Effective fumigation with methyl bromide can be ensured if the recommended Ct product has been reached or exceeded. The Ct product is calculated by the time in hours (h) that the concentration has been present, and is recorded in gram hours per cubic metre (gh/m3). If the gas concentration within the enclosure were to remain constant, the Ct product could be estimated simply by multiplying the concentration by the exposure time. The Ct product then has to be calculated by adding together the component Ct products obtained from the average concentration of sequential observations and multiplying by the time interval between them. The best approximation of true total Ct product is obtained with a large number of concentration observations in an exposure. However, practical constraints often limits the number of observations that can be made. Concentrations should be measured at about 2, 4, 12, and 24 hours after dosing. If a 48-hour exposure is used, readings at about 36 and 48 hours should also be taken. A Ct product cannot be calculated on fewer than two concentration measurements. If only two readings are possible the first must be taken after gas mixing is complete and the second must indicate a quantifiable concentration (that is, more than zero or a trace).
In fumigations under gas-proof sheeting where gas loss rates are very high, the Ct product is best calculated by using the geometric mean. this is done by multiplying together two observed gas concentrations (as grams per cubic metre), taken one after the other then multiplying the square root of their number by the time interval (in hours) between the readings. This can be expressed as the equation.
(1) 
(g h/m3)
where
Tn is the time the first reading was taken in hours
Tn+1 is the time the second reading was taken in hours
Cn is the concentration reading at Tn in g/m3
Cn+1 is the concentration reading at Tn+1 in g/m3
Ctn,n+1 is the calculated Ct product between Tn and Tn+1 in g h/m3
The Ct product obtained from a series of readings may then be added to calculate the cumulative Ct product for the whole of exposure period. It is this value that is used to indicate the successor failure of a fumigation. The calculation is easily carried out on a simple electronic calculator with a square root function.
In well sealed enclosures that have passed a pressure test where gas loss rates are low, the Ct product may be calculated by using the arithmetic mean. This is done by adding together two observed gas concentrations (as grams per cubic metre), taken one after the other, and multiplying half of this number by the time interval (in hours) between the two readings. This can be expressed as the equation:
(2) 
Tn is the time the first reading was taken in hours
Tn+1 is the time the second reading was taken in hours
Cn is the concentration reading at Tn in g/m3
Cn+1 is the concentration reading at Tn+1 in g/m3
Ctn,n+1 is the calculated Ct product between Tn and Tn+1 in g h/m3
The Ct products obtained from a series of readings may then be added to calculate the cumulative Ct product for the fumigation (see example 3). It is this value that is used to indicate the success or failure of a fumigation.
It possible to add gas during the course of an exposure to maintain a minimum gas concentration and so achieve a prescribed or statutory Ct product.
Note: Whichever method of calculating the Ct product is used, it is important the gas within the enclosure is well mixed and the concentration have become approximately even by the time the first concentration reading used in the calculation (e.g. 2 hours in a bag stack) have been taken. Pairs of observations containing a zero or unquantifiable low (e.g. trace) concentration cannot be used to obtain a valid contribution towards a cumulative Ct product.
Worked examples of Ct calculation
The following examples (based on hypothetic methyl bromide fumigation) are given to illustrate the steps needed to calculate Ct products using either equation 1 or 2 above.
EXAMPLE 1
A fumigation under gas poor sheets with a high loss rate, where the Ct product is calculated on the basis of equation 1. This is the type of result that will be expected in many commercial fumigations or where the commodity is very sorbitive.
Readings:
|
Time (hours) |
Time step (hours) |
Concentration (g/m³) |
Ct product (g h/m³) |
Cumulative Ct (g h/m³) |
Comments |
|
0.0 |
- |
- |
- |
- |
End of gassing |
|
2.0 |
2.0 |
20.0 |
* |
0.0 |
Ct cannot be calculated |
|
4.0 |
2.0 |
15.5 |
35.2 |
35.2 |
|
|
12.0 |
8.0 |
6.2 |
78.4 |
113.6 |
|
|
24.0 |
12.0 |
2.0 |
42.3 |
155.9 |
|
|
36.0 |
12.0 |
trace |
** |
155.9 |
Ct cannot be calculated |
|
48.0 |
12.0 |
0.0 |
** |
155.9 |
Ct cannot be calculated |
* No contribution to Ct as gas most probably not mixed by this time and sample may not be representative of concentrations as a whole.* * Ct for this time period cannot be calculated as final value is less than a quantifiable concentration.
Example of Calculation
Using equation 1 for the period from 2 to 4 hours
That is, the Ct for the period between the observations = the time between the observation x the square root of the product of the concentrations at the two observation times.
EXAMPLE 2
A fumigation with a very high loss rate where top up gas is added to ensure that the required Ct product is achieved. Here the Ct product is calculated using Equation 1. This is the type of result that can be expected from a poorly sealed under-sheet fumigation, or a fumigation of a very sorptive commodity where a contractual or quarantine target dose (either Ct or minimum concentration over a set time) has been specified.
Readings:
|
Time (hours) |
Time step (hours) |
Concentration (g/m³) |
Ct product (g h/m³) |
Cumulative Ct (g h/m³) |
Comments |
|
0.0 |
- |
- |
- |
- |
End of gassing |
|
2.0 |
2.0 |
20.0 |
* |
0.0 |
Ct cannot be calculated |
|
4.0 |
2.0 |
15.5 |
35.2 |
35.2 |
|
|
7.0 |
3.0 |
10.0 |
37.3 |
72.5 |
Top up started |
|
8.0 |
1.0 |
19.5 |
14.0 |
86.5 |
Top up finished |
|
15.0 |
7.0 |
10.0 |
97.7 |
184.2 |
Top up started |
|
16.0 |
1.0 |
15.5 |
12.3 |
196.6 |
Top up finished |
|
24.0 |
8.0 |
4.0 |
63.0 |
259.6 |
|
|
36.0 |
12.0 |
trace |
** |
259.6 |
Ct cannot be calculated |
|
48.0 |
12.0 |
0.0 |
** |
259.6 |
Ct cannot be calculated |
* No contribution to Ct as gas most probably not mixed by this time and sample may not he representative of concentrations as a whole.** Ct for this time period cannot be calculated as final value is less than a quantifiable concentration.
EXAMPLE 3
A fumigation in a well sealed enclosure hat has passed the pressure test and where the gas loss rate is low. Here the Ct product is calculated using Equation 2. This type of fumigation is only likely to occur in an extremely well sealed enclosure with a relatively non-sorptive commodity.
Readings:
|
Time (hours) |
Time step (hours) |
Concentration (g/m³) |
Ct product (g h/m³) |
Cumulative Ct (g h/m³) |
Comments |
|
0.0 |
- |
- |
- |
- |
End of gassing |
|
2.0 |
2.0 |
19.8 |
* |
0.0 |
Ct cannot be calculated |
|
4.0 |
2.0 |
19.7 |
39.5 |
39.5 |
|
|
12.0 |
8.0 |
19.0 |
154.8 |
194.3 |
|
|
24.0 |
12.0 |
18.1 |
222.6 |
416.9 |
|
|
36.0 |
12.0 |
17.2 |
211.6 |
628.6 |
|
|
48.0 |
12.0 |
16.4 |
201.6 |
830.2 |
|
* No contribution to Ct as gas most probably not mixed by this time and sample may not be representative of concentrations as a whole.
Example of calculation
Using equation 2 for the period from 2 to 4 hours
That is the Ct for the period between the observations = the time between the observation x the sum of the concentrations at the two observation times - 2.0.
RESULTS OF METHYL BROMIDE MONITORING PROGRAMME AT ARUSHA*
* Users of the PHYTOGUIDE can use these results to calculate the Ct products achieved during this fumigation, and note whether the fumigation would have been successful, or not.
Gas concentrations in mg/l recorded during fumigation of 130 tonnes maize using methyl bromide at 32 g/m3
|
24 hour exposure |
Time (hours) | ||
|
Sampling positions |
3.5 |
6 |
23 |
|
1 |
47,3 |
38,1 |
21,8 |
|
2 |
50.0 |
19.4 |
19.4 |
|
3 |
9.9 |
11.9 |
14.3 |
|
4 |
10.2 |
12.6 |
11.9 |
|
5 |
17.3 |
15.0 |
14.3 |
|
6 |
15.0 |
14.3 |
18.7 |
|
7 |
8.5 |
8.8 |
11.6 |
|
8 |
33.3 |
53.4 |
13.9 |
Graph 1 Methyl bromide fumigation Arusha (Dosage rate 32/m3)
RESULTS OF PHOSPHINE MONITORING PROGRAMME
Gas concentrations in mg/l recorded during fumigations at Arusha of 100 tonnes of maize using phosphine applied at 3 g/tonne
|
Stack 1, 5-day exposure |
| ||||||||||
|
|
Time (hours) | ||||||||||
|
Sampling Positions |
1 |
18 |
25 |
43 |
51 |
66 |
72 |
91 |
98 |
116 | |
|
1 |
0.10 |
0.70 |
1.03 |
1.66 |
1.83 |
2.15 |
2.29 |
2.33 |
2.40 |
2.33 | |
|
2 |
0.14 |
0.67 |
0.99 |
1.65 |
1.86 |
2.15 |
2.29 |
2.33 |
2.40 |
2.33 | |
|
3 |
0.01 |
0.55 |
0.86 |
1.56 |
1.77 |
2.09 |
2.24 |
2.28 |
2.40 |
2.32 | |
|
4 |
0.18 |
0.67 |
1.01 |
1.64 |
1.88 |
2.17 |
2.39 |
2.34 |
2.40 |
2.33 | |
|
5 |
0.09 |
0.75 |
1.09 |
1.64 |
1.91 |
2.18 |
2.37 |
2.34 |
2.40 |
2.35 | |
|
Stack 2, 7 day exposure |
| ||||||||||
|
|
Time (hours) | ||||||||||
|
Sampling positions |
3 |
20 |
27 |
42 |
51 |
67 |
73 |
91 |
98 |
116 |
164 |
|
1 |
0.11 |
0.84 |
1.18 |
1.80 |
2.01 |
2.21 |
2.33 |
2.31 |
2.40 |
2.25 |
1.95 |
|
2 |
0.14 |
0.82 |
1.17 |
1.83 |
2.06 |
2.24 |
2.36 |
2.33 |
2.40 |
2.26 |
1.94 |
|
3 |
0.07 |
0.80 |
1.08 |
1.83 |
2.00 |
2.25 |
2.32 |
2.34 |
2.40 |
2.23 |
1.96 |
|
4 |
0.08 |
0.76 |
0.99 |
1.73 |
1.92 |
2.25 |
2.38 |
2.40 |
2.40 |
2.29 |
1.98 |
|
5 |
0.09 |
0.86 |
1.06 |
1.85 |
2.02 |
2.25 |
2.36 |
2.40 |
2.40 |
2.30 |
1.93 |
Gas concentrations in mg/l recorded in Dar es Salaam, during fumigations of 100 tonnes of maize using phosphine applied at 2 g/tonnes
|
Stack 1, 5-day exposure |
| |||||||||
|
|
Time (hours) | |||||||||
|
Sampling positions* |
17 |
22 |
41 |
47 |
64 |
70 |
89 |
114 |
| |
|
1 |
0.77 |
1.57 |
1.71 |
1.74 |
1.56 |
1.56 |
1.38 |
1.23 |
| |
|
2 |
1.51 |
1.56 |
1.80 |
1.74 |
1.58 |
1.57 |
1.38 |
1.23 |
| |
|
3 |
1.67 |
1.69 |
1.81 |
1.73 |
1.58 |
1.57 |
1.37 |
1.23 |
| |
|
4 |
1.74 |
1.68 |
1.80 |
1.73 |
1.58 |
1.55 |
1.37 |
1.22 |
| |
|
5 |
1.64 |
1.55 |
1.82 |
1.74 |
1.59 |
1.56 |
1.38 |
1.22 |
| |
|
Stack 2, 7 day exposure |
| |||||||||
|
|
Time (hours) | |||||||||
|
Sampling positions |
18 |
23 |
42 |
48 |
65 |
71 |
90 |
115 |
129 |
161 |
|
1 |
1.22 |
1.67 |
1.57 |
1.79 |
1.64 |
1.60 |
1.41 |
1.23 |
1.10 |
0.96 |
|
2 |
1.44 |
1.74 |
1.89 |
1.82 |
1.68 |
1.64 |
1.43 |
1.26 |
1.10 |
0.97 |
|
3 |
1.59 |
1.77 |
1.90 |
1.77 |
1.68 |
1.64 |
1.43 |
1.26 |
1.10 |
0.99 |
|
4 |
1.38 |
1.72 |
1.90 |
1.82 |
1.68 |
1.64 |
1.45 |
1.27 |
1.13 |
0.99 |
|
5 |
1.54 |
1.73 |
1.92 |
1.84 |
1.69 |
1.64 |
1.46 |
1.27 |
1.14 |
0.99 |
* Sampling positions as at Arusha
Graph 2 Phosphine fumigation - Dodoma (Dosage rate 2 g/tonne)
Graph 3 Phosphine fumigation - Dar es Salaam (Dosage rate 2g/tonne)
