INDOOR AIR AS A COLLECTIVE FACTOR OF PRODUCTION

Transcription

1 INDOOR AIR AS A COLLECTIVE FACTOR OF PRODUCTION Arne Jönsson Secondary Vocational Training, Härnösand, Sweden Abstract The theory for a collective factor of production is applied to indoor air in an office. A collective factor is the same to all. In an office all workers breathe air of the same quality. The theory is adapted to measurements of dissatisfied and to the marginal cost for outdoor air. The loss of production is expressed as a function of both the number of disturbed (dissatisfied) and of a loss of production for every worker. A worker has a loss if the concentration is higher than his threshold value or his sensitivity. This makes the loss sensible to new odours since they change both the number of disturbed and the loss per disturbed. The theory is tested against measurements of production and it explains why the average loss per worker with body odour at the economic optimum concentration is only a promille and why a more irritating odour increases the loss to a percent of the production. The theory also explains why it is better to reduce the source strength of pollutants than to increase the outdoor air rate. To reduce the loss of production from 1,82 SEK/h pers to 0,17 SEK/h pers with more outdoor air an increase from 15 to 91 l/s pers is necessary. This costs an additional 2840 SEK/yr pers at the construction of the building. To reduce the source strength costs about 1000 SEK/yr pers. It is less expensive to reduce the source strength. (1 USD = 7 SEK) Keywords: collective, factor of production, office, indoor air, odour, economics 1 Introduction The theory about collective goods was introduced bye economists before It explains the indoor temperature in MU-dwellings or block of flats with collective control of the indoor temperature Jönsson (2006). A form of collective control is common supply water temperature control for a building. If the theory is used for indoor temperature as a collective factor of production then it explains the indoor temperature in offices Jönsson (2009). It also gives that % of the households in Swedish MU-dwellings are disturbed by the indoor temperature but only % of the workers in an office are disturbed by the indoor temperature. A household or a worker must have a temperature below his threshold to be disturbed and he is more disturbed if the temperature is more below the threshold. If the temperature is over his threshold he is not affected by the temperature at all, unless it is too high. The temperature thresholds are changed to concentration thresholds in the indoor air. In the field of ventilation this is similar to the concept of acceptable or acceptable to a part of the population. This has been used for ventilation since at least the 1930-ties. In this paper the theory of collective goods and collective factors of production is applied to indoor air and adapted to measurements of dissatisfied. It is tested against measurements of productivity.

2 2 Collective factor of production A collective factor of production is the same to all workers in an office, like the indoor temperature or the indoor air. The cost for the factor is not changed if more workers use the factor. This is not fully true when body odour is the dominant source of pollution. The loss of production for an individual Li SEK/h pers from polluted air depends on the concentration and the sensibility of the individuals to the pollutant. The individuals only loses production at concentrations above the values where they are disturbed c*1i Fig. 1. The sum of loss for n workers L SEK/h follows Eq.(1) if the concentration of pollutant 1 c1 ppm is above the thresholds c* 1i for all workers. Concentration where pollutant 1 disturbs the first most sensible individual 1 is c* 11 ppm. Concentration where pollutant 1 disturbs the least sensible of n individuals is c* 1n ppm. Consequence factor for loss of production from pollutant 1 on individual 1 p 11 SEK/h ppm, pers. p1i = 0 if c1 < c*1i. (1) Li SEK/h p11 p12 p1n ppm c*11 c*12 c*1n Concentration, c1 Figur 1. Individual loss of production for n workers as function of the concentration c1 of pollutant 1 in ppm The sum of loss of production Eq.(1) from all workers is differentiated and shown in Fig. 2. All workers are supposed to have the same p 1. SEK/h ppm p1 ppm c*11 c*12 c*1n Concentration, c1 Figur 2. Differential of sum of loss of production for n workers as function of the concentration c1 of pollutant 1 in ppm. The sum of loss of production is represented bye the area under the lines in Fig. 2. The area under the dotted line is the loss of production calculated as if everybody was disturbed. This overestimates the loss of production at low concentrations. If there are many workers n and if c*11 = 0

3 then the differential of sum of losses from pollutant 1 can be described with the continuous function in Fig. 3. SEK/h ppm n p1 dis1 ppm Concentration, c1 Figur 3. The area under the curve represents the sum of loss of production for all workers as a continuous function of c1 The share of the disturbed workers dis1 can be written with Eq.(2) as long as dis1 < 1. The constant k 1 ppm -l 1 is found from an adaptation to measurements of dissatisfied. dis 1 = k 1 c 1 l1 (2) The loss of production L is the area under the curve in Fig. 3. It can be found from the integral in Eq.(3). (3) The loss of production L in an office at the concentration c 1 follows Eq.(4). (4) Dissatisfied may not have the same meaning as disturbed in Eq.(2) but here they are equal. 3 Adaption to measurements 3.1 Adaption to measurements with body odour The percentage dissatisfied bye body odour expressed as CO 2 concentration in ppm can be found in Berg-Munch et al. (1984). "A ventilation rate around 8 l/s pers is required to satisfy 80 % of people entering a space". The percentage dissatisfied has been determined from questions to the occupants. 20 % dissatisfied visitors means a CO 2 concentration of 800 ppm. If the CO 2 concentration in the outdoor air is 300 ppm then the CO 2 concentration at 20 % dissatisfied is 500 ppm over the outdoor concentration and the outdoor air rate is 8 l/s person. This is the relative concentration c 1r = 1 (no dimension). Eq.(2) is rewritten as a function of the relative concentration in Eq. (5), Eq. (6), Eq. (7) and Eq. (8). c1 = 500 ppm * c1r (5) (6)

4 (7) (8) The loss of production in average per person Lm SEK/h pers as function of the relative outdoor air rate qr is finally Eq.(9). 3.2 Adaption to measured percentage of dissatisfied Knudsen et al. (1994) gives the percentage of dissatisfied with bio effluents as function of the relative concentration. The relative concentration zero gives 0 % dissatisfied, concentration 1 gives 20 % and 6 gives 60 % dissatisfied. This gives Eq. (10). (9) dis1 = 0,2 * c 1r 0,61 0,2 = k 1 (500 ppm) l1 and l 1 = 0,61 (10) 3.2 Adaption to the marginal cost To determine p1 in Eq.(9) an outdoor air rate of 10 or 15 l/s pers is assumed to be optimal. Since the marginal loss is equal to the marginal cost for outdoor air at optimum then the marginal loss can be determined. If a high outdoor air rate is optimal it means that odours are valued to give a high loss of production. The marginal cost for outdoor air was calculated in Jönsson (1995). The investment in a ventilation system with 1,25 m 3 /s supply and return air (100% outdoor air) with heat recovery in an office building with 50 rooms is 1 MSEK. If half the investment depends on the outdoor air rate and the annuity is 0,074 then the cost of capital is SEK/ m 3 /s, yr. The cost of operation (heat and maintenance) is SEK/ m 3 /s, yr during work hours 2000 h/yr. Then it will cost 37,4 SEK/ l/s yr or 0,019 SEK/ l/s h to increase the outdoor air rate at the design of the building. The fixed investment is 0,015 SEK/ h. The price of a work hour is 250 SEK/h. The marginal cost as function of the outdoor air rate 0,019 SEK/l/s h is rewritten for one relative outdoor air rate: 0,019 SEK /l/s h * 8 l/s = 0,152 SEK/h. The differential of the loss Eq.(9) in average per person with regard to qr is Eq.(11). If the optimum with only body odour pollutant 1 is 10 l/s pers then p1 = 0,0027 SEK/ h ppm. If the optimum is 15 l/s pers then p1 = 0,0078 SEK/h ppm. If the optimum outdoor air rate is between l/s pers then the average loss per person Lm SEK/h pers from pollutant 1 as function of the relative outdoor air rate qr is Eq.(12). (11) The loss of production at optimum 10 l/s pers is 0,12 SEK/h pers in average. According to Eq.(10) it is the 17 % disturbed who gives the loss. The other 83 % are not affected. A disturbed person loses 0,12 SEK/h / 0,17 = 0,70 SEK/h pers in average for the group of disturbed. In Jönsson (1995) the loss of production at optimum 10 l/s pers was 374 SEK/yr pers during 2000 h or 0,19 SEK/h pers if the loss was linear to the concentration. The loss of production at optimum 15 l/s pers is 0,17 SEK/h pers. The relative loss is 0,17 / 250 = 0,0007. (12)

5 Figur 4. Loss of production in SEK/h pers, cost of ventilation and sum as function of outdoor air rate in l/s pers. The optimal outdoor air rate is 10 l/s person 4 Calculation of loss from body and carpet odour Wargocki et al. (2000) determined the percentage of dissatisfied and the productivity in a mixture of body and carpet odour at 3 outdoor air rates, Table 1. Long term effects to health are not included, only short-term loss of production. Table 1: Percentage dissatisfied and production at different outdoor air rates Outdoor air Dissatisfied Productivity rate Body body+carpet Speed, norm. body+carpet Knudsen Wargocki Typing Add Proof reading l/s pers % % ,8 221,1 5, ,6 232,9 5, ,9 237,7 5,41 Loss of production in average per person Lm in odour 2, body+carpet from Eq.(13) as function of the relative outdoor air rate qr. The function for dis Eq.(2) is adapted to 58 % at 3 l/s and to 29% at 30 l/s. It gives Eq.(14). (13) dis2 = 0,43 * c r 0,30 0,43 = k 2 (500 ppm) l2 and l 2 = 0,30 (14)

6 Odour 2 dissatisfies 29/9 = 3,2 as many workers at 30 l/s as odour 1 according to Table 1. This is the reason to assume that the consequence factor p2 is 3,2 times higher than p1. If the optimum for body odour is 10 l/s pers then p2 = 3,2 * 0,0027 SEK/h ppm = 0,0086 SEK/h ppm. If the optimum for body odour is 15 l/s pers then p2 = 3,2 * 0,0078 SEK/h ppm = 0,025 SEK/h ppm. If the optimum outdoor air rate for body odour is between 10 and 15 l/s pers then the loss of production in average per person Lm SEK/h pers in body+carpet odour is between Eq.(15). With only body odour the loss of production if optimum is 10 l/s pers is 0,12 SEK/h pers in average or 0,12 / 250 = 0,00048 and 17 % is disturbed. With both body and carpet odour at optimum 10 l/s pers the loss is 1,08 SEK/h pers and 40 % are disturbed. The average relative loss is 1,08 / 250 = 0,0043 of the price of a work hour. A disturbed person loses in average 1,08 / 0,40 = 2,7 SEK/h pers. If 15 l/s pers is optimal then 1,82 SEK/h pers in average is lost at 15 l/s pers with both body and carpet odour and 36 % are disturbed. The average relative loss is 1,82 / 250 = 0,072. The most sensitive person loses 6,66 SEK/h, pers. (15) 5 Test against measurements with body and carpet odour The loss of production according to this theory is compared to the measured work rates for typing, addition and proof reading from Wargocki et al. (2000) in Table 1. Figur 5. Relative loss in average calculated according to Eq.(15) (curves) and measured relative loss of production (points) as function of the outdoor air rate in l/s pers

7 A loss relative to the production at 30 l/s pers is calculated for the three activities and for the theoretical losses assuming that the optimal outdoor air rate is 10 or 15 l/s pers. The relative losses at the price of a work hour 250 SEK/h are shown in Fig. 5. The loss of production measured at 3 l/s in the presence of the carpet is 3-6 %. The theory gives a loss of 6 % (14,8 SEK/h pers) and 58 % disturbed if the optimum is 15 l/s pers. The loss in average for a disturbed person is 14,8 / 0,58 = 25,5 SEK/h or 10 %. 6 Test against change of carpet In this case it has probably been decided that it is more economic to change the carpet than to increase the outdoor air rate. Do the theory predict this? If the optimal outdoor air rate with only body odour is 15 l/s pers then the loss of production is 0,17 SEK/h pers at 15 l/s pers. This is 20 seconds a day and person. The average loss for one of the 14 % disturbed is 2 minutes and 20 seconds a day. Both body and carpet odour gives a loss of 1,82 SEK/h pers. Then the removal of the carpet will increase production with 1,82 0,17 = 1,65 SEK/h pers or with 3220 SEK/yr pers. To change the carpet costs about 5000 SEK/workplace or 1000 SEK/workplace yr. To reduce the loss of production from 1,82 SEK/h to 0,17 SEK/h with more air an increase from 15 to 91 l/s pers is needed according to Eq.(15). This costs an additional 2840 kr/yr workplace if it had been done with the price of ventilation at the construction of the building. It is less expensive to change the carpet. The introduction of the carpet odour increases the loss from promilles (0,7 ) to percent (0,72 %) of the production. 7 Conclusion The loss of production from odours depends on the number of disturbed and on the loss per disturbed. The loss for a collective increase more than linear with the concentration as long as the number of disturbed is below 100 %. Odours change both the number of disturbed and the loss per disturbed. This makes the loss sensible to different odours. The differential of the loss of production goes to zero at zero concentration. This theory says that small concentrations do not give any loss below the lowest threshold value. If it is optimal to use 15 l/s pers to reduce body odour then the loss is 0,17 SEK/h pers or 0,0007 of the production in average for all and 14 % is disturbed. If an odour that makes three times as many disturbed also increases the loss three times for a disturbed person then the loss increases to 1,82 SEK/h pers or 0,007 of the production in average and 36 % is disturbed. The theory explains why it is less expensive to change the carpet, than increase the outdoor air rate. To describe the loss of production from different pollutants it is necessary to know the percentage disturbed and the loss for the disturbed individuals. This considers the individual sensibilities to different odours or pollutants. 8 References Berg-Munch, B., Clausen, G., Fanger, P.O. (1984) Ventilation requirements for the control of body odour in spaces occupied by women, Indoor Air 84, Stockholm, Sweden, Vol. 5 p Jönsson, A. (1995) Economic analysis of ventilation in an Office Building, Indoor air quality in practice, 1995, Oslo, Norway, p

8 Jönsson, A. (2006) Indoor temperature as a collective goods, Cold Climate 2006, Moscow, Russia, Section 1. Jönsson, A. (2009) Indoor temperature as a collective factor of production, Cold Climate HVAC 2009, Sisimiut, Greenland Knudsen, H.N., Clausen, G., Fanger, P.O., (1994) Characterisation of sensory emission rates from materials, Healthy Buildings 94, Proceeding of the 3rd International Conference, Budapest, Hungary, Vol. 1, p Wargocki, P., Wyon, D.P., Fanger, P.O. (2000) Productivity is affected by the air quality in offices, Healthy Buildings 2000, Vol. 1, p