Exergy Analysis of a Sugarcane Crop: A Planting-to-Harvest Approach

Abstract

The objective of this study was to conduct an exergy analysis of sun–plant interactions in sugarcane using mathematical models, aiming to estimate plant production and exergy flows and describe their photosynthetic efficiency during sugarcane cultivation. Sugarcane productivity was determined based on the Brazilian BRCANE model. The efficiency of this crop was evaluated through a simple control volume, where the exergy of solar radiation serves as the sole energy input, and the exergy of the culms and straw represents the useful exergy. The findings revealed an average second-law efficiency of 5% for sugarcane photosynthesis production from solar radiation, with an estimated harvest of approximately 16.29 kWh/m² of useful extended exergy after a year, and an estimated water consumption of 111.2 m³/ton of harvested stalks. Moreover, this study highlights that exergy efficiency varies significantly in response to seasonal changes. The method developed here can be utilized in future studies to estimate mass and energetic flows and exergy analyses.

1. Introduction

Applying the second law of thermodynamics to living beings has become the focus of several publications over the past decades [1]. The main areas of concern have been thermal comfort, pathologies, and sports performance. This article has a similar purpose but focuses on another realm: plant and biomass production. Specifically, it aimed to evaluate the exergy efficiency of sugarcane under a context of fleet electrification and changes in the global energy matrix. Brazilian society has a unique scenario for this transition as it is highly dependent on biofuels (with a lower carbon footprint than fossil fuels) [2]. Sugarcane can be used to produce sugar, ethanol, and electricity [2]. Other potential products include ammonia fertilizers [3], electricity from the correct disposal or gasification of vinasse [4], biogas [5], and beverages.

One of the main studies on plants from an exergy perspective was conducted by Attorre et al. [6] using Pinus sylvestris as a validation model. The control volume was the whole plant, and the authors considered part of the soil and atmosphere in the immediate surroundings of the plants. According to the authors, the resulting solar exergetic efficiency, ranging from 2% to 5%, depended on the age of the plants and increased as the plants matured. In a different study, Silva et al. [7] used chloroplasts as a control volume and observed that the most significant exergy destruction occurred within these organelles, presenting an efficiency of 12%. They also applied the second law of thermodynamics to the light and dark stages of photosynthesis. They segregated the stages of photosynthetic reactions, such as ATP synthesis, and considered the losses through transpiration, metabolism, and photorespiration. After studying each electrochemical reaction comprising photosynthesis, the authors obtained an overall efficiency of 3.9% considering only photosynthetically active radiation.

Another study on the subject was conducted by Saboohi et al. [8], who carried out an exergy analysis focused on soil–plant interactions and observed that they were responsible for 2.5% of the exergy waste of organisms. They also conducted several analyses of the second law of thermodynamics, applying it to the dissolution of minerals in the soil, precipitation, fertilization, the correction of soil acidity, and the reaction of some pollutants. The study concluded that the exergy expenditure of mining was responsible for 17.8% of all exergy destruction attributed to the plant–soil interaction. Furthermore, a prime study conducted by Petela [9] explored a plant from an exergy perspective by considering leaves as the control volume. This was probably the first time that several input variables, such as radiation and irradiation to and from plant leaves, were analyzed. Additionally, the author [9] examined the flow rates of water (transpiration) and chemical elements. The predicted exergy efficiency, or degree of perfection, obtained was approximately 2.6% for glucose production.

Considering this background, the present study focused on the exergy analysis of sugarcane, which is commonly used in Brazil for biofuel production (ethanol), sugar production, and electricity generation. Fully understanding plant growth is essential to comprehend how much incident solar irradiation may be transformed into valuable products, such as glucose, bagasse, and other parts used in biorefineries. With this, quality indicators are obtained in the energy conversion processes for sugarcane, considering everything from radiation to the final use. Hence, a study that may follow this article is a comparison of different forms of renewable energy (for the same area), which may promote energy planning analyses for transitioning vehicle fleets to give a better combination in the national energy matrix. This article is the first step toward creating an energy policy, since ethanol is one path to decarbonize the vehicle fleet. In addition, the analysis of these indicators can contribute to the rational use of energy in society. This manuscript compiles information and procedures for estimating mass, energy, and exergy transfers related to sugarcane cultivation. It proposes a method for estimating sugarcane transpiration (water control) and straw mass production (a useful product). The exergy analysis is a distinguishing feature of this work as a rational tool to assess the inefficiencies of the plant.

2. Thermodynamic Model

To better understand the exergy interactions between sugarcane and the sun, it is necessary to carry out a temporal analysis of plant development. Therefore, a phenomenological model is required. Several methods for assessing plant development are available in the literature. Some cover more than one type of harvest, such as the Agro-Ecological Zone, determined by Doorenbos et al. [10], whereas others were built explicitly for sugarcane, such as that proposed by Machado [11]. The BRCANE model developed by Barbieri [12] was used as the basis for this study. The BRCANE model was selected as it was developed for sugarcane, is up to date, and is continuously evolving, as shown by Barbieri et al. [13]. This model aims to assess the maximum dry matter production in sugarcane, without taking water or nutritional absence into consideration. Moreover, pests and biological damage to plants were not considered either. As a result, maximum sugarcane production was estimated, with climatic conditions and geographic positioning as the only limiting variables. The method was validated for the varieties RB72 454, NA 56-79, CB 41-76, CB 47-355, CP 51-22, Q138, and Q141, according to Barbieri [12].

Geographic positioning and climatic conditions are important factors for this model because it is possible to estimate the amount of solar radiation that reaches the ground if these data are available. The first step in computing this radiation is finding the fraction of clean days. After computing this information together with the Angström–Prescott equation (which relates solar irradiation and sun hours), the radiation on the ground (I_g) was calculated following Equation (1):

$$I_g=I_0\left(A+B\frac{n}{N}\right),$$

(1)

where I₀ is the solar radiation at the top of the atmosphere (MJ/[m² day]), A and B are the coefficients of the Angström–Prescott equation, n is the actual insolation at the analyzed location (h), and N is the photoperiod (h), which can be calculated using Equation (2). There, $\theta$ is the latitude of the analyzed location (^o) and $\delta$ is the solar declination on the analyzed day (^o).

$$N=0.1333arccos\left[-tan\left(\delta \right)tan\left(\theta \right)\right]$$

(2)

The solar declination was calculated with Equation (3):

$$\delta =23.45°sen\left(\frac{2\pi }{365}\left(d{ay}_i-80\right)\right).$$

(3)

With these data, it was also possible to calculate the fraction of the day that was cloudy (F), according to Equation (4).

$$F=\left(1-\frac{n}{N}\right).$$

(4)

The city of Campinas (São Paulo, Brazil), which was selected as the reference for this analysis, is located at a latitude of 22.82° S and presents values of A = 0.23 and B = 0.56 for the coefficients of the Angström–Prescott equation. Solar radiation at the top of the atmosphere was calculated as described by Pereira et al. [14] and is shown in Equation (5), where d is the number of days in the period.

$$\begin{gathered} I_0=37.6 \left(1+0.033cos\left(\frac{2\pi d}{365}\right)\right) \left(\left(\frac{\pi }{180}\right)arccos\left(-tan\delta tan\theta \right)sen\left(\delta \right)sen\left(\theta \right)+ \\ sen\left(-tan\delta tan\theta \right) cos \left(\delta \right) cos\left(\theta \right)\right). \end{gathered}$$

(5)

Using data from Climate-Data [15], the minimum and maximum temperature and humidity values of Campinas for each month of the year were obtained. This information is important to calculate degree-days, a concept widely used in growth and development analysis of crops, which cannot be measured solely as a function of time. For the same period, different results may be obtained because of seasonality as crops develop differently in winter and summer. In summary, the degree-days variable describes the phenomenological age of the plant and not its chronological age. For the climatic conditions of Campinas, the amount of degree-days (DD) was calculated according to Equation (6):

$$DD=\frac{{(T_{max}-T_b)}^2}{2(T_{max}-T_{min})}.$$

(6)

Equation (6) was corrected based on the length of the day, as shown in Equation (7):

$${DD}_{corr}=\frac{DD\times N}{12},$$

(7)

where T_b is the base temperature of the crop, which according to Barbieri [12] is 20 °C. The result of Equation (5) indicates the value of degree-days for a single day in the study period. Therefore, for a period of one week, DD must be multiplied by seven, whereas for a month, DD must be multiplied by the number of days in the month in question. After defining the climatic and geographic parameters, the model focuses on crop development. At the beginning of development, the crop has a minimal leaf area, which means that little radiation is absorbed and converted into biomass. As plants grow, the leaf area increases until it reaches adulthood. To analyze this behavior, the leaf area index (LAI) was proposed by Watson [16] as the ratio between the canopy leaf area and the projected area on the soil. It is a dimensionless variable that is of great importance in botany and, because it is directly related to plant development, there are different indices for each plant stage. Usually, the LAI is measured; however, for this analysis, it was necessary to estimate this index. Barbieri [12] correlated LAI values with DD values and obtained Equation (8). This function is only valid for $\Sigma DD>80$; otherwise, LAI = 0.

$$LAI=\frac{3.71}{1+e^{3.149-0.00711\cdot \Sigma DD}}-0.15.$$

(8)

Having defined the geoclimatic characteristics and the behavior of leaf growth, the BRCANE [13] model defines the carbohydrate production for a clear day (CB_c) and a cloudy day (CB_n), as shown in Equations (9) and (10), respectively. These equations were simplified, adjusted to work with radiation in MJ/m² day, and calculated in kg/ha day:

$${CB}_c=409.1N\times ln\left(\frac{1+\frac{128\cdot I_0}{1560\cdot N}}{1+\frac{155\cdot I_0}{\mathrm{34,320}\cdot N}}\right),$$

(9)

$${CB}_n=409.1N\times ln\left(\frac{1+\frac{233\cdot I_0}{7800\cdot N}}{1+\frac{41\cdot I_0}{\mathrm{24,960}\cdot N}}\right).$$

(10)

Leegood et al. [17] showed that CO₂ assimilation by plant leaves varies with temperature, motivating the insertion of a correction coefficient based on temperature for carbohydrate production (C_ct and C_nt). To correct this, the BRCANE model proposes Equations (11) and (12) for clear and cloudy days, respectively, where T is the mean period temperature (K):

$$C_{ct}=\frac{-0.29{\left(T-271\right)}^2+17.3\left(T-271\right)-186.4}{60.39},$$

(11)

$$C_{nt}=\frac{-0.29\left(T-273\right)²+17.3(T-273)-186.4}{60.39}.$$

(12)

With Equations (9)–(12), the model concludes that the maximum dry matter production (CB_max, kg/ha) is given using Equation (13):

$${CB}_{max}=d\left[F\times {CB}_n\times C_{n\left(t\right)}+\left(1-F\right)\times {CB}_c\times C_{c\left(t\right)}\right].$$

(13)

The CB_max in Equation (13) was estimated for the maximum LAI, considered by Barbieri et al. [13] as 5; therefore, it was necessary to correct this production for the LAI at the analyzed moment. This correction is expressed in Equation (14):

$$C_{LAI}=0.645 e^{-1\times {\left(\frac{\left(\sum DDcorr-900\right)}{500}\right)}^2}+0.988 e^{-{\left(\frac{\left(\sum DDcorr-1868\right)}{1080}\right)}^2}.$$

(14)

Photosynthetic capacity decreases with leaf age, regardless of crown position, light intensity, or photoperiod [18]. Therefore, it is important to correct Equation (13) for leaf age. The BRCANE model suggests Equation (15) as a correction:

$$C_i=0.6+\frac{\mathrm{73,000}}{{\Sigma DD}^{2.5}}.$$

(15)

Having established Equations (13)–(15), the model proposes a corrected carbohydrate production (CBC), given in Equation (16):

$$CBC={CB}_{max}\times C_{LAI}\times C_{i \left(cane\right)}\times C_{i \left(leaf\right)}.$$

(16)

In the case of leaves, when $\sum {DD}_{corr}<$ 127, the correction value for age is equal to 1. For values of $\sum {DD}_{corr}$ between 127 and 490, Equation (15) should be adopted. For $\sum {DD}_{corr}>$ 490, the correction value for age is 0.7567. After defining the production of carbohydrates, the model focuses on evaluating the storage of these sugars. Barbieri [12] considers that to store 1 g of dry matter, it is necessary to photosynthesize 1.27 g of carbohydrates; that is, the metabolic expenditure of the plant to synthesize 1 g of dry matter is 0.27 g. Thus, the energy efficiency of the process is 79%. Like all living beings, plants also have an energy expenditure due to basal metabolism, that is, the energy needed for the plant to remain alive. Barbieri [12] calls this metabolism Maintenance Respiration and describes it as Equation (17):

$$C_{rm}=1-R_{max}\times C_{rt}\times C_{ri},$$

(17)

where $R_{max}$ is the maximum value of respiration estimated by Medina et al. [19], who found a value of 0.023 g of dry matter for the maintenance of 1 g of live dry matter. $C_{rt}$ is the correction of respiration due to temperature. For temperatures greater than 30 °C, this index is considered equal to 1. Contrastingly, $C_{ri}$ is the correction of respiration due to plant age. When $\sum {DD}_{corr}>$ 372, this correction is considered equal to 1. These indexes are expressed as Equations (18) and (19):

$$C_{rt}=e^{-4.11+0.1383\times (T-273)},$$

(18)

$$C_{ri}=1.26\times {0.9994}^{\Sigma DD}.$$

(19)

The BRCANE model states that the accumulated dry matter at the end of the day is equal to that at the beginning of the day multiplied by the maintenance respiration correction; therefore, at the end of a period of d days, the total accumulated dry matter is given as Equation (20):

$$MST={(MS}_0-P_{straw})\times C_{rm}^d+\frac{\overline{MS}\left(C_{rm}^d-1\right)}{\left(C_{rm}-1\right)}+P_{straw},$$

(20)

where $MST$ is the total dry matter produced at the end of day $d$, ${MS}_0$ is the dry matter at the beginning of the period, calculated by dividing the CBC from Equation (16) by 1.27, $\overline{MS}$ is the daily average dry matter produced, and P_straw is the mass of the straw, as described below. After defining the plant development, it was necessary to understand crop harvesting. The model proposed by Barbieri et al. [13] divides the plant into three main structures: roots, leaves, and culms, which represent the only structure harvested. This study considered the maximum utilization of the stalk, such that no stumps remain in the field. To calculate the culm mass, it was fundamental to estimate the mass of the other structures. The mass of the leaves was estimated with Equation (21):

$$M{P}_{leaves}=\frac{0.259 MST}{1+e^{9.62-0.00881(200+\sum DD)}}.$$

(21)

Leaves were divided into two categories: green leaves and straw. The mass of the green leaves was estimated considering the LAI, as shown in Equation (8). The dry matter specific mass found in leaves by Pinto et al. [20] was 13.5 m²/kg, or 740 kg/ha; in other words, 13.5 m² of leaves are required for each kilogram of them. Thus, this article presents the calculation estimation of green leaves, and adjusted the maturity correction factor (denominator of the equation) used by Barbieri et al. [13], converging in Equation (22):

$$P_{green.leaves}=\frac{740 LAI }{1+e^{9.62-0.00881(200+\sum DD)}}.$$

(22)

Using the function describing total leaf production and green leaf production, it was possible to calculate straw production, as shown in Equation (23). The straw composition was assumed to be approximately 10% water.

$$P_{straw}=P_{leaves}-P_{green. leaves}$$

(23)

For roots, the model uses Equation (24):

$$P_{roots}=MST\times \left(-9\times {10}^{-8}{\sum DD}^2+2.17\times {10}^{-4}\sum DD\right).$$

(24)

As a final approximation, the yield in kg/ha was calculated following Equation (25):

$$P_{culms}=MST-P_{leaves}-P_{roots}$$

(25)

Using data obtained from the BRCANE [13] model, it was possible to estimate sugarcane transpiration. Petela [9] proposes that the transpiration flow of a plant is proportional to the assimilated CO₂ flow through photosynthesis, while the assimilation of CO₂ is known to be proportional to the produced carbohydrate. Simplifying Petela’s original equation and considering the atmospheric pressure as 936 mbar and the carbon concentration in the atmosphere as 414.7 ppm, the transpiration during the study period was estimated according to Equation (26), the equation proposed in this work.

$$m_{transp}=8.34CBC\left(P_{sT}-{\phi }_0{P}_{s0}\right),$$

(26)

where $m_{transp}$ is the transpiration (kg/ha) and $P_{sT}$ is the water saturated pressure on leaf temperature (mbar), assuming that the leaf temperature is 2 °C warmer than the air temperature. $P_{s0}$ is the water saturated pressure on air temperature and ${\phi }_0$ is the relative humidity. Plants use water for photosynthesis and for hydration; 70% of sugarcane mass is considered water. Additionally, the water content is proportional to the dry matter produced (MST). Therefore, the hydration and photosynthetic water ($m_{HP}$) was estimated according to Equation (27):

$$m_{HP}=2.933\left(MST-{MS}_0\right).$$

(27)

This model assumes that during the photoperiod, the temperature difference between the leaf and the environment is 2 °C, whereas the leaf temperature is equal to the air temperature outside of the photoperiod. This temperature difference determines plant convection, which was evaluated by Petela [9], who considered the heat transfer coefficient to be 3 W/m² K. The total leaf area is twice that of the canopy, so it can be calculated as 2$·$LAI. It is also assumed that temperature differences only occur when there is solar radiation; therefore, for period d, the heat transferred by convection can be estimated according to Equation (28):

$$q_{conv}=12 LAI\times n\times d.$$

(28)

The assimilation of CO₂ during the study period was related to dry matter production according to Equation (29):

$$m_{{CO}_2}=1.467\left(MST-{MS}_0\right).$$

(29)

With the data obtained from the described model, it was possible to conduct an exergy analysis for sugarcane. According to Lior and Zhang [21], the total exergy efficiency is defined as the ratio between the exergy outputs and the exergy inputs. In the case of photosynthesis, ${\eta }_{photosynthetic}$, the primary exergy input is solar radiation, $B_{solar}$. The exergy outputs consist of convection, $B_{convection}$, radiation, $B_{radiation }$, and transpiration, $B_{transpiration}$, emitted by the plant, as well as the glucose, $B_{glucose}$, produced through the photosynthetic process. Therefore, photosynthetic exergy efficiency can be expressed using Equation (30):

$${\eta }_{photosynthetic}=\frac{B_{convection}+B_{rad iation}+B_{transpiration}+B_{glucose}}{B_{solar}}.$$

(30)

Lior and Zhang [21] also defined the concept of useful exergy efficiency, which is the ratio between the useful exergy outputs and the exergy inputs. For sugarcane the useful products considered in this context are the millable structures of the plant, namely the culms and leaves. The roots are left in the soil and are considered as lost exergy, along with transpiration, radiation, and convection (Figure 1).

The daily exergy of solar radiation was calculated using Equation (31), as stated by Petela [9], where $T_0$ is the reference temperature, assumed as 293 K, and $T_1$ is the temperature of the sun, 5778 K.

$$B_{solar \left(ground\right)}=I_g\times n\times d\left[1-\frac{4}{3}\frac{T_0}{T_1}+\frac{1}{3}{\left(\frac{T_0}{T_1}\right)}^4\right].$$

(31)

As defined by Petela [9], the exergy owing to heat convection is given as Equation (32):

$$B_{convection}=12 LAI\times n\times d\times \left(1-\frac{T_0}{T_p}\right),$$

(32)

where $T_p$ is the temperature of the plant. Petela [9] defined the exergy emitted by a plant owing to radiation in w/m², making it necessary to adjust it to Wh/m², as shown in Equation (33):

$$B_{Radiation}=F_{LAI}\times n\times d\frac{5.667·{10}^{-8}}{60}\left(3{T_p}^4+T^4-4T^3{T}_p\right),$$

(33)

where $F_{LAI}$ is defined as the value of LAI when LAI < 1 and is defined as 1 when LAI > 1. The exergy related to transpiration was defined by Petela [9], as shown in Equation (34):

$$B_{transpiration}=\frac{m_{transp}}{36}\left(h-h_0-T_0\left(s-s_0\right)+\frac{R}{M_{H_{2}O}} T_0 ln\left(\frac{1}{{\phi }_0}\right)\right),$$

(34)

where $h$ and $s$ are the enthalpy and entropy of water at a given plant temperature ($T_p$), respectively, $R$ is the universal gas constant, 8.314 kJ/(kmol K), and $M_{H_{2}O}$ is the molar mass of water. In this case, it was necessary to adjust the units of measurement. Finally, Petela [9] defined the exergy related to the production of glucose converted into dry matter as follows in Equation (35):

$$B_{glucose}=\frac{CBC}{{648\times 10}^4}\left(\mathrm{2,942,570}+1409.5\left(T_0-293\right)+\mathrm{430,227}\left(\left(T_p-T_0\right)-T_0 ln\left(\frac{T_p}{T_0}\right)\right)\right)$$

(35)

After being produced via photosynthesis, glucose is transformed into other sugarcane components. As culms and straw are not entirely composed of glucose, the exergy of glucose cannot be used to describe these products. In this case, the approximation used by Palacios-Bereche et al. [22] was used, which states that the exergy of straw is 4905 Wh/kg and that of culms is 5335 Wh/kg on a dry basis at 298 K and 1 bar. Therefore, the useful exergetic efficiency, ${\eta }_{useful}$, was calculated as the exergy of the harvested products, stalk, and straw divided by the exergy of the sun (B_solar), as shown in Equation (36):

$${\eta }_{useful}=\frac{{4905P}_{leaves}+5335P_{culms }}{B_{solar}}.$$

(36)

To produce sugarcane, several agricultural operations involving cultivations are necessary. Moya et al. [23]. state that 1600 GJ are required to produce 2300 tons of stalks. This value is considered to estimate the extended exergy of sugarcane.

3. Results

Using the model described above, a simulation was carried out, obtaining the estimated maximum productivity, the week of the year when planting should be performed to achieve maximum productivity, and the consequences of altering the cultivation time. Figure 2 shows the maximum productivity for a cycle of 52 weeks, obtained by repeating the simulation while varying the week of bud break from 1 to 52.

The maximum productivity occurred when the first planting took place in week 49 of the year, with a production of 24.2 tons of dry stalks or 80.7 tons of harvested sugarcane. A simulation was subsequently performed with planting in week 49 of the year (Figure 3).

Sugarcane leaves require special attention during analysis. These were previously divided into two categories: green leaves and straw. Considering that straw has only a 10% water content, the presented model estimated a ratio of approximately 138 kg of straw produced for every ton of harvested culms. Figure 4 illustrates the behavior of sugarcane leaves during plant development.

The method used in this study did not consider water stress, so plants had the entire volume of water available for consumption. Under these conditions, plant transpiration accounted for approximately 98.7% of total water consumption. The model estimated a maximum water consumption of 111.2 L/kg of culms produced, which is equivalent to a maximum rainfall requirement of 897 mm throughout the planting cycle. Figure 5 illustrates the daily and cumulative water consumption of the simulated sugarcane crops.

By calculating the exergetic flows, it was observed that the exergy of glucose and transpiration flows contributed the most to the exergetic efficiency of photosynthesis, as shown in Figure 6. Figure 7 shows the behavior of photosynthetic exergetic efficiency during the maturation of the sugarcane crop. On average, the exergetic efficiency was 5%, reaching peaks close to 8.3%.

By analyzing the exergetic flow and disregarding all lost flows, such as transpiration, radiation, convection, and the roots left in the soil, Figure 8 was plotted. In the figure, the useful exergetic flow of sugarcane is the sum of the exergy contained in the culms and the leaves. This useful exergy reached values close to 17.86 kWh/m², representing a utilization of only 1.2% of all the radiation that reaches the ground.

The exergy required for production, according to Moya et al. [23], and considering the presented culm production, is 1.56 kWh/m². Therefore, the extended exergy of sugarcane is 16.29 kWh/m² for a 52-week cycle.

4. Discussion

The method employed in this study was very useful for simulating the best possible conditions for sugarcane production, without water stress or other issues that decrease productivity. The data obtained aligned with reality and were consistent with results reported in previous literature. A maximum stalk production of 80.7 tons/ha was observed for a 52-week cycle in Campinas, with an estimated water consumption of 111.2 m³/ton of harvested stalks.

The model, in addition to estimating the maximum potential sugarcane production, also helps determine the best time for planting to achieve maximum productivity. These values may vary depending on the chosen cultivation duration.

The relationship between straw and stalks was in accordance with the literature, 13.8%, agreeing with the results obtained by Santos et al. [24]. In addition, it properly reflects the onset of dry leaf production, which typically occurs around the 490 degree day mark, happening after the 12th week after planting.

The water consumption we found of 11.12 mm/ton was slightly higher than the 8.5 mm/ton found in a previous study [25], which was expected because it represents an estimate of the maximum consumption, given that the plant does not have water in abundance.

Evaluating the useful extended exergy obtained solely from the harvest of stalks and leaves, the balance was positive, with 16.29 kWh/m² harvested for a 52-week cycle. It is understood that this value will decrease when the leaves and stalks are sent to a biorefinery to produce biofuels and electricity; however, positive values are still expected, as the exergetic inputs not originating from sugarcane in a biorefinery are very small [26].

The average exergetic efficiency of photosynthesis was 5%, peaking at approximately 8.3%. For comparison, solar photovoltaic systems have an exergy efficiency ranging between 4% and 25% [27], with an average of approximately 11%. This means that a solar photovoltaic system can be five times more efficient than a sugarcane crop and certainly more efficient than the exergy of the ethanol generated from the same crop.

The method developed here can be used in future studies, not only for estimating the maximum production of sugarcane but also for estimating water consumption, heat exchange with the environment, and, most importantly, exergetic analyses, providing indicators of the quality of energy conversion in sugarcane metabolic processes in an energy transition scenario, serving as a tool for intelligent decision-making.

5. Conclusions

The present study proposes quality indicators for sugarcane energy conversion that can be applied to strategic decision-making regarding intelligent land use, providing data to enhance the comparison between sugarcane biofuels and other sustainable energy sources. The average exergy efficiency of a sugarcane plant is around 5.0%.