**PROCESS
OPTIMIZATION OF SAMPLING AND DETERMINING THE UNCERTAINTY ASSOCIATED WITH THE
PROPERTIES OF SOLID FUELS FOR COCOMBUSTION**

**OPTIMIZACIÓN DEL PROCESO DE
MUESTREO Y DETERMINACIÓN DE LA INCERTIDUMBRE ASOCIADA
A LAS PROPIEDADES DE COMBUSTIBLES SÓLIDOS PARA COCOMBUSTION**

**JOSE ANTONIO PAZÓ**

*Dep. Mechanical Engineering, University of Vigo, Spain , jpazo@uvigo.es*

**ENRIQUE GRANADA**

*Dep. Mechanical Engineering, University of Vigo, Spain , egranada@uvigo.es*

**ANGELES SAAVEDRA**

*Dep. Statistics, University of Vigo, Spain , saavedra@uvigo.es*

**XIAN ESTEVEZ**

*Dep. Mechanical Engineering. University of Vigo, Spain , xian@uvigo.es*

**ROBERTO COMESAÑA**

*Dep. Mechanical Engineeringl, University of Vigo, Spain , robcomesana@uvigo.es*

**Received for review June 16 ^{ th}, 2009, accepted
December 6^{ th}, 2009, final version December 21^{ th}, 2009**

**ABSTRACT**: This paper presents the process used to
determine the statistical uncertainty associated with eight different
properties of solid fuels for co-combustion tests of moisture and ash. Provides
a map of sampling to determine the sample sizes in the light of the
uncertainties that are considered acceptable. The values obtained show that
despite the heterogeneity of the fuel itself, a well-planned campaign of samples
can extrapolate the properties of the samples from the entire lot with an
uncertainty controlled and quantified.

**KEYWORDS:** co-combustion, sampling, uncertainty.

**RESUMEN: **En este trabajo se presenta
el proceso empleado para la determinación estadística de la incertidumbre
asociada a diversas propiedades de ocho combustibles sólidos para co-combustión
a partir de los ensayos de humedad y cenizas. Se establece un mapa de muestreo
que permite determinar los tamaños muestrales en función de las incertidumbres
que se consideren aceptables. Los valores obtenidos permiten afirmar que a
pesar de la heterogeneidad propia de dichos combustibles, una campaña de
muestreos bien planificada permite extrapolar las propiedades obtenidas de las
muestras a la totalidad del lote analizado con una incertidumbre controlada y
cuantificada.

**PALABRAS
CLAVE:** co-combustión,
muestreo, incertidumbre.

In today's society, air
pollution has become an issue of particular interest, the Kyoto Protocol sets limits on
emissions of greenhouse gases [1]. Measures to assess and reduce emissions
appear as a priority. Co-combustion is an alternative technique in which the
fossil fuel used in a boiler is replaced by biomass.
This option achieves the benefit of the environmental advantages of biomass
burning instead of the use of fossil fuels like coal. The technologies employed
in co-combustion are direct co-combustion, indirect co-combustion and
co-combustion in parallel [2]. In the direct co-combustion type, the biomass is
introduced into the boiler. The two fuels are burned together. Indirect
co-combustion requires the biomass to be processed prior to an independent
device of external combustion or gasification. Then, products generated by each
process and fuel are introduced into the boiler. These systems reduce the
problems that may arise in the boiler by using a fuel other than that for which
it was designed. In parallel co-combustion the biomass is burned in a separate
boiler. The main advantages of co-combustion highlighted by different authors
[2-7] are: Reduction of the percentage of CO_{2} emitted into the
atmosphere per Joule produced, because the CO_{2} emissions related to
biomass burning are considered to be neutral. Reduced emissions of SO_{2},
as a result of the low sulfur content of biomass and a positive effect on NO_{x} emissions. Reduction of the dependence on fossil fuels by using local
agricultural and forest waste. An increase in operation flexibility with respect
to plants that burn only biomass. The major drawbacks are the cost of
additional facilities and potential negative effects of biomass burning, such
as decreased performance, increased corrosion and increased fouling [2]. The
intrinsic heterogeneity of the biomass increases the complexity to define
systems that allow an objective knowledge of their technical characteristics.
The types of biomass are analyzed in the study of diverse backgrounds, variable
presentation and packaging of different forms. There are extensive published
data [8-11] on different sampling methods to provide answers to the problems
associated with the materials on which this work is based. A sampling theory
should be suitable to answer the questions of how to select a sample and how
much material must be taken [8]. It is often necessary to obtain small samples
from large lots. These great reductions require a careful sampling and sample
reduction. Some of the most important factors to consider working with solid
materials are the phenomena of segregation and stratification (fig 1) [10]. A
good sampling method should be able to get a representative sample without the
influence of these phenomena. In order to know their technical characteristics,
a study method was designed. In this method each material with different
origins, appearance or packaging, is considered as a lot.

**
Figure
1.** Different segregation states for the same sample. The left picture shows a high
degree of segregation. The image on the right shows the opposite case

The moisture content and ash of solid biomass are chosen for the study; moisture as a feature related to the material and processes for storage, as well as environmental conditions and ashes as a feature associated with the material.

The objectives of this work are find out the values of moisture and ash contents of each lot tested, as well as the uncertainty associated with the number of samples. Once the above parameters are known, the minimum number of samples required for an error and a given level of reliability will be determined. Moisture content influences the low heating value, which affects the performance of the device, and the ashes are critical to the effects of fouling and corrosion of heat exchangers [2, 12-14].

**2. METHODOLOGY **

**2.1 Materials
**Materials from
agriculture and forestry were selected for the study, covering a broad spectrum
of solid biomass which could be used as fuel in processes of co-combustion. The
materials of agricultural origin were stored in big-bags. The materials of
forest origin pellets were stored in sacks.

The materials of agricultural origin selected were: pine kernel shell, almond shells, hazelnut shell and crush olive stones. The materials of forest origin were selected as follows: Pellets of pine, oak pellets, brasica pellets and poplar pellet.

design also takes into account that these materials were supplied in sacks or pallets of big-bag. It is considered that the nominal

maximum size "d" of the material sampled is 0.02 m [15], so the tube sampler should have an increased ability to collect no less than [16]:

V_{min} = 0.05 ∙ d = 0 05 ∙
20 = 1 dm^{3} = 10^{-3} ∙ m^{3}

The tube sampler is composed of three parts (see fig 2). The first part is the outer tube which presents a series of six holes; each rotated 30 degrees to the previous hole. The holes are 80x30mm and the greatest dimension is in the direction of the axis. The second piece is the inner tube which can be rotated within the outer tube which enables the holes to be closed while the tube is inserted in the sample, and then opened when the device is in the correct position for collecting the sample. The third piece is joined onto the tip of the outer tube to facilitate the penetration of the device in the sack of material under study. This cone is removable for easy cleaning of the instrument. The design of this instrument is based on the standard [17] and the work of Pierre Gy [16].

**
Figure 2.** 3D picture and
drawing of the tube sampler

* 2.2.1 Procedure for lots in
big-bag*9 samples of
approximately 10

* 2.2.2 Procedure for lots in bags
of pellets*Samples of about 10

numbers [17]. Samples were obtained by firstly introducing the tube sampler from a corner of the bag to the opposite corner below and secondly from opposite corners in the other direction. The two samples from each bag were mixed and stored in the same bottle, thereby obtaining five bottles of each sample material.

In the case of pellets of pine and oak the process was analogous but samples from the same bag were not mixed, therefore ten sample bottles were obtained. The bottles used to store the samples are made of polypropylene, wide-necked with a lid and screw top and therefore air tight.

**2.3 Reduction of the samples
**For samples that were
subjected to laboratory tests, it was necessary to reduce their size; the
process was the same for all samples.

1. 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 there are studies that indicate that for cocombustión this particle size is sufficient even with pulverized coal [18, 19]. The olive stone samples do not receive this treatment because they are already crushed when delivered. The ground samples were stored back in the original bottles.

2. The sample is divided in similar parts using a slotted box, called a Boerner divider, which separates them into smaller samples. In Table 1 rounded average weights of the samples selected for analysis of each material are shown. Once a sample is selected, it is separated by half. One part is subjected to testing in order to determine the moisture content and the other is stored.

**Table 1.** Rounded average
weight of the samples

3. The determination of
moisture content was carried out. Dry samples were returned to the bag 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 a
particle size less than 3∙10^{-3}m,
to determine the ash content.

4. The sample obtained in the previous step is divided into two parts, one of which is sealed in a bag, and the other used to determine the ash content.

**3. TESTS **

**3.1 Moisture**

The method used is 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
have no corrosion phenomena and no moisture adsorption, are used.

The samples are weighed using the “Great Series
VXI-110” scales with 0.100 kg maximum and precision of 10^{-8}kg. The
empty tray is weighed. Then the sample is uniformly distributed over the
surface of the tray with about 10^{-3}kg/10^{-4}m^{2}.
The weighed samples of each material are simultaneously introduced in the oven
at a temperature of 105ºC. The time spent on stabilising these conditions is
180 minutes to ensure constant mass. Moisture content on wet basis (M_{ar})
is obtained by the following expression [20].

Where the different m_{i} (10^{-3} kg) indicate:

m

_{1}: Empty tray.

m_{2}: Tray and sample before drying.

m_{3}: Tray and sample after drying.

m_{4}: Reference tray at room temperature before drying.

m_{5}: Tray after drying when reference is still hot.

m_{6}: Moisture packing where applicable.

Where the different m_{i} (10^{-3} kg) indicate:

m

_{1}: empty crucible.

m_{2}: crucible and sample.

m_{3}: crucible and ash.

Where ** a_{i}** is the concentration
of component

where ** HI_{L}= CH_{L}•M_{L}/N_{F}** is
the heterogeneity invariant. Taking into account the expression of

In view of the above
expressions, it is easy to deduce that ** σ^{2} (FE)** is zero if,
and only if, some of the following two conditions holds: the sample is the
whole lot,

with ** a_{n}** the concentration of
component

Y and Z are
nondimensional parameters which characterize the size of groups and
distribution of components in the lot, respectively. Since ** Y≥0** and

Since both errors are independent, the variance
of the sampling error can be expressed as the sum of the variances: ** σ^{2}(SE)= σ^{2}(FE)+σ^{2 }(SGE**). The variance of the grouping and
segregation error cannot be calculated, but as the relationship:

Assuming that the sampling error follows a
normal distribution, i.e.: ** SE~N(0,σ(SE))**, we can ensure with a confidence level of 95%:

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

The following conclusions can be inferred from the above equation, with a confidence level of 95%:

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

2. If we set a maximum sampling error, the mass of the sample should be:

3. Regardless of the material, a direct relationship between increases in the maximum error of sampling and the mass of the sample is observed:

For example, an increase of 50% mass reduction of the sample represents a maximum sampling error of 18.35%.

4. By setting a maximum error and
considering a constant sample mass, we can ask wonder about what is the effect
of the fragment size ** F_{i}** on the sampling error.
Logic suggests that using a single piece of mass

So, the sampling error has an upper limit calculated as:

and it can be seen that when ** k** tends to infinity, the sampling
error tends to zero.

where ** a_{m}**, the concentration of component in the sample, is
obtained by averaging the concentrations of the extracts:

For the calculations shown below,
the mass of the fragment is assumed as a dimensionless unit of mass ** M_{i}=1**, so that the mass sample is
represented as sampling units

**5. RESULTS**

Table 2, shows the values of moisture in % and ash for each material tested.

**Table
2.** Values of moisture and ash in % for each material tested

The medium, maximum, and minimum value of moisture and ash content in %, are shown respectively in figure 3.

**
Figure 3.** Medium, minimum
and maximum values (%) of moisture content and ash

The moisture value observed in hazelnut shell, pine nut, almond and olive stones, is similar. These materials were presented in big-bag. The pellets presented in sacks, also have humidity values, with the exception of brassica pellets, which contain a higher percentage of humidity. The high ash content in the brassica pellets is significant. The results also show a significant uniformity in the average values of the ashes of hazelnut shells (1.10%), pinion (1.32%) and almond (1.17%). The lowest ash percentage is found in oak, olive stones and pine pellets. These values make these pellets best suited for burning in boilers. In poplar pellets, a high ash value, was found. Figure 4 illustrates the values of the variances of moisture and ash for the materials studied.

**
Figure 4.** Variances of
moisture and ash

By analyzing the value of the variances of moisture and ash obtained for the different materials, we can conclude that the sampling plans should take into account what the properties to be studied are, as well as their accuracy and reliability. For example, materials like olive stone, pellets of pine and oak have a very low variance for the ashes, but, on the other hand, have significant values for the moisture content. It can also be seen that the values obtained for the variances of moisture and ash, indicate that there are independent variables. A surprising case is that of almond shell and pine, which show very contrasting values of variance for the two properties. This fact requires different sampling plans, if we want to obtain the same accuracy and reliability in the results. As the moisture of the material depends on its own characteristics and external actions to which it was subjected, a greater value for their variances was expected, than the variances associated with the ashes. This hypothesis was confirmed in only five of the materials.

By applying the
statistical treatment described above to the sample data, the values of ** HI_{L}** shown in Table 3 are obtained.

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

With these values, it can be deduced that the maximum sampling error for a fixed sample mass and the mass of a minimum sample size has a fixed sampling error. These results are given in Tables 4 and 5, for data of humidity, and Tables 6 and 7 for details of ashes. With these Tables, it is possible to determine the maximum permissible error for a sample size, which is necessary for the determination of moisture and ash respectively (Tables 4 and 6), or alternatively, for a predetermined sample size, the maximum error made can be determined.

**Table 4.** Moisture. Minimum
sample mass, expressed as N_{m} sampling units, sampling error for a
determined maximum sampling error

**Table 5.** Moisture maximum
sampling error for a simple mass, expressed as N_{m} sampling
determined units

**Table 6.** Ashes. Minimum
sample mass, expressed as N_{m} sampling units, sampling error for a
determined maximum sampling error

**Table 7.** Ashes maximum
sampling error for a simple mass, expressed as N_{m} sampling
determined units

The sampling errors have a certain correlation with the results of variance in Figure 4. Those materials with large sample variance will, in general, have a higher sampling error. In the case of the correlation between the moisture sampling error (Tables 4-7) and sample variance (Fig. 4) it is 0.69. In the case of ash, the correlation increases to 0.85. Then, it can be deduced that the sample variance is a more qualitative than quantitative indication of the sampling errors, but in no case, can be estimated. The perfect correlation (1.00) exists between the coefficient of variation (sample standard deviation between sample mean) and the sampling error.

In determining properties of a lot, a sampling plan for each property to be studied should be designed and the sampling error that is made with the chosen sampling process should be determined. This is crucial in order to discover the subsequent propagation of error in future calculations with the set property value. In particular, biomass fuels, despite being heterogeneous materials, with an appropriate sampling procedure, the experimental error associated with different properties, can be reasonably limited. In other words, we can say that, despite the heterogeneity of the fuel itself, a well-planned campaign of samples can extrapolate the properties of the samples from the entire lot with a controlled, analyzed and quantified uncertainty.

In this work, it can be seen that, despite the fact that the sample variance of a property of a material is an indication of the level of heterogeneity, this does not accurately quantify the error committed. To do this, a determination of the statistical uncertainty associated with this property, which allows us to quantify this error precisely, is necessary.

Eight biomass fuels and a map of sampling to determine the sample sizes in the light of the uncertainties which are considered acceptable and vice versa have been established. These techniques, the sampling procedure and statistical determination, can be extrapolated to any solid material in granular form with approximately homogeneous sizes.

**7. ACKNOWLEDGMENTS**

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

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