A mixed-integer optimization approach for polygeneration energy systems design

Computers and Chemical Engineering 33 (2009) 759–768

Contents lists available at ScienceDirect

Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

A mixed-integer optimization approach for polygeneration energy systems design Pei Liu a , Efstratios N. Pistikopoulos a,∗ , Zheng Li b a b

Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 10 March 2008 Received in revised form 20 August 2008 Accepted 21 August 2008 Available online 29 August 2008 Keywords: Polygeneration Mixed-integer nonlinear programming (MINLP) Design optimization

a b s t r a c t A mixed-integer nonlinear programming (MINLP) model is developed for the design optimization of polygeneration energy systems. A suitable superstructure is introduced, based on partitioning a general polygeneration energy system into four major blocks, for each of which alternative available technologies and types of equipment are considered. A detailed case study, involving a coal-based polygeneration plant producing electricity and methanol, is presented to demonstrate the key features and applicability of the proposed approach. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction Polygeneration is considered a potentially attractive technology for energy utilization, as it could provide feasible solutions to the worldwide problems of excessive green house gas (GHG) emissions and ever-increasing depletion of fossil fuels (Li, Ni, Zheng, & Ma, 2003; Ni & Johansson, 2004; Ni, Li, & Yuan, 2000; U.S. Department of Energy, 1999, 2001; Yamashita & Barreto, 2005). A typical polygeneration plant produces electricity and chemical synthesis products, in particular alternative fuels, such as methanol, dimethyl ether (DME) and hydrogen. Fig. 1 shows an example of a polygeneration process producing electricity and methanol (National Energy Technology Laboratory, 2003). Polygeneration energy systems are considered to be superior to conventional stand-alone plants. Their advantages lie in three main aspects: • Energy efficiency: due to the tight integration of the power generation and the chemical synthesis sections, the overall energy utilization of a polygeneration plant is expected to be higher than the overall efficiency of stand-alone plants, producing the same products.

∗ Corresponding author at: Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, Roderic Hill Building, South Kensington Campus, London SW7 2AZ, UK. Tel.: +44 20 75946620; fax: +44 20 75941129. E-mail address: [email protected] (E.N. Pistikopoulos). 0098-1354/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2008.08.005

• Alternative fuels and energy carriers: chemical products produced by a typical polygeneration plant can be used as substitutions for traditional liquid fuels; for example, methanol for gasoline, DME for diesel oil. Hydrogen can also be a product. • Cost-effective emissions reduction: the large-scale of polygeneration energy systems is expected to result in cost-effective solutions for the implementation of CO2 capture and sequestration (CCS) units. Due to the high degree of integration and coupling between the power generation and chemical synthesis parts, determining the optimal configuration and design of a polygeneration energy system is quite a challenging task. Different process designs have been reported in literature. Ma, Ni, Li, and Ren (2004) and Ma, Ni, Li, and Ren (2004) proposed a group of sequential and parallel process designs for a coal-based polygeneration plant producing electricity and methanol. By comparing energy efficiency and economic characteristics, they concluded that the sequential design with a once-through methanol synthesis unit exhibits optimal overall performance. Liu, Gao, and Li (2006) tested the dynamic behaviour of the processes designed by Ma et al. under varying power loads, and concluded that a parallel process design will have better performance under certain operating conditions. Liu, Liu, Li, Ni, and Xu (2006) developed a novel process design producing electricity and DME from natural gas, in the context of determining a better way to transport natural gas from West China to East China. Chen, Jin, and Gao (2006) compared the energy and energy efficiencies between polygeneration plants producing electricity and

760

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

Fig. 1. A polygeneration energy system producing electricity and methanol.

DME and stand-alone DME plants, and concluded that the energy saving ratio in a polygeneration plant could be as high as 16.6%. Besides general processes producing electricity and chemical fuels, there are also other forms of polygeneration process designs for specific purposes, such as exploring the potential of coal-gas generated in coke ovens in iron and steel industry, and combining an ammonia process with a coal-based power generation process for higher energy utilization rates (Zhang, Ni, & Li, 2004; Zhang, Gao, Jin, & Cai, 2006). While the reported works above have significantly advanced our understanding of polygeneration from a design perspective, they share a common limitation—they either focus on specific technologies, or mostly focus on specific requirements/conditions. In this context, it is important to provide a general systematic methodology for the design of coal-based polygeneration energy systems, which could be applicable for different technology, design and operational requirements. In this work, building on our earlier work for the strategic planning of polygeneration energy system (Liu, Gerogiorgis, & Pistikopoulos, 2007), we present the building blocks of such a general methodology, featuring a superstructure representation and a comprehensive mixed integer optimization model formulation. The paper is structured as follows. The superstructure representation is described. The mathematical model is presented then, followed by detailed study of a polygeneration plant for the production of methanol and electricity. 2. Superstructure representation A general superstructure representation of a polygeneration plant is shown in Fig. 2, consisting of four blocks: gasification, chemical synthesis, gas turbine, and heat recovery steam generator (HRSG) and steam turbine. The superstructure acts as the overriding model, capturing all the possible alternatives and intersections between process components. For each block, several alternative technologies and types of equipment are available for selection. All combinations of these technologies and types of equipment form the design space of the plant. The optimal process design will then correspond to the best combination of these components, obtained by eliminating existence of units and links between them. To further illustrate the model superstructure and its utilization in modelling, a four-block superstructure of a coal-based polygeneration process producing electricity and methanol is discussed in

Fig. 2. General polygeneration energy system superstructure.

some detail below. Fig. 3 shows the superstructure and all alternative technologies and types of equipment for each block. The function of the gasification block is to prepare clean synthesis gas (syngas) for downstream utilization by gasifying feedstocks, usually coal, in a high temperature, high pressure, and reductive atmosphere. The crude syngas consists mainly of hydrogen, carbon monoxide, carbon dioxide, hydrogen sulphide (H2 S), carbonyl sulphide (COS), unconverted carbon, and ash. The hot crude syngas can either be quenched by cold water or cooled through a series of radiative and convective heat exchangers where heat can be recovered and used for power generation. Once it is cooled down, slag is removed and fine solid particles of unburned carbon are separated and recycled. After that, the syngas goes through a cleanup process to remove acid components which are extremely hazardous to downstream units and catalysts. Depending on the temperature of the syngas entering the cleanup process, two types of cleanup technologies are available, cold gas cleanup (CGCU) and hot gas cleanup (HGCU). In the model superstructure, the gasification block is further divided into two sub-blocks, representing the cooling part and the cleanup part. Technologies and types of equipment for the gasification block are denoted by • Q: quench. • LRC: low temperature radiative and convective cooling. • HRC: high temperature radiative and convective cooling.

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

761

Fig. 3. Superstructure representation of a polygeneration plant producing electricity and methanol.

• CC: cold syngas cleanup. • HC: hot syngas cleanup.

energy of the hot gas to mechanical work. Typical technologies and types of equipment for this block are given by

Syngas leaving the gasification block enters the methanol synthesis block. There are two kinds of commercially matured methanol synthesis technologies. According to the phase of synthesis reaction, they are known as gas phase methanol synthesis (GPMeOH) and liquid phase methanol synthesis (LPMeOH). In a GPMeOH reactor, reactants are in gas phase and react with each other on the surface of solid catalysts. In an LPMeOH reactor, gaseous reactants resolve in inert oil with solid catalyst particles being suspended in. The methanol synthesis progress typically consists of mainly three reactions, where only two of them are independent, as follows:

• GT1: gas turbine with first-stage inlet temperature at 1703 K. • GT2: gas turbine with first-stage inlet temperature at 1589 K. • GT3: gas turbine with first-stage inlet temperature at 1473 K.

CO + 2H2 → CH3 OH

(1)

CO2 + 3H2 → CH3 OH + H2 O

(2)

CO + H2 O → CO2 + H2

(3)

Besides the main reactor, some auxiliary units are needed to ensure an optimal performance for the reactor. First of all, since the synthesis reactions are highly exothermic, heat released in the synthesis reaction should be either recovered for power generation or absorbed by cooling water to obtain an isothermal operation. For the ease of controlling the reaction heat, GPMeOH has an upper limit for the carbon monoxide content in reactants and needs a water gas shift reactor before it to adjust the composition of the feeding syngas. However, LPMeOH reactors do not have such a constraint. Therefore, a water gas shift reactor always exists before a GPMeOH reactor. Secondly, both GPMeOH and LPMeOH reactors can achieve maximum conversion rate at approximately 5% for the carbon dioxide volume fraction, making the catalyst staying at the most active level. With this requirement, a carbon dioxide removal unit is usually needed before the reactor. Typical technologies and types of equipment for the methanol synthesis block are denoted by • • • •

WG: water gas shift reactor. CR: carbon dioxide removal unit. GPMeOH: gas phase methanol synthesis. LPMeOH: liquid phase methanol synthesis.

Fluegas leaving the methanol synthesis block enters the gas turbine block for power generation. This block consists of a combustion chamber where fuel burns with pressurized air to produce pressurized hot gas, an air compressor that compresses air into the combustion chamber, and a turbine that transforms the thermal

The exhausted gas leaving the gas turbine block enters HRSG where its heat is recovered to generate steam for the steam turbine, where the thermal energy in the steam is transformed into mechanical work. Technologies and types of equipment for this block are given by • LHR: low heat recovery technology with exhaust gas temperature of 450 K. • HHR: high heat recovery technology with exhaust gas temperature of 400 K. Based on such a superstructure representation, a mathematical model can be developed, as discussed next. 3. Mathematical model The mathematical model comprises the physical representation of each one of the four blocks in the superstructure representation discussed in the previous section, along with an appropriate objective function. Mixed-integer logical conditions are also employed, associated, for example, with selection of technologies, types of equipment and connectivity restrictions. Nomenclature notation is listed in Appendix A. 3.1. Gasification block Mass composition, temperature and pressure of the fuel stream fed to the gasification block are given by z(ie) =

Tf =





z0 (ft, ie)yf (ft)

(4)

ft

Tf,0 (ft)yf (ft)

(5)

ft

Pf =

 ft



Pf,0 (ft)yf (ft)

(6)

ft

yf (ft) = 1

(7)

762

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

where z0 , Tf,0 , and Pf,0 are mass composition, temperature, and pressure of the feeding fuel ft, respectively, and yf is a binary variable representing the selection of ft. Physical properties of other feeding streams, like water or steam, and oxygen or air, can be expresses in a similar way. Key operational parameters of the gasifier are given as follows: Rwaterfuel =



Rwaterfuel,0 ygas (gft)



RO2 fuel,0 ygas (gft)

= UAH maf + 2MWH mogfwater MWO morawsg (xCO + 2xCO2 + xH2 O + xCOS + xCH3 OH ) = UAO maf + MWO (mogfwater + 2mogfO2 XO2 )

(a3)

(9)

2MWN morawsg xN2 = UAN maf + 2MWN mogfO2 XN2

(a4)

MWS morawsg (xH2 S + xCOS ) = UAS maf

(a5)

gft

Cgas (rs) =

Tgas =





Cgas,0 (rs, gft)ygas (gft)

(10)

marawsg = morawsg



MWi xi ,

i

gft

Tgas,0 ygas (gft)

(a2)

(8)

gft

RO2 fuel =

MWH morawsg (2xH2 + 2xH2 O + 4xCH4 + 2xH2 S + 4xCH3 OH )

i = N2 , H2 , CO, CO2 , H2 O, CH4 , H2 S, COS, CH3 OH

(a6)

(11)

gft

Pgas =





Pgas,0 ygas (gft)

(12)

gft

ygas (gft) = 1

(13)

gft

where Rwaterfuel,0 , RO2 fuel,0 , Cgas,0 , Tgas,0 , Pgas,0 are specific technical parameters for gasification technology gft, whose physical meanings are presented in Appendix A. Eq. (13) guarantees that one and only one gasification technology is selected. Using these parameters, mass relations between the feeding steams of the gasifier can be set up, as follows: magfwater = maf Rwaterfuel magfO2 = maf RO2 fuel

(14) (15)

Mass balances connecting the feedstocks of the gasifier and the crude syngas are then built on an elementary basis: f (z(ie), maf , magfwater , magfO2 , marawsg ) = 0

(16)

The mole flowrate and the mass flowrate of the crude syngas can be connected to each other through its mole composition and the molecular weight of its components: f (marawsg , morawsg , xrawsg ) = 0

(17)

Eq. (16) is on an elementary basis, while Eq. (17) is on a component basis. Considering the fact that more types of components exist in the crude syngas than elements in the feedstocks, ratios of mole fractions between certain components in the crude syngas, which are associated with a particular type of gasification technology, are added. f (xrawsg , ˛gas ) = 0

(18)

Specific enthalpy and enthalpy can be expressed as a function of mole composition, temperature and pressure, as follows: hrawsg = h(Tgas , pgas , xrawsg )

(19)

Hrawsg = morawsg hrawsg

(20)

Explicit forms of Eqs. (16)–(19) depend on the specific type of feed fuel ft selected. For example, for a coal-feed gasifier, five elements exist in the feeding fuel, namely carbon, hydrogen, oxygen, nitrogen, and sulphur. Crude syngas consists of N2 , H2 , CO, CO2 , H2 O, CH4 , H2 S, COS and CH3 OH. Representations of these equations are shown below: MWC morawsg (xCO + xCO2 + xCH4 + xCOS + xCH3 OH ) = UAC maf

(a1)

xH2 O = ˛H2 O/H2 xH2

(a7)

xCH4 = ˛CH4 /H2 xH2

(a8)

xCO2 = ˛CO2 /CO xH2

(a9)

hi = h0i + At + B

t2 t3 t4 E +C + D − + F − H, 2 3 4 t

i = N2 , H2 , CO,

CO2 , H2 O, CH4 , H2 S, COS, CH3 OH

t=

T 1000

hrawsg =

(a10)

(a11)



xi hi ,

i

i = N2 , H2 , CO, CO2 , H2 O, CH4 , H2 S, COS, CH3 OH

(a12)

Parameters in Eq. (a10) can be obtained from NIST Chemistry Webbook (NIST, 2005). A capacity constraint is added to size the gasifier, as follows: maf − Fgas ≤ 0

(21)

Selection of technologies for the gasifier cooler, sizing of the cooler and physical properties of the syngas leaving the cooler were also modelled in a similar way as for the gasifier. Heat recovered in the gasifier cooler is given by Hcooler = Hcoolsg − Hrawsg

(22)

The recovered heat is used for power generation. The amount of power generation depends on the temperature and pressure of the working fluid carrying it and the working process in the HRSG and steam turbine block. Instead of going into extensive technical details of heat transfer and fluid engineering, which is not the focus of this model, all the influential factors involved in generating power from the recovered heat are incorporated in a single parameter cooler , defined as the ratio of the power generated by the recovered heat to the total amount of the recovered heat. Thus the power generated indirectly from the gasifier cooler is given by Wcooler = Hcooler cooler

(23)

Note that in case various technologies are not compatible, mixed integer logical constraints are added. For example, a hot gas cleanup unit can never be used after a quench cooler, instead, it requires a cooler using high-temperature radiative and convective technology, which can be represented as follows: ycleanup (HC) − ycooler (HRC) ≤ 0

(24)

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

Calculations of physical properties, mole composition, mass flowrate, and enthalpy for streams in the other blocks are derived in a similar way, hence omitted in the following. Only mathematical expressions with unique characteristics to the particular case are depicted below. 3.2. Chemical synthesis block Leaving the cleanup unit, the clean syngas is split into two streams. One goes through an optional water gas shift reactor, and the other is bypassed, both mixing together again after the water gas reactor. Mole composition of the stream going through the reactor is changed through the water gas shift reaction CO + H2 O → CO2 + H2

(25)

while the bypassed stream keeping unchanged. This is a means of adjusting the mole composition of the syngas according to the requirements of the methanol synthesis reactor. The degree of adjustment depends on the design parameter of split ratio Rsplit given by the following equation: f (Rsplit , maclsg , xclsg , xwgsg ) = 0

(26)

The syngas then goes through a carbon dioxide removal unit, where the fraction of carbon dioxide in the syngas is adjusted to an appropriate level for the best performance of the catalysts in the methanol synthesis reaction, given by

763

combustion chamber with a large amount of compressed air to produce gas with sufficient high temperature and pressure. Mathematically, the combustion procedure is expressed as an oxidation reaction with excessive oxygen. Assuming complete combustion takes place in the combustion chamber, all carbon monoxide and hydrogen in the fuel gas is converted to carbon dioxide and steam. The selection of gasification technologies determines the temperature and pressure of the gas entering and leaving the gas turbine, denoted by T1 and p1 , and T4 and p4 , respectively. Through energy balance, the mass flowrate of the air flowing into the compressor of the gas turbine is a function with respect to T1 , the mass flowrate of the fuel gas, and its mole composition, given by f (maair , mafg , xfg , T1 ) = 0

(32)

For a typical fuel gas consisting of CO, CO2 , H2 , H2 O, O2 , N2 , and trace amount of CH4 , COS, CH3 OH, H2 S, a set of equations of explicit form of Eq. (32) are given as follows: mofg + moair = mogas1

(32a)

mofg (xfg,CO + xfg,CO2 + xfg,CH4 + xfg,COS + xfg,CH3 OH ) = mogas1 xgas1,CO2

(32b)

mofg (xfg,H2 + xfg,H2 O + 2xfg,CH4 + xfg,H2 S + 2xfg,CH3 OH ) = mogas1 xgas1,H2 O

(32c)

(27)

mofg xfg,N2 + moair XN2 = mogas1 xgas1,N2

(32d)

After the carbon dioxide removal, the syngas goes to the methanol synthesis reactor to produce methanol. Gas phase synthesis technology has a strict upper limit on the mole fraction of carbon monoxide in the syngas, given by reactions (1)–(3), as follows:

mofg (xfg,H2 S + xfg,COS ) = mogas1 xgas1,SO2

(32e)

xsg (CO2 ) = xsg,0 (CO2 )

xsg (H2 ) − (2xsg (CO) + 3xsg (CO2 )) ≥ (ymeoh (GPMeOH) − 1)U



Rmeoh,0 (pmeoh, meoh)y(meoh)

(29)

meoh

Using these parameters, mass balance between the incoming syngas and product gas is given by f (mosg , xsg , mopg , xpg , Rmeoh ) = 0

= mogas1 (2xgas1,O2 + 2xgas1,CO2 + xgas1,H2 O + 2xgas1,SO2 )

(28)

Parameters of the reactor, such as the conversion rate of reactants, depend on the selection of synthesis technologies, given by Rmeoh (pmeoh) =

mofg (xfg,CO + 2xfg,CO2 + xfg,H2 O + xfg,COS + xfg,CH3 OH ) + moair XO2

(30)

hfg,i = h0i + Atfg + B

2 tfg

2

+C

3 tfg

3

+D

4 tfg

−

4

E + F − H, tfg

i = CO, CO2 , H2 , H2 O, O2 , N2 , CH4 , COS, CH3 OH, H2 S tfg =

Tfg



xfg,i hfg,i ,

i

One realization of (30), based on mass balances established in reactions (1)–(3), is shown below as an example:

i = CO, CO2 , H2 , H2 O, O2 , N2 , CH4 , COS, CH3 OH, H2 S

mosg (xsg (H2 ) − 2Rmeoh (CO)xsg (CO) − 3Rmeoh (CO2 )xsg (CO2 ))

hair,i = h0i + Atair + B

= mopg xpg (H2 )

(31)

Crude methanol produced in the synthesis reactor goes through a series of distillation columns to produce methanol as a final product, either of fuel degree or chemical degree. Mathematically, this process is formulated as splitting the crude product into two streams. One stream contains mainly methanol and a minor content of water, depending on the product degree, whilst the other stream includes all the other components in the crude methanol. The mass flowrate of the final product methanol, or its production rate, must meet its market demand, given by Eq. (47). 3.3. Gas turbine block The exhausted gas leaving the synthesis block, also known as fuel gas, goes to the gas turbine block, where it combusts in the

(32g) (32h)

1000

hfg =

(32f)

2 tair

2

+C

3 tair

3

+D

4 tair

4

−

(32i)

E + F − H, tair

i = O2 , N2

(32j)

Tair 1000

(32k)

tair = hair =



xair,i hair,i ,

i = N 2 , O2

(32l)

i

hgas1,i = h0i + Atgas1 + B

2 tgas1

2

i = CO2 , H2 O, O2 , N2 , SO2

tgas1 =

Tgas1 1000

+C

3 tgas1

3

+D

4 tgas1

4

−

E + F − H, tgas1 (32m)

(32n)

764

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

hgas1 =



xgas1,i hgas1,i ,

i = CO2 , H2 O, O2 , N2 , SO2

(32o)

i

mofg hfg + moair hair = mogas1 hgas1

(32p)

Now that the flowrate of the air flowing through the compressor and its physical properties at the inlet and outlet point of compressor are known, the compression work consumed by the compressor can be expressed as a function of them: Wgc = f (maair , T1 , p1 , p2 )

Wgc =

isen

maair Cp T1



p2 p1

−1/



−1

(35)

A set of equations of explicit form of Eq. (35) are presented below: 2 tgas4

2

+C

3 tgas4

3

+D

4 tgas4

4

−

E tgas4

(35a)

(35b)

xgas4,i hgas4,i ,

i = CO2 , H2 O, O2 , N2 , SO2

(35c)

i

xgas4,i = xgas1,i ,

i = CO2 , H2 O, O2 , N2 , SO2

Wgt = mogas1 (hgas1 − hgas4 )

(35d) (35e)

3.4. HRSG and steam turbine block Gas leaving the gas turbine enters the HRSG and steam turbine block, where its heat is recovered in the HRSG and transformed to mechanical work in the steam turbine. An overall efficiency, denoted by st , is used to represent different technologies for HRSG and the steam turbine, given by st =



Income =



PriceP(p) × ProRate(p) × OpTime

(41)

Total costs of equipment include annual depreciated investment cost, fixed O&M cost, and variable O&M cost, as follows: CostEquip =

st,0 (hst)yst (hst)

(36)



Inv(e) + OMFix(e) + OMVar(e)

(42)

e

Assuming there are ei kinds of technologies or types of equipment e available for a certain block or unit, the investment costs are expressed as

+ F − H,

Tgas4 = 1000

hgas4 =

(40)

Income from the sale of products is given by

Inv(e) =

i = CO2 , H2 O, O2 , N2 , SO2



Profit = Income − CostEquip − CostFuel

(34)

Wgt = f (magas1 , xgas1 , T1 , p1 , T4 , p4 )

tgas4

The objective function of the model is the annual profit of the polygeneration plant over lifetime, given by

p

The mechanical work generated by the gas turbine is a function of the mass flowrate of the gas flowing through the gas turbine, its composition, and its physical properties at the point before and after the turbine, denoted by

hgas4,i = h0i + Atgas4 + B

3.5. Objective function

(33)

The realization of Eq. (33) is shown below (Al-Hamdan & Ebaid, 2006): 1

The electricity generation should meet its market demand, given by Eq. (47).



UInv0 (e, ei) × F(e, ei)

(43)

ei

0 ≤ F(e, ei) ≤ y(e, ei) × UL



y(e, ei) = 1

(44) (45)

ei

Eq. (44) ensures that if a technology or type of equipment is not selected, its corresponding capacity is zero, whilst if it is selected, the operation capacity can take any value between zero and the upper limit. Eq. (45) makes sure that one and only one kind of technology or type is selected for a piece of equipment. Equations for calculating the fixed and variable O&M costs are similar, omitted here for conciseness. Expense on purchase of fuels is expressed as below: CostFuel =



PriceF(ft) × FuelRate(ft) × OpTime

(46)

ft

Assuming there is an upper bound and lower bound for market demands, the production rate should meet the following constraints: LDemand(p) ≤ ProRate(p) ≤ UDemand(p)

(47)

st

3.6. Overall model

Work generated by the steam turbine is thus given by Wst = Hgas4 st

(37)

So far, all streams of the mechanical work consumed and generated in the process have been presented, based on which the net work generated by the process is given by W = Wgt + Wst + Wcooler + Wmeoh − WASU − Wgc

(38)

where WASU is the work consumption in the air separation unit (if there is one) which provides oxygen for the gasifier. It is a function of the mass flowrate of the oxygen steam to the gasifier (MartinezFrias, Aceves, Smith, & Brandt, 2004). The mechanical work is transformed to electricity through a generator, and the electricity generation is given by E = WG

(39)

By gathering all the terms together, we obtain the following mathematical model, shown in (p). Note that some approximations and simplifications have been made in the model, based on which we can remove redundant technical details and focus on the most important points. Firstly, we assume that reactions (1)–(3) are all the chemical reactions taking place in a methanol synthesis reactor, and there are no side reactions. Secondly, some minor quantities are neglected as they are too small compared with others and have little impact on the mass and energy balance of the process, even though technically they may be crucial. For example, steam streams extracted from steam turbines to cool gas turbine blades are essential for the operation of a gas turbine, but they are small in quantity and have little influence on energy efficiency,

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

thus these cooling streams are not taken into account in the node. max

Profit

s.t.

z(ie) = Tf =





Table 1 Ultimate analysis of Illinois #6 coal (wt.%, dry) C H O N S Ash

z0 (ft, ie)yf (ft)

ft

Tf,0 (ft)yf (ft)



765

71.72 5.06 7.75 1.41 2.82 11.24

ft

Pf =



Pf,0 (ft)yf (ft)

Table 2 Conversion rates of methanol synthesis

ft

yf (ft) = 1



ft

Rwaterfuel =

Rwaterfuel,0 ygas (gft)

RO2 fuel,0 ygas (gft)



gft

Cgas (rs) =





Cgas,0 (rs, gft)ygas (gft)

gft

Tgas,0 ygas (gft)

(p)

gft

ygas (gft) = 1

gft

.. . ycleanup (HC) − ycooler (HRC) ≤ 0 xsg (H2 ) − (2xsg (CO) + 3xsg (CO2 )) ≥ (ymeoh (GPMeOH) − 1)U Rmeoh (pmeoh) = st =

 st

Inv(e) =



Rmeoh,0 (pmeoh, meoh)y(meoh)

meoh

st,0 (hst)yst (hst)



CO2 to methanol

Gas phase Liquid phase

0.446 0.128

0.199 0.0075

2000; Floudas, Aggarwal, & Ciric, 1989; Sahinidis & Tawarmalani, 2005). Eq. (p) can be primarily used in the context of scenario analysis of various options for every polygeneration systems. Different objectives, other than profit, can also be included, such as environmental indicators (see for example Hugo, Rutter, Pistikopoulos, Amorelli, & Zoia, 2005), thereby transforming (p) into a multi-objective optimization model. The effect of uncertainty in the model parameters can also be studied—here developments in the area of optimization under uncertainty and uncertainty analysis can be explored, such as multi-parametric programming (Pistikopoulos, Georgiadis, & Dua, 2007), or global sensitivity analysis (Kontoravdi, Asprey, Pistikopoulos, & Mantalaris, 2005; Rodriguez-Fernandez, Kucherenko, Pantelides, & Shah, 2007). These topics contribute our current research focus in this area. In the following, a detailed case study will be presented for a polygeneration plant producing electricity and methanol.

UInv0 (e, ei)F(e, ei) 4. A Polygeneration plant for electricity and methanol—a case study

ei

0 ≤ F(e, ei) ≤ y(e, ei)UL



CO to methanol

gft

RO2 fuel =

Tgas =

Technology

y(e, ei) = 1

ei

Eq. (p) is a mixed-integer nonlinear programming (MINLP) formulation. It is also non-convex due to the presence of the bilinear terms in mass balance calculations. Therefore, global optimization techniques for MINLP problems are needed here to obtain a global optimum. These techniques can either be applied directed to the model, or indirectly through commercial solvers such as BARON to obtain a global optimum (Adjiman, Androulakis, & Floudas, 1997; Adjiman, Androulakis, & Floudas,

We consider a polygeneration plant as shown in Fig. 3, to produce electricity and methanol. The market demand for methanol is assumed to vary between 400 and 700 tons/day, and the electricity demand is between 100 and 300 MW. The following specifications are considered: • All four blocks of technologies and types of equipment as outlined in the previous sections are considered for selection. • Eleven chemical compounds are involved, namely O2 , N2 , H2 , CO, CO2 , H2 O, CH4 , H2 S, SO2 , COS, and CH3 OH.

Table 3 Temperature and pressure loss for each technology Unit

Technology

Temperature (K)

Pressure/pressure loss (bar)

Syngas cooler

Quench Low temperature radiative and convective High temperature radiative and convective

491 477 813

−1 −3.3 −3.3

Syngas cleanup unit

Cold cleanup Hot cleanup

320 840

−4.6 −5.6

Water gas shift reactor

Water gas shift

473

−1

Methanol synthesis

Gas phase Liquid phase

523 523

−5.5 −5.5

Gas turbine

Gas turbine technology 1 Gas turbine technology 2 Gas turbine technology 3

1703 1589 1473

19 18 17

HRSG and steam turbines

High heat recovery Low heat recovery

400 450

1.05 1.05

766

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

Table 4 Economic parameters Parameter

Value

Coal price ($/ton) Methanol ($/ton) Electricity price ($/kW h) Investment cost for the gasifier ($/((kg/s coal) years)) Investment cost for the cooler, quench ($/((kg/s syngas) years)) Investment cost for the cooler, low temperature radiative and connective ($/((kg/s syngas) years)) Investment cost for the cooler, high temperature radiative and connective ($/((kg/s syngas) years)) Investment cost for the cleanup unit, low temperature ($/((kg/s syngas) years)) Investment cost for the cleanup unit, high temperature ($/((kg/s syngas) years)) Investment cost for the water gas shift reactor ($/((kg/s syngas) years)) Investment cost for the CO2 removal unit ($/((kg/s syngas) years)) Investment cost for the methanol synthesis unit, gas phase ($/((kg/s syngas) years)) Investment cost for the methanol synthesis unit, liquid phase ($/((kg/s syngas) years)) Investment cost for the gas turbine compressor ($/((kg/s air) years)) Investment cost for the gas turbine, technology 1 ($/((kg/s gas) years)) Investment cost for the gas turbine, technology 2 ($/((kg/s gas) years)) Investment cost for the gas turbine, technology 3 ($/((kg/s gas) years)) Investment cost for the HRSG and steam turbines, technology 1 ($/((kg/s gas) years)) Investment cost for the HRSG and steam turbines, technology 2 ($/((kg/s gas) years))

35 340 0.06 28,500

15 binary variables, 299 continuous variables, 293 equations (107 nonlinear) and 20 inequality constraints. The model was solved using both DICOPT and BARON. For DICOPT, when a feasible starting point is provided, it takes 1.1 s of solver time and 9 major iterations to obtain an optimum, which DICOPT claims to be local optimum. For BARON, after providing proper lower bounds and upper bounds for all variables and scaling all variables and equations, it takes 506.2 s and 137 iterations to claim a global optimum, which is the same with the solution obtained from DICOPT. Model results indicate the following:

3,000 45,000

30,000

• The plant uses low temperature radiative and convective technology for the cooling of the crude syngas, followed by a low temperature cleanup unit. The methanol synthesis part uses gas phase synthesis technology with a water gas shift reactor before it. The power generation unit uses gas turbine technology one which has the highest first stage temperature and pressure, together with the technology of high heat recovery for the HRSG and the steam turbine. • 2991 tons of coal/day are consumed for the production of 300 MW electricity and 700 tons/day of methanol, with an annual profit of $140.6 m (electricity: $117.0 m, methanol: $64.5 m, fuel expense: $28.4 m, equipment $12.6 m). • Table 5 summarizes the results of the analysis for different combinations of technologies employed for comparison purpose. The results indicate that the combination of gas phase methanol synthesis and high efficient power generation on technologies are preferable. In most configurations, the use of liquid phase methanol synthesis results in methanol production below its maximum market demand value of 700 tons/day. On the other hand, liquid phase methanol synthesis options are in general more cost-effective due to its low operating pressure, leading to less consumption of compression work in the air separation unit. • Table 6 summarizes the results of a simple sensitivity analysis that was carried out on the effect of a change of a key parameter on the profitability and coal consumption of the best technology combination observed. We considered that parameters follow normal distribution and have nominal values with known standard deviations, as given in Table 6. Note that amid operating time, electricity price and demand greatly influence the profitability of the plant, whereas the price of methanol and its market demand play a less dominant role. Note also that the price of coal has the most dominant effect.

20,000 40,000 5,000 5,000 15,000 20,000 2,000 3,000 2,500 2,000 3,000 2,500

• In the gasification block, Texaco gasification technology is applied to the gasifier, which uses dry pulverized coal, pure oxygen, and steam from power generation sector as main feedstocks. The gasification temperature and pressure is 1371 ◦ C and 42 bar, respectively. Parameters of the gasification and power generation units are from NETL’s report of Texaco IGCC case study (Shelton & Lyons, 1998). • Technical parameters used in the model are listed in Tables 1–3. Table 1 depicts the characteristic of the coal considered. Table 2 shows the conversion ratios of gas phase and liquid phase methanol synthesis technologies, whereas Table 3 outlines the corresponding operating conditions. • Economic parameters for prices and unit costs are listed in Table 4. A time horizon of 30 years is considered for depreciation, with an annual operating time of 6500 h. The overall model is implemented in GAMS (GAMS Development Corporation). See http://www.gams.com/dd/docs/ bigdocs/GAMSUsersGuide.pdf for the details. The model involves

An interesting observation can be made in relation to the conversion ratio of the methanol synthesis. Note that its increase does not lead to a decrease of the coal consumption but rather to an increase. This can be explained as follows. Since the conversion ratio is already sufficiently high, its further increase will only result in making the fluegas stream exiling the synthesis reactor to have a lower value of its flowrate and heating value. As a result, more coal consumption is required to generate more syngas for power

Table 5 Model results for technology combinations Technology combination

Power (MW)

Methanol (ton/d)

Coal (ton/d)

Profit (million dollar)

LRC–CC–WG–GPMeOH–GT1–HHR LRC–CC–WG–GPMeOH–GT1–LHR LRC–CC–WG–GPMeOH–GT2–HHR LRC–CC–WG–GPMeOH–GT3–HHR Q–CC–WG–GPMeOH–GT1–HHR LRC–CC–LPMeOH–GT1–HHR Q–CC–LPMeOH–GT1–HHR Q–CC–LPMeOH–GT2–LHR Q–CC–WG–LPMeOH–GT3–LHR

300 300 300 300 300 300 300 300 300

700 700 700 700 700 474 588 673 700

2991 3050 3173 3460 3618 2567 3182 3643 4113

140.6 139.9 137.7 133.2 136.9 125.0 131.4 133.5 129.6

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

767

Table 6 Sensitivity Analysis Parameters

Nominal value

Standard deviation

Coal consumption

Profit

Annual operating time (h) Market demand for electricity, upper bound (MW) Market demand for electricity, lower bound (MW) Market demand for methanol, upper bound (t/d) Market demand for electricity, lower bound Coal price ($/t) Electricity price ($/kWh) Methanol price ($/t) Investment cost (k$/(kg/s)/y) O&M costs (k$/(kg/s)/y) Temperature at first stage of gas turbine (K) Energy efficiency of HRSG and steam turbines Conversion ratio of methanol synthesis

6500 300 100 700 400 35 0.06 340 227 22.7 1703 0.454 0.645

650 30 10 70 40 3.5 0.006 34 22.7 2.27 170.3 0.0454 0.0645

0 0.628 0 0.190 0 0 0 0 0 0 −0.738 −0.157 0.031

0.656 0.363 0 0.239 0 −0.121 0.501 0.276 −0.045 −0.009 0.190 0.035 −0.005

generation. This extra amount of coal consumption cannot be compensated by the enhanced efficiency of the methanol synthesis block, hence the overall coal consumption increases. Interestingly, increasing the conversion ratio of the methanol synthesis does not lead to less coal consumption but the other way round. This is because the conversion ratio is already sufficiently high, further increase will only make the fluegas leaving the synthesis reactor to have lower flowrate and heating value. More coal consumption is therefore required to generate more syngas to keep the power generation. This extra amount of coal consumption cannot be compensated by the enhanced efficiency of methanol synthesis, thus the overall coal consumption increases. Acknowledgements The authors would like to gratefully acknowledge the financial support from BP and its contribution in the inception, progress, and completion of this research study. Pei Liu would also like to thank Kwoks’ Foundation for providing scholarship. Appendix A Sets e ei ft gft hst ie p rs

Equipment Technology for a piece of equipment Available fuel feedstocks Gasification technologies Available technologies for HRSG and steam turbines Elements in a fuel feedstock Product Key chemical compounds in the syngas

Variables Binary variable y Continuous variables  C CostEquip CostFuel E F FuelRate H Income Inv OMFix OMVar P Profit ProRate R T

Energy efficiency Key mole ratios in the crude syngas Investment cost and O&M cost on equipment Cost on fuel Electricity generation rate Equipment capacity Fuel consumption rate Enthalpy Sale of products Investment cost Fixed O&M cost Variable O&M cost Pressure Annual profit of a polygeneration plant Production rate Ratio Temperature

W ma mo h x z

Mechanical work Mass flowrate Mole flowrate Specific enthalpy Mole composition Mass fraction for an element in the fuel feedstock of the gasifier

Parameters ˛ 0  Cp LDemand MW OpTime P0 PriceF PriceP R0 T0 U UA UDemand UInv0 UL X z0

Key mole ratios in crude syngas Energy efficiency Adiabatic coefficient Specific heat capacity at a constant pressure Lower bound for market demand Molecular weight Operation time per year Pressure Fuel price Product price Ratio Temperature A large positive number Ultimate analysis of feeding fuel, on a weight basis Upper bound for market demand Unit investment cost Upper limit for process capacity Mole composition Mass fraction for an element in a fuel feedstock

Subscripts ASU G O2 fuel air cleanup clsg cooler coolsg f fg gas gas1 gas4 gc gfO2 gfwater gt isen meoh pg pmeoh rawsg sg split st waterfuel wgsg 1 4

Air separation unit Generator Oxygen and fuel feeding streams to a gasifer Air entering a gas turbine Syngas cleanup unit Clean syngas Syngas cooler Cooled syngas Feeding fuel stream to a gasifier Fuel gas entering a gas turbine Gasifier Gas at the inlet of a gas turbine Gas at the outlet of a gas turbine Gas turbine compressor Feeding oxygen stream to a gasifier Feeding water stream to a gasifier Gas turbine Isentropic procedure Methanol synthesis Product gas after methanol synthesis Parameters for methanol synthesis Raw syngas Syngas for the chemical synthesis reaction Split ratio for the water gas shift reaction Steam turbine Water and fuel feeding streams to a gasifier Syngas after water gas shift reaction Inlet point of a gas turbine Outlet point of a gas turbine

768

P. Liu et al. / Computers and Chemical Engineering 33 (2009) 759–768

References Adjiman, C. S., Androulakis, I. P., & Floudas, C. A. (1997). Global optimization of MINLP problems in process synthesis and design. Computers and Chemical Engineering, 21, S445–S450. Adjiman, C. S., Androulakis, I. P., & Floudas, C. A. (2000). Global optimization of mixed-integer nonlinear problems. AIChE Journal, 46(9), 1769–1797. Al-Hamdan, Q. Z., & Ebaid, M. S. Y. (2006). Modeling and simulation of a gas turbine engine for power generation. Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, 128(2), 302–311. Chen, B., Jin, H. G., & Gao, L. (2006). Study of DME/power individual generation and polygeneration. Kung Cheng Je Wu Li Hsueh Pao/Journal of Engineering Thermophysics, 27(5), 721–724. Floudas, C. A., Aggarwal, A., & Ciric, A. R. (1989). Global optimum search for nonconvex NLP and MINLP problems. Computers and Chemical Engineering, 13(10), 1117–1132. GAMS Development Corporation. GAMS—A user’s guide. Retrieved January, 2008, from http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf. Hugo, A., Rutter, P., Pistikopoulos, S., Amorelli, A., & Zoia, G. (2005). Hydrogen infrastructure strategic planning using multi-objective optimization. International Journal of Hydrogen Energy, 30(15), 1523–1534. Kontoravdi, C., Asprey, S. P., Pistikopoulos, E. N., & Mantalaris, A. (2005). Application of global sensitivity analysis to determine goals for design of experiments: An example study on antibody-producing cell cultures. Biotechnology Progress, 21(4), 1128–1135. Li, Z., Ni, W., Zheng, H., & Ma, L. W. (2003). Polygeneration energy system based on coal gasification. Energy for Sustainable Development, 7(4), 57–62. Liu, G. J., Liu, Y., Li, Z., Ni, W. D., & Xu, H. Y. (2006). Design and analysis of a new dimethyl ether-electric power polygeneration system. Dongli Gongcheng/Power Engineering, 26(2), 295–299. Liu, P., Gao, J., & Li, Z. (2006). Performance alteration of methanol/electricity polygeneration systems for various modes of operation. Dongli Gongcheng/Power Engineering, 26(4), 587–591. Liu, P., Gerogiorgis, D. I., & Pistikopoulos, E. N. (2007). Modeling and optimization of polygeneration energy systems. Catalysis Today, 127(1–4), 347–359. Ma, L. W., Ni, W., Li, Z., & Ren, T. J. (2004a). Analysis of the polygeneration system of methanol and electricity based on coal gasification (1). Power Engineering, 24(3), 451–456. Ma, L. W., Ni, W., Li, Z., & Ren, T. J. (2004b). Analysis of the polygeneration system of methanol and electricity based on coal gasification (2). Power Engineering, 24(4), 603–608.

Martinez-Frias, J. M., Aceves, S. M., Smith, J. R., & Brandt, H. (2004). Thermodynamic analysis of zero-atmospheric emissions power plant. Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, 126(1), 2– 8. National Energy Technology Laboratory (2003). Commercial-scale demonstration of the liquid phase methanol (LPMEOH) process (A DOE Assessment). United States. Ni, W., & Johansson, T. B. (2004). Energy for sustainable development in China. Energy Policy, 32(10), 1225–1229. Ni, W., Li, Z., &Yuan, X. (2000). National energy futures analysis and energy security perspectives in china—strategic thinking on the energy issue in the 10th fiveyear plan (FYP). Workshop on East Asia Energy Futures, Beijing. NIST (2005). NIST Chemistry WebBook. NIST Standard Reference Database Number 69, from http://webbook.nist.gov/chemistry/. Pistikopoulos, E. N., Georgiadis, M. C., & Dua, V. (2007). Multi-parametric programming: Theory, algorithms, and applications Weinheim: Wiley-VCH. Rodriguez-Fernandez, M., Kucherenko, S., Pantelides, C., & Shah, N. (2007). Optimal experimental design based on global sensitivity analysis. Computer-Aided Chemical Engineering, 24 Sahinidis, N. V. & Tawarmalani, M. (2005). BARON 7.2.5: Global Optimization of Mixed-Integer Nonlinear Programs, User’s manual. Retrieved January, 2008, from http://www.andrew.cmu.edu/user/ns1b/baron/bibliography.html. Shelton, W. & Lyons, J. (1998). Texaco Gasifier IGCC Base Cases, US Department of Energy. U.S. Department of Energy (1999). Vision 21 program plan: Clean energy plants for the 21st century. Washington, DC. U.S. Department of Energy (2001). Vision 21 fossil fuels options for the future. Retrieved January, 2008, from http://fossil.energy.gov/programs/powersystems/publications/Strategic Plans/2001/mypp 2001 vision21.pdf. Yamashita, K., & Barreto, L. (2005). Energyplexes for the 21st century: Coal gasification for co-producing hydrogen, electricity and liquid fuels. Energy, 30(13), 2453–2473. Zhang, X., Gao, L., Jin, H., & Cai, R. (2006). Design and analysis of coal based ammoniapower polygeneration. Dongli Gongcheng/Power Engineering, 26(2), 289– 294. Zhang, Y., Ni, W., & Li, Z. (2004). Research on superclean polygeneration energy system of iron and steel industry. In Proceedings of the Seventh IASTED International Conference on Power and Energy Systems, November 28–December 1. Clearwater Beach, FL, United States, Anaheim, CA, United States: Acta Press.