A method of estimation of the caloric value of the biomass. Part II – energy balance of biomass production

When establishing a plantation of energy crops, a number of decisions regarding planned technology and plant selection should be made. Using the complex calculation algorithms, it is possible to determine the amount of energy needed to establish, run and liquidate the plantation. An analysis of the technological process and the specifics of the examined plants allows to determine the set of the most important features determining the yield size, and ultimately the energy efficiency of the planned production. When conducting field production, the influence of climatic conditions should also be taken into account, for example using a hydrothermal coefficient. The most difficult element of the planned project is to determine the size of the expected yield. Using the above relationships, a mathematical model can be used which, while maintaining the range of the system variables, allows to determine the amount of the expected energy value of the crop.


INTRODUCTION
The research results presented in the literature and published studies on the methods of energy inputs calculating refer to the assessment of conducted or completed biomass production. Only sporadically, there are algorithms that allow to perform theoretical calculations of energy inputs before plantation establishing [22]. However, they contain significant simplifications concerning e.g. fuel consumption, machine performance, etc. Comprehensively developed algorithms will allow optimization of biomass production technologies, which according to many authors is a particularly important issue [9,18,19].
Optimization of technological processes is possible only after recognizing and understanding the depende-ncies occurring in them. The undertaking of optimiza-tion measures is often preceded by the construction of models. Creating the models including biological pro-cesses is a complicated problem. Currently, two groups of models are created most often. The first group contains the models concerning the relationship between the conditions of the habitat and the yielding of plants, the second group are models concerning the optimization of technological processes. Model presented by Cabelguenne [3] refers to the growth and yield of maize, sunflower, sorghum, wheat under water and nitrogen stress. Villalobos [24] developed a simulation model of sunflower cultivation using, for example, the physio-logical properties of this plant. The model is corrected on a current basis based on up-to-date meteorological data. A similar model was created by Lòpez-Cedròn [12] defining the yield of maize biomass and grains in the aspect of water deficit. The model gives good results when it is possible to adjust the input factors, in this case the watering. Complex models are also created, e.g. APSIM developed for many plant species [21]. This model makes it possible to determine the yield of plants based on their physiological features, growth conditions, e.g. soil conditions, humidity, availability of nitrogen. In addition, photoperiodism, the type of photosynthesis, etc. are taken into account. The model aims to create general principles that would allow to obtain a satisfactory result with the introduction of lower number of data.
Attempts are made to construct the models that can determine the relationship between the size of energy inputs and crop yields. The verifiability of these models is possible provided they are used in objects with controlled atmosphere, which in practice is limited to greenhouse crops [5]. Some models are also introduced in case of biomass obtaining for energy purposes. Most often, these are the IBSAL [11] and MILP models [8].
The IBSAL method concerns an application of a mathematical apparatus for the analysis and optimization of complex biomass supply systems, optimization of harvesting, storage and processing networks. It can be considered that this method optimizes, in economic and energy terms, the logistics of biomass obtaining and processing. The MILP method makes it possible to determine the conditions under which transport of waste biomass from forestry production is profitable. This depends on the dispersion of biomass sources, production volume, transport distances, biomass transport and processing manners. Similarly to the previous method, it deals with the broadly understood logistics of biomass harvesting and processing. The optimization is based on an economic or energy calculation.
Summing up, it can be concluded that the presented models allow either determining the size of the plant yield based on physiological and habitat factors, or determining the amount of energy expenditure on the logistics of biomass obtaining and processing for energy purposes. On their basis, however, it is not possible to determine the impact of energy inputs on the energy value of the crop. Therefore, it is necessary to develop a model that would allow to determine these relationships.

ENERGY BALANCE OF BIOMASS OBTAINING
When performing the energy balance of biomass production, its basic components should be determined, i.e., the energy value of the yield and the amount of energy necessary to produce it. The methods of an evaluation of crop energy value are discussed in detail in the article "A method of estimation of the caloric value of the biomass. Part I -biomass energy potential" [14].
When assessing the energy consumption of biomass production technology, a method of process analysis can be used, which involves determining a sequence of subsequent treatments and technological operations. Then, the total energy expenditure is determined [22].
In practice, it is good to divide the technological process of production into individual stages and evaluate them separately. Typical stages that can be distinguished are as follows: − establishing a plantation, − running a plantation (e.g. care, fertilization), − harvesting, − liquidation of the plantation.
The energy expenditures incurred for establishing a plantation are quite large, especially in the case of perennial crops. For this reason, they should be accounted for proportionally over all years of plantation use or all collection cycles -if the harvest occurs every few years (e.g. basket willow). A similar rule applies to energy expenditures incurred for the liquidation of plantation.
When conducting the energy evaluation of a technological treatment, it can be performed using two methods. When the planned treatment is evaluated, the tabular values for, e.g. machine performance should be used. These capacities should be selected according to the area of the field on which the treatment will be performed. The Muzalewski's study can be used in this case [13]. Such an approach generates some inaccuracies, however, it is usually sufficient at the planning stage. When assessing the actually used technology or single treatment, it is advisable to perform direct measurements. Machine performance should be determined using simplified timing. This method is more accurate, but it can only be used on existing plantations.
Some examples of algorithms used in the evaluation of agrotechnical procedures are presented below. Sewage sludge fertilization is often used in the energy plant production technology. The relationships presented by formulas (1), (2), (3) can be used when calculating the efficiency of the fertilizer set [15]: (3) The number of transport means needed to receive the crop is calculated from the formula (4) [10]: The time required to mow the crop is calculated from the formula (5): Determining the amount of energy expenditure of a given treatment, the value of energy brought in by the used aggregate is taken into account, calculating it separately for the tractor and the cooperating machine, then adding the components obtained.
The energy input of the tractor's work is calculated using the formula 6 [1], individual energy consumption indices were adopted according to Wójcicki [23] (6): The energy expenditures of the machines' operation are calculated using the formula (7) [1], unit energy consumption indices were adopted according to Wójcicki [23]: The amount of fuel consumed can be calculated using the formula (8) [7]: In practice, it is better to directly measure the amount of fuel consumed, this allows you to minimize the error. The energy expenditure of the examined technology is calculated using the formula (9) [1,23]: The values of unit energy consumption indicators, presented in Table 1, are most often taken after Wójcicki [23].
The energy value of human labor is difficult to determine. Various ways of its determination and unit indices are presented in the literature on the subject. It can be assumed in some simplification, that one hour of human labor is an equivalent of 80 MJ [6].
The summary in the assessment of the analyzed technologies is the energy efficiency index, which can be determined according to the formula (10) [4]: (10) It is most often used to compare different technologies or plants in terms of energy efficiency.
In economic practice, we are interested in the amount of energy that can be obtained from the surface unit. The parameter that applies here is the net energy value, calculated according to the formula (11) [20]: (11)

MATHEMATICAL MODEL
Summary and generalization of energy dependencies in the production of biomass is the development of mathematical models of its cultivation. The creation of models makes it possible to estimate the energy value of the crop depending on pre-determined factors. When developing the model, it is very important to correctly determine the relationships between the examined traits and the plant yield and its energy value and to select the determinants.
An example of modeling in biomass production can be the model proposed by Piskier [16] for an evaluation of the energy value of topinambour grown for fuel.
Data for model development were collected in 2005-2009. The amount of energy inputs and the energy value of topinambour yield were determined according to the method proposed by Piskier [14] and the relationships given above. Rainfall and temperature were monitored throughout the duration of the experiment. The parameter synthetically describing the relation between rainfall and temperature is a hydrothermal coefficient, calculated according to the dependence proposed by Bartoszek and Banasiewicz [2], formula (12): HT 10 .
Detailed studies showed a significant relationship between the topinambour yield and the hydrothermal coefficient value determined during the growing season, i.e., from May to October, for this reason it was included in the model.
The characteristics of the research object were adopted after Polański [17].
The research object was biomass (topinambour), the following were accepted as input values:  Table 2.
The form of the model included an effect of: energy inputs incurred for the establishment of the plantation, its fertilization, care and hydrothermal coefficient on the yield energy value formula (13): ( On the basis of theoretical considerations and the data analysis carried out, a linear-quadratic algebraic model with a quadruple interaction was adopted as the model, which after the creation and calculation of coefficients assumed the form of formula (14): An effect of selected input factors on the energy value of the crop is presented in Figure 1.