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Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant
Applied Energy 88 (2011) 1366–1376
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant G. Barigozzi, A. Perdichizzi, S. Ravelli ⇑ Department of Industrial Engineering, Bergamo University, Italy
a r t i c l e
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Article history: Received 9 January 2010 Received in revised form 1 August 2010 Accepted 27 September 2010 Available online 29 October 2010 Keywords: Wet and dry condenser Cooling tower Air condenser Off-design optimization
a b s t r a c t In Brescia, Italy, heat is delivered to 70% of 200.000 city inhabitants by means of a district heating system, mainly supplied by a waste to energy plant, utilizing the non recyclable fraction of municipal and industrial solid waste (800,000 tons/year, otherwise landfilled), thus saving annually over 150,000 tons of oil equivalent and over 400,000 tons of CO2 emissions. This study shows how the performance of the waste-to-energy cogeneration plant can be improved by optimising the condensation system, with particular focus on the combination of wet and dry cooling systems. The analysis has been carried out using two subsequent steps: in the first one a schematic model of the steam cycle was accomplished in order to acquire a knowledge base about the variables that would be most influential on the performance. In the second step the electric power output for different operating conditions was predicted and optimized in a homemade program. In more details, a thermodynamic analysis of the steam cycle, according to the design operating condition, was performed by means of a commercial code (ThermoflexÓ) dedicated to power plant modelling. Then the off-design behaviour was investigated by varying not only the ambient conditions but also several parameters connected to the heat rejection rate, like the heat required from district heating and the auxiliaries load. Each of these parameters has been addressed and considered in determining the overall performance of the thermal cycle. After that, a complete prediction of the cycle behaviour was performed by simultaneously varying different operating conditions. Finally, a MatlabÓ computer code was developed in order to optimize the net electric power as a function of the way in which the condensation is operated. The result is an optimum set of variables allowing the wet and dry cooling system to be regulated in such a way that the maximum power is achieved. The best strategy consists in using the maximum amount of heat rejection in the wet cooling system to reduce the operational cost of the dry one. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The cooling system in a power plant rejects heat at approximately twice the rate at which electric power is generated [1]. It is important to underline that, since energy flows in power plants are typically high, small improvements to the cooling system can lead to large fuel savings and consequently efficiency enhancement [2]. The effectiveness of a cooling system can be quantified through the condensing steam pressure: the lower the pressure the greater the effects. The present study was inspired by the operation of a waste-toenergy cogeneration plant placed in Brescia, Northern Italy (Fig. 1). Attention was drawn to the condensing units because of the combined wet and dry cooling system (Fig. 2): it is composed of an air cooled condenser (AC) in parallel with a water cooled condenser. In ⇑ Corresponding author. Tel.: +39 035 2052346; fax: +39 035 2052077. E-mail address: [email protected] (S. Ravelli). 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.09.023
the latter, the cooling water taken from the condenser passes through a wet mechanical draft tower (CT) and returns to the condenser. The obvious advantage of a closed-loop system is the reduction in the water demand at the expense of larger operational costs. Nevertheless environmental regulations and the increasing scarcity of natural water supplies make both the AC and the CT convenient [3]. The way in which the heat rejection takes place in an AC does not need to be deeply investigated: the critical element of the plant is the CT. Although the basic parts of the tower can easily be described and understood, heat and mass transfer processes are very complex. The temperature of the circulating water is reduced by bringing it into direct contact with air: the cooling is attained partly by the evaporation of a fraction of the water flow rate and partly by the transfer of sensible heat [4]. Each water particle is surrounded by a film of saturated air which is considered to be at the same temperature as the water; the air is heated and becomes saturated with moisture as it passes through the tower. In
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Nomenclature AC AUX CT CWP d DH HP
LP m n P RH Tamb W&D
air condenser auxiliaries cooling tower cooling water pump design district heating high pressure
the heat transfer process more then two-thirds of the heat is transferred by evaporation with the rest being transferred by convection. In many works a great effort has been made to model the physical situation within a CT: since films and droplets of water are in constantly changing configuration there is no theoretical investigation capable of simulating such a complex phenomenon without simplifying assumptions. It could be described by a set
Fig. 1. View of the waste-to-energy cogeneration plant placed in Brescia, Northern Italy.
low pressure flow rate rotational speed net power relative humidity ambient temperature wet and dry layout
of differential equations [5–8], with the help of CFD modelling [9,10], or by the NTU methods [11,12]. All cited papers think about the CT as a standalone component. According to different viewpoints it could be considered as a device which can minimize the environmental impact in the process industry thanks to the recirculation of the cooling water [13,14] or increase the efficiency of a power plant [15]. The present study complies with the last approach and wants to show the effect of a wet and dry condensation system on the performance of a cogenerative plant. At author’s knowledge, no works concerning this field can be documented. This paper offers an original contribution not only for considering a split system for air condenser and wet cooling tower but also for defining an optimization procedure whose aim is to maximize the net electric power for any operating condition. Consequently the power consumption of all auxiliaries was accurately estimated. It is necessary to remember that a mechanical draft CT uses fans to provide the required volume of airflow: their cost is an additional expense to be considered. With respect to a natural draft CT, where the circulation is ensured by the density difference existing between the heated, moist air and the fresh air, the mechanical draft CT can be built with relatively less expensive materials but requires higher operation and maintenance costs. The major problems are associated with fogging and recirculation. However the risk of recirculation is reduced if the fan is located on the top of the tower, because of the high discharge velocity. Furthermore, pumps with variable speed are required in order to guarantee the most favourable mass flow rate of cooling water. Another issue dealing with the operation of a CT is the plume formation: when the atmosphere is too cold and humid to absorb the moisture in the exhaust air from the CT, it fol-
Fig. 2. Schematic of a split system for air condenser and wet cooling tower [16].
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lows that the excess moisture condenses and the water droplets become visible. Nevertheless the plume is not a pollutant, many ways to avoid it are well documented in technical papers [16]. In spite of that, plume abatement is not widely applied since it is a very expensive feature. 2. Power plant and design operating conditions The present investigation refers to the thermal cycle of a wasteto-energy 80 MWe cogeneration plant. The flue gas from the combustion of the municipal solid waste, downstream of materials recovery, enters the heat recovery steam generator to produce steam. This steam then passes through a steam turbine, as shown in Fig. 3: the turbine is split up into a high pressure (HP) section and a low pressure (LP) one, by allowing the steam extraction for district heating (DH). The remaining steam flow rate goes to condensation passing into an AC or into a water condenser. The heat transferred between the steam side and the cooling water is rejected in a mechanical draft CT. Two pumps in parallel connection ensure the adequate circulation of the cooling water in a closed loop. All pumps and fans operate under inverter control so that their rotational speed can be continuously varied. Finally the two condensate flows mix together and go to the deareator. The elements marked with letters a–e symbolize the connection between the cycle components through pipes. Each pipe is characterised by a specific pressure drop, mainly depending on its geometric features. The scheme presented in Fig. 3 included some simplifications in comparison with the real plant. The heat recovery steam generator and the feed water heater were not considered since the analysis was focused on the condensation system, with a steam production at a constant mass flow rate, pressure and temperature. Moreover, a simplified modelling of the steam extractions from the HP turbine was performed: a single steam extraction feeding both DH, feed water heaters and combustion air pre-heaters was used instead of modelling three different extractions. Anyway, the model assured the same steam flow rate entering the LP turbine as in real operating conditions. Table 1 reports the main cycle parameters at design conditions. The analysis has been carried out for a constant steam production
Table 1 Reference cycle design parameters. Ambient temperature (°C) Ambient pressure (bar) Ambient R.H. (%) HP turbine inlet pressure (bar) HP turbine inlet temperature (°C) HP turbine inlet steam flow rate (t/h) DH heat load (MW) AC fan load (%) CT fan load (%) Water cooled condenser pumps load (%) Gross power output (MW)
15 1.01325 60 72 450 345 22.8 100 100 80 81.5
of 345 t/h entering the HP turbine at 72 bar and 450 °C. In the design condition the steam fraction going to the DH is about 9.56% of the turbine inlet steam flow rate, supplying 22.8 MWt. Steam fraction going to condensation is about 76% of turbine inlet steam mass flow rate. Between high and low pressure turbines, a crossover valve (1) is used to control steam extraction and HP turbine downstream pressure. A second valve (2) placed before the water cooled condenser is closed when ambient temperature is under 10–12 °C (i.e. provided that the AC is able to fully condense the steam), so all the steam flow rate goes to the AC. This plant layout has been defined as ‘‘dry” (Dry), with reference to the cooling system, in opposition to the ‘‘wet and dry” configuration (W&D) described before.
3. Simulation method Heat rejection to the ambient, net power output and cycle efficiency can vary because of atmospheric conditions (temperature and RH), implying a modification in both AC and CT behaviour, but also because of the thermal load required by DH. The final effect is a change in the steam flow rate going through the condenser. Moreover, the LP turbine back pressure (and the HP one, even if in a limited way) can be changed by a different control strategy of the condensation system. When a W&D configuration is used, this control strategies may be complicated, involving several parameters. In fact, heat rejection can be varied changing both AC and CT fans rotational speed as well as cooling water pumps
Fig. 3. Thermal cycle layout with the Wet and dry cooling system.
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rotational speed through inverters. An optimization strategy was thus developed in order to find out the best control strategy, i.e. the combination of fans and pumps rotational speeds leading to the maximum net power output, whatever the operating conditions may be. This optimization process was carried out by an in house developed MatlabÓ code, taking the net power output P as the objective function. The user is first required to choose the plant configuration (Dry or W&D), the ambient conditions (temperature T and relative humidity RH), and the heat demand from DH. The program first makes use of these input data to correct the net power output from the design (Pd) to the off design point (P) by means of a few coefficients (k). The net power P is then further corrected using polynomial functions, each one taking into account for the influence of the following parameters: the AC fan speed nAC, the CT fan speed nCT and the cooling water pump speed nCWP. The implemented procedure attempts to find a constrained minimum of a scalar function (P) of several variables (nAC, nCT and nCWP), each one depending on ambient and DH conditions, starting at an initial estimate (P0). The minimum is thus subjected to the linear inequalities Ax 6 b. The resulting problem to be solved consisted in
min funðPÞ ¼ kT amp kRH kDH Pd P3i¼1 ðAi n3i þ Bi n2i þ C i ni þ Di Þ
Table 2 LP turbine design data. Inlet pressure (bar) Inlet steam flow rate (t/h) Exit enthalpy before exhaust loss (kJ/kg) Dry exhaust loss (kJ/kg) Exhaust volume flow (m3/s) Annulus area (m2)
1.118 281.8 2313.5 19.34 602 3.06
ð1Þ
ni being the three already mentioned fluid machinery rotational speeds, ki the correction factors for ambient conditions and DH and Ai to Di the polynomial interpolation coefficients describing the net power output P dependency on each influence parameter. The code finally gives the AC fan speed, the CT fan speed and the cooling water pumps speed which optimize the net power production. Each considered variable is subjected to the constraints listed in Table 9. In particular, the ambient temperature can vary between 10 °C and 35 °C in the W&D configuration, a range typically encountered in Northern Italy in the warmest seasons (i.e. from April to October), and from 5 °C up to 15 °C in the Dry configuration, operating in the October–April time period. An overlap of 5 °C was maintained to check for the effective convenience of moving from W&D to Dry configurations. A 10–100% fans operational range in the W&D case was considered, reducing to 40–100% for the Dry case. This was chosen to avoid freezing and to comply with the plant’s everyday routine operation. Also the range of the heat demand from DH is limited, depending on the considered condensation asset: in the W&D layout the heat load varies between 20 MW and 100 MW, while in the Dry layout it varies from 60 MW up to 160 MW, resulting in a very large variation of mass flow rate going to condensation. In order to resolve the model for any possible operating condition occurring during the year, thus defining both ki and polynomial coefficients values, a detailed database containing the power plant off-design thermodynamic performances was generated; an interpolation method was then used to rapidly calculate the polynomial coefficients. 4. Power plant performance database The power plant simulation software ThermoflexÓ, tuned with performance data provided by the manufacturers, has been used to build up the plant model necessary to generate the data base cycle performance, according to different operating conditions. It should be noted that each cycle component needed a specific design according to features which did not necessarily match each other. A design procedure was carried out in order to define mass, heat balances and sizing of each cycle component, followed by a comparison between simulation results and manufacturer data.
Fig. 4. LP turbine leaving loss as a function of the exhaust volume flow.
In order to obtain a realistic simulation many details were included in the model. One of the most critical components to be sized was the LP turbine, whose design data are listed in Table 2. In fact, to correctly predict its off-design behaviour, the exhaust losses were evaluated as a function of the exhaust volume flow (Fig. 4). The design point is located close to the loss minimum condition, where it is supposed to be. The inlet pressure control to LP turbine, defined as sliding, lets the pressure vary with the steam flow rate. On the contrary, pressure at the inlet of the HP turbine is fixed and does not depend on the steam flow rate. Tables 3–5 summarized the design parameters for the most relevant cycle components (AC, water cooled condenser and CT, respectively) and the corresponding sizing procedure results. In the water cooled condenser a condensate subcooling of about 5 °C was introduced in order to match the experimental data. This can be related both to a not proper design of this component and to the way in which it is connected to the LP turbine exhaust diffuser. In fact, a long channel connects the LP turbine exit with the water cooled condenser, generating high pressure losses, and probably a non uniform steam distribution over the condenser heat transfer surfaces. Once all components were sized according to design values and their stand alone off-design performance verified against manufacturers data, they were connected as reported in Fig. 3 to build up the whole plant model, and operated in off-design conditions. Pressure drops in connection pipes were estimated from DCS data and
Table 3 AC design data. Condenser pressure (bar) Condensate subcooling (°C) Air temperature rise (°C) Air flow rate (t/h) Fan efficiency (%) Fan power consumption (kW)
0.095 0 16.8 21,215 70 1160
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developed in order to understand the way each relevant parameter influences the net power output. The second goal was the assessment of the superposition effect applicability to the present analysis. Finally, the optimization of net power output as a function of condensing system operational parameters was carried out for the two investigated condensing system configurations (Dry and W&D), whatever ambient conditions and DH requirements.
Table 4 Water cooled condenser design data. Condenser pressure (bar) Condensate subcooling (°C) Cooling water temperature rise (°C) Cooling water mass flow rate (t/h) Pump efficiency (%)
0.13 4.8 10.1 7370 85
Table 5 CT design data.
5.1. Model validation
Cooling tower approach to wet bulb temperature (°C) Air wet bulb temperature rise in wet section (°C) Number of cells Cooling water mass flow rate (t/h) Air mass flow rate (t/h) Fan power consumption (kW)
6.2 12.2 3 12,000 7695 560.8
plant lay-out schemes (Table 6). The combination of wet and dry cooling systems implies that a portion of the exhaust steam may condense by the water condenser and another portion may condense by air in the AC. A balancing splitter was chosen to govern the exhaust steam allocation so as to balance the turbine exit pressure: the basic idea is that both the condensers, except of the piping connections pressure drops, work at the same pressure level.
5. Results and discussion As a first step of this investigation, the power cycle model was validated against operational data. Then a parametric analysis was Table 6 Pressure drops in pipes (with reference to Fig. 2). Pipes
Pressure drop (dP/P)
(a) (b) (c) (d) + (e)
0.08 0.07 0.001 0.5 + 0.5
The model was first run at the plant design condition, considered as a reference, and also under different ambient conditions and DH requirements, in order to evaluate its prediction capability. Table 7 compares computed and measured data for three different operating conditions of the W&D configuration. All the reported cases refer to a full condensing asset, corresponding to the minimum steam extraction for DH. Table 8 compares the model results against the cycle performance data provided by the turbine manufacturer, for the Dry configuration. The reported cases show three values of the steam flow rate entering the HP turbine and different DH requirements. In particular, case 1 refers to a steam extraction for DH of about 60% of the HP turbine inlet flow, corresponding to an heat demand of about 55 MWt while, in case 2 and case 3, the steam extraction for DH is relatively low (about 20% of HP turbine inlet flow), corresponding to an heat demand of about 20 MWt. The model prediction capability was verified by comparing computed and measured LP turbine exhaust steam temperature values as well as AC, cooling water condenser and CT inlet and outlet temperature values. The net power production cannot be directly compared, due to the fact that the HP turbine steam extractions were not simulated in a detailed way, leading to an overestimation of the computed HP turbine power. Few other cases were considered to validate the W&D model but they were not included in the paper. For all the cases, a good agreement was found between model results and measurements: the maximum difference is lower than ±8%, as shown in Tables 7 and 8. In the W&D case, the simulation provides also the steam sharing between the two condensers: approximately 54% of the steam
Table 7 Comparison between model results (M.) and experimental data (Exp.) – W&D. Variables
Case 1 M.
Ambient temperature (°C) Turbine inlet flow rate (t/h) CT flow rate (t/h) Exhaust steam flow rate (t/h) Exhaust steam temperature (°C) Condensate temperature from AC (°C) Cooling water temperature to the CT (°C) Cooling water temperature from CT (°C) Condensate temperature from water condenser (°C) Steam temperature to water condenser (°C) Steam flow rate to AC (t/h)
22.1 345 7437.5 270 43.8 42.3 30.8 22.3 36.3 41.1 140
Case 2 Exp.
M.
250 44.7 44.3 32.6 25 38.3 42.3 –
16.4 370 7370 292 41.2 39.7 28.1 19.6 33.6 38.4 159
Case 3 Exp.
M.
Exp.
267 43.1 42.2 27.7 20 34.5 40.1 –
14.5 318 7350 286 39.4 37.9 25.6 18.8 31.1 36.2 159
275 40.5 39.3 27.1 20.5 33 37.8 –
Table 8 Comparison between model results and cycle data provided by the turbine manufacturer – dry. Case 1 Model Turbine inlet flow rate (t/h) Turbine inlet pressure (bar) Steam flow rate to AC (t/h) Exhaust steam temperature (°C)
212 60 87.2 35.5
Case 2 Ref.
Model
35
245.5 60 200.3 46.7
Case 3 Ref.
Model
Ref.
47.5
370 76.3 281.7 56.5
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flow rate goes to the air cooled condenser in the tested operating conditions (i.e. with minimum steam extraction for DH). Unfortunately, this information is not made available by DCS. 5.2. Parametric analysis Afterwards a parametric analysis was accomplished, starting from the design point (see Table 1), to assess the thermal cycle performance over a complete range of operating conditions. Taking into consideration both the plant layouts (W&D and Dry), several test cases were executed by varying the parameters listed in Table 9. In particular, the ambient temperature Tamb was varied with 5 °C steps in a range depending on the plant layout. Relative humidity RH variation was only considered in the hottest climate, i.e. in the W&D configuration. The AC and CT fan loads and pumps loads were also included, ruling the heat transfer in both condensers and in the CT. Finally, also the effect of the heat demand from DH was evaluated. All ranges reported in Table 9 are large enough to cover the whole plant operational field. The study initially focused on the effects of each input variable on some selected outputs (net power output P, auxiliaries power consumption PAUX, LP turbine exhaust pressure pout and steam fraction to AC, mAC/mLP) in order to verify the behaviour of each component and if a superposition rule can apply at least to some of the considered variables. Moreover, the numerous simulations constitute a fundamental database to derive the mathematical relation between the net power (object function of the optimization process) and a combination of inputs. 5.2.1. W&D configuration Figs. 5–9 show the influence of the aforementioned parameters on some selected outputs from the W&D model. In each picture the net power output is normalized using the design value, while AC and CT fans load as well as cooling water pumps load are computed as the ratio between the actual and the maximum fluid machinery rotational speed. Fig. 5a shows the normalized net power output variation versus Tamb and RH. As expected, P/Pd decreases with rising RH. The effect becomes more and more appreciable with increasing temperature. This is consistent with the LP turbine exhaust steam pressure behaviour shown in Fig. 5b: the condensing pressure increases with ambient temperature making turbine power decrease, while the auxiliary power consumption (not shown) remains practically unchanged. In the worst condition, the combined effect of high RH = 100% and Tamb = 35 °C causes a large increase in turbine exhaust pressure (up to 0.17 bar) and a significant reduction of about 2% in net power output with respect to design condition. The influence of the AC fan load on the cycle performance is shown in Fig. 6. An optimum fan load maximizing the net power output can be easily identified (Fig. 6a), whose value progressively increases with Tamb. This optimum condition is a compromise between the auxiliaries power consumption increase (Fig. 6b), almost independent from ambient temperature, and the exhaust pressure decrease (Fig. 6c), the latter strongly influenced by Tamb. It is worth
Table 9 Parametric analysis ranges. Input variables
Wet and dry
Dry
Ambient temperature (°C) Relative humidity (%) Air condenser fan load (%) Cooling tower fan load (%) Cooling water pumps load (%) DH heat load (MW)
10–35 20–100 10–100 10–100 20–100 20–100
5–10 20–100 40–100 – – 60–160
Fig. 5. RH and Tamb influence on (a) normalized net power output and (b) exhaust steam pressure – W&D.
noting that fan regulation according to the maximum load is not the right way to get the highest power production: the power gain due to the reduction in condensing pressure is not enough to compensate the increase in fan power consumption. So fan load ranging from 30% to 80% was found to give the best performance. It is obvious that the steam flow rate entering the AC increases with raise in fan load and consequently in fan speed (Fig. 6d). A very similar plant behaviour was also found varying the CT fan load (Fig. 7), thus controlling the heat rejection in the water cooled condenser. A CT fan load increase at constant ambient temperature initially gives rise to an exhaust pressure decrease (Fig. 7c) that, coupled to a small PAUX increase (Fig. 7b), results in a relevant P/Pd augmentation (Fig. 7a). Note that the CT fan power input (PCT,d = 561 kW) is less than half the AC fans one (PAC,d = 1160 kW). The progressive increase of PAUX counteracts the beneficial exhaust pressure decrease, that also stabilizes due to increased leaving losses, giving the net power output a decreasing trend. Also the full load operation of CT fan is not a good approach to achieve the maximum power. Even at the highest investigated ambient temperature, the fan load should not exceed 70%. Of course, the AC steam fraction decreases increasing the CT fan load (Fig. 7d).
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Fig. 6. AC fan load and Tamb influence on (a) normalized net power output, (b) auxiliary power consumption, (c) exhaust steam pressure and (d) AC steam fraction – W&D.
The amount of heat exchanged in the water condenser can be regulated also by varying the cooling water flow rate through a change in pumps rotational speed (Fig. 8). The plant behaviour for variable pump load is not different than before, as the effect on exhaust pressure is almost unchanged. Fig. 8a shows that the choice of cooling water flow rate exceeding the design point (corresponding to an 80% pump load) produces an increase in the net power only for high temperature (35 °C). At low ambient temperature the circulation pumps should be run at partial speed to reduce the power consumption: a pump load lower than 33% is enough for a temperature range between 10 °C and 20 °C. The influence of the DH heat demand on cycle performance in shown in Fig. 9. P/Pd linearly reduces with an increase in the heat demand from DH up to 85 MW. This is mainly due to the reduction in the power produced by the LP turbine, as a result of a decreasing steam flow going into it, even if the LP turbine exhaust pressure progressively decreases (Fig. 9b). Increasing the DH heat load further, P quickly decreases. This is due to the crossover valve closing strategy, resulting in a constant HP turbine exhaust pressure, as reported in Fig. 10. Concerning the way in which the exhaust steam is shared into the two condensers, Fig. 9c shows, as expected, that an increasing steam mass flow rate goes through the water cooling system as the ambient temperature in-
creases. The steam distribution at constant temperature and variable DH heat requirement instead depends on the ambient temperature level: at the lowest temperature of 10 °C the AC steam fraction increases with rising DH heat load. The opposite occurs at the highest temperature of 35 °C. This behaviour is consistent with the water cooled condenser better performances with rising air temperature. 5.2.2. Dry configuration In the coldest period of the year (5–15 °C) the AC receives the whole exhaust steam flow rate. Thus the investigation has been restricted to ambient temperature, to the AC fan load and to the heat demand from DH. Fig. 11 reports some of the parametric analysis results for the Dry configuration. The effects of air temperature on net power output are not reported as they are very similar to those given for the W&D layout, even though the influence is less marked, as a result of more favourable ambient conditions. On the contrary, the effect of the AC fan load on net power output greatly differs from the W&D behaviour: in fact, if Tamb varies between 5 °C and 15 °C, the AC fan should be operated according to the maximum load to get the highest power production. The regulation of fans speed, so as to reduce the auxiliary power consumption, is convenient
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Fig. 7. CT fan load and Tamb influence on (a) normalized net power output, (b) auxiliary power consumption, (c) exhaust steam pressure and (d) AC steam fraction – W&D.
in hard weather conditions. As far as the DH is concerned, no significant matters deserve notation; in fact the Dry layout reacts in the same way as the W&D layout to variation in the heat demand from DH. 5.3. Optimization of the cycle performance The performed parametric analysis demonstrated that the superposition rules do not apply either to the W&D or to Dry configuration. Nevertheless, this analysis provided a detailed data base for plant performance evaluation at different operating conditions. This data base was then included in an optimization procedure whose final target was the selection of a set of fans and pumps loads to operate the condensing system in such a way that the maximum power is achieved at different ambient conditions and DH heat demands. 5.3.1. W&D configuration Figs. 12 and 13 report the results of the condensing system optimization procedure for the W&D configuration. In particular, Fig. 12 shows the optimum load of CT fan, AC fan and pumps by varying air temperature, while Fig. 13 shows the combining effects
of the AC fan load and the DH heat load or RH on the optimum net power output. From the optimized AC and CT fans behaviour (Fig. 12) it can be deduced that, if Tamb < 15 °C, the condensation heat is more efficiently dissipated in the AC: in fact, in this condition, the optimized AC fan load (60–70%) is higher than the CT fan load (45.7–47.5%). On the contrary, if Tamb is hotter, the water cooling system ensures the greatest results in terms of power production: the optimized CT fan load (86.8–100%) is now higher than the AC fan load (40– 80%). The optimization of the W&D layout led to the following major suggestions: – The pumps rotational speed should gradually increase with Tamb, passing from about 33% at 10 °C to 100% at 35 °C. – Similarly, the CT fan rotational speed should be raised from 45% to 87% while Tamb increasing up to 20 °C and maintained at the highest level (100%) if Tamb exceeds 25 °C. – Concerning the AC fan rotational speed, the range between 40% and 80% is confirmed to provide the best performance. In the warmest conditions the plant should be regulated according to the following logic: heat rejection has to be performed as
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Fig. 8. Cooling water condenser pumps load and Tamb influence on (a) normalized net power output, (b) exhaust steam pressure – W&D.
much as possible by the cooling water; the rest of the condensation heat has to be discarded in the AC. This complies with the auxiliary power consumption: at full load, the AC fan uses more than twice the CT fan electricity. So, to sum up, an increase in temperature shifts condensation from the dry to the wet cooling system. The shift point is between 15 °C and 20 °C. The heat demand from DH and the ambient RH do not affect the optimal point but the objective function value at the optimal point. As shown in Fig. 13, the increase in both the DH heat load and the RH causes the optimized net power scaling down, while maintaining the same optimum condition, in terms of CT, AC, and pumps load. This is valid whatever the ambient temperature may be. 5.3.2. Dry configuration The optimization of the plant working according to the dry layout required a smaller effort since the objective function depends on one single variable. The AC fan load which maximizes the net power, by varying ambient temperature, is shown in Fig. 14. Unlike the previous case, steam extraction to DH influences the optimal point at intermediate temperatures (0–5 °C). In this range, the AC fan load can be reduced to 60% if a great part of the steam flow
Fig. 9. DH heat load and Tamb influence on (a) normalized net power output, (b) exhaust steam pressure and (c) AC steam fraction – W&D.
feeds the DH, otherwise it would be set to 80%. At warmer temperature (10–15 °C) the AC fan must work at full load.
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Fig. 10. DH heat load and Tamb influence on HP turbine exhaust pressure (W&D).
Fig. 13. Optimized normalized net power output: influence of (a) DH heat load and (b) RH – W&D. Fig. 11. AC fan load and Tamb influence on normalized net power output – dry.
Fig. 12. Optimized cooling water flow pumps load and CT and AC fans load for different Tamb – W&D.
Fig. 14. Optimized AC fan load for different Tamb – dry.
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6. Conclusions A detailed simulation of a wet and dry condensing system installed in a steam power cycle for district heating was developed. A parametric analysis was carried out in order to check the influence of ambient conditions, DH heat demand and condensation heat transfer (i.e. AC, water cooled condenser and CT fans and pumps rotational speeds) on plant thermodynamic performances, and particularly, on net power output. No superposition rules could be applied, but several parameters simultaneously influences in a combined way the net power output. For example, the way the CT fan load influences the net power output depends on the ambient temperature as well as on the AC fan load. Thus, a wide data base of cycle thermodynamic performances was carried out, covering all the possible operating conditions. This data base was included in an in house developed optimization code providing the condensing system control strategy giving the maximum net power output for each ambient condition and DH requirement. The air cooled condenser resulted the best way to reject heat if the ambient temperature is lower than 15 °C. At higher ambient temperature, the condensation should exploit the cooling capacity of the tower as much as possible while discarding the remaining heat in the air cooled condenser. This strategy uses the maximum available amount of heat rejection in the cooling tower to reduce the cost of the air condenser. Another result is about the cooling water pumps rotational speed: it would be simultaneously increased with ambient temperature. The AC fan load providing the best performance in terms of net power came out to be between 40% and 80%. The increase in both heat demand from DH and in ambient RH was found to scale downwards the power production without having an effect on the optimum condition. The prediction and the optimization of the thermal cycle performance have been achieved by fixing flow rate, temperature and pressure of the steam entering the high pressure turbine. An interesting hint on how to improve the model lies in consider-
ing variable steam conditions and their effect on cycle power output. References [1] Conradie AE, Kroger DG. Performance evaluation of dry-cooling systems for power plant applications. Appl Therm Eng 1996;16:219–32. [2] Smrekar J, Oman J, Sirok B. Improving the efficiency of natural draft cooling towers. Energy Convers Manage 2006;47:1086–100. [3] El-Wakil MM. Powerplant technology. NewYork: McGraw-Hill; 1984. [4] Mohiuddin AKM, Kant K. Knowledge base for the systematic design of wet cooling towers. Part I: Selection and tower characteristics. Int J Refrig 1996;1:43–51. [5] Fisenko SP, Petruchik AI. Toward to the control system of mechanical draft cooling tower of film type. Int J Heat Mass Transfer 2005;48:31–5. [6] Brin AA, Petruchik AI, Fisenko SP. Mathematical modeling of evaporative cooling of water in a mechanical-draft tower. J Eng Phys Thermophys 2002;75:1332–8. [7] Fisenko SP, Brin AA, Petruchik AI. Evaporative cooling of water in a mechanical draft cooling tower. Int J Heat Mass Transfer 2004;47:165–77. [8] Fisenko SP, Brin AA. Simulation of a cross-flow cooling tower performance. Int J Heat Mass Transfer 2007;50:3216–23. [9] Rafat AW, Masud B. CFD simulation of wet cooling towers. Appl Therm Eng 2006;26:382–95. [10] Milosavljevic N, Heikkila P. A comprehensive approach to cooling tower design. Appl Therm Eng 2001;21:899–915. [11] Soylemez MS. On the optimum performance of forced draft counter flow cooling towers. Energy Convers Manage 2004;45:2335–41. [12] Qureshi BA, Zubair SM. A complete model of wet cooling towers with fouling in fills. Appl Therm Eng 2006;26:1982–9. [13] Bloemkolk JW, Van der Schaaf RJ. Design alternatives for the use of cooling water in the process industry: minimization of the environmental impact from cooling systems. J Cleaner Prod 1996;1:21–7. [14] Harte R, Kratzig WB. Large-scale cooling towers as part of an efficient and cleaner energy generating technology. Thin-Walled Struct 2002;40: 651–664. [15] Ganan J, Rahman Al-Kassir A, Gonzales JF, Macias A, Diaz MA. Influence of the cooling circulation water on the efficiency of a thermonuclear plant. Appl Therm Eng 2005;25:485–94. [16] Lindahl PA, Jameson RW. Plume abatement and water conservation with the wet/dry cooling tower. In: Proceedings of the Cooling Tower Institute annual meeting; 2003.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant G. Barigozzi, A. Perdichizzi, S. Ravelli ⇑ Department of Industrial Engineering, Bergamo University, Italy
a r t i c l e
i n f o
Article history: Received 9 January 2010 Received in revised form 1 August 2010 Accepted 27 September 2010 Available online 29 October 2010 Keywords: Wet and dry condenser Cooling tower Air condenser Off-design optimization
a b s t r a c t In Brescia, Italy, heat is delivered to 70% of 200.000 city inhabitants by means of a district heating system, mainly supplied by a waste to energy plant, utilizing the non recyclable fraction of municipal and industrial solid waste (800,000 tons/year, otherwise landfilled), thus saving annually over 150,000 tons of oil equivalent and over 400,000 tons of CO2 emissions. This study shows how the performance of the waste-to-energy cogeneration plant can be improved by optimising the condensation system, with particular focus on the combination of wet and dry cooling systems. The analysis has been carried out using two subsequent steps: in the first one a schematic model of the steam cycle was accomplished in order to acquire a knowledge base about the variables that would be most influential on the performance. In the second step the electric power output for different operating conditions was predicted and optimized in a homemade program. In more details, a thermodynamic analysis of the steam cycle, according to the design operating condition, was performed by means of a commercial code (ThermoflexÓ) dedicated to power plant modelling. Then the off-design behaviour was investigated by varying not only the ambient conditions but also several parameters connected to the heat rejection rate, like the heat required from district heating and the auxiliaries load. Each of these parameters has been addressed and considered in determining the overall performance of the thermal cycle. After that, a complete prediction of the cycle behaviour was performed by simultaneously varying different operating conditions. Finally, a MatlabÓ computer code was developed in order to optimize the net electric power as a function of the way in which the condensation is operated. The result is an optimum set of variables allowing the wet and dry cooling system to be regulated in such a way that the maximum power is achieved. The best strategy consists in using the maximum amount of heat rejection in the wet cooling system to reduce the operational cost of the dry one. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The cooling system in a power plant rejects heat at approximately twice the rate at which electric power is generated [1]. It is important to underline that, since energy flows in power plants are typically high, small improvements to the cooling system can lead to large fuel savings and consequently efficiency enhancement [2]. The effectiveness of a cooling system can be quantified through the condensing steam pressure: the lower the pressure the greater the effects. The present study was inspired by the operation of a waste-toenergy cogeneration plant placed in Brescia, Northern Italy (Fig. 1). Attention was drawn to the condensing units because of the combined wet and dry cooling system (Fig. 2): it is composed of an air cooled condenser (AC) in parallel with a water cooled condenser. In ⇑ Corresponding author. Tel.: +39 035 2052346; fax: +39 035 2052077. E-mail address: [email protected] (S. Ravelli). 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.09.023
the latter, the cooling water taken from the condenser passes through a wet mechanical draft tower (CT) and returns to the condenser. The obvious advantage of a closed-loop system is the reduction in the water demand at the expense of larger operational costs. Nevertheless environmental regulations and the increasing scarcity of natural water supplies make both the AC and the CT convenient [3]. The way in which the heat rejection takes place in an AC does not need to be deeply investigated: the critical element of the plant is the CT. Although the basic parts of the tower can easily be described and understood, heat and mass transfer processes are very complex. The temperature of the circulating water is reduced by bringing it into direct contact with air: the cooling is attained partly by the evaporation of a fraction of the water flow rate and partly by the transfer of sensible heat [4]. Each water particle is surrounded by a film of saturated air which is considered to be at the same temperature as the water; the air is heated and becomes saturated with moisture as it passes through the tower. In
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Nomenclature AC AUX CT CWP d DH HP
LP m n P RH Tamb W&D
air condenser auxiliaries cooling tower cooling water pump design district heating high pressure
the heat transfer process more then two-thirds of the heat is transferred by evaporation with the rest being transferred by convection. In many works a great effort has been made to model the physical situation within a CT: since films and droplets of water are in constantly changing configuration there is no theoretical investigation capable of simulating such a complex phenomenon without simplifying assumptions. It could be described by a set
Fig. 1. View of the waste-to-energy cogeneration plant placed in Brescia, Northern Italy.
low pressure flow rate rotational speed net power relative humidity ambient temperature wet and dry layout
of differential equations [5–8], with the help of CFD modelling [9,10], or by the NTU methods [11,12]. All cited papers think about the CT as a standalone component. According to different viewpoints it could be considered as a device which can minimize the environmental impact in the process industry thanks to the recirculation of the cooling water [13,14] or increase the efficiency of a power plant [15]. The present study complies with the last approach and wants to show the effect of a wet and dry condensation system on the performance of a cogenerative plant. At author’s knowledge, no works concerning this field can be documented. This paper offers an original contribution not only for considering a split system for air condenser and wet cooling tower but also for defining an optimization procedure whose aim is to maximize the net electric power for any operating condition. Consequently the power consumption of all auxiliaries was accurately estimated. It is necessary to remember that a mechanical draft CT uses fans to provide the required volume of airflow: their cost is an additional expense to be considered. With respect to a natural draft CT, where the circulation is ensured by the density difference existing between the heated, moist air and the fresh air, the mechanical draft CT can be built with relatively less expensive materials but requires higher operation and maintenance costs. The major problems are associated with fogging and recirculation. However the risk of recirculation is reduced if the fan is located on the top of the tower, because of the high discharge velocity. Furthermore, pumps with variable speed are required in order to guarantee the most favourable mass flow rate of cooling water. Another issue dealing with the operation of a CT is the plume formation: when the atmosphere is too cold and humid to absorb the moisture in the exhaust air from the CT, it fol-
Fig. 2. Schematic of a split system for air condenser and wet cooling tower [16].
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lows that the excess moisture condenses and the water droplets become visible. Nevertheless the plume is not a pollutant, many ways to avoid it are well documented in technical papers [16]. In spite of that, plume abatement is not widely applied since it is a very expensive feature. 2. Power plant and design operating conditions The present investigation refers to the thermal cycle of a wasteto-energy 80 MWe cogeneration plant. The flue gas from the combustion of the municipal solid waste, downstream of materials recovery, enters the heat recovery steam generator to produce steam. This steam then passes through a steam turbine, as shown in Fig. 3: the turbine is split up into a high pressure (HP) section and a low pressure (LP) one, by allowing the steam extraction for district heating (DH). The remaining steam flow rate goes to condensation passing into an AC or into a water condenser. The heat transferred between the steam side and the cooling water is rejected in a mechanical draft CT. Two pumps in parallel connection ensure the adequate circulation of the cooling water in a closed loop. All pumps and fans operate under inverter control so that their rotational speed can be continuously varied. Finally the two condensate flows mix together and go to the deareator. The elements marked with letters a–e symbolize the connection between the cycle components through pipes. Each pipe is characterised by a specific pressure drop, mainly depending on its geometric features. The scheme presented in Fig. 3 included some simplifications in comparison with the real plant. The heat recovery steam generator and the feed water heater were not considered since the analysis was focused on the condensation system, with a steam production at a constant mass flow rate, pressure and temperature. Moreover, a simplified modelling of the steam extractions from the HP turbine was performed: a single steam extraction feeding both DH, feed water heaters and combustion air pre-heaters was used instead of modelling three different extractions. Anyway, the model assured the same steam flow rate entering the LP turbine as in real operating conditions. Table 1 reports the main cycle parameters at design conditions. The analysis has been carried out for a constant steam production
Table 1 Reference cycle design parameters. Ambient temperature (°C) Ambient pressure (bar) Ambient R.H. (%) HP turbine inlet pressure (bar) HP turbine inlet temperature (°C) HP turbine inlet steam flow rate (t/h) DH heat load (MW) AC fan load (%) CT fan load (%) Water cooled condenser pumps load (%) Gross power output (MW)
15 1.01325 60 72 450 345 22.8 100 100 80 81.5
of 345 t/h entering the HP turbine at 72 bar and 450 °C. In the design condition the steam fraction going to the DH is about 9.56% of the turbine inlet steam flow rate, supplying 22.8 MWt. Steam fraction going to condensation is about 76% of turbine inlet steam mass flow rate. Between high and low pressure turbines, a crossover valve (1) is used to control steam extraction and HP turbine downstream pressure. A second valve (2) placed before the water cooled condenser is closed when ambient temperature is under 10–12 °C (i.e. provided that the AC is able to fully condense the steam), so all the steam flow rate goes to the AC. This plant layout has been defined as ‘‘dry” (Dry), with reference to the cooling system, in opposition to the ‘‘wet and dry” configuration (W&D) described before.
3. Simulation method Heat rejection to the ambient, net power output and cycle efficiency can vary because of atmospheric conditions (temperature and RH), implying a modification in both AC and CT behaviour, but also because of the thermal load required by DH. The final effect is a change in the steam flow rate going through the condenser. Moreover, the LP turbine back pressure (and the HP one, even if in a limited way) can be changed by a different control strategy of the condensation system. When a W&D configuration is used, this control strategies may be complicated, involving several parameters. In fact, heat rejection can be varied changing both AC and CT fans rotational speed as well as cooling water pumps
Fig. 3. Thermal cycle layout with the Wet and dry cooling system.
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rotational speed through inverters. An optimization strategy was thus developed in order to find out the best control strategy, i.e. the combination of fans and pumps rotational speeds leading to the maximum net power output, whatever the operating conditions may be. This optimization process was carried out by an in house developed MatlabÓ code, taking the net power output P as the objective function. The user is first required to choose the plant configuration (Dry or W&D), the ambient conditions (temperature T and relative humidity RH), and the heat demand from DH. The program first makes use of these input data to correct the net power output from the design (Pd) to the off design point (P) by means of a few coefficients (k). The net power P is then further corrected using polynomial functions, each one taking into account for the influence of the following parameters: the AC fan speed nAC, the CT fan speed nCT and the cooling water pump speed nCWP. The implemented procedure attempts to find a constrained minimum of a scalar function (P) of several variables (nAC, nCT and nCWP), each one depending on ambient and DH conditions, starting at an initial estimate (P0). The minimum is thus subjected to the linear inequalities Ax 6 b. The resulting problem to be solved consisted in
min funðPÞ ¼ kT amp kRH kDH Pd P3i¼1 ðAi n3i þ Bi n2i þ C i ni þ Di Þ
Table 2 LP turbine design data. Inlet pressure (bar) Inlet steam flow rate (t/h) Exit enthalpy before exhaust loss (kJ/kg) Dry exhaust loss (kJ/kg) Exhaust volume flow (m3/s) Annulus area (m2)
1.118 281.8 2313.5 19.34 602 3.06
ð1Þ
ni being the three already mentioned fluid machinery rotational speeds, ki the correction factors for ambient conditions and DH and Ai to Di the polynomial interpolation coefficients describing the net power output P dependency on each influence parameter. The code finally gives the AC fan speed, the CT fan speed and the cooling water pumps speed which optimize the net power production. Each considered variable is subjected to the constraints listed in Table 9. In particular, the ambient temperature can vary between 10 °C and 35 °C in the W&D configuration, a range typically encountered in Northern Italy in the warmest seasons (i.e. from April to October), and from 5 °C up to 15 °C in the Dry configuration, operating in the October–April time period. An overlap of 5 °C was maintained to check for the effective convenience of moving from W&D to Dry configurations. A 10–100% fans operational range in the W&D case was considered, reducing to 40–100% for the Dry case. This was chosen to avoid freezing and to comply with the plant’s everyday routine operation. Also the range of the heat demand from DH is limited, depending on the considered condensation asset: in the W&D layout the heat load varies between 20 MW and 100 MW, while in the Dry layout it varies from 60 MW up to 160 MW, resulting in a very large variation of mass flow rate going to condensation. In order to resolve the model for any possible operating condition occurring during the year, thus defining both ki and polynomial coefficients values, a detailed database containing the power plant off-design thermodynamic performances was generated; an interpolation method was then used to rapidly calculate the polynomial coefficients. 4. Power plant performance database The power plant simulation software ThermoflexÓ, tuned with performance data provided by the manufacturers, has been used to build up the plant model necessary to generate the data base cycle performance, according to different operating conditions. It should be noted that each cycle component needed a specific design according to features which did not necessarily match each other. A design procedure was carried out in order to define mass, heat balances and sizing of each cycle component, followed by a comparison between simulation results and manufacturer data.
Fig. 4. LP turbine leaving loss as a function of the exhaust volume flow.
In order to obtain a realistic simulation many details were included in the model. One of the most critical components to be sized was the LP turbine, whose design data are listed in Table 2. In fact, to correctly predict its off-design behaviour, the exhaust losses were evaluated as a function of the exhaust volume flow (Fig. 4). The design point is located close to the loss minimum condition, where it is supposed to be. The inlet pressure control to LP turbine, defined as sliding, lets the pressure vary with the steam flow rate. On the contrary, pressure at the inlet of the HP turbine is fixed and does not depend on the steam flow rate. Tables 3–5 summarized the design parameters for the most relevant cycle components (AC, water cooled condenser and CT, respectively) and the corresponding sizing procedure results. In the water cooled condenser a condensate subcooling of about 5 °C was introduced in order to match the experimental data. This can be related both to a not proper design of this component and to the way in which it is connected to the LP turbine exhaust diffuser. In fact, a long channel connects the LP turbine exit with the water cooled condenser, generating high pressure losses, and probably a non uniform steam distribution over the condenser heat transfer surfaces. Once all components were sized according to design values and their stand alone off-design performance verified against manufacturers data, they were connected as reported in Fig. 3 to build up the whole plant model, and operated in off-design conditions. Pressure drops in connection pipes were estimated from DCS data and
Table 3 AC design data. Condenser pressure (bar) Condensate subcooling (°C) Air temperature rise (°C) Air flow rate (t/h) Fan efficiency (%) Fan power consumption (kW)
0.095 0 16.8 21,215 70 1160
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developed in order to understand the way each relevant parameter influences the net power output. The second goal was the assessment of the superposition effect applicability to the present analysis. Finally, the optimization of net power output as a function of condensing system operational parameters was carried out for the two investigated condensing system configurations (Dry and W&D), whatever ambient conditions and DH requirements.
Table 4 Water cooled condenser design data. Condenser pressure (bar) Condensate subcooling (°C) Cooling water temperature rise (°C) Cooling water mass flow rate (t/h) Pump efficiency (%)
0.13 4.8 10.1 7370 85
Table 5 CT design data.
5.1. Model validation
Cooling tower approach to wet bulb temperature (°C) Air wet bulb temperature rise in wet section (°C) Number of cells Cooling water mass flow rate (t/h) Air mass flow rate (t/h) Fan power consumption (kW)
6.2 12.2 3 12,000 7695 560.8
plant lay-out schemes (Table 6). The combination of wet and dry cooling systems implies that a portion of the exhaust steam may condense by the water condenser and another portion may condense by air in the AC. A balancing splitter was chosen to govern the exhaust steam allocation so as to balance the turbine exit pressure: the basic idea is that both the condensers, except of the piping connections pressure drops, work at the same pressure level.
5. Results and discussion As a first step of this investigation, the power cycle model was validated against operational data. Then a parametric analysis was Table 6 Pressure drops in pipes (with reference to Fig. 2). Pipes
Pressure drop (dP/P)
(a) (b) (c) (d) + (e)
0.08 0.07 0.001 0.5 + 0.5
The model was first run at the plant design condition, considered as a reference, and also under different ambient conditions and DH requirements, in order to evaluate its prediction capability. Table 7 compares computed and measured data for three different operating conditions of the W&D configuration. All the reported cases refer to a full condensing asset, corresponding to the minimum steam extraction for DH. Table 8 compares the model results against the cycle performance data provided by the turbine manufacturer, for the Dry configuration. The reported cases show three values of the steam flow rate entering the HP turbine and different DH requirements. In particular, case 1 refers to a steam extraction for DH of about 60% of the HP turbine inlet flow, corresponding to an heat demand of about 55 MWt while, in case 2 and case 3, the steam extraction for DH is relatively low (about 20% of HP turbine inlet flow), corresponding to an heat demand of about 20 MWt. The model prediction capability was verified by comparing computed and measured LP turbine exhaust steam temperature values as well as AC, cooling water condenser and CT inlet and outlet temperature values. The net power production cannot be directly compared, due to the fact that the HP turbine steam extractions were not simulated in a detailed way, leading to an overestimation of the computed HP turbine power. Few other cases were considered to validate the W&D model but they were not included in the paper. For all the cases, a good agreement was found between model results and measurements: the maximum difference is lower than ±8%, as shown in Tables 7 and 8. In the W&D case, the simulation provides also the steam sharing between the two condensers: approximately 54% of the steam
Table 7 Comparison between model results (M.) and experimental data (Exp.) – W&D. Variables
Case 1 M.
Ambient temperature (°C) Turbine inlet flow rate (t/h) CT flow rate (t/h) Exhaust steam flow rate (t/h) Exhaust steam temperature (°C) Condensate temperature from AC (°C) Cooling water temperature to the CT (°C) Cooling water temperature from CT (°C) Condensate temperature from water condenser (°C) Steam temperature to water condenser (°C) Steam flow rate to AC (t/h)
22.1 345 7437.5 270 43.8 42.3 30.8 22.3 36.3 41.1 140
Case 2 Exp.
M.
250 44.7 44.3 32.6 25 38.3 42.3 –
16.4 370 7370 292 41.2 39.7 28.1 19.6 33.6 38.4 159
Case 3 Exp.
M.
Exp.
267 43.1 42.2 27.7 20 34.5 40.1 –
14.5 318 7350 286 39.4 37.9 25.6 18.8 31.1 36.2 159
275 40.5 39.3 27.1 20.5 33 37.8 –
Table 8 Comparison between model results and cycle data provided by the turbine manufacturer – dry. Case 1 Model Turbine inlet flow rate (t/h) Turbine inlet pressure (bar) Steam flow rate to AC (t/h) Exhaust steam temperature (°C)
212 60 87.2 35.5
Case 2 Ref.
Model
35
245.5 60 200.3 46.7
Case 3 Ref.
Model
Ref.
47.5
370 76.3 281.7 56.5
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flow rate goes to the air cooled condenser in the tested operating conditions (i.e. with minimum steam extraction for DH). Unfortunately, this information is not made available by DCS. 5.2. Parametric analysis Afterwards a parametric analysis was accomplished, starting from the design point (see Table 1), to assess the thermal cycle performance over a complete range of operating conditions. Taking into consideration both the plant layouts (W&D and Dry), several test cases were executed by varying the parameters listed in Table 9. In particular, the ambient temperature Tamb was varied with 5 °C steps in a range depending on the plant layout. Relative humidity RH variation was only considered in the hottest climate, i.e. in the W&D configuration. The AC and CT fan loads and pumps loads were also included, ruling the heat transfer in both condensers and in the CT. Finally, also the effect of the heat demand from DH was evaluated. All ranges reported in Table 9 are large enough to cover the whole plant operational field. The study initially focused on the effects of each input variable on some selected outputs (net power output P, auxiliaries power consumption PAUX, LP turbine exhaust pressure pout and steam fraction to AC, mAC/mLP) in order to verify the behaviour of each component and if a superposition rule can apply at least to some of the considered variables. Moreover, the numerous simulations constitute a fundamental database to derive the mathematical relation between the net power (object function of the optimization process) and a combination of inputs. 5.2.1. W&D configuration Figs. 5–9 show the influence of the aforementioned parameters on some selected outputs from the W&D model. In each picture the net power output is normalized using the design value, while AC and CT fans load as well as cooling water pumps load are computed as the ratio between the actual and the maximum fluid machinery rotational speed. Fig. 5a shows the normalized net power output variation versus Tamb and RH. As expected, P/Pd decreases with rising RH. The effect becomes more and more appreciable with increasing temperature. This is consistent with the LP turbine exhaust steam pressure behaviour shown in Fig. 5b: the condensing pressure increases with ambient temperature making turbine power decrease, while the auxiliary power consumption (not shown) remains practically unchanged. In the worst condition, the combined effect of high RH = 100% and Tamb = 35 °C causes a large increase in turbine exhaust pressure (up to 0.17 bar) and a significant reduction of about 2% in net power output with respect to design condition. The influence of the AC fan load on the cycle performance is shown in Fig. 6. An optimum fan load maximizing the net power output can be easily identified (Fig. 6a), whose value progressively increases with Tamb. This optimum condition is a compromise between the auxiliaries power consumption increase (Fig. 6b), almost independent from ambient temperature, and the exhaust pressure decrease (Fig. 6c), the latter strongly influenced by Tamb. It is worth
Table 9 Parametric analysis ranges. Input variables
Wet and dry
Dry
Ambient temperature (°C) Relative humidity (%) Air condenser fan load (%) Cooling tower fan load (%) Cooling water pumps load (%) DH heat load (MW)
10–35 20–100 10–100 10–100 20–100 20–100
5–10 20–100 40–100 – – 60–160
Fig. 5. RH and Tamb influence on (a) normalized net power output and (b) exhaust steam pressure – W&D.
noting that fan regulation according to the maximum load is not the right way to get the highest power production: the power gain due to the reduction in condensing pressure is not enough to compensate the increase in fan power consumption. So fan load ranging from 30% to 80% was found to give the best performance. It is obvious that the steam flow rate entering the AC increases with raise in fan load and consequently in fan speed (Fig. 6d). A very similar plant behaviour was also found varying the CT fan load (Fig. 7), thus controlling the heat rejection in the water cooled condenser. A CT fan load increase at constant ambient temperature initially gives rise to an exhaust pressure decrease (Fig. 7c) that, coupled to a small PAUX increase (Fig. 7b), results in a relevant P/Pd augmentation (Fig. 7a). Note that the CT fan power input (PCT,d = 561 kW) is less than half the AC fans one (PAC,d = 1160 kW). The progressive increase of PAUX counteracts the beneficial exhaust pressure decrease, that also stabilizes due to increased leaving losses, giving the net power output a decreasing trend. Also the full load operation of CT fan is not a good approach to achieve the maximum power. Even at the highest investigated ambient temperature, the fan load should not exceed 70%. Of course, the AC steam fraction decreases increasing the CT fan load (Fig. 7d).
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Fig. 6. AC fan load and Tamb influence on (a) normalized net power output, (b) auxiliary power consumption, (c) exhaust steam pressure and (d) AC steam fraction – W&D.
The amount of heat exchanged in the water condenser can be regulated also by varying the cooling water flow rate through a change in pumps rotational speed (Fig. 8). The plant behaviour for variable pump load is not different than before, as the effect on exhaust pressure is almost unchanged. Fig. 8a shows that the choice of cooling water flow rate exceeding the design point (corresponding to an 80% pump load) produces an increase in the net power only for high temperature (35 °C). At low ambient temperature the circulation pumps should be run at partial speed to reduce the power consumption: a pump load lower than 33% is enough for a temperature range between 10 °C and 20 °C. The influence of the DH heat demand on cycle performance in shown in Fig. 9. P/Pd linearly reduces with an increase in the heat demand from DH up to 85 MW. This is mainly due to the reduction in the power produced by the LP turbine, as a result of a decreasing steam flow going into it, even if the LP turbine exhaust pressure progressively decreases (Fig. 9b). Increasing the DH heat load further, P quickly decreases. This is due to the crossover valve closing strategy, resulting in a constant HP turbine exhaust pressure, as reported in Fig. 10. Concerning the way in which the exhaust steam is shared into the two condensers, Fig. 9c shows, as expected, that an increasing steam mass flow rate goes through the water cooling system as the ambient temperature in-
creases. The steam distribution at constant temperature and variable DH heat requirement instead depends on the ambient temperature level: at the lowest temperature of 10 °C the AC steam fraction increases with rising DH heat load. The opposite occurs at the highest temperature of 35 °C. This behaviour is consistent with the water cooled condenser better performances with rising air temperature. 5.2.2. Dry configuration In the coldest period of the year (5–15 °C) the AC receives the whole exhaust steam flow rate. Thus the investigation has been restricted to ambient temperature, to the AC fan load and to the heat demand from DH. Fig. 11 reports some of the parametric analysis results for the Dry configuration. The effects of air temperature on net power output are not reported as they are very similar to those given for the W&D layout, even though the influence is less marked, as a result of more favourable ambient conditions. On the contrary, the effect of the AC fan load on net power output greatly differs from the W&D behaviour: in fact, if Tamb varies between 5 °C and 15 °C, the AC fan should be operated according to the maximum load to get the highest power production. The regulation of fans speed, so as to reduce the auxiliary power consumption, is convenient
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Fig. 7. CT fan load and Tamb influence on (a) normalized net power output, (b) auxiliary power consumption, (c) exhaust steam pressure and (d) AC steam fraction – W&D.
in hard weather conditions. As far as the DH is concerned, no significant matters deserve notation; in fact the Dry layout reacts in the same way as the W&D layout to variation in the heat demand from DH. 5.3. Optimization of the cycle performance The performed parametric analysis demonstrated that the superposition rules do not apply either to the W&D or to Dry configuration. Nevertheless, this analysis provided a detailed data base for plant performance evaluation at different operating conditions. This data base was then included in an optimization procedure whose final target was the selection of a set of fans and pumps loads to operate the condensing system in such a way that the maximum power is achieved at different ambient conditions and DH heat demands. 5.3.1. W&D configuration Figs. 12 and 13 report the results of the condensing system optimization procedure for the W&D configuration. In particular, Fig. 12 shows the optimum load of CT fan, AC fan and pumps by varying air temperature, while Fig. 13 shows the combining effects
of the AC fan load and the DH heat load or RH on the optimum net power output. From the optimized AC and CT fans behaviour (Fig. 12) it can be deduced that, if Tamb < 15 °C, the condensation heat is more efficiently dissipated in the AC: in fact, in this condition, the optimized AC fan load (60–70%) is higher than the CT fan load (45.7–47.5%). On the contrary, if Tamb is hotter, the water cooling system ensures the greatest results in terms of power production: the optimized CT fan load (86.8–100%) is now higher than the AC fan load (40– 80%). The optimization of the W&D layout led to the following major suggestions: – The pumps rotational speed should gradually increase with Tamb, passing from about 33% at 10 °C to 100% at 35 °C. – Similarly, the CT fan rotational speed should be raised from 45% to 87% while Tamb increasing up to 20 °C and maintained at the highest level (100%) if Tamb exceeds 25 °C. – Concerning the AC fan rotational speed, the range between 40% and 80% is confirmed to provide the best performance. In the warmest conditions the plant should be regulated according to the following logic: heat rejection has to be performed as
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Fig. 8. Cooling water condenser pumps load and Tamb influence on (a) normalized net power output, (b) exhaust steam pressure – W&D.
much as possible by the cooling water; the rest of the condensation heat has to be discarded in the AC. This complies with the auxiliary power consumption: at full load, the AC fan uses more than twice the CT fan electricity. So, to sum up, an increase in temperature shifts condensation from the dry to the wet cooling system. The shift point is between 15 °C and 20 °C. The heat demand from DH and the ambient RH do not affect the optimal point but the objective function value at the optimal point. As shown in Fig. 13, the increase in both the DH heat load and the RH causes the optimized net power scaling down, while maintaining the same optimum condition, in terms of CT, AC, and pumps load. This is valid whatever the ambient temperature may be. 5.3.2. Dry configuration The optimization of the plant working according to the dry layout required a smaller effort since the objective function depends on one single variable. The AC fan load which maximizes the net power, by varying ambient temperature, is shown in Fig. 14. Unlike the previous case, steam extraction to DH influences the optimal point at intermediate temperatures (0–5 °C). In this range, the AC fan load can be reduced to 60% if a great part of the steam flow
Fig. 9. DH heat load and Tamb influence on (a) normalized net power output, (b) exhaust steam pressure and (c) AC steam fraction – W&D.
feeds the DH, otherwise it would be set to 80%. At warmer temperature (10–15 °C) the AC fan must work at full load.
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Fig. 10. DH heat load and Tamb influence on HP turbine exhaust pressure (W&D).
Fig. 13. Optimized normalized net power output: influence of (a) DH heat load and (b) RH – W&D. Fig. 11. AC fan load and Tamb influence on normalized net power output – dry.
Fig. 12. Optimized cooling water flow pumps load and CT and AC fans load for different Tamb – W&D.
Fig. 14. Optimized AC fan load for different Tamb – dry.
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6. Conclusions A detailed simulation of a wet and dry condensing system installed in a steam power cycle for district heating was developed. A parametric analysis was carried out in order to check the influence of ambient conditions, DH heat demand and condensation heat transfer (i.e. AC, water cooled condenser and CT fans and pumps rotational speeds) on plant thermodynamic performances, and particularly, on net power output. No superposition rules could be applied, but several parameters simultaneously influences in a combined way the net power output. For example, the way the CT fan load influences the net power output depends on the ambient temperature as well as on the AC fan load. Thus, a wide data base of cycle thermodynamic performances was carried out, covering all the possible operating conditions. This data base was included in an in house developed optimization code providing the condensing system control strategy giving the maximum net power output for each ambient condition and DH requirement. The air cooled condenser resulted the best way to reject heat if the ambient temperature is lower than 15 °C. At higher ambient temperature, the condensation should exploit the cooling capacity of the tower as much as possible while discarding the remaining heat in the air cooled condenser. This strategy uses the maximum available amount of heat rejection in the cooling tower to reduce the cost of the air condenser. Another result is about the cooling water pumps rotational speed: it would be simultaneously increased with ambient temperature. The AC fan load providing the best performance in terms of net power came out to be between 40% and 80%. The increase in both heat demand from DH and in ambient RH was found to scale downwards the power production without having an effect on the optimum condition. The prediction and the optimization of the thermal cycle performance have been achieved by fixing flow rate, temperature and pressure of the steam entering the high pressure turbine. An interesting hint on how to improve the model lies in consider-
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