2.2.3. Experimental Procedure

Bed length was kept constant packing the column with the same HC volume same of the inert material volume used for the blank test.

Adsorption experiments were performed with two different feed mixtures (CO2 + N2 and CO2 + CH4). The PSA operating pressure varied up to 5 bars.

Tests with CO2 + N2 were carried out at 2, 3, 4, and 5 bar with 100 NmL/min of CO2 and 80 NmL/min of N2 (carrier gas). The regeneration step was performed with N2 at 280 NmL/min. A mass flow meter (MFM) quantified the total amount of the gas mixture leaving the column. During the adsorption tests, V-A, V-B, and V-C valves were kept open. The configuration for regeneration after each run was as follows: V-A and V-G closed, V-H switched for a quick depressurization and then repositioned, V-G re-opened, and N2 injected until no CO2 was detected. The blank tests were carried out in the same way.

Tests with CO2 + CH4 mixture were carried out at 2 and 5 bar with 76 NmL/min of CO2 and 76 NmL/min of CH4. The flow rate of N2 during the regeneration step was 280 NmL/min. The experiments were carried out as previously described, with CH4 in the inlet flow rate instead of N2. V-D and V-A operated simultaneously. The regeneration step lasted until no CH4 was detected at the column outlet.

All tests were repeated almost five times. The synopsis is reported in Table 1.


**Table 1.** Synopsis of tests conditions.

## 2.2.4. Mathematical Model

The mathematical model for determining the amount of the adsorbed CO2 was extensively described in Di Felice et al. [45]. The blank test highlighted the domination in the response curve of a flow-mixing in the ancillary equipment and provided a means of confronting the gas outlet responses to the CO2 capture characteristics of the bed itself. A simple descriptive FOPDT model (first order plus dead time model) of the gas phase allows extracting the response of the particle phase from the measured gas phase response of the entire system under CO2 capture conditions. The response curve gives the molar total gas holdup, viz, the product of the total molar throughput of gas and the area enclosed by the response curve and normalized ordinate 1 (Figures 2 and 3).

The response curve may be used to evaluate the total amount of CO2 present in the whole system as a function of time (i.e., its holdup: the moles of CO2 that entered the system at time *t* minus those that left). The CO2 holdup in the solid phase of the bed (i.e., the CO2 captured by the hydrochar) is merely the total holdup of the entire system minus the holdup of the gas phase of the entire system [45]. Adsorption performance in CO2/CH4 tests was evaluated estimating recovery, purity, and selectivity [22]. The gas recovery rate is the ratio of the quantity of gas recovered after the column to the fed quantity:

$$\text{Recovery}(i) = \left(\int\_0^t (y\_i \, q)\_{\text{OUT}} \, dt\right) \left(\int\_0^t (y\_i \, q)\_{\text{BLANK}} \, dt\right) \tag{1}$$

The purity is defined by the quantity of the gas during the saturation phase divided by total gas leaving the column at the same time.

$$\text{Purity}(i) = \left(\int\_0^t (y\_i \, q)\_{\text{OUT}} \, dt\right) \Big/ \left(\int\_0^t q\_{\text{OUT}} \, dt\right) \tag{2}$$

where *yi* is the molar fraction of the specific gas and *q* is the total gas flow.

The selectivity is expressed as follows:

$$\text{Selocity} = \frac{\text{mol}\_{\text{CO}\_2} / \text{kg}\_{\text{adsorbed}}}{\text{mol}\_{\text{CH}\_4} / \text{kg}\_{\text{adsorbed}}} \tag{3}$$

#### **3. Results and Discussions**

The assessment of new porous carbon material should be based on its adsorption properties, evaluated through the well-established procedures. Table 2 lists the results of the BET analysis.


**Table 2.** BET and BJH results of all materials tested.

The surface area and the average diameter of the pore *Dav,BJH* (obtained as <sup>4</sup>·VBJHa/ABET, where VBJHa is the BJH desorption pore volume and ABET is the BET surface area) are critical parameters for physical adsorption. In general, the higher the superficial area, the better the sorbent capacity.

The increase of porosity is also highlighted by SEM-EDS images (Figure 2), where, in the left-hand side (Figure 2a,c,e), the original wood structure is always present after hydrothermal treatment with several typical pits [46] and, at higher magnification (3000 and 10,000×), 10 μm macropores are also visible. On the right-hand side (Figure 2b,d,f), after the activation procedure, as expected, a well-developed sponge structure is evident at increasing magnification (400, 2000, and 10,000×).

**Figure 2.** Scanning electron microscopy (SEM) images of HC\_200\_0 (left-hand side: (**<sup>a</sup>**,**c**,**d**) and HCA\_200\_0 (right-hand side: (**b**), (**d**,**f**) at di fferent magnification: (**<sup>a</sup>**,**b**) 400×; (**c**) 3000×; (**d**) 2000×; (**<sup>e</sup>**,**f**) 10,000<sup>×</sup>.

The EDS analysis, not reported here, shows the carbon as the main element with a distributed trace of chlorine, owing to the HCl washing step of the activation method.

As far as the time course of the outflowing CO2 and CH4 concentration is concerned, a sigmoidal behavior was observed for all tests and at all values of the operating pressure, as shown in Figure 3. The recorded signals are reported as a normalized value, that is, divided by the inlet concentration.

**Figure 3.** CO2/N2 adsorption curves at (**a**) 2 bar; (**b**) 3 bar; (**c**) 4 bar; and (**d**) 5 bar.

By inspection of Figure 3, the time of first detection (arrows) depends evidently on the operating pressure. The translation of blank curves is inherent in the operating modality of the apparatus and depends linearly on the pressure (data not reported for the sake of brevity). The translation of the response curves suffers from the superimposition owing to the presence of the adsorbent bed. The difference between the two delays increases steadily. Table 3 is a synopsis of all the results.

The sorbent capacity of the activated hydrochar obtained at 200 ◦C and 0 min is higher than that of the corresponding material recovered after 120 min of retention in the HTC reactor. The results of the BET analysis confirm this finding, where the 0 minute sample shows a specific area as high as 210% (3.1 time bigger) and an average pore diameter decreased by 27% in comparison with sample HCA\_200\_120. These results warn that the HTC reaction time is a crucial parameter and that the existence of a possible optimal retention time will be worth study, and in the further developments, it will be coupled with a cost optimization aimed at industrial exploitation of the results.

On the other hand, the performances of non-activated hydrochar denounce of an adsorbent capacity of an order of magnitude lower, and are thus not acceptable for industrial applications.


**Table 3.** CO2 sorbent capacity.

\* Mean ± standard deviation.

Figure 4 shows typical adsorption curves obtained with the activated hydrochar at 2 and 5 bar (a and b, respectively) and the mixture CH4/CO2. Blank runs are reported as a reference. Arrows signal the time of the first detection. Both diagrams show that, in the blank runs, the CO2 and CH4 signals are indistinguishable. On the contrary, in the presence of a hydrochar bed, a selectivity appears evident, as proven by the temporal separation of the arrows. Methane appears first in the column outlet regardless of the operating pressure. The delay between the two signals is an increasing function of the operating pressure, and in any case, it is sufficiently broad for envisaging the development of an industrial process. All of this evidence proves that hydrochar is a suitable medium for separating the mixture by selective adsorption.

**Figure 4.** CO2/CH4 adsorption curves at (**a**) 2 bar and (**b**) 5 bar.

Table 4 quotes the obtained selectivities and recoveries calculated using Equations (1)–(3). The obtained selectivities confirm that CO2 is preferred to CH4. The performance of hydrochar is worse than that obtainable with commercial porous sorbents such as zeolites or activated carbons [22]. As expected, the methane recovery is relatively low with a purity of 95% (Italian regulation for network injection) regardless of the investigated operating pressure. The doubling of recovery obtained with a purity of 70% is a valuable result because of energetic applications.


**Table 4.** Summary of the results of the adsorption tests (mixture CO2/CH4).

Figure 5 reports the averaged CO2 sorbent capacity for the two samples of activated hydrochar as a function of the corresponding partial pressure in the gas phase. Data fit well to the Langmuir equation [47].

$$\text{CO}\_{2\text{Sorbert capacity}} = \left(\text{C}\_{\text{Max}^\circ} \text{p}\_{\text{CO}\_2}\right) / \left(\text{K} + \text{p}\_{\text{CO}\_2}\right) \tag{4}$$

**Figure 5.** CO2 sorbent capacity vs. pCO2.

The regressions are reported as solid lines in the explored range and as dotted lines in the extrapolated ones. A wider partial pressure range should be explored to ascertain the correct equilibrium law. For the present paper, this preliminary investigation gives valuable information for steering future studies.

The regression parameters are reported in Table 5.

**Table 5.** Synopsis of regression parameters for Langmuir equation.


Figures 6 and 7 compare the performances of the hydrochars to those of traditional solid materials and those of some innovative materials, as reported in the literature [22,40,48–54]. As a general finding, data on PSA at 1 bar appear in the literature sparingly, even for traditional sorption media. Figure 6 reports a possible comparison of the hydrochar sorption capacity. It appears that, despite the different capture techniques, the data of "HCA\_200\_0\_calc" at 1 bar (calculated by Equation (4)) are comparable with those of the literature. On the other hand, the comparison with PSA experiments conducted on zeolites, activated carbon, and fly ash shows that, at the same operating conditions, the HCA exhibits much better results in terms of CO2 capture capacity.

**Figure 6.** Comparison of CO2 sorbent capacities with literature data obtained with batch equilibrium method (BPL: commercial activated carbon [48]; C35N400: ammonia-treated activated carbon [49]; G-900: activated graphite fibers [50]; MFB-600: N-doped activated carbon [51]; RN-800: ammonia-treated activated carbon [52]; RFL-500: N-doped porous carbon [53]; DO-88-M: activated carbon from petroleum pitch [54]; AS-2-600: sawdust-based porous carbon [40]).

**Figure 7.** Comparison of CO2 sorbent capacities with literature data obtained with the dynamic experimental method (pressure swing adsorption (PSA)) (A1, A2, A3, A4, B1, B2: zeolites from fly ash; SG: commercial silica gel; AC: commercial activated carbon; 13X: commercial zeolite [22]).

Figure 7 shows that the HCA\_200\_0 has the best CO2 sorbent capacity: 6.569 mmol/g, threefold concerning the best performance of traditional sorbents [22]. Another significant result appears in Figure 7. Hydrochars prepared after 120 min of HTC reaction halve their performance, even though remaining well above commercial zeolites and similar materials. This suggests investing in further research aimed to ascertain if a reaction time exists, which maximizes the sorption capacity. This more-in-depth investigation is of the utmost importance for industrial-scale process optimization.

All of the results here reported highlight the concrete possibility of exploiting the residual biomass as an adsorption medium for biogas upgrading and encourages continuing research in this way.
