doi:10.1016/j.biosystemseng.2005.09.002 SE—Structures and Environment
Ventilation Flow in Pig Houses measured and calculated by Carbon Dioxide,
Moisture and Heat Balance Equations
V. Blanes; S. Pedersen
Research Centre Bygholm, Danish Institute of Agricultural Sciences, Schu¨ttesvej 17, DK-8700, Horsens, Denmark; e-mails: [email protected], [email protected]
(Received 29 April 2005; accepted in revised form 7 September 2005; published online 21 October 2005)
Ventilation flow in commercial livestock buildings can be estimated by means of relatively simple indirect methods based on carbon dioxide (CO2), moisture or heat balances. However, ventilation flow on an hourly basis forthese balances needs adjustment fordiurnal variation in animal CO2and heat production.
This work examines the agreement between ventilation flow measured in a pig house over a period of 41 days and that estimated from the three balances, on a 24 h and on an hourly basis.
The study shows that, all three methods can give reasonably good estimations of the ventilation flow on an hourly basis. On average, the calculated ventilation flow was 8% lower than measured ventilation flow for the CO2balance, and 9% lowerforthe moisture and heat balances.
A good agreement between measured and calculated ventilation flow was obtained on a 24-h basis (coefficient of determination R2between 092 and 097) and on an hourly basis (R2between 083 and 092). The study indicates that the agreement between measured and estimated ventilation flow on an hourly basis can be improved by taking into account the diurnal variation in CO2, moisture and heat production. r2005 Silsoe Research Institute. All rights reserved
Published by ElsevierLtd
1. Introduction
Ventilation flow in livestock buildings is related with two important aspects of the animal production. Firstly, it determines indoor climate and air quality inside the house, and so it affects the comfort of the animals. Secondly, ventilation rate is also connected with environmental issues, as it has a great influence on gas emission rates from animal houses.
As a consequence, ventilation flow in an animal house is a fundamental variable in the calculation of climatisa-tion systems and gas emission rates, and so it is important to determine it in a reliable way.
Direct measurement and indirect methods can both be used to estimate ventilation flow in a mechanically ventilated livestock building. However, direct measure-ment has several important drawbacks. Accurate registration requires the use of measuring fans installed in series with ventilation fans. Unfortunately, the large numberand the location of ventilation fans in real
livestock buildings make theiruse very difficult in practice.
The estimation of ventilation flow by indirect methods based on balance equations avoids these drawbacks by calculating the ventilation flow from some specific parameters of the indoor and the outdoor air, whose measurement is not so complicated and time-consuming as the direct measure of ventilation rate. Three different balances are possible (CO2 balance, moisture balance and heat balance) depending on the parameter being measured (CO2 concentration, content of moist-ure or temperatmoist-ure, respectively). However, these balance methods require an accurate prior determina-tion of the producdetermina-tion of CO2, latent heat and sensible heat from the animals, which also take part in the equations.
Therefore, it is a question of interest to assess the reliability of the balance methods to estimate the ventilation flow in livestock buildings, by com-paring the estimated ventilation flows, from the three
1537-5110/$30.00 483 r2005 Silsoe Research Institute. All rights reserved
balances, with the real ventilation flow, in order to validate the method and reinforce the credibility of the results.
In previous works, some authors have dealt with different aspects of this matter. In that sense, Pedersen
et al. (1998) investigated the agreement between the ventilation flow calculated from the CO2, moisture and heat balances in houses forcattle, pigs and laying hens, but a comparison with the real ventilation flow was not carried out. Pedersen and Gaardbo Thomsen (2000)
used the moisture and heat balance equations to estimate the heat production in a broiler house.
Schauberger et al. (2000) applied the three balances to predict the indoor climate in a finishing pig unit.Liet al. (2005) compared the ventilation flow measured and calculated from CO2balance in a laying hen house. In resume, as far as is known, there are very few works that compare the measured ventilation flow in a livestock building, and the ventilation flow calculated from the balance equations.
The production of CO2, moisture and heat from the animals, depend on different factors (live mass, energy
intake,etc.), and it has been demonstrated that it is also related with the animal activity which varies diurnally (Van Ouwerkerk & Pedersen, 1994; Pedersen & Rom, 1998;Niet al., 1999a;Jeppsson, 2002;Chwaliboget al., 2004;Sousa & Pedersen, 2004).
Nonetheless, most of the values and equations forthe calculation of CO2, moisture and heat produc-tion from the animals, that can be found in literature have been obtained from long-term experiments (more than 24 h), and so they assume intrinsically a diurnal average animal activity. As a result, calculating ventila-tion flow from balance equaventila-tions, on less than a 24-h basis, from literature data, without any adjustment foranimal activity, can make the balance method inaccurate.
The main objective of this work is to examine the agreement between ventilation flow measured in a pig house overa period of 41 days and ventilation flow calculated from CO2, moisture and heat balances, on a 24-h basis and on an hourly basis. The agreement on an hourly basis is improved by taking into account the diurnal variation of animal activity.
Notation A relative animal activity
A0CO2 coefficient forthe diurnal adjustment of the CO2production due to animal activity A0
moist coefficient forthe diurnal adjustment of moisture production due to animal activity A0
heat coefficient forthe diurnal adjustment of the heat production due to animal activity a,b,c
andd
constants forthe activity models
Cprod production of CO2on a 24-h basis, m3h
1 Cind concentration of CO2 in the indoorair,
p.p.m.
Cout concentration of CO2 in the outdoorair, p.p.m.
Eintake daily feed energy intake, W
Hind content of moisture in the indoor air, kg[H2O] m
3 [air]
Hout content of moisture in the outdoor air, kg[H2O] m
3 [air]
h time of day (24 hourclock), h hmin time of day with minimum activity, h
hsp specific heat of air, J kg1K1 hvap heat of vaporization of water, J kg1
ks correction factor for sensible heat at house level
L corrected latent heat production at house level, W
m live mass, kg
S corrected sensible heat production at house level, W
Strans transfer of sensible heat through the build-ing, W
Srad heat gain due to the thermal radiation transmitted through the ceiling, W
Sslurry heat gain owing to the difference of tem-peratures between the slurry and the indoor air, W
T airtemperature,1C Tind indoorairtemperature,1C
Tout outdoorairtemperature,1C
VCO2 ventilation flow calculated from CO2
bal-ance, m3h1
Vmoist ventilation flow calculated from the moist-ure balance, m3h1
Vheat ventilation flow calculated from the heat balance, m3h1
Vmeasured measured ventilation flow, m3h1
Ftot total heat production for fattening pigs at 201C, W
F
tot total heat production at temperatures dif-ferent to 201C, W
F
sen sensible heat production at house level, W F
lat latent heat production at house level, W r airdensity, kg m3
2. Heat production and animal activity 2.1. Total, sensible and latent heat production
In a recent report (CIGR, 2002), an equation forthe calculation of total heat lossFtotin W forfattening pigs at 201C is presented [Eqn (1)] wheremis the live mass in kg andEintakeis the feed energy intake in W:
Ftot¼509m075þ ð1 ð047þ0003mÞÞðEintake509m075Þ (1) In that equation, the total heat loss in W is calculated as the sum of heat loss formaintenance (509m075) and heat loss for growth (second part of the equation). For a live mass above 106 kg the factor(047+0003m) should be fixed at 079.
The total heat production Ftot in W at temperatures different from 201C can be calculated from Eqn (2) (CIGR, 2002):
Ftot¼Ftotþ0012Ftotð20TÞ (2) whereTis the air temperature in1C.
Pigs lose heat as sensible heat, due to the temperature gradient between their body temperature and the surrounding air, and as latent heat, by evaporation from respiratory tracts. However, the partition of the total heat into sensible and latent heat at house level is different to the sensible and latent heat at animal level. Sensible and latent heat at house level depends on the housing conditions, as part of the sensible heat produced by the animals can be used for the evaporation of wet surfaces inside the building.
The following equations [Eqns (3) and (4)] were proposed in the same report (CIGR, 2002) forthe calculation of sensible F
senand latentF
latheat produc-tion in W at house level forfattening pigs on partly slatted floor (at normal housing conditions of Northern Europe): F sen¼062F tot115 10 7T6 (3) F lat¼F totF sen (4)
The heat production expressed in heat production units (originally defined as the heat production of a dairy cow), is shown inFig. 1, where 1 heat production unit (hpu) is equal to 1000 W of total heat produced by the animals at 201C.
A further adjustment can still be necessary if the housing conditions are slightly different from the previously mentioned. A correction factor ks forthe sensible heat production S in W at house level, was introduced inPedersenet al. (1998), forthat adjustment [Eqn (5)]. The adjusted latent heatL in W can then be
obtained by Eqn (6):
S¼ksFsen (5)
L¼F
totS (6)
2.2. Carbon dioxide production
The CO2 production in a pig house is important because it can be used forcalculation of the ventilation flow.
The CO2production is the addition of that emitted by the animals in the respiration, and that released by the slurry.
Van Ouwerkerk and Pedersen (1994) estimated that the total CO2production in animal houses was between 017 and 020 m3h1
hpu1
, and in average of 0185 m3h1
hpu1
. In that work, it was considered that 4% of the total CO2 production came from the slurry. That value of 0185 m3h1
hpu1
was 135% higher than the value of 0163 m3h1
hpu1
that was recom-mended previously inCIGR (1984).
A value of 0185 m3h1hpu1 forthe total CO2 production was used also inPedersenet al. (1998), who found that it provided a good agreement between ventilation flow calculated from the CO2 balance and the heat and moisture balances, and in Sousa and Pedersen (2004), where those authors stated that using a CO2production of 0185 m3h
1
hpu1 gave ventilation rates of the same level as measured by the measuring fans.
However, Ni et al. (1999a) found that the CO2 production of a pig of 105 kg of body weight was equal to 8129 g h1
(that is approximately 0173 m3h1 hpu1
), and the CO2 production from the slurry, in a partly
0 200 400 600 800 1000 1200 1400 0 10 20 30 40 Ambient temperature, °C Sensible heat Latent heat Total heat
Heat production per hpu, W
Fig. 1. Distribution of total heat as sensible and latent heat for fattening pigs on partly or fully slatted floor (CIGR, 2002); hpu,
slatted pig house, was on average about 34% of the CO2 emitted by the animals (Niet al., 1999b).
2.3. Animal activity models
Animal activity shows daily cycles, according to the different animal actions (feeding, moving, resting, etc.) during every 24-h period.
There are several alternatives to quantify the animal activity. One possibility is to assess it by sensing systems with passive infrared detectors (Pedersen & Pedersen, 1995). To obtain the diurnal pattern of the animal activity, the absolute measurement can be expressed in relation to daily average, to get the relative animal activityA.
However, if it is not possible to measure the animal activity, the relative animal activity can be approxi-mated directly, by one of the following diurnal variation models (CIGR, 2002): the single sinusoidal model or ‘one maximum model’ [Eqn (7)] and the double sinusoidal model or‘two maxima model’ [Eqn (8)]:
A¼1asin 2p 24ðhþ6hminÞ (7) A¼1asin 2p 24ðhþ6hminÞ bsin 2p c ðhdÞ (8) where:his the time of day (24 hourclock), h;hminis the time of day with minimum activity, h; and,a,b,candd, are constants.
As the production of CO2, moisture and heat is positively related with the animal activity, the hourly adjustment coefficients for production at every specific hourA0
CO2;A
0
moistand A 0
heat (forthe CO2, moisture and heat production, respectively) follow a similar pattern as the relative animal activity (measured or estimated).
3. Materials and methods 3.1. Experimental room
The investigation was carried out in an experimental building forfattening pigs (Fig. 2), at Research Centre Bygholm (Danish Institute of Agricultural Sciences). The house is provided with four pens with partially slatted floor. The room is equipped with a neutral pressure mechanical ventilation system that consisted of one inlet and one outlet unit with fan. Incoming air passes through the inlet pipe, and enters the room through a circular horizontal inlet slot, placed in the centre of the room at 22 m above the floor.
The building is insulated and the different materials that compose the walls, the ceiling and the floorwere taken into account in the estimation of the coefficients of heat transmission orU-values.
The duration of the experiment was 41 days, starting in November month, therefore winter conditions can be considered.
Two products (maize silage and straw) were used as rooting materials for the pigs, during two different periods. In that respect, it is known that when maize silage is used in the pen as a rooting material, the pigs eat part of it every day. In the calculation of the total heat production [Eqn (1)], an increase in the energy intake, has been considered owing to that ingestion.
The slurry was removed twice during the 41 days: in the middle of the experiment and at the end.
3.2. Animals
The experiments were carried out with 40 pigs in the first 25 days and then reduced to 28 pigs, to make more space due to increased live mass. The initial average body weight was 805 kg increasing to 1225 kg after41 days. The pigs were fed ad libitum, with feed whose composition was 68% of grain, 16% of soya bean cake, 10% wheat bran and 6% of others. The feed intake was measured daily.
3.3. Registrations
3.3.1. Indoor and outdoor climate
Climate measurements comprise temperature, humid-ity and CO2 concentration of the indoor and the outdoor air, and solar radiation outside of the building. Adjacent building Experimental room Computer room 2 .35 m 2 .56 m 4 .6 m 11 m
Forthe balance calculations on an hourly basis, the difference between indoor and outdoor temperature perhourwas calculated as an average of 12 data, and in the case of humidity and CO2differences, as averages of six data. Solar radiation was measured at hourly intervals.
3.3.2. Activity
The animal activity was measured by three passive infrared sensors (Pedersen & Pedersen, 1995) located inside of the room.
3.3.3. Ventilation flow
Ventilation flow in the outlet pipe was measured Vmeasuredin m3h1by a measuring fan (FANCOM) that records 12 measurements per hour. Ventilation flow on an hourly basis was calculated as average of those measurements.
3.4. Carbon dioxide, moisture and heat balance equations The CO2, moisture and heat balance equations are based on the conservation of mass and energy in the building, understeady-state conditions.
The CO2balance can be expressed by the following equation [Eqn (9)]: VCO2¼ CprodA0 CO2 ðCindCoutÞ106 (9) where:VCO2 is the ventilation flow in m
3
h1from CO2 balance;Cprod is the production of CO2in m3h
1 on a 24-h basis; andCindandCoutare the CO2concentrations in the indoorand outdoorairin p.p.m.
In this work, a value of 0185 m3h1 hpu1
forthe total CO2production in the farm has been used for the CO2 balance. The suitability of this value is discussed below.
The ventilation flow can be calculated also from the moisture balance [Eqn (10)]:
Vmoist¼
3600A0 moistL hvapðHindHoutÞ
(10) where: Vmoist is the ventilation flow from moisture balance in m3h1
; Hind and Hout are the contents of moisture in the indoor and outdoor air in kg[H2O] m3[air] and hvap is the heat of vaporisation of waterin J kg1
, that can be obtained, according to the indoortemperature Tind in 1C from the expression:
ð2501242TindÞ 103:
Finally, the balance equation forthe sensible heat is described by Eqn (11):
Vheat¼
3600ðAheatSþStransþSradþSslurryÞ
hsprðTindToutÞ (11)
where: Vheat is the ventilation flow in m3h1 from the sensible heat balance;Strans is the transfer of sensible heat in W through the building (negative when it is heat loss); Srad is the heat gain in W due to the thermal radiation transmitted through the ceiling;Sslurryis the heat gain in W owing to the difference of temperatures between the slurry (when it is excreted) and the indoor air; Tout is the temperature of the outdoor air in1C;hspis the specific heat of airin J kg1
K1
; andr is the airdensity in kg m3 . The solar radiation affecting the roof varies over the daytime, and a certain space of time is required to sense its effect in the indoor air. The outdoor temperature also varies diurnally, although this variation is slower. In this work, a time delay for the heat gain due to the thermal radiation, and for the heat loss of sensible heat through the building, has been considered. On the other hand, it is known that only a specific fraction of the energy from the total thermal radiation is transmitted through the ceiling. That proportion has also been included in the calculations. Regarding the heat gain from the slurry, an initial slurry temperature of 391C (equal to the body temperature of the pigs) was used.
When these balances [Eqns (9), (10) and (11)] are performed on a 24-h basis, A0 CO2; A 0 moist and A 0 heat are equal to 1.
Finally, note that, theoretically, all three calculated ventilation flow, should give the same value, and equal to the measured ventilation flow, as it is indicated in the following expression [Eqn (12)]:
VCO2¼Vmoist¼Vheat¼Vmeasured (12)
4. Results
4.1. Live mass, energy intake and total heat production
Table 1shows the results on live mass, energy intake and total heat production from the animals, over the experiment period.
Table 1
Live mass,energy intake and heat production (average for every week)
Week Live mass, kg Energy intake Heat production, W
MJ day1 W Maintenance Total
1 846 470 544 142 253 2 932 474 548 153 252 3 1011 475 550 162 250 4 1082 475 550 171 251 5 1146 479 554 178 257 6 1203 483 559 185 263 509m075
4.2. Animal activity measured and estimated from diurnal variation models
Measured animal activity has been expressed in terms of relative activity (in relation to average activity for every day) and then averaged over 41 days. Relative animal activity from measured data (Fig. 3) indicates that a low, and relatively constant, animal activity occurs from 20:00 to 3:00. The minimum animal activity during a 24-h period is about 25% lower than the daily average. On the other hand, relative animal activity shows two maxima during the day, probably affected by the times of the day when the feeders are replenished. These two maxima are relatively close to each other. This can be associated with the shortness of daylight in the winterperiod.
Relative animal activity (averaged over 41 days) has been approached by two different activity models: the single sinusoidal model and the double sinusoidal model (Fig. 3).
The correlation coefficients between the measure-ments and the estimations are shown inTable 2, where two cases are considered for each model. In the first case, we have used in the equations, the standard
coefficients proposed in CIGR (2002). In the second case, we have found the optimum coefficients: those that minimise the standard deviations of the differences between measured and estimated animal activity.
The great improvement (coefficient of determination R2 from 055 to 095) in the double sinusoidal model when the coefficients are optimised is mainly related to the change in the coefficient c which determines the distance between the two daily maxima foranimal activity. The inaccuracy when using the CIGR coeffi-cients is probably connected to the fact that, in that case, the coefficients were estimated according to average annual conditions. However, this work has been carried out underwinterand natural lighting conditions, and so the time between the two daily maxima has to be reduced from 11 to about 6 h.
On the otherhand, as measured animal activity shows two main maxima during the day, the double sinusoidal model, when using the appropriate coefficients, fits betterthan the single sinusoidal model.
In conclusion, it can be stated that in general terms, the diurnal variation in animal activity can be explained both by the single sinusoidal modelðR2¼088Þand by the double sinusoidal modelðR2¼095Þ:
0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time, hours after midnight
Relative activity
Fig. 3. Diurnal variation in relative animal activity: , measured; , single sinusoidal model; , double sinusoidal model; (activity models from optimised coefficients)
Table 2
Values for the constantsa,b,cand d,and the time of the day with minimum activity hminin h in the activity models; and the
coefficients of determinationR2
for the correlation between measured and estimated animal activity
Single sinusoidal model Double sinusoidal model
a (hmin), h R2 a b c d (hmin), h R2
Standard 02 2 078 02 015 11 113 2 055
4.3. Comparison between measured and calculated ventilation flow
The relation between calculated and measured venti-lation flow, is shown in Table 3. The pigs get straw as rooting material in the first part of the experiment and maize silage in the last part but no offset on calculated ventilation flow is observed, why all 41 days measure-ments are considered in the analyses as a whole.
Table 3 presents the results from two different approaches in the calculation of the ventilation flow, namely: no adjustment of the partition between sensible and latent heatðks¼1Þ;and adjustment of the partition by applying a correction factorksof 093.
Table 3 shows that, when no correction is applied (ks¼1), ventilation flows from moisture balance and from heat balance are in disagreement. However, in theory, moisture and heat balances should provide the same ventilation flow. That disagreement can be attributed to an inaccuracy in the estimation of the partition of the total heat into sensible and latent heat, as it is known that that division is highly influenced by the housing conditions. In this work, the same ventila-tion flow from the heat and the moisture balance is achieved when applying a correction factor ks of 093. That means that 7% of the sensible heat produced by the animals [calculated according to CIGR (2002)
equations], is used to evaporate water from wet surfaces (drinking water, slurry, etc.) inside the animal house.
Ventilation flow calculated from the CO2 balance is, on average, 8% lower than averaged measured ventila-tion flow (Table 3). This result indicates that the value of 0185 m3h1hpu1forthe total CO2production should be reconsidered and slightly adjusted to improve the estimation of the ventilation flow from the CO2balance. In that sense, a perfect agreement between estimated and measured ventilation flow would involve consider-ing a total CO2production in the house, equal to 0201 m3h1
hpu1 .
However, in any case, that increase in the total CO2 production seems not to be related with an under-estimation of the slurry emissions, as it has not been observed any development in the differences between measured and calculated ventilation flow, as the days passed and the slurry was being accumulated in the house (maximum depth of 06 m).
In Table 4, the standard deviation s in m3h1, and correlation coefficients R2 between measured and calculated ventilation flow are shown. Four cases are considered depending on the adjustment criteria by animal activity being applied. In the first case, estimated ventilation flow was calculated from animal emissions not adjusted by activity. In the following three cases, those emissions were adjusted by measured activity, activity from the double sinusoidal model and activity from the single sinusoidal model, respectively.
In the calculations that provide the results shown in
Table 4, the relation between measured animal activity A and the coefficients forthe adjustment of CO2, moisture and heat production on an hourly basis (A0CO2; A0moistandA0heat) were optimised, just like the coefficients of the single and the double sinusoidal models (a,b,c,d and hmin), which define the diurnal variation of those productions. The correction factor ks of 093 was also applied, according to the results presented inTable 3.
The results indicate that the agreement between measured and calculated ventilation flow is generally high (Table 4), but the agreement can be improved by including in the calculations the diurnal variation on the production of carbon dioxide, moisture and heat by the animals. When adjusting the equations by measured Table 3
Relation between calculated and measured ventilation flow from different correction factorsksof the sensible heat
Balance Ratio of calculated/measured airflow
ks¼1 ks¼093
CO2 092 092
Moisture 082 091
Heat 098 091
Table 4
Standard deviationsin m3h1,and coefficient of determinationR2for the correlation between measured and calculated ventilation flow on hourly basis
Balance Not adjusted by activity Adjusted by measured
activity
Adjusted by activity from double sinusoidal model
Adjusted by activity from single sinusoidal model
s R2 s R2 s R2 s R2
CO2 189 079 139 090 125 092 126 092
Moisture 254 066 180 083 174 084 179 084
activity, between 83% and 90% of the total variation of the ventilation flow can be explained by balance equations; and between 84% and 92% when using the single orthe double sinusoidal model.
A comparison between measured ventilation flow and ventilation flow calculated from the CO2, moisture and
heat balances, adjusted by activity from the single sinusoidal model, is shown inFig. 4, by way of example. Regarding the ability of the different balances to provide accurate ventilation flow, Table 4 shows that CO2 and heat balances provide better results than moisture balance. The correlation coefficient from
y = 0.909x R2 = 0.92 y = 0.908x R2 = 0.84 y = 0.902x R2 = 0.87 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 Measured ventilation flow, m3 h−1
Measured ventilation flow, m3 h−1
Measured ventilation flow, m3 h−1
Calculated ventilation flow from
CO 2 balance, m 3 h − 1 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500
Calculated ventilation flow from
moisture balance, m 3 h − 1 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500
Calculated ventilation flow from
heat balance, m 3 h − 1 (a) (b) (c)
Fig. 4. Measured and calculated ventilation flow on hourly basis from: (a) carbon dioxide, (b) moisture and (c) heat balance adjusted by activity from single sinusoidal model; R2, coefficient of determination
moisture balance when ignoring the diurnal variation of activity, is relatively low ðR2¼066Þ: Nonetheless, ventilation rate from moisture balance also shows a high correlation when considering the diurnal variation ðR2¼084Þ:
The standard deviations of the differences between measured and calculated flow (Table 4), are about 11–12% of the average measured ventilation flow (1285 m3h1) when considering the CO2 and heat balance, and about a 15% in the case of the moisture balance.
R2 = 0.97 y = 0.915x R2 = 0.97 R2 = 0.92 y = 0.921x y = 0.905x 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Measured ventilation flow, m3 h−1
Measured ventilation flow, m3 h−1
Measured ventilation flow, m3 h−1
Calculated ventilation flow from
CO 2 balance, m 3 h − 1 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
Calculated ventilation flow from
moisture balance, m 3 h − 1 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
Calculated ventilation flow from
heat balance, m 3 h − 1 (a) (b) (c)
Fig. 5. Measured and calculated ventilation flow on 24-h basis from: (a) carbon dioxide, (b) moisture and (c) heat balance; R2, coefficient of determination
When calculating the ventilation flow from the heat balance [Eqn (11)], we have taken into consideration some different factors (the thermal radiation that is transmitted to the indoor air, a time delay in the solar radiation and in the heat loss, and the heat gain from the slurry) that take part of the heat balance in the real farm, but whose importance is unknown. Including these factors makes the calculation more complicated and therefore it is interesting to analyse if they involve a relevant improvement in the estimation of the ventila-tion flow.
Table 5 shows the correlation coefficients that have been obtained forthe heat balance (not adjusted and adjusted from the single sinusoidal model) as the calculation was refined.
Considering a time delay in the heat transmission did not mean any change in the standard deviation and the coefficient of determination under winter conditions.
Finally, Fig. 5 shows linear regressions and coeffi-cients of determination between measured and calcu-lated ventilation flows (from the three balances), on a 24-h basis.
4.4. Sensitivity analysis
The measurement of each parameter that takes part in the balance equations inevitably entails a measurement error, which involves a lack of precision in the estimated ventilation flow. Table 6 shows the sensitivity of the calculated ventilation flow to inaccuracies in the measurement of temperature, relative humidity, CO2 concentration, coefficient of heat transmission, solar radiation and the live mass of the animals.
As seen in Table 6, an error of 10% in estimated ventilation flow corresponds approximately to an error of 11C in the measurement of temperature, 3% for the relative humidity or 150 p.p.m. for the CO2 concentra-tion.
5. Conclusions
In this work, a comparison between measured ventilation flow in a pig house during 41 days, and ventilation flow calculated from CO2, moisture and heat Table 6
Sensitivity analysis (% change in calculated ventilation flow)
Parameter Basic value (average of 41 days) Increment Change in airflow, %
CO2balance Moisture balance Heat balance
Temperature indoor 1761C 11C 12 13 11 Temperature outdoor 421C 11C 0 0 95 RHindoor71% 1% 0 35 0 RHoutdoor97% 1% 0 37 0 CO2conc. indoor1900 p.p.m. 50 p.p.m. 36 0 0 CO2conc. outdoor390 p.p.m. 50 p.p.m. 39 0 0 U-valuey 043 W/m2K 10% 0 0 10 Solarradiation z 10% 0 0 01 Live mass 1036 kg 10% 13 13 14 RH, relative humidity.
yU-value, coefficient of heat transmission.
zThe maximum value of solar radiation for the whole period was 198 W m2
, and the transmission of the energy from the solar radiation has been set as 10% of the total radiation measured every hour.
Table 5
Effect of the sun radiation on the standard deviation s in m3h1,and coefficient of determination R2 between measured and ventilation flow calculated from heat balance (not adjusted and adjusted from the single sinusoidal model)
Factors considered in the heat balance (besides the heat emission from the animals)
Not adjusted Adjusted from single sinusoidal
model
s R2 s R2
Heat transmission 168 084 153 087
Heat transmission+solar radiation 164 085 153 087
Heat transmission+solar radiation+time delay in the effect of solarradiation
balances has been carried out. Results indicated that, in general terms, ventilation flow calculated from the three balances were in good agreement, although they were slightly lowerthan measured ventilation flow.
(1) Ventilation flow estimated from CO2balance (from 0185 m3h1
hpu1
of CO2) on an hourly basis was, on average, 8% lower than the averaged measured ventilation flow. To bring a perfect agreement between estimated and measured ventilation flow would involve considering a total CO2production in the house, equal to 0201 m3h1hpu1.
(2) Ventilation flow estimated from both, moisture and heat balances, on an hourly basis, were on average 9% lowerthan the averaged measured ventilation, by converting 7% of sensible heat into latent heat. (3) The values forthe coefficient of determinationR2for
the correlation between measured and estimated ventilation flow, on an hourly basis, without adjustment foractivity, were 079 forthe CO2 balance, 066 forthe moisture balance and 085 for the heat balance.
(4) The agreement on an hourly basis can be improved by including in the calculations the diurnal variation in the CO2, moisture and heat production (e.g. values of R2 of 092, 084, 087, forthe CO2, moisture and heat balance, respectively, for a single sinusoidal variation in animal activity).
(5) The diurnal variation in animal activity can be fairly explained by both, a single sinusoidal model (R2¼088) and by a double sinusoidal model (R2¼095).
(6) The values forthe coefficient of determinationR2for the correlation between measured and calculated ventilation flow on a 24-h basis were: 097, forthe CO2and the moisture balance, and 092 forthe heat balance.
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