, C 
vg – gas velocity, m/s 
vtoluene – relative volume, - 
w – mass fraction, - 
 – absorption rate, kg/(m3·s) 
–frost thickness, m 
ρ–  density, kg/m3 
ε – porosity, - 

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