Applied Energy 89 (2012) 474–481 Contents lists available at SciVerse ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant Mandhapati Raju a,1, Siddhartha Kumar Khaitan b,⇑ a b Optimal CAE Inc., Plymouth, MI 48170, United States Iowa State University, Electrical and Computer Engineering Dept., Ames, IA 50014, United States a r t i c l e i n f o a b s t r a c t Article history: Received 17 November 2010 Received in revised form 12 August 2011 Accepted 12 August 2011 Available online 8 September 2011 An accurate dynamic simulation model for compressed air energy storage (CAES) inside caverns has been developed. Huntorf gas turbine plant is taken as the case study to validate the model. Accurate dynamic modeling of CAES involves formulating both the mass and energy balance inside the storage. In the ground reservoir based storage bed, the heat transfer from the ground reservoir plays an important role in predicting the cavern storage behavior and is therefore taken into account. The heat transfer coefficient between the cavern walls and the air inside the cavern is accurately modeled based on the real tests data obtained from the Huntorf plant trial tests. Finally the model is validated based on a typical daily schedule operation of the Huntorf plant. A comparison is also made with the results obtained from adiabatic and isothermal assumptions inside the cavern to gain further insights. Such accurate modeling of cavern dynamics will affect the design of the cavern storage beds for future explorations. Ó 2011 Elsevier Ltd. All rights reserved. Keywords: CAES Huntorf Cavern Simulation Heat transfer coefficient 1. Introduction There is an increasing need to harness the renewable energy sources to reduce the nation’s dependence on fossil fuels, oils and natural gas. On the other hand renewable energy from sources like solar, wind, and tidal is inherently intermittent and thus nondispatchable leading to non-optimal operation. Therefore proven storage technology is very crucial for technical viability and economic feasibility of renewable energy sources. Current available storage technologies include potential energy (e.g. compressed air energy storage [1–6], pumped hydro storage [7,8]), kinetic, thermal, chemical energy storage (e.g. hydrogen [9]), batteries [10], super capacitors [11], flywheels [12] and superconducting magnetic energy storage (SMES) [13]. For large scale storage applications, pumped hydro storage and compressed air storage are the most viable technologies. However pumped hydro storage is found to have certain adverse environmental effects [7]. As compared to other storage options (pumped hydro power and batteries), CAES has a lower capital and maintenance cost [14,15]. Hence CAES has received lot of attention in the recent times [4–6,16]. Historically CAES has been deployed for grid management applications such as load shaving, load following, load shifting and regulation. Earlier investigations focussed on peak shaving and load-levelling applications in conjunction with base-load ⇑ Corresponding author. Tel.: +1 515 294 5499. E-mail addresses: raju192@gmail.com (S. Kumar Khaitan). 1 Tel.: +1 216 526 8384. (M. Raju), skhaitan@iastate.com 0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.08.019 thermal and nuclear power plants [17,18]. The technology for CAES has a proven past although there are only two CAES plants in the world namely the 290 MW plant belonging to E.N Kraftwerke, Huntorf, Germany, 1978 [1], and the 110 MW plant of Alabama Electric Corporation (AEC) in McIntosh, Alabama, USA, 1991 [2]. Both the plants have served us well over last two decades without any problem. Recent global climatic concerns, widespread renewable portfolios and initiatives for a greener tomorrow open a host of newer opportunities of application domains for large scale storage technologies such as CAES. Combining renewables with large scale storage technology such as CAES has the potential to increase the penetration [19] of the intermittent sources. Currently, power generators are used, on average, approximately 55% of the time due to the variability of peak and off peak demand. During peak demand times, power suppliers use costly generators which increase the cost of energy for the customers. Although a CAES turbine still requires some natural gas to heat the compressed air that drives the turbine, it is less than one third of the amount used by a conventional combustion turbine. Power generators are also able to produce fossil fuel generated power during the night when green house gases are least harmful and the stored energy can be used during the day. Compressed air energy storage can be achieved using manually dug underground salt caverns, naturally occurring aquifers, depleted wells, manually built storage tanks and so on. The dynamics of compressed air storage depends on the type of storage bed. In naturally occurring aquifers, porous media modeling is required to accurately model the storage bed. There is intimate contact between the bed and the compressed air leading to heat transfer M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 between the bed and the air. Previous modeling effort has been done by [20] to model the porous media based aquifer storage. However, the heat transfer inside the aquifer has not been modeled. In the case of underground salt caverns, there is heat transfer between the air in the cavern and the salt ground reservoir at the cavern walls. Depending on the quantity of the heat transfer and the operation of the cavern, the temperature of the cavern will vary. While designing the volume of the cavern for a particular project, the operating temperature and pressure inside the cavern, plays an important role in addition to the designed number of full load operating hours of the turbine [1]. However the temperature inside the cavern is dependent on the heat transfer taking place between the compressed air in the cavern and ground reservoir. Fluctuations in this temperature can affect the operating capacity of the cavern storage, which has to be taken into account while designing the cavern storage volume. In future, adiabatic compressed air storage systems are to be driven only by cleanly-sourced power. The heat generated by the compression is also to be stored and be mixed with the compressed air streaming out to the expansion turbine. The accurate prediction of temperature inside the cavern is even more important in the case of adiabatic compressed air storage. In reality, adiabatic storage is difficult to achieve due to heat transfer to the surrounding reservoir. The temperature of the stored air being high in the case of adiabatic compressed air storage systems, the heat transfer will play an important role in designing such systems. In this paper, an accurate dynamics simulation model is developed for compressed air energy storage. Heat transfer to and from the cavern walls is taken into account. Huntorf CAES system is taken as a sample case study. The heat transfer coefficients are estimated based on comparison with test runs reported on Huntorf CAES storage plant. Once having obtained the heat transfer coefficients, the dynamic performance of the Huntorf cavern storage is obtained for a typical daily schedule operation of the plant and the results are compared with the experimental results. The importance of including accurate heat transfer model is further illustrated by comparing the results obtained from isothermal and adiabatic assumptions inside the cavern. turbine operation; air is removed from the cavern. In principle, both the compressor and the turbine can be operated simultaneously. The mass and the energy balance equations inside the cavern are given below. Air is assumed to be ideal gas. In the operating range of pressures (46–66 bar) and temperatures (around 50 °C) within the cavern, ideal gas assumption for air is nearly valid [21]. The mass and energy balance are written over the control volume enclosing the air in the cavern. Fig. 2 shows the control volume enclosing the cavern storage bed. 3.1. Mass balance _ out _ in m dq m ¼ dt V 3.2. Energy balance Energy balance is written over the control volume enclosing the air in the cavern as dðMUÞ _ out Hout hamb Acav ern ðT T amb Þ _ in Hin m ¼m dt P q dH ¼ C p dT ð3Þ ð4Þ Substituting Eqs. (3) and (4) in Eq. (2) leads to qcp _ in dT m dP hamb Acav ern þ þ cp ðT T in Þ ðT T amb Þ ¼ 0 dt dt V V ð5Þ The first term in the above equation is the rate of heat accumulation in the cavern air. The second term is the rate of convective heat flux into the cavern due to the incoming air. The third term is the heat of compression and the last term is the heat transfer from the ambient. Tin is the temperature of the incoming air from the compressor, P is the pressure inside the cavern and V is the volume of the cavern. The heat transfer coefficient and the area of heat transfer are not easy to determine. It has to be estimated based on trial experiments. Both of them are lumped together to obtain the following equations qcp Compressed air is physically stored in a cavern. During the compressor operation, air is pressurized into the cavern and during the ð2Þ The left-hand side of this equation is the rate of increase in internal energy of the cavern air, the first two terms on the righthand side of the equation represents the net rate of enthalpy change between the incoming air and the outgoing air, the third term represents the heat loss from the cavern air to the cavern surroundings. M is the mass of the air in the cavern, Hin is the specific enthalpy of the incoming air, Hout is the specific enthalpy of the outgoing air, hamb is the heat transfer coefficient between the cavern wall and the air, Acavern is the area of heat transfer between the air and the cavern wall, T is the temperature of the air and Tamb is the cavern wall temperature. For an ideal gas U ¼H 3. Modeling CAES ð1Þ q is the density of air inside the cavern and min is the mass flow rate of the incoming air from the compressor and mout is the mass flow rate of the out-going air to the turbine and V is the volume of the cavern . 2. Schematic A CAES plant mainly consists of (1) compressor train, (2) motorgenerator unit, (3) gas turbine and (4) underground compressed air storage. Fig. 1 shows the schematic of a CAES plant. During lowcost off-peak low load periods, motor consumes the grid power or power from the renewable source to compress and store air in the underground cavern. Later, during peak load periods, the process is reversed. The compressed air is discharged from the storage tank and is sent to combustion chambers to burn the natural gas. The resulting combustion gas is then expanded in the 2-stage, high pressure and low pressure gas turbines to generate electricity. The electricity generated is fed back to the grid to meet the peak load. In a pure gas turbine power station, around two-thirds of the output is needed for compressing the combustion air. In a CAES power station, however, no compression is needed during turbine operation because the required enthalpy is already included in the compressed air. This has two advantages: (1) during off-peak periods cheaper power can be used for compression; (2) the gas turbine can generate thrice the electricity as compared to the conventional gas turbine. 475 _ in dT m dP þ þ heff ðT T amb Þ ¼ 0 cp ðT T in Þ dt dt V ð6Þ heff is the effective heat transfer coefficient with the units (W/m3 K). Eqs. (1) and (6) constitute the mass and balance energy equations for the compressed air storage in caverns. 476 M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 Power Grid Exhaust After-cooler Motor HP Turbine LP Turbine Compressor Generator Fuel(Natural Gas) Salt Dome Cavern Fig. 1. Main components of a CAES plant. min H in Table 1 Operating conditions for the Huntorf plant [1]. mout H out hamb Aamb (T – Tamb ) Operating condition Value Unit Gas turbine Rated turbine power Air consumption Inlet pressure HP turbine Inlet temperature HP turbine Inlet pressure LP turbine Inlet temperature LP turbine Fuel 290 417 42 550 11 825 Natural gas MW kg/s bar °C bar °C Compressor Air flow rate Rated compressor power Temperature at exit of after cooler Pressure at exit of after cooler 108 60 50 46–72 kg/s MW °C Bar Cavern Volume of the cavern storage Cavern operating pressure Maximum cavern pressure Maximum discharge rate Cavern wall temperature 300,000 46–66 72 10 50 m3 Bar Bar bar/h °C Fig. 2. Schematic of control volume enclosing the cavern storage bed. To validate these model equations, Huntorf air storage gas turbine plant is taken as a case study. The following section outlines the methodology adopted to validate the model for this case study. 4. Huntorf – a case study Data collected from the Huntorf project as given in Table 1 is taken as case study to validate our model. Fortunately some of the real test data from the Huntorf plant is reported in the literature [22], which helped the authors to thoroughly validate the model. In particular 2 data sets are extracted from [22]. First data set is to use the trail runs conducted to examine the thermodynamic behavior of the cavern air storage (refer Fig. 4.2 of [22]). It is reported that the heat transfer takes place at the peripheral zone of the contact between cavern wall and the bulk air. Further the irregular shape of the cavern wall surface led to an increased heat transfer with the cavern surroundings, thereby leading to an increase in storage capacity. This data set is used to evaluate the unknown heat transfer coefficient in Eq. (6). This is presented in Section 4.1. The next data set is the typical power production schedule during a single day operation (see Fig. 4.1 of [22]). The pressure variation inside the cavern during this operation is also provided. The power consumption/production schedule is used to determine the compressor and turbine mass flow rates which is provided as input to the model. Knowing the accurate heat transfer coefficients, the cavern pressure and temperature can be determined accurately. The pressure variation in the cavern predicted by the model is compared with the observed pressure data. This is presented in Section 4.2. Finally the results are compared with the results obtained from the adiabatic and isothermal assumptions to demonstrate the errors that might be expected from such assumptions. 4.1. Evaluating heat transfer coefficients In this section Fig. 4.2 of [22] is taken as guideline to estimate the heat transfer coefficients accurately. Preliminary comparisons with the Huntorf test data set revealed that a constant heat transfer coefficient assumption is unable to reproduce the observed cavern behavior. This is to be expected since the mass flow rate is changing. In general, the heat transfer coefficient is dependent on the flow velocity. The flow velocity is affected by the charging 477 M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 NuL;FC ¼ 0:023ðReÞ0:8 ðPrÞn ð7Þ Since the flow velocities are dependent on the mass flow rate, Eq. (7) could be written as _ in m _ out j0:8 NuL;FC / jm ð8Þ In Eqs. (7)–(9), NuL,FC is the Nusselt number based on forced convection, Re is the Reynolds number, Pr is the Prandtl number. Hence the heat transfer coefficient can be roughly approximated as _ in m _ out j0:8 heff ¼ a þ bjm ð9Þ The constant term a represents the heat transfer coefficient caused by natural convection in the absence of any net flow in/ out of the cavern. The unknown coefficients a and b can be obtained by comparison with the cavern tests. These coefficients are weak functions of temperature but given the fact that the temperature variation in the cavern is not very high, they can be assumed to be fairly constant. If the temperature variation is large, even more accurate correlations are required. In such a case, a more detailed CFD modeling may be required to accurately study the temperature and pressure variation inside the cavern. However for the current study, a lumped parameter correlation based on Eq. (9) is a good approximation. Fig. 4.2 of [22] provides dynamics of the cavern during a trial discharge experiment where the cavern is vented out to the atmosphere. Up to 5 h, the cavern is discharged at a constant rate of 417 kg/s and then the discharge mass flow rate continually drops. Fig. 3 shows the mass flow variation as a function of time. This data is extracted from [22]. Based on this discharge mass flow as an input to the model, the cavern pressure and temperature are simulated. The coefficients a and b are tuned in such a way that a good match between the experimental and model results are obtained. Thus Eq. (9) becomes 500 _ in m _ out j0:8 heff ¼ 0:2356 þ 0:0149jm ð10Þ Fig. 4 shows the comparison of the experimental results and the simulation model results. Quite accurate match between the experimental and simulation model results are obtained for the given choice of a and b as shown in Eq. (10). Fig. 4a shows the variation of pressure with time. Since air is continually discharged from the cavern, the pressure decreases with time. After 5 h, the rate of decrease of pressure decreases since the mass flow discharge continually drops after 5 h. Fig. 4b shows the temperature inside the cavern. As air is discharged from the cavern, the temperature of the air in the cavern decreases as a result of gas expansion. Simultaneously heat is also transferred from the cavern walls to the air. The cavern wall is assumed to be at 50 °C. The initial temperature of the air inside the cavern is assumed to be at 33 °C. Heat is transferred from the cavern wall to the cavern air which is at lower temperature. The temperature drops rapidly till 5 h when the discharge is maximum. After 5 h, the discharge rate drops continuously and so the heat of expansion reduces and the heat transfer from the wall increases causing a lower decrease rate in temperature. Interestingly at around 10 h, the temperature reaches a minimum and it starts increasing. This implies the rate of heat transfer from the cavern wall dominates the rate of heat loss from gas expansion. This interesting trend is well captured by the model. In order to demonstrate the necessity of an accurate heat transfer model inside the cavern, comparison is made with the current model results with the other two possible model assumptions – isothermal and adiabatic. Both the above two model assumptions are at the two extremes. The thermodynamics inside the cavern will be in between the two extremes. Fig. 5 shows the comparison of the current model results with the isothermal and adiabatic models. Note that in the case of isothermal assumption, the cavern temperature is assumed to be constant at the initial temperature of 33 °C. Fig. 5a shows the pressure variation inside the cavern for the three models. The maximum pressure difference between the experimental and the isothermal model is around 6 bar. Given the 80 pressure (bar) and discharging characteristics of the cavern. The heat transfer inside the cavern is a combination of forced convection (induced by the incoming or outgoing air) and natural convection (due to buoyancy effect). Due to lack of information on heat transfer correlation for flows inside storage bed, the well known heat transfer correlations for flows inside tubes are taken as guidelines. The forced convection heat transfer coefficient is proportional to the convective mass flow rate inside the cavern given by Dittus–Boelter equation [23]. Model Experimental 60 40 0 400 5 10 15 time (hr) 50 300 temperature (C) mass flow rate (kg/s) 20 200 100 0 5 10 15 time (hr) Fig. 3. Experimental data showing the discharge rate as a function of time. Model Experimental 40 30 20 10 0 0 5 10 15 time (hr) Fig. 4. Comparison of model and experimental results for the discharge tests. 478 M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 mass flow rate (kg/s) 250 turbine operation compressor operation 0 -250 -500 0 5 10 15 20 time (hr) Fig. 7. Mass flow rates during a single day of Huntdorf plant. Fig. 5. Comparison of experimental results for the discharge tests with adiabatic and isothermal assumptions. 3500 grid power w/o CAES grid power with CAES Power (MW) 3000 dynamics during actual plant operation. Fortunately, experimental data is provided during a typical daily schedule operation of the Huntorf plant. Ref. [22] provides the grid power demand at the electric grid both with and without the operation of the Huntorf plant as shown in Fig. 6. Based on the data provided in [1], it is assumed that for an intake of 108 kg/s during compressor operation, 60 MW of power is consumed by the compressor. The compressed air is cooled in an after-cooler down to 50 °C (approximately corresponds to the salt wall temperature of the cavern) before entry into the cavern [1]. Similarly, a discharge rate of 417 kg/s runs a turbine which produces an output power of 290 MW. Based on these assumptions, the flow rates during compressor operation and turbine operation are estimated. It is also assumed that the power is directly proportional to the mass flow rates. 2500 5. Results and discussion 2000 1500 0 5 10 15 20 25 time (hr) Fig. 6. Typical grid power operation of Huntdorf during a single day. operating pressure of the cavern is the range of 20–70 bar, this pressure difference can lead to a significant error in the design calculations for the estimation of cavern volume and in estimating the operational characteristics of the cavern. Similarly for the adiabatic assumption, the maximum pressure difference is around 10 bar. Fig. 5b shows the temperature variation inside the cavern. The isothermal model gives a temperature difference of around 25 °C. The adiabatic model gives a very low temperature prediction of around -100 °C at the end of 16 h discharge. The discharge flow rates are huge (average 300 kg/s in 16 h). This caused a huge under-prediction in the temperature for the adiabatic assumption. Hence it is to be noted that if the flow rates are high, the adiabatic assumption will give very misleading results. 4.2. Validation of the cavern storage model Once having obtained the values of the heat transfer correlation coefficients, the model is ready to accurately simulate the cavern Fig. 7 shows the mass flow rates thus calculated based on the above assumptions. The solid lines indicate the compressor operation and the dotted lines indicate the turbine operation. Cavern intake flow rates are treated as positive and cavern discharge flow rates are treated as negative. Fig. 8 shows the comparison of the model results with the actual Huntorf results for pressure variation inside the cavern during a daily schedule operation. Fig. 8a shows the pressure variation inside the cavern. Fig. 8b shows the variation of temperature inside the cavern. As shown in Fig. 8a, the simulated pressure variation matches quite closely with the actual pressure variation inside the cavern as reported in [22]. The pressure increases during the compressor operation due to the fact that mass inside the cavern increases. During compressor operation, the temperature inside the cavern increases due to heat of compression. Similarly the pressure decreases during the turbine operation due to fact that mass is discharged from the cavern and the temperature decreases resulting from cooling due to expansion. Ref. [22] does not report the temperature variation inside the cavern. Using the model, the temperature inside the cavern can be well predicted. It is to be noted that the good match observed in the pressure variation between the simulation and the observed values is due to the incorporation of accurate heat transfer model in the energy balance equation. Fig. 9 shows the comparison of the observed pressure with the simulated model and the isothermal and adiabatic models. Fig. 9a shows the pressure variation. It is clear from the figure that the 479 pressure (bar) M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 75 model 70 Experiment 65 60 55 50 45 40 35 0 5 10 15 20 25 15 20 25 time (hr) temperature (K) 350 340 330 320 310 0 5 10 time (hr) Fig. 8. Cavern pressure and temperature variation during a single day operation. actual model experimental isothermal model adiabatic model pressure (bar) 60 55 50 0 5 10 15 20 25 time (hr) 360 actual model isothermal model adiabatic model temperature (K) 350 340 330 320 310 0 5 10 15 20 25 time (hr) Fig. 9. Comparison of the cavern characteristics for the current model with the adiabatic and isothermal models. 480 M. Raju, S.K. Khaitan / Applied Energy 89 (2012) 474–481 heat gained from the reservoir (kW) 2000 0 -2000 -4000 -6000 -8000 -10000 0 5 10 15 20 time (hr) Fig. 10. Heat loss to the reservoir during daily operation of the cavern. isothermal and adiabatic models compare poorly with the actual one. In addition, the prediction of temperature inside the cavern is quite different for all the three models showing the importance of using an accurate heat transfer model. Fig. 10 shows the heat transfer rate from the cavern walls to the air inside the cavern. The cavern wall is 323 K. As shown in Fig. 8b, the temperature of the cavern air is higher than 323 K during the compressor operation. During this phase, heat is lost to surroundings through the cavern walls. The cavern surface act as a heat sink during this phase. During the turbine operation, the temperature inside the cavern decreases and reaches a stage where the temperature drops below 323 K. Then the heat is transferred from cavern surroundings to the air inside the cavern. This is depicted in Fig. 10 as a shift from negative values to positive values. The heat transfer rate is in the order of a few megawatts. This heat transfer has to be taken into account for accurate calculations while designing cavern storage beds. This current simulation model can be used to conduct feasibility studies of the CAES technology for various practical scenarios. The efficiency of a CAES system can be improved by identifying the waste heat losses and reusing it in the system. For example, the waste heat of the exhaust gases from the LP turbine can be used for preheating the air at the inlet of the HP combustor. Similarly, the heat losses from the after-cooler during compressor operation can be stored in suitable storage materials like PCM’s, concrete and reused later. Feasibility studies can also be done for hybrid CAES systems with renewable energy sources like wind and solar. The optimal design parameters and operating conditions of the cavern storage can be estimated based on the types of the renewable energy sources available, energy available from such sources and the nature of their intermittency. The current storage model can also be modified appropriately for using it in hydrogen storage applications [24] and other applications. 5.1. Technical and economical issues There are various technical challenges to be met to bring the CAES technology to the real market. First, is the choice of the air storage system (mines, reservoir, salt domes, etc.). The geological factors play an important role in the selection of proper air storage systems. The size of the storage system needed for optimal performance of the CAES system might become technically unfeasible depending on the local conditions [25]. Efficient recuperator systems are needed to extract the waste heat from the exhaust gases to increase the efficiency of the CAES system. The usage of fuel could be further reduced with semi-adiabatic systems using efficient storage and heat recuperation. In principle, the usage of fuel could be totally eliminated with advanced adiabatic systems. However, this would require advanced research on high heat production by compressors, heat capture and transmission systems [26]. The current air driven turbine designs are based on the steam driven turbine technology and hence the operating conditions of the CAES system are limited. Although the technical challenges are there, the real concern is how to address these issues in a cost effective way because bulk storage systems like CAES have high capital cost. Thus, economic feasibility of the CAES is an important bottleneck in the implementation of the technology. The economics of the CAES plant design is affected by the location of the CAES plant and the plant operational costs. The CAES plant should be located such that there is geographical suitability for CAES storage, easy delivery of natural gas or a suitable fuel, suitable infrastructure for electric transmission network. The plant operational costs include on-peak and off-peak electricity costs, ancillary service revenues and fuel prices. The economics is further affected by the ability to capture multiple revenue streams and environmental regulations. Detailed cost analysis models need to be developed to justify the development of the bulk storage CAES systems [26]. 6. Conclusions Accurate modeling of compressed air storage cavern is done by including the mass and energy balance inside the cavern. It is shown that heat transfer plays an important role in determining the behavior of the cavern. Data from Huntorf cavern operation is used to validate this model. By incorporating accurate heat transfer model, the cavern behavior can be accurately simulated. 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