Ahsan A. Two Phase Flow, Phase Change and Numerical Modeling

Подождите немного. Документ загружается.

Thermal Energy Storage Tanks Using Phase Change Material (PCM) in HVAC Systems

559

where S is heat flux through the PCM capsule wall, which is calculated as follows:

()

θθ

=−

(13)

The heat from the PCM to the circulating air was calculated by heat convection on the

surface of the PCM containers. The convection coefficient was calculated using the following

empirical equation for a flat surface (Incorpera et al. 1996):

0.8

0.037Re PrNu = (14)

The heat transfer between a container of PCM and air in the duct was enhanced by fins

extended toward the air. The fins increased the surface 18.2 times as compared to a flat surface.

The heat balance among the air entering the room, the heat transfer from outdoor air, and

the internal heat gain determined the temperature of room is as follows:

()()

rorir

cUA V

θθ θθ

=−+−

(15)

Charging was conducted for three hours, from 5:00 to 8:00, followed by ordinary air

conditioning from 9:00. Discharging started at 13:00 and ended at 16:00. The charging hours

were set to be equal to the discharging hours. The inlet temperature to the PCM storage tank

for the charging operation was 12°C, and the inlet temperature to the room (

) during

ordinary air conditioning was 16°C. No temperature control was performed during the

discharging operation. During the ordinary air conditioning, the air flow rate to the room

was controlled in order to maintain the temperature of the room at 26°C. The mixture

quantities were 50, 100, 150, 200, 250, 300, 350, and 400 kg.

The room temperature was set to 25°C, as calculated by solving the heat balance for the heat

transfer through walls and windows, internal heat, and release of stored cooling from the

PCM. The calculation was conducted for two days for each condition. The results shown

herein are the results for the second day.

Fig. 19. Section and plan of the building used for simulation

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.

13:00 16:00

Fig. 22. Index used to evaluate the investigated effect

Thermal Energy Storage Tanks Using Phase Change Material (PCM) in HVAC Systems

561

100

150

200

250

300

350

400

MT17

MT19

MT21

MT23

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

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

of room surface (or 5.4 kg/m

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

: Archimedes number at the inlet

c : specific heat

: diameter of the inlet of the tank

dz : thickness of PCM

g : gravitational acceleration

h: convective coefficient

: heat removed from a storage tank

: heat removed until the outlet temperature reaches the limit temperature

IPF : (Ice Packing Factor) ratio of ice volume to tank volume (= V

ice

)

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

: velocity of inlet water

u: velocity of water inside the tank

U : average overall heat transfer coefficient

V : airflow rate to the room

: volume of tank

ice

: volume of ice

x : length in the flow direction,

: response-based efficiency

: system efficiency

: volumetric efficiency

: initial temperature

: temperature of the inlet water

out

: temperature of the outlet water

: limit temperature to the coils of the air handling units

Δθ

: equivalent temperature difference for ice storage (= L • IPF/c)

Δθ

: temperature difference of the coils of the air handling units

: density of inlet water

: density of water at the initial temperature

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

: temperature of air

: temperature of PCM

: 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.

Heat Transfer and Phase Change in Deep CO

Injector for CO

Geological Storage

Kyuro Sasaki and Yuichi Sugai

Department of Earth Resource Engineering, Kyushu University

Japan

1. Introduction

capture and storage (CCS) is expected to reduce CO

emissions into the atmosphere.

Various underground reservoirs and layers exist where CO

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

gas with roughly twice volume

compared with CH

gas originaly stored (Yee et al., 1993). However, the coal matrix is

swelling with adsorption CO

and its permeability is reduced. Supercritical CO

has a

higher injection rate of CO

into coal seams than liquid CO

because its viscosity is 40%

lower than the liquid CO

(see Harpalani and Chen, 1993).

The Japanese consortium carried out the test project on Enhanced Coal Bed Methane

Recovery by CO

injection (CO

–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

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

This chapter provides a numerical model of heat transfer and calculation procedure for the

prediction of CO

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. Prediction model for CO

injection temperature

2.1 CO

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

injection with a vertical injection well (injector). The reservoir

with radius R and thickness h

, is saturated with water and open with constant pressure at

its outer boundary. Assume omitting well pressure loss, the initial CO

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)

BH R

BH BH WH

wR w

PP gxdx

Kh r

ρρ

−

==+



⋅







(1)

where ρ(x,t) and ρ

BH =

ρ(H,t) are CO

density in the injector and bottom hole respectively, g is

acceleration of gravity, r

is outer radius of the bottom hole, K

is reservoir permeability,

and P

are pressures at well head, bottom hole and outer boundary, μ

is water

viscosity in the reservoir, and H is length of vertical injector. The reservoir’s initial pressure

is also equal to P

After starting CO

injection, the CO

mass flow rate M(t) and bottom hole pressure P

(t) are

changing with elapsed time t, since bottom hole pressure depends on CO

density

distribution through the injector and water is replaced with CO

. Therefore, flow rate after

becoming steady-state Q is given with P

and CO

viscosity μ

at t = ∞.

()

() () ; () () (,)

BH R

BH BH WH

wR w

PP gxdx

Kh r

ρρ

∞−

∞= ∞ ∞= ∞+ ∞



⋅







(2)

Fig. 1. Schematic radial flow model for injected CO

into a reservoir filled with water

Generally, CO

viscosity (30°C, 15MPa) is much smaller than water (roughly 1/30), thus the

flow rate increases with t. Furthermore, viscosity of supercritical CO

is smaller than liquid

. On the other hand, the flow rate Q strongly depends on reservoir permeability times

height (=K

). Especially coal seams have relatively low permeability of order 10

-15

. It

has been reported by some projects that permeability of coal seams decreased with rough

ratio of 1/10 to 1/100 after CO

injection due to swelling of coal matrix by CO

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

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

injection, and possibly needed to prevent heat

loss from the tubing.

Heat Transfer and Phase Change in Deep CO

Injector for CO

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

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

/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

temperature and pressure at the bottom hole.

1. Natural convection in the annulus, filled with N

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

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

injection.

Temperature (liquid/supercritical)

(quasi-steady state)

ection rate:

M (t)

a)Phase chan

e and enthalp

chan

e of supercritical CO

(Pressure, Temperature,

Properties)

Casin

temperature:

Initial strata

temperature

Tem

erature:

Tem

erature distribution in strata

e) Unstead

temperature chan

e with time in

rock formation

d) Natural convection heat transfer and thermal

radiation in annulus

b) Insulatin

characteristic of ar

as and

thermal radiation heat transfer

)

Heat conduction at

oints of tubin

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

-ECBMR pilot-test site). CO

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).

ln ln ln

cao cai tuo

cai ruo tui

Steal

Steal tui i

rrr

rr r

Nu r

λλλα

+++

⋅

(4)

ln ln ln ln ln

cao cai thco thci tho

cai thco thci tho thi

Steal u

Steal Ar Steal thi thi

rrrrr

rr r rr

Nnr

λλλλλα

+++++

⋅⋅

(5)