### Material preparation for the anaerobic fermentation

Both materials were prepared similar for the anaerobic fermentation process: the material was subject to dimension reduction with a Retsch SM2000 grinding device to a dimensions of 1 – 2 mm. The selected materials for the experiments were placed inside the anaerobe reactors through the means of a submersible pump, the ratio between the solid and liquid material being 75 kg to 2000 L. The internal agitation occurred by the means of a bubble system, inserted at the bottom of each reactor and by using as agitation factor a part of the produced biogas. The pH corrections were accomplished using a lime suspension with a correction of the pH-value of 12 – 13. The suspension was inserted inside the reactors by means of dosing pumps (Hanna Instruments, model BL20). The obtained biogas was analyzed with a Delta 1600 S – IV gas analyzer for CO_{2} and CH_{4} composition with an accuracy domain of +/−5% of reading both for CH_{4} and CO_{2}.

### Laboratory analysis

*For the determination of moisture content*, the used equipments are: Sartorius AC211 laboratory balance with four decimal precision, weighing dishes, a desiccator and a drying oven (model DHG-9040, A Series). The substrates were systematically weighted with the balance before, during and after the drying process until stable mass. The period of time inside the drying oven was between 2 and 4 hours.

The used formula for the determination is:

{M}_{\mathit{ad}}=\frac{({m}_{2}-{m}_{3})}{({m}_{2}-{m}_{1})}\xb7;100

(1)

*m*_{
1
} = is the mass in grams of the empty dish

*m*_{
2
} = is the mass in grams of the empty dish plus sample before drying

*m*_{
3
} = is the mass in grams of the empty dish plus sample after drying

At least three determinations for each material were achieved.

*For the determination of ash content* the used equipments are: Sartorius AC211 laboratory balance with four decimal precision, weighing dishes, a desiccator and a furnace (model L1206 – Caloris Group). The empty dishes were inserted inside the furnace at 815°C for a period of 2 – 3 hours. The materials were measured with the balance, put inside the empty dishes and inside the furnace for approximately 2 hours. After the process was finished, the materials were put near the furnace for 10 minutes to cool and then inside the desiccator for 10–15 minutes. After those steps, the materials are weighed again.

The proposed formula for the determination is:

{A}_{d}=\frac{({m}_{3}-{m}_{1})}{({m}_{2}-{m}_{1})}\xb7100\xb7\frac{100}{100-{M}_{\mathit{ad}}}

(2)

*m*_{
1
} = is the mass in grams of the empty dish

*m*_{
2
} = is the mass in grams of the empty dish plus sample

*m*_{
3
} = is the mass in grams of the empty dish plus ash

*M*_{
ad
} is the% moisture content of the test sample used for determination.

Again at least three determinations for each material were carried out.

*For the determination of the calorific value* there was used a Sartorius 320 laboratory balance with four decimal precision, a calorimeter bomb model IKA C 5000, metal dishes for the bomb, cotton fuses, a pellet press, a ion chromatograph model Dionex IC 20, distilled water and glass bottles for the liquid samples. A quantity of about 0.7 grams of material was pressed inside the pellet press, weighed without the cotton fuse, and introduced inside the bomb. After approximately 40 minutes, the sample was removed from the bomb, washed with 100 ml distilled water and the registered value indicated by the apparatus is inserted into a protocol. The liquid sample was further analyzed inside the ion chromatograph for chlorine, sulphur and nitrates and the obtained values are used for correcting the initial values, together with hygroscopic humidity and ash content. Again, one mentions that at least three determinations for each material were made.

*Determining of major and minor elements* was based on a two step method. First, each sample was introduced inside a hot press, at a temperature level of 140°C and a force of 50 kN for a period of 330 sec. For the second step, the pressed materials were inserted into a MagiXPro X – Ray Fluorescence Spectrometer for a period of 20 minutes / sample for major elements and 1.5 hours / sample for the minor elements. The results were stored and imported via PC.

For the determination of C and N content the LECO TruSpec CHN analyzer was used, with dedicated software and a Sartorius 320 laboratory balance. Before the determination, a general analysis of the system was made, through blind tests and standard materials for equipment calibration. The obtained values were used for recalculation of the results up to their constancy and the average value was considered.

### Mathematical analysis

The correlation coefficient used for data analysis was developed based on real laboratory data, as resulted from the two anaerobic digestion experiments. By analyzing the set of experimental data, it was assumed that the dependence between the biogas production and pH and temperature of the substrates is best to be evaluated by means of the regression coefficient. Also the analysis by means of histograms between the biogas volumes (quantity) generated under different temperature and pH values was proposed.

In general agreement to the basic theory and the application developed in [14], was used the following general formula for the correlation coefficient:

R=\frac{\frac{1}{N}\left[\sum _{i}{x}_{i}{y}_{i}-\sum _{i}{x}_{i}\sum _{i}{y}_{i}\right]}{\frac{1}{N}\sqrt{\left[\sum _{i}{\left({x}_{i}-\frac{1}{N}\sum _{i}{x}_{i}\right)}^{2}\right]\left[\sum _{i}{\left({y}_{i}-\frac{1}{N}\sum _{i}{y}_{i}\right)}^{2}\right]}}

(3)

where:

x_{i,} y_{i} with i = 1, 2, … N, are sample values of the measured quantities (physical values) for which the correlation coefficients are calculated. In particular they represent the substrate pH value during anaerobic digestion, as a function of produced biogas volume [m^{3}/day] and the substrate temperature during anaerobic digestion process [°C] as a function of produced biogas volume [m^{3}/day].