Introduction

Energy demand and consumption are increased due to an increase in population and economic growth. Also, the non-renewable energy resource is limited, and it harms the environment. The environmental issue is the main concern for every government in non-developed and developed countries (Atabi et al. 2014; Abanades et al. 2021).

To solve this problem, the usage of renewable energy resources is considered by many countries. Among this type of energy, biomass plays an important role due to availability and sustainability in any region of the world (Ahmadi et al. 2020; Cao et al. 2022). Due to various types of biomass regions, the local usage of biomass is widely spread (Situmorang et al. 2019; Abanades et al. 2022). This utilization can be divided into many categories such as heating (Herbes et al. 2018), electrical power production(Scarlat et al. 2018), upgrading to biomethane (Ryckebosch et al. 2011), transportation(Faaij 2006), and hydrogen production (Armor 1999). Electrical power generation from biogas resources is a relatively new technology in the world while it is more common in developed countries. This new technology includes gas turbine (GT)(Mohammadpour et al. 2021), internal combustion engine (ICE) (Nindhia et al. 2021), micro-gas turbine (MGT) (Sung et al. 2017), fuel cell (Hosseini 2020; Ding et al. 2019). Also, these systems can be used as combined heat and power (CHP) (Damyanova and Beschkov 2020), combined cooling and power (CPC)(Gholizadeh et al. 2019), and cogeneration (Movahed and Avami 2020) systems by utilizing the heat energy from the hot exhaust gas of the system (Quaschning 2019). Among these mentioned technologies, an MGT is an attractive option due to lower NOx emissions and flexibility to meet different load needs. Microturbines' size ranges are from 70 kW to over 250 kW(Mozafari et al. 2010). They can be used for different applications, especially dispersed power generation (DPG) systems to meet loads of the residential, commercial, and office buildings (Ehyaei and Bahadori 2007). Also, they have the flexibility to produce heat and cooling energies in the CHP (Ehyaei and Mozafari 2010) and CHPC states (Scarlat et al. 2018).

The application of biogas for MGT has been investigated in many research studies (Goulding and Power 2013). Renzi et al. (Renzi et al. 2017) examined the performance of a 100 kW MGT powered by syngas derived from biomass. It was shown that the overall efficiency of the MGT powered by the syngas was 27.2%., while this efficiency for natural gas was 28.6%. Furthermore, it was concluded that using the steam injection system increased electric power production, since, by variation of the injected steam from 0 to 58 g/s, the output electrical power generation changed from 100 to 129 kW. Kim et al. (Kim et al. 2017) investigated the utilization of a biogas fuel on an MGT incorporated with an organic Rankine cycle (ORC). They presented that the MGT produced 7.4MWh heat and electrical energy annually while in combination with ORC the 8.5 MWh electrical energy was produced. In a similar study, Hosseini et al. (Hosseini et al. 2016) investigated energy and exergy analyses for a system that included an ORC and MGT powered by biogas. The electrical output power of this hybrid system was 1.4 MW while 1 MW electrical power was produced by GT and the rest of 0.4 MW was generated by the ORC cycle. The results of this study showed by increasing the gas turbine efficiency from 76 to 88% the overall energy efficiency varied from 43 to 54%, and exergy efficiency varied from 36 to 47%, respectively. Sevinchan et al. (Sevinchan et al. 2019) did energy and exergy evaluations of a biogas-fueled multigeneration system. This system includes ORC, MGT, absorption chiller, water separation unit, and recovery boiler. The results indicated that the system energy and exergy efficiencies are 72.5% and 30.4%, respectively. Bo et al. (Bo et al. 2019) investigated the energy and exergy analyses of three different configurations MGT, and ORC for electrical production, MGT and ejector refrigeration cycle (ERC), and MGT + ORC + ERC for electrical and cooling energy production. They showed that R600 as a working fluid was the worst choice for the combination of MGT + ORC while it was the best choice for the combination of an MGT + ORC + ERC. Bruno et al. (Bruno et al. 2009) compared 6 configurations of MGC, an absorption chiller to produce power and cooling energies in the sewage treatment plant. They selected the best scenario. Basrawi et al. (Basrawi et al. 2015) developed an economic methodology for biogas-fueled MGT unit sizing. They found that a combination of three types of MGT has the highest energy efficiency and the system net present value (NPV) ranges between 2.6 and 3.1 million $. Basrawi et al. (Basrawi et al. 2012) investigated the combination of the biogas-fueled MGT located in the sewage treatment plant. They found that the number of units of MGT depends on the scale of the plant.

Rajaei et al. (Rajaei et al. 2017) did a feasibility study of micro-gas turbine units powered by biogas to meet the electrical, cooling, and heating energy needs of a rural building. Results showed the electricity cost produced by this system is around 0.446 US$/kWh. Furthermore, Rasul and Sajjad (Rasul et al. 2015) examined biogas-fueled MGT to cover the energy requirements of a residential building in Australia. The combination of MGT with solid oxide fuel cells (SOFC) attracts the attention of researchers in current years. Moller and Rokni (Bang-Møller and Rokni 2010) the performance of the combination of SOFC and MGT is better than each system that worked individually. They also found that (Bang-Møller et al. 2011) the combination of the SOFC, MGT, and gasifier energy efficiency is around 50.1% and it is higher than the combination of the SOFC, and gasifier (36.4%), and the combination of the MGT, and gasifier (28.1%). Wongchanapai et al. (Wongchanapai et al. 2013) did the energy and exergy analyses of direct biogas-fueled SOFC integrated by an MGT in CHP mode. They showed that increasing the compressor ratio, increases the electrical power but it decreases the useful heat generation. The combination of the SOFC, MGC, and ORC fueled by biogas is investigated by Karimi et al. (Karimi et al. 2020). Results of this research showed that the optimized system produced 329 kW electricity and 56 kW heat rate, respectively. Ebrahimi and Moradpoor (Ebrahimi and Moradpoor 2016) investigated a CHP system including SOFC, MGT, and ORC. They found that the system energy efficiency is higher than 65%. Kalina cycle (KC) was introduced as a power cycle to utilize the low-temperature energy source (Zhuang et al. 2021). The working fluid of this cycle is a mixture of ammonia and water. This cycle could be powered by different energy resources such as geothermal (Wei et al. 2015), solar (Mehrpooya et al. 2018), and waste heat in several industries(Zare et al. 2015). The usage of KC for heat recovery can be applied to various systems such as internal combustion (IC) engine (Mohammadkhani et al. 2019), diesel engine (Larsen et al. 2014), cement industry (Júnior et al. 2019), gas cycle (Feng et al. 2020). An exergoeconomic assessment of a superheated Kalina cycle powered by exhaust and coolant of a Diesel engine was performed by Mohammadkhani et al. (Mohammadkhani et al. 2019). The outcome of this study revealed that this cycle was able to generate 21.74 kW electrical power from the waste heat of a 98.9 kW Diesel engine. Also, the energy and exergy efficiencies of this cycle were calculated as 25.55% and 55.52%, respectively. Moreover, the cost of the generated power in the Kalina turbine was 15.52 cents/kWh. In another study, the assessment of a specific KC named as Split-cycle process of a KC based on exhaust heat recovery of a large marine engine was performed. The results of this study suggested that the KC with a split-cycle process obtained a thermal efficiency of 23.2% when using reheat compared to 20.8% for a conventional KC (Larsen et al. 2014). An integration hybrid of a supercritical carbon dioxide Brayton cycle and a KC powered by waste heat recovery of a marine engine was examined. The outcome of this study showed that the proposed system reduced the average annual fuel consumption of marine power generation auxiliary engines 16.6% (Feng et al. 2020).

A careful assessment of the previous research reveals that the combination of the MGT and superheated Kalina cycle (SKC) has not been investigated, while the SKC has higher efficiency with the high-temperature source. In this study, an SKC is coupled with the MGT to utilize the heat from the exhaust hot gas of the MGT. This proposed system is powered by biomass. Also, the heat produced in the gasifier is utilized to meet the heat loads of the consumers. This proposed system is evaluated by 4E analyses. In summary, this research covers the following research gap:

  • Proposing of the new cycle consists of the biogas powered by the MGT and SKC to improve the energy efficiency

  • Energy, Exergy, Economic, exergoenvironmental analysis of this cycle

The conceptual layout of the proposed cycle is shown in Fig. 1.

Fig. 1
figure 1

The conceptual layout of the proposed cycle

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Material and methods

System description

Figure 2 shows the schematic diagram of the proposed system. In this proposed system, the biomass (point 1) is reacted with air (point 2) to produce syngas (point 3) in the gasifier. The energy of the hot syngas (point 4) is utilized by water (points 21&22). Then, the syngas is pressurized with a booster compressor (BC) (point 5) and it is reacted with the air (point 7) in the combustion chamber (CC) to produce hot gas (point 8). The hot gas rotates the gas turbine (GT) and generator (G) to produce electricity (points 8&9). The heat of the exhaust hot gas is recovered in the superheater and boiler of the SKC (points 9,10,11). In the SKC, the mixture of ammonia and water is pressurized by a pump (points 20&12) and it is heated by the boiler (point 13). After the mixture goes through a separator and ammonia (point 14) and water (point 17) are separated. The ammonia superheats in the superheater (point 15) and it rotates the turbine (point 16). The water pressure (point 17) is throttled by the valve (point 18) and it is mixed with ammonia (point 19). Then, the heat of the mixture (point 19) is transferred to the cooling water (points 20, 23, and 24). The electrical power in this proposed system is produced via turbine and GT and it is consumed via a compressor (point 6&7) and pump.

Fig. 2
figure 2

The schematic diagram of the proposed system

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The following assumptions can be considered in this study (Mozafari et al. 2010; Ehyaei and Bahadori 2007; Ehyaei and Mozafari 2010; Karimi et al. 2020; Gholamian et al. 2018):

1. The system operates at the steady-state condition.

2. The heat losses in types of equipment are neglected.

3. The pressure loss in the MGT is assumed 2%.

4. The pressure loss in the SKC is ignored.

5. The ambient conditions are considered 101.103 kPa pressure and 298 K temperature.

6. The compressor and gas turbine polytrophic efficiency is assumed 85% in the MGT.

7. The heat exchanger effectiveness factor is 85%.

8. The pump and turbine polytrophic efficiencies in the SKC are 85%.

9. Pinch temperature is 20 K.

Energy modeling

The following reaction can be considered in the gasifier (Jarungthammachote and Dutta 2007; Soltani et al. 2013; Cao et al. 2020):

$$ CH_{a} O_{b} N_{c} + wH_{2} O + m \left( {O_{2} + 3.76N_{2} } \right) \to n_{{H_{2} }} H_{2} + n_{CO} CO + n_{{CO_{2} }} CO_{2} + n_{{H_{2} O}} H_{2} O + n_{{CH_{4} }} CH_{4} + n_{{N_{2} }} N_{2} . $$
(1)

\(C H_{a} O_{b} N_{c}\) shows the general chemical formula for biomass. The parameters a, b, c show the content of the H, O, and N in the biomass considering the elemental analysis. \(w\) depicts the moisture content. m displays the amount of the inlet air. Considering the mass balance in Eq. 1 for the C, H, O, and N the following relation can be obtained (Jarungthammachote and Dutta 2007; Soltani et al. 2013; Karim et al. 2021):

$$ n_{CO} + n_{{CO_{2} }} + n_{{CH_{4} }} = 1 $$
(2)
$$ 2n_{{H_{2} }} + 2n_{{H_{2} O}} + 4n_{{CH_{4} }} = a + 2w $$
(3)
$$ n_{CO} + 2n_{{CO_{2} }} + n_{{H_{2} O}} = b + w + 2m $$
(4)
$$ 2n_{{N_{2} }} = c + 7.52m $$
(5)

Also, the following equilibrium reactions are considered (Jarungthammachote and Dutta 2007; Soltani et al. 2013):

$$ C + 2H_{2} \leftrightarrow CH_{4} $$
(6)
$$ CO + H_{2} O \leftrightarrow CO_{2} + H_{2} $$
(7)

Equations 6 and 7 are related to the methane and water/gas reactions.

The related equilibrium constants are calculated by Jarungthammachote and Dutta (2007); Soltani et al. 2013; Noorpoor et al. 2016):

$$ K = \frac{{n_{{CH_{4} }} n_{{{\text{tot}}}} }}{{(n_{{H_{2} }} )^{2} }} \left( {\frac{{P_{g} }}{{P_{o} }}} \right) = \exp \left( {\frac{ - \Delta G}{{R_{u} T_{{{\text{gasifier}}}} }}} \right) $$
(8)
$$ K = \frac{{n_{{CO_{2} }} n_{{H_{2} }} }}{{n_{CO} n_{{H_{2} O}} }} = \exp \left( {\frac{ - \Delta G}{{R_{u} T_{{{\text{gasifier}}}} }}} \right). $$
(9)

P and T show the pressure and temperature. \(\Delta G\) shows the changes in the Gibbs free energy. \(R_{u}\) means the global gas constant. The mass and energy balance relations for the MGT are presented in Table 1.

Table 1 The MGT mass and energy balance relations for each component
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In Table 1, h, \(m\)and η are specific enthalpy, mass flow rate, and component efficiency. The subscripts C, CC, GT, and BC are the compressor, combustion chamber, gas turbine, and booster compressor, respectively. The combustion reaction can be obtained:

$$ C_{w} H_{x} O_{y} N_{z} + r_{a} \left( {x_{{o_{2} }} O_{2} + x_{{N_{2} }} N_{2} } \right) \to y_{{CO_{2} }} CO_{2} + y_{{N_{2} }} N_{2} + y_{{o_{2} }} O_{2} + y_{{H_{2} O}} H_{2} O $$
(10)
$$ y_{{CO_{2} }} = w $$
(11)
$$ y_{{N_{2} }} = { }r_{a} x_{{N_{2} }} + \frac{z}{2} $$
(12)
$$ y_{{H_{2} O}} = \frac{x}{2} $$
(13)
$$ y_{{O_{2} }} = r_{a} x_{{O_{2} }} + \frac{y}{2} - y_{{CO_{2} }} - \frac{{y_{{H_{2} O}} }}{2} $$
(14)
$$ r_{a} = \frac{{n_{{{\text{Air}}}} }}{{n_{{{\text{Fuel}}}} }} $$
(15)

\(x_{i}\) and \(y_{i}\) present the mass and mole fractions of i. \(r_{a}\) depicts the air/fuel ratio.

The concentration, mass, and energy balance equations for the SKC are shown in Table 2.

Table 2 The mass, concentration, and energy balance equations for the SKC
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Tables 2x denotes the ammonia mass ratio. The net power production for the MGT and total system can be calculated by:

$$ \dot{W}_{{\text{net,MGT}}} = \dot{W}_{GT} - \dot{W}_{C} - \dot{W}_{BC} $$
(16)
$$ \dot{W}_{{\text{net,sys}}} = \dot{W}_{GT} - \dot{W}_{C} - \dot{W}_{BC} + \dot{W}_{T} - \dot{W}_{P} $$
(17)

The energy efficiency for the MGT/gasifier and the system can be obtained by:

$$ \eta_{{\text{en,MGT/gasifier}}} = \frac{{\dot{W}_{{\text{net,MGT}}} + \dot{m}_{22} \left( {h_{22} - h_{21} } \right)}}{{\dot{m}_{1} LHV}} $$
(18)
$$ \eta_{{\text{en,sys}}} = \frac{{\dot{W}_{{\text{net,sys}}} + \dot{m}_{22} \left( {h_{22} - h_{21} } \right)}}{{\dot{m}_{1} LHV}} $$
(19)

LHV means the lower heating value of biomass.

Exergy modeling

A specific exergy equation is written below (Lazzaretto and Tsatsaronis 2006; Bejan et al. 1996):

$$ ex = \sum x_{i} ex_{{{\text{chi}}}} + \frac{{V^{2} }}{2} + gz + \left( {h - h_{0} } \right) - T_{0} \left( {s - s_{0} } \right) + T_{0} \sum x_{i} R_{i } \ln y_{i} $$
(20)

x and ex are defined as a mass fraction and specific exergy. z, V, and g are defined as height, velocity, and gravitational acceleration. y and s denote mole fraction and entropy. Abbreviations ch, i, and 0 present as a chemical, species, and dead state condition Tables 3 and 4 show the exergy destruction rate (EDR) equations for the MGT/gasifier, and the SKC.

Table 3 The EDR equations for each component
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Table 4 The EDR equations for the SKC
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The exergy efficiency for jlthe MGT/gasifier and the system can be obtained by:

$$ \eta_{{\text{ex,MGT/gasifier}}} = \frac{{\dot{W}_{{\text{net,MGT}}} + \dot{m}_{22} \left( {ex_{22} - ex_{21} } \right)}}{{\dot{m}_{1} e_{x1} }} $$
(21)
$$ \eta_{{\text{ex,sys}}} = \frac{{\dot{W}_{{\text{net,sys}}} + \dot{m}_{22} \left( {ex_{22} - ex_{21} } \right)}}{{\dot{m}_{1} ex_{1} }} $$
(22)

The biomass chemical exergy can be obtained by Kotas (2013):

$$ e_{ch} = \beta \left( {{\text{LHV}} + \omega h_{{{\text{fg}}}} } \right) $$
(23)
$$ \beta = \frac{{1.0438 + 0.1882 \times \left( {H/C} \right) - 0.2509 \times \left( {1 + 0.7256 \times \left( {H/C} \right)} \right) + 0.0383 \times \left( {N/C} \right)}}{{1 - 0.3035 \times \left( {N/C} \right)}} $$
(24)

hfg denotes the enthalpy of vaporization.

Economic modeling

The proposed system annual income can be obtained by Bellos et al. (2019); Tzivanidis et al. 2016):

$$ CF = Y_{{{\text{elec}}}} k_{{{\text{elec}}}} + Y_{{{\text{heating}}}} k_{{{\text{heating}}{.}}} $$
(25)

k denotes products specific costs that are equal to 0.11 (Nami et al. 2018) and 0.04 (Alizadeh et al. 2020)$/kWh for electrical and heating energy.

The system’s capital cost is calculated by Bellos et al. (2019); Tzivanidis et al. 2016; Makkeh et al. 2020):

$$ C_{0} = C_{{{\text{MGT}}}} + C_{{{\text{SKC}}}} + C_{{\text{gasifier }}} + C_{{{\text{heater}}}} $$
(26)

C shows the installation and investment costs. The operation and maintenance cost is assumed 3% of the initial cost (Bellos et al. 2019; Tzivanidis et al. 2016).

The effect of the inflation rate can be seen by Shafer (2017):

$$ C_{n} = C_{0} \left( {1 + i} \right)^{n} $$
(27)

n depicts the number of years. i shows the inflation rate (3.1%) (Statista. 2021).

The simple payback period (SPP) is obtained (Bellos et al. 2019; Tzivanidis et al. 2016):

$$ {\text{SPP}} = \frac{{C_{n} }}{CF} $$
(28)

The payback period (PP) is obtained by Bellos et al. (2019); Tzivanidis et al. 2016):

$$ {\text{PP}} = \frac{{{\text{ln}}\left( {\frac{{C_{F} }}{{CF - r.C_{n} }}} \right)}}{{{\text{ln}}\left( {1 + r} \right)}}. $$
(29)

r shows the factor of discount (3%).

The net present value (NPV) can be calculated by Bellos et al. (2019); Tzivanidis et al. 2016):

$$ NPV = CF\frac{{\left( {1 + r} \right)^{N} - 1}}{{r\left( {1 + r} \right)^{N} }} - C_{n} $$
(30)

N presents the project lifetime (25 years).

The internal rate of return (IRR) can be obtained (Bellos et al. 2019; Tzivanidis et al. 2016; Edalati et al. 2016):

$$ {\text{IRR}} = \frac{CF}{{C_{n} }}\left[ {1 - \frac{1}{{\left( {1 + {\text{IRR}}} \right)^{N} }}} \right] $$
(31)

Table5 shows the cost function for the different components.

Exergoenvironmental assessment

To investigate the system from exergy and environmental point of views, exergoenvironmental analysis can be used (Han et al. 2020; Lv et al. 2020; Shamoushaki et al. 2021). The exergoenvironment factor can be obtained by Ratlamwala et al. (2013); Midilli and Dincer 2009; Aliehyaei et al. 2015):

$$ f_{ei} = \frac{{\dot{E}_{destruction} }}{{\sum \dot{E}x_{in} }} $$
(32)

This factor shows the ratio of exergy destruction rate divided into the inlet exergy rate. This factor demonstrates that increasing this factor causes more exergy destruction rate that has negative effects on the environment (Ashari et al. 2012).

The environmental damage effectiveness index is expressed as (Ratlamwala et al. 2013; Midilli and Dincer 2009):

$$ \theta_{ei} = f_{ei} .{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\eta_{ex} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\eta_{ex} }$}} $$
(33)

The exergy stability index is obtained by Ratlamwala et al. (2013); Midilli and Dincer 2009):

$$ f_{es} = \frac{{\dot{E}_{{{\text{destruction}}}} }}{{\dot{E}x_{{{\text{output}}}} + \dot{E}_{{{\text{destruction}}}} + 1}}\theta_{ei} = f_{ei} .{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\eta_{ex} .}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\eta_{ex} .}$}} $$
(34)

Results and discussion

In this section, the results of the energy, exergy, economic, and exergoenvironmental analyses are presented. The biomass type is bean straw and its chemical formula can be shown as CH1.5611O0.7842N0.0166 (Kanagarajan 2015). For the mathematical modeling purpose, one computer program is written in the engineering equation solver (EES). For consideration of the thermodynamic properties, the functions that existed in the EES are used. The initial design data are presented in Table 5 (Mozafari et al. 2010; Gholamian and Zare 2016).

Table 5 The inlet design data
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Model validation

Since the proposed system is novel, the validation of the whole system is not achievable. So, all of the subsystems are validated individually. For validation of the gasifier, Ref. (Kanagarajan 2015) is considered. Table 6. 3 of that reference is noticed, the biomass is considered as a bean straw. The biomass feed is 0.1294 kg/s and the intake air molar is equal to 0.0006 kmole/kmole biomass. Figure 3 shows the result of comparison between the data presented in Ref. (Kanagarajan 2015) and the output data of the computer model developed for the research. The root mean square error (RMSE) is around 3.4%.

Table 6 The cost function for different components
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Fig. 3
figure 3

The result of comparison between the data presented in the ref and the computer model for the gasifier products

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For validation of the micro-gas turbine model, Ref. (Mozafari et al. 2010) is noticed. The inlet information presented in Table 2 of that reference is noticed. The electrical power production by the MGT in Ref. (Mozafari et al. 2010) is 29.9 kW. This value is calculated by the computer program around 29.05 kW. The error is around 2.8%. The SKC is validated by Ref. (Wang et al. 2019). The inlet data depicted in Table 1 of this reference are considered. Table 7 presents the comparison results between the output data of the computer model and reference (Wang et al. 2019) for the SKC.

Table 7 The SKC results comparison of the present research and reference (Wang et al. 2019)
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Energy and exergy assessment

Table 8 presents the thermodynamic properties at every point of the cycle. Figure 4 depicts the annual electrical energy and heat produced by the MGT, gasifier, and the system. The MGT produces 1.639 GWh of electrical energy annually. The heather in the line of the gasifier produces 1.724 GWh of heating energy. The 2.302 GWh of electrical energy is produced by the SKC through a year if it is added to the MGT. From Fig. 4, it can be understood that adding the SKC to the MGT increased the electrical power production by around 140%. The ratio of heat to electrical energy for the total system is 43.7%.

Table 8 The thermodynamic properties at every point of the cycle
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Fig. 4
figure 4

The annual electrical and heating energy produced by the MGT, gasifier, and total system

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The MGT and system energy and exergy efficiencies are depicted in Fig. 5. Adding the SKC to MGT fueled by biogas increases the system energy efficiency from 30.7% to 51.7%. This increase is about 69.4% which is a considerable increase. For the system exergy efficiency, a similar trend can be seen. It means that adding the SKC to the MGT increases the system exergy efficiency from 26.1% to 50.8%. This increase is about 93.1% (nearly twice). In general, the system exergy efficiency in both cases is lower than the system energy efficiency. The concept of heat (recovered in a heater located in the line of biogas) differs from the work and power. The exergy rate of the heat is always much lower than the electrical power exergy rate.

Fig. 5
figure 5

The MGT + gasifier, and system energy and exergy efficiencies

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The percent of the EDR for each component of the system and the subsystem is depicted in Fig. 6. The first circle shows the percent of the EDR in the line of biogas for the gasifier and heater. It is obvious that 57.01% of this value is related to the gasifier and the remaining part (42.99%) is related to the heater. The high percent of the gasifier EDR is related to the chemical reaction in the gasifier that normally has a considerable amount of exergy destruction rate. The second circle shows the percent of the EDR in each component of the MGT. The highest percent of EDR is occurred in the CC due to the combustion reaction that takes place in the CC. The lowest percent of the EDR belongs to the BC due to the lowest flow rate of the biogas that goes through it. The EDR of the GT is lower than the compressor, since the GT is a power production component and this production is reduced from the GT exergy destruction rate. The third circle is related to the percent of the EDR in every component of the SKC. The high percent of the EDR is related to the components that the heat transfer takes place in them (condenser (43.0%), boiler (29.4%), and SH (15.1%)). The lowest percent belongs to the pump (0.1%) due to the low mass flow rate of the working fluid. In comparison between cycles (fourth circle), the highest percent of the EDR is related to the SKC (63.65%) after it, the MGT and the gasifier line have 27.63% and 8.73% of the EDR, respectively.

Fig. 6
figure 6

The percent of the EDR in the gasifier line, MGT, SKC, and the total system

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2.3 Economic evaluation

The NPV, PP, SPP, and IRR for the system and MGT + gasifier is presented in Table 9.

Table 9 The NPV, PP, SPP, and IRR for the system, and MGT + gasifier
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Table 10 shows that adding the SKC to the MGT + gasifier improves the economic factors. This means that adding the SKC increases the initial cost but due to an increase in system electrical power production, the system's economic benefit is improved, since the cost of products overcomes the extra initial cost of the system. For example, the NPV is improved from 2.179 to 6.04 million $. Also, the PP and SPP are decreased from 9.071 and 7.84 to 4.615 and 4.25 years, respectively. The system IRR is increased from 0.1201 to 0.2341.

Table 10 The chemical formula, molecular weight, and LHV for different biomasses (Kanagarajan 2015; Basu 2010)
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Exergoenvironmental assessment

Figure 7 shows the exergoenvironmental factors (fei, θei, fes) for the MGT + gasifier and system.

Fig. 7
figure 7

The exergoenvironmental factors (fei, θei, fes) for the MGT + gasifier and system

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Considering Fig. 7, the fei is increased from 0.29 to 0.79 by adding the SKC, since the EDR is increased by adding any components. Similar to the fei, the θei is increased from 1.09 to 1.56 by adding the SKC. Adding the SKC increases the fes from 0.52 to 0.61, since this coupled system increases the system EDR and the output exergy rate, simultaneously. But the increase in system EDR overcomes the increase in output exergy rate in this system. So, this factor is increased. From the exergoenvironmental point of view, it is suitable that the fei, θei, and fes have the lowest value. So, increasing these factors is not suitable.

Extension of the study to other biomasses

For evaluation of the other biomasses, Table 10 can be considered (Kanagarajan 2015; Basu 2010). Table 10 shows the chemical formula, molecular weight, and LHV for different biomasses.

Figure 8 shows the MGT + gasifier, and system energy and exergy efficiencies for various biomasses depicted in Table 10. Among different biomasses, case 4 (Alfalfa), has the highest energy and exergy efficiencies for the MGT + gasifier and system. This biomass has the lowest LHV. Case 3 (wheat straw) has the lowest energy and exergy efficiencies for the MGT + gasifier and the system. Unlike case 4, this biomass has the highest LHV.

Fig. 8
figure 8

The MGT + gasifier, and system energy and exergy efficiencies for various biomasses

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Figure 9 shows the MGT + gasifier, and system exergoenvironmental factors (fei, θei, fes) for various biomasses depicted in Table 10. The reverse trend of Fig. 8 can be seen.

Fig. 9
figure 9

The MGT + gasifier and system exergoenvironmental factors (fei, θei, fes) for various biomasses

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Conclution

Due to the environmental pollution and depletion of non-renewable energy resources, the utilization of renewable energy resources has been considered by researchers. Among the type of renewable energy resources, biomass has a priority due to durability, stability, and accessibility in different regions of the world. Also, improving the system performance powered by biomass is another beneficial point. One method to improve the system performance is the utilization of the exhaust hot gas produced by the system. In this paper, the integration of the MGT biomass-fueled with the SKC was investigated. The energy, exergy, economic, and exergoenvironmental assessments were done about this system and the main parameters were calculated and compared. The main results of this article are:

  • This system produced 3.94 and 1.72 GWh electrical and heating energy. The ratio of heating to electrical energy was 44%.

  • Adding the SKC to MGT biomass-fueled improved the system energy and exergy efficiencies from 30.7% and 26.1% to 51.7% and 50.8%, respectively.

  • Exergoenvironmental analysis showed that adding the SKC to MGT + gasifier is not beneficial, since all of the exergoenvironmental factors were increased.

  • Adding the SKC to the MGT + gasifier decreased the PP and SPP from 9.1 and 7.8 years to 4.6 and 4.2 years.

  • The integration increased the system NPV from 2.18 to 6.04 million $.

  • In this integration, the SKC has the highest amount of exergy destruction rate.

For future research in this regard, the SKC can be placed by different cycles such as ORC or Goswami to investigate the system performance by different configurations. Also, the combination of different renewable energy resources such as biomass plus solar energy or biomass plus geothermal energy can be examined.