# Problems

11.1 A farmer with 50 pigs proposed to use biogas generated from their wastes to power the farm's motor car.

a Discuss the feasibility of doing this. You should calculate both the energy content of gas and the energy used in compressing the gas to a usable volume, and compare these with the energy required to run the car.

b Briefly comment on what other benefits (if any) might be gained by installing a digester.

You may assume that a 100 kg pig excretes about 0.5 kg of volatile solid (VS) per day (plus 6 kg water), and that 1 kg of VS yields 0.4 m3 of biogas at STP.

11.2 Studies show that the major energy consumption in Fijian villages is wood which is used for cooking on open fires. Typical consumption of wood is 1 kg per person per day.

a Estimate the heat energy required to boil a two-litre pot full of water. Assuming this to be the cooking requirement of each person, compare this with the heat content of the wood, and thus estimate the thermal efficiency of the open fire. b How much timber has to be felled each year to cook for a village of 200 people?

Assuming systematic replanting, what area of crop must the village therefore set aside for fuel use if it is not to make a net deforestation? Hint: refer to Table 11.4. c Comment on the realism of the assumptions made, and revise your estimates accordingly.

11.3 a A butyl rubber bag of total volume 3.0m3 is used as a biogas digester. Each day it is fed an input of 0.20m3 of slurry, of which 4.0 kg is volatile solids, and a corresponding volume of digested slurry is removed. (This input corresponds roughly to the waste from 20 pigs.)

Assuming that a typical reaction in the digestion process is C12H22O11 + H2O baTa 6CH4 + 6CO2

and that the reaction takes 7 days to complete, calculate (i) the volume of gas (ii) the heat obtainable by combustion of this gas for each day of operation of the digester (iii) how much kerosene would have the same calorific value as one day's biogas? b The reaction rate in the digester can be nearly doubled by raising the temperature of the slurry from 28 (ambient) to 35 °C. (i) What would be the advantage of doing this? (ii) How much heat per day would be needed to achieve this? (iii) What proportion of this could be contributed by the heat evolved in the digestion reaction?

11.4 a Write down a balanced chemical equation for the conversion of sucrose (C12H22O11) to ethanol (C2H5OH). Use this to calculate how much ethanol could be produced in theory from one tonne of sugar. What do you think would be a realistic yield? b Fiji is a small country in the South Pacific, whose main export crop is sugar. Fiji produces 300 000t/y of sugar, and imports 300 0001

of fossil petroleum fuel. If all this sugar were converted to ethanol, what proportion of petroleum imports could it replace?

11.5 Consider a pile of green wood chips at 60% moisture content (wet basis) and weighing 11. What is the oven-dry mass of biomass in the pile?

The biomass has a heat of combustion of 16 MJ per oven-dry kg. This is the 'gross calorific value' corresponding to the heat output in a reaction of the type

The net calorific value (or 'lower heating value') is the heat evolved when the final water is gaseous; in practice this is the maximum thermal energy available for use when biomass is burnt.

i The pile is left to dry to 50% moisture content (wet basis), when it looks much the same but has less water in it.

ii The pile is left to dry for a few more weeks, and reaches 20% m.c. (w.b.), at which stage it has shrunk a little in volume and much in mass.

For each situation calculate the total mass of the pile, the net heat energy available from burning the pile, and its net calorific value per wet kg.

11.6 Figure 11.8 shows total (cumulative) carbon above ground in a plantation and in the atmosphere as trees grow and are harvested. For the same situation sketch the corresponding curves for annual emissions of CO2 by sources and removals by sinks. (These are the terms in which greenhouse gas inventories are compiled for purposes of the UN Framework Convention on Climate Change and its Kyoto Protocol.)