## Plant size range calculations (Chapter 2)

Plant size range calculations (Chapter 2)

1.2 Plant size range calculations

1.2.1     For the smallest plant size (“size 1”) in the range:

i.          The minimum daily substrate feeding (min sub fee1) is equal to the minimum required gas production for the smallest installation divided by the specific gas production:min sub fee1 = min gas prod1 / spec gas prod.
Or: min sub fee1 = 1.00 / 0.040 = 25 [kg dung day]

ii.          A feeding of dung of 25 [kg dung / day] requires with a 1:1 dung to water ratio an equal amount of water. The minimum feeding(min fee1) to the plant thus arrives at 50 [ltr / day].

iii.         For the situation in which the daily feeding corresponds with the minimum feeding amount for which the plant will be designed, the hydraulic retention time is maximal (HRT max). The required digester volume (dig vol1) is equal to the hydraulic retention time multiplied by the daily feeding: dig vol1 = HRTmaxxmin fee1.

Or: dig vol1 = 60 x 50 = 3,000 [ltr]

iv.         For the situation in which the daily feeding corresponds with the maximum feeding amount for which the plant will be designed, the hydraulic retention time is minimal (HRTmin). The maximum feeding (max fee2), then, equals the digester volume divided by the minimum hydraulic retention time: max fee1 = dig vol / HRTmin

Or: max fee1 = 3,000 / 40 = 75 [ltr/day]

v.         A maximum feeding of 75 [ltr/day], with a dung / water ratio of 1:1, then requires a maximum substrate feeding (max sub fee1) of 37.5 [kg/day].

vi          The maximum gas production of this installation equals the maximum substrate feeding (max sub fee1) multiplied by the specific gas production: max gas prod1 = max sub fee1 x spec gas prod.

Or: max gas prod1 = 37.5 x 0.040 = 1.5 [m3 biogas/day]

vii         The required gas storage volume for this plant then is 60% of the maximum daily gas production.

Or: gas stor vol1 = 0.6 x 1.5 = 0.9 [m3]

viii        The resulting main dimensions of plant size 1 then are:
Digester volume:          3,00 m3
Gas storage volume:    0.90 m3
Total plant volume:      3.90 m3

1.2.2     For the second smallest plant size (“size 2”) in the range:
i.          For a range of plant sizes, the minimum daily feeding for the next size (min sub fee2) is equal to the maximum feeding for the next smallest installation (max sub fee1). The minimum feeding for plant size 2 then equals 75 [ltr/day] or, for the maximum substrate feeding (max fee2), 37.5 [kg dung/day].
ii.          The minimum gas production for size 2, consequently, is equal to the maximum gas production of size 1, and equal to the minimum feeding multiplied by the specific gas production: min gas prod2 = min sub fee2 x spec gas prod.

Or: min gas prod2 = 37.5 x 0.040 = 1.5 [m3 biogas/day]

ii.          Similar to 1.21. ii, for the situation in which the daily feeding corresponds with the minimum feeding amount for which the plant will be designed, the hydraulic retention time is maximal (HRT max). The required digester volume (dig vol2) is equal to the maximum hydraulic retention time multiplied by the daily feeding: dig vol2 = HRTmax x min fee2.

Or: dig vol2 = 60 x 75 = 4,500 [ltr]

iii.         For the situation in which the daily feeding corresponds with the maximum feeding amount for which the plant will be designed, the hydraulic retention time is minimal (HRTmin). The maximum feeding (max fee2), then, equals the digester volume divided by the minimum hydraulic retention time: max fee2 = dig vol2 / HRTmin

Or: max fee1 = 4,500 / 40 = 112,5 [ltr/day]

This corresponds with a maximum substrate feeding (max sub fee2) for this size of 56.25 [kg dung/day]

vi          The maximum gas production of this installation equals the maximum substrate feeding (max sub fee2) multiplied by the specific gas production: max gas prod2 = max sub fee2 x spec gas prod.

Or: max gas prod2 = 56.25 x 0.040 = 2.25 [m3 biogas/day]

vii         The required gas storage volume for this plant then is 60% of the maximum daily gas production.

Or: gas stor vol2 = 0.6 x 2.25 = 1.35 [m3]

viii        The resulting main dimensions of plant size 2 then are:

Digester volume:          4,50 m3

Gas storage volume:    1.35 m3

Total plant volume:      5.85 m3

This is an approximation; in reality a similar amount of feeding will generate slightly more biogas in a larger installation as the retention time is longer.

### Biogas Plant Design (Chapter 3)

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