Domestic biogas plants Sizes and dimensions ( Chapter 1)
1 Plant size range.
As each situation differs in terms of e.g. gas requirement or available feeding material, a unique plant size could be calculated for each household. For larger dissemination programmes, however, this would be impractical. Therefore, most such programmes work with a limited number of plant sizes that are expected to cover the demand of (most) households. The following example shows how to develop a plants size range with the lowest number of sizes covering a certain demand scope.
1.1 Plant size parameters.
Although size calculations can become very complicated, for domestic application the following parameters suffice to arrive at a practical plant size range
Parameter

Explanation

Values used

Dung/water ratio

Theoretically, the dung / water ratio depends on the total solids (TS) concentration of the dung, whereby optimum fermentation results are claimed at 6 to 7% TS. The TS of dung varies considerably, for livestock in development countries TS values in the 10 to 15% (cattle) and 15 to 20% (pigs) range are reported.

The TS values suggest a dung / water ratio of a little under 1 : 1 for cattle dung and 1 : 2 for pig dung. For practical reasons.A 1 : 1 ratio has the advantage that households can easily measure the amount of required process water.

Specific gas production

The specific gas production of dung depends on the type and quality of dung.

For cattle, typically 1 kg of dung fed to a digester produces about 40 litres of biogas per day. Values for other substrates will differ; pigs, poultry and human excreta typically have higher yields.

Minimum gas production

Depending on construction costs and gas demand pattern, below a certain nominal gas production the investment becomes uninteresting for the household.

One cubic meter of biogas daily will render 2.5 to 3.5 stove hours. This could, depending on family size, suffice for e.g. breakfast and lunch preparation, and would then provide a meaningful contribution.

Hydraulic Retention Time

The hydraulic retention time (HRT) is the period the dung/water mix fed to the installation remains in the plant. As the fermentation process works better at higher ambient temperatures, installations in warmer climates can work with a shorter HRT and vice versa. As a longer HRT requires a larger digester volume, plants become more expensive to construct.

Typical HRTs for domestic (simple) biogas plants are 40 to 60 days for warm climates and 50 to 75 days for temperate climates.

Gas storage volume

Biogas is generated more or less continuously, but consumption in households typically takes place during 3 or 4 periods during the day. The generated gas needs to be stored in the installation.

For the gas storage volume, a fixed share of the maximum amount of daily generated gas, 60% is taken

The table summarizes the values of the main design parameters. As the aim is to develop a plant size range, the hydraulic retention time is applied as a minimum and maximum value.
Calculation examples hereunder use parameter values for a warm climate
digester parameters 
Domestic biogas plants Sizes and dimensions ( Chapter 1
Plant size range calculations (Chapter 2)
Biogas Plant Design (Chapter 3)
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 fee_{1}) is equal to the minimum required gas production for the smallest installation divided by the specific gas production:min sub fee_{1} = min gas prod_{1} / spec gas prod.
Or: min sub fee_{1} = 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 fee_{1}) 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 vol_{1}) is equal to the hydraulic retention time multiplied by the daily feeding: dig vol_{1} = HRTmaxxmin fee_{1}.
Or: dig vol_{1} = 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 fee_{2}), then, equals the digester volume divided by the minimum hydraulic retention time: max fee_{1} = dig vol / HRTmin
Or: max fee_{1} = 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 fee_{1}) of 37.5 [kg/day].
vi The maximum gas production of this installation equals the maximum substrate feeding (max sub fee_{1}) multiplied by the specific gas production: max gas prod_{1} = max sub fee_{1} x spec gas prod.
Or: max gas prod_{1} = 37.5 x 0.040 = 1.5 [m^{3} biogas/day]
vii The required gas storage volume for this plant then is 60% of the maximum daily gas production.
Or: gas stor vol_{1} = 0.6 x 1.5 = 0.9 [m^{3}]
viii The resulting main dimensions of plant size 1 then are:
Digester volume: 3,00 m^{3}
Gas storage volume: 0.90 m^{3}
Total plant volume: 3.90 m^{3}
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 fee_{2}) is equal to the maximum feeding for the next smallest installation (max sub fee_{1}). The minimum feeding for plant size 2 then equals 75 [ltr/day] or, for the maximum substrate feeding (max fee_{2}), 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 prod_{2} = min sub fee_{2} x spec gas prod.
Or: min gas prod_{2} = 37.5 x 0.040 = 1.5 [m^{3} 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 vol_{2}) is equal to the maximum hydraulic retention time multiplied by the daily feeding: dig vol_{2} = HRTmax x min fee_{2}.
Or: dig vol_{2} = 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 fee_{2}), then, equals the digester volume divided by the minimum hydraulic retention time: max fee_{2} = dig vol_{2} / HRTmin
Or: max fee_{1} = 4,500 / 40 = 112,5 [ltr/day]
This corresponds with a maximum substrate feeding (max sub fee_{2}) for this size of 56.25 [kg dung/day]
vi The maximum gas production of this installation equals the maximum substrate feeding (max sub fee_{2}) multiplied by the specific gas production: max gas prod_{2} = max sub fee_{2} x spec gas prod.
Or: max gas prod_{2} = 56.25 x 0.040 = 2.25 [m^{3} biogas/day]
vii The required gas storage volume for this plant then is 60% of the maximum daily gas production.
Or: gas stor vol_{2} = 0.6 x 2.25 = 1.35 [m^{3}]
viii The resulting main dimensions of plant size 2 then are:
Digester volume: 4,50 m^{3}
Gas storage volume: 1.35 m^{3}
Total plant volume: 5.85 m^{3}
[1]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.
Domestic biogas plants Sizes and dimensions ( Chapter 1
Plant size range calculations (Chapter 2)
Biogas Plant Design (Chapter 3)
Biogas Plant Design
Biogas Plant Design (Chapter 3)
2 Plant design
biogas plant formula 
A simple plant design similar to the designs in Vietnam (KT), Cambodia (modified Dheenbandu) or Tanzania (modified Camartec) is used for this example.
Plant Layout 
In this hemispherical design, the digester volume is the volume under the lower slurry level(LSL), and the gas storage volume is the volume between the lower and higher slurry level (HSL).
For all plants with internal gas storage, the gas storage volume in the plant is equal to the volume of the compensation volume
2.1 Total plant volume
Dome Radius 
digester volume dimensions 
As pic 1 shows, part of the dome volume, over the higher slurry level, is not used by a well functioning installation. The volume, often referred to as “dead volume” is required, however, to accommodate the floating layer on top of the slurry. In addition, when gas production is less then nominal (cold seasons) or when gas is slowly leaking, the higher slurry level can rise (up to overflow level). For that reason, the total plant volume used for dimensioning should be higher than the plant size range volume results. For this example, 20% addition is allowed for this dead volume. Hence, taking plant size 1 for the example, the total plant volume (digester + gas storage + dead volume) arrives at 3.90 x 1.2 = 4.68 m^{3}_{.}
2.2 Dome radius
The dome radius, R dome, follows from: R dome = (V tot / 2/3 π)^{1/3}. For plant size 1, then:
R dome_{1} = (4.68 / ^{2}/_{3} π)^{1/3 }= 1.3 [m]
2.2 Calculating digester volume dimensions
This calculation serves to find the upper level of the digester volume, or the height of the lower slurry level (LSL) in the dome. For this, the digester volume (calculated at 3.00 m^{3} in 1.2.1 iii) can be seen as the total dome volume minus the volume of the “dome cap”. In this way V dig cap_{1} = V dome_{1} – V dig_{1}.
Or: V dig cap_{1} = 4.68 – 3.00 = 1.68 [m^{3}]
To apply the formula V dome cap equals ^{π}/_{6} x h x (3a^{2} + h^{2}), the dome (R dome = 1.3 [m]) has to be draw precisely on scale. Through “trial and error”, then, you should find when h = 0.7 [m] a will be 1.66 [m],
and V dome cap_{1} = ^{π}/_{6} x 0.7 x (3 x 1.66^{2} + 0.7^{2}) = 1.66 [m^{3}] .
The digester volume, then, results in V dig_{1} = Vdome_{1} – Vdome cap_{1}
Vdig_{1} = 4.68 – 1.66 = 3,02 [m^{3}] which is close to the design volume of 3.00 [m^{3}]. The LSL equals Rdome_{1} minus a_{1}; LSL_{1}= 1.30 – 0.70 = 0.60 [m]
gas storage volume dimensions 
2.3 Calculating gas storage volume dimensions
The gas storage volume should be at least 0.90 [m^{3}] (see 1.2.1 vii).
The volume of a segment of a sphere is:
V segment = ^{π}/_{6 }x (3R1^{2} + 3R2^{2} + h^{2}) x h
R1 is equal to a(from 2.3); R1 thus equals to 1.66 [m].
To find R2 you’ll have to use the drawing again, and measure h and R2 . You’ll find that when h = 0.25 [m] then R2 = 0,97 [m] and
Vseg1 = ^{π}/_{6 }x (3 x 1.16^{2} + 3 x 0.97^{2} x 0.25^{2}) x 0.25 = 0.91 [m^{3}].
2.4 Plant dimensions
From the above follows for plant size 1 that:
R dome = 0.130 [m]
LSL = 0.130 – 0.70 = 0.60 [m]
HSL = 0.60 + 0.25 = 0.85 cm
Whereby:
The LSL is also the height of the manhole entry in the plant (beam height or, for Vietnam, outlet pipe height)
The HSL is also to floor level height of the compensation chamber.
2.4 Overflow height.
The height of the overflow determines:
 the maximum pressure in the plant;
 the extent to which slurry can reach into the gas dome pipe, and;
 of course, the height determines the dimensions of the compensation chamber.
For the positioning of the overflow, there are two schools of thought:
1 The overflow should be positioned under the bottom of the dome pipe. This will avoid slurry reaching the bottom of the gas dome pipe. Slurry can reach the bottom of the dome pipe when plants are leaking gas or when, for temperature reasons or other, the gas production is significantly lower than the gas consumption over a prolonged period of time.
2 The overflow should be positioned higher than the bottom of the dome pipe. This allows a higher maximum pressure in the plant and makes the compensation chamber dimensions more economic. Slurry entering the dome pipe, then, is an indication of a mistake in the construction of the operation of the installation, and should be remedied.
In this example the overflow is placed 5 cm under the top of the dome.
overflow and pressure height 
2.5 Pressure height check
The pressure height is the maximum pressure that the installation can produce. This maximum pressure is limited by the LSL; when pressure increases to the point whereby the LSL is pushed down further below the beam / outletpipe level, biogas will escape through the compensation chamber.
As shown in the picture, the pressure height (ph) is the difference between overflow height (oh) and LSL.
Compensation chamber dimensions 
ph_{1} = 1.25  0.60 = 0.65 [m].
2.6 Compensation chamber dimensions
The volume of the compensation chamber (V cc) shall be equal to the plant’s gas storage volume. In case of “size 1”, then, V cc shall be 0.9 [m^{3}]. Following the earlier position that the overflow level should be lower that the top of the dome, the compensation chamber height (cch) is the difference between the overflow height (oh) and the higher slurry level (HSL) (= compensation chamber floor level).
For the example size 1, the compensation chamber height then is 1.25 – 0.85 = 0.40 [m].
Assuming a cylindrical compensation chamber, the radius of the compensation chamber (R cc) follows from:
R cc = (V cc / (π x cch))^{1/2}.
Or: R cc_{1} = (0.90 / (π x 0.40))^{1/2} = 0.84 [m]
2.7 Inlet floor and inlet pipe
To avoid reflux, the inlet floor height (ifh) should be higher than the overflow height (oh). For the example for plant size 1, ifh is 0.15 [m] higher than oh.
To avoid biogas escaping through the inlet pipe (toilet connection!), the top of the inlet entering the dome should be below the LSL. At the same time the inlet pipe height (iph) should not be too close to digester floor to prevent obstruction by debri. Typically, the iph should be about 0.30 [m] above the digester floor.
Finally, the inlet / pipe layout should allow entering a long stick in case of inlet pipe blockage.
Inlet floor and inlet pipe 
Domestic biogas plants Sizes and dimensions ( Chapter 1
Plant size range calculations (Chapter 2)
Biogas Plant Design (Chapter 3)
Thanks for such information Felix ter Heegde (http://www.ppre.unioldenburg.de/download/Biogas/Biogas2011/03_20110427_Biogas_plant_sizes_and_dimensions.docx)