Energy-demand analysis for a dairy-farm with a biogas plant operating in either self-sufficient or spot-market mode

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1 Energy-demand analysis for a dairy-farm with a biogas plant operating in either self-sufficient or spot-market mode Michael Jack, George Estcourt, and Per Nielsen The aim of this study is to determine how much biogas is required to fulfil the energy needs (electricity and heat) at a dairy farm in New Zealand. We consider two specific modes of operation for a dairy farm with a biogas digester/generator system: 1) a self-sufficient mode, where the dairy farm is run completely off-grid, and 2) a spot-market mode, where electricity is traded on the spot market and emergency backup is provided. From the electricity and heat demands of these modes of operation we determine the minimum energy requirements (in the form of biogas) that need to be met from an anaerobic digester using the effluent produced on the farm. The main difference between the two modes of operation is that the production in the "self-sufficient" mode is determined by the electricity demand. If electricity demand is high (milking time) more waste heat is produced by the engine than can be utilized and it has to be "dumped". On the other hand if the electricity demand is low (night time) an additional boiler is required to maintain the temperature in the digester. In the other "spot market" mode, the system is run on heat demand. In this case the heat demand determines the amount of electricity produced and if it is not enough to cover load (milking time), electricity is purchased from the grid. On the other hand, if too much electricity is produced during periods of high heat demand and low electricity demand (night) the excess is sold to the grid Heat demand of a biogas digester Biogas generation from dairy farm effluent is greatly enhanced at temperatures of 35 and 55 deg C. There are two energy demands due to heating this effluent in a tank: firstly, the energy required to heat the effluent to the required temperature and secondly, the energy required to overcome heat losses through the tank walls. The number of watts to heat the effluent from T w to T with a flow rate, f, is given by Q heat =f C (T-T w ), where C is the specific heat of the effluent, which we take to be the same as water. The heat loss on the other hand is given by Q loss =A(T-T )/R, where A is the surface area of the tank, R is the R-value of the wall insulation and T is the temperature of the surroundings. Assuming a tank of volume V (in cubic metres), the flow rate in litres per second is given by f=1v/t R, where t R is the residence time of the effluent in the tank in seconds. The minimum surface area for a cylindrical tank of fixed volume is given by setting the radius to (V/2π) 1/3, this gives an area of A=3(2π) 1/3 V 2/3. The total heat demand (in watts) is therefore 1VC Q = t R 1/ 3 3(2π ) V R 2 / 3 ( T T ) + ( T T ) W If, in addition, we assume there is a heat recovery system in place with efficiency k, then T w =kt. Energy demand.

2 Different modes of operation have different energy demands in terms of heat and electricity. Let us denote the energy demand on the fuel at time t by D(t) (measured in watts). This demand will need to be met by the biogas produced from the effluent. We define two convenient parameters that measure different aspects of the required energy: the energy per litre of the effluent, and the energy per cow per day. Energy concentration In order to quantify the potential energy that can be extracted from the effluent we define a quantity φ given in units of joules per litre. This quantity is a function of the biogas production rate, the energy content of the biogas, and the dilution of the solid manure. Here we treat these as unknown parameters. To determine φ s lower bound we compare it to the energy demand. Assuming there is enough storage for the gas and given the average flow f, we can write the requirement that the effluent have enough energy to meet the demand as D φ, f 1 D = T T D( t) dt where D is the average demand, determined by integrating over some period T (taken to be one day). In this treatment we ignore seasonal changes, and assume that there is some method of getting biogas production started again after winter. The result of the work below will be a quantity D / f which represents the lowest possible energy concentration of the effluent for the demands of a particular mode of operation. Energy per cow In addition to the required energy concentration of the effluent we also need to quantify the total energy that is required for each mode of operation. A convenient measure is the energy demand per cow. If N is the number of cows then D / N is the demand per cow per day. Defining the energy available per cow per day as h, the requirement that we have enough energy to meet the demand is h D / N. Note that D / N is proportional to D / f in the case when V (and therefore f) is proportional to N. Here we treat the more general case when this is not necessarily true due to other sources of biomass. Self-sufficient mode In self-sufficient mode we need to meet the electricity demand of the dairy farm, we also need to meet the heat demand of heating the effluent to maintain biogas production. When electricity demand is high the waste heat from the engine producing electricity will be enough to provide this heat. However, when the electricity demand is low the engine is not producing sufficient heat to cover the heat demand. The cheapest technology to fill the gap which makes most efficient use of

3 the biogas is likely to include a boiler. We therefore assume that in addition to an engine that can generate electricity from the biogas we also have a boiler available to top up the heating if required. Given an electricity demand, E(t,N), where N is the number of cows we have k elec D 1 (t) f = E(t,N), where k elec is the efficiency factor of the engine and is the ratio of electricity to fuel in energy units. As the waste heat from the engine is also used to heat the effluent tank the heat demand equation has the form l heat D 2 (t) f= max[q(v)- k heat D 1 (t) f,], where l heat (k heat ) is the heat efficiency of the boiler(engine). Obviously, one does not need to run the boiler if the engine is meeting the heat demand and this is taken into account by the function max[x,] which means the maximum of x and. Inserting the first equation this can be written as l heat D 2 (t) f= max[q(v)- k heat E(t,N) /k elec,]. The total energy demand is, therefore E( t, N) 1 k heat E( t, N) D ( t) = + max Q( V ),. kelec lheat kelec Demand is a minimum if the engine can supply all the heat for the effluent tank. Integrating over a period and dividing by f we can determine D / f. As f is proportional to V, selecting a cow number N, a tank volume V and a residence time t R, completely specifies the required energy demand that needs to be supplied by the effluent. We now consider some example farms of specific size. We assume engine sizes of 2 el for a dairy farm with N=27 cows, 3e for N=4,65,7 and 6e for 14 based on approximate peak demand.. Measured electricity demand curves were not available so we consider model electricity demand curves and as such they should be taken as indicative rather than exact. These are shown in figure 1. 5 N=14 84 h N=7 426 h N= h N=4 264 h 2 1 N= h Time (hours) Figure 1: Electricity demand profiles (effluent pump is assumed not to run concurrent with milking). Total daily demand in h is shown on each subplot. In figure 2 and 3 we show the demand in kj per litre and the demand per cow per day for various sized tanks (5, 1, 2 m 3 ) and various numbers of cows (27, 4, 65,7,14). We have assumed a heat recovery of 6% (i.e. k=.6), k heat =.5,

4 C=4.2 kj/(kg deg C), T =8 deg, a residence time of 4 weeks for 35 deg C and 2 weeks for 55 deg C, and a R-value for the tank insulation of R=2 m 2 K/W. The decreasing demand with increasing volume is simply the result of larger tanks requiring less energy content per litre of effluent. The gas production rate is likely to be at least doubled at the higher temperature and at 35 deg C residence times are chosen to be 4 weeks to increase the biogas yield from a given litre of effluent. Of course, there is a trade-off in increasing the residence time as it also requires an increase in the volume of the tank. Energy concentration (kj/litre) N=27 N=4 N=65 N=7 N= N=27 N=4 N=65 N=7 N=14 Figure 2: Energy demand at T=35 deg C. The coloured bars show the different volumes: 5/1/2 cubic metres shown in light-blue/lilac/pink. Energy concentration (kj/litre) N=27 N=4 N=65 N=7 N= N=27 N=4 N=65 N=7 N=14 Figure 3: Energy demand at T=55 deg C. The coloured bars show the different volumes: 5/1/2 cubic metres shown in light-blue/lilac/pink.

5 The percentage of the heat supplied by the boiler for the various volumes and numbers is shown in figure 4. Heat supplied by boiler (%) T=35 C N=27 N=4 N=65 N=7 N=14 Heat supplied by boiler (%) T=55 C N=27 N=4 N=65 N=7 N=14 Figure 4: Percentage of heat supplied by boiler. The coloured bars show the different volumes: 5/1/2 cubic metres shown in light-blue/lilac/pink. Spot-market mode In this mode of operation electricity is purchased and sold by the dairy farm on the spot market. The generator runs most of the time at a constant load supplying just enough heat to the effluent tank via waste heat from the engine. When emergency power is required it can be run at full power for short stretches of time (say one milking) on stored gas. The energy demand on the fuel in the absence of an emergency is given by Q( V ) D = Which is related to the generated electricity by G(t)=k elec D. As the heat demand is not time-dependent we have put D ( t) = D. Note that this demand is also independent of the number of cows. If it is possible to ignore the heat loss term, (due to size of tank or thermal insulation) this simplifies even more, and we have D C( T TW ) CT (1 k) = =, f kheat kheat giving a simple requirement for the energy potential of the effluent per litre. In figure 5 and 6 we show the demand in kj per litre and kj per cow per day for various sized tanks for the two temperatures 35 deg and 55 deg. We have assumed a heat recovery of 6% (i.e. k=.6), k heat =.5, C=4.2 kj/(kg deg C), T =8 deg, a residence time of 4 weeks at 35 deg and 2 weeks at 55 deg, and a R-value for the tank insulation of R=2 m 2 K/W. k heat

6 Energy concentration (kj/litre) N=27 N=4 N=65 N=7 N= N=27 N=4 N=65 N=7 N=14 Figure 5: Demand at 35 deg C. The coloured bars show the different volumes: 5/1/2 cubic metres shown in light-blue/lilac/pink. Energy concentration (kj/litre) N=27 N=4 N=65 N=7 N= N=27 N=4 N=65 N=7 N=14 Figure 6: Demand at 55 deg C. The coloured bars show the different volumes: 5/1/2 cubic metres shown in light-blue/lilac/pink. The demand in kj per litre reduces with increasing volume due to the fact that the heat loss through the tank depends on surface area rather than volume. In contrast, the demand in kj per cow increases rapidly with increasing volume. Emergency operation is an additional energy demand. Suppose that once a month there is an emergency where we have to run the dairy operation for four hours from the start of one milking. This demand is given by D E 1 = t k 2 elec t 1 E( t, N) dt where t 2 is a period of one month and t 1 is four hours of milking time.

7 The increased demand in the case V=5 m 3 and T=55 deg C is shown in figure 7 for various numbers of cows. The electricity demand is taken to be the same as in the self-sufficient mode above. Energy concentration (kj/litre) N=27 N=4 N=65 N=7 N= N=27 N=4 N=65 N=7 N=14 Figure 7: Demand at 55 deg C for a volume of V=5 cubic metres. Red bars include backup storage for one emergency milking a week. Case Study To illustrate how the above results may be utilized for a particular farm, we consider and example farm of N=4 cows. We estimate that the amount of effluent under normal operating conditions is 14 m 3 /day (or f I =.16 litres/sec) this could possibly be reduced to a minimum of 4 m 3 /day (or f II =.46 litres/sec) by scraping instead of washing down the dairy shed. Let us refer to these two possible flow rates as case I and II. If we choose the temperature in the digester to be 35 deg C and the residence time to be 4 weeks this fixes the volume of the tank in the two cases to V I = f I t R =387 m 3 and V II =112 m 3. Using the same assumptions as above the heat demand in the two cases is given by Q I =13.3 and Q II =4.4. In spot market mode the total energy demand is twice the heat demand, assuming k heat =.5. The demand per cow per day is given by 5.8 MJ and 1.9 MJ in case I and II, respectively. In self-sufficient mode, the demand per cow per day is 1MJ and 8.1MJ in case I and II, respectively. This fixes the demand side of the problem. To determine the feasibility of these case we need to compare these with the effluent energy content. Suppose the effluent yields.16 m 3 of biogas per cow per day, and the energy content of the biogas is 22.7 MJ/m 3 then we see that the effluent s energy value is h=3.7 MJ/day per cow. As this is greater than 1.9 MJ this demonstrates the feasibility of the spot-market mode of operation for case II considered above and shows that, if the assumption we have made here are correct, for the system to run in self-sufficient mode the effluent will need to be supplemented from other sources to increase its energy content per cow.

8 On the other hand, from figure 5 we see that even for a volume of 2 m 3 the spotmarket mode is still viable, which corresponds to a flow rate of 7 m 3 /day, or half normal operation. Conclusions In conclusion, we have determined the energy demands of a dairy-farm operating a biogas digester in both self-sufficient and spot-market modes. From this analysis we have extracted the energy concentration of the effluent in kj per litre and the energy per cow in kj per day that is necessary to sustain these modes of operation. The spot market mode of operation requires substantially less energy than the self-sufficient mode. It also makes more efficient use of fuel as all waste heat is utilized, however, as the effluent is a waste product this may not be a major concern. The stop-start operation of the self-sufficient mode may increase wear and tear on the engine. This could be improved by changing operations so as to yield a more even load over the day. A more even load would also increase efficiency as the waste heat from the engine would provide a larger percentage of the heat for the effluent tank. The economic returns of the self-sufficient operation are obviously the entire avoided electricity costs. In the spot market case, buying from the spot market can reduce costs by 8% as discussed in our previous report. In addition one can gain additional cost reduction by selling excess electricity to the grid and avoiding price spikes by utilizing the engine. In both cases there is an additional economic benefit of installing a biogas plant brought about by the ability to operate the dairy shed independent of the grid for short periods of time, thus mitigating the risk of a black-out. In the analysis of the self-sufficient mode we have not taken into account start up voltage spikes. The engines sizes we have assumed will not cope with large start-up spikes, however, there exists equipment to prolong start up times and therefore reduce these spikes.

Energy supply and demand analysis of a biogas electricity plant for a dairy farm

Energy supply and demand analysis of a biogas electricity plant for a dairy farm Introduction George Estcourt, Michael Jack and Per Nielsen (9 January 26) In this report we study a dairy farm generating