Two Phase Flow Phase Change and Numerical Modeling Part 20 pdf

Two Phase Flow, Phase Change and Numerical Modeling 560 Fig. 20. Schematic diagrams of the HVAC systems used in the simulations The results are shown in Figure 21 for 100 and 400 kg of PCM. In the left-hand figure, the PCM mixture was cooled to air temperature (12°C) as soon as the charging operation started. During the discharging operation, the stored heat was not large enough to maintain the room temperature. Consequently, the room temperature was raised to 35°C. The right- hand figure shows the results for 400 kg. The temperature during charging and discharging operations decreased gradually due to latent heat. The stored heat had sufficient capacity to maintain the room temperature near the set point. Fig. 21. Comparison of temperature fluctuation using 100 kg or 400 kg of PCM Room temp. 28 C 13:00 16:00 A 26 C Fig. 22. Index used to evaluate the investigated effect Thermal Energy Storage Tanks Using Phase Change Material (PCM) in HVAC Systems 561 50 100 150 200 250 300 350 400 MT17 MT19 MT21 MT23 0 2 4 6 8 10 12 14 16 18 Temp. deviation; "A" of Fig 5 Quantity of PCM [kg] Fig. 23. Relationship among the index, the materials, and the quantities 3.4 Discussion The purpose of this system was to control the temperature increase while the refrigeration machines were stopped. The evaluation of the system focused on the degree to which the temperature fluctuated. Assuming that 28°C is the allowed indoor temperature, the area A shown in Figure 22, which is the difference between the room temperature and 28°C, was used as an index of temperature deviation. This index increases as the temperature in the room increases. Figure 23 shows the relationship between the index, the quantity of PCM, and the PCM mixture. The temperature deviation decreased as the quantity of PCM mixture increased. The index or the temperature deviation was very small for 400 kg of PCM, which was equivalent to 5.4 kg/m 2 of PCM. The differences among the various materials were not significant. The index was larger for materials with higher melting temperatures (MT23, MT21). Because of its lower melting temperature, the most effective material was MT19. Moreover, MT 17 melted too quickly. In the system discussed in the present paper, the PCM would be maintained in containers and installed in air ducts. The heat transfer between the surface of the container and the air in the duct would be a significant problem. Since thermal conductivities of paraffin waxes are small, the material would not be sufficiently melted or frozen, unless some enhancements, such as fins, were adopted. Although, in the present study, fins were adopted, for real applications, the structure of the container should be simple in order to decrease the cost of construction. In the present study, there was no consideration of the humidity because the program only treated the heat transfer problem. The humidity has a large influence on thermal comfort. The dew point of 26°C and RH 50% air is lower than 17°C, so the humidity of the room would increase during the discharging operation. The humidity should be calculated because the sensible heat load is relatively small in an office building. 4. Conclusions Thermal energy storage systems are used to shift peak heat load to off-peak hours. The performance depends on the design and installation of such systems. The performances of two types of TES, which use ice and paraffin waxes, were analyzed. Ice storage systems Two Phase Flow, Phase Change and Numerical Modeling 562 were analyzed as HVAC system components, and a storage system using paraffin waxes was evaluated for use by a passive method. Ice-on-coil and slurry ice storage system were considered. Several definitions of efficiency as indices of evaluation were discussed. The temperature response of an ice-on-coil storage system depends on the mixing condition. Large Archimedes numbers at the inlet result in a longer duration of low outlet temperature. The effects of the operating conditions on the energy and response-based efficiencies were also examined. The response-based efficiency was more sensible to the normalized inlet enthalpy flow rate. For the slurry ice storage tank, the time at which the outlet temperature reached 4°C varied according to experimental conditions. Since the ice in the slurry ice tank consisted of tiny floating particles, the higher velocity could enhance heat transfer and result in lower outlet temperatures For storage system using paraffin waxes, an air distribution system with the PCM tank in the air ducts was proposed. The system was used for cooling and could take advantage of discounted electricity rates at night. The materials that could be used in the system, were obtained by mixing paraffin waxes and fatty acids. The thermal properties of the materials were measured. The melting temperature could be controlled by adjusting the concentration of each material, although the latent heat of the measured mixtures was less than that of the pure paraffin wax. The system performance was examined through a computer simulation, and the necessary quantity of material was evaluated. The PCM was cooled from 5:00 to 8:00 am using discounted electricity. The stored heat was discharged from 13:00 to 16:00, when the peak load of cooling occurred. As the refrigeration machines were stopped during this period, the temperature of the room fluctuated. The temperature deviation was taken as an index, and the system was evaluated. For an ordinary office building in Nagoya City, which is located in the same climate as major cities with more than two million inhabitants in Japan, 400 kg of PCM for 73.8 m 2 of room surface (or 5.4 kg/m 2 of PCM) could maintain the room temperature to be constant without any cold source operation. The melting temperature suitable for the system was approximately 19°C, which could be achieved using MT19. 5. Nomenclature A : wall surface area Ar in : Archimedes number at the inlet c : specific heat d in : diameter of the inlet of the tank dz : thickness of PCM g : gravitational acceleration h: convective coefficient H t : heat removed from a storage tank H tc : heat removed until the outlet temperature reaches the limit temperature IPF : (Ice Packing Factor) ratio of ice volume to tank volume (= V ice /V 0 ) L : heat of fusion of water Nu : Nusselt number Pr : Prandtl number q : heat flow from coil Q*: dimensionless enthalpy flow rate Q : flow rate of inlet water Thermal Energy Storage Tanks Using Phase Change Material (PCM) in HVAC Systems 563 Re : Reynolds number T, t : time Tc : limit temperature to the coils of the air handling units u in : velocity of inlet water u: velocity of water inside the tank U : average overall heat transfer coefficient V : airflow rate to the room V 0 : volume of tank V ice : volume of ice x : length in the flow direction, η : response-based efficiency η 0 : system efficiency η v : volumetric efficiency θ 0 : initial temperature θ in : temperature of the inlet water θ out : temperature of the outlet water θ c : limit temperature to the coils of the air handling units Δθ i : equivalent temperature difference for ice storage (= L • IPF/c) Δθ 0 : temperature difference of the coils of the air handling units ρ : density of inlet water ρ 0 : density of water at the initial temperature ρ ice : density of ice Δ ρ : density difference between the inlet water to the tank and the initial temperature of water in the tank λ : thermal conductivity θ a : temperature of air θ p : temperature of PCM θ r : temperature of the room * indicates a dimensionless value 6. References Barnard, N and Setterwall, F, (2003), Thermal Mass and Night Ventilation - Utilising "hidden" Thermal Mass, Proceedings of Workshop IEA Annex 17, Indore. Mar. 2003. Feldman, D, Shapirom, M M, Banu, D and Fuks, C J, (1989), Fatty Acids and Their Mixtures as Phase-Change Materials for Thermal Energy Storage. Solar Energy Material, Vol. 18, Issue 3-4, pp. 201-216. ISSN 0927-0248 Feldman, D, Banu, D, and Hawes, D W, (1995), Development and Application of Organic Phase Change Mixtures in Thermal Storage Gypsum Wallboard, Solar Energy Materials and Solar Cells, Vol. 36, Issue 2, pp. 147-157. ISSN 0927-0248 He, B, Gustafsson, M, and Setterwall, F, (1999), Tetradecane and Hexadecane Binary Mixtures as Phase Change Materials (Pcms) for Cool Storage in District Cooling Systems. Journal of Energy, Vol. 24, Issue 12, 1015-1028. ISSN: 0360-5442 Incropera, F and DeWitt, D, (1996), Fundamentals of Heat and Mass Transfer, John Wiley & Sons., ISBN 0-471-30460-3, New York Two Phase Flow, Phase Change and Numerical Modeling 564 Kauranen, P, Peippo, K, and Lund, P D, (1991), An Organic PCM Storage System with Adjustable Melting Temperature. Solar Energy, Vol. 46, Issue 5, pp. 275-278. ISSN: 0038-092X Lin, K, Zhang, Y, and Jiang, Y, (2003), Simulation and Evaluation of the Thermal Performance of PCM Wallboard Rooms Located in Different Climate Regions of China in Summer, Proceedings of the ASME/JSME Thermal Engineering Joint Conference: 71, Hawaii, Mar. 2003 Mehling, H, (2002), News on the Application of PCMs for Heating and Cooling of Buildings. Proceedings of Workshop IEA Annex 17, Tokyo, Sept. 2002. Shilei, L, Neng, Z, and Gouhui, F, (2006), Impact of Phase Change Wall Room on Indoor Thermal Environment in Winter. Energy and Buildings, Vol. 38: 18-24. Tamblyn, R T, (1977), Thermal storage: it saves and saves and saves. ASHRAE Transaction Vol. 83, Part 1, pp.677-684, ISSN: 0001-2505 Yamaha, M, Shuku, K, and Misaki, S, (2001), A Study on Thermal Characteristics of Thermal Storage Tank Using Phase Change Material Installed in an Air Distribution System, Transaction of AIJ. No. 549, pp. 51-57. ISSN 1348-0685. 25 Heat Transfer and Phase Change in Deep CO 2 Injector for CO 2 Geological Storage Kyuro Sasaki and Yuichi Sugai Department of Earth Resource Engineering, Kyushu University Japan 1. Introduction CO 2 capture and storage (CCS) is expected to reduce CO 2 emissions into the atmosphere. Various underground reservoirs and layers exist where CO 2 may be stored such as aquifers, depleted oil and gas reservoirs as well as unmined coal seams. Coal seams are feasible for CCS because coal can adsorb CO 2 gas with roughly twice volume compared with CH 4 gas originaly stored (Yee et al., 1993). However, the coal matrix is swelling with adsorption CO 2 and its permeability is reduced. Supercritical CO 2 has a higher injection rate of CO 2 into coal seams than liquid CO 2 because its viscosity is 40% lower than the liquid CO 2 (see Harpalani and Chen, 1993). The Japanese consortium carried out the test project on Enhanced Coal Bed Methane Recovery by CO 2 injection (CO 2 –ECBMR) at Yubari City, Hokkaido, Japan during 2004 to 2007 [Yamaguchi et al. (2007), Fujioka et al.(2010)]. The target coal seam at Yubari was located about 890 to 900 m below the surface (Yasunami et al., 2010). However, liquid CO 2 was injected from the bottom holes because of heat loss along the deep injection tubing. The absolute pressure and temperature at the bottom hole was approximately 15.5MPa and 28°C. The regular tubing was replaced with thermally insulated tubing that included an argon gas layer but the temperature at the bottom was still lower than the critical temperature of CO 2 . This chapter provides a numerical model of heat transfer and calculation procedure for the prediction of CO 2 temperature and pressure that includes a phase change (supercritical or liquid) by considering the heat loss from the injector to surrounding casing pipes and rock formation. Furthermore, this study provides numerical simulation results of the temperature distribution of the coal seam after the injection of CO 2 . 2. Prediction model for CO 2 injection temperature 2.1 CO 2 flow rate injected into a reservoir As shown in Fig. 1, a schematic radial flow model in a reservoir, such as coal seam or aquifer, is targeted for CO 2 injection with a vertical injection well (injector). The reservoir with radius R and thickness h R , is saturated with water and open with constant pressure at its outer boundary. Assume omitting well pressure loss, the initial CO 2 mass flow rate , M(0), at time t = 0, that is injected into the reservoir from its bottom hole, is equal to radial water flow rate in the reservoir [Michael et al. (2008) and Sasaki & Akibayashi (1999)], Two Phase Flow, Phase Change and Numerical Modeling 566 0 (0) (0) ; (0) (0) ( ,0) ln 2 H BH R BH BH WH w wR w PP M PP gxdx R Kh r ρρ μ π − ==+  ⋅    (1) where ρ(x,t) and ρ BH = ρ(H,t) are CO 2 density in the injector and bottom hole respectively, g is acceleration of gravity, r w is outer radius of the bottom hole, K w is reservoir permeability, P WH , P BH and P R are pressures at well head, bottom hole and outer boundary, μ w is water viscosity in the reservoir, and H is length of vertical injector. The reservoir’s initial pressure is also equal to P R . After starting CO 2 injection, the CO 2 mass flow rate M(t) and bottom hole pressure P BH (t) are changing with elapsed time t, since bottom hole pressure depends on CO 2 density distribution through the injector and water is replaced with CO 2 . Therefore, flow rate after becoming steady-state Q is given with P BH and CO 2 viscosity μ f at t = ∞. 0 () () () ; () () (,) ln 2 H BH R BH BH WH f wR w PP M PP gxdx R Kh r ρρ μ π ∞− ∞= ∞ ∞= ∞+ ∞  ⋅    (2) Fig. 1. Schematic radial flow model for injected CO 2 into a reservoir filled with water Generally, CO 2 viscosity (30°C, 15MPa) is much smaller than water (roughly 1/30), thus the flow rate increases with t. Furthermore, viscosity of supercritical CO 2 is smaller than liquid CO 2 . On the other hand, the flow rate Q strongly depends on reservoir permeability times height (=K w h R ). Especially coal seams have relatively low permeability of order 10 -15 m 2 . It has been reported by some projects that permeability of coal seams decreased with rough ratio of 1/10 to 1/100 after CO 2 injection due to swelling of coal matrix by CO 2 adsorption [Clarkson et al. (2008) and Sasaki et al. (2009)]. 2.2 Unsteady heat conduction equation Figure 2 shows schematic diagram of radial heat loss from a vertical injection well (injector) that is consisting tubing pipe, casing pipes and well annulus. CO 2 is flowed down through the tubing pipe, and injected from bottom of the well with perforated holes. The annulus between two coaxial pipes is not used for CO 2 injection, and possibly needed to prevent heat loss from the tubing. Heat Transfer and Phase Change in Deep CO 2 Injector for CO 2 Geological Storage 567 In present analytical approaches, inside area of the casing pipe is assumed as quasi-steady and outer region of the casing pipe (r ≥r cao ) is analyzed by unsteady equation of heat conduction. For the outer cement and rock region at a level, Fourier’s second law in cylindrical coordinates (r, x) is expressed as; 222 222 11 rr aa t r rr x r rr θθθθ θθ  ∂∂∂∂ ∂∂ =++≅+  ∂∂∂∂ ∂∂  (3) ｗhere θ (°C) is rock temperature, t(s) is elapsed time, r(m) is radius, a r (m 2 /s) is the heat diffusivity of rock. Heat conduction in vertical direction, x, can be omitted by comparing with that of radial direction. Analytical solution has been presented by Starfield & Bleloch (1983) for unsteady-state rock temperature distribution around underground airways. Especially, they presented a method to simulate internal surface temperature using with Biot number and elapsed time factor function of Fourier number (see section 2.7). Fig. 2. Schematic diagram of radial heat flow from a vertical injection well (cross section) 2.3 Four thermal phenomena considered along CO2 injection well Figure 3 shows a schematic of heat transfer phenomena at an injection well. Four thermal phenomena were considered for the construction of the numerical model that is used for predicting CO 2 temperature and pressure at the bottom hole. 1. Natural convection in the annulus, filled with N 2 or water, increases heat transfer from tubing to casing, cement and rock formation. The heat transfer coefficient or Nusselt number at a specific depth is determined by using a formula reported by. Choukairy et al. (2004). 2. The thermal performance of insulated tubing containing an argon shield layer was evaluated by considering the vertical convection flow of argon, thermal radiation between inner surfaces of the argon layer and thermal conduction at the tubing joints. Thermal characteristics of the insulated tubing are able to be corrected against the Two Phase Flow, Phase Change and Numerical Modeling 568 original heat conductivity of argon gas using a number n determined by a field test and also by well logging data (see section 2.5). 3. The CO 2 phase was determined by its specific enthalpy which can be calculated from the pressure, temperature and heat loss along the well. 4. An unsteady analytical solution of the outer-surface temperature of casing pipe, expressed with Eq.(1), can be applied against the elapsed time from the start of CO 2 injection. CO 2 Temperature (liquid/supercritical) (quasi-steady state) In j ection rate: M (t) a)Phase chan g e and enthalp y chan g e of supercritical CO 2 (Pressure, Temperature, Properties) Casin g temperature: T W Initial strata temperature T 0 h c CO 2 Tem p erature: T f Tem p erature distribution in strata e) Unstead y temperature chan g e with time in rock formation d) Natural convection heat transfer and thermal radiation in annulus b) Insulatin g characteristic of ar g on g as and thermal radiation heat transfer c ) Heat conduction at j oints of tubin g p i p es Fig. 3. Heat transfer phenomena from fluid flow in injector to surrounding rock formation 2.4 Overall thermal conductivity of the quasi-steady state region of the injection well Figure 4 shows an example of the well structure (Yubari CO 2 -ECBMR pilot-test site). CO 2 heat loss occurs during flow down to the bottom and propagates through various cylindrical combinations of steels and fluids with various thermal properties in the well configuration. To evaluate heat loss the overall heat conductivity that consists of conductivities of well materials and convective heat transfer rates of fluid flows that are contained in the well are important. Equations (4) and (5) represent single tubing and thermally insulated tubing, respectively (Nag, 2006). 1 ln ln ln 1 cao cai tuo cai ruo tui Steal f Steal tui i rrr rr r Nu r λ λλλα = +++ ⋅ (4) 1 ln ln ln ln ln 1 cao cai thco thci tho cai thco thci tho thi Steal u f Steal Ar Steal thi thi rrrrr rr r rr Nnr λ λλλλλα = +++++ ⋅⋅ (5) [...]... liquid phase change Fig 13 Comparisons of bottom hole temperature and pressure (BHT and BHP) that were simulated by heat conduction and heat convection models with monitored values (Model 200 5) 578 Two Phase Flow, Phase Change and Numerical Modeling Figures 14 and 15 show comparisons of CO2 temperature and pressure between simulations and the well logging data for injection conditions of 68.54°C, 9MPa and. .. Transfer and Phase Change in Deep CO2 Injector for CO2 Geological Storage 573 Fig 8 Elapsed time factor vs Fourier number Fig 9 CO2 pressure-specific enthalpy and phase diagram calculated with PROPATH (200 8) for 10 to 100 °C and 1 to 100 MPa (○; Critical point; 31.1°C and 7.38MPa) 2.8 Numerical equations for the determination of the CO2 specific enthalpy Changes in CO2 temperature and phase (gas, liquid and. .. diagram 580 Two Phase Flow, Phase Change and Numerical Modeling Fig 18 CO2 density and specific enthalpy vs depth (Model 200 6) 3.4 All usage of thermal insulated tubing (Model 200 7) In 200 7, the all injection tubing pipe was replaced with thermally insulated tubing of 890 m in length and the annulus was filled with water Figure 13 shows numerical calculation results for Model 200 7 The predicted temperature... Issues 3-4, 1 June 201 0, pp 287-298, ISSN 0166-5162 Rohsenow, W., Hartnett, J & Cho, Y (1998) An Introduction to Heat Transfer (May 1998), McGraw-Hill Professional, ISBN-10 0070535558 Michael, A M., Khepar, S D & Sondhi, S K (200 8) Water Wells and Pumps, Tata McGrawHill, ISBN(13) 978-0-07-065706-9, New Delhi 584 Two Phase Flow, Phase Change and Numerical Modeling Nag, P.K (200 6) Heat And Mass Transfer... range 1 to 100 MPa, that is calculated by PROPATH (200 8), is shown in Fig 9 The specific enthalpy of CO2 decreases with depth x by heat loss from CO2 flow to the formation around the injection well Δq = 2πλ (T w − T f )Δx (20) 574 Two Phase Flow, Phase Change and Numerical Modeling where Tf is the CO2 temperature in the tubing, ∆x is the length of the element and Tw is the temperature at the outer surface... using the well models consisting of two copper pipes with different diameters as shown in Fig 6 Hot water at 40 to 60 °C was circulated through the inner pipe instead of CO2 Pipe temperatures were measured by Tthermocouples that were placed on the pipe surfaces Figure 7 shows experimental results 572 Two Phase Flow, Phase Change and Numerical Modeling obtained for Nu and compared with those from Choukairy’s... insulated tubing was determined to be n = 4 or λ = 0.21W/m°C based on the well logging temperature at the Yubari CO2-ECBMR test site and the measurement data were obtained from the heater response test carried out in the test field 570 Two Phase Flow, Phase Change and Numerical Modeling Fig 5 Thermal conductivity correction factor for shielding with argon gas (*; spec value provided by a steel pipe maker)... 14 Comparison between logged temperature and simulation results for Model 200 6 (Logging data was obtained on August 28, 200 6 (11:08 to 13:46) at the Yubari ECBMR test site) Fig 15 Comparison between logged pressure and simulation results (Model 200 6) (Logging data was obtained on August 28 ,200 6 (11:08 to 13:46) at the Yubari test site) Heat Transfer and Phase Change in Deep CO2 Injector for CO2 Geological... 3.3 Thermal insulated tubing partly used at the well head and bottom (Model 200 6) For the case of Model 200 6 of Yubari ECBMR test, numerical simulations at 0, 22 and 68 days are shown in Figure 16 Figures 17 and 18 show the Nusselt number, the heat conductivity, the density and the specific enthalpy versus depth after 1 day Fig 16 CO2 temperature distribution vs depth (Model 200 6) Fig 17 Nusselt number... connected thermal insulated tubing pipes 20 m in length were used partially in 200 5 -200 6 and totally in 200 7 The insulated tubing includes argon gas shield layer is enclosed between inner and outer pipes to prevent heat loss from inside ideally with low thermal conductivity of argon gas; 0.116 W/m°C However, joints between pipes are not shielded, and natural gas convection flow in the shield is expected to . monitored values (Model 200 5) Two Phase Flow, Phase Change and Numerical Modeling 578 Figures 14 and 15 show comparisons of CO 2 temperature and pressure between simulations and the well logging. hole, is equal to radial water flow rate in the reservoir [Michael et al. (200 8) and Sasaki & Akibayashi (1999)], Two Phase Flow, Phase Change and Numerical Modeling 566 0 (0) (0). design and installation of such systems. The performances of two types of TES, which use ice and paraffin waxes, were analyzed. Ice storage systems Two Phase Flow, Phase Change and Numerical Modeling