2.2.1. Biochemical Methane Potential Test

Biochemical methane potential (BMP) tests were performed using an automatic methane potential test system (BPC Instruments AB, AMPTS® II, Lund, Sweden) presented in Figure 2. The system consists of 15 reactors (500 mL) with agitation (2) placed in water batch (1), gas volume meters (4) as well as a built-in data acquisition system that can be displayed on PC (5). Due to the presence of CO2 absorption units filled with NaOH solution (4), only CH4 volume was measured.

**Figure 2.** Biochemical methane potential test equipment AMPTS II, 1—water bath, 2—reactors with agitation, 3—CO2 absorption units, 4—gas volume meters, 5—computer.

A biomethane potential test took 21 days and was performed twice. Each replication consists of two reactors filled with digestate; two reactors filled with digestate and FW, and two reactors filled with digestate, FW, and biochar according to the matrix presented in Table 2. For each reactor, 300 g of liquid digestate was used. For each reactor (excluding the first two), 3.96 g of dry FW mixture was added, and for reactors with BC, 0.1982 g of dry biochar was added. As a result, the substrate to inoculum ratio (SIR) was 0.4 by VS (or 0.25 by TS), the total solids in the reactors were 6.53–6.59%, and biochar share in FW was 5% (by total solids). At the beginning and end of the test, ph and electrical conductivity (EC) was measured using a ph/EC meter (Elmetron, CPC-411, Zabrze, Poland).

**Table 2.** Anaerobic digestion experiment matrix, D—digestate, FW—food waste, BC\_—specific biochar derived under the following conditions: temperature, ◦C/residence time, min./pressure, bar.


D—digestate; FW—food waste mixture, BC\_300/60/0—biochar produced at 300 ◦C in 60 min and atmospheric pressure, BC\_300/60/15—biochar produced at 300 ◦C in 60 min and overpressure pressure of 15 bars, BC\_400/60/0—biochar produced at 300 ◦C in 60 min and atmospheric pressure, BC\_400/60/150—biochar produced at 300 ◦C in 60 min and overpressure pressure of 15 bars, HTC280—biochar/hydrochar produced in hydrothermal carbonization process at 280 ◦C in 60 min at a pressure of up to 15 bars.

The SIR of 0.4 was chosen due to works of [21,22], which show that, for FW, the optimal SIR varies from 0.33 to 0.5, while a 5% BC share in food waste by TS was chosen due to our previous work [18]. In addition, a 5% share of biochar addition considered in the current study is equal to biochar addition of 0.05 gBC × gTSsubstrate<sup>−</sup>1, or 0.65 gBC × <sup>L</sup><sup>−</sup>1.

#### 2.2.2. Materials and Process Residue Analysis

All material used in the study was subjected to moisture content, total solids, volatile solids, and ash content determination [23]. The moisture content and total solids were determined using the laboratory dryer (WAMED, model KBC-65W, Warsaw, Poland), according to the PN-EN 14346:2011 standard [24], while volatile solids and ash content were determined using the muffle furnace (SNOL, 8.1/1100, Utena, Lithuania) according to the PN-EN 15169:2011 standard [25]. Additionally, biochars were analyzed for pH and EC. The measurements were performed in measured in solution: 1 g of dry mass to 10 mL of deionized water, after 30 min since being mixed [26].

FW mixture was additionally subjected to ultimate analysis for determination of the elemental composition (C, H, N, S, O). The ultimate analysis was performed using a CHNS analyzer (PerkinElmer, 2400 CHNS/O Series II, Waltham, MA, USA) according to 12902:2007 [27]. The oxygen content was calculated by the difference according to Equation (2):

$$O = 100 - \mathcal{C} - H - N - S - A\mathcal{C} \tag{2}$$

where:

*O*—oxygen % share in dry mass, %; *C*—carbon % share in dry mass, %; *H*—hydrohen % share in dry mass, %; *S*—sulfur % share in dry mass, %; *AC*—ash % share in dry mass, %.

The elemental composition was used for the calculation of theoretical biogas composition and the theoretical biochemical methane potential (TBMP). Calculations were done according to Boyle modification of Buswell and Mueller stoichiometric formulas, Equation (3) [28]:

$$\begin{array}{ll} \text{C}\_{a}\text{C}\_{b}\text{H}\_{b}\text{N}\_{d}\text{S}\_{d} + & \left(a - \frac{b}{4} - \frac{c}{2} + \frac{3d}{4} + \frac{e}{2}\right)\text{H}\_{2}\text{O} \\ & \rightarrow \left(\frac{a}{2} + \frac{b}{8} - \frac{c}{4} - \frac{3d}{8} - \frac{e}{4}\right)\text{CH}\_{4} + \left(\frac{a}{2} - \frac{b}{8} + \frac{c}{4} + \frac{3d}{8} + \frac{e}{4}\right)\text{CO}\_{2} + dNH\_{3} + eH\_{2}\text{S} \end{array} \tag{3}$$

where:

*CaHbOcNdSe*—elemental composition of the substrate, C—carbon, H—hydrogen, O—oxygen, N—nitrogen, S—sulphury, and *a*, *b*, *c*, *d*, *e* stands for molar % share of specific elements of the volatile solids of biomass [29].

*H*2*O*—water needed for substrate decomposition, mol;

*CH*4—methane, mol;

*CO*2—carbon dioxide, mol;

*NH*3—ammonia, mol;

*H*2*S*—hydrogen sulfide, mol.

The mols of biogas products (*CH*4, *CO*2, *NH*3, *H*2*S*) were recalculated for volume in standard conditions (*p* = 1013.25 hPa, *T* = 273.15 K) by multiplication obtained mols by 22.415 obeying Avogadro's law. Knowing the elemental composition of substrates and the molar mass of each element, the mass of 1 mol of the substrate was calculated. Next, the volume of each gas component was divided by the mass of 1 mole of substrate used for its production, providing a result in dm<sup>3</sup> per gram of dry substrate. Then, knowing the volatile solids of a substrate, results were recalculated to dm3 of gas per gram of volatile solids of a substrate.

Additionally, the FW biodegradability was calculated using data of cumulative methane production and theoretical maximum methane production following Equation (4) [30], and CH4 production effect, Equation (5):

$$BD = \frac{EBMP}{TBMP} \times 100\tag{4}$$

where:

*BD*—biodegradability of FW obtained in the methane fermentation process, %; *EBMP*—experimental biochemical methane potential, ml × gVS<sup>−</sup>1; *TBMP*—theoretical biochemical methane potential, ml × gVS<sup>−</sup>1;

$$\text{CH}\_4 \text{production } effect = \frac{\text{CH}\_4}{\text{CH}\_4} \text{with } \text{BC} - \text{CH}\_4 \text{ without } \text{BC} \times 100 \tag{5}$$

where:

*CH*<sup>4</sup> *production e f f ect*—change of CH4 produced after biochar addition to the process, %; *CH*4*with BC*—CH4 produced from a sample without biochar added, ml; *CH*4*without BC*—CH4 produced from a sample with biochar added, ml.
