The data collection has been done through various methods including literature reviews concerning biogas plant designs and biogas production using different biodegradable wastes either as a single substrate or co-digested with other wastes, questionnaires, interviews, and observation. Primary data was collected through a baseline survey that included a questionnaire and personal observations in and around Phalombe secondary school where the study was carried out.

Secondary data was collected through literature reviews that included books, journals/articles, and websites. Data gathered from the literature review was used to determine the type of biogas plantto be used at Phalombe Secondary School. The Floating drum, Fixed dome, and the Polythene tube biodigester are three main digesters used worldwide. Each type of the three biogas plants mentioned above was thoroughly evaluated and the best design suitable for use at Phalombe Secondary school was selected using the Ranking method. Data for daily feeding material (DFM) was collected from both surrounding households and the administrator of the school. Also collected were data on the number of times of cooking per day at the school, number of staff and students at the school, disposal of kitchen waste, and annual temperatures of Phalombe district. All this data was required to come up with an appropriate design of a biogas plant that could supply Phalombe Secondary School with the right amount of gas for cooking and lighting. Other design considerations were based on the hydraulic retention time (HRT) and total solids (TS) content in the manures. From the literature review, the TS value desired is 8% and HRT is greater than 20 days. From this information, a TS value of 8% and HRT of 40 days was used in the design calculations for the biogas plant to be constructed at Phalombe Secondary School.

The energy demand assessment has been done through a questionnaire, interviews, and site visit, therefore, data for energy demand (ED) for cooking and lighting was also collected. This helped to know how much electrical energy (EE) per day was being used by the school for lighting in the school classrooms, staff houses, kitchen, laboratories, and hostels. Also collected were data on the amount of firewood the school was using per school term. The electrical energy demand (EED) and the ED for firewood were then summed up and converted into biogas equivalence. It was from this sum of ED that the calculations for the size of the biogas plant were based. The respondents of the questionnaire on EED at the school for lighting were the head teacher of the school and other members of staff on duty during evening study times at the school. On the demand for firewood, the respondent of the questionnaire was the head cook. The respondents for ED for lighting at staff houses of the school were the head teacher and his fellow members of staff who are housed in the school compound.

The EED requirement was based on EE used by the staff members for lighting in their houses, EE used in the classrooms and offices for lighting during study times, EE used in the laboratories, student hostels, student kitchen, dining hall/canteen, and storeroom where kitchen facilities are kept. The EED in kilowatt-hour (kWhr) was summed up and converted to ED in Joules per day. This was then being converted to biogas flow rate per day (m³ per day) as biogas equivalent from ED. Wood energy demand was calculated based on the amount of firewood the school is using in an academic term or year. This was then converted to the amount of firewood the school uses per day. Using the firewood to biogas-equivalent conversion, it came up with the amount of biogas in cubic meter (m³) required per day (m³ per day) for cooking in the kitchen as an alternative source of energy. The total amount of biogas required per day at the school for cooking and lighting was calculated by summing up the biogas equivalence for electrical lighting and firewood to biogas equivalent in m³ per day. Using the sum of biogas equivalence per day required at the school for cooking and lighting, the amount of HW required per day to be fed into the digester was determined. Based on the total amount of substrate to be fed into the biodigester (HW and CFW) and an estimated HRT of 40 days, the sizing of the biodigester, Gasometer, and the Digestate Collecting Tank was carried out. Detailed calculations are shown in the next section (section 2.5.3).

The tool used for this method was literature reviews on the common types of biogas plants in use globally for biogas production namely the Floating drum, Fixed dome, and the Polythene tube biodigester. The information of these types of biogas plants was gathered in terms of construction methods, availability of materials used in construction, the durability of materials, gas pressure holding ability, gas leakage through walls, gas pressure capacity, their life span, gas holding capacity, maintenance costs, their versatility in terms of construction(in high or low weather conditions), methane emission from each type, and other factors that should be considered when designing a biogas plant were sourced through this literature search. Each type of the three biogas plants mentioned above was thoroughly evaluated and the best design suitable for use at Phalombe Secondary school was selected. Based on literature detailed information about each of the three types of biogas plants, the fixed dome was selected [12] [14]. Although high skilled labor is required in the construction of a fixed dome biodigester, it has several advantages over the other types of biodigesters in AD [15]. Therefore, it was the preferred choice in the design selection. It consists of a digester with a fixed, non-movable gas holder that sits on top of the digester. When gas production starts, the slurry is displaced into the overflow tank. Gas pressure increases with the volume of the gas stored and the height of the difference between the slurry level in the digester and the slurry level in the compensation tank. There are no rusting steel parts in its construction hence long life (20 years or more). The plant is constructed underground, protecting it from physical damage and saving space. The underground digester is protected from low temperatures at night and cold seasons [12] [16].

A Biogas software called Online Biogas App (OBA) was used to simulate biogas production from the amount of substrate that was calculated/estimated in the design. The biogas yield was calculated from stoichiometry calculation, based on substrate compositions using OBA. Graphical presentations were drawn from the averaged results. All statistical work was done in Microsoft Excel 2016 (Microsoft Corporation, USA) and Past statistical software (version 4.03).

Using HW and CFW separately as substrates and then using the mixture as substrate simulations were run (Figures 3-5). The results were as follows Simulation 1: Theoretical biogas production from HW, Simulation 2: Theoretical biogas production from CFW, and Simulation 3: Theoretical biogas production from co-digestion of HW and CFW as shown in Table 6, Table 7, and Table 8 respectively.

As described from the above tables, in simulation 1, the macromolecular composition of HW is 11%, 15%, 15%, and 3% for carbohydrates, Ash, Lipids, and Protein respectively. The total volume of biogas produced was 185,000 L per kg (185 m³ per kg) from which the amount of CH₄ produced was 118,000 L per kg (118 m³ per kg) representing 64% CH₄ from the total biogas produced. The amount of CO₂ produced was 66,400 L per kg (66.4 m³ per kg) representing 35.9% of the total gas produced. In simulation 2, the macromolecular composition of CFW is 45%, 0%, 40%, and 15% for carbohydrates, Ash, Lipids, and Protein respectively. The total volume of biogas produced was 58,900 L per kg (58.9 m³ per kg) from which the amount of CH₄ produced was 36,300 L per kg (36.3 m³ per kg) representing 61.6% CH₄ from the total gas produced. The amount of CO₂ produced was 22,600 L per kg (22.6 m³ per kg) representing 38.4% of the total biogas produced. In simulation 3, the macromolecular composition of the mixture was 56%, 15%, 30%, and 18% for carbohydrates, Ash, Lipids, and Protein respectively. The biogas production from co-digestion was high compared to HW and CFW digestion alone. However, the %CH₄ was low compared to them. The total volume of biogas produced was 265,000 L per kg (265 m³ per kg) from which the amount of CH₄ produced was 157,000 L per kg (157 m³ per kg) representing 59% CH₄ from the total gas produced. The amount of CO₂ produced was 109,000 L per kg (109 m³ per kg) representing 41% of the total biogas produced. All digesters presented high degradability with 90%.

Figure 6 and Figure 7 show pie charts and bar charts for the mole fraction of methane in dry biogas produced from co-digestion of HW and CFW.

The two graphs above show that single digestion of HW and CFW gives results of 64% and 61.6% respectively. When the two types of wastes are co-digested, they also give a fairly good result of 59%; a figure which is within the bracket of 55% - 65% CH₄ composition [30] [32]. From the simulation results 1 and 2, it can be seen that both substrates (HW and CFW) have the potential of producing enough biogas, with gas constituent compositions well comparable [33] [34]. Similarly, if the two substrates are co-digested, it can also be seen that enough CH₄ is well comparable to the constituent compositions presented by [32] [35].

The study [36] reported that the quantity and quality of biogas produced from biodegradable wastes largely depend on the nature and composition of the digester feedstock, temperature, organic loading rate, HRT, and C/N ratio. Proper management of the production process is also of great importance. This simulation exercise did not show the C/N ratio. In general, anaerobic microbes utilize carbon 25 - 30 times faster than nitrogen. So for efficient biogas production, the C/N ratio in the feedstock should be maintained at 20 - 30:1 [9] [37] [38]. This is the optimal value that can give out enough CH₄ gas. However, the designer of this study will use rice straw/bran to improve the C/N ratio during the anaerobic co-digestion of these wastes. Plants such as rice straw have a high percentage of carbon. For example, rice straw has a C/N ratio of 70:1 [39] such that it can be mixed with materials of low C/N ratio such as HW to maintain this optimum C/N ratio thereby increasing the CH₄ yield.

In the study of co-digestion of food waste and human excreta for biogas production [40], the value of biogas generated from a 40-liter laboratory-scale AD was 84,750 cm³ (0.08475 m³) comprising 58% CH₄ and 24% CO₂ with a mesophilic temperature range of 22˚C - 30.5˚C throughout the study. The simulated results of this design study obtained a CH₄ value of 59% which is slightly higher than what was found in this laboratory experiment. However, it was argued that if a higher temperature, in this case, 50˚C - 60˚C was reached during the AD process a higher percentage value of CH₄ yield would have been maintained because methane methanogenic bacteria which is responsible for CH₄ production work efficiently at a mesophilic temperature of 30˚C - 40˚C and thermophilic temperature of 50˚C - 60˚C.

The study suggested the temperature of below 30˚C slowed the development of methanogenic bacteria responsible for CH₄ production, hence low yield. In the study of [41] which was done to find out the yield of CH₄ when fruit vegetable waste and food wastes were digested separately in anaerobic conditions, methane yields for fruit vegetable waste and food waste in m³ per kg-VS were 35% and 60% respectively. This shows that there is potential in food wastes for CH4 production. The results are also very comparable with the value obtained through simulation of biogas production in CFW (61.6%). A study of [42] reported that with a proper organic loading rate into the biodigester, the highest CH₄ production yield was 64%. Therefore, the simulation results of this design agree with those of this study. In the study of [18], a biodigester of volume 2.5 m³, gasometer volume of 0.7 m³, and digestate volume of 2.5 m³ were designed. With an HRT of 30 days, the total gas produced was 0.6108 m³, with maximum gas production of 0.037 m³ per day while the maximum biogas potential was 0.771 m³. This study has designed a biogas of volume 62 m³. Mathematically it can be proved that if a 2.5 m³ biodigester produces 0.037 m³ per day of biogas, then a 61 m³ biodigester will produce

( 0.037 ÷ 2.5 ) m 3 × 62 / day = 0.9176   m 3   per dayof biogas (40)

We can assume that with an HRT of 40 days as per this design, the volume of biogas produced in the digester will be more than 0.9176 m³ per day. Taking this value of 0.9176 m³ per day of biogas production, it means that to satisfy the demand of biogas at Phalombe secondary school which is currently at 42.85 m³ per day as per the researcher’s calculations, then this demand will be met within 47 days. But this is when the HRT is 30 days. Therefore, with an HRT of 40 days as per this design and the addition of rice straw to the substrate to improve the C/N ratio, then the demand can be met in less than 47 days. Therefore, this is a viable design. It must also be mentioned here that proper management of the whole biogas production process is very vital to achieve good results. Table 9 shows standard sizes (models) of fixed dome biogas plants used in Bangladesh.

According to Table 9 from these articles, we can compare the effective digester volumes and their respective rated biogas production with the new design. It can be seen that if a digester of volume 11.8 m³ produces 4.8 m³ of biogas per day, then from the new design of 62 m³ digester we can get:

4.8   m 3   per day × ( 62 ÷ 11.8 ) = 25.2   m 3   per dayof biogas (41)

The energy demand at Phalombe Boarding School is found to be 42.85 m³ per day. So at the rate of 25.2 m³ per day of biogas, this demand can be meet within a very short period.

If we use conversion factors in Figure 8 we can calculate CH₄ production from the biogas energy demand in this design.

From the table in Figure 8, 1 m³ of biogas = 0.65 m³ of CH₄. Therefore the 25.2 m³ per day of biogas, CH₄ produced will be 0.65 m³ × 25.2 m³ per day = 16.38 m³ per day

From this value, it can be assumed that meeting the demand of 42.85 m³ per day can be achieved in 3 days after the HRT which in this design is 40 days. A study [45] proved that the best HRT is below 44 days because after this day biogas production becomes stable for some time and then drops. Also, studies [23] [25] showed the same effect of HRT. So, an HRT of 40 days for this design is a good time for digestion since by the time this day is reached production of biogas will be at its peak and the yield will be stable from the 44^th day.Using the value of 25.2 m³ per day of dry biogas, the Mole fraction of CH₄ in dry biogas can be calculated as follows:

Amount of dry biogas production per day = 25.2 m³.

Amount of Methane production per day = 16.38 m³.

Then the Mole fraction of CH₄ in dry biogas will be (16.38 ÷ 25.2) × 100% = 65%.

This value of the mole fraction of CH₄ is approximately the same as the values found in the simulation results. Therefore, the volume of this biogas plant designed in this study will be able to meet energy demand at Phalombe Boarding Secondary school.

Source: study Article [43] [44].

Initial investment costs for a fixed dome biogas digester may seem to be high. However, it has more advantages than the other types of biogas plants namely. The amount of firewood used by Phalombe Secondary school per term is 60 tons. In three terms it uses 180 tons of firewood. One ton costs US$16.67. Therefore 180 tons cost US$3000. The school spends US$344 on electricity per month. A school term is approximately 4 months. This means that the school spends a total of US$1032 per term. The school has three academic terms, so the total amount of money spent on electricity in one academic year is approximately US$3096.

If these two expenditures are summed up (firewood plus electricity), the total expenditure in one academic year is approximately US$6096. The cost of installing a biogas plant at the school is approximately US$5277.57. This amount is less than the amount of money the school spends on firewood only in one academic year and it can be used to construct the biogas plant at the school. Therefore, the use of a biogas plant will not only curb deforestation in the district but also make great savings on the money the school is currently spending on firewood and electricity. This money can be used for other school requirements. Moreover, according to the Indian Agriculture Research Institute (ICAR), a single biogas plant with a capacity of 2.8 m³ can save a woodland area of 0.12 ha per year. Therefore, with this designed biogas plant whose capacity is 62 m³, it can save a forest area of 2.66 ha of woodland per year in the Phalombe district.