Optimal Gas Turbine Integration to the Process Industries - American

Ind. Eng. Chem. Res. 1999, 38, 4317-4329

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Optimal Gas Turbine Integration to the Process Industries Jussi Manninen† and X. X. Zhu* Department of Process Integration, UMIST, P.O. Box 88, Manchester, M60 1QD, U.K.

Deregulated electricity markets provide good opportunities for the process industries to seek benefits by importing or exporting electricity. Gas turbine is a very good option for increasing power generation capacity due to its high power-to-heat ratio and relatively low investment cost. In this paper, a new systematic methodology for gas turbine integration is presented. The methodology employs mathematical programming in a systematic manner. The first stage is a screening stage, where promising gas turbine integration options and the optimal size range for a gas turbine are identified. These options with the model of the existing plant form a superstructure, which is optimized to get an initial design. In the second stage, constraint analysis identifies the dominant constraining units in the existing system. Relaxing these constraints and introducing new options are then considered in updating the superstructure, subject to further optimization. With this strategy, we effectively solve a much smaller optimization problem while guaranteeing good solution quality from this iterative approach. Introduction The main objective for considering gas turbine integration to the process industries is to reduce the operational costs of a site. The reduction in operational cost is partially due to the increased thermal efficiency of the site, which results in fuel savings, and partially due to the increased power-to-heat ratio, which enables the site to produce more electricity for the same amount of heat requirement. More importantly, increased power production capability can provide the site flexibility in dealing with importing and exporting electricity in the deregulated electricity markets. Gas turbine integration can also help cut down flue gas emissions as a result of the improved efficiency of a cogeneration system. Integration of gas turbines to an existing site is not a trivial task. It involves simultaneous grass root design of a gas turbine system and retrofit of an existing system to accommodate the gas turbine system. During this design process several complex issues need to be taken into account to ensure a successful integration. These issues include (i) selecting the most appropriate gas turbine, (ii) determining the optimal gas turbine integration scheme, (iii) considering changes to the existing system to exploit synergy effects, (iv) taking into account operational characteristics and hardware constraints of a site, and (v) considering external economic factors. Townsend and Linnhoff (1983a,b) considered gas turbine integration through use of gas turbine exhaust for individual processes, and they developed the concept of grand composite curve for analysis of gas turbine integration. Building upon this method, Dhole and Linnhoff (1993) attempted to address the gas turbine integration in the site context. In both cases, the designer can use graphical tools to estimate the size of a gas turbine for satisfying either directly or indirectly the process requirements. However, although the above methods can provide quick estimates, they may give a

false estimate of the true potential, since these methods do not take into account the constraints of existing site equipment, operational constraints, and options to modify an existing system to better accommodate a gas turbine system. On the other hand, research has been carried out in using mathematical programming to solve the problem of gas turbine integration. These methods are divided into two main categories: flow sheet synthesis and operational optimization. In flow sheet synthesis, the main emphasis has been on grass root design of utility systems (Papoulias and Grossmann, 1983; Bruno et al., 1998; Wilkendorf et al., 1998). In these methods gas turbine and heat recovery steam generator are considered as one of several options for satisfying a given power and heat demand. Singh et al. (1998) investigated the problem of retrofitting an existing total site for reducing flue gas emissions using gas turbine integration as one of the major options. All of the above methods, except that of Wilkendorf et al. (1998), do not consider multiple operational aspects. On the other hand, operational optimization methods take into account multiple operations, which are defined by tariffs, demands, and so forth in different periods. Ito et al. (1988, 1995) presented MILP planning models for optimizing gas turbine-based power systems. Hui and Natori (1996) proposed a multiperiod MILP model for operational optimization and maintenance scheduling of utility systems. In this present work, the two distinguished aspects, flow sheet synthesis (design aspects) and operational optimization (operation aspects) are combined. This allows us to simultaneously consider grass root design of the gas turbine system and its integration with the existing system, while at the same time performing operational optimization to achieve the best economic performance. Problem Definition

* Author for correspondence. E-mail: [email protected]. Phone: +44 161 200 4398. Fax: +44 161 236 7439. † Current address: VTT Energy, P.O. Box 1603, FIN-40101 Jyva¨skyla¨, Finland.

The problem can be stated as follows. Given an industrial site, the objective is to find the gas turbine integration scheme that minimizes total cost including

10.1021/ie990260t CCC: $18.00 © 1999 American Chemical Society Published on Web 09/28/1999

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Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999

Figure 1. Gas turbine integration options.

operational cost and capital investment for a gas turbine system. Gas turbines can be integrated either to a utility system, process furnaces, or directly to processes. The integration is subject to internal constraints (e.g. hardware limits) and external constraints (e.g. fuel availability, constraints for power export and import, and electricity tariffs). Multiple operational characteristics in terms of changes in heat and power demands and tariffs are taken into account. Modifications to existing processes and utility systems are also considered for improving the economics of the integration. The main characteristics of the problem are discussed in more detail as follows. What Size and Type of Gas Turbine To Select? Selection of the size and type of the gas turbine is the key issue to be addressed in this problem. Gas turbines are available at discrete sizes. Currently there are around 100 different gas turbines available on the market. They are of two main types, namely industrial and aeroderivative gas turbines. Industrial gas turbines are heavy-duty single-shaft machines, while the aeroderivative turbines are modified twin-shaft aircraft engines. The aeroderivative turbines have higher efficiency than the industrial type, but they are more expensive. Selection of the most suitable gas turbine is mainly based on the tradeoff between efficiency and capital cost in the range of possible operation scenarios. It should be noted that the aeroderivative turbines tend to have a lower exhaust temperature and exhaust oxygen content than the industrial ones, which can limit their use in some applications. Which Integration Scheme To Chose? There are various alternatives for integrating a gas turbine to an existing site. Selection of the most appropriate integration scheme determines the majority of benefit from the use of gas turbine. These options can be classified into four main schemes (Allen and Kovacik, 1984; Shallice, 1985) (Figure 1): (1) use gas turbine exhaust to raise steam in a heat recovery steam generator (HRSG); (2) use gas turbine exhaust as combustion air in furnace or boiler; (3) use gas turbine exhaust directly for process heating; (4) use gas turbine as a process driver either directly or indirectly. Each of the integration schemes requires some additional capital expenditure. The first two options are the most common ones. Shallice (1985) discussed gas turbine integration with both furnaces and steam systems, and provided engineering and economic evaluation criteria for gas turbine integration. How to Address Operational Characteristics? The capital cost of the gas turbine integration depends on the selected gas turbine and the integration scheme. To justify the capital expenditure, operational savings

should result from gas turbine integration. The operational characteristics of the site and external economic factors have a paramount influence on the amount of savings that can be achieved by gas turbine integration. The main characteristics are as follows: (1) existing hardware (e.g. how many boilers, turbines, etc.) and their capacity constraints; (2) fuel availability and prices of fuel and electricity; (3) operational scenarios of the plant, which determine the seasonal heat and electricity demand. What Changes to Make To Enhance the Profit of an Overall Plant? Although significant economic benefits could be obtained by gas turbine integration alone, it may be beneficial to look at changes to both the utility system and processes to make the integration more profitable. To do this, we need to identify equipment or processes, which limit the full potential of the gas turbine integration. The purpose is to find dominant constraining units, which impose the biggest economic penalty, and how to overcome or relax these constraints. Gas Turbine Exhaust Utilization. Dedicated discussions for gas turbine exhaust are given here to provide more insights for gas turbine integration. Gas turbine exhaust is well suited for heat recovery and firing, since it has a high temperature (450-600 °C) and contains plenty of oxygen (12-15% per volume). There are three distinct firing modes, namely unfired, supplementary fired, and fully fired. In the unfired mode the sensible heat of the flue gas is used in a heat recovery steam generator (HRSG). In supplementary firing the temperature of flue gas is raised to 850-900 °C. Generally the same HRSG (with a convection section only) can be used in both unfired and supplementary fired modes. The main purpose of using supplementary firing is to provide flexibility for satisfying fluctuating steam demands without affecting the gas turbine performance. Supplementary firing provides the incremental steam at a very high marginal efficiency, which can exceed 100%. In full firing practically all of the oxygen is consumed and the flue gas temperature is raised to around 15001700 °C. This requires a radiant heat-transfer section in addition to a convection section in the heat recovery unit. The major tradeoff in the HRSG design is between the heat recovery efficiency and the capital cost. The heat recovery efficiency can be enhanced by increasing the number of pressure levels and by minimizing the temperature difference at pinch points, but at the same time the heat exchanger area is increased. Increased heat exchanger area also increases pressure drop, which decreases the gas turbine output. Integrating a gas turbine with an existing boiler or furnace can be more complicated than integration with a HRSG. In some cases the modification costs of the boiler or the furnace may become prohibitive. When a gas turbine is integrated with a boiler or a furnace, the gas turbine exhaust is used as preheated combustion air. The exhaust contains less oxygen than air, which usually leads to a lower flame temperature, even though the degree of air preheat is higher. Lower flame temperature results in a reduced duty in the radiant heattransfer section, while the convective duty remains practically constant. This creates an imbalance between the radiant and convective sections. Modifications may be necessary in order to cope with the new balance. Technical aspects of integrating gas turbines with fired

Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4319

Figure 2. New design methodology.

heaters have been discussed by Iaquaniello et al. (1984), Shallice (1985), and Cooke and Parizot (1991).

Figure 3. Example of screening results.

New Methodology for Gas Turbine Integration to Process Industries General. To address effectively all the issues mentioned above, we propose a sequential iterative methodology based on the use of mathematical programming. The overview of the methodology is presented in Figure 2. The first stage is a screening stage, where promising gas turbine integration options and the optimal size range for a gas turbine are identified. These options with the model of the existing plant form a superstructure, which is optimized to get an initial design. This design does not consider any changes to the existing plant except those required by the integration schemes. In the second stage, constraint analysis identifies the dominant constraining units in the existing system. Relaxing these constraints and introducing new options are then considered in updating the superstructure. This procedure can be repeated until no promising options can be found. The proposed method differs from existing general superstructure-based methods in that relevant options are identified systematically and are used as the basis to generate a reduced superstructure. The procedure reflects the nature of practical engineering design practice in generating design options evolutionarily. In the early stage, we set up design objectives and have a certain level of understanding of major aspects. However, in the early stage, we have limited understanding of complex interactions and synergy between a gas turbine system and existing systems. This understanding is improved through the design process, which gradually reveals promising options. These options form the basis to build a relevant superstructure, which is updated when new options appear at any design stages. With this strategy, we effectively solve a much smaller optimization problem while considering all relevant design options. Screening Stage. The purpose of this stage is to determine the promising range of gas turbines to be considered. It is performed using parametric optimization individually for each integration option, gas turbine type, and gas turbine fuel. For the furnace integration case the gas turbine exhaust flow is fixed to match the flue gas flow of each furnace. For the HRSG integration case, the model is optimized at several discrete gas turbine outputs. Figure

Figure 4. Integration superstructure.

3 shows an example as to how an integration option is determined initially. In the example of Figure 3 the objective is to maximize annual savings by integrating a gas turbine. For each of the integration options the maximum economic potential is determined by optimizing the overall model, including the existing plant. By obtaining several optimal points for different gas turbine output, we can clearly see a trend in the economic performance of each option as a function of the gas turbine output. In the example in Figure 3, it can be seen that the best options are to integrate a gas turbine of around 30 MW either with one of the furnaces or to a HRSG, since this yields the biggest savings. Similarly, the pay back time for the investment can be plotted against gas turbine output. Sensitivity analysis regarding changing prices of fuel, electricity, and capital can also be performed easily at this stage. Integration with Necessary Changes. At this stage we want to select a gas turbine from a discrete set of real gas turbines within the size range determined by the screening stage. Thus, the formulation becomes a mixed-integer model (MILP). Gas turbines with the promising integration options form a superstructure (Figure 4). The superstructure allows the gas turbine exhaust to be simultaneously used for both furnace and HRSG. Optimization of this superstructure gives the initial design. Identification of Design Changes. The need for changing the existing utility system design arises when the optimization in the integration stage indicates that some of the existing utility equipment reached their

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trial gas turbines and LP2 with aeroderivative gas turbines, are presented first. The two design models, MILP1 for integration without changes and MILP2 for integration with changes, are presented thereafter. Screening Models (LP1 and LP2). Mass Balances.

∑

mi,j )

i∈IN(i,k)

lo up e mi,j e mi,j mi,j

Figure 5. Possible changes to the existing system.

capacity limits. To identify which pieces of equipment impose dominant constraints for gas turbine integration, we need to investigate the marginal values of relaxing these constraints. The marginal values are defined by changes in the objective value versus one unit change (e.g. 1 t/h or 1 MW) in the capacity for these constrained units. In such a way we can identify the dominant constraints and relax them in the further optimization. It should be noted that we use marginal values as an indicator of dominant constraints and let the optimization determine the degree of relaxation of these constraints. As we consider multioperation aspects, marginal values can also change from one operation to another. The time-weighed average of marginal values over all the periods is calculated and used as a benchmark. Integration with Synergistic Design Changes. Once the dominant constraining units have been identified, design changes can be proposed to overcome the bottlenecks. Figure 5 illustrates some of possible changes. There are basically two ways to overcome a bottleneck. The first option is to increase the capacity of constrained units. In this case a slack variable is assigned to each constrained unit and the capital cost of the capacity increase is defined as a function of the slack variable. Alternatively the structure of the utility system can be changed to get around the bottleneck. A local superstructure can be constructed to address these options, and the structural decisions are made using binary variables to indicate the existence of new units or connections. In some cases the capacity of certain units (e.g. steam turbine drives) is fixed. In this case the turbine can be replaced by, for example, an electric motor. On the process side we can investigate process HEN retrofit using the Network Pinch technique proposed by Asante and Zhu (1997) or explore opportunities for steam substitution (e.g. use MP steam to replace currently used HP steam) (Makwana et al., 1998). At the same time we may want to revise the gas turbine selection. This could be done in cases where the proposed changes could change the electricity consumption of the site. Once the promising change options are determined, the overall superstructure is modified. The optimization of this superstructure gives an improved design. Mathematical Models General. The screening models (LP1 and LP2) are linear programming (LP) models, and the integration models (MILP1 and MILP2) are mixed integer linear programming (MILP) models. The mathematical models for screening and design are presented as follows. The nomenclature is provided in Appendix A. The screening models, LP1 with indus-

∑

∀j ∈ J, k ∈ K

mi,j

(1)

i∈OUT(i,k)

∀i ∈ I, j ∈ J

(2)

All the process units (i ∈ I) are connected to a steam or condensate header (k ∈ K). The mass balance is calculated around the steam and condensate headers for every operational scenario (j ∈ J). It should be noted that all the process units are modeled such that at most one inlet and one outlet is allowed. Also all connections between headers and external flows, like imported steam, are modeled as process units. Mixers and splitters are modeled as headers. Fuel and Electricity Constraints. min Qf,j e

∑

f gtf max Qi,f,j + (Qgt + Qsf j )‚zf e Qf,j

i∈FURN,BOIL

Wmin e j

∀f ∈ F, j ∈ J (3)

Wi,j + Wgt - Wp e Wmax ∑ j i∈TUR

∀j ∈ J (4)

Both furnaces and boilers can use several fuels at the same time. Use of any fuel (f ∈ F) in the boilers and furnaces (Qf), in a gas turbine (Qgt), and in supplementary firing (Qsf) can be constrained for any operational scenario. The binary parameter zgtf indicates whether a fuel is used in a gas turbine and supplementary firing. Similarly bounds can be assigned for the net shaft work production of the site. Industrial Gas Turbines.

Qgt ) (2.84 × 10-3)Wgt + 7.33

(5)

mgt ) (2.9 × 10-3)Wgt

(6)

Tgt ) (0.4 × 10-3)Wgt + 493.42

(7)

cgt ) (195.1 × 10-3)Wgt + 2529.2

(8)

Aeroderivative Gas Turbines.

Qgt ) (2.35 × 10-3)Wgt + 7.75

(9)

mgt ) (3.1 × 10-3)Wgt

(10)

Tgt ) -10-3Wgt + 512.24

(11)

cgt ) (295.5 × 10-3)Wgt + 2002.2

(12)

Equations 5-12 are developed from this work for estimating fuel consumption (Qgt), exhaust mass flow (mgt), exhaust temperature (Tgt), and capital cost (cgt) for industrial and aeroderivative gas turbines. The gas turbines have been divided into two groups because these two types have different characteristics and capital costs. The models are based on published data of gas turbines on ISO conditions and using natural gas as fuel (Gas Turbine World, 1997; www.gas-turbines.com, 1996). In the case of using a fuel with a low


Feedwater Heaters.

∀j ∈ J, i ∈ FWH (19)

mi,j∈BLEED(i,i) ) afi‚mi,j + bfi

Figure 6. Willans line.

heating value, it is assumed that the performance of a gas turbine does not change, and the exhaust mass flow is kept constant by bleeding excess air from the compressor. Auxiliary Gas Turbine Equations.

mgt ) mgt,furn + mgt,stack + mgt,hrst j j j Wp ) ap‚Qgt

∀j ∈ J

(13)

∀i ∈ TUR, j ∈ J (15)

Following Chou and Shih (1987), extraction steam turbines are decomposed into simple turbines operating between steam mains. Steam Boilers.

∆hsi Qi,j ) mi,j‚ ηi

∑f

f Qi,f,j ) Qi,j

∑

mjgt,furn )

m0i ‚zfurn ‚zi,j i

∀j ∈ J

(20)

i∈FURN

‚ffuel,gt + (1 - zfurn )]‚Q0i ‚zi,j Qi,j ) [zfurn i i i ∀j ∈ J, i ∈ FURN (21) f ) Qi,j ∑f Qi,f,j

(14)

The gas turbine exhaust can be simultaneously directed as combustion air to a furnace, to a HRSG, and to a bypass stack (eq 13). By introducing the bypass stack, we can consider operational scenarios, when a furnace or a HRSG is not in operation but the gas turbine can still be used in stand-alone mode with the exhaust directed to a bypass stack. It is assumed in eqs 5-12 that the fuel pressure is higher than the pressure of compressed air. If a fuel with lower pressure than that required is to be used in a gas turbine, the shaft work required to compress the fuel (Wp) is added to the shaft work requirement. Steam Turbines. The behavior of existing steam turbines is described using the Willans line (Church, 1950) (Figure 6). Although the Willans line is a linear function, it takes into account the nonlinear change of isentropic efficiency as a function of load.

Wi,j ) ni‚mi,j - Wloss i

Feedwater heaters are modeled as process units between condensate and feedwater headers. Bleed streams for feed heaters are modeled as additional process units, which take steam from a steam header to a condensate or feedwater header. Equation 19 relates the bleed steam flow on the left-hand side to the feedwater flow on the right-hand side. Furnaces.

∀j ∈ J, i ∈ FURN

(22)

f gt furn fuel,gt 0 e [si,f ‚zi ‚fi + si,f ‚(1 - zfurn )]‚Q0i ‚zi,j Qi,f,j i ∀f ∈ F, j ∈ J, i ∈ FURN (23)

The binary parameter zfurn is used in eq 20 for selecting a candidate furnace for integration and setting the exhaust flow for the gas turbine to match the furnace flue gas flow (m0). For process furnaces the duty is fixed for each scenario. If a furnace is integrated with a gas turbine, the fuel consumption of the furnace is then a fraction (ffuel,gt) of original fuel consumption (Q0) (eq 21). It is assumed that the furnace duty remains constant after integration. The binary parameter z is input data, which indicates whether a furnace is used in an operational scenario or not. In the case of integrating a multifuel furnace with a gas turbine, new fuel ratios (sgt) can be defined in order to get as close to the nominal flame temperature as possible (eq 23). In practice this implies increasing the use of high calorific value fuels. Heat Recovery Units.

∀j ∈ J

(24)

∀r ∈ R, j ∈ J

(25)

) mgt,hrsg ‚cpgt‚Tg Qgt,tot j j

∑

c ) Qr,j

c mi,j‚∆hi,r

i∈HR(r,i) m

∀j ∈ J, i ∈ BOIL ∀j ∈ J, i ∈ BOIL

(16) (17)

p Qr)m,j ) Qgt,tot j

c ) ∀f ∈ F, j ∈ J, i ∈ BOIL (18)

The efficiency of each boiler (η) is assumed to be constant over the operation range. The fuel consumption (Q) is the sum of all the fuels (Qf) used in a boiler. If a boiler has multifuel capability, upper and lower bounds are assigned for the share of each fuel.

∀r ∈ R, j ∈ J (26)

p g (Tmaxin + ∆Tmin)‚cpgt‚mgt,hrsg Qr,j r j

h

min f max ‚Qi,j e Qi,f,j e si,f ‚Qi,j si,f

c Qr,j ∑ r)1

Qc,max r

∑r Rr‚

Tlm r

+ ψ‚mgt,max ∑r mmax r

+ φ‚

c e Qc,max Qr,j r

∑

∀r ∈ R, j ∈ J (27)

mi,j e mmax r

∀j ∈ J, r ∈ R ∀j ∈ J, r ∈ R

(28) (29) (30)

i∈HR(r,i)

e mgt,max mgt,hrst j

∀j ∈ J

(31)

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The total heat available from the gas turbine exhaust to the HRSG is calculated in eq 24. The parameter Tg is used instead of the actual temperature to avoid a bilinear formulation, and it is updated between iterations. The cumulative heat transferred (Qp) until section r is the difference between the initial heat content of the flue gas Qgt,tot and the summation of the heating duties from the first section to the section r. Equation 27 ensures that the minimum temperature difference is not violated. The right-hand side of the equation calculates the minimum allowable heat content for the flue gas, which the actual heat content must exceed. The capital cost (eq 28) is a linear approximation of the cost function proposed by Foster-Pegg (1986), which correlates the cost as a function of effective heat-transfer area, steam flow, and flue gas flow. The cost parameter R can take different values depending on the nature of the interval in question. For example, a superheating section requires more expensive material than the evaporating section, and this is reflected in the value of R. The values used in this work can be found in Appendix B. The logarithmic mean temperature difference (Tlm) is given as a parameter, and it is updated in each iteration. Cost functions would be simpler if they were based solely on steam production rate or flue gas flow, but they fail to reflect the important effect of temperature driving force on the required surface. The variables in the cost equation (Qc,max, mmax, mgt,max) represent the highest values for heat duty and mass flows, as defined in eqs 29-31. Supplementary Firing. sf

Qsf j

mi,j ) η ‚ HP ∆h

∀j ∈ J, i ∈ SF

gt,hrsg Qsf ‚cpgt‚(Tsf - Tg) j e mj

∀j ∈ J

(32) (33)

A HRSG is designed in an unfired mode. To evaluate rigorously the effect of supplementary firing on the steam production, we would have to simulate the behavior of a HRSG at off-design conditions. Instead, the effect of supplementary firing is estimated by introducing a supplementary firing process unit. The behavior of this unit is based on following assumptions: (1) Supplementary firing will only change the production of the highest pressure steam in a HRSG. (2) The change in production rate is a linear function of the fuel used in supplementary firing. The supplementary firing unit is connected to the same header as the highest pressure steam from the HRSG. The production rate is calculated in eq 32. The amount of supplementary firing is constrained by the highest allowable exhaust temperature after firing (typically 850-900 °C). Objective Function. The objective function is to minimize the overall annual cost.

(Wreq - ∑ Wi,j + Wp - Wgt)‚tj‚cej + ∑ j j∈J i∈TUR f f f ( Qi,f,j + ∑ Qi,f,j )‚cf,j ‚tj + ∑ ∑ ∑ j∈J f∈F i∈BOIL i∈FURN c (Qgt + Qjsf)‚cgtf‚tj + ∑ ∑ ai,j ‚mi,j‚tj + (cgt‚fi + ch + ∑ j∈J j∈J i∈CS Wp‚cc + ∑ cfurn‚zifurn)‚fa (34) i∈FURN

OBJ )

Figure 7. Solution strategy for screening models.

The first part of objective function determines the operational cost or benefit caused by electricity import or export. The second part is the annual fuel cost and also costs assigned for process unit flows, like steam import and export costs and the makeup water cost. The third part is the annual capital cost from the gas turbine and its accessories, the HRSG cost, and the furnace modifications. Remarks on Models. The screening model with industrial gas turbines (LP1) consists of eqs 1-8 and 13-34. The screening model with aeroderivative gas turbines (LP2) consists of eqs 1-4 and 9-34. The overall solution strategy for screening is illustrated in Figure 7. In the solution strategy described in Figure 7, a gas turbine fuel is first selected and screening is performed for all candidate furnaces. For each candidate furnace, two optimization runs are performed (LP1 and LP2). Through the comparison between the results of LP1 and LP2, we can determine which type of gas turbines


(industrial versus aeroderivative gas turbines) is more appealing for integration. After all candidate furnaces have been considered, screening for HRSG integration is performed for a given output range [W0 - Wup] at ∆W increments, where W0 is the smallest gas turbine to be considered. This loop is continued until all candidate fuels have been considered. Nonlinear terms appear in eqs 24, 28, and 33 involving Tg and Tlm. To avoid the nonlinearity, the nonlinear terms are linearized by treating these two variables as parameters. An iterative strategy using sequential linear programming (SLP) is developed for solving models LP1 and LP2, which is explained as follows: (1) Solve the problem using initial guesses for the parameters Tg and Tlm. (2) Update the values of the parameters using the newly generated results (Tg ) Tgt, Tlm is calculated on the basis of the flue gas and steam temperatures around each heat recovery section). (3) Solve it using updated values. (4) Stop if the objective value remains the same; otherwise, go back to step 2. The methodology has been developed aiming at industrial applications. Therefore, we apply sequential linear programming (SLP) to solve the original nonlinear and nonconvex model (NLP). We have compared the solution quality of this approach against that of a nonlinear formulation for several cases. The differences of SLP and NLP solutions were within 3%, which is acceptable for screening purposes. Design Models (MILP1 and MILP2). Equations Dedicated to MILP1 (No Changes Considered to an Existing System). Fuel and Electricity Constraints. min Qf,j e

∑

f Qi,f,j +

i∈BOIL,FURN

Wmin j

e

∑

Wi,j +

i∈TUR

∑ Qf,gf‚ygtg + Qf,jsf e Qf,jmax

g∈G

∑ ∑

∑

mgt,furn ) j Qi,j ) [

gt Wgt g ‚yg

p f Wg,f ‚yg,f

i 0 i yg,j ‚ffuel,gt + si,f ‚(1 - ∑ yg,j )]‚Q0i ‚zi,j ∑ i g∈G g∈G

∀f ∈ F, j ∈ J, i ∈ FURN (45)

Supplementary Firing. Similar to eqs 32 and 33, the following two equations are used for supplementary firing. With these two equations it is assumed that any of the available fuels for the gas turbine can be used for supplementary firing.

mi,j ) ηsf

e

∀j ∈ J (36)

∑ ygtg ) 1

∀j ∈ J, i ∈ SF

(46)

∀j ∈ J

(47)

sf Qf,j e mgt,hrsg ‚cpgt‚(Tsf - Tg) j

Objective Function for MILP1. The objective function is to minimize the total annual cost.

f yg,f )1

(38)

OBJ )

g∈G f∈GTF

∀g ∈ G

(39)

f∈GTF i yg,i e1

(40)

g∈G i∈FURN i yg,i - ygt ∑ g e 0 i∈FURN

∆hHP

(37)

g∈G

f yg,f ) ygt g

∑

sf Qf,j ∑ f∈GTF

f∈GTF

Gas Turbine Equations.

∑ ∑

∀j ∈ J, i ∈ FURN (44)

f GT Qi,f,j e [si,f ‚

Wmax j

∀j ∈ J (43)

i + (1 - ∑ yg,j )]‚Q0i ‚zi,j ∑ yg,ji‚ffuel,gt i g∈G

g∈G

g∈G

∑ ∑

i m0i ‚yg,j ‚zi,j ∑ ∑ g∈G i∈FURN

∀f ∈ F, j ∈ J (35)

g∈G f∈GTF

∑

turbine must be selected (eq 37). Sometimes it may be beneficial to use two small gas turbines instead of a bigger one. In this case the twin gas turbine can be considered as one of the optional gas turbines. Of the available fuels for a gas turbine, only one is selected, which is controlled using the binary variable yf (eqs 38 and 39). Integration with any of the furnaces is controlled by the binary variable yi. The implication of eq 40 is that one of the furnaces can be integrated with one gas turbine. Equation 41 makes sure that the furnace can only be integrated with the selected gas turbine. Furnaces. The following three equations are similar to eqs 20, 21, and 23. The only difference is the presence of binary variables (y) for gas turbine and furnace selection.

∀g ∈ G

gt gt,furn ygt + mgt,hrsg + mgt,stack ∑ g ‚mg ) mj j j g∈G

(41) ∀j ∈ J (42)

In the integration models real gas turbines are given as a discrete set with their data given as parameters. The data include shaft work, fuel consumption, exhaust flow, and temperature. The selection of a gas turbine is controlled by the binary variable ygt, and only one gas

p f (Wreq - ∑ Wi,j + ∑ ∑ Wg,f ‚yg,f ∑ j j∈J i∈TUR g∈G f∈GTF f + ∑ Wgtg ‚ygtg )‚tj‚cej + ∑ ∑ ( ∑ Qi,f,j g∈G j∈J f∈F i∈BOIL f f f f sf f Qi,f,j )‚cf,j ‚tj + ∑ ∑ ( ∑ Qf,g ‚yg,f + Qf,j )‚cf,j ‚tj + ∑ i∈FURN j∈J f∈GTF g∈G c gt i ai,j ‚mi,j‚tj + (ch + ∑ cgt ∑ ∑ g ‚yg ‚fg + j∈J i∈CS g∈G p c f furn i W ‚c ‚y + cg,i ‚yg,i)‚fa (48) ∑ ∑ ∑ ∑ g,f g,f g,f g∈G f∈GTF g∈G i∈FURN

Equations Dedicated to MILP2 (Changes Considered to an Existing System). Electricity Constraint. gt p f Wi + ∑ Wgt ∑ g ‚yg - ∑ ∑ Wg,f‚yg,f + i∈TUR g∈G g∈G f∈GTF d Wi,j - ∑ Wi,j ‚ypi e Wmax ∀j ∈ J (49) ∑ j i∈OT i∈DR

e Wmin j

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Mass Flow Relaxation for Constrained Units. lo up + mi,j - δi,j e mi,j e mi,j + δi,j + g δi,j δmax i

∀i ∈ I, j ∈ J ∀i ∈ I, j ∈ J

(50) (51)

+ and δi,j are slack variables for deThe variables δi,j creasing and increasing the capacity of a process unit, respectively. They are by default fixed to zero. However, if the need arises for changing the bounds, the slack variables can be relaxed. In the case of increasing capacity of a process unit, an additional variable δmax is introduced, which takes the largest value of capacity increase over all operational scenarios. This variable is used in the objective function to determine the capital cost associated with capacity increase. Optional Modules.

∀j ∈ J, i ∈ (OM - DR)

up e0 mi,j - ypi ‚mi,j lo δi,j ) ypi ‚mi,j

∀j ∈ J, i ∈ DR

up e0 mi,j - (1 - ypi )‚mi,j p + cfix ci ) ai‚mmax i i ‚yi

mi,j e mmax i

∀j ∈ J, i ∈ DR ∀i ∈ OM

∀j ∈ J, i ∈ OM

(52) (53) (54) (55) (56)

The ability to introduce new process units or replace existing ones is controlled by the binary variable yp. It takes the value one when a new unit is introduced and zero otherwise. In a general case, where the capacity of a unit is not fixed, eq 52 is used to control the flow through the unit. In the case of a steam turbine driver, the load is fixed for each of the operational scenarios; that is, the upper and lower bounds on mass flows are set equal. If an alternative driver, for instance an electric motor, is preferred, yp takes the value one. The slack variable δ- is forced to take the value of the lower mass flow bound when the binary variable yp equals one in eq 53. Equation 54 ensures that the mass flow is set to zero. Objective Function for MILP2. The objective function is to minimize the total annual cost. d (Wreq + ∑ Wi,j ‚ypi - ∑ Wi,j + ∑ j j∈J i∈DR i∈TUR p f gt gt e W ‚y W ‚y ∑ ∑ ∑ g,f g,f g g - ∑ Wi,j)‚tj‚cj + g∈G f∈GTF g∈G i∈OT f f f ( Q + Q )‚cf,j ‚tj + ∑ ∑ ∑ i,f,j i∈FURN ∑ i,f,j j∈J f∈F i∈BOIL ∑ ∑ ( ∑ Qf,gf‚yg,ff + Qf,jsf)‚cf,jf‚tj + ∑ ∑ ai,jc‚mi,j‚tj + j∈J f∈GTF g∈G j∈J i∈CS gt i ( ∑ ci + ∑ δmax ‚csi + ch + ∑ cgt i g ‚yg ‚fg + i∈OM i∈I g∈G p c f furn i W ‚c ‚y + cg,i ‚yg,i)‚fa (57) ∑ ∑ ∑ ∑ g,f g,f g,f g∈G f∈GTF g∈G i∈FURN

OBJ )

Remarks on Design Models. Equations 1-4, 1519, 22, 24-31, and 35-48 form the complete model for MILP1, which is used to optimize gas turbine integration without considering modifications to the existing system. MILP2 consists of eqs 1, 3, 4, 15-19, 22, 2431, 35, 37-47, and 49-57. This MILP model considers gas turbine integration allowing changes to the existing system. The iterative solution strategy is virtually the same as that for models LP1 and LP2. In this strategy,

Figure 8. Flow sheet of the plant.

MILP1 is first used to determine the optimal size of the gas turbine together with the optimal integration scheme. Basically, this stage determines the design aspects for integrating a gas turbine system. The decision made in the MILP1 stage is further examined and reoptimized in the MILP2 stage, where optional steam turbines and process drivers are considered and they are allowed to have options of switch on or off (eqs 52-56). In addition to these, identification of dominant constraints in the existing system is carried out by means of introducing slack variables (eqs 50 and 51). Analysis of the dominant constraints may give potential design changes to the existing system, and these changes are introduced to the previous superstructure. Consequently, the MILP2 model is updated with the newly introduced change options and it is optimized again to obtain an improved design. Case Study The case study comprises the utility system and five process furnaces (F1-F5) of an oil refinery. The simplified flow sheet is shown in Figure 8. Furnace F1 is not a single furnace but a group of three furnaces located side by side. An HP steam is generated in the five boilers (B1-B5) and by some of the processes. Processes also generate and use lower pressure steam. An HP steam is used to generate shaft work in the three steam turbines (TG1-TG3) and to operate the steam turbine process drives (D1-D5). The utility system also contains additional features such as venting of LP steam, returning condensates, and so on, which are included in the model. Four fuels are available at the site: natural gas, fuel oil, and low- and medium-Btu refinery gas. The boilers can use any of the available fuels, and the furnaces use the refinery gases as fuel. The objective is to minimize the annual operating cost considering (1) three operational scenarios, (2) gas turbine integration with any of the furnaces and/or with a HRSG, (3) the capacity constraints of the utility system and the furnaces, (4) changes in fuel availability and prices in the operational scenarios, and (5) using either natural gas or medium-Btu refinery gas as the gas turbine fuel. The medium-Btu gas is available at 10 bar, and it has to be compressed to 25 bar if it is to be used in the gas turbine. This incurs a work penalty of 250 kW per m3 of gas. The cost of the compressor is estimated at $4000/ kW. The gas turbine is to be used for base load generation at the rated capacity. Exporting electricity is not allowed in this study. The current electricity consumption of the site is around 48 MW, of which the steam turbines produce 18 MW, leaving therefore a maximum of around 30 MW to be produced by the gas turbine.


Figure 9. Annual savings for HRSG option. Figure 11. Specific installation cost for HRSG option.

Figure 10. Simple payback time for HRSG option.

For the process furnaces it is found by simulation that in the case of integration the flame temperature can be kept constant by increasing the share of medium-Btu refinery gas. In the case of integrating with a HRSG, the same fuel is to be used in both gas turbine and supplementary firing. Appendix B contains details of the main operational constraints of the site. Screening. The purpose of screening is to find the optimal size range for the gas turbine and to select the most economic fuel for the gas turbine. The main selection criteria are the annual savings in operational cost and the simple payback time. We will also look at the influence of changing the price ratio between electricity and natural gas. The base price ratio is 6.25, and the modified ratio is 3.75, which corresponds to increasing the natural gas price by 25% and decreasing the price of electricity by 25%. A total of 8 optimization runs are performed per integration scenario, which equals 4 runs per a fixed price ratio. The runs correspond to the following options: (1) industrial gas turbine using natural gas, (2) industrial gas turbine using medium-Btu refinery gas, (3) aeroderivative gas turbine using natural gas, and (4) aeroderivative gas turbine using medium-Btu refinery gas. Integration with HRSG. For each of the optimization runs, the performance is calculated for the gas turbine sizes 5, 10, ..., 30 MW. The results are shown in Figures 9 and 10. The figures show the performance of the worst and best options. All the other options fall between these two. In all cases the best performance is achieved by the aeroderivative gas turbine using refinery gas. The worst performance is by an industrial gas turbine using natural gas. The variation in specific installation cost is shown in Figure 11. Integration with Furnaces. In each optimization run, the performance is calculated for each of the individual furnaces. The gas turbine exhaust flow is fixed to the nominal flue gas flow of each furnace, and shaft work is calculated for this given exhaust flow by the continuous gas turbine models. The results are shown in Figures 12 and 13. For both price ratios, the best performance is achieved by an industrial gas turbine using refinery gas. A natural-gas-fired aeroderivative gas turbine causes the

Figure 12. Annual savings for furnace option.

Figure 13. Simple payback time for furnace option.

worst performance for the high price ratio. For the low price ratio the worst performance is by a natural-gasfired industrial gas turbine. The differences in shaft work for specific furnace integration cases are due to the different characteristics of gas turbine types and the work penalty for compressing refinery gas. Summary of Screening. The best individual option is to integrate furnace F1 with an industrial gas turbine using refinery gas as fuel. The operational savings including the annual capital cost of the investment is between $4 × 106 and $8 × 106/year depending on the price ratio used. The simple payback time of the investment is between 1.3 and 1.8 years. For HRSG integration, the range of operational savings is between $6 × 106 and $7.5 × 106/year with a payback time of 1.7-1.9 years. In all of the cases the optimal gas turbine size is around 25-30 MW. The payback curves (Figures 10 and 13) are fairly flat between 15 and 30 MW for the best option, so in the case of not finding a real gas turbine of optimal size, any gas turbine within that range could have a payback time less than 2.5 years. If for some reason combined integration with a furnace and a HRSG was not allowed, both integration options by themselves would result in large operational savings with a short payback time. In that case the two options to be considered in subsequent steps would be either integration with furnace F1 or integration with a HRSG using a gas turbine closest to 30 MW. In this study, however, we are looking at the possibility of combined integration, and therefore, we retain the possibility of integrating a gas turbine with any of the furnaces and a HRSG.

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Figure 14. Initial integration superstructure. Figure 15. Improved design. Table 1. Gas Turbine Data gas turbine

output (MW)

exhaust flow (kg/s)

efficiency (%)

price ($1000)

GT1 GT2 GT3

27 26 26

83 122 81

37 28 35

11600 7400 11200

Table 2. Process Units with Largest Marginal Values process unit

marginal value ($1000/(t/h), year)

TD3 TD5 TD4 TG1 (LP-condensing) TD2

-29.81 -29.81 -27.16 +23.56 -21.94

Integration with Necessary Changes. Within the optimal size range determined by screening, we find three gas turbines (GT1-GT3), of which GT1 and GT3 are aeroderivative ones and GT2 is an industrial one. The gas turbine data are shown in Table 1. A superstructure is constructed, which allows any of the gas turbines to be simultaneously integrated with any of the furnaces and a HRSG producing both HP and MP steam. The superstructure is shown in Figure 14. The superstructure is optimized, and the following results are obtained using the base price ratio: (1) GT2 is integrated with furnace F1 and a HRSG producing 41 t/h of HP steam in supplementary fired mode. (2) Annual savings including the capital cost for the investment are around $7.5 × 106. (3) The investment cost is $20 × 106 ($761/kWe). (4) The simple payback time of the investment is 1.5 years. The optimization is also performed using the lower price ratio. The design remains unchanged from the one with the base price ratio, and only the economics change. The annual savings change to $3.8 × 106, and the payback time increases to 2.1 years. This design does not consider any additional design changes to the existing utility system. The next step is to investigate promising design changes, which might bring additional economic benefit. Identification of Design Changes. From the results of the previous runs, we identify the constrained process units and calculate their annual marginal values. The process units with the highest marginal values are shown in Table 2. Note that a positive marginal value indicates the objective could be improved by increasing the capacity while a negative value indicates a benefit could be achieved by decreasing the capacity. The optimization result also indicates that the condensing end of steam turbine TG1 has reached its capacity limit. The positive marginal value indicates that it could be beneficial either to increase its capacity or to install an additional condensing turbine. On the

Table 3. New Optional Process Units new process unit

output (MW)

price ($1000)

electric motor for TD2 electric motor for TD3 electric motor for TD4 electric motor for TD5 condensing turbine gas turbine (GT4)

9 10 15 1 10 38.6

1400 1600 2300 170 1500 10500

other hand, the steam turbine drivers have negative marginal values, suggesting that it may be beneficial to switch off some of the drivers and use electrical motors instead. Integration with Synergistic Design Changes. On the basis of the previous analysis, we will introduce potential design changes to the existing system. The changes include options of using electric motors instead of steam turbine drives. Since this will potentially increase the electricity consumption of the site, the option of installing a new condensing turbine and a bigger gas turbine is also considered. Table 3 contains data on the proposed design changes. These options are added to the existing superstructure, which is optimized to get the improved design. The improved design gives the following results: (1) GT2 is integrated with furnace F1 and a HRSG producing 41 t/h of HP steam in supplementary fired mode. (2) TD2 is replaced by an electric motor. (3) The annual savings including the capital cost for the investment are around $7.55 × 106 (+$50 × 103). (4) The investment cost is $21.4 × 106 (+1.4 × 106) ($814/kWe). (5) The simple payback time of the investment is still 1.5 years. The replacement of TD2 yields an annual savings of $50,000. The main reason for the positive effect of replacing the drive is that the TG2 and TG3 turbines, which were run at part load in the previous design, are now run at full load for most of the time. As the efficiency of steam turbines increases with increasing load, the power production efficiency of the plant is also increased. The improved design is shown in Figure 15. Conclusions A new methodology for gas turbine integration to an existing site has been presented. The methodology employs a stepwise approach to reduce the complexity of the design problem and to provide insights. The methodology utilizes mathematical programming to address multiple tradeoffs simultaneously. It differs from the existing methods, however, by simultaneously considering operational optimization and retrofit of the existing system in connection with grass root design of the gas turbine system. In this way, the gas turbine system can be optimally fitted into the existing site, thus maximizing its economic potential.


The methodology starts with the top-level screening, which establishes the optimal gas turbine size range, and provides an estimate for the economic viability of gas turbine integration. On the basis of the screening results, the most promising integration options are built into a superstructure together with a selection of gas turbines within the optimal size range. Hence, the superstructure size can be reduced and the number of candidate gas turbines kept small, which will in turn make the problem easier to solve. The results from the optimized superstructure give an initial design. This design is analyzed in order to locate existing process units, which economically constrain the design the most. Once the constraining units have been identified, design options are added to the existing superstructure to overcome the constraints and to improve the economics of the design. The revised superstructure is optimized to get an improved design. This analysis and design loop can be continued until no major options can be identified. Appendix A: Nomenclature for the Mathematical Models Nomenclature for Screening Models (LP1 and LP2) General Indices F ) {f/fuels} I ) {i/process units excluding headers} J ) {j/operational scenarios} K ) {k/steam and condensate headers} R ) {r/sections of heat recovery steam generator} Process Unit and Fuel Sets BOIL ) {i/steam boilers; BOIL ⊂ I} CS ) {i/units with cost attached; CS ⊂ I} FURN ) {i/process furnaces; FURN ⊂ I} GTF ) {f/fuels for gas turbine; GTF ⊂ F} TUR ) {i/steam turbines; TUR ⊂ I} Connection Sets IN ) {(i ∈ I, k ∈ K)/process unit i feeds to mains k} OUT ) {(i ∈ I, k ∈ K)/process unit i feeds from mains k} BLEED ) {(i ∈ I, i ∈ I)/process unit i provides steam for process unit i} HR ) {(r ∈ R, i ∈ I)/process units i in HRSG section r} Continuous Variables cgt ) capital cost of gas turbine ($1000) ch ) capital cost of HRSG ($1000) mi,j ) mass flow of water or steam through process unit i ∈ I in scenario j ∈ J (kg/s) mrmax ) maximum mass flow of steam through a section r ∈ R in HRSG (kg/s) mgt ) exhaust flow of gas turbine (kg/s) mjgt,furn ) exhaust flow from gas turbine to furnace in scenario j ∈ J (kg/s) mjgt,hrsg ) exhaust flow from gas turbine to a HRSG in scenario j ∈ J (kg/s) mgt,max ) maximum exhaust flow to a HRSG (kg/s) mjgt,stack ) exhaust flow from gas turbine to bypass stack in scenario j ∈ J (kg/s) Qi,j ) total fuel consumption of process unit i ∈ (BOIL, FURN) in scenario j ∈ J (kW) Qcr,j ) heat transferred in section r ∈ R of HRSG in scenario j ∈ J (kW) Qrc,max ) maximum transferred heat in HRSG section r ∈ R (kW) Qfi,f,j ) consumption of fuel f ∈ F in process unit i ∈ (FURN,BOIL) in scenario j ∈ J (kW)

Qgt ) fuel consumption of gas turbine (kW) Qjgt,tot ) heat content of gas turbine exhaust available for HRSG in scenario j ∈ J (kW) Qpr,j ) cumulative heat transferred until section r ∈ R of HRSG in scenario j ∈ J (kW) Qsfj ) consumption of fuel by supplementary firing in scenario j ∈ J (kW) Tgt ) exhaust temperature of gas turbine (°C) Wi,j ) shaft work produced by steam turbine i ∈ TUR in scenario j ∈ J (kW) Wgt ) shaft work of gas turbine (kW) Wp ) shaft work requirement of fuel compression for gas turbine (kW) Parameters aci,j ) cost coefficient for costing flow through unit i ∈ CS for scenario j ∈ J ($/(kg s)) afi ) coefficient for bleed steam amount of feedwater heater i ∈ I (kg steam/kg water) ap ) coefficient for fuel compression (kW/kW) bfi ) constant for bleed steam amount for feedwater heater i ∈ I (kg/s) cc ) capital cost coefficient for gas turbine fuel compressor ($1000/kW) cej ) price of electricity for scenario j ∈ J ($/kWh) cff,j ) price of fuel f ∈ F for scenario j ∈ J ($/kWh) cfurn ) furnace modification cost ($1000) cgtf ) cost of gas turbine fuel ($/kWh) cpgt ) specific heat capacity of gas turbine exhaust (kJ/ kgK) fa ) annualization factor fi ) installation factor for gas turbine ffuel,gti ) coefficient for fuel burned in furnace i ∈ FURN when integrated with a gas turbine [0,1] m0i ) nominal flue gas flow for furnace i ∈ FURN (kg/s) mloi,j ) lower bound for mass flow through process unit i ∈ I in scenario j ∈ J (kg/s) mupi,j ) upper bound for mass flow through process unit i ∈ I in scenario j ∈ J (kg/s) ni ) specific work produced by steam turbine i ∈ TUR Q0i ) nominal fuel consumption of furnace i ∈ FURN (kW) Qmaxf,j ) maximum availability of fuel f ∈ FUEL in scenario j ∈ J (kW) Qminf,j ) minimum amount of fuel f ∈ FUEL to be consumed in scenario j ∈ J (kW) s0i,f ) nominal share of fuel f ∈ F in furnace i ∈ FURN [0,1] sgti,f ) share of fuel f ∈ F in furnace i ∈ FURN when integrated with gas turbine [0,1] smaxi,f ) maximum share of fuel f ∈ F in boiler i ∈ BOIL [0,1] smini,f ) minimum share of fuel f ∈ F in boiler i ∈ BOIL [0,1] tj ) duration of scenario j (1000h) Tg ) temperature of gas turbine exhaust (°C) Tlmr ) logarithmic mean temperature difference in HRSG section r ∈ R (°C) Tmaxinr ) highest temperature of steam entering section r ∈ R in HRSG (°C) Tsf ) maximum allowable exhaust temperature after supplementary firing (°C) W0 ) initial gas turbine output in screening (kW) Wlossi ) loss term of steam turbine i ∈ TUR (kW) Wmaxj ) maximum own shaft work production in scenario j ∈ J (kW) Wminj ) minimum own shaft work production in scenario j ∈ J (kW) Wreqj ) site shaft work requirement in scenario j ∈ J (kW) Wup ) final gas turbine output in screening (kW) zi,j ) operational status of furnace i ∈ FURN in scenario j ∈ J (0,1) zfurni ) integrate furnace i ∈ a FURN with a gas turbine (0,1) zgtff ) use fuel f ∈ FUEL in gas turbine (0,1) Rr ) cost coefficient for area cost in HRSG section r ($1000/ (kW K))

4328


∆hci,r ) specific enthalpy difference in process unit i ∈ I in HRSG section r ∈ R (kJ/kg) ∆hHP ) specific enthalpy difference of HP steam in HRSG (kJ/kg) ∆hsi ) specific enthalpy difference between steam outlet and feedwater inlet in boiler I ∈ BOIL (kJ/kg) ∆Tmin ) minimum temperature difference (°C) ∆W ) output increment in screening (kW) φ ) cost coefficient for HRSG ($1000/(kg s)) ηi ) efficiency of boiler i ∈ BOIL [0,1] ηsf ) coefficient for supplementary firing efficiency ψ ) cost coefficient for HRSG ($1000/(kg s)) Nomenclature for Design Models (MILP1 and MILP2)

The nomenclature for these models follows closely that of the screening models. Additional definitions only are reported here. General Indices

Wgtg ) shaft work production of gas turbine g ∈ GT (kW) Wpg,f ) shaft work requirement needed for compressing fuel f ∈ GTF for gas turbine g ∈ GT (kW)

Appendix B: Data for the Case Study Table 4. Electricity, Fuels and Makeup Water operation 1 operation 2 operation 3 duration (h) electricity demand (MW) electricity price ($/MWh) availability of medium-BTU gas (m3/s) price of medium-BTU gas (¢/m3) availability of low-BTU gas (m3/s) price of low-BTU gas (¢/m3) price of natural gas (¢/m3) price of fuel oil ($/ton) price of makeup water (¢/ton)

DR ) {i/optional drivers; DR ⊂ OM} GTF ) {f/fuels for gas turbine; GTF ⊂ F} OM ) {i/optional process modules; OM ⊂ I} OT ) {i/optional steam turbines; OT ⊂ OM} Continuous Variables ci ) capital cost of an optional module i ∈ OM ($1000) Qsff,j ) consumption of fuel f ∈ GTF by supplementary firing in scenario j ∈ J (kW) σ-i,j ) slack variable for negative capacity change in process unit i ∈ I in scenario j ∈ J (kg/s) σ+i,j ) slack variable for positive capacity change in process unit i ∈ I in scenario j ∈ J (kg/s) σmaxi ) slack variable for maximum positive capacity change in process unit i ∈ I (kg/s) Binary Variables yfg,f ) selection of fuel f ∈ GTF for gas turbine g ∈ GT ygtg ) selection of gas turbine g ∈ GT yig,i ) integration of gas turbine g ∈ GT with furnace i ∈ FURN yip ) selection of optional process units i ∈ OM

HP steam generation (t/h) HP steam consumption (t/h) MP steam generation (t/h) MP steam consumption (t/h) LP steam generation (t/h) LP steam consumption (t/h)

1500 45.0 70 10.13

6.4

6.4

8.0

21.6

21.6

8.4

3.2 11.2 74.0 72.0

3.2 11.2 74.0 72.0

5.0 11.2 74.0 72.0

operation 1

operation 2

operation 3

160.2 79.4 49.2 251.1 17.9 88.1

150 85.0 51.0 240.0 16.0 85.0

170 75.0 43.0 260.0 18.0 93.0

Boilers B1 max. steam flow (t/h) specific steam duty (kW/(t/h)) efficiency (%) share of medium-BTU gas (min, max) share of low-BTU gas (min, max) share of natural gas (min, max) share of fuel oil (min, max)

B3

B4

81.6 712.0

81.6 712.0

B2

90.7 746.0

108.9 712.0

136.1 712.0

B5

96.0 0, 0.5

80.0 0, 0.5

77.0 0, 0.6

84.0 0, 0.3

89.0 0, 0

0, 0.5

0, 0.5

0, 0

0, 0.6

0, 0

0, 0.77

0, 0.71

0, 0.6

0, 0.6

0, 0

0.23, 0.23 0.29, 0.29 0.4, 0.98 0.4, 0.83 1, 1 Furnaces

fuel consumption (MW) flue gas flow (kg/s) efficiency (%) share of medium-BTU gas (normal, integrated) share of low-BTU gas (normal, integrated)

F1

F2

F3

F4

F5

159.2 81.2 96.0 0.45, 0.86 0.55, 0.14

46.8 25.5 80.0 0.15, 0.42 0.85, 0.58

24.1 12.5 77.0 0.38, 0.76 0.62, 0.24

89.3 48.7 84.0 0.15, 0.42 0.85, 0.58

65.7 33.7 89.0 0.42, 0.82 0.58, 0.18

Steam Turbines

Parameters ai ) cost coefficient for capital costing of flow through unit i ∈ OM ($/(kg s)) cfixi ) capital cost constant of an optional module i ∈ OM ($1000) ccg,f ) capital cost coefficient for compressor of fuel f ∈ GTF for gas turbine g ∈ GT ($1000/kW) cfurng,i ) modification cost for integrating furnace i ∈ I with gas turbine g ∈ G ($1000) cgtg ) capital cost of gas turbine g ∈ GT ($1000) csi ) specific cost for increasing capacity for unit i ∈ I ($1000/(kg s)) fig ) installation factor for gas turbine g ∈ GT mgtg ) exhaust flow of gas turbine g ∈ GT (kg/s) Qff,g ) consumption of fuel f ∈ GTF by gas turbine g ∈ GT (kW) Tgt ) temperature of gas turbine exhaust (°C) Wdi,j ) shaft work requirement of an added electrical motor i ∈ DR in scenario j ∈ J (kW)

2000 52.0 70 13.52

Steam Production and Consumption

G ) {g/gas turbines} Process Unit and Fuel Sets

5000 48.5 70 13.52

specific work (kW/(t/h)) work loss (kW) minimum flow (t/h) maximum flow (t/h)

TG1HP

TG1MP

TG1LP

TG2

TG3

75.45 977.3 11 144

68.0 1021.9 4 80

81.39 253.7 4 52

84.2 153.6 27 75

93.62 1255.6 20 20

Steam Turbine Drivers TD1 flow (t/h) TD2 flow (t/h) TD3 flow (t/h) TD4 flow (t/h) TD5 flow (t/h)

operation 1

operation 2

operation 3

135.6 80.5 75 90 21.3

140 75 70 85 20

130 85 78 95 23

Cost Coefficients and Modification Costs gas turbine installation factor coefficient R for superheater ($1000/(kW/K)) coefficient R for evaporators and economizer ($1000/(kW/K)) coefficient φ ($1000/(t/h)) coefficient ψ ($1000/(kg/s)) modification cost for furnaces ($1000)

1.5 13 6.5 5.91 1.184 26% of cost of integrated gas turbine


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Received for review April 13, 1999 Revised manuscript received July 9, 1999 Accepted July 20, 1999 IE990260T

Optimal Gas Turbine Integration to the Process Industries - American

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