The mathematical CT was developed with the help of a Microsoft Excel worksheet. The tool consists of fundamental arithmetic equations, and the solutions of these equations are integrated to forge a chain of equations. Thus, a few selected parameter values are sufficient to generate a required solution as an output. The few selected parameters were retention time (RT, days), Daily Feed (DF, kg/day), and TOF. The input value of RT typically ranges from 10 to 40 days. The DF value is the total amount of feed that would be added to the digester daily. DF was converted from kg to Nm3 with the help of the typical density of the feedstock. The converted value was retained as Daily Feed Volume (DFV, Nm3/day). The selection of TOF describes a host of parameters related to a particular feedstock. Each feedstock has a characteristic value of percentage of total solids (TS, %), percentage of volatile solids to total solids (VS, % TS), and Biochemical Methane Potential (BMP, Nm3/kg VSadded).
2.1. Digester Dimensions
The input values of parameters, RT and DFV, facilitate the calculation of the volume of the digester (DV, Nm3).
(1)
The DV was considered to be 80% of the total volume of the digester (TDV). The volume for the gas storage (GSV) was allotted the remaining 20%.
(2)
The TDV calculated from equation (1) was utilized as the volume of the digester in the three BDD as follows:
For Chinese BDD,
(3)
Where, D is the diameter of the digester (m)
For Hemisphere BDD,
(4)
Where, D is the diameter of the digester (m)
For Deenbandhu BDD,
(5)
Where, r is the radius of the digester (m), k is the depth of the curved base (m).
After attaining the fundamental values such as diameter and radius, dimensioning of other dependent values (such as height, dome height, base depth, etc.) was calculated for each digester. The fixed dome BDD was selected to be modeled for their advantages of simple design, absence of moving parts, and long-life span.
2.2. Methane Production
Methane production is directly proportional to the VS present in the feedstock. The CT was formulated to calculate the amount of methane produced every day based on the DF. The VS added to the digester was computed based on the TS and the VS of the given feedstock. For calculation of VSadded in kg/day, DF was multiplied with the TS and the VS to find its fraction in the DF by the following formula:
(6)
BMP of feedstock represents the maximum volume of methane produced per kg of VS present in the substrate. Hence, the total amount of VSadded to the digester on daily basis assists in the calculation of the total volume of methane produced daily (VMP). The VMP is expressed in the units of Nm3/day.
(7)
The TS, VS, and BMP are the characteristic values that determine the volume of methane produced by a particular feedstock. Table 1 contains these characteristic values for a few TOF obtained from various studies. The values in Table 1 are the mean values of the data gained from the studies and are incorporated in the CT.
Table 1 The characteristic values of the various TOF used in the CT
TOF
|
TS (%)
|
VS (% of TS)
|
BMP (Nm3/kg VSadded)
|
Reference
|
Food Waste
|
20.000
|
95.000
|
0.480
|
[12, 13]
|
OFMSWa
|
27.000
|
84.500
|
0.415
|
[14]
|
Dairy Manure
|
16.322
|
69.372
|
0.242
|
[15 – 18]
|
Dairy Slurry
|
7.593
|
77.707
|
0.211
|
[18, 19]
|
Poultry Manure
|
47.598
|
73.004
|
0.258
|
[15 – 20]
|
Pig Manure
|
26.704
|
75.366
|
0.263
|
[15, 18, 21, 22]
|
Maize Silage
|
32.094
|
93.706
|
0.417
|
[18, 23 – 26]
|
WWTPb Sludge
|
4.482
|
74.274
|
0.323
|
[18, 27 – 30]
|
aOrganic Fraction of Municipal Solid Waste, bWastewater Treatment Plant
The composition of biogas generally contains 60% of methane in its total volume [31]. Hence, for computation of volume of biogas produced (VBP, Nm3/day), VMP was utilized as the following formula:
(8)
The VBP indicated the estimated volume of biogas produced every day for the given input values.
2.3. Implementation of Co-digestion in the CT
Co-digestion is the process of anaerobic digestion of two or more TOF simultaneously. The CT was programmed for co-digestion of two TOF. Two separate DF input options were provided with the ability to select a TOF for each DF input option. The DFV was calculated by the addition of the two DF inputs. The VBP of individual TOF was calculated independently with the help of the characteristic values from Table 1. The summation of individual VBP of the two TOF resulted in the total VBP.