Productivity Model of Herbal Bioenergy Cultures Depending on Biometric Indicators of Overhead Mass

The research was carried out on the territory of c. Tsenzhiv of Yamnytsya territorial community of Ivano-Frankivsk region on sod-podzolic degraded soils according to the generally accepted research methods. The productivity of miscanthus and switchgrass depends on the biometric indicators of plants, namely the height of plants and the number of stems. Correct models of miscanthus and switchgrass productivity are calculated depending on the dose of sewage sludge. For miscanthus, the correlation coefficient r = 0.952 and for switchgrass r = 0.951, which indicates a high linear relationship between plant height, number of stems and productivity. The dry matter yield in grass energy crops varies according to fertilizer application. The productivity of the agrophytocenosis of miscanthus is much higher than that of switchgrass. With the addition of sewage sludge at a dose of 40 t/ha, the dry matter yield under the same growing conditions in the agrophytocenosis of miscanthus is 12.2 t/ha, or 3.3 t/ha higher than the productivity of agrophytocenosis switchgrass. The use of composts based on SS + straw (3: 1)) – 30 t/ha + N30K55, has a significant impact on yield, providing the highest productivity of miscanthus – 13.0 t/ha, and switchgrass – 9.6 t/ha. In order to obtain stable biomass productivity of grass energy crops (miscanthus and switchgrass), it is advisable to use compost of sewage sludge and straw in a ratio of 3: 1 at a dose of 30 t/ha. Thus, two important problems are partially solved, namely increasing the productivity of energy crops and utilizing municipal waste (sewage sludge).


INTRODUCTION
Today, humanity is facing new challenges that need to be addressed urgently: the depletion of traditional energy sources, the rising cost of their production, pollution at an increasing rate due to their extraction, transportation and consumption; formation of excessive amounts of organic waste of industrial, agricultural and household origin  Turhollow 1991]. All of this has reached alarming proportions and is a factor in the impact on global climate change.
One of the ways to partially overcome such problems is to increase the share of renewable energy sources in the overall balance of energy resources, in particular raw bioenergy resources. Ukraine has significant resource potential for biomass production for energy purposes, which can allow the country to become a platform for innovative solutions in this area and attract investment. This encourages new approaches and the development of integrated technologies in the cultivation of bioenergy crops, which will make a significant contribution to strengthening energy security, improving soil condition and improving the environmental situation in the country

Analysis of recent research and publications
Almost 200 million tons of conventional fuel are consumed annually in Ukraine, while the production from natural sources is only 80 million tons. With such an imbalance between the consumption of energy raw materials from different sources, biofuels constitute the potential energy resource [Pysarenko et al. 2017 Herbaceous miscanthus and switchgrass, which are relatively new for Ukraine bioenergy cropsare characterized by a height of more than 1.5-2.5 m, a strong root to a depth of 2.0 m and more, and leave a large number of root and postharvest residues in the soil. This allows growing such crops in the areas that are not used in traditional crop production, degraded and marginalized soils, including those with low groundwater levels, ensuring not only rational land use, but also stabilizing the soil cover, preventing the spread of its degradation processes. and man-made pollution  In the initial periods of vegetation, the need of miscanthus and switchgrass plants in the application of mineral fertilizers is relatively low, due to the root system, which is significantly branched and penetrates quite deep into the soil. This allows intensively absorbing nutrients, including from deeper layers of soil. In addition, the nutrients that accumulate in the rhizomes of miscanthus can be recycled in subsequent vegetation cycles [ Under the current conditions of agricultural production in Ukraine, given the lack of organic fertilizers for traditional crop production, nontraditional types of organic raw materials can be sources of increasing organic matter resources in the soil under bioenergy crops. The waste from public utilities, namely sludge from wastewater treatment plants, which is accumulated in excess in Ukraine, can be used as fertilizer provided their environmental safety and permissible content of heavy metals, pollutants and other pollutants , Van Loocke 2012.
The introduction of sewage sludge under bioenergy crops has significant prospects and allows solving the problem of utilization of its accumulated significant reserves in municipal utilities, as well as helps to provide plants with the necessary macro-and micronutrients. After all, sewage sludge itself contains a significant amount of essential nutrients for plant growth and development [Lopushniak et al.2021a It is important to study the patterns related to the productivity formation of bioenergy crops for the introduction of various types of sewage sludge to further increase biomass production and stabilize the energy balance of the country.
The aim of the research was to study the patterns of formation of productivity of bioenergetic grass crops under different fertilizer systems in combination with sewage sludge (SS) and compost based on them, applied on degraded soils under conditions of sufficient moisture.

MATERIALS AND METHODS
The research was carried out on the territory of c. Tsenzhiv of Yamnytsya territorial community of the Ivano-Frankivsk region on sod-podzolic degraded soils according to generally accepted research methods. The content of humus in the soil was determined using the Turin method, the hydrolytic acidity and the amount of absorbed bases were determined with the Kappen method and Kirsanov's method, respectively, the content of Trace elements and heavy metals in the plant were determined using standard methods (atomic absorption). The chemical composition of the studied soil and composts with SS and straw was determined using devices based on X-ray fluorescence and magneto-optical effects. EXPERT 3L analyzer was used, which allowed controling all studied indicators with an accuracy of 0. The schemes of field experiments with culture of miscanthus and switchgrass were the same and included the following options: 1) Without fertilizers -control; 2) N 60 P 60 K 60 ; 3) N 90 P 90 K 90 ; 4) SS -20 t/ha + N 50 P 52 K 74 ; 5) SS -30 t/ha + N 30 P 33 K 66 ; 6) SS -40 t/ha + N 10 P 14 K 58 ; 7) Compost (SS + straw (3: 1)) -20 t/ha + N 50 P 16  Options 3-8 are balanced for the introduction of basic nutrients -the introduction of nitrogen, phosphorus and potassium was 90 kg/ha. Sewage sludge, which was used in the research, was taken from overflowing silt maps of Ivano-Frankivsk «Ekotechprom» in the village Yamnytsia, Ivano-Frankivsk region. Its acidity was pH -8.1. Nitrogen content -0.66%; phosphorus -2.51; potassium -2.16% (based on dry matter), and trace elements in mobile form: copper -14.9 mg/kg; cobalt -3.9; zinc -7.2 mg/ kg of dry mass of sewage sludge , Lopushniak et al. 2021a].
In addition to the direct use of sewage sludge as fertilizer, studies used the compost made from straw. Composting SS with organic raw materials, such as straw, helps to bind excess nutrients, conversion of mobile compounds of pollutants into a strongly bound form, humification of organic residues, release of excess moisture from raw materials, improving sanitation and hygiene [Batsmanova et al. (Table 1).
Under the conditions of the experiment, miscanthus was planted manually according to the scheme of 0.5×0.7 m. At the same time, rhizomes with 5-6 growth buds were used for better rooting. The depth of earning rice was 0.12-0.15 m. During the first 16-18 months, the plant usually forms a strong root system, but the closure of plants in rows does not occur. At plant heights of 0.15-0.20 m, loosening between rows was carried out to control the spread of weeds. The following year, owing to a good root system, a significant increase herbage was formed. During this period, the energy crop is very competitive with weeds and does not require additional cultivation between rows. Plant development takes place within three years During this period, the humidity of the stems decreases to 17%. It was in December that the plants were mowed, weighed and samples were taken for laboratory analysis.
Switchgrass was sown by hand with a distance between rows of 0.5 m to a depth of 0.04-0.05 m. The plant is characterized by slow shoots. Many weeds have sprouted during this time, so it was necessary to control weeds manually. Three inter-row treatments were carried out at the sites every 8 to 10 days. After the switchgrass plants reached a height of more than 0.3 m, no cultivation was carried out. The most desirable period for harvesting switchgrass as well as miscanthus is December-February. In December, the plants were mowed, productivity records were taken and samples were collected for laboratory experiments [Lopushniak et al. 2021a, Lopushniak et al. 2021b]. In the early spring, after the cessation of late frosts, aisles were treated and SS were applied according to the experimental scheme.
The area of the accounting area is 35 m 2 , the total area is 63 m 2  Depending on the weather conditions of the growing season and the use of fertilizers, the biometric indicators of miscanthus and switchgrass plants were marked by certain changes (Fig. 1).
Over the years of research, the average height of miscanthus plants ranged from 1.33 to 2.04 m. In the options where sewage sludge was added at a dose of 20-40 t/ha, plant height increased, compared to the control, by 0.17-0.42 m, respectively. With the addition of a mixture of sewage sludge and straw (3: 1)) -20 t/ha + N 50 P 16 K 67 plant height increased by 0.57 m compared to option 1, and was 1.9 m. For all years of research, the highest rate of stem height miscanthus provided a option where a mixture was used (SS + straw (3: 1)) -30 t/ha + N 30 K 55 (variant 8), which averaged 2.04 m, which is 0.7 m higher than the control option , Lopushniak et al. 2021b].
During the years of research, the average height of switchgrass plants varied from 1.10  On average, over the years of research with the use of organic fertilizers and composts based on them, the differences in the productivity of the vegetative mass of bioenergy crops were noted in the studied results (Table 2).
On average, during 2016-2020 studies, the productivity of the vegetative mass of miscanthus in the options with the addition of sewage sludge (options 4-6) was 23.5-25.1 t/ha, which is 0.5-2.1 t/ha increased by of options where fertilizers were applied at a dose of N 60-90 P 60-90 K 60-90 (options 2 and 3). Application of a mixture based on SS and straw (options 7-8) productivity of vegetative mass was 26.0-26.9 t/ha, which is 3.9-4.8 t/ha more than the results of studies of control option 1. The dry yield of miscanthus plants were 10.0-13.0 t/ha, depending on fertilizer options. With the addition of sewage sludge (options 4-6) to the soil, the dry plant yield was 10.6-12.2 t/ha, which is 0.6-2.2 t/ ha more than in the result of the studied option 1. SS together with straw (options 7-8) in the soil; the yield of dry mass of the plant was at the level of 12.8-13.0 t/ha, which is 2. According to the results of correlationregression analysis, it was found , Lopushniak et al., 2021b] that the productivity of miscanthus depends mostly on the height of plants with coefficients of determination and correlation R 2 = 0.80, r = 0.81, as well as the number of stems (R 2 = 0.77, r = 0.88) The multiple regression equation can have the following form: y = 8.6563 + 0.1328x (1) where: x is the height of plants, cm; y -yield of dry plant, t/ha; and y = 5.9968 + 0.034x (2) where: x is the number of plants, pcs/m 2 ; y -yield of dry plant, t/ha , Lopushniak et al. 2021b].
The connection between the dry mass yield of the plant, plant height and the number of miscanthus stems was proven; it was determined that these indicators are interdependent, i.e. the dry plant mass yield increases along with plant height and the dry plant mass yield increases with the number of stems per m 2 [ The results obtained during the study suggest that the height of the switchgrass plant is 1.45-1.56 m in the variants with the addition of sewage sludge at a dose of SS -40 t/ha + N 10 P 14 K 58 (option 6) and with the addition of a mixture of SS + straw (3: 1)) -30 t/ha + N 30 K 55 (option 8).
According to the results of correlationregression analysis, it was determined that the yield of switchgrass depends on the height of the plant for the coefficient of determination R 2 = 0.86 and the correlation coefficient r = 0.83 and the number of stems for the coefficient of determination R 2 = 0.89 and correlation coefficient r = 0.94 , Lopushniak et al. 2021b]. The regression equations can have the following form: y = 0.04524x + 2.1964 (plant height and productivity) (3) where: x is the height of plants, cm; y -yield of dry plant, t/ha (Fig. 3a). y = 0.13284x + 8.6563 (number of stems and productivity) (4) where: x is the number of plants, pcs/m 2 ; y -yield of dry plant, t/ha (Fig. 3b).
In order to determine the nature of multiple correlation, the methods of multiple linear regression analysis were used, the results of which are shown in Figures 4 and 5.
Thus The yield of dry mass of switchgrass plants from plant height and number of plants can be expressed by the equation: z = 6.2494 + 0.034x + 0.057y (5) where: z is the dry matter yield of switchgrass, t/ha; x -height of plants, cm; y -number of plants, pcs/m 2 . The dependence of the productivity of miscanthus plants on plant height and number of stems can be represented by the equation: z = 9.2014 + 0.1496x + 0.0056y (6) where: z is the dry matter yield of miscanthus, t/ ha; x -height of plants, cm; y -number of plants, pcs/m 2 .
The mathematical models for determining the productivity of switchgrass and miscanthus, as well as multiple regression coeffi cients are signifi cant, because the actual value of the t-criterion exceeds the theoretical value at 5% level of signifi cance , Lopushniak et al. 2021b].
As can be seen from Table 3, the coeffi cient of determination R 2 for the model of switchgrass productivity depending on the dose of sewage sludge is 0.903, and for miscanthus -0.905, which indicates that these mathematical models explain about 90 -91% variability ]. The level of statistical signifi cance (signifi cance) is equal to p = 0.002, which corresponds to the given framework of high statistical reliability, namely p <0.05. One of the most important indicators in the presented table is the average relative absolute error, which shows how much the mathematical model could be wrong when estimating performance. The absolute value of this error is 2.7% for switchgrass and 3.5% for miscanthus, which is quite an acceptable result.