*2.3. Pre-Digestion Farm Activities*

This study considered the direct and indirect energy inputs for the co-digestion feedstock prior to digestion. For the grass silage feedstock, energy inputs in cultivation, harvesting, recovery and digester feeding were accounted for and are described in Tables 2 and 3. The calculations used in Table 2 were based on the land being ploughed every seven years to maintain grass productivity. For the dairy cow manure feedstock, the energy inputs related to its collection, loading and transportation from the farm's cattle housing and milking parlour to the digester were also accounted. According to Berglund [35], the energy input in loading and transporting liquid manure is 2.5 MJ t−<sup>1</sup> km−1. The model used this figure and an estimated distance of 500 m between the manure storage and digester to calculate energy consumption. The system boundary assumed that the digestate produced from the AD process was spread as fertiliser on the farms' own land.


**Table 2.** Fuel consumption by machinery in grass cultivation. Reproduced from [36], Elsevier: 2008.

**Table 3.** Energy consumed and CO2 emitted from raw materials. Reproduced from [36], Elsevier: 2008.


a Assumed, application rate of mineral fertilizer according to [37]; b Average pesticide applied to grass reported by [38].

### *2.4. Operation of the Biogas Plant*

The biogas available for potential recovery in an AD plant is largely dependent on the fraction of volatile solids (VS) in the feedstock, high fractions of VS correlate to higher biogas production [39]. The VS content represents the portion of organic solids that can be digested in the feedstock, while the remainder of the solids is fixed [40]. Using the feedstock physical and chemical properties described in Table 4, the biogas flowrates per kg of VS were quantified using the Boyle–Buswell stoichiometric relationship described in Equation (1) [41]. This methodology assesses the biogas potential of organic

solids through the AD process. As this methodology considers the total content of VS to be biologically degraded, it can lead to an overestimation of the biogas produced from the feedstock in comparison to real-world case studies [42]. Nevertheless, Boyle–Buswell has been commonly applied in literature as an effective indicator to gauge biogas potential [21,43,44]. The subsequent methane yield was 0.6376 m<sup>3</sup> CH4 kg−<sup>1</sup> VS from dairy cow manure and 0.822 m<sup>3</sup> CH4 kg−<sup>1</sup> VS from grass silage.

$$\mathrm{C\_6H\_6O\_6N\_6S\_6} + \left(a - \frac{b}{4} - \frac{\epsilon}{2} + \frac{\gamma d}{4} + \frac{\epsilon}{2}\right) \mathrm{H\_2O} \rightarrow \left(\frac{a}{2} + \frac{b}{8} - \frac{\epsilon}{4} - \frac{\gamma d}{8} - \frac{\epsilon}{4}\right) \mathrm{CH\_4} + \left(\frac{a}{2} - \frac{b}{8} + \frac{\epsilon}{4} + \frac{\gamma d}{8} + \frac{\epsilon}{8}\right) \mathrm{CO\_2} + d\mathrm{NH\_3} + \epsilon \mathrm{H\_2S} \quad \text{(1)}$$

**Table 4.** Physical and chemical properties for dairy cow slurry and grass silage.


a DS is dry solids; b VS is volatile solids; c Characteristics of grass and manure are based on [21]; d Ultimate analysis of dry and ash free cow manure reported by [41,42]; e Ultimate analysis of grass silage as presented in [45].

The plant simulated consisted of a mesophilic continuously stirred tank reactor (CSTR) with all biogas produced used in a combined heat and power (CHP) unit. The annual operating time of the plant was assumed to be 8000 h (91% of the year), allowing for routine maintenance and repair, as reported in the literature [46–48]. The hydraulic retention time of the plant was 25 days [49]. Based on the rate of biogas flow, it was possible to size the required CHP unit using Equation (2) [50]. The CHP unit was assumed to have an electrical efficiency of 30% and a thermal efficiency of 55%, which is typical for similar sized systems [35,48,51,52].

Berglund and Börjesson [35] reported that the primary power consumption in the operation of an AD plant is the pumping and stirring of feedstock (7.2 kWh <sup>t</sup>−1). The net electricity produced via the CHP unit was first used to meet the electrical demand of the farm, with surplus electricity exported to the national grid. The energy required to heat and maintain the digester's temperature was calculated using Equation (3). The plant's heat losses (hl) were estimated using Equation (4). The heat transfer coefficients of the plant's construction materials correspond to the following: floating cover (1.0 W m2.◦C); 6 mm steel plate "sandwich" with 100 mm insulation (0.35 W m2.◦C); 300 mm concrete floor in contact with earth (1.7 W m2.◦C) (Zhang, 2013). Equation (5) describes the energy required to heat the digester feedstock (q). The operating temperature of the digester was assumed to be constant at 40 ◦C, with the temperature of the incoming feedstock at 10 ◦C [53].

$$\text{CHP capacity (kW}\_{\ell}) = \frac{\text{Rig gas production } \left(\text{m}^3\right) \times \left[\text{Cauchy/k value of } \log \text{sa} \left(\frac{\text{M}^2}{\text{Na}^2} / 3.6\right)\right]}{\text{Operational full load} \left(\frac{\text{k}}{\text{y}}\right)} \times \text{Electrical efficiency (\%),} \tag{2}$$

Total heat requirement for the process = *hl* + *q*, (3)

$$
\delta l = \mathcal{U} \, A \, \Delta \mathcal{T},
\tag{4}
$$

where hl is heat loss (kJ s<sup>−</sup>1); U is the overall coefficient of heat transfer (W m<sup>−</sup><sup>2</sup> K); A is the cross-sectional area through which heat loss occurs (m2); ΔT is temperature drop across the surface area (◦C).

$$
\eta = \mathbb{C} \bigotimes \Delta \Upsilon\_{\prime} \tag{5}
$$

where *q* is the energy required for heating feedstock (kJ s<sup>−</sup>1); *C* is the specific heat of the feedstock (kJ kg−<sup>1</sup> ◦C−1); *Q* is the volume to be added (m3); ΔT is the outside and inside temperature di fference (◦C).

### *2.5. Final use of Energy Produced*

The energy produced in the form of electricity and heat via the CHP unit was used in four main areas. These include: (i) the operation of AD plant; (ii) satisfying the dairy enterprises energy demand; (iii) exported to the national grid (electricity); (iv) exported to district heating system (thermal energy). The energy demand of the farm was calculated by using the energy requirements per litre of milk, as reported in the literature [54]. The average yield of an Irish dairy cow was assumed to be 5000 litres [55]. The thermal energy generated by the CHP unit was understood to displace kerosene, which is the primary heating fuel on Irish farms [54].

The heat produced that exceeds the needs of the plant and the farm has a number of potential local applications, such as drying woodchips, use in the horticulture sector, or in local industry. Another promising option is its use in a district-heating scheme, where heat generated is distributed from a central location through a network of insulated pipes to nearby residential and commercial energy users. Although these systems are not common in Ireland, this study has selected this technology to demonstrate its potential applicability. The study assumed that the thermal energy supplied to the scheme displaces kerosene, which is commonly used to heat residential homes in Ireland [54]. Equation (6) was used to describe the heat transfer capacity of the pipework utilised, with the subsequent heat losses calculated using Crane's methodology [56]. An average distance of 300 m was assumed between the CHP unit and the residential housing for this study.

$$Q = \pi \, r^2 \,\mathrm{v} \,\, \Delta \mathrm{T} \,\mathrm{C} \tag{6}$$

where *Q* is heat transfer capacity of pipe (kW); *r* is internal pipe radius (mm); v is the fluid velocity (m<sup>3</sup> s<sup>−</sup>1); ΔT is temperature di fference between the flow and return (◦C); C is the specific heat of fluid (kJ kg−<sup>1</sup> ◦C−1).
