The analyses are based on the experimental results of the SUT in Spain collected in 1982 (Haaf et al., 1983; Haaf, 1984). The key dimensions and data of the Spanish prototype are shown in Table 1.

There are two different places to coat photocatalyst, on the ground or on the surface under the canopy. In the following analysis, we assume that the photocatalyst is coated on the ground surface. Air is supplied to the chimney from the entrance of the collector similar to a greenhouse along the radial direction. In this process, it contacts the photocatalyst coated on the ground and the methane is degraded. Based on the data in Table 1, it is estimated that the amount of air flowing through the collector is 729 m³/s. If the concentration of methane in the atmosphere is 1.8 ppm, it means nearly 74.5 kg of methane per day and 761 Tonnes of CO₂ equivalent per year flowing through this SUT.

Furthermore, if photocatalysis is combined with an up-scaled SUT of 200 MW (i.e. R_c = 3,500 m, H_T = 1,000 m and R_T = 65 m), it can provide 38 km² GH area. According to Schlaich et al.’s report (Schlaich et al., 2005), despite the considerable dimensional differences between a 200 MW SUT and the Spanish 50 kW SUT, the main thermodynamic parameters are similar in both cases. Therefore, it is reasonable to assume that the 200 MW SUT has the same temperature rise and tower outlet velocity as the Spanish SUT. The amount of air passing through the collector can be calculated as 2 × 105 m³/s. The amount of methane is 2.0 × 104 kg per day, and nearly 2.1 × 10⁵ Tonnes of CO₂ equivalent per year flowing through a single SUT.

In order to simplify the problem, there are two assumptions: 1) only methane reacts on the surface, and there is no multi-component competitive reaction; 2) the reaction is uniform along the radial direction at the same R (R is the distance from the collector center).

Many researchers have described the adsorption and photocatalytic reaction step for CH₄ total oxidation. The following analysis is based on data form Haeger et al. (2004a) and Chen et al. (2016).

In Haeger et al.’s report (Haeger et al., 2004b), the kinetics of the total oxidation of methane were studied in a continuous-stirred tank reactor with titanium dioxide as the photocatalyst. The model established by Andreas Haeger et al. can be expressed as, r A I = B B 1 C ( C H 4 ) 1 + B 1 C ( C H 4 ) ⋅ B 2 C ( O 2 ) 1 + B 2 C ( O 2 ) . (1)

The parameter values in the above model are as follows: B = 0.537 × 10 − 6  mol · W − 1 s − 1 B 1 = 2.42   m 3 / mol B 2 = 4.60   m 3 / mol , (2) where, r _AI is the reaction rates per absorbed irradiation intensity and geometric surface area of the active plate, mol·W⁻¹ s⁻¹. The product of r _AI and light intensity I is the reaction rate r(CH₄), mol·m⁻² s⁻¹; C(CH₄)and C(O₂) are the concentration of CH₄ and O₂ respectively, mol/m³. Plotting C(CH₄)/r _AI vs. C(CH₄), a straight line is achieved (Figure 3).

If the zenith solar intensity is 1120 W/m², the intensity of light with wavelength less than 400 nm can be estimated to be 56 W/m² according to the solar spectrum at sea level. Eq. 1 is used to predict initial reaction rate of 4.8 × 10^–9 mol m⁻² s⁻¹ at atmospheric methane concentration of 1.8 ppm.

For the 50 kW SUT in Spain, the ground under collector provides 46735 m² reaction area. It means that 2.2 × 10^–4 mol/s of methane can be removed (i.e. 0.31 kg/day), which is far less than the amount of methane flowing through the collector at nearly 74.5 k/day (i.e. 0.4% of removal rate).

If photocatalysis is combined with 200 MW SUT, the methane removal capacity is 0.18 mol/s, that is, 252 kg/day of methane removal, which is also less than the amount of methane flowing through the collector at 2.0 × 104 kg/day (i.e. 1.3% of removal rate).

Fortunately, beside the less effective TiO₂ photocatalyst, there are recent progress on much more effective new photocatalysts for methane oxidation. For example, in Chen et al.’s report (Chen et al., 2016), the photocatalytic methane oxidation over ZnO doped with 0.1 wt% Ag (noted as 0.1-Ag-ZnO) follow pseudo-first-order kinetics. A fitting equation can be obtained by plotting k (the rate constant) with C₀ (the initial methane concentration) (Figure 4). The rate constant k and the initial reaction rate can be predicted to be 1.69 min⁻¹ and 3.04 ppm/min at atmospheric methane concentration of 1.8 ppm. Considering the area of the reaction surface (a 7 cm diameter disc) and the volume of reactor (a 0.45 L cylinder vessel), it is estimated that the reaction constant k and initial reaction rate are 0.0035 m/s and 2.36 × 10^–7 mol m⁻² s⁻¹, respectively.

Calculations of methane removal rate based on 0.1-Ag-ZnO photocatalysts is summarized in Table 2 and compared with those based on TiO₂. In the 50 kW SUT, methane can be removed at a rate of 15.2 kg/day (i.e. 20% of removal rate). And in a 200 MW SUT, methane can be removed at a rate of 1.24 × 104 kg/day (i.e. 62% of removal rate).

Because of the concentration gradient of methane between bulk fluid and photocatalyst surface, there is a mass transfer flux which are controlled by advection and diffusion (Fogler, 2016). For the present case, the direction of air flow is radial and parallel to the ground, so the mass transfer caused by bulk fluid motion does not need to be considered. The molar diffusive flux of methane can be written as following equation: W ( C H 4 ) = h m ( C ( C H 4 ) − C s ( C H 4 ) ) , (3) where C(CH₄) is the averaged methane concentration, mol/m³; C_s(CH₄) is the methane concentration in the air next to the air–photocatalyst interface, mol/m³; h_m is the mass transfer coefficient, m/s.

Because heat transfer and mass transfer are analogous, correlations for Nusselt and Sherwood numbers are also analogous. Therefore, when the correlation for Nusselt number (Nu), Prandlt number (Pr) and heat transfer coefficient (α) is found based on the data from experiments, the correlation for Sherwood number (Sh), Schmidt number (Sc) and mass transfer coefficient (h_m) can be obtained by simple replacement. If the Pr equals Sc, then Nu equals Sh.

For 50 kW SUT, based on the temperature rise, the heat transfer rate is 24,300 kW (de Richter et al., 2017), heat transfer coefficient can be calculated as below α = Q A   Δ T , (4) where Q is the heat transfer rate, kW; A is the heat transfer area, m²; and ΔT is the logarithmic mean temperature, K. Δ T = ( T g − T a i r , i n ) − ( T g − T a i r , o u t ) ln T g − T a i r , i n T g − T a i r , o u t , (5) T _g is the temperature of the ground, T _air,in is the inlet temperature and T _air,out is the outlet temperature of the collector respectively. Nu number can be calculated by N u = α L c h a r λ , (6) where L _char is the characteristic length, m, L _char = 2H_c. λ is air thermal conductivity, W·m⁻¹K⁻¹. According to the definition of Sh, Eq. 7 can be used to calculate the mass transfer coefficient h _m . h m = S h   D C H 4 , a i r   L c h a r , (7) where D _{CH4, air} is the diffusion coefficient, m²/s.

If the concentration of methane on the surface of photocatalyst is assumed to be zero and the concentration of methane in the bulk air is kept at 1.8 ppm, the average rate of mass transfer is 1.1 × 10^–6 mol m⁻² s⁻¹ calculated from Eq. 3. The main parameters and calculation results are summarized in Table 3.

Sherwood (Sh) number correlations can also be expressed by Sh = constant × Re ^m × Sc ⁿ , where Re is Reynolds number. Since the air flowing under the collector is turbulent, according to the literature (Zukauskas and Slanciauskas, 1987), we use the equation Sh = 0,032 × Re ^0.8 × Sc ^0.43 to calculate Sh.

Table 4 shows the velocity V_c, Re, Sh, and the corresponding mass transfer coefficients at different positions under the collector of a 50 kW SUT system, which can be used for qualitative analysis of mass transfer under collector. It can be seen that at the entrance to the collector, the air velocity is the lowest and the corresponding mass transfer rate constant is the smallest. As the air flows to the center of the collector, the velocity increases and mass transfer coefficient also increases. It is because the higher velocity enhances the air turbulence, which helps to enhance the mass transfer of methane in the air, so the mass transfer coefficient increases. The mass transfer coefficient ranges from 0.0019 to 0.0191 m/s, which is in accordance with the previous results calculated by Reynolds analogy. The mass transfer rates at different positions of the collector can be estimated according to Eq. 3 and list in Table 4.

In the same way, Re, Sh, h_m, W(CH₄) of 200 MW SUT can be calculated easily, and listed in Table 5. Compared with 50 kW SUT, 200 MW SUT has higher air velocity and mass transfer rate.

To evaluate the mass transfer process comprehensively, it is essential to calculate the average mass transfer coefficient. Because there is not enough data of heat transfer to obtain the average mass transfer rate coefficient by Reynolds analogy method, the average mass transfer rate coefficient is obtained by calculating the average flow rate. The velocity of the air under the collector can be written as following equation: d R d t = G 2 π R H c , (8) where t is the residence time, min; G is the volumetric flow rate at the outlet of the tower, m³/s; H c  is the average canopy height .  

From Eq. 8, it can be estimated that the residence time of air under the collector is 10 min for 200 MW SUT. The average velocity is obtained by dividing the collector radius by the residence time. The mass transfer rate coefficient obtained from the average velocity is shown in Table 5.

By comparing the mass transfer rate W(CH₄) with the reaction rate r(CH₄), we can determine the rate-limiting step. 1) if W(CH₄) >> r(CH₄), reaction is the bottleneck of the whole process; 2) if W(CH₄) << r(CH₄), mass transfer is rate-limiting step, 3) if W(CH₄) and r(CH₄) are very close, it means that the reaction and mass transfer have equivalent influence and jointly control the whole process.

According to photocatalytic data from TiO₂, the photocatalytic decomposition rate of methane is 4.8 × 10^–9 mol m⁻² s⁻¹. No matter for 50 kW SUT or 200 MW SUT, even the minimum W(CH₄) at the collector entrance is much greater than r(CH₄), so photocatalytic reaction is the rate-limiting step.

The reaction rate based on 0.1-Ag-ZnO is 2.16 × 10^–7 mol m⁻² s⁻¹, which is close to the diffusion rate. Therefore, for 50 kW SUT, catalytic reaction is the rate-limiting step in the area near the collector inlet, while diffusion is the rate-limiting step in the centre of the collector. For 200 MW SUT, photocatalytic reaction is the rate-limiting step under the whole collector.

According to Eq. 1, the apparent reaction rate constant K_app can be estimated by the following equation for Haeger et al.’s model (Haeger et al., 2004a). K a p p = I B B 1 1 + B 1 C ( C H 4 ) · B 2 C ( O 2 ) 1 + B 2 C ( O 2 ) . (9)

The mass conservation equation together with the boundary conditions can be written as − G d C ( C H 4 ) 2 π R   d R = K a p p C s ( C H 4 ) (10) K a p p C s ( C H 4 ) = h m ( C ( C H 4 ) − C s ( C H 4 ) ) (11) R= R coll , C ( C H 4 ) = C in ( C H 4 ) , (12) where R _coll is the radius of the collector; C _in (CH₄) is the inlet methane concentration; K _app is the rate constant of apparent reaction, m/s.

The solution to Eq. 10 is C s ( C H 4 ) = 1 1 + K a p p / h m C ( C H 4 ) (13) C o u t ( C H 4 ) = C i n ( C H 4 ) e − K a p p A r / ( ( 1 + K a p p / h m ) G ) , (14) where A _r is the surface area of reaction, m². C_out(CH₄) is the methane concentration in the outlet air. The methane removal effectiveness of a SUT can be characterized by the fractional conversion. ε = C i n ( C H 4 ) − C o u t ( C H 4 ) C i n ( C H 4 ) , (15) If methane is completely decomposed, ε is 1. If no methane is decomposed, ε is 0.

The number of mass transfer units (NTU_m) is defined as, N T U m = A r G ( 1 / K a p p + 1 / h m ) , (16) Equation 16 is often used to assess the number of mass transfer units in a process that contains both physical mass transfer and chemical reaction. ε can then be written as ε = 1 − e − N T U m . (17)

The calculation results of NTU_m and ε are shown in Table 6. If the photocatalytic technology is applied to 50 kW SUT, the methane removal rates are 0.44 and 17.5% with TiO₂ and 0.1-Ag-ZnO respectively, which are lower than the results previously analysed (de Richter et al., 2017) and the methane removal rates calculated in Table 2. The main reason is that the previously analysed results only consider the mass transfer process, while the removal rate in Table 2 only considers the photocatalytic reaction kinetics. But in fact, the whole process involves both photocatalytic reaction and mass transfer process. The methane removal rates in a 200 MW SUT are 1.4 and 42.5% with TiO₂ and 0.1-Ag-ZnO respectively.

With the understanding of relevant mass transfer and kinetic phenomena, it is found that the overall rate of methane oxidation is limited by the adsorption and oxidation step rather than the diffusion of the species to the surface in most scenarios. Therefore, the future efforts should focus on improvement of photocatalytic materials.

The above analysis is based on two typical photocatalysts for methane oxidation, i.e. less effective TiO₂ and more effective 0.1-Ag-ZnO sample. It is found that the process is almost unfeasible due to the relatively low methane removal rate on TiO₂. However, for 200 MW SUT, the methane removal rate can reach 42.5% if 0.1-Ag-ZnO is used. Figure 5 shows the methane removal rates can be further enhanced if even higher reaction rates can be achieved by developing even more advanced photocatalysts. For example, if the reaction rate reaches 1 × 10^–5 mol m⁻² s⁻¹, the methane removal rate of 200 MW SUT can reach 73%. The development of photocatalysts with high reaction rate is undoubtedly the primary task.

In addition to types of photocatalysts, we can also take some other strategies to improve the photocatalytic reaction rate, such as increasing the loading amount (i.e. reaction area). There are different ways to apply photocatalysts, e.g. on the surface under the canopy, or on the ground or both. Multi-layer roof is another method that can effectively increase the reaction area (Pretorius, 2007; de Richter et al., 2016), as shown in Figure 6. It should be pointed out that although the multi-layer roofs can effectively increase the reaction area, if too many layers are needed for sufficient contact area, perhaps poorer mass transfer would occur due to slower air flow and thicker boundary layers. The intensity of sunlight will also be weakened.

If the reaction rate of the photocatalyst is large enough to meet the reaction requirement only by coating part of the collector, it is suggested that the photocatalyst should be positioned toward the outer rim of the collector rather than the center. Under the collector, with the air flow to the center, the velocity steadily rises. The rise of velocity intensifies the air turbulence, which is beneficial to the mass transfer process. But it also reduces the contact time between methane and photocatalyst. Since the reaction is the bottleneck of the whole process, it is reasonable to coat the catalyst on the periphery of the collector.

Light availability and penetration to the catalyst could present a further limitation, according to the quantum efficiency of the photocatalytic reaction. During photocatalytic process where photons strike photocatalyst surface, stimulate charge carriers inside photocatalyst and then the charge carriers move to photocatalyst surface and react with CH₄ molecules. Apparent quantum yield (AQY), defined in Eq. 18, is widely used in heterogeneous photocatalysis (solid/liquid or solid/gas systems) to quantify the efficiency of photocatalysts or photocatalytic processes. AQY = the number of reacted electrons the number of incident photons . (18)

Assuming that only UV light can be used for the total oxidation of methane, and the ground under collector (46,760 m²) are equipped with photocatalysts, all methane passing through 50 kW SUT can be removed with an AQY of 5.2%. Similarly, we calculated the required AQY of 1.7% for a 200 MW SUT which has a greenhouse area of 3.8 × 107 m², summarized in Table 7.

Another challenge of solar photocatalysis is night operation. On the ground under canopy, a thermal energy storage layer can be applied to store heat during the day and to release heat at night, driving airflow and allowing electricity production 24 h/day with no-intermittency (Ming et al., 2021). As a consequence, there can be some feasible strategy to utilize a small part of generated power to drive photocatalysis at night. Among those possibilities, at least two options for photocatalytic research are directly related.

1) Using artificial illumination at night onto all/part of the existing photocatalytic areas. In this option, almost all research outcomes about photocatalyst will stand and be applicable.

1) Height of the tower

The tower height not only determines the energy output of SUT, but also affects the outlet velocity, which is related to the amount of air flowing through SUT, the velocity and the residence time of air under the collector.

It can be seen from Eq. 19 that the outlet air speed of the tower increases with the increase of tower height, which means that more air will flow through the SUT collector with high tower, and the contact time between methane and photocatalyst is shorter Therefore, on the premise of meeting the energy output requirements, lower tower is conducive to improve the methane removal rate. v = 2 g H T Δ T T a . (19)

2) Radius of Collector

The large radius collector can provide larger contact area and longer residence time, but at the same time, it reduces the inlet velocity and thus weakens the mass transfer. For the process in which photocatalytic reaction is the rate-limiting step, it is suggested to build a collector with large radius. But larger collectors mean higher investment and maintenance costs. Therefore, the collector radius needs to be considered comprehensively. It should be pointed out that from the perspective of energy output, there is an up-limit on the radius of the collector, larger radius than that will not produce more power output (Li et al., 2012).

In respect to the reaction rate, although methane oxidation is an exothermal reaction, Chen et al. conducted experiments under different temperatures and concluded that temperature fluctuation has little effect on the photo-oxidation process (Chen et al., 2016). At the mass transfer side, status of air flow is the major factor for mass transfer. Air flow under the collector mainly depends on temperature change (∆T) and tower height (H_T) (Schlaich et al., 2005), and the influence of ambient temperature (T_a) on ∆T and H_T is negligible. Therefore, it is believed that temperature might not be a major influencer for air flow and thus should not be a major influencer for mass transfer.