Thermodynamic evaluation and optimization of a cogeneration energy system integrated with steam network

Introduction

Today, energy demand is growing at a considerable rate worldwide. Conventionally, fossil fuels have been the primary source for meeting this ever-growing demand (Ghazizadeh, Ghorbani, Shirmohammadi, Mehrpooya, & Hamedi, 2018). As a result of these fuels' utilization, the enormous volume of greenhouse gases is considered to be amongst the most dangerous threats to the environment (Bahram Ghorbani, Roshani, Mehrpooya, Shirmohammadi, & Razmjoo, 2020; Hamedi, Shirmohammadi, Ghorbani, & Sheikhi, 2015; SHEIKHI, GHORBANI, SHIRMOHAMMADI, & HAMEDI, 2014).  The data published in World Energy Outlook, 2019 (Mohn & Policy, 2020), greenhouse gas (GHG) is mostly released by the power sector, which solely releases over 40 percent of energy-related carbon dioxide (CO₂) emissions. In particular, 30% of the CO₂ emission related to the energy sector is released by power plants burning coal. Therefore, a tremendous amount of effort is put by energy researchers into an efficient and clean energy system that is based on renewable energy and reduces the production of CO₂ emissions. 

Solar, wind, hydro, biomass and bio-energy, geothermal, and other renewable energy resources can be utilized for a clean and sustainable generation of electricity (Ebadollahi et al., 2020; B Ghorbani, Shirmohammadi, Mehrpooya, & Assessments, 2020; Kolahi, Nemati, & Yari, 2018; Ranjbar, Nemati, & Kolahi, 2018). Because of the belief that biomass is carbon-neutral fuel, it is one of the most favorable alternatives to fossil fuels (Gustavsson & Svenningsson, 1996). Because of the everlasting nature of replanting, biomass is considered to be a renewable energy source. In recent years, the biomass gasification process has seen several advancements, and now it can be used to convert solid biomass to gaseous fuels utilized for power generation (Ebrahimi, Ghorbani, & Ziabasharhagh, 2020; Ebrahimi, Ghorbani, Ziabasharhagh, & Rahimi, 2020). Generally, there are two methods for consuming biomass energy: Combustion and Gasification. In combustion, a combustor is used to combust solid biomass, and the heat in the combustion products is utilized for operating power cycles, organic Rankine cycle (ORC), and gas turbine (GT) cycle, etc. Gasification is the second method, which through it the solid biomass convert into syngas, a combustible gas mixture. Hydrogen (H₂), carbon monoxide (CO), methane (CH₄), water vapor (H₂O), carbon dioxide (CO₂), and nitrogen (N₂) are among the main components of syngas (Hu et al., 2016). Afterward, this syngas, also called producer gas, is used in different power systems as fuel. The gasification method is believed to be much more efficient than the combustion process (Niasar, Ghorbani, Amidpour, & Hayati, 2019; Shariati Niasar et al., 2017). Because of the advantages of biomass-fueled cogeneration energy systems, today, these systems are considered one of the most prominent options for meeting the demands of power and heating/cooling in an efficient and environmentally friendly manner. One of the essential advantages of cogeneration is power, heating or cooling, from a solo source simultaneously (Pirmohamadi, Ghaebi, Ziapour, & Ebadollahi, 2021; Rostamzadeh, Ebadollahi, Ghaebi, Shokri, & management, 2019). The heating can be achieved by utilizing waste energy from the prime mover exit which can be used in hot water and steam production and also space heating.

Fuel cells have advantages that have made favorable options for power generating. In addition to high efficiency, the fuel's chemical energy directly converses to power without any necessary combustion. High-temperature fuel cells are the most favorable option for designing biomass gasification-based energy systems (Radenahmad et al., 2020) due to the similarity of the high-performance cell's operational temperature to the biomass gasification process (Archer & Steinberger-Wilckens, 2018). Among this type of fuel cells, solid oxide fuel cell (SOFC) is a high potential (Tafazoli, Shakeri, Baniassadi, & Babaei, 2017) and an appropriate option that can be efficiently integrated with a gas turbine (GT), steam turbine (ST), organic Rankine cycle (ORC), Kalin Cycle (KC), Stirling engine, supercritical CO₂ (s-CO₂) cycle, and other energy conversion technologies. Besides, SOFC yields byproducts like heat, which can be utilized by cogeneration facilities.

SOFC/GT systems have been studied by researchers in several papers that have analyzed the performance of these systems considering different fuels, temperature levels, and arrangements. For example, Cheddie et al. (Cheddie, 2011) integrated SOFC and a gas turbine power plant capable of 10 MW power generation in an indirect manner that resulted in 4.65 ¢/kWh per—unit of energy cost. They also carried out the same analysis using semi-direct coupling and anode recycling (Cheddie & Murray, 2010). In 2008, Akkaya et al. (Akkaya, Sahin, & Huseyin Erdem, 2008) conducted a thermodynamical simulation of SOFC and CHP turbines under stable conditions. In another study, Akkaya and Sahin (Akkaya & Sahin, 2009) devised a steady-state mathematics model of integrating solid-state oxide fuel and organic Rankine cycle (ORC). In 2014, Calindro et al. (Caliandro, Tock, Ensinas, & Marechal, 2014) analyzed a SOFC/GT system from a multi-objective thermal economy perspective. Improving electricity efficiency and minimizing investment costs were among the objectives of this research. According to the results, the SOFC/GT system's power generation efficiency is up to 50%, which is high, but the SOFC/GT system still has a high exhaust temperature. Significant progress has been made in the thermal efficiency and economy of SOFC/GT systems, but still, the exhaust gas from SOFC/GT is not utilized appropriately. Using this exhaust gas, a waste heat recovery cycle helps to improve system efficiency. The system's total energy conversion efficiency can be improved by recovering the SOFC/GT waste heat (Larminie & Dicks, 2000; Meng et al., 2017). In another study, Ghorbani and Khoshgoftar Manesh analyzed an IRSOFC-GT-ORC Hybrid System from the thermodynamic, exergetic, exergoeconomic, and advanced energetic points of view. The results showed that net power and overall cycle efficiency increased by 1.1 MW and 7.7% compared to the basic SOFC-GT comparison. Exergy efficiency also was increased by 3.6 % rather than the initial base case (S. Ghorbani & Khoshgoftar Manesh, 2020).

There are two primary purposes for using waste heat in power plants: heating liquid water and heating coal in gas units. Reducing this heat results in increasing efficiency and reducing emissions (Iglesias Garcia, Ferreiro Garcia, Carbia Carril, & Iglesias Garcia, 2018; Moradi et al., 2019). Many researchers have been done about reducing the heat dissipated in different units of an energy system in recent years. This waste heat can be a result of combustion in the GT (Kadhum, 2016). It also can be a result of reducing heat produced in combustion engines. The waste heat is recognized as low-grade waste heat, and its reduction can lead to a decrease in environmental pollution and lower carbon dioxide and similar gasses release. Reducing fuel consumption can also result in a decrease in the emission rate of pollutants. The utility part is one of the crucial parts of any process system. The generation of power is necessitated for the process, and steam production occurs at different levels of the process (Arghandeh, Amidpour, & Khodaei, 2009). 

The optimization of the solar heat and power (CHP) system has become the subject of further research in recent years (Bahram Ghorbani et al., 2019). For example, the Cuckoo Search algorithm is utilized for optimizing decision variables (M. H. Khoshgoftar Manesh & Ameryan, 2016). As a matter of fact, fuel consumption reduction results in decreasing both costs and environmental emissions. A steam grid is used to produce the power and steam necessitated for the process. Steam efficiency will have effects on the efficiency of the whole process. Also, an accurate site utility design can lead to a reduction in investment costs and also saving more energy. For example, Khoshgoftar Manesh and Noori Shemirani (Mohammad Hasan Khoshgoftar Manesh & Noori Shemirani, 2017) simulated and optimized utilities in an oil refinery concerning exergetic, exergoeconomic, and environmental analyses. According to their study results, the annual cost was declined to 42% in the best scenario.

Several studies have been made about reducing low-temperature waste in units previously mentioned (Wang, Wang, & Zhang, 2012). The amount of waste heat dissipated from industrial units reduces, resulting in saving energy and preventing further environmental pollution (Varbanov, Doyle, & Smith, 2004). Zheng et al. (Zheng et al., 2017) conducted a feasibility study on a low-grade heat recovery cycle in the petrochemical industry. According to statistics, low-temperature heating comprises 50% of heat dissipation from each industrial sector (Jouhara et al., 2018). Using the Rankine cycle for recovering waste heat in various industrial sectors is one of the first solutions that can be proposed. However, it is not economically feasible to recover low-temperature waste using a Rankine cycle (Johnson & Choate, 2008).

According to the given literature review, the integration of renewable resources with industrial steam networks has not been thoroughly investigated. Thus, In this study, a biomass-based cogeneration scheme integrated with a steam network is assessed and evaluated from the thermodynamic viewpoint, and afterward, an optimization study is performed to find the optimum design conditions.

2. Systems description

In Fig. 1, the layout of the proposed integrated cogeneration system is depicted. According to this figure, the devised set-up encompasses these components: a BG, a SOFC module, a GT cycle, and an SN. The following describes each unit:

In BG, biomass is fed into the gasifier at ambient condition (state 5). A compressor is used to boost the low-pressure steam extracted from the SN to the necessitated high-pressure steam. Simultaneously, a fragment of the compressed air (state 3) is led into the gasifier also. After the syngas is generated (state 6), which is a result of gasification processes in the gasifier, it splits into two streams: the first stream is guided into the combustion chamber (CC) of the GT cycle (state 8), at the same time as the second one is injected into SOFC (state 7).

In the SOFC module, a recuperator is utilized for preheating the rest of the compressed air at state 4. Afterward, this preheated air is guided into the cathode part of the SOFC module (state 9). Simultaneously, the syngas generated in the gasifier is directed to the anode part of the module and then being utilized in the methane reforming process for producing CO and enriching H₂. A reaction occurs between CO and steam during the water shifting process, and then it transforms into CO₂. It is worthy to note that through moving from cathode to anode, ions of O₂ are combined with H_2, which results in the generation of steam. Meantime, electricity is generated through the movement of electrons from the anode toward the cathode. A percentage of the released heat during the electrochemical reaction is utilized to satisfy the direct internal reforming process's thermal demands. The rest of the heat mentioned earlier is used to warms up the residual reactants and the FC (fuel cell) products. When the electrochemical reaction comes to an end, the unreacted syngas and the surplus air are released from the anode and cathode compartments, respectively. Afterward, these two released gases enter the combustion chamber. The flue gas exiting from the combustion chamber (state 12) is utilized to preheat the air stream and then is guided into the gas turbine (state 13).

In the GT cycle, an air compressor (AC) is used to compress the air at ambient pressure (state 1). Afterward, the produced compressed air splits into two flows: The first one is guided into the aforementioned preheating process using a recuperator and then goes into the SOFC module, while the second flow part is guided into the gasifier. For providing shaft power of the AC, the flue gases at the recuperator's outlet (state 12) are expanded through a gas turbine.  Also, surplus power for direct users is generated by this expansion. At the final step, while their temperature has been decreased, the flue gases leave the gas turbine and then are guided into a heat recovery steam generator (HRSG). In the HRSG, steam necessitated for gasification and heating loads for wide-site utility sectors are generated simultaneously.

Auxiliary fuel is necessary to provide a surplus amount of load that the HRSG unit needs for heating and steam generation purposes. In the integration of SN/HRSG, NG is utilized as this necessary auxiliary fuel. There are four stages in the process of power and heating generation along with steam supplement: very high pressure (VHP), high pressure (HP), medium pressure (MP), and low pressure (LP). To achieve this goal, three steam turbines (STs) are utilized at each stage in which the expansion process for power generation takes place in STs.  To adjust the mass flow rate of steam exchanged between successive stages, an expansion device is used, which is also known as a letdown process. After the necessitated steam for each utility center is extracted at each stage, a fraction of residue is bypassed for the gasification process's steam supply.

Figure 1: Schematic of the proposed biomass-based cogeneration system.

Methodology

Before developing the thermodynamic models, some assumption is necessary to be made. The following represent general assumptions (Bezaatpour, Rostamzadeh, Bezaatpour, & Ebadollahi, 2021; Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018; Ghaffarpour, Mahmoudi, Mosaffa, Farshi, & management, 2018; Smith, 2005; Sun, Doyle, & Smith, 2015; Sun, Smith, & Research, 2015; M. Taheri, A. Mosaffa, & L. G. J. E. Farshi, 2017):

• The system is operating in a steady-state.
•  The air consists of 79% and 21% of N₂ and O₂, respectively.
• Heat losses between all the heat exchangers, pipelines, and the environment are not taken into account.
• In the SOFC, the pressure at the anode and the cathode is assumed to be constant and equal. Similarly, the pressure drop of the heat exchanger remains constant.
• All the reactions reach chemical equilibrium before leaving the SOFC.
• Fuel and air are assumed to be ideal gas.
• The only electrochemically active species is hydrogen.
• Potential and kinetic energy effects are assumed to be negligible.
• Isentropic efficiency of the GT and AC is assumed to be 80% and 75%, respectively. For all steam turbines, a variable isentropic efficiency related to input load is assumed.
• The desuperheating process of the Superheated steam in the deaerator uses water.
• The acid dew point of the flue gases leaving the GT is 120 .
• The pressure of deaerators is set on 1.02 bar, and its temperature is saturated liquid at this pressure.
• For steam recovery, all processes taking place in the SN unit use desuperheater steam. The temperature of all elements in the SN is set below 570 .
• The steam generation process uses boiler feed water (BFW) at the deaeration temperature.

Energy analysis

To evaluate the devised system's performance, each element is considered a control volume and mass and energy balance equations to be employed for them individually (Bahram Ghorbani, Hamedi, & Amidpour, 2016). The general form of mass and energy balance equations at steady state for inlet and outlet streams of a control volume with heat transfer and work interactions can be articulated as follows:

Biomass gasification 

Pine sawdust (PSD) is selected as biomass for the devised system (Altafini, Wander, & Barreto, 2003; Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018). The critical characteristics of PSD are listed in Table 1. The following relation can be used for computing compressed air temperature ( ) (Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018; M. Taheri, A. Mosaffa, & L. G. Farshi, 2017):

In this relation, represents the compressor ratio ( ),  shows the air temperature at ambient condition,  is the specific heat ratio, and  represents the isentropic efficiency of the compressor, which is computed by the following relation:

The following reaction shows the chemical reaction in the gasifier, which takes place due to the supply of biomass and high-temperature steam and air (Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018):

the coefficient a₁ is equal to 1 for every single atom of carbon in biomass fuel.  To compute the coefficients a₂, a_3, and a₄, mole ratios should be used as follows:

The definition of stoichiometric air-fuel ratio ( ) is shown in Eq. (8). Also, the relative air-fuel ratio ( ) and can be used to determine the actual air-fuel ratio ( ) as shown in Eq. (9) (Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018; Srinivas, Gupta, & Reddy, 2009):

In these relations,  is equal to 0.1.

The coefficients  and  can be calculated by the following relations, respectively (Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018):

In Eq. (11),  represents the steam-fuel ratio. Considering atom balances on carbon, hydrogen, oxygen, and nitrogen, the following relations can be written about coefficients a_1-4:

To obtain the composition of the produced syngas, there are six unknown and four equations. Therefore, in order to compute the unknowns, two more equations are necessitated. These equations are developed from equilibrium reactions, as follows:

Because of the stable methane molecule, the methane steam reforming reaction has an endothermic nature. A high process temperature is needed to shift the dissociation reaction's equilibrium composition to the right side. On the contrary, the water gas shift reaction is exothermic, and therefore to shift the equilibrium to the right side, the process temperature should be as low as possible. Eqs (12-15) can be rewritten in terms of two unknown coefficients, i.e., b₁ and b₂:

The following relation can be used to compute the total number of species in products:

In Eqs (23) and (24), are the equilibrium constants of the reforming reaction  and water shift reaction  are computed:

The following relation shows the equilibrium constant based on Gibbs energy:

In this relation,  represents the Gibbs free energy for each reaction and can be calculated as follows:

Solid oxide fuel cell (SOFC)

Mass and energy balance equations are used to develop the thermodynamic modeling framework (C. Ozgur Colpan, Hamdullahpur, Dincer, & Yoo, 2010; Ghaffarpour, Mahmoudi, Mosaffa, Farshi, et al., 2018; Guo, Yu, Li, & Zhao, 2020). Considering the above assumptions, the following three reactions occur in the SOFC:

It is assumed that the reforming reaction is fully developed, and therefore, the methane is wholly converted in the process. This reaction's full development is because of the high temperature of the reactor and the catalyst effect. It is assumed that the shifting reaction is considered to will reach a thermodynamic equilibrium state. the equilibrium constant in this state can be given by:

In Eq. 31, A, B, C, D, and E represent the constant values (See Table 2), and T is the fuel cell's operating temperature.

In order to compute the output voltage V_cell of SOFC, the irreversible loss of each part should be subtracted from the ideal reversible voltage V_Nernst:

In this relation, V_cell and V_Nernst, represent the actual output voltage and the ideal reversible voltage, respectively. V_act, V_conc, and V_ohm are the activated polarization overvoltage, the concentration polarization overvoltage, and the ohmic polarization overvoltage. The reversible ideal voltage V_Nernst is defined as the voltage without current passing through the SOFC external circuit. The following relation expresses the V_Nernst:

Butler-Volmer equation is used for computing the activated polarization overvoltage:

In this relation, n_e represents the number of exchanged electrons.

The concentration polarization overvoltage is expressed in the following relations:

where i_as and i_cs represent the anodic and cathodic limiting current density, respectively.

Ohm's law is used in the following relation to calculate ohmic polarization overvoltage:

Eq. 37 is used for calculating the electrochemical reaction rate in Eq. (37):

In this relation, r_H2 represents the H₂ electrochemical reaction rate. A, J, E_A, and F represent effective reaction area, the current density, activation energy, and Faraday constant, respectively. The steam-to-carbon ratio (STCR) of the anode stream is expressed as:

The following relation is used to compute the SOFC fuel utilization ratio of SOFC (U_f):

where n_i represents the molar flow rate of H₂, CH₄, CO, H₂O.

The power output of the SOFC stack is calculated as follows

N, in this relation, represents the total number of cells. A represents the active area of a single fuel cell. The values and constants for electrochemical reaction calculation are shown in Table 2.

In Eq. 41, the general energy conservation equation is represented:    

Then In SOFC, the energy balance equation can be written as follows:

where W_SOFC represents the SOFC power output.

Combustor and gas turbine module

Since the content of CH₄ is not enough to carry on the combustion process in the combustor, some surplus amount of syngas is bypassed from the gasifier (state 8). Therefore, Eq (43) can be used to express the reaction taking place in the combustion chamber (Ghaffarpour, Mahmoudi, Mosaffa, & Farshi, 2018):

In this Equation,  represents the sum of mole rate at states 9 and 7.

At the outlet GT, the gas temperature can be computed by the following relation:

In this relation,  represents the isentropic efficiency of gas turbine and  represents the flue gas specific heat ratio, which can be calculated as follows:

In Table. 3, necessitated data for simulation and modeling of the proposed cogeneration system are listed.

Steam network

A fully detailed representation of steam network modeling is represented and described in our previous work (Amiri, Sotoodeh, & Amidpour, 2021). Also, the targeting algorithm implemented in this study is represented in Fig. 2.

Figure 2: Targeting algorithm for the proposed system in the steam network.

Performance evaluation

The energy efficiency of the proposed system can be described as follows:

where,  is the net power which is described as follows:

Model Validation

In this study, Engineering Equation Solver (EES) is used to establish the performance of the proposed cogeneration system (Klein & Nellis, 2012). The current computational and experimental results in the literature are used to evaluate the validity of this model. For gasification and SOFC, the comparisons between the modeling results are represented in Table 4 and Fig. 3, which show good accuracy.

Figure 3: Comparison of SOFC modeling outcomes between the present study and Colpan et al. (C Ozgur Colpan et al., 2007).

Table 5: Verification of simulation results for the steam network (power calculation).

Table 5: Verification of simulation results for the steam network (power calculation).

Table 6: Verification of simulation results for the steam network (power calculation).

Finally, for evaluating the steam network, the results of simulations are compared with Sun et al. (Sun, Doyle, et al., 2015). In Tables 5 and 6, the results of this validation for mass flow rate and power are shown, respectively. As can be deduced from this comparison, a good agreement exists between the results of the two studies.

4. Result and discussion

The main results of the energy analysis of the reckoned cogeneration system are listed in Table 7. According to the results, the net electricity is augmented by approximately 52% after integrating the combined SOFC/GT system with the steam network. Besides that, 235.266 MW heating energy can be produced along with 72.3 MW amount of net power. Finally, the energy efficiency of this system is 54.35%, which shows much more performance compared to the standalone SOFC/GT scheme.

Table 7: Performance indicators of the present study.

Moreover, steam network targeting results are depicted in Fig. 4.

Figure 3: Results of simulation for steam network targeting for a maximum steam temperature of 570 .

Parametric study of steam network side

A parametric study is applied to investigate the impact of pressure headers of the steam network. The variations of energy efficiency with various steam network pressure headers are depicted in Fig. 4. According to this figure, it can be deduced that with increasing , the energy efficiency is raised since the extraction ratio of the first turbine increases remarkably. In the HP header case, the energy efficiency decreases with the increase of HP, which is due to the more significant effect of heating load decrease than the impact of power augmentation. Similarly, as pressure increases in MP headers, the power generated by steam turbines and the heating capacity decreases since expansion ratios of superior turbines decreases. As expected, VHP headers have a higher impact on efficiency since

Figure 4: Impact of steam network headers on energy efficiency.