Performance of a Novel Steam Generation System Using a Water-zeolite Pair for Effective Use of Waste Heat From the Iron and Steel Making Process

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To reduce CO2 emission from the iron and steel making process, a novel steam generation system using waste hot water is proposed to use waste heat effectively from the process. This system adopts a direct heat exchange method for the adsorption heat pump to increase the heat transfer rate between the adsorbent and heat transfer fluid. In this study, the performance of the system is evaluated according to the mass of steam generated during the cyclic operation. The regeneration process is first studied taking the transport phenomena in the generator into account. The mass of steam generated is then estimated based on the distributions of water content and temperature in the generator. The results from the model exhibit good agreement with the experimental results. The effect of the operating conditions on the performance of the steam generation process is studied. It was found that there was an appropriate regeneration time to maximize the mass of steam generated during the cycle. For the effective use of adsorption heat, reuse of the water drained from the steam generation process (Drainage Recycling) is proposed. As a result, recycling the drainage water is a practical and helpful method to improve the performance of the system.

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ISIJ International, Vol. 55 (2015), No. 2, pp. 448–456

# Performance of a Novel Steam Generation System Using a Water- zeolite Pair for Effective Use of Waste Heat From the Iron and Steel Making Process

Koichi NAKASO, Yuuki TANAKA, Shotaro ESHIMA, Shunsuke KOBAYASHI and Jun FUKAI *

Department of Chemical Engineering, Graduate School of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka,
819-0395 Japan.

( _Received on August 6, 2014; accepted on September 25, 2014_ )

To reduce CO2 emission from the iron and steel making process, a novel steam generation system
using waste hot water is proposed to use waste heat effectively from the process. This system adopts a
direct heat exchange method for the adsorption heat pump to increase the heat transfer rate between the
adsorbent and heat transfer fluid. In this study, the performance of the system is evaluated according to
the mass of steam generated during the cyclic operation. The regeneration process is first studied taking
the transport phenomena in the generator into account. The mass of steam generated is then estimated
based on the distributions of water content and temperature in the generator. The results from the model
exhibit good agreement with the experimental results. The effect of the operating conditions on the
performance of the steam generation process is studied. It was found that there was an appropriate
regeneration time to maximize the mass of steam generated during the cycle. For the effective use of
adsorption heat, reuse of the water drained from the steam generation process (Drainage Recycling) is
proposed. As a result, recycling the drainage water is a practical and helpful method to improve the performance of the system.

KEY WORDS: effective use of waste heat; steam generation; adsorption heat pump; numerical.

1. Introduction

Efforts in energy conservation research are pursued
because of the limitation of fossil fuel and the environmental issues of global warming. The steel industry is one of the
largest energy-consuming manufacturing industries. Large
amount of waste water at less than 100°C and exhaust gas
at less than 200°C, in particular, are released from the iron
and steel making processes. The reduction of CO2 emission
from the process is also an important issue for the steel
industry. Although some strategies for the separation and
reduction of CO2 in the exhaust gas from the process have
been proposed recently as shown in Fig. 1, 1,2) another
energy source for the separation and reduction of CO2 is
required. For stable and economic operation, effective use of
waste heat from the iron and steel making process, in
particular thermal energy storage, is necessary. Because heat
transfer phenomena are governed by the temperature
difference between the heat source and heat sink, a method
to upgrade the temperature level of waste heat is a key
technology for the effective use of waste energy. The heat
pump system is one of the promising methods for upgrading
the temperature level. There are several types of heat pump
systems. The mechanical heat pump is generally used for air

- Corresponding author: E-mail: jfukai@chem-eng.kyushu-u.ac.jp
DOI: http://dx.doi.org/10.2355/isijinternational.55.448

conditioning and refrigeration. To raise the temperature
level, the mechanical heat pump is not always suitable
because of the lack of durability of the system components.
A chemical heat pump uses the reaction heat from reversible
reactions. Because its working temperature depends on the
chemical reaction, a chemical heat pump can be used from
low to high temperatures.

The authors focused on the adsorption heat pump using a

Fig. 1. Concept of the reduction in CO2 emission from the iron and
steel making process using the novel steam generation system. (Online version in color.)

ISIJ International, Vol. 55 (2015), No. 2

zeolite-water pair, which is classified as a chemical heat
pump, to upgrade the temperature level of the waste hot
water. In particular, the authors adopted a direct heat
exchange method for the adsorption heat pump system to
overcome the low heat transfer rate between the packed bed
and heat transfer fluid. 3–6) Figure 2 shows the schematic of
the cycle for the novel adsorption heat pump. At the start of
the process, the steam generator with a dry adsorbent is
evacuated using a vacuum pump to avoid air-entrained
steam. Saturated water vapor at low pressure is then
introduced as the preheating process. By adsorbing water
vapor, the temperature of the adsorbent is increased.
Subsequently, hot water is introduced to the dry adsorbent
as an adsorbate and a heat transfer fluid. The direct contact
of water and zeolite results in the evaporation of excess
water by releasing adsorption heat from the zeolite. When
the steam generator is full of water, the steam generation
process is terminated. After draining the residual water
between the adsorbent particles, regeneration of the
adsorbent is started. Drying and desorption of the adsorbent
occur continuously by introducing dry gas. After the
regeneration process, the adsorbent returns to its initial state.
Waste heat can be used in the novel steam generation system
for generating the saturated water vapor in the preheating
processes, for heating feed water in the steam generation
processes, and for heating dry gas in the regeneration
processes. In the direct heat exchange method, the large
surface area of adsorbent particles can be used for the
convection heat transfer as well as the reaction. In our previous studies, superheated steam at 0.1–0.4 MPa was generated using water at 80°C and dry gas at 130°C with

laboratory-scale apparatus using zeolite as the adsorbent. 3–5)

In addition, the generation of steam under the cyclic operation of steam generation and regeneration processes was
demonstrated experimentally. 6)

In this study, the performance of the system using a
water-zeolite pair was numerically investigated in terms of
the mass of steam generated during the cyclic operation. To
predict the progress of the regeneration process, a mathematical model for each process was developed and compared with the experimental results. The mass of the steam
generated in the cyclic steam generation and regeneration
processes was studied. As shown in Fig. 2, the steam generation process strongly depends on the progress of the
regeneration process. The regeneration process was first
numerically studied under various conditions. The result of
each calculation of the regeneration process was used as the
initial condition of the steam generation process. Accordingly,
the mass of steam generated was calculated under various
regeneration conditions. The effect of the operating conditions on the mass of steam generated was investigated.

2. Experiment

Figure 3 shows a schematic of the experimental apparatus, which consists of a cylindrical generator, water reservoir, feeding pump, compressor, drier, gas heater, condenser,
an electronic balance, and a humidity meter. The generator
was made of stainless steel 100 mm high and 78 mm in
inner diameter. K-type thermocouples were inserted into the
generator to monitor the transient temperatures. Cylindrical
particles of Zeolite 13X of about 0.27 kg were used as

Fig. 2. Schematic of the cycle for the novel steam generation system. (Online version in color.)

Fig. 3. Schematic of the experimental apparatus. (Online version in color.)

ISIJ International, Vol. 55 (2015), No. 2

adsorbent. In the steam generation process, the generated
steam was condensed by the condenser to obtain the mass
of steam generated. The stainless steel pipe line was heated
using electric heating cables to prevent condensation of the
steam generated. In the regeneration process, dry air from
the compressor was heated to a preset temperature and then
introduced through the generator for pushing the wet gas
out. The temperature, dew point and superficial velocity of
dry air were 140°C, –50°CDP (3.94 Pa), and 0.57 Nm/s,
respectively. To observe the effect of the regeneration time
on the mass of steam in the cycle operation, the regeneration
time was changed from 600 to 3 600 s.

To validate the numerical model for the regeneration
described in the following section, another experiment on
regeneration was carried out using another generator for which
the inner diameter was 21 mm because of the limitation of the
flow rate of the compressor. The temperature, dew point and
superficial velocity of dry air were 80–130°C, –50°CDP, and
1–1.6 m/s, respectively. To reduce the effect of the remaining
water in the gap between the particles on the regeneration, the
wet particles were wiped before packing into the generator.
This is because any remaining water sometimes results in nonuniform distribution of voids in a packed bed. To measure the
water content of the adsorbent during the regeneration, the
humidity of the outlet gas was measured using the humidity
meter. The relative humidity of the outlet air was almost 100%
at the beginning of the process because evaporation of free
water took place all over the packed bed. Therefore, the
humidity meter was used instead of the condenser. To prevent
condensation in the humidity meter, the outlet gas was heated
before introduction to the meter.

3. Mathematical Model

3.1. Calculation of the Regeneration Process
A mathematical model considering transport phenomena
during the regeneration process was developed. As seen in
Fig. 2, the regeneration process mainly takes place along the
flow direction, that is, the axial direction of the cylindrical
generator. Therefore the regeneration process was studied
using a one-dimensional mathematical model. Figure 4
shows the computational domain. For the governing
equations, the following conservation equations of mass and
energy for solid and gas were considered. The mass
conservation of water vapor was especially solved to
consider the rate of regeneration in the calculations. Ergun’s

∂ _P_ g ⎧ ( −ε b ) 2 ⎛

= −⎨ ⎪ 150 1 3
∂ _z_ ⎩ ⎪ ε b ⎜⎜⎝

_P_ g ⎧ ( −ε b ) ⎛ μ g ⎞ −ε b ⎛ ρ g _u_ ⎞

∂ _z_ = −⎨ ⎪ ⎩ ⎪ 150 1 ε b3 ⎜⎜⎝ _d_ p2 ⎟⎟+⎠ 1.75 1 ε b3 ⎜⎜⎝ _d_ p ⎟⎟⎠

equation was used instead of the momentum conservation
equation for gas.

The mass conservation of gas phase (i = g) and water
vapor (i = v, v ⊂ g) are given by the following equation:

ε b ∂ρ i = − ∂ ( ρ i _u_ ) +δ iv ε b ∂ ⎛ v ∂ρ v ⎞ (1 −ε b ) ρ z

_z_ ⎝ ⎜ _D_ ⎠ ⎟−

v

∂

i i

( ρ i _u_ ) +δ iv ε b ∂ ⎛ v ∂ρ v ⎞ (1 −ε b ) ρ z _S_ reg,

_z_ _D_ ⎠ ⎟−

ρ _z_ i _u_ ) +δ iv ε b ∂∂ _z_ ⎛⎝ ⎜ _D_ v ∂∂ρ _z_ v ⎞⎠ ⎟− (1 −ε b ) ρ z _S_

∂ρ i (

= − ∂
∂ _t_

∂ρ _z_ i _u_ ) +δ iv ε b ∂∂ _z_

⎛ ∂

⎝ ⎜ _D_ ∂

⎝ ⎜

(1 −ε b ) ρ z _S_ reg,

( _i_ = _v_ , _g_ )

⎞

⎠ ⎟− (1

∂

iv b v

_t_ ∂ _z_ iv b ∂ _z_ ⎝ ⎜ _D_ v ∂ _z_ b

( _i_ =

_i_ = _v_ ,

.. (1)

where εb, ρ, _t_, _u_, _D_, and _S_ reg is the porosity of the packed
bed, density, time, superficial velocity, diffusivity, and rate
of regeneration, respectively. δiv indicates Kronecker’s delta
because the second term on the right hand side of Eq. (1) is
the diffusion of water vapor in the gas phase. It should be
noted that gas consists of air and water vapor (g [gas] = a

[air] + v [water vapor]). Assuming an ideal gas, the gas state
equation was used to convert the density to the pressure:

ρ i

wi _P_ i

= _M_

_R_ _T_ g

_R_

wi i

.............................. (2)

_TP_ gi ,

where _M_ w, _R_ and _T_ are the molecular weight, gas constant
and temperature, respectively. Accordingly, Eq. (1) is
expressed by the following equation:

⎫
⎬ ⎪

⎭ ⎪

⎞⎟⎟= − _MR_ wi ∂∂ _z_

⎠

_M_

wi i

ε

_M_

∂ ⎛ _P_ i ⎞ _M_ wi ∂ ⎧⎨ ⎪ ⎛ _P_ i ⎞ _u_
∂ _t_ ⎜⎜⎝ _T_ g ⎟⎟= −⎠ _R_ ∂ _z_ ⎩ ⎪ ⎜⎜⎝ _T_ g ⎟⎟⋅⎠

⎛

⎜⎜
⎝

⎞

⎧⎛ _P_ i ⎞
⎨ ⎪

⎩ ⎪ ⎜⎜⎝ _T_ g ⎟⎟⋅⎠

b wi i

⎞

_R_ ∂ _t_

_P_ i
_T_ g

⎛

⎜⎜
⎝

_R_ ∂ _z_

⎩ ⎪ ⎝

- (1 −ε b ) ρ z _S_ reg, (i = v, g)

+δ iv ε b _M_ wi ∂ ⎧⎨ ⎪ v ∂ ⎛ _P_ v ⎞⎫⎬ ⎪ - (1 −ε b ) ρ z

_z_ _D_ ⎜⎜ ⎟⎟

.. (3)

⎫
⎬ ⎪

⎭ ⎪

v

_T_ g

⎞

∂
∂ _z_

⎛

⎜⎜
⎝

_M_ wi ∂ ⎧⎨ ⎪ v ∂ ⎛ _P_ v ⎞⎫⎬ ⎪ - (1 −ε b ) ρ z _S_ reg, (i = v, g

_z_ _D_ ⎜⎜ ⎟⎟

wi

_R_ ∂ _z_ ⎨ ⎪ _D_ v ∂ _z_

⎩ ⎪

∂ ⎧⎨ ⎪ v ∂ ⎛ _P_ v ⎞⎫⎬ ⎪ - (1 −ε b ) ρ z _S_
∂ _z_ ⎩ ⎪ _D_ ∂ _z_ ⎜⎜⎝ _T_ g ⎟⎟⎠⎭ ⎪

⎧ ∂ ⎛ _P_ v ⎞
⎨ ⎪ v

⎩ ⎪ _D_ ∂ _z_ ⎜⎜⎝ _T_ g ⎟⎟⎠

⎩ ⎪

The energy conservation of the gas phase (i = g), and
solid (zeolite, i = z) were given by the following equation:

pi i i

ρ i

∂ρ _z_ i _uT_ i ) + ϕ i ∂∂ z

⎛ ∂ _T_

⎝ ⎜ λ i ∂ _z_

⎝ ⎜

⎞

⎠ ⎟

⎞

ϕ i λ i

z ⎝ ⎜ λ i ∂ _z_ i

_c_ pi ∂ _T_ i

ϕ i ρ i _c_ pi _T_ i = −δ ig

∂ (

( _c_ pi ρ i _uT_ i )

( _c_ pi ρ i _uT_ i

_T_ i

i

∂

i i pi

∂∂ _Tt_ i = −δ ig ∂ ( _c_ pi ∂ρ _z_ i _uT_ i ) + ϕ i ∂∂ z ⎛⎝ ⎜ λ i ∂∂ _Tz_ i

_T_ i = −

∂ _t_

_t_

_z_

i i

+ ( - 1) δ iz ( 1 −ε b ) _ha_ p ( _T_ z
+δ iz Δ _H_ reg (1 −ε b ) ρ z _S_ reg,

+ (

δ iz

b p z g

1) iz ( 1 −ε b ) _ha_ p ( _T_ z - _T_ g

Δ _H_ reg (1 −ε b ) ρ z _S_ reg,

..... (4)

−ε b ) _ha_ p ( _T_ z - _T_ g )

(1 −ε b ) ρ z _S_ reg, (i = g, z)

iz reg b z reg

where, ϕ, _c_ p, λ, _a_ p, _h_, and Δ _H_ reg indicate the volume fraction,
heat capacity, thermal conductivity, specific surface area,
heat transfer coefficient, and enthalpy of regeneration,
respectively. The fourth term on the right hand side of Eq.
(4) is energy consumption resulting from the regeneration.

For the momentum conservation of gas, Ergun’s equation 7)

was used:

⎜⎜
⎝

1.75 1 −ε b ⎛ ρ g

⎜⎜

_u_

∂

g b

⎧ ( −ε b ) 2 ⎛ μ g ⎞ −ε
⎨ ⎪ 150 1 3 2 1.75 1 3

ε ⎜⎜ ⎟⎟+ ε

( −ε b ) 2 ⎛ μ g ⎞ −ε b ⎛ ρ g

150 1 ε b3 ⎜⎜⎝ _d_ p2 ⎟⎟+⎠ 1.75 1 ε b3 ⎜⎜⎝ _d_ p

μ g ⎞ −ε b

.75 1

⎞

⎫
⎬ ⎪

⎭ ⎪

⎫
⎬ ⎪

⎞

_u_

⎜⎜
⎝

2g 1.75 1 3 b

⎟⎟+ ε

g

_d_

...(5)

_z_ ⎩ ⎪ ε b3 ⎝ _d_

⎞⎟⎟+⎠ 1.75 1 ε− b ε 3 b ⎛⎜⎜⎝

⎩ ⎪

ε b

b g

3 2

⎜⎜

ε b

where, μ and _d_ p are the viscosity and particle diameter,
respectively.

The regeneration consists of drying and desorption. It
depends on the water content of zeolite. It was assumed that
the drying takes place at higher than the saturated amount
of water adsorbed on zeolite ( _x_ - _x_ sat). It is defined by
assuming that boundary layer around a zeolite particle is
dominant, and given by the following equation:

⎛

⎜
⎝

−ε b ε b ⎞⎟⎠ _MRT_ w,vg _a_ ρ p _k_ zgz ( _P_ v sat ( _T_ z ) - _P_ v )

w,v

_S_ reg = − ⎛⎜ ε b ⎞⎟ _M_

= − ⎜⎝ 1 - b ε b ⎟⎠ _MRT_ w,vg ρ p zgz ( _P_ v sat ( _T_ z ) - _P_ v

_a_ p _k_

p gz

b

⎞

reg = − ⎜ b ⎟ w,v ( _P_ v sat ( _T_ z ) - _P_ v

. ...... (6)

1 - b ε b ⎟⎠ _RT_ w,vg ρ z ( _P_ v sat ( _T_ z )

_RT_ g

where _k_ gz is mass transfer coefficient.

Fig. 4. Computational domain and boundary conditions. The rate of desorption at lower than _x_ sat is based on the

ISIJ International, Vol. 55 (2015), No. 2

Table 1. Physical properties and parameters in the calculations.

ρz [kg/m 3 ] 1047 *1

εb [–] 0.46

λz [W/(m·K)] 0.15 *1

_c_ pz [J/(kg·K)] 823

λw [W/(m·K)] 0.67

_c_ pw [J/(kg·K)] 4200

ρw [kg/m 3 ] 971

λv [W/(m·K)] (8.74 × 10 –5 ) _T_ - (8.34 × 10 –3 )

_c_ pv [J/(kg·K)] (–5.3047 × 10 –1 ) _T_ + (2.245 × 10 –3 )

μv [Pa s] (3.97 × 10 –8 ) _T_ - (2.4374 × 10 –6 )

λa [W/(m·K)] (7.15 × 10 –5 ) _T_ + (5.0667 × 10 –3 )

_c_ pa [J/(kg·K)] (4.6609 × 10 –4 ) _T_ 2 - (2.5413 × 10 –1 ) _T_ + 1 040

μa [Pa s] (3.9683 × 10 –8 ) _T_ + (6.7698 × 10 –6 )

_L_ [kJ/kg-water] (–1.443 × 10 –3 ) ( _T_ –273.15) 2 - 2.292 ( _T_ –273.15) + 2 501

_Q_ [kJ/kg-water] 1350

energy balance based on the local temperature and water
content profiles at the final state of the regeneration process.

For the preheating process shown in Fig. 2(3), the temperature of the adsorbent is increased by the adsorption of water
vapor. The energy balance for a unit mass of zeolite during
the preheating process is given by the following equation:

+ _c_ pw _x_ 2 )( _T_ z2 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 1)( _T_ z1

( _c_ pz + _c_ pw _x_ 2 )( _T_ z2 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 1)( _T_ z1 - _T_ ref )

_c_ pz + _c_ pw _x_ 2 )( _T_ z2 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 1)( _T_ z1 - _T_

pz pw 2 z2 ref pz pw 1 z1 ref

= ( _x_ 2 −

pw p

2 − _x_ 1){ _c_ pw ( _T_ p h - _T_ ref ) + _L_ ph} + Δ _H_ ads ( _x_ 2 − _x_ 1)

( _x_ 2 − _x_ 1){ _c_ pw ( _T_

_x_ 2 − _x_ 1){ _c_ pw ( _T_ p

...(8)

(for drying)

Δ _H_ reg [kJ/kg-water] =

⎧ _L_ (for drying)
⎨
⎩ _L_ + _Q_ (for desorption)

_L_ + _Q_

_L_

Δ _H_ ads[kJ/kg-water] = _Q_

_A_ [1/s] 4.0 × 10 5

_E_ [J/mol] 3.5 × 10 4

_N_ [–] 3

*1 Density and thermal conductivity of zeolite are the effective values for a
zeolite pellet, which are considered pore inside the particle.

measurement data from thermal analysis:

where subscript 1 and 2 indicate the initial and final states
of the preheating process, respectively. The first and second
terms on the left hand side of Eq. (8) are the enthalpy of the
packed bed after and that before the preheating process,
respectively. The first term on the right hand side of Eq. (8)
is the input energy from saturated vapor introduced into the
adsorbent for preheating. The second term is the adsorption
heat. _T_ ref, _L_, and Δ _H_ ads are the reference temperature, latent
heat and enthalpy of adsorption, respectively. It should be
noted that the sensible heat of water vapor in the void of the
packed bed is ignored in this study because its enthalpy is
less than 0.3% of total enthalpy supplied. _x_ and _T_ are the
averaged local water content and temperature, respectively.
For example, _x_ 1 and _T_ z2 are given by:

## ∫

_x dv_ 1

_Tz_ 2 _dv_

................. (9)

_T_

1 _z_ 2
and _T_ z2 = _V_ R

_V_ R

_x_ 1

## ∫ x dv 1

= _V_ R and _T_ z2 =

_V_ R

R
## ∫

_V_ R

_z_
_V_ R

R

1 z2

_dv_

⎛ − _E_ ⎞
= − _A_ exp ⎜ ⎟ ( _x_ - _x_ eq

................. (7)

_S_ reg = − _A_ exp ⎛⎜ − _E_ ⎞⎟ ( _x_ - _x_ eq ) _N_

⎝ _RT_ z ⎠

_E_

exp ⎜ ⎟ ( _x_ - _x_ eq )

⎝ _RT_ z ⎠

where, _V_ R is the volume of the steam generator. Based on
the adsorption equilibrium for a water-zeolite pair, _x_ 2 after
preheating is given by _x_ 2 = _f_ ( _P_ ph, _T_ z2). When the local ( _x_ 2 –
_x_ 1) value is negative, adsorption would not take place in this
region. That is, _T_ z2 = _T_ z1 and _x_ 2 = _x_ 1 are given, respectively.
From Eq. (8), the averaged adsorbent temperature after the
preheating process _T_ z2 is given by

⎜
⎝

⎞

_x_ eq indicates the equilibrium water content of zeolite, which
is expressed by the function of the partial pressure of water
vapor and temperature _x_ eq = _f_ ( _P_ v, _T_ z).

For the initial conditions, uniform distributions of
pressure _P_ ini, temperature _T_ ini and water content _x_ ini were
assumed. Boundary conditions are also shown in Fig. 4. The
physical properties are summarized in Table 1 . The
discretization of all governing equations in space was based
on a finite volume method. The time deviation terms were
discretized using an implicit scheme. Considering the
effects of the grid number and time step on the calculation,
the typical grid number and time step were 200 for _z_ max =
0.1 m and 1 × 10 –3 s, respectively.

3.2. Estimating the Mass of Steam Generated
To understand the performance of the system, the mass of
the steam generated in the cyclic steam generation and
regeneration processes was studied. According to a previous
study, a system satisfied the energy balance in the steam
generation process. 6) This implies that the mass of steam
generated can be estimated based on the energy balance
between the initial and the final states of the steam generation process. While the initial state of the steam generation
process strongly depends on the local distributions of temperature and water content in the zeolite after the regeneration process, the final state of the steam generation process
is independent of the regeneration process. In this study, the
mass steam generated was therefore estimated using the

.........................................(11)

where the first term on the left hand side of Eq. (11) indicates the final state of the steam generation process. As seen
in Fig. 2(5), the steam generator is full of water at the end
of the steam generation process. Therefore, _x_ f indicates the
“full” water content, which means the adsorbed water and
free water in the particle. ( _m_ d/ _m_ z) is the mass of water
between the particles per unit mass of zeolite. Subscript 3
indicates the final state of the steam generation process. The
first term on the right hand side of Eq. (11) is the enthalpy
of the input water. {( _x_ f – _x_ 2) + ( _m_ d/ _m_ z) + ( _m_ v/ _m_ z)} indicates

...(10)

_T_

= pz pw 1 z1 2 1

_c_ pz + _c_ pw

( _c_ pz + _c_ pw _x_ 1) _T_ z1 + ( _x_ 2 − _x_ 1)( _c_ pw _T_ ph + Δ _H_ ads + _L_ ph )

_c_ pz + _c_ pw _x_ 1) _T_ z1 + ( _x_ 2 − _x_ 1)( _c_ pw _T_ ph + Δ _H_ ads + _L_

pz pw 1 z1 2 1 pw ph ads ph

+ _c_ pw _x_ 1) _T_ z1 + ( _x_ 2 − _x_ 1)( _c_ pw _T_ ph + Δ _H_ ads +

z2 _c_ pz + _c_ pw _x_

Equations (9) and (10) and the equation of adsorption equilibrium are solved simultaneously.

After the preheating process, water is introduced into the
packed bed (see Fig. 2(4)). The energy balance during the
steam generation process is given by

+ _c_ pw{ _x_ f + ( _m_ d / _m_ z )}]( _T_ z3 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z2

[ _c_ pz + _c_ pw{ _x_ f + ( _m_ d / _m_ z )}]( _T_ z3 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z2 - _T_ ref )

_c_ pz + _c_ pw{ _x_ f + ( _m_ d / _m_ z )}]( _T_ z3 - _T_ ref ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z2 - _T_

pz pw f d z z3 ref pz pw 2 z2 ref

_c_ pw

_c_

{

d z z3 ref pz pw 2 z2

( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v / _m_ z )}( _T_ w,in - _T_ ref )

( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v / _m_ z )}( _T_ w,in - _T_

f 2 d z v z w,in ref

- _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v / _m_ z )}( _T_ w,in

2 d z v z w,in ref

){ _c_ pw ( _T_ v - _T_ ref ) + _L_ v} +Δ _H_ ads ( _x_ 3 - _x_ 2 )

- ( _m_ v / _m_ z ){ _c_ pw ( _T_ v

( _m_ v / _m_ z ){ _c_ pw ( _T_ v - _T_ ref )

_m_ v / _m_ z ){ _c_ pw ( _T_ v - _T_

v z pw v ref

ISIJ International, Vol. 55 (2015), No. 2

the mass of input water per unit mass of zeolite. ( _m_ v/ _m_ z) is
the mass of steam generated per unit mass of zeolite. The
second term on the right hand side of Eq. (11) is the enthalpy
of the steam, which is assumed to be saturated steam at
temperature _T_ v. The third term on the right hand side of Eq.
(11) is the adsorption enthalpy. Here, _x_ 3 = _x_ sat. Based on the
experiment, the average temperature at the end of the steam
generation process _T_ z3 is given by the following equation
assuming a linear temperature profile in the generator.

mass of zeolite at _n_ th cycle is given by:

- _c_ pw ⎨ ⎪ ⎩ ⎪ ( _x_ f - _x_ 2 ) + ⎜⎝ 1

⎧⎨ ⎪ ( _x_ f - _x_ 2 ) + ⎛⎜ ε b ⎞⎟⎛⎜ ρ w ⎞⎟

⎩ ⎪ ⎝ 1 −ε b ⎠⎝ ρ z ⎠

⎩ ⎪

⎛

⎜⎜
⎝

( _n_ )

⎞

⎟⎟ =
⎠

_m_

1

v

⎟⎟ = ( _n_

- _T_ w,in( _n_ ) ) +

( _T_ v - _T_ w,in( _n_ ) )

_m_ z ⎠ _c_ pw ( _T_ v - _T_ w,in( _n_ ) ) + _L_

z pw v w,in v

⎡Δ _H_ ads ( _x_ 3 - _x_ 2 ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z3( _n_ )

z3( _n_ ) - _T_ z2

⎣ ⎢

Δ _H_ ads ( _x_ 3 - _x_ 2 ) - ( _c_ pz + _c_ pw _x_ 2

- _x_ 2 ) - ( _c_ pz +

( _x_ 3 - _x_ 2 ) - (

_H_ ads ( _x_ 3 - _x_ 2 ) - ( _c_ pz + _c_ pw _x_

)( _T_ z3( _n_ ) - _T_ z2 )

_T_ z3( _n_ ) - _T_

ads 3 2 pz pw

.... (17)

ε b ⎞⎛ ρ w ⎞⎫

⎬ ⎪

( _T_ z3( _n_ ) - _T_ w,in( _n_ ) ) ⎥⎥⎦

⎤

⎞

⎭ ⎪

ρ w

( _x_ f - _x_ 2 )

⎛

⎜
⎝

b

_c_ pw ( _x_ f - _x_

ε b

pw f

2 ⎝ 1

⎞

⎟
⎠

⎛

⎜
⎝

ρ w ⎞⎫

⎟ ⎬ ⎪

ρ z ⎠⎭ ⎪

w

= _T_ v + _T_ w,in
2

_T_ z3 = _T_ v + _T_

In the same way, a linear temperature profile is assumed at
the end of the steam generation process. _T_ z3 for the _n_ th cycle
is therefore given by using the temperature of the saturated
steam _T_ v and the temperature of the input water for the _n_ -th
cycle _T_ ( _n_ ),

........................... (12)

The mass of water between the particles per unit mass of
zeolite ( _m_ d/ _m_ z) is given by {εb/(1–εb)}(ρw/ρz), and is the
same as the mass of drainage water after the steam generation process. Accordingly, the mass of steam generated per
unit mass of zeolite is given by:

_T_ w,in( _n_ )

( _n_ )

w,in

( _n_ )

_T_ z3( _n_ ) = _T_ v + _T_

( _n_ ) v w,in

........................... (18)

= _T_ v +
2

⎛

⎜
⎝

⎡

⎣ ⎢

1

_m_ v ⎞⎟ = 1
_m_ z ⎠ _c_ pw ( _T_ v - _T_ w,in ) + _L_

v

⎞

1

⎟ =
⎠ _c_ pw ( _T_ v - _T_ w,in ) +

( _T_ v - _T_ w,in )

z pw v w,in v

Δ _H_ ads ( _x_ 3 - _x_ 2 ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z3 - _T_ z 2

- _x_ 2 ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z3

_T_ z3( _n_ )

( _n_ )

_H_ ads ( _x_ 3 - _x_ 2 ) - ( _c_ pz + _c_ pw _x_ 2 )( _T_ z3 - _T_ z

)

3 2 pz pw 2

ads 3 2 pz pw 2 z3

( _n_ + 1)

...(13)

( _m_ (v _n_ ) / _m_ z )

⎧⎨ ⎪ ( _x_ f - _x_ 2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟

⎩ ⎪ ⎝ 1 −ε b ⎠ ⎝ ρ z ⎠

_c_ pw ⎧⎨ ⎪ ( _x_ f - _x_ 2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟⎫⎬ ⎪ ( _T_ z3 - _T_ w

⎩ ⎪ ⎝ 1 −ε b ⎠ ⎝ ρ z ⎠⎭ ⎪

⎤

_T_ ( _n_

- _c_ pw ⎨ ⎪ ⎩ ⎪ ( _x_ f - _x_ 2 ) + ⎜⎝ 1

b

⎞

⎫⎬ ⎪

⎭ ⎪

( _x_ f - _x_ 2 ) + ⎜ b ⎟ ⎜ w ⎟ (

z3 w ,

, in )

w,in

pw f

⎛

⎜
⎝

ε b

⎤

⎥
⎥⎦

⎩ ⎪

⎞

⎟
⎠

⎛

⎜
⎝

ρ w

ρ z

w

3.3. Calculation of Reuse of the Drainage Water
(Drainage Recycling, DR)
After the steam generation process, water at higher than
input temperature remains in the void of the packed bed. It is
then released from the generator as drainage water (see Fig.
2(6)). This is helpful when this drainage water is used as the
input water in the next cycle. In this study, the reuse of the
drainage water, called Drainage Recycling (DR) is studied. In
the _n_ th steam generation process, the drainage water of the previous (( _n_ - 1) th ) cycle is first introduced and then the normal
input water (which is the same as the first cycle) is fed to fill
the packed bed of adsorbent. Therefore, the enthalpy of the _n_ th

input water per unit mass of zeolite is expressed by:

- _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in( _n_ )

pw{( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in( _n_ ) - _T_ ref

_c_ pw{( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in( _n_ ) - _T_

{( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in( _n_ ) - _T_ ref )

pw d z

ref

_c_ pw ( _m_ d / _m_ z

( _m_ d / _m_ z )(

( _n_ -1)

( _n_

_n_ -1)

)

_T_ z3( _n_ -1) - _T_

+ _c_ pw{( _x_ f - _x_ 2 ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in(1)

( _n_ )

( _n_ ) (1)

In the calculation of DR, Eqs. (15)–(18) are solved simultaneously. When the averaged water content is higher than its
saturated value, steam cannot be generated. In this case, the
temperature of water after the _n_ th cycle _T_ z3( _n_ ) is calculated
using Eq. (17) considering ( _m_ (v _n_ ) / _m_ z ) = 0. The temperature
of the input water in the (( _n_ + 1) th ) cycle _T_ w,in( _n_ + 1) is then calculated using the Eqs. (15) and (16).

The temperature of the drainage water depends on the
temperature of the steam generated. Before the drainage
water is released from the generator, the temperature of the
remaining water ranges from _T_ w,in to _T_ v. When the drainage
water is released from the generator under atmospheric pressure, its maximum temperature is limited to 100°C. Such a
limited case is called the “Limited DR”. On the other hand,
the ideal no-limitation case is called the “Full DR”.

4. Results

4.1. Comparison between the Model and Experiment
for the Regeneration Process
The numerical results from the model were compared
with the experimental results for validation. Figure 5 shows
the comparison between the calculation and experiment for
the regeneration process. The initial temperature and water
content were 25°C and 0.6 kg-water/kg-zeolite, respectively.
Three gas inlet conditions were studied. As seen in the
figure, there is a little difference between calculated water
content and experimental one at the initial stage of the
regeneration process especially for the higher flow rates. To
study the reason of the difference, the effect of the heat loss
on the calculated results was studied considering the heat
transfer between adsorbent and ambient air. However, there
was little difference between the calculation results. The difference between calculation and experiment is probably due
to the distribution of the flow velocity of the regeneration
gas. However the calculation could reasonably predict the
temperature at the center of the generator as well as the
water content of zeolite.

4.2. Effect of Regeneration Time on the Mass of Steam
Generated in the Cyclic Operations
Performance of the system is discussed in terms of the
mass of steam generated in the cyclic operation under

_c_ pw{( _x_ f - _x_ 2 ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in(1) - _T_

{( _x_ f - _x_ 2 ) + ( _m_ v( _n_ ) / _m_ z )}( _T_ w,in(1) - _T_ ref )

... (14)

pw f 2 v z w,in ref

where _T_ z3( _n_ -1) is the temperature of drainage water at ( _n_ 1) th cycle. ( _m_ (v _n_ ) / _m_ z ) is the mass of steam generated at the
_n_ th cycle per unit mass of zeolite. The temperature of the _n_ th

_T_ z3( _n_

( _n_ -1)

( _m_ (v _n_ ) / _m_ z )

input water _T_ w,in( _n_ ) is therefore expressed by

_T_ w,in( _n_ )

( _n_ )

w,in

_T_ w,in( _n_ ) = γ _T_ z3( _n_ -1) + (1 −γ ) _T_

( _n_ )

= γ _T_ z3( _n_ -1) + (1 −γ ) _T_ w,in(1)

( _n_ -1)

w,in

................... (15)

where:

γ =

( _m_ d / _m_ z )

( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z )

d z

( _x_ f - _x_ 2 ) + ( _m_ d / _m_ z ) + ( _m_ v( _n_ ) / _m_ z

- _x_ 2 ) + ( _m_ d / _m_ z ) +

( _m_ d / _m_ z )

f 2 d z v z

⎛ ε

⎜
⎝ 1
=

ρ w

ρ z

( _n_ )

⎞

⎛

⎜
⎝

ε b

b

⎞

⎟
⎠

⎛

⎜
⎝

⎞

⎟
⎠

ε b

⎧⎨ ⎪ ( _x_ f - _x_ 2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟⎫⎬ ⎪

⎩ ⎪ ⎝ 1 −ε b ⎠ ⎝ ρ z ⎠

_m_

...... (16)

ρ z

ρ w

+ ⎛ ⎜

⎛ ⎜

⎝

v

⎞

w

⎞

b

( _x_ f - _x_ 2 )

⎜
⎝

ε b

- _x_ 2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟⎫⎬ ⎪ + ⎛ ⎜ _m_ v( _n_ )

⎝ 1 −ε b ⎠ ⎝ ρ z ⎠⎭ ⎪ ⎝ _m_ z

2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟⎫⎬ ⎪ + ⎛ ⎜ _m_ v( _n_ ) ⎞⎟

⎝ 1 −ε b ⎠ ⎝ ρ z ⎠⎭ ⎪ ⎝ _m_ z ⎠

⎩ ⎪

_x_ f - _x_ 2 ) + ⎛⎜ ε b ⎞⎟ ⎛⎜ ρ w ⎞⎟⎫⎬ ⎪ + ⎛ ⎜ _m_ v( _n_ )

⎞

⎟
⎠

⎛

⎜
⎝

ρ z

⎫⎬ ⎪

⎭ ⎪

According to Eq. (13), mass of steam generated per unit

ISIJ International, Vol. 55 (2015), No. 2

Fig. 5. Comparison between experiments and calculations for the regeneration process. (Online version in color.)

Fig. 6. Calculated distributions of the water content of zeolite and temperature at various regeneration times ( _T_ g,in =
140°C, _u_ g,in = 0.57 Nm/s, _x_ ini = 0.7 kg-water/kg-z, _T_ z,ini = 80°C, _z_ max = 0.1 m).

various regeneration conditions. When the time for the
regeneration was inadequate, the mass of steam generated in
the following steam generation process would decrease. As
a first step, the effect of the regeneration time on the mass
of steam generated in the cyclic operations was studied. As
an example, Fig. 6 shows the distributions of solid temperature and water content at various regeneration times. The
operating condition was set based on the cycle experiment.
An increase in temperature and decrease in water content
occurred simultaneously from the gas inlet ( _z_ = _z_ max = 0.1
m) with time. Accordingly, the regeneration of zeolite proceeded from the gas inlet. For example, from the result of
_t_ reg = 1 000 s, while desorption took place in most parts of
the generator, drying still took place near the gas outlet.
From the results, drying finished at about 1 200 s.

Figure 7 shows the relationship between the mass of
steam generated and the regeneration time _t_ reg. To calculate
the mass of steam generated, the distributions of temperature and water content at each _t_ reg, shown in Fig. 6, were
used. Steam generation under atmospheric pressure with nopreheating case was assumed based on the experimental
conditions. As seen in Fig. 7(a), the calculated mass of
steam increased with the regeneration time and reached the
saturated value of about 0.12 kg-steam/kg-zeolite. This
implied that there was an appropriate regeneration time to
maximize the mass of steam generated during the cycle. To

Fig. 7. Effect of the regeneration time on the mass of steam generated and the mean steam generation rate ( _T_ g,in = 140°C, _u_ g,in =
0.57 Nm/s, _x_ ini = 0.7 kg-water/kg-z, _T_ z,ini = 80°C, _z_ max = 0.1
m, _T_ w,in = 80°C, _T_ v = 100°C, No-preheating case).

ISIJ International, Vol. 55 (2015), No. 2

assess the appropriate regeneration time clearly, the mean
steam generation rate (MSGR) was introduced. This is
defined as the mass of steam generated during the cycle
period, that is, the sum of the regeneration time _t_ reg and the
time for the steam generation _t_ sg. In fact, _t_ sg changed with
the mass of steam generated because the water was fed at
the constant feeding rate. In this calculation, the average
time for the steam generation was set to 389 s based on the
experiment. The results are shown in Fig. 7(b). The mean
steam generation rate exhibited a maximum value of 6.0 ×
10 –5 kg-steam/(kg-zeolite·s) at the regeneration time of
1 200 s. It should be noted that when the mean steam generation rate was maximum, all the drying of the adsorbent
was complete as shown in Figs. 6 and 7(c). After this
moment, the rate of regeneration slowed because the rate of
desorption depending on ( _x_ eq – _x_ ) was much lower than that
of drying. Therefore the increasing rate of ( _m_ v/ _m_ z) changed
at this moment. That was why there was the maximum value
of the MSGR.

The experimental data are also plotted in Fig. 7. When the
regeneration time is short, calculated mass of steam and
MSGR are higher than the experiment. This difference
could be attributed to the estimation of the progress of the
regeneration process. As discussed in the previous section,
the present calculation for the regeneration process tends to
estimate slightly lower water content. This could affect the
estimation of mass of steam generated during the cyclic
operation. Although the heat loss and sensible heat of the
generator were considered in the other calculations, these
effects were little according to the calculated results. However the calculated data exhibited similar tendencies to the
experiment. From the results, the maximum mean steam
generation rate was important information for deciding the
appropriate regeneration condition.

4.3. Effect of Drainage Recycling on the Mass of Steam
Generated
Figure 8 (a) shows the effect of the number of DR cycles
on the mass of steam generated. The dashed and solid lines
indicate the Limited DR and Full DR, respectively. The first
cycle (cycle number = 1) implied the No-DR case. The mass

of steam generated increased as the number of DR cycle
increased. It should be noted that the effect of the number
of DR cycle was significant for the first four cycles. This
was because the temperature of water in the generator at the
end of steam generation was fully developed for the first
four cycles, as shown in Fig. 8(b). The temperature of the
inlet water increased from 80°C to 110°C with the Full DR
cycle. In the following results for the DR case, the cycle
number was set to 10 to remove the effect of the cycle number of DR on the mass of steam generated.

Figure 9 shows the effect of DR on the mass of steam
generated and the MSGR under various regeneration times.
The calculation was done for _T_ g,in = 120°C, _u_ g,in = 0.7 Nm/s,
_T_ v = 160°C and _z_ max = 0.1 m. The time for steam generation
was assumed 600 s for calculating the MSGR. As seen in
the figure, an increase in the maximum value of the MSGR
and a decrease in the appropriate regeneration time at which
the maximum MSGR was reached, occurred simultaneously
when applying DR. The maximum MSGR was 1.7 times
higher than for the No-DR case.

Figure 10 shows the relationship between the preset
steam temperature and the maximum mean steam generation rate. Each set of data shown in the graph indicates the
maximum value of MSGR obtained for each operating condition and for _t_ reg < 3 000 s. The effect of DR on the maximum mean steam generation rate was significant for the
higher steam temperature. In particular, the Full DR was
clearly effective than the Limited DR. According to the
results, it can be said that the effect of the temperature of
the feed water on the mass of steam generated was significant. When water at higher temperatures is not available in
the practical process, DR is the more effective and helpful
method.

The effect of the fraction of voids on the mass of steam
generated with/without DR was studied. Generally the fraction of void in the packed bed ranges from 0.4 to 0.8. Moreover, in a practical application, an increase in the voids of
the packed bed might be necessary because the pressure
drop of dry gas for the regeneration process should be
reduced. The effect of fraction of voids on the mass of steam
generated is shown in Fig. 11 . For the initial conditions of

Fig. 8. Effect of recycling of the drainage water on the steam generation process ( _T_ g,in = 120°C, _u_ g,in = 0.7 Nm/s, _x_ ini = 0.7
kg-water/kg-z, _t_ reg = 2 500 s, _z_ max = 0.1 m, _T_ v = 160°C, _T_ w,in = 80°C).

ISIJ International, Vol. 55 (2015), No. 2

Fig. 11. Effect of the fraction of voids on the mass of steam generated with drainage recycling ( _T_ z,ini = 120°C, _x_ ini = 0.1 kgwater/kg-zeolite, _T_ v = 160°C, _T_ w,in = 80°C).

Fig. 9. Effect of the regeneration time on the mass of steam generated and the mean steam generation rate ( _T_ g,in = 120°C, _u_ g,in =
0.7 Nm/s, _x_ ini = 0.7 kg-water/kg-z, _z_ max = 0.1 m, _T_ v = 160°C,
_T_ w,in = 80°C).

Fig. 12. Comparison of methods of water feeding in terms of the
mass of adsorbent and the mass of water supplied during
the steam generation process ( _T_ z,ini = 120°C, _x_ ini = 0.1 kgwater/kg-zeolite, _T_ v = 160°C, _T_ w,in = 80°C).

Fig. 10. Maximum steam generation rate at various steam temperatures ( _T_ g,in = 120°C, _u_ g,in = 0.7 Nm/s, _x_ ini = 0.7 kg-water/kg-z,
_z_ max = 0.1 m, _T_ v = 160°C, _T_ w,in = 80°C).

the calculation, uniform distributions of temperature and
water content were assumed and shown in the figure. From
the results, the effect of fraction of voids on the mass of
steam can be reduced by applying the DR. While steam cannot be generated for the fraction of voids of more than 0.6
in the No DR case, considerable steam can be expected for
the Full DR case. It should be noted that the difference
between the Limited DR and Full DR cases was significant
especially for higher volume fractions. Thus the Full DR
and not the Limited DR was required for the severe conditions of steam generation.

Consequently, the novel steam generation system can
generate not only high-temperature steam but also water at
a higher temperature. The DR proposed in this study is the
method to convert the sensible heat of drainage water to
high-temperature steam. It would be ideal if as small volume
as possible of the feed water could be supplied to cover the
adsorbent. One method to realize the ideal case is to feed
water from the top of packed bed of the adsorbent. However,
this is generally difficult, as demonstrated in our previous
study. 4) Figure 12 shows the mass of steam generated using
various feeding methods. Figure 12(a) shows the mass of
steam generated per unit mass of zeolite. Figure 12(b) shows
the mass of steam generated per unit mass of feed water.
_m_ w,in is the averaged mass of water supplied to the generator

ISIJ International, Vol. 55 (2015), No. 2

during ten cycles. “Partial” indicates there is no drainage
water at the end of the steam generation process. “Water
free” is the ideal case, that is, there is no residual water
including free water in the particle at the end of the steam
generation process. As seen, DR exhibits better performance
than “Partial”. This is because the reuse of drainage water
can substantially reduce the mass of feed water. Therefore,
DR is a powerful and practical method of approaching the
ideal operation of the novel steam generation system.

5. Summary

The performance of the novel steam generation system
has been studied for the application of effective use of waste
heat from the iron and steel making process. Because the
performance strongly depends on the regeneration process,
a numerical model for the regeneration process has been
developed taking transport phenomena in the zeolite packed
bed into account. The model is found to be satisfactory in
predicting the temperature and water content in the packed
bed during the regeneration process. Based on the results of
the regeneration process, the mass of steam generated during cyclic operation is estimated. As a result, the appropriate
regeneration time to maximize the mean steam generation
rate during the cycle is identified. Furthermore, reuse of the
drainage water of the steam generation process, that is,
Drainage Recycling has been proposed to effectively use the
waste heat of the process. Because this method can be followed without any special modifications in the packed bed,
it is more practical than existing methods of performance
improvement. The effect of Drainage Recycling on steam
generation is more pronounced especially for severe conditions such as a higher fraction of voids in the packed bed.

Acknowledgements

This work was partially supported by the NEDO project
under the Research and Development Program for Innovative
Energy Efficiency Technology, and by the Japan Society for
the Promotion of Science (JSPS) Grants-in-Aid for Scientific
Research (C) 25420923.

Nomenclature

_A_ = Frequency factor [1/s]
_a_ p = Specific surface area [m 2 /m 3 ]
_c_ p = Specific heat [J/kgK]
_D_ = Diffusion coefficient [m 2 /s]
_d_ p = Particle diameter [m]
_E_ = Activation energy [J/mol]
_h_ = Heat transfer coefficient [W/m 2 K]
_k_ gz = Mass transfer coefficient [m/s]
_L_ = Latent heat [J/kg-water]
_M_ w = Molecular weight [kg/mol]
_m_ = Mass [kg]
_N_ = Order of the reaction [–]
_P_ = Pressure [Pa]
_Q_ = Enthalpy of adsorption/desorption [kJ/kg-water]

_R_ = Gas constant [J/mol K]

_S_ reg = Rate of regeneration [kg-water/kg-zeolite·s]
_t_ = Time [s]
_T_ = Temperature [K]
_u_ = Superficial velocity [m/s]
_V_ R = Volume of the steam generator [m 3 ]
_v_ = Volume [m 3 ]
_x_ = Water content [kg-water/kg-zeolite]
_z_ = Coordinate [m]
γ = mass ratio of drainage to water supplied [–]
δ ij = Kronecker’s delta [–]
ε = Porosity [–]
Δ _H_ = Reaction enthalpy [J/kg-water]
λ = Thermal conductivity [W/mK]
μ = Viscosity [Pa·s]
ρ = Density [kg/m 3 ]
ϕ = Volume fraction [–]

Superscript

( _n_ ) = Cycle number

Subscripts

a = Air
ads = Adsorption

b = Packed bed
d = Drainage
eq = Equilibrium

f = Full
g = Gas phase

i = Index
j = Index
in = Inlet
ini = Initial
max = Maximum

out = Outlet

p = Particle
ph = Preheating

R = Reactor
ref = Reference
reg = Regeneration

sat = Saturated

sg = Steam generation

v = Water vapor
w = Water

z = Zeolite

REFERENCES

1) Y. Kato: _ISIJ Int._, 50 (2010), 181.
2) T. Miwa and H. Okuda: _J. Jpn. Inst. Energy_, 89 (2010), 28 (in Japanese).
3) E. Oktariani, A. Noda, K. Nakashima, K. Tahara, B. Xue, K. Nakaso
and J. Fukai: _Int. J. Energ. Res._, 36 (2012), 1077.
4) E. Oktariani, K. Tahara, K. Nakashima, A. Noda, B. Xue, A. T.
Wijayanta, K. Nakaso and J. Fukai: _J. Chem. Eng. Jpn._, 45 (2012),
355.
5) B. Xue, K. Tahara, K. Nakashima, A. Noda, E. Oktariani, A. T.
Wijayanta, K. Nakaso and J. Fukai: _J. Chem. Eng. Jpn._, 45 (2012),
408.
6) B. Xue, Y. Iwama, Y. Tanaka, K. Nakashima, A. T. Wijayanta, K.
Nakaso and J. Fukai: _Exp. Therm. Fluid Sci._, 46 (2013), 54.
7) S. Ergun: _Chem. Eng. Prog._, 48 (1952), 89.
8) A. Gorbach, M. Stegmaier and G. Eigenberger: _Adsorption_, 10 (2004),
29.

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