# Reduced Integration Optimization Model for Coupled Elevated-Pressure Air Separation Unit and Gas Turbine in Oxy-combustion and Gasification Power Plant

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## Abstract

For the promising and green oxy-combustion and gasification power plant, the most efficient and assessable approach for further improvements on the current situation with less investment turned to be process optimization and integration. In this work, the gap of systematic analysis of air separation unit (ASU) and gas turbine (GT) integrations in integrated gasification combined cycle (IGCC) power plant has been fulfilled in the elevated-pressure ASU operation conditions beyond discrete case studies. Based on the conventional rigorous mathematical simulation, a series of model reductions have been proposed and applied to increase the computational flexibility. To validate the reduced model, a base case is built and settled as the benchmark, which is consistent with the industrial experiences. Afterwards, based on the reduced model, the effects of air integration on the thermal performance of IGCC power plant have been explored under the conditions of various nitrogen injection levels. The individual influences of nitrogen injection level on IGCC plant efficiency have been explored as well. To achieve best IGCC performance, the optimization of coupled air integration and nitrogen injection as a whole is completed. Based on the proposed reduced model, the three dimensional figure about systematics analysis of integration optimization for IGCC power plant is generated for the first time. Based on its two-dimensional top view, the feasible regions are identified and optimal solution is generated through nonlinear programming problem solver based on enhanced generalized reduced gradient method.

## Keywords

Optimization Reduced model Integrated gasification combined cycle Air separation unit## Nomenclature

- FR
_{air, GT} Flow rate of air injection to GT compressor.

- FR
_{air, cooling} Flow rate of the compressed air for GT cooling.

- FR
_{air, com} Flow rate of compressed air for GT combustion.

- FR
_{n, ST} Flow rate of stream going through steam turbine.

- \( {G}_f^0 \)
Standard Gibbs free energy of formation.

*G*_{system}Total Gibbs free energy of the system.

*H*_{f ‐ coal}Enthalpy of formation for feed coal.

*H*_{f, i}Enthalpy of formation for feed component

*i*.- \( {H}_{298.15}^o \)
Standard enthalpy of formation at 298.15 K and 1 atm.

- LHV
_{coal} Lower heating value of the feed coal.

*n*_{coal}Total mole flow rate of feed coal.

*P*_{MAC}Discharge pressure of main air compressor.

*P*_{GTC}Discharge pressure of GT compressor.

*P*_{GTT}Discharge pressure of GT turbine.

*P*_{GT, 0}Inlet air pressure of GT compressor.

*P*_{GT, com}Inlet combusted gas’s pressure.

*P*_{HPC}Operation pressure of high-pressure column.

*P*_{ST,out}Total power output of steam turbine.

*r*_{com}Isentropic index of exhausted combusted gas.

*S*_{GT}GT compressor surge margin.

*T*_{out}The outlet syngas temperature.

*T*_{GT, com}Inlet combusted gas’s temperature.

*T*_{GT, 0}Inlet air temperature of GT compressor.

*T*_{GTC, isen}Outlet temperature after isentropic process from GT compressor.

*T*_{GTT, isen}Outlet temperature after isentropic process from GT turbine.

*T*_{HPC, con}Temperature of high-pressure column condenser.

*T*_{LPC, reb}Temperature of low-pressure column reboiler.

*T*_{MAC, isen}^{`}Outlet temperature after isentropic process from MAC.

*W*_{MAC}Main air compressor’s work consumption.

*W*_{GTT}The work generation of GT turbine.

*η*_{is, GTC}Isentropic efficiency of the GT compressor.

*η*_{is, GTT}Isentropic efficiency of the GT turbine.

*η*_{is}Isentropic efficiency of the main air compressor.

## Introduction

With the progress of science and technology, electricity power has become the cornerstone of global economic growth and social development, which leads to its persistently increasing demand and supply. For example, the electricity generation of the whole world has been increased more than 30% from 18,358.1 to 24,097.7 TWh in the decasas from 2005 to 2015 (BP global company 2016). As one of the most potential power generation technologies, integrated gasification combined cycle (IGCC) power plant has been recognized as a rare existing opportunities to fulfill the requirements of energy dissipation and waste production simultaneously. It’s almost perfect environmental performance has been demonstrated in the last decade, which mainly attributes to the implement of pre-combustion cleaning other than common post-combustion cleaning in conventional pulverized coal (PC) plant. However, this promising and sustainable technology still requires improvements in terms of process economics to become fully competitive in commercial scale (Christou et al. 2008). The investigations has identified the cost of electricity (CoE) as the greatest barrier for the global acceptance of IGCC power plant.

To overcome this bottleneck, the decrements of corresponding capital costs and operational costs are essential and necessary. Unfortunately, to achieve lower capital cost through applying advanced technology, market penetration and economy of scale still needs plenty of efforts and resources as a valuable but difficult long-term task. Therefore, improving IGCC plant power efficiency and benefiting the decrement of its operational cost have become only a subsistent approach to figure out the dilemma. Even though many key blocks of IGCC plant has been explored and improved for decades so far, the advanced technology of process optimization and integration still provide the opportunities for further plant efficiency enhancement due to the complicated configurations of IGCC power plant.

IGCC power plant mainly consists of gasification, power, and air separation unit (ASU) islands. The three islands are closely connected and deeply interacted with each other. The IGCC power island is the one directly related with electricity power generation, which relies on the combined cycle technology. While, due to the limitations of high capacity and high product purity, energy-intensive cryogenic ASU technology is the most common choice to apply in the ASU island of the current IGCC plant. As one of the significant portions in the power island, gas turbine (GT) may connect with the ASU island in the state-of-art design of current IGCC plant for overall efficiency improvements. Therefore, the interactions between ASU and GT in IGCC should attract more attention (van der Ham and Kjelstrup 2010). Many integration details are introduced by Smith and Klosek (Smith and Klosek 2001) such as air integration and nitrogen injection.

The estimation index, integration degree, is described by the ratio of flow rate for integration against the total flow rate. According to the practice of single-air integration, less than 15% air integration degree can satisfy the requirement of ASU feed (Todd 2000). If only this is considered, the net power generation is steadily reduced in the lower integration degree (Farina and Bressan 1999). However, in the higher degree, the reduction is still there because of less GT power generation. Foster Wheeler Corporation analyzed this balance using GE 9001 FA GT and concluded the most efficient integration degree is 46% (Farina and Bressan 1999). Meanwhile, the study taken by Air Products and Chemicals, Inc. indicates that the optimal integration degree should be in the range of 25 and 50% (Smith et al. 1996). This conclusion is based on both the cost and efficiency optimization.

When both the air integration and nitrogen injection are taken into consideration, the problem becomes more complicated. Frey and Zhu (Frey and Zhu 2006) examined different combinations of air and nitrogen integration in 2006 and concluded that the system with nitrogen integration only is better than that with two integrations together. Lee (Lee et al. 2009) reports a conclusion to support the high integration degree considering both of the system performance and operation limitation of GT. And they claim that a high nitrogen supply ratio can only be acceptable in high air integration degree. Emun (Emun et al. 2010) also suggested the nitrogen integration degree could be as high as possible for higher IGCC efficiency.

What’s more, ambient operation pressure assumptions of IGCC ASU island were frequently occupied in the previous case studies. For example, (Wang et al. 2010) have studied the influences of air extraction rate and nitrogen injection rate for ambient-pressure ASU. Cormos (Cormos 2010) have investigated of ASU and GT integration through case studies operating at 0.237 MPa. However, the rare discussed elevated operation pressure of ASU seems to be more beneficial to the IGCC power plant compared with ambient operation pressure. Because IGCC power plant is used to operate at the pressure range from 10 to 40 bar for most blocks except ASU. To fulfill this gap, the integration schemes with ASU operation conditions located into elevated-pressure range have been emphasized in this work. And according to comprehensive literature review and conjecture, elevated-pressure ASU working around 10 bar is supposed to be more suitable of being a part of whole IGCC plant.

Even though IGCC plant performance enhancements through air integration and nitrogen injection between ASU and GT individually or simultaneously have been confirmed, and among the literature review, it is certain that the various integration degrees have great influences on the efficiency increments and CoE decrease. However, there is still no systematic analysis of ASU and GT integrations. Almost all of existing conclusions were generated by the comparisons of discrete case studies. What’s more, for each work, the assumed integration degrees lie behind all cases used to be concentrated into specific small ranges. Therefore, the comprehensive relationships between integration conditions and IGCC plant performance have not been clearly illustrated. The primary cause of this status is the lack of proper optimization model for wide integration degree range. Even though commercial process simulators have integrated many functions as convenient toolsets, their non-open sources nature have limited their flexibility and achieving profound integration explorations. According to previous experiences, the complicated IGCC process simulations built on commercial simulators like Aspen Plus, PRO II, and Themoflex have too many variables and constraints to be converged at optimal integration schemes. Therefore, there is a requirement of suitable models considering both prediction accuracy and flexibility to overcome existing barrier of this large-scale optimization problem, especially to achieve comprehensive analysis of ASU and GT integration in IGCC system.

To sum up, there is a gap of systematic analysis of ASU and GT integrations in IGCC power plant among wide integration degrees above discrete case studies, especially in the elevated-pressure ASU operation conditions. Hence, in this work, a series of model reductions are proposed and applied on the conventional rigorous mathematical process simulations. Based on the reduced model, a systematic analysis of coupled elevated-pressure ASU and GT considering air integration and nitrogen injection will be completed. The impacts of different integration degrees on overall IGCC power plant performances will be identified. And finally, the optimal integration degrees will be generated for EP ASU and GT system as a part of IGCC power plant.

## Process Description and Rigorous Modeling

### Process Description of IGCC Power Plant

The coal or other fuel-like biomass is crushed and supplied into the gasifier, where it is partially oxidized. The feed could be slurry or solid particles are delivered by gas (like nitrogen). The steam or feed water would be necessary especially for the dry feed scheme. If pure oxygen is used as oxidant instead of air, there will be an air separation unit (ASU). The operating pressure and temperature of gasifier are different based on the fuel supplied and gasifier type, which are in the range of 1 to 40 bar and 1100 to 1600 °C. Gasification product, the crude syngas, is mainly composed of H_{2}, CO, CO_{2}, CH_{4}, H_{2}S, and H_{2}O. Besides the chemical energy, the crude syngas contains large amount of sensible heat at high temperature and pressure. To prepare the crude syngas for cleaning at near ambient temperature, cooling or water quench devices are necessary. The syngas cooler could recover the sensible heat to increase the thermal efficiency, while the water quench scheme is cheap. The clean syngas goes to drive gas turbine (GT) including combustion with additional oxygen and injected nitrogen. The heat of fuel gases from GT is used to generate superheated steam in the heat recovery steam generator (HRSG). A steam turbine (ST) is driven by that steam to produce additional power. The GT and ST process plus HRSG consist of the combined cycle (CC), which is originally used in modern natural gas-fired power plants. As shown in Fig. 1, all the blocks mentioned above could be classified into three functional parts. Firstly, gasification island converts the fuel to syngas. While the syngas is combusted to generate power in the power island, which is also known as CC process. What’s more, the ASU island is used as auxiliary system, which connects each block by supplying nitrogen and oxygen.

### Integration Framework of Air Separation Unit and Gas Turbine

Feed streams for the isobaric combustor include not only the oxidizing agent (compressed air) and the fuel (pretreated syngas) but also the nitrogen from ASU and the water vapor to moisten the syngas. After that, the exhausted combustion gas at high temperature and pressure is delivered to the following turbine for power generation. A shaft is used to connect the turbine and compressor. The exhausted gas from the turbine still has the sensible heat at the temperature of about 700 K (Boyce 2011), which will be recovered by the other IGCC blocks.

As the byproduct from ASU, N_{2} is used to vent but actually has other chances to utilize in IGCC plant, like in the GT. It can be achieved by direct injection or premixing with the fuel stream (syngas). The benefit is keeping the optimal turbine operation temperature and reducing the emission of NO_{x}. Another dilution option is steam injection, which has the advantage of the low cost for syngas humidification. Air integration means the total or partial ASU air requirement being supplied by the extraction of GT compressor discharged air. Its advantages lie on the higher compressor efficiency and smaller ASU device size.

### Modeling of Gasification Island

The modeling of gasifier is built on the assumptions of equilibrium state. The specific assumptions are uniform gasification temperature, fast gasification reaction rate, and non-tar formation. The high-quality coal with certain amount of carbon is assumed as feedstock and only the carbon element is considered in the reaction. The crude syngas is assumed as a mixture of CO, CO_{2}, H_{2}, CH_{4}, COS, H_{2}S, NO, and N_{2}O. The Gibbs free energy minimization model is built where the syngas composition is calculated simultaneously with the equilibrium temperature in adiabatic statement.

*n*

_{coal}is the total mole flow rate of feed coal.

*H*

_{f − coal}(

*T*

_{0}) means the enthalpy of formation for feed coal in

*T*

_{0}(kJ kmol

^{−1}). While the rest of the lefthand side of Eq. (1) stands for the total input enthalpy of other feed besides coal. In that,

*H*

_{f, i}(

*T*

_{0}) stands for the enthalpy of formation for feed component

*i*at

*T*

_{0}.

*n*

_{i}means the mole flow rate of that feed component

*i*. The outlet syngas temperature (

*T*

_{out}) is taken as the gasification temperature. And the temperature of reactants (

*T*

_{0}) is assumed to be 298 K in this work. Reported by De Souza-Santos (De Souza-Santos 2010), the enthalpy of formation for the solid fuels, like coal, could be calculated. In this work, the

*H*

_{f − coal}(

*T*

_{0}) can be expressed by Eq. (2).

_{coal}is the lower heating value of the feed coal (kJ kmol

^{−1}) and

*H*

_{f, i}(

*T*

_{0}) is the enthalpy of formation of the gaseous product

*i*in

*T*

_{0}. Gaseous products are produced from the complete combustion of feed coal with oxygen.

^{−1}), the standard Gibbs free energy of formation in

*T*for component

*i*, is calculated by Eq. (3).

*i*from standard state to system state at

*T*(K), represented by \( \varDelta {H}_{f,i}^0(T) \) and\( \varDelta {S}_i^0(T) \), are calculated based on Eqs. (4), (5) and (6).

^{−1});

*A*,

*B*,

*C*,

*D*,

*E*, and

*H*are constant coefficients supplied by the National Institute of Standards and Technology (NIST) chemistry database (Lemmon et al. 2005). In Eq. (4),

*T*is the gasification temperature (K).

*G*

_{system}, which is defined by Eq. (7), is minimized.

^{−1}),

*n*

_{i}(mole) is amount of component

*i*of the system.

*T*(K) is system temperature and

*R*is gas constant. With ideal gas assumption, \( {\widehat{f}}_i \) is related with system mole composition

*y*

_{i}and pressure

*P*(Pa):

When at low pressures, \( {f}_i^0 \) is taken as the standard state pressure. \( {G}_{f,i}^0 \), is calculated based on Eq. (3).

### Modeling of Power Island

*T*

_{GTC, isen}is the outlet temperature after the isentropic process (K);

*T*

_{GT, 0}and

*P*

_{GT, 0}are the inlet air temperature (K) and pressure (atm). While

*P*

_{GTC}is the discharge pressure of the compressor (atm) and

*r*

_{air}is the isentropic index of air. The outlet temperature of GT compressor corrected by introducing the isentropic efficiency could be defined as Eq. (10):

*η*

_{is, GTC}is the isentropic efficiency of the GT compressor;

*H*(

*T*

_{GT, 0}) is the enthalpy of injected air in

*T*

_{GT, 0}(kJ mol

^{−1});

*H*(

*T*

_{GTC, actual}) is the enthalpy of compressed air in

*T*

_{GTC, actual}(kJ mol

^{−1}) and

*H*(

*T*

_{GTC, isen}) is the enthalpy of compressed air in

*T*

_{GTC, isen}, (kJ mol

^{−1}).

*T*

_{GTC, actual}, the output temperature after isentropic compression considering efficiency (K). Based on industrial experiences, GT compressor is more efficient than others in CC unit due to its higher compression ratio (Kapat et al. 1994).

*W*

_{GTC}), MW could be calculated as Eq. (11):

_{air, GT}is the flow rate of air injection to GT compressor (kmol h

^{−1}). The compressed air should be split into two parts, where one for oxidization in the later syngas combustion and the rest one for the GT combustor and turbine blade cooling purpose. The relationship of different options could be identified by Eqs. (12) and (13).

_{air, cooling}is the flow rate of the compressed air for GT cooling (kmol h

^{−1}); FR

_{air, com}is the flow rate of compressed air for GT combustion (kmol h

^{−1}); and

*R*

_{cooling}is in the range from 0 to 1, which stands for the degree of GT cooling.

Equation (14) stands for the mass balance between the input and output stream of combustor for element *j*. The input streams involved are syngas, which is analyzed and calculated based on Chapter 2, and compressed air. While the output ones are complete oxidation of carbon (CO_{2}), hydrogen (H_{2}O), and nitrogen as an insert gas. Hence *j*-set contain the carbon, hydrogen, oxygen and nitrogen element. And total *i*-set contain CO, CO_{2}, H_{2}O, H_{2}, O_{2}, and N_{2} for input and CO_{2}, H_{2}O, and N_{2} for output. While Eq. (15) means that the differences between the total enthalpy of the input and output streams are the summary of the syngas lower heat value (LHV). With those two balances, the enthalpy and composition out of GT combustor are generated. The combustion temperature (*T*_{GT, com} in K) could be calculated using exhausted gas enthalpy. Due to industrial practices, exhausted gas from GT combustor to the turbine for power generation is at high temperature (1300 to 1600 K) and high pressure (10 to 20 atm) (Farmer and De Biasi 2010).

*T*

_{GTT, isen}is the outlet temperature after the isentropic process (K);

*T*

_{GT, com}and

*P*

_{GT, com}are the inlet combusted gas temperature (K) and pressure (atm). While

*P*

_{GTT}is the discharge pressure of GT turbine (atm) and

*r*

_{com}is the isentropic index of exhausted combusted gas.

*η*

_{is, GTT}is the isentropic efficiency of the GT turbine;

*H*(

*T*

_{GT, com}) is the enthalpy of injected stream in

*T*

_{GT, com}(kJ mol

^{−1});

*H*(

*T*

_{GTT, actual}) is the enthalpy of outlet stream in

*T*

_{GTT, actual}(kJ mol

^{−1}) and

*H*(

*T*

_{GTT, isen}) is the enthalpy of outlet stream in

*T*

_{GTC, isen}(kJ mol

^{−1}).

*T*

_{GTT, actual}is the output temperature after isentropic expansion considering efficiency (K).

*W*

_{GTT}), MW could be calculated by Eq. (18), which is similar as Eq. (11).

_{com, GT}is the flow rate of exhausted combusted gas from GT combustor (kmol h

^{−1}), which equals summary of FR

_{i, out}. What’s more, as one of essential control variables, GT compressor surge margin (

*S*

_{GT}) is described by Eq. (19).

*S*

_{GT}could guarantee the successful operation of GT as a part of power island. Finally, the total power output of GT,

*P*

_{GT,out}(MW) can be calculated by Eq. (20).

The process of steam turbine is proposed including HRSG, cooler, turbines, and pumps. The combusted fuel gas from GT unit is injected to HRSG, where the sensible heat of fuel gas is recovered. The feed water is heated, evaporated, and heated again through HRSG, and finally converts to superheated steam at high temperature and pressure. The efficiency of HRSG is defined as the ratio of output and input enthalpy, which is around 90%. The superheated steam goes through several turbines to expand to lower temperature and pressure steam for power generation. The modeling of ST turbine is similar as GT turbine and it is idealizing the expansion then adding the efficiency. Isentropic process is assumed for ideal turbine expansion as before but using Water97 database for property calculation.

*E*

_{in, n, ST}stands for the entropy of inlet stream injected into turbine or pump

*n*(J mol

^{−1}K

^{−1}).

*E*

_{in, n, ST}stands for the entropy of outlet stream from turbine or pump

*n*(J mol

^{−1}K

^{−1}). The entropy is determined by the temperature and pressure conditions based on Water97 add-in. What’s more, the isentropic efficiency of turbine or pump

*n*is added, as defined by Eq. (22). This equation is similar as Eq. (11).

*η*

_{is, n, ST}is the isentropic efficiency of turbine or pump

*n*in ST;

*H*(

*T*

_{in, n, ST}) is the enthalpy of inlet stream in

*T*

_{in, n, ST}(kJ mol

^{−1});

*H*(

*T*

_{out, n, ST, actual}) is the enthalpy of outlet stream in

*T*

_{out, n, ST, actual}(kJ mol

^{−1}) and

*H*(

*T*

_{out, n, ST, isen})is the enthalpy of outlet stream in

*T*

_{out, n, ST, isen}(kJ mol

^{−1}).

*T*

_{out, n, ST, isen}, the temperature after isentropic process calculated by Eq. (21) (K). While

*T*

_{out, n, ST, actual}represents the output temperature after isentropic process considering efficiency (K).

*n*could be calculated by Eq. (23), which is similar as Eq. (11).

_{n, ST}is the flow rate of stream going through turbine or pump

*n*(kmol h

^{−1}).

_{2}O from the steam to water phase. Therefore, the relationship between inlet and outlet stream of cooler is described by Eqs. (24) and (25).

*P*

_{in, cooler}and

*P*

_{out, cooler}is the inlet and outlet stream’s pressure (atm).

*ΔP*

_{cooler}is the pressure loss of cooler (atm).

*T*

_{sat}is the statured temperature in

*P*

_{out, cooler}, which is generated by Water97 add-in (K). While

*ΔT*

_{cooler}is the approach temperature of cooler assumed as constant 5 K. Finally,

*T*

_{out, cooler}, the outlet temperature of cooler (K) is calculated and acted as input value of first pump model. All in all, the total power output of ST,

*P*

_{ST,out}(MW) can be calculated by Eq. (26).

*n*-set contain every turbine and pump in ST unit.

### Modeling of ASU Island

*T*

_{MAC, isen}is the outlet temperature after the isentropic process (K);

*T*

_{0}and

*P*

_{0}are the inlet air temperature (K) and pressure (atm). While

*P*

_{MAC}is the discharge pressure of the compressor (atm), and

*r*is the isentropic index.

*P*

_{MAC}can be calculated as below:

*P*

_{HPC}is the operation pressure of high pressure column (HPC) in ASU (atm), and

*dP*is the pressure difference for preventing pressure loss (atm).

*η*

_{is}is the isentropic efficiency of the MAC;

*H*(

*T*

_{0}) is the enthalpy of injected air in

*T*

_{0}(kJ mol

^{−1});

*H*(

*T*

_{MAC, actual}) is the enthalpy of compressed air in

*T*

_{MAC, actual}(kJ mol

^{−1}), and

*H*(

*T*

_{MAC, isen}) is the enthalpy of compressed air in

*T*

_{MAC, isen}, (kJ mol

^{−1}).

*T*

_{MAC, actual}, the output temperature after actual compression process (K), can be calculated by Eqs. (4) and (5). MAC work consumption (

*W*

_{MAC}), MW, could be calculated as:

*F*

_{ASU}is the flow rate of air injection to ASU (kmol h

^{−1}). The cooling duty (

*Q*

_{MAC}, MW) is calculated by the enthalpy difference as Eq. (31).

*H*

_{inlet}represents the total enthalpy of inlet streams of MHEX including compressed air and both product streams of LPC (kJ h

^{−1}). The

*H*

_{outlet}represents the total enthalpy of outlet streams of MHEX including cryogenic compressed air and both product streams of LPC after being heated up (kJ h

^{−1}) as well. The temperature of outlet stream could be calculated by its enthalpy and compositions.

*y*

_{i}is the mole fraction in gas phase for component

*i*and

*x*

_{i}is its mole fraction in liquid phase.

*P*is the pressure of the selected system (atm), namely the column operation pressure. And \( {P}_i^{\theta } \) is the saturated vapor pressure of

*i*in the system temperature (

*T*) (atm), which could be calculated by the Antoine equation shown by Eq. (34).

*T*is the system temperature, namely the tray temperature;

*A*

_{i},

*B*

_{i}, and

*C*

_{i}are the coefficients reported by Mallard (Mallard 2003).

*T*

_{HPC, con}and

*T*

_{LPC, reb}are the temperature of HPC condenser (K) and LPC reboiler (K). While 2 K is approach temperature according to the real application (Smith and Klosek 2001).

Finally, the products are the nitrogen from the top of LPC and the oxygen from the bottom of LPC. Both of them are assumed as the gas phase. And the consequential treatment for downstream purpose are only compression as last step. The simulation of product compression is using the same method of MAC modeling, which are represented by Eqs. (16) and (17).

## Model Reductions and Optimization Framework

### Model Reductions

The conventional rigorous mathematical model of IGCC power plant mentioned above has the potential bi-level optimization trouble due to the implement of the Gibbs free energy minimization model. To overcome this barrier of systematic analysis for process integration optimization, a series of model reductions are proposed and applied on the basis of the simulation mentioned above.

According to the analysis of our previous work (Wang et al. 2018), a reduced equilibrium model for IGCC gasification unit is introduced. Under the assumption of a steady state isothermal gasification process, the feed stock, coal, could be expressed by the empirical formulated as C_{x}H_{y}O_{z}, where *x*, *y*, and *z* are constant coefficients relying on coal species. All gasification reactions occur simultaneously and the properties for gas is assumed to follow the law of ideal gas in thermodynamics. Water gas shift reaction (WGSR) is assumed to achieve the equilibrium before the syngas goes out of the gasifier. The potential components in syngas are CO, CO_{2}, H_{2}, CH_{4}, and H_{2}O. The feed conditions and reaction conditions, such as temperatures and pressures, are known as input information in reduced model.

*n*

_{C ‐ coal}is the mole flow rate of carbon from coal, similarly for other items starting with

*n*

_{C−}. While the mole flow rate of oxygen and hydrogen in the feed are expressed by the items starting with

*n*

_{O−}and

*n*

_{H−}, respectively. The input water or steam is distinguished from output steam in syngas by different subscripts −in and −out.

*T*can be calculated (Liu et al. 2018). The Gibbs free energy of WGSR, \( \varDelta {G}_r^0(T) \), can be calculated by Eq. (39).

*K*

_{eq}) of WGSR can be calculated by Eq. (40).

*R*is the gas constant equal to 8.314 J mol

^{−1}K

^{−1}, and

*T*is the gasification temperature in

*K*. Because the equilibrium of WGSR could be achieved,

*K*

_{eq}can be related with syngas compositions by Eq. (41).

_{2}, H

_{2}, CO, and H

_{2}O in the product syngas from IGCC gasification unit.

*Q*

_{HPC, con}) and LPC reboiler (

*Q*

_{LPC, reb}) should be equal as well, as shown by Eq. (43).

Once the relationship between the top tray of HPC (condenser) and bottom tray of the LPC (reboiler) has been built, it is necessary to identify the connection for the rest one. According to cryogenic ASU configurations, the top product stream of HPC is injected into the top tray of the LPC. Under the requirement of 99% oxygen and nitrogen product purity, the results show that the stream from the top tray of HPC will be stay above 99% for different operation pressure.

### Integration Indicators

^{−1}); while \( {\mathrm{FR}}_{{\mathrm{N}}_2,\mathrm{ASU}} \) is the mole flow rate of nitrogen product generated by ASU (kmol h

^{−1}). \( {R}_{N_2} \) should be in the range from 0 to 1.

*R*

_{cooling}is introduced to express the amount of compressed air for GT cooling. In this section, additional portion should be introduced to represent the amount of compressed air for integration. Therefore, the corresponding ratio is described in Eq. (45).

_{air, ASU}is the flow rate of compressed air through GT compressor for ASU feed (kmol h

^{−1}). Similar with

*R*

_{cooling},

*R*

_{air}, which stands for the degree of integration using compressed air, is still in the range from 0 to 1.

What’s more, for the injection dilution of GT combustor, the nitrogen stream should be almost pure and the steam should be evaporated from pure water. Besides controlling by flame temperature, the mole fraction of the steam is limited to avoid the potential damage for the turbine blade (Bolland and Stadaas 1995). While the purification of minerals in the injected steam, which is used to prevent the corrosion in turbine and increase the gas heat transfer coefficient, should be taken care of in order to keep the turbine in good conditions.

### Objective Functions

*P*

_{out}(MW), for IGCC power plant can be calculated by Eq. (46).

*P*

_{GT, out}and

*P*

_{ST, out}(MW) stand for the overall power output of GT and ST. While

*W*

_{ax}(MW) stands for all auxiliary work of compressors and pumps in power plant. Finally, the estimation index of the IGCC plant performance is identified as the overall efficiency

*η*

_{all}:

*η*

_{all}is set as the objective function of the simulations.

## Results and Discussions

### Reduced Model Validation and Benchmark Establishment

The ultimate analysis of fed coal (daf) (Deutch and Monis 2007)

Components | Mass fraction |
---|---|

Carbon | 0.8052 |

Hydrogen | 0.0553 |

Oxygen | 0.0792 |

Nitrogen | 0.0153 |

Sulfur | 0.0428 |

The key assumptions of IGCC power plant in the reduced model

Items | Values |
---|---|

Gasification island | |

Gasification temperature (K) | 1473 |

Gasification pressure (bar) | 42 |

Flow rate of fed coal (kg s | 30 |

Clean syngas temperature (K) | 600 |

Power island | |

GT compressor efficiency (%) | 95 |

GT combustor pressure (bar) | 11 |

Maximum GT combustor temperature (K) | 1600 |

Compressed air ratio for GT cooling (%) | 11.8 |

Pressure of superheated steam from HRSG (bar) | 100 |

Temperature of superheated steam from HRSG (K) | 900 |

ASU island | |

HPC operation pressure (bar) | 10.5 |

LPC operation pressure (bar) | 3 |

Split ratio of compressed air (%) | 95 |

Air flow rate of ASU (kmol h | 32,000 |

Results of IGCC power plant simulation

Items | Values |
---|---|

Net power output of GT | 279.5 MW |

Net power output of ST | 208.4 MW |

Work consumption of ASU | 62.7 MW |

Net power output of plant | 411.5 MW |

Total LHV input | 934.5 MW |

Overall efficiency | 44.03% |

### Individual Influences of Air Integration on IGCC Plant

It is concluded that with the increment of air integration degree the IGCC plant efficiency keeps decreasing due to the decrease of mass flow rate through GT turbine. As more and more compressed air extracted to ASU, the gross power output of GT declined and corresponding power output of ST decreased as well. Therefore, the plant efficiency achieved the best performance at the point without any integration. If only air integration is considered, higher integration degree leads to worse thermal performance. Actually, these observations are consistent with the situation using ambient-pressure ASU.

According to Fig. 4, higher air integration degree could achieve better IGCC performance. Due to the full nitrogen injection, the augmentation effect of GT becomes obvious and decrease of mass flow rate turns to be a negligible factor for IGCC plant efficiency until the integration degree of 0.57. Before this inflection point, the power output of GT has been reached the upper limitation while the ST power generation keeps increasing with the increment of the combusted gas’s sensible heat. After the inflection point, the influences of air integration are reflected on the rate of overall plant efficiency change. However, the highest efficiency has been achieved at total air integration in this total nitrogen injection situation.

According to Fig. 5, the changes of the relationships under different nitrogen injection levels are obvious. The inflection points keep moving with the increase of the nitrogen injection level. Under the situations of low nitrogen injection, the inflection points are not obvious since the GT mass flow rate and power output have not reached the upper limitations. While with the nitrogen injection level going up, the augmentation effect of GT approaches to the saturation point. However, in most cases with nitrogen injection, the more air integration the better for IGCC plant performance.

### Individual Influences of Nitrogen Injection on IGCC Plant

It is concluded that with the increment of nitrogen injection level the IGCC plant efficiency keeps decreasing and its rate of change becomes larger and larger. In the situation without air integration, the nitrogen injection has positive impacts on the power output of GT while holds the negative effect on ST power generation. The mass flow rate of GT increases with more and more nitrogen injected and causes more and more GT power output. While the decline of the combusted gas’ sensible heat leads to the decrement of ST power output. All in all, the plant efficiency achieved the best performance at the point without any integration. If only nitrogen injection is considered, higher injection level leads to worse thermal performance.

To understand the individual influences of nitrogen injection on IGCC power plant performance, the relationships between plant efficiency and nitrogen injection level have been explored through reduced model in the situations with different air integration degree. The trends are illustrated in Fig. 7 as well.

According to Fig. 7, the changes of the relationships under different air integration degrees are obvious. If the air integration degree is between 0 and 1, there turns to be many inflection points in the trends. The inflection points keep moving with the increase of the air integration degree. Under the situations of high air integration, the inflection points are not obvious since the GT mass flow rate and power output have not reached the upper limitations. However, in most situations, the more nitrogen injection the better for IGCC plant performance.

### Optimization of Coupled Air Integration and Nitrogen Injection on IGCC Plant

During the analysis of individual integration influences, the coupling effects of air integration degree and nitrogen injection level are obvious. If best IGCC performance needs to be achieved, the optimization of coupled air integration and nitrogen injection as a whole becomes extremely necessary. Based on the proposed reduced model, the 3D figure of systematics analysis of integration optimization for IGCC power plant is generated for the first time.

In Fig. 9, the area in gray demonstrate the situation with IGCC plant efficiency lower than 44% in this work. While the yellow field is the opposite and has been recognized as the feasible range of following optimization. With both of the air integration degree and nitrogen injection level as variables, the optimal conditions with maximum IGCC plant efficiency is generated. The well-developed NLP solver has been used in this optimization, which is developed based on enhanced generalized reduced gradient (GRG) method (Wang et al. 2017). GRG method has been originally proposed in 1969 to solve NLP problem with nonlinear constraints in efficient way (Abadie 1969). Lasdon (Lasdon et al. 1978) improved the GRG method by involving the concept of quasi-Newton method for search direction. Kao (Kao 1998) compared the performances of several different common NLP solvers, which supports the superior properties of the one using GRG method. It has been concluded that NLP solver based on GRG method is widely accepted and qualified to optimize the reduced model of IGCC power plant. The optimal conclusion for this elevated-pressure ASU and GT system as a part of IGCC power plant is fully integration in both air integration and nitrogen injection aspects.

## Conclusions

In this work, the gap of systematic analysis of ASU and GT integrations in IGCC power plant has been fulfilled in the elevated-pressure ASU operation conditions beyond discrete case studies. Based on the conventional rigorous mathematical simulation, a series of model reductions have been proposed and applied to increase the computational flexibility. To validate the reduced model, a base case is built and settled as the benchmark, which is consistent with the IGCC plant performance according to industrial experiences. Afterwards, based on the reduced model of IGCC power plant, the effects of air integration on the thermal performance of IGCC power plant have been explored. The situations with none and total nitrogen injection have been explored firstly. The change of relationships between air integration degree and IGCC plant efficiency has been illustrated under various nitrogen injection levels. The individual influences of nitrogen injection level on IGCC plant efficiency have been explored as well. To achieve best IGCC performance, the optimization of coupled air integration and nitrogen injection as a whole is completed. Based on the proposed reduced model, the 3D figure of systematics analysis of integration optimization for IGCC power plant is generated for the first time. Based on its 2D top view, the feasible regions are identified through the curves of inflection points and optimal solution is generated through nonlinear programing problem solver based on enhanced GRG method. Finally, the total integration in both aspects is generated as the best choice for elevated-pressure ASU and GT system as a part of IGCC power plant.

## Notes

### Funding information

Financial supports provided by RGC-GRF Grant No. 16211117 is gratefully acknowledged. The National Natural Science Foundation of China (U1662126) and (21476180) are gratefully acknowledged as well.

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