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# Sizing of the Biogas Plant

## Overview

The size of the biogas plant depends on the quantity, quality and kind of available biomass and on the digesting temperature. The following points should be considered.

## Determinig Gas Demand for Domestic Use

The gas demand can be defined on the basis of energy consumed previously. For example, 1 kg firewood then corresponds to 200 l biogas, 1 kg dried cow dung corresponds to 100 l biogas and 1 kg charcoal corresponds to 500 l biogas.

The gas demand can also be defined using the daily cooking times. The gas consumption per person and meal lies between 150 and 300 liter biogas. For one liter water to be cooked 30-40 l biogas, for 1/2 kg rice 120-140 l and for 1/2 kg legumes 160-190 l are required.

Compared to other gases, biogas needs less air for combustion. Therefore, conventional gas appliances need larger gas jets when they are used for biogas combustion. About 5.7 liters of air are required for the complete combustion of one liter of biogas, while for butane 30.9 liters and for propane 23.8 liters are required.

## Sizing the Digester

The size of the digester, i.e. the digester volume Vd, is determined on the basis of the chosen retention time RT and the daily substrate input quantity Sd.

$V_{\text{d}}=S_{\text{d}}*R_{\text{T}}$ [ m3 = m3/day × number of days ]

The retention time, in turn, is determined by the chosen/given digesting temperature. For an unheated biogas plant, the temperature prevailing in the digester can be assumed as 1-2 Kelvin above the soil temperature. Seasonal variation must be given due consideration, however, i.e. the digester must be sized for the least favorable season of the year. For a plant of simple design, the retention time should amount to at least 40 days. Practical experience shows that retention times of 60-80 days, or even 100 days or more, are no rarity when there is a shortage of substrate. On the other hand, extra-long retention times can increase the gas yield by as much as 40%.

The substrate input depends on how much water has to be added to the substrate in order to arrive at a solids content of 4-8%.

Substrate input (Sd) = biomass (B) + water (W) [m3/d]

In most agricultural biogas plants, the mixing ratio for dung (cattle and / or pigs) and water (B:W) amounts to between 1:3 and 2:1.

## Calculating the Daily Gas Production G

The amount of biogas generated each day G [m3 gas/d], is calculated on the basis of the specific gas yield Gy of the substrate and the daily substrate input Sd.

The calculation can be based on:

1. The volatile solids content VS

G = VS × Gy(solids) [ m3/d = kg × m3/(d×kg) ]

1. the weight of the moist mass B

G = B × Gy(moist mass) [ m3/d = kg × m3/(d×kg) ]

1. standard gas-yield values per livestock unit LSU

G = number of LSU × Gy(species) [ m3/d = number× m3/(d×number) ]

The temperature dependency is given by:

Gy(T,RT) = mGy × f(T,RT)

where

Gy(T,RT) = gas yield as a function of digester temperature and retention time
mGy = average specific gas yield, e.g. l/kg volatile solids content
f(T,RT) = multiplier for the gas yield as a function of digester temperature T and retention time RT

As a rule, it is advisable to calculate according to several different methods, since the available basic data are usually very imprecise, so that a higher degree of sizing certainty can be achieved by comparing and averaging the results.

## Establishing the Plant Parameters

The degree of safe-sizing certainty can be increased by defining a number of plant parameters:

### Specific gas production Gp

i.e. the daily gas generation rate per m3 digester volume Vd, is calculated according to the following equation

Gp = G ÷ Vd [ (m3/d) / m3 ]

The digester loading Ld is calculated from the daily total solids input TS/d or the daily volatile solids input VS/d and the digester volume Vd:

$Ld_{\text{T}}={\frac {TS/d}{V_{\text{d}}}}$ [ kg/(m3 d) ]

$Ld_{\text{V}}={\frac {VS/d}{V_{\text{d}}}}$ [ kg/(m3 d) ]

Then, a calculated parameter should be checked against data from comparable plants in the region or from pertinent literature.

## Sizing the Gasholder

The size of the gasholder, i.e. the gasholder volume Vg, depends on the relative rates of gas generation and gas consumption. The gasholder must be designed to:

• cover the peak consumption rate gcmax (->Vg1) and
• hold the gas produced during the longest zero-consumption period tzmax (->Vg2)

Vg1 = gcmax × tcmax = vcmax Vg2 = Gh × tzmax

with

gcmax = maximum hourly gas consumption [m3/h] tcmax = time of maximum consumption [h] vcmax = maximum gas consumption [m3] Gh = hourly gas production [m3/h] = G ÷ 24 h/d tzmax = maximum zero-consumption time [h]

The larger Vg-value (Vg1 or Vg2) determines the size of the gasholder. A safety margin of 10-20% should be added:

Vg = 1.15 (±0.5) × max(Vg1,Vg2)

Practical experience shows that 40-60% of the daily gas production normally has to be stored.

The ratio Vd ÷ Vg (digester volume ÷ gasholder volume) is a major factor with regard to the basic design of the biogas plant. For a typical agricultural biogas plant, the Vd/Vg-ratio amounts to somewhere between 3:1 and 10:1, with 5:1 - 6:1 occuring most frequently.