Article pubs.acs.org/IECR
Design of Entire Energy System for Chemical Plants Cheng-Liang Chen* and Chih-Yao Lin Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC ABSTRACT: This paper presents a systematic methodology for the synthesis of an entire energy system for chemical plants, which explores the interactions between the steam network and the heat recovery networks of process plants. The energy system is designed not only to meet the heating and power demands from an individual chemical process, but also to consider possibilities of energy transfer among holistic sites. In this paper, energy utilization across different plants is studied. Specifically, indirect and direct energy integration strategies are adopted for the design of the whole energy system to maximize the possible integration. With the energy integration strategies for the overall systems, the utility consumption can be reduced and the total annualized cost minimized. Case studies are presented to demonstrate the applicability and significant economic benefits of the proposed model when applied to industrial problems.
1. INTRODUCTION During the past few decades, extensive and numerous research efforts have made considerable contributions to the energy system design for chemical plants in order to decrease the energy waste and reduce the environmental impact. The energy system design of chemical plants can generally be divided into two parts: the steam network of steam power plants and the heat recovery network of process plants. This task can be accomplished with energy integration techniques. To address the design issues of steam systems, several related studies have been published in the literature. In general, these methods could be classified into two categories. The first is based on thermodynamic principles and heuristics rules to synthesize the steam distribution network (SDN) of steam plants. Nishio et al.,1 and Chou and Shih2 took gas-steam cycles into account to get the maximum overall thermal efficiency. However, the main drawback of these approaches was that the results with highest thermal efficiency might lead to high capital costs. Therefore, it seems impractical for the economic concern. The second depends on the superstructure-based mathematical formulation to find the best design through the optimization procedure. Papoulias and Grossmann3 proposed a mixedinteger linear programming (MILP) method to solve the design problem. The MILP formulation was derived by fixing operating conditions such as pressures and temperatures. Later, Bruno et al.4 developed a mixed-integer nonlinear programming (MINLP) model to have sufficient accuracy for the implementation to actual industrial problems. Furthermore, Hui and Natori,5 and Iyer and Grossmann6 presented multiperiod approaches for the synthesis of steam systems under multiple periods. However, the steam level optimization was not considered in their work. Moreover, Chang and Hwang7 proposed an multiobjective strategy for waste minimization in steam plants. Recently, Aguilar et al.8,9 developed a generic modeling framework for energy equipment, where the part-load operating models of equipment were established to estimate the unit efficiencies under different operating conditions. Thus, the structural and operational conditions of system plants could be considered as variables in the model and could be optimized simultaneously. © 2012 American Chemical Society
On the other hand, the heat recovery system is one of the most important issues to study for enhancing the energy saving in the process industries. Many techniques, such as the insightbased pinch design method10−14 and the superstructure-based mathematical programming approach15−21 have been proposed for addressing the heat recovery system. The former used a graphical method to analyze the process stream properties for maximizing the heat recovery or determining the requirement of hot/cold utilities, while the latter directly found the optimal heat exchanger networks (HEN) through a proposed superstructure-based model. Moreover, Hui and Ahmad22 focused on the heat integration between different plants for enhancing the possibilities of heat recovery. In addition, Rodera and Bagajewicz23 further considered the synthesis of multipurpose heat exchanger networks, which were capable of operating stand-alone and/or integrated plants. It should be noted that the studies mentioned above addressed both the steam system and the heat recovery system sequentially. Papoulias and Grossmann24 first proposed a simultaneous design strategy, where the transshipment model of heat integration was embedded into the formulation to account for the possible heat integration and its utility consumption. However, some design variables such as the temperature of steam headers in the model were treated as prespecified values, and the energy use from processes to the steam system was not considered. Afterward Dhole and Linnhoff25 introduced the concept of total site integration to describe a set of processes served by a central steam system, where the targeting procedure was developed for sites involving several processes. Then, Hui and Ahmad26 extended this concept to address a similar problem by the targeting method, where the exergetic approach was proposed for total site integration. This approach showed that reducing the exergy loss in a HEN will ultimately benefit the power generation in the steam system. Subsequently, Klemeš et al.27 and Bandyopadhyay et al.28 applied Special Issue: APCChE 2012 Received: Revised: Accepted: Published: 9980
November 22, 2011 March 27, 2012 March 28, 2012 March 28, 2012 dx.doi.org/10.1021/ie202716q | Ind. Eng. Chem. Res. 2012, 51, 9980−9996
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Article
Figure 1. Steam distribution network superstructure.
demands, respectively. For each region process, process integration technique is used to address the heat recovery system, where energy recovery is accomplished to reduce the utility consumption. In particular, the cost can be reduced further with the integrated energy system considering energy recovery across plants or/and regions. The objective of this study is to design an integrated energy system of an entire plant at minimum cost. This work includes the optimum energy utilization that determines the energy distribution between individual systems and layouts of a steam plant and individual region processes.
the site utility grand composite curve method to estimate the cogeneration potential of a total site. Thereafter, some publications29−31 have also addressed the steam system design with the total site integration, where the pinch technology or trans-shipment model of heat integration was embedded into the formulation. However, the network design focused on only the steam system. The synthesis of the heat recovery system was not considered in these studies. In this paper, the objective is to design the entire energy system, including the overall steam network and the heat recovery networks, in order to optimize the use of energy among different plants. In the proposed integrated model, energy can be distributed and transferred between a center steam power plant and various process plants, or even between adjacent process plants, where the energy from processes is regarded as an alternative energy source that can be exploited and exchanged. On the basis of the proposed superstructures for the steam system and the heat recovery network, the design problem can be formulated as an MINLP for minimizing the total annualized cost (TAC) of the entire system. Numerical examples are studied to illustrate the potential application of the proposed model in industrial problems.
3. MODEL FORMULATION In this section, an integrated energy system design model is proposed to synthesize the network and determine the operating condition by the combination of steam system model and heat recovery system model. The superstructures of SDN for steam system and HEN for heat recovery system developed respectively by Papoulias and Grossmann3 and Yee et al.16 are modified in this study for getting more integration opportunities. 3.1. Steam System Model. Figure 1 shows a superstructure of SDN which is constructed to incorporate all possible flow connections. Steam is generated in steam boilers, and collected and distributed via the steam headers. This is expanded in steam turbines to provide steam at high, medium, or low pressures. Therefore, steam is available at different pressures and temperatures. Some processes use steam, while others generate steam. For the former case, the steam power plant provides appropriate level of steam to satisfy the requirements. Steam is imported to a certain steam level header in a steam plant for the latter condition. The generation of power might be through a steam turbine or a gas turbine. In this part, the equipment model to determine the performance of units is taken from Aguilar et al.8 3.1.1. Boiler. Steam can be generated with fired (b ∈ 4)) or heat recovery steam generator (HRSG) (b ∈ /)). Equation 1 states the mass balance of a boiler, where the boiler feedwater
2. PROBLEM STATEMENT The problem addressed in this paper can be briefly stated as follows: Consider a chemical plant that is divided into several regions/ plants (r ∈ 9), which is due to the location limitation or the process difference. In a certain region r, there exist a set of hot process streams (h ∈ /r) to be cooled and a set of cold process streams (c ∈ *r) to be heated. Each hot and cold stream’s heat capacity flow rates (CP) and initial and target temperatures are given and specified. Besides, each regional process may need power imported to maintain the operation of equipment. The entire energy system for chemical plants is normally divided into logically identifiable regions which consist of the steam system and the process systems. The main energy supplied to process plants is from a steam plant that produces steam and generates electricity for satisfying heating and power 9981
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Table 2. Performance Model for Gas Turbine8
entering the boiler b equals the steam to the steam header i and the effluent of blowdown water. The blowdown water is treated as fix φ fraction of steam output and extracted at saturated liquid condition. Equation 2 is the energy balance around the boiler. Therein, qb is the total energy given to the boiler feedwater, Hdeaer, denotes various enthalpy terms. Details about the hbi and Hsat,l i performance models for boiler and HRSG units are listed in Tables 1 and 4.
w gt = C gtq gt − (Agt C gt − 1)W gt,d − (Bgt C gt) f gt = αgtQ gt,d − β gt(Q gt,d − q gt)
Q gt,d = Agt W gt,d + Bgt ⎛ Q gt,d − q gt ⎞ ⎟⎟ T gt = T gt,d⎜⎜1 − k gt Q gt,d ⎠ ⎝ wgt: gas turbine power output (kW) Wgt,d: design gas turbine power output (kW) qgt: gas turbine fuel input (kW) Qgt,d: design gas turbine fuel input (kW) Tgt: part-load GT exhaust temp (°C) Tgt,d: design GT exhaust temp (°C) fgt: GT exhaust mass flow (kg/s) four types of GT consuming natural gas, low heating value of 44650 kJ/kg
Table 1. Performance Model for Multifuel Bolier8 b ⎞ ⎛ qb qfb2 qfm f1 q b = ⎜ b + b + ··· + b ⎟ − Db,avg ⎜B Bf 2 Bfm ⎟⎠ ⎝ f1 b ⎞ ⎛ qb qfb2 qfm f1 f b (Δhb + Δhb,ecoF bd) = ⎜ b + b + ··· + b ⎟ − Db,avg ⎜B Bf 2 Bfm ⎟⎠ ⎝ f1
numerical parameters
qb: heat added to the water (kW) qbfm: net heat released by fuel fm (kW) f b: steam output from a boiler (kg/s) Fbd: blowdown to steam output ratio Δhb: enthalpy difference between boiler feedwater and outlet steam conditions (kJ/kg) Δhb,eco: enthalpy difference across boiler economizer (kJ/kg) natural gas fuel oil units b
B Db
1.113 1.383
fbbfw =
∑ fbi
+
i∈0
fbbfw H deaer
1.072 1.422
∑ fbibd
+ qb =
Agt (−) 2.9066 Bgt (kW) 1366.2 Cgt (−) 0.6281 four control schemes used
MW
∑ fbi hbi + ∑ i∈0
∀b∈)
∀ b ∈ ), i ∈ 0
∑ zbi
∑ b ∈ /)
fgb
high flow rate regulation
αgt (kg/kJ) βgt (kg/kJ)
0.0011226 0.00
0.0011226 0.000953
0.0011226 0.001035
0.0011226 0.001500
∑
Tgb
∀g∈. (7)
∑ wgj
∀ g ∈ .: (8)
The following constraints are imposed to reflect physical and practical limitations of the equipment. Equations 9 and 10 define the unit capacity that must comply with maximum and minimum limits. Equation 11 depicts the operation range of the temperature.
(4)
Ω̲ g zgb ≤ fgb ≤ Ω̅ g zgb
Γ̲ g zgj ≤ wgj ≤ Γ̅g zgj Φ̲ g zgb ≤ Tgb ≤ Φ̅g zgb
∀ g ∈ ., b ∈ /)
∀ g ∈ .:, j ∈ 1 ∀ g ∈ ., b ∈ /)
(9) (10) (11)
where zgb and zgj are binary variables reflecting whether or not the connections exist. Ω̲g, Γ̲g, Φ̲g, Ω̅ g, Γ̅ g, and Φ̅ g are the minimum and the maximum capacities for gas turbines, respectively. It is mentioned that the exhaust of a gas turbine is recovered by the HRSG. Following constraints are imposed to restrict the connection between gas turbine g and HRSG b. If a gas turbine is chosen, a corresponding HRSG is automatically included, and vice versa.
(5)
3.1.2. Gas Turbine. Gas turbines can generate electricity (g ∈ .,) or shaft work (g ∈ .:), where the corresponding unit performance models are listed in Table 2. To reduce the fuel consumption, the hot exhaust may be sent to the HRSG unit b as heat input to increase the steam generation. The corresponding relations (eqs 6 and 7) are derived below. fg =
medium flow rate regulation
(3)
∀b∈)
i∈0
low flow rate regulation
j∈1
where zbi is a binary variable and Ω̲b and Ω̅ b are the minimum and the maximum capacities, respectively. The steam flow rate is zero without the installation of boiler unit. Equation 5 is the constraint for boiler and steam header, which states that a boiler generates one level of steam. Therefore, only one connection can exist between boiler b and steam header i with the boiler b selected, where zb is a binary variable reflecting whether or not the boiler exists. zb =
2.5422 1019.3 0.6428
no air flow regulation
wg =
Depending on the capacity of units, the constraint is imposed in the boiler formulation, that is, Ω̲bzbi ≤ fbi ≤ Ω̅ bzbi
2.5254 3.0830 1366.2 1019.3 0.6281 0.6428 to regulate exhaust flow
Equation 8 depicts that a gas turbine can generate power to satisfy shaft work demand j.
i∈0
∀ b ∈ ), i ∈ 0
aero drives
b ∈ /)
(2)
fbibd = φfbi
heavyweight drives
regression coefficients
Tg =
(1)
fbibd Hisat,l
aero gensets
Assume GT operated at sea level, 15°C, 60% of relative humidity (ISO conditions).
∀b∈)
i∈0
heavyweight gensets
zg =
∑
zgb
∀g∈. (12)
b ∈ /)
∀g∈.
zb = (6)
∑ zgb b∈.
9982
∀ b ∈ /) (13)
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Table 4. Performance Model for HRSG8
where zg is a binary variable reflecting whether or not the gas turbine installed. Equation 14 is a constraint which describes that a gas turbine satisfies a certain shaft work demand. zg =
∑ zgj
unfired mode (UF) f ufΔhuf,sh = Fuf,radCpuf,exhfgt(Tgt − Tuf,sh) f uf(Δhuf,sh + Δhuf,eva) = Fuf,radCpuf,exhfgt(Tgt − Tuf,eco) f ufΔhuf,net = Fuf,radCpuf,exhfgt(Tgt − Tuf,stk) Tuf,eco = Tuf,sat + ΔTmuf Δhuf,net = Δhuf,sh + Δhuf,eva + (1 + Fuf,bd)Δhuf,eco f uf: steam production from UF-HRSG (kg/s) Fuf,rad: radition losses factor for UF-HRSG Fuf,bd: blowdown to steam output ratio in UF-HRSG Cpuf,exh: average specific heat for GT exhaust gases (kJ/kg°C) Tuf,sh: gas temperature at superheater steam inlet in UF-HRSG (°C) Tuf,eco: gas temperature at economizer steam inlet in UF-HRSG (°C) Tuf,sat: saturation temperature for the steam produced inside UF-HRSG (°C) Tuf,stk: gas stack temperature of UF-HRSG (°C) ΔTmuf: minimum temp difference between gas and steam/water in UF-HRSG (°C) Δhuf,sh: steam enthalpy difference across the superheater in UF-HRSG (kJ/kg) Δhuf,eva: steam enthalpy difference across the evaporator in UF-HRSG (kJ/kg) Δhuf,eco: steam enthalpy difference across the economizer in UF-HRSG (kJ/kg) Δhuf,net: net steam enthalpy difference across the UF-HRSG (kJ/kg) supplementary-fired mode (SF)
∀ g ∈ .: (14)
i∈1
3.1.3. Steam Turbine. A steam turbine can convert the steam energy into power and produce steam at lower pressure levels. The corresponding performance models can be found in Table 3. Following logic constraints ensure feasible functioning within the given minimum/maximum operating loads. Table 3. Performance Model for Steam Turbine8 w st = Δhst,is
Lst + 1 st Ast f − LstW st,d − (Lst + 1) st Bst B
qst = f st (hst,in − 0.838Δhst,is) + 809.721 Lst = aL + bLΔTst,sat Ast = a0 + a1ΔTst,sat Bst = a2 + a3ΔTst,sat
f fuHLHV = Fsf,radCpsf,exhfgt(Tfir − Tgt) fsfΔhsf,sh = Fsf,radCpsf,g( fgt + f fu)(Tfir − Tsf,sh) fsf(Δhsf,sh + Δhsf,eva) = Fsf,radCpsf,g( fgt + f fu)(Tfir − Tsf,eco) fsfΔhsf,net = Fsf,radCpsf,g( fgt + f fu)(Tfir − Tsf,stk) Tsf,eco = Tsf,sat + ΔTmsf Δhsf,net = Δhsf,sh + Δhsf,eva + (1 + Fsf,bd)Δhsf,eco f fu: fuel flow required to reach the maximum firing temperature in SF-HRSG (kg/s) fsf: steam production from SF-HRSG (kg/s) Fsf,rad: radition losses factor for SF-HRSG Fsf,bd: blowdown to steam output ratio in SF-HRSG HLHV: low or net specific heat content of the supplementary fuel in SF-HRSG (kJ/kg) Cpsf,exh: average specific heat for GT gases between exhaust and firing temp (kJ/(kg °C)) Cpsf,g: specific heat for the SF gases between firing and minimum stack temp (kJ/(kg °C)) Tfir: firing temperature in SF-HRSG (°C) Tsf,sh: gas temperature at superheater steam inlet in SF-HRSG (°C) Tsf,eco: gas temperature at economizer steam inlet in SF-HRSG (°C) Tsf,sat: saturation temperature for the steam produced inside SF-HRSG (°C) Tsf,stk: minimum stack temperature of SF-HRSG (°C) ΔTmSf: minimum temp difference between gas and steam/water in SF-HRSG (°C) Δhsf,sh: steam enthalpy difference across the superheater in SF-HRSG (kJ/kg) Δhsf,eva: steam enthalpy difference across the evaporator in SF-HRSG (kJ/kg) Δhsf,eco: steam enthalpy difference across the economizer in SF-HRSG (kJ/kg) Δhsf,net: net steam enthalpy difference across the SF-HRSG (kJ/kg)
wst: shaft output (kW) Wst,d: design shaft output (kW) qst: steam heat discharge (kW) fst: steam flow rate (kg/s) ΔTst,sat: inlet−outlet saturation temperature difference across the turbine (°C) Δhst,sat: insentropic inlet−outlet enthalpy difference across the turbine (kJ/kg) back-pressure turbines condensing turbines units −0.000021 0.297263 1.601699 −0.001596 −0.010000 0.000326
a0 a1 a2 a3 aL bL
10.000 7.000 1.312466 −0.000910 0.224361 −0.000777
zt ≥ zii ′ t
∀ i ,i′ ∈ 0, i < i′, t ∈ ;
Ω̲t zii ′ t ≤ fii ′ t ≤ Ω̅ t zii ′ t
Γ̲ t zii ′ t ≤ wii ′ t ≤ Γ̅t zii ′ t
∀ i , i′ ∈ 0, i < i′, t ∈ ;
∀ i , i′ ∈ 0, i < i′, t ∈ ;
kW kW/°C − 1/°C − 1/°C
(15) (16) (17)
where zt and zii′t are binary variables reflecting whether the unit installed or connections between headers exist. Ω̲t, Γ̲t, Ω̅ t, and Γ̅ t are the minimum and the maximum capacities for steam turbines, respectively. Steam turbines can generate electricity (t ∈ ;,) or shaft work (t ∈ ;:). Equation 18 describes the shaft power demand of the process is satisfied with the steam turbine.
∑
wii ′ t =
i , i ′∈ 0
∑ wtj
∀ t ∈ ;:
j∈1
3.1.4. Deaerator. In this unit, water needs to be treated to remove the dissolved gas before it can be used for steam generation. Equations 21 and 22 describe the mass and energy balance around this unit. Its inlet streams may come from the low pressure steam, condensate return from processes, or water makeup. After water treatment, the boiler feedwater may be sent to the boiler, let-down station, or the processes for steam generation, where Ω̲D and Ω̅ D are the minimum and the maximum capacities, respectively.
(18)
i i
Ω̲ D ≤
∑ fi i∈0
c
+f +f
w
≤ Ω̅ D
+ fild + f ips
+ f ipd + fi + f ivent
∀i∈0
i ′> i
(24)
∑ fbi hbi + ∑ ∑ fi′ it hi′it + ∑ fi′i hi′ + fild H deaer + f ips hi ps
(23)
b∈)
i ′∈ 0 t ∈ ;
i ′∈ 0
i ′< i
3.1.5. Steam Header. Equations 24 and 25 describe the mass and energy balances around the steam header to ensure the total amount of flow rate/enthalpy entering header equals that leaving. The inlet streams might be from boiler, steam turbine, previous header, let-down station, or process steam generation, while outlet steams might flow to steam turbine, next lower pressure header, process demand and deaerator, or vent to environment. It is mentioned that the flow can be distributed through steam turbines or let-down stations, if there is a requirement for steam expansion. Steam flow through the steam turbines should normally be maximized in order to maximize the power generation. However, a steam balance must be maintained, and let-down stations are still important degrees of freedom in the optimization. f ii′ means the steam flow from header i to header i′. Steam expanding through a let-down station might be able to bypass a flow constraint in a steam turbine somewhere in the system and increase the power generation indirectly. The letdown stations also have desuperheaters. f ldi is the boiler feedwater used for reducing superheat of steam let-down to level i. When steam is let down from a high to a low pressure under adiabatic conditions, the amount of superheat increases. Desuperheating can be achieved by the injection of boiler feedwater under temperature control, which evaporates and reduces the superheat. Moreover, if the let-down has desuperheating, the increases the steam flow after expansion. Although let-down flows decrease the cogeneration opportunity, they can provide more degrees of freedom to bypass bottlenecks in the steam system.
= (∑
i ′< i
∑ fii′t
i ′∈ 0 t ∈ ; i ′> i
+
∑ fii′
i ′∈ 0
+ f ipd + fi + f ivent )hi
∀i∈0
i ′> i
(25)
Steam property determination is important, especially when steam is used for power generation. Without sufficient superheat, condensation will take place in the steam turbine and hence cause damage to the turbine. Also, if the steam turbine is exhausting to a steam header, then it is desirable to have some degree of superheat in the outlet to maintain some superheat in the outlet low-pressure steam header. This is because the steam might also be used through lower pressure steam turbines for power generation. Thus, The variable enthalpy is employed which depends on pressure and temperature (hi = f n(Ti, Pi)). Moreover, steam turbine performance is related to the inlet and outlet conditions. In other words, steam properties may be determined/optimized through the design procedure. 3.1.6. Power Balance. Gas turbines, steam turbines and electric motors (m ∈ 4) are used to meet the required power demands. Equation 26 ensures that the actual power delivered by all the drives attached to common shaft meets the corresponding demands.
∑ g ∈ .:
wgj +
∑ t ∈ ;:
wtj +
∑ m∈4
wmj = wjdem,s
∀j∈1 (26)
Equation 27 depicts the overall power balance, where gas turbines and steam turbines generate electricity to satisfy devices or process demands. Electricity might be exported to chemical or power plants when the steam plant generates more than needed. On the other hand, electricity might be 9984
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treated as variables. The total flow balances for the split heat capacity flow rates in stage k are stated as follows. For steam generation streams, the water stream f ihk for steam generation is provided from the deaerator, and each steam generation exchanger can provide one pressure level for a certain steam header.
imported from power plants if the steam plant generates less than needed.
∑
wg +
g ∈ .,
∑ ∑
wii ′ t + w imp,e = w dem,e
i , i ′∈ 0 t ∈ ;, i
