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Accurate determination of the properties of biomass is of particular interest in studies on biomass combustion or cofiring. The aim of this paper is to develop a methodology for prompt analysis of heterogeneous solid fuels with an acceptable degree of accuracy. Special care must be taken with the sampling procedure to achieve an acceptable degree of error and low statistical uncertainty. A sampling and error determination methodology for prompt analysis is presented and validated. Two approaches for the propagation of errors are also given and some comparisons are made in order to determine which may be better in this context. Results show in general low, acceptable levels of uncertainty, demonstrating that the samples obtained in the process are representative of the overall fuel composition.

Global concern about environmental protection has grown considerably in the last few decades, culminating in the Kyoto Protocol [

Several different technologies are normally applied in cofiring processes [_{2} due to the closed carbon cycle; the low sulfur content of biomass helps minimize SO_{2} emissions, and NO_{x} also shows a positive trend. Cofiring increases the operational flexibility of the process, reducing dependence on fossil fuels such as coal, but its main drawbacks are the additional cost of adapting combustion facilities and the increase in fouling and corrosion of equipment [

To avoid some of these problems, it is important properly to define the composition of the biomass used for cofiring. This is made more difficult by the high intrinsic heterogeneity of solid biofuels, so a well-defined measurement methodology must be developed to ensure declared characteristics with an acceptable, clearly defined level of uncertainty. Many reference studies have been published dealing with this issue [

The present paper presents a new methodology for solid biomass fuel sampling and error determination independently of the origin, appearance and packaging of the batch. To validate this procedure, prompt analysis of different biofuels is carried out. Moisture, volatile matter and ash content are obtained directly from a series of samplings and fixed carbon content is inferred from them. Moisture content influences the low heating value, ash is critical in the effects of fouling and corrosion [

Since fixed carbon content can be calculated as a function of moisture, volatile matter and ash content, the uncertainties of these last three properties propagate the uncertainty of fixed carbon. In this paper a new approach for approximating error propagation is derived. This expression is compared to the traditional formula that can be seen in [

All materials manipulations were developed in the same laboratory and by the same analyst. As the materials exposure after sampling to environmental conditions are less than half an hour in the worst case, we ignore the effects of environmental variations in the material properties (temperature and relative humidity variations in the laboratory are considered insignificant in such a short period of time). Laboratory instruments have been verified and calibrated in order to assure the accuracy of the experimental methodology. Errors registered during the realization of the experiments are considered to be non-systematic errors and therefore related to the precision of the experiment. These latest errors are quantified in the total sampling error.

Several different materials from agriculture and forestry were selected for the study, covering a broad spectrum of solid biomass which could be used as fuel in cofiring processes. The agricultural materials were stored in big-bags and the forestry materials, in pellet form, were stored in sacks. The materials of agricultural origin selected were pine kernel shells, almond shells, hazelnut shells and ground olive stones. The materials of forest origin were pine pellets, oak pellets, brassica pellets and poplar pellets.

Depending on the material, sampled masses vary from 320 × 10^{−3} kg to 730 × 10^{−3} kg. Fuel samples were obtained through a tube sampler, which was designed to work with all kinds of solid biomass. In its construction special attention was paid to the fact that biofuels are supplied in sacks or big-bag. The nominal maximum size “d” of the material sampled is taken as 20 mm [_{min} = 0.05 × d = 0.05 × 20 = 1 dm^{3} = 10^{−3} m^{3} [

The tube sampler comprises three parts (

The different biomasses contained in big-bags (1.5 m^{3} approximately) were Hazelnut shell, Pine nut shell, Almond shell and ground Olive stone, each biomass in its own big-bag. Nine samples of approximately 10^{−3} m^{3} volume were extracted [

The different biomasses contained in sacks (0.025 m^{3} approximately) were poplar pellets (nine sacks), brassica pellets (25 sacks), oak pellets (10 sacks) and pine pellets (24 sacks). Samples of about 10^{−3} m^{3} volume were collected from 5 selected sacks using a table of random numbers [

The samples that were laboratory tested had to be reduced in size; the process was the same for all samples:

The selected samples were completely ground in a RETSCH SM-100 grinder, using a 6 mm nominal square step sieve. This filter was chosen because this particle size is large enough to be used even for cofiring with coal [

The sample was divided into similar parts using a slotted box called a Boerner divider, which separated them into smaller samples.

The moisture content was determined. Dry samples were stored in new bags from which the sample for the ash test was obtained. Before testing, the sample was ground in a mill with IKA MF 10.2, with an impact grinding head, producing particle sizes of less than 3 × 10^{−3} m, to determine the ash content.

The dry samples obtained in the previous step were divided into two parts, one of which was used to determine the volatile matter content and the other to determine the ash content, except for hazelnut shell, oak and pine pellets samples, which were studied wet.

The method used was oven drying (Nabertherm) of the wet sample obtained by the reduction procedure described above. Aluminium trays with an interior diameter of 0.093 m which were free from corrosion and had no moisture adsorption were used.

The samples were weighed using the “Great Series VXI-110” scale, which is accurate to 10^{−8} kg. The empty tray was weighed, then the sample was uniformly distributed over the surface of the tray with less than 10^{−3} kg/10^{−4} m^{2}. The weighed samples of each material were simultaneously placed in the furnace at a temperature of 105 °C. The time spent on stabilizing these conditions was 180 minutes, to ensure constant mass. Moisture content when wet (M_{i)} was obtained by the following equation [_{i} (10^{−3} kg) indicate:
_{1}

Empty tray

_{2}

Tray and sample before drying

_{3}

Tray and sample after drying

_{4}

Reference tray at room temperature before drying

_{5}

Tray after drying when reference is still hot

_{6}

Moisture of the packing if necessary

The ash is the residual inorganic mass which remained after combustion of a biofuel sample at a controlled temperature of 550 ± 10 °C in oven air until constant mass was established [_{2} and Al_{2}O_{3} crucibles were used as recipients. Their properties include chemical stability, low mechanical strength expansion at high temperature and thermal shock resistance [^{−4} kg/10^{−4} m^{2}, the smallest amount tested was 10^{−3} kg. To weigh the samples, scales accurate to 10^{−8} kg were again used. The sample was ground and passed through the 3 MF 3 mm sieve. Before the tests, the crucibles were placed in the oven at 550 ± 10 °C for 60 min. The sample was placed in the crucible and uniformly distributed over the bottom surface. The dry sample and crucible were weighed and then put into the oven when cold in order to start the test. A heating rate of 5 °C/min to 250 °C was programmed. Once finished, the temperature was kept at 250 °C for 60 min to evaporate the volatiles. With the same heating rate, the temperature was increased to 550 ± 10 °C and held for 360 min. The ash content when dry, Ai, was calculated by [_{i} (10^{−3} kg) indicate:
_{1}

empty crucible.

_{2}

crucible and sample.

_{3}

crucible and ash.

The volatile matter content was determined using a special furnace (CARBOLITE ELF 11/68) with a maximum temperature of 1100 °C [

Crucible tips fitted perfectly and the sample was uniformly distributed over their inner surfaces. Volatile matter content was determined by weight difference, as shown in ^{−8} kg
_{1}

Mass of the empty crucible with the lid

_{2}

Mass of the crucible with lid and the sample before heating

_{3}

Mass of the crucible with lid and the sample after heating

Following [

The fundamental error is related to the constitutional heterogeneity, is never zero and is the minimum sampling error that can be made. The variance in the fundamental error can be expressed as:
_{L} is the heterogeneity invariant given by:

In view of the above expressions, it is easy to deduce that the variance of the fundamental error is zero if, and only if, the sample is the whole batch, _{m}_{L}_{i}_{L}_{F}

The segregation and grouping error is related to distributional heterogeneity. The variance in the grouping and segregation error, σ^{2} (^{2} (^{2} (

Assuming that the sampling error follows a normal distribution,

Finally, assuming that M_{m} <<<M_{L}, it is easy to get to:

Using the latest inequality some useful bounds, with a confidence level of 95%, can be inferred for the sampling error and the mass of the sample:

If the mass of the sample is constant, the sampling error has an upper bound of a maximum sampling error given by:

If a maximum sampling error is set then the mass of the sample should be:

More details about these results can be seen in [

Since the percentage of fixed carbon can be obtained directly from the other properties of the materials (

Here _{max}_{max}_{max}

On the other hand, using the linear relationship between the properties, some simple arithmetic can be used to get a new expression for the heterogeneity invariant of fixed carbon:
_{L} stands for the heterogeneity invariant and

By applying expression 6 it is easy to show the following relationship between the heterogeneity invariant of the properties:

Finally, using expression 10 a second approximation for the sampling error can be obtained:

The results of the experimental tests are compiled in this section.

A look at the variance in the properties for all the samples in

It can be concluded from an analysis of the variances in moisture and ash obtained for the different materials that the sampling methodology is somewhat dependant on the nature of the biofuel. The properties of each material need to be taken into account if adequate accuracy and reliability are to be achieved. For example, materials such as olive stones, pine pellets and oak pellets have a very low variance for ash. On the other hand, their moisture contents vary significantly. The results for almond shell and pine nut shell are surprising, with contrasting variance levels for the two properties. This calls for different sampling plans if the same accuracy and reliability levels are to be achieved in the results. As the moisture in each material depends on its inherent characteristics and on external actions to which it is subjected, greater variances were expected than for ash. This hypothesis was confirmed in only five of the materials.

A correlation analysis of the properties of the biofuels was conducted and no statistically significant correlations were found. This means that the figures for one property, say moisture, cannot be explained by the figures for the others,

For the calculations shown below, the fragment is assumed to be a dimensionless unit of mass M_{i} = 1, so that the mass sample is represented as N_{F} sampling units. To determine the accuracy of the approximations deduced in the previous section, and since the exact sampling error is impossible to determine, the figures for of _{1} (_{2} (_{max}

_{max}_{1} (

Values of _{2} (^{−1}, with a negligible p-value, which indicates a significant correlation between the maximum sampling error and this second approximation. Notice that to calculate _{1} (_{2} (

By applying the statistical treatment described above to the sample data, the values of HI_{L} shown in

Given a maximum acceptable sample error, with these tables it is possible to establish a minimum sample size for determining levels of moisture, ash, volatiles and fixed carbon, respectively with a confidence level of 95%, (

When the representative properties of heterogeneous biomass substances are determined in batches, a sampling methodology must be established for each property. This paper introduces a new sampling process and provides a statistical analysis, defining a sampling error or level of uncertainty associated with the properties measured. This is crucial for learning the subsequent propagation of error in future calculations with the set property level. The new methodology is validated by means a prompt analysis variance analysis.

Although they are heterogeneous materials, the biofuels studied here show reasonable limits. In other words, despite the heterogeneity of the fuel itself a well-planned campaign of samples can extrapolate the properties of samples from the entire batch with a controlled, analyzed, quantified level of uncertainty.

The paper also shows that sample variance cannot accurately quantify error levels. The statistical uncertainty associated with this property needs to be determined for errors to be quantified precisely. The sampling procedure and statistical determination techniques can be extrapolated to any other solid material in granular form with approximately homogeneous sizes.

Sampling errors are significantly correlated with sample variances. Thus, materials with high levels of sample variance will, in general, have higher sampling errors. In the case of moisture, the correlation coefficient between the sampling error and the sample variance is 0.69. Correlation increases to 0.79 for ash, 0.96 for volatiles and up to 0.98 for fixed carbon. It can thus be deduced that sample variance is more of a qualitative than a quantitative indicator of sampling errors but that in no case can it be estimated. Perfect correlation (1.00) is achieved between the coefficient of variation (ratio of the standard deviation to the mean) and the sampling error. This result applies to all materials and is a consequence of the mathematical expression of the heterogeneity invariant and, therefore, of the expression used to obtain the maximum sampling error.

The correlation coefficients between the maximum sampling errors obtained for the different properties were calculated. Only the correlation between moisture and ashes seemed to be significant, with a coefficient of −0.76. Further study of the data leads to the conclusion that this figure is a consequence of the atypical behaviour of the almond shell. When this single observation is omitted the coefficient changes to −0.48. In view of these coefficients, the maximum sampling error of a given property should not be approximated from the maximum sampling errors of the other properties. This might explain the lack of correlation between _{max}_{1}(

This work was funded partly by project 08DPI003303PR for the first and second author and by project PGIDIT07PXIB300191PR of the Xunta de Galicia and by the project MTM2008-03129 of the Ministry of Science and Innovation for the third author.

Different segregation states for the same sample. The picture on the left shows a high degree of segregation while the one on the right shows the opposite case.

3D illustration and technical drawing of the tube sampler.

Moisture, Ash and Volatiles variances.

Rounded-off average weight of the samples.

Hazelnut shell (Hs) | 21.7 × 10^{−3} |
8.5 × 10^{−3} |
23.1× 10^{−3} |

Pine nut shell (Pns) | 17.9 × 10^{−3} |
6.8 × 10^{−3} |
6.9 × 10^{−3} |

Almond shell (As) | 23.9 × 10^{−3} |
9.2 × 10^{−3} |
9.8 × 10^{−3} |

Ground olive stone (Gos) | 18.1 × 10^{−3} |
7.8 × 10^{−3} |
7.8 × 10^{−3} |

Poplar pellets (Pp) | 14.0 × 10^{−3} |
8.2 × 10^{−3} |
6.2 × 10^{−3} |

Brassica pellets (Bp) | 13.9 × 10^{−3} |
3.1 × 10^{−3} |
6.3 × 10^{−3} |

Oak pellets (Op) | 21.7 × 10^{−3} |
8.8 × 10^{−3} |
20.2 × 10^{−3} |

Pine pellets (Pin) | 19.0 × 10^{−3} |
10.1 × 10^{−3} |
17.8 × 10^{−3} |

Levels of moisture, ash and volatile content in the biofuels tested in %.

^{2} | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Moist | 12.264 | 12.055 | 11.961 | 12.189 | 11.876 | 12.075 | 11.998 | 12.038 | 11.934 | 12.043 | 0.01 | ||

Hs | Ash | 1.037 | 0.878 | 0.937 | 0.956 | 0.897 | 0.993 | 1.002 | 1.149 | 0.929 | 0.975 | 0.00 | |

Volati | 64.418 | 64.568 | 64.960 | 64.452 | 64.932 | 64.556 | 64.937 | 64.572 | 64.993 | 64.710 | 0.05 | ||

Moist | 12.063 | 12.102 | 12.184 | 12.419 | 12.208 | 12.695 | 12.701 | 12.683 | 12.154 | 12.357 | 0.07 | ||

Pns | Ash | 1.258 | 1.264 | 1.210 | 1.119 | 1.171 | 1.094 | 1.103 | 1.091 | 1.093 | 1.156 | 0.00 | |

Volati | 67.149 | 67.334 | 67.043 | 66.889 | 66.555 | 66.030 | 66.685 | 66.599 | 66.493 | 66.753 | 0.15 | ||

Moist | 12.621 | 12.632 | 12.562 | 12.628 | 12.533 | 12.589 | 12.643 | 12.643 | 12.498 | 12.594 | 0.00 | ||

As | Ash | 0.858 | 1.078 | 1.560 | 1.248 | 0.851 | 0.896 | 1.181 | 0.802 | 0.749 | 1.025 | 0.07 | |

Volati | 68.731 | 68.024 | 67.849 | 68.611 | 68.577 | 68.897 | 68.620 | 68.766 | 68.523 | 68.511 | 0.12 | ||

Moist | 12.629 | 12.658 | 12.812 | 12.394 | 12.416 | 12.623 | 12.698 | 12.764 | 12.595 | 12.621 | 0.01 | ||

Gos | Ash | 0.477 | 0.501 | 0.485 | 0.451 | 0.460 | 0.465 | 0.502 | 0.475 | 0.517 | 0.481 | 0.00 | |

Volati | 69.656 | 70.206 | 69.345 | 69.783 | 69.814 | 70.206 | 69.503 | 69.761 | 69.547 | 69.758 | 0.08 | ||

Moist | 8.025 | 8.044 | 7.701 | 7.816 | 8.016 | 7.920 | 0.02 | ||||||

Pp | Ash | 2.507 | 2.809 | 2.957 | 2.633 | 2.796 | 2.740 | 0.03 | |||||

Volati | 73.479 | 73.744 | 74.902 | 74.639 | 73.548 | 74.062 | 0.43 | ||||||

Moist | 10.301 | 9.907 | 10.344 | 10.005 | 10.070 | 10.125 | 0.03 | ||||||

Bp | Ash | 8.903 | 8.807 | 8.430 | 8.828 | 8.764 | 8.746 | 0.03 | |||||

Volati | 66.593 | 66.768 | 66.461 | 66.850 | 66.790 | 66.692 | 0.02 | ||||||

Moist | 7.568 | 7.515 | 7.479 | 7.742 | 7.595 | 7.549 | 7.182 | 7.302 | 7.675 | 7.453 | 7.506 | 0.02 | |

Op | Ash | 0.704 | 0.722 | 0.711 | 0.707 | 0.705 | 0.746 | 0.753 | 0.741 | 0.735 | 0.696 | 0.722 | 0.00 |

Volati | 73.239 | 72.985 | 73.812 | 72.723 | 72.968 | 72.987 | 73.310 | 73.259 | ---------- | 73.052 | 73.148 | 0.09 | |

Moist | 7.350 | 7.209 | 7.605 | 7.449 | 7.288 | 7.366 | 7.063 | 7.695 | 7.411 | 7.348 | 7.378 | 0.03 | |

Pin | Ash | 0.482 | 0.485 | 0.439 | 0.485 | 0.492 | 0.485 | 0.480 | 0.455 | 0.491 | 0.485 | 0.478 | 0.00 |

Volati | 74.757 | 74.595 | 74.908 | 74.566 | 74.708 | 74.748 | 75.081 | 74.475 | 74.415 | 74.320 | 74.657 | 0.05 |

It was not possible to calculate the fixed carbon content of the oak pellet in sample nine (Op) because the sample became corrupted during the process to determine the volatiles content. This lack of information was of course taken into account in the calculations.

Calculated fixed carbon in wet basis.

^{2} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Hs | 22.281 | 22.500 | 22.142 | 22.402 | 22.296 | 22.376 | 22.063 | 22.241 | 22.144 | 22.272 | 0.0197 | |

Pns | 19.531 | 19.300 | 19.562 | 19.573 | 20.066 | 20.181 | 19.511 | 19.628 | 20.260 | 19.735 | 0.1166 | |

As | 17.789 | 18.266 | 18.029 | 17.512 | 18.039 | 17.618 | 17.556 | 17.789 | 18.230 | 17.870 | 0.0805 | |

Gos | 17.238 | 16.635 | 17.358 | 17.372 | 17.310 | 16.706 | 17.297 | 17.001 | 17.341 | 17.140 | 0.0834 | |

Pp | 15.990 | 15.403 | 14.440 | 14.912 | 15.639 | 15.277 | 0.3723 | |||||

Bp | 14.203 | 14.519 | 14.765 | 14.317 | 14.375 | 14.436 | 0.0468 | |||||

Op | 18.489 | 18.778 | 17.998 | 18.828 | 18.732 | 18.719 | 18.755 | 18.698 | --------------- | 18.800 | 18.644 | 0.0683 |

Pin | 17.411 | 17.710 | 17.047 | 17.501 | 17.512 | 17.401 | 17.377 | 17.375 | 17.683 | 17.848 | 17.487 | 0.0500 |

Maximum sampling errors and two approximations for fixed carbon, assuming a sample size of one unit.

_{max} |
_{1}( |
_{2}( | |
---|---|---|---|

Hs | 1.65E-02 | 2.23E-01 | 3.30E-02 |

Pns | 4.52E-02 | 1.74E-01 | 6.42E-02 |

As | 4.15E-02 | 6.77E-01 | 6.44E-02 |

Gos | 4.40E-02 | 1.21E-01 | 4.99E-02 |

Pp | 9.90E-02 | 1.66E-01 | 1.14E-01 |

Bp | 3.71E-02 | 7.01E-02 | 5.31E-02 |

Op | 3.66E-02 | 9.48E-02 | 4.93E-02 |

Pin | 3.36E-02 | 1.14E-01 | 4.42E-02 |

Pearson correlation coefficients between maximum sampling error and two approximations for fixed carbon, assuming a sample size of one unit. P-values in brackets.

_{max} |
_{1}( |
_{2}( | |
---|---|---|---|

_{max} |
1 | ||

_{1}( |
−3.64E-02 (0.93) | 1 | |

_{2}( |
9.77E-01 (0.000) | 1.11E-01 (0.79) | 1 |

Values for the intrinsic heterogeneity of moisture and ash concentrations observed in different biomass materials.

_{L} | ||||
---|---|---|---|---|

Hs | 9.21E-05 | 6.38E-03 | 1.22E-05 | 3.54E-05 |

Pns | 4.28E-04 | 3.46E-03 | 3.13E-05 | 2.66E-04 |

As | 1.55E-05 | 5.97E-02 | 2.28E-05 | 2.24E-04 |

Gos | 1.11E-04 | 1.79E-03 | 1.59E-05 | 2.52E-04 |

Pp | 3.02E-04 | 3.21E-03 | 6.36E-05 | 1.28E-03 |

Bp | 2.81E-04 | 3.53E-04 | 4.67E-06 | 1.80E-04 |

Op | 4.40E-04 | 7.14E-04 | 1.58E-05 | 1.75E-04 |

Pin | 5.44E-04 | 1.13E-03 | 8.61E-06 | 1.47E-04 |

Moisture. Minimum sample mass, expressed as N_{m} sampling units, sampling error for a determined maximum sampling error.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
9.21E-05 | 4.28E-04 | 1.55E-05 | 1.11E-04 | 3.02E-04 | 2.81E-04 | 4.40E-04 | 5.44E-04 | |

Maximum error | 0.001 | 7.08E+02 | 3.29E+03 | 1.19E+02 | 8.50E+02 | 2.32E+03 | 2.16E+03 | 3.38E+03 | 4.18E+03 |

0.005 | 2.83E+01 | 1.31E+02 | 4.76E+00 | 3.40E+01 | 9.27E+01 | 8.64E+01 | 1.35E+02 | 1.67E+02 | |

0.01 | 7.08E+00 | 3.29E+01 | 1.19E+00 | 8.50E+00 | 2.32E+01 | 2.16E+01 | 3.38E+01 | 4.18E+01 | |

0.05 | 2.83E-01 | 1.31E+00 | 4.76E-02 | 3.40E-01 | 9.27E-01 | 8.64E-01 | 1.35E+00 | 1.67E+00 |

Moisture. Maximum sampling error for a sample mass, expressed as N_{m} sampling units, fixed.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
9.21E-05 | 4.28E-04 | 1.55E-05 | 1.11E-04 | 3.02E-04 | 2.81E-04 | 4.40E-04 | 5.44E-04 | |

Sample size | 1 |
2.66E-02 | 5.73E-02 | 1.09E-02 | 2.92E-02 | 4.81E-02 | 4.65E-02 | 5.82E-02 | 6.47E-02 |

10 |
8.41E-03 | 1.81E-02 | 3.45E-03 | 9.22E-03 | 1.52E-02 | 1.47E-02 | 1.84E-02 | 2.04E-02 | |

100 |
2.66E-03 | 5.73E-03 | 1.09E-03 | 2.92E-03 | 4.81E-03 | 4.65E-03 | 5.82E-03 | 6.47E-03 | |

200 | 1.88E-03 | 4.05E-03 | 7.71E-04 | 2.06E-03 | 3.40E-03 | 3.29E-03 | 4.11E-03 | 4.57E-03 |

Ash. Minimum sample mass, expressed as N_{m} sampling units, sampling error for a determined maximum sampling error.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
6.38E-03 | 3.46E-03 | 5.97E-02 | 1.79E-03 | 3.21E-03 | 3.53E-04 | 7.14E-04 | 1.13E-03 | |

Maximum error | 0.001 | 4.90E+04 | 2.66E+04 | 4.58E+05 | 1.38E+04 | 2.47E+04 | 2.71E+03 | 5.49E+03 | 8.66E+03 |

0.005 | 1.96E+03 | 1.06E+03 | 1.83E+04 | 5.52E+02 | 9.88E+02 | 1.08E+02 | 2.19E+02 | 3.47E+02 | |

0.01 | 4.90E+02 | 2.66E+02 | 4.58E+03 | 1.38E+02 | 2.47E+02 | 2.71E+01 | 5.49E+01 | 8.66E+01 | |

0.05 | 1.96E+01 | 1.06E+01 | 1.83E+02 | 5.52E+00 | 9.88E+00 | 1.08E+00 | 2.19E+00 | 3.47E+00 |

Ashes. Maximum sampling error for a sample mass, expressed as N_{m} sampling units, fixed.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
6.38E-03 | 3.46E-03 | 5.97E-02 | 1.79E-03 | 3.21E-03 | 3.53E-04 | 7.14E-04 | 1.13E-03 | |

Sample size | 1 |
2.21E-01 | 1.63E-01 | 6.77E-01 | 1.17E-01 | 1.57E-01 | 5.21E-02 | 7.41E-02 | 9.31E-02 |

10 |
7.00E-02 | 5.16E-02 | 2.14E-01 | 3.71E-02 | 4.97E-02 | 1.65E-02 | 2.34E-02 | 2.94E-02 | |

100 |
2.21E-02 | 1.63E-02 | 6.77E-02 | 1.17E-02 | 1.57E-02 | 5.21E-03 | 7.41E-03 | 9.31E-03 | |

200 | 1.57E-02 | 1.15E-02 | 4.79E-02 | 8.30E-03 | 1.11E-02 | 3.68E-03 | 5.24E-03 | 6.58E-03 |

Volatiles. Minimum sample mass, expressed as N_{m} sampling units, sampling error for a determined maximum sampling error.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
1.22E-05 | 3.13E-05 | 2.28E-05 | 1.59E-05 | 6.36E-05 | 4.67E-06 | 1.58E-05 | 8.61E-06 | |

Maximum error | 0.001 | 9.34E+01 | 2.40E+02 | 1.76E+02 | 1.22E+02 | 4.89E+02 | 3.59E+01 | 1.22E+02 | 6.62E+01 |

0.005 | 3.74E+00 | 9.61E+00 | 7.02E+00 | 4.88E+00 | 1.96E+01 | 1.44E+00 | 4.87E+00 | 2.65E+00 | |

0.01 | 9.34E-01 | 2.40E+00 | 1.76E+00 | 1.22E+00 | 4.89E+00 | 3.59E-01 | 1.22E+00 | 6.62E-01 | |

0.05 | 3.74E-02 | 9.61E-02 | 7.02E-02 | 4.88E-02 | 1.96E-01 | 1.44E-02 | 4.87E-02 | 2.65E-02 |

Volatiles. Maximum sampling error for a sample mass, expressed as N_{m} sampling units, fixed.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
1.22E-05 | 3.13E-05 | 2.28E-05 | 1.59E-05 | 6.36E-05 | 4.67E-06 | 1.58E-05 | 8.61E-06 | |

Sample size | 1 |
9.66E-03 | 1.55E-02 | 1.32E-02 | 1.10E-02 | 2.21E-02 | 5.99E-03 | 1.10E-02 | 8.13E-03 |

10 |
3.06E-03 | 4.90E-03 | 4.19E-03 | 3.49E-03 | 6.99E-03 | 1.89E-03 | 3.49E-03 | 2.57E-03 | |

100 |
9.66E-04 | 1.55E-03 | 1.32E-03 | 1.10E-03 | 2.21E-03 | 5.99E-04 | 1.10E-03 | 8.13E-04 | |

200 | 6.83E-04 | 1.10E-03 | 9.37E-04 | 7.81E-04 | 1.56E-03 | 4.24E-04 | 7.80E-04 | 5.75E-04 |

Fixed carbon. Minimum sample mass, expressed as N_{m} sampling units, sampling error for a determined maximum sampling error.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
3.54E-05 | 2.66E-04 | 2.24E-04 | 2.52E-04 | 1.28E-03 | 1.80E-04 | 1.75E-04 | 1.47E-04 | |

Maximum error | 0.001 | 2.72E+02 | 2.04E+03 | 1.72E+03 | 1.94E+03 | 9.81E+03 | 1.38E+03 | 1.34E+03 | 1.13E+03 |

0.005 | 1.09E+01 | 8.18E+01 | 6.88E+01 | 7.75E+01 | 3.92E+02 | 5.52E+01 | 5.37E+01 | 4.53E+01 | |

0.01 | 2.72E+00 | 2.04E+01 | 1.72E+01 | 1.94E+01 | 9.81E+01 | 1.38E+01 | 1.34E+01 | 1.13E+01 | |

0.05 | 1.09E-01 | 8.18E-01 | 6.88E-01 | 7.75E-01 | 3.92E+00 | 5.52E-01 | 5.37E-01 | 4.53E-01 |

Fixed carbon. Maximum sampling error for sample mass, expressed as N_{m} sampling units, fixed.

Hs | Pns | As | Gos | Pp | Bp | Op | Pin | ||
---|---|---|---|---|---|---|---|---|---|

_{L} |
3.54E-05 | 2.66E-04 | 2.24E-04 | 2.52E-04 | 1.28E-03 | 1.80E-04 | 1.75E-04 | 1.47E-04 | |

Sample size | 1 |
1.65E-02 | 4.52E-02 | 4.15E-02 | 4.40E-02 | 9.90E-02 | 3.71E-02 | 3.66E-02 | 3.36E-02 |

10 |
5.21E-03 | 1.43E-02 | 1.31E-02 | 1.39E-02 | 3.13E-02 | 1.17E-02 | 1.16E-02 | 1.06E-02 | |

100 |
1.65E-03 | 4.52E-03 | 4.15E-03 | 4.40E-03 | 9.90E-03 | 3.71E-03 | 3.66E-03 | 3.36E-03 | |

200 | 1.17E-03 | 3.20E-03 | 2.93E-03 | 3.11E-03 | 7.00E-03 | 2.63E-03 | 2.59E-03 | 2.38E-03 |