Full text of DOI:10.1007/BF03187022

growth model was not founded. Zhao et al.[10] observed
the HCFC-141b hydrate formation process with a micro-
scope.
In agglomeration state physics, fractal and fractal
dimension can preferably describe some nonreversible
growth process far from the equilibrium state such as
phase transition and self-similarity in critical phe-
nomena[11,12]. Applying fractal theory, Min[13] founded the
nucleation-limited aggregation model of BaNO3 crystalli-
zation growth, and Zhang[14] founded the nucleation ag-
gregation model.
HFC-134a refrigerant gas
hydrate formation process
and RIN model
ZHAO Yongli1,2, GUO Kaihua2, LIU Xiaocong2,
FAN Shuanshi2, SHU Bifen2 & GE Xinshi1
1. Department of Thermal Engineering, University of Science and Tech-
nology of China, Hefei 430070, China
2. Guangzhou Institute of Energy Conversion, Chinese Academy of
Sceinces, Guangzhou 510070, China;
Correspondence should be addressed to Guo Kaihua (e-mail: guokh@
ms.gies.ac.cn)
In this paper, a morphology experiment on HFC-
134a hydrate formation is reported and a series of macro-
scopic formation process photos are provided. A model of
growth is also proposed according to the fractal theory.
Abstract
In this paper, the macroscopic visualization
experiments of HFC-134a refrigerant gas hydrate formation
are investigated. According to the macroscopic photos and
Mori’s microscopic photos of HFC-134a hydrate formation
process, the mechanism of gas hydrate formation is analyzed.
A random inducement nucleation model is presented to de-
scribe the hydrate formation process. The factors affecting
the fractal growth dimension in the model, such as step,
branch increment and angle, are discussed.
1
Experiment
(ν) Experimental apparatus. The low-temperature
visualization experimental system is composed of a test
chamber, a cooling system, a heating system, a data ac-
quisition control system, and a digital photo system. The
apparatus is shown in fig. 1.
Keywords: refrigerant gas hydrate, crystallization, formation proc-
ess photos, RIN model.
Gas hydrate are crystalline compounds that are
formed when water and gas or volatile liquid come in
contact under conditions of high pressure and low tem-
perature. Hydrates are formed in a highly structured sys-
tem where all the water molecules are hydrogen bonded in
a crystal cavity and the gas molecule dissolves in the cav-
ity and interacts with the water through van der Waals
forces. Refrigerant gas hydrates can be effectively formed
at appropriate temperature (5ćü12ć) with large reac-
Fig. 1. Schematic of experimental apparatus. 1, Compressor; 2, con-
denser; 3, capillary; 4, evaporator; 5, thermocouple; 6, thyristor; 7, heater;
8, hydrate reactor; 9, digital video camera; 10, glass chamber; 11, com-
puter; 12, data acquisition and control system.
tion heat (320ü430 kJ/kg). Because of their particular
thermodynamic properties, refrigerant hydrates have been
considered as one of the most promising cool storage me-
dia for air conditioning systems[1,2]. Natural gas hydrates
are being regarded as future potential energy sources be-
cause of findings of a great amount of natural gas hydrates
in the ocean[3,4]. The formation processes of gas hydrate
have become an important and pressing subject in energy
and environment research field as well as in natural gas
industry.
The test chamber is made of hollow windows to in-
sulate heat from outside. A moisture absorbent is put in
the interlayer of the hollow windows to absorb water va-
por in the interlayer and to prevent water frost forming
inside when temperature becomes low. The cooling sys-
tem is a small refrigerator. The heating pipe is controlled
by a thyristor. In the chamber, six thermocouples were
placed to measure the temperature, which was controlled
through a HP data acquisition and control system.
A continually focused digital video camera (Pana-
sonic NV-DX100EN) is used to observe the HFC-134a
hydrate formation process. The digital photo caught by the
camera was input in the computer through a photo acqui-
sition card (DC-30Plus).
The formation of gas hydrate takes place in a multi-
phase (refrigerant gas phase, refrigerant liquid phase, liq-
uid water phase, and solid hydrate phase) system. The gas
hydrate formation process is characterized by a low
phase-diffusion speed, a long inducement time, a large
supercooling, and a low formation rate. Many articles of
dynamic research of gas hydrate formation have been
(ξ) HFC-134a hydrate macroscopic formation pho-
tos. The hydrate reactor is cylindrical and has inner
volume of 1.5h10ꢀ5 m3. The front and back faces of the
ü
found[3 7]. The formation morphology studies are mainly
included in Makagon’s thesis[4]. Mori[8,9] obtained the
HFC-134a hydrate formation process photos but the
Chinese Science Bulletin Vol. 46 No. 1 January 2001
1425

NOTES
reactor are made of two pieces of Plexiglas which were
mounted on the stainless steel cylindrical wall with two
flanges. The distance between the two pieces of Plexiglas
is 6.0h10ꢀ3 m. Water and HFC-134a were fed into the
reactor. Then the reactor was put in the test chamber
which had been set at 0.5ć. When the temperature in the
reactor was stable, the digital photos system was taken
continuously. The formation process photos are shown in
fig. 2.
Fig. 2. Morphology of HFC-134a gas hydrate formation process.
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Chinese Science Bulletin Vol. 46 No. 1 January 2001

Fig. 3. Morphology of HFC-134a gas hydrate microscopic formation process (h10) (T=(5.2f0.1)ć, p=(0.482f0.011) MPa).
(a) t = 0 s; (b) t = 2 s; (c) t = 6 s; (d) t = 11 s.
The liquid density of HFC-134a is 1.294h103 kg/m3
tween HFC-134a and water at 5.2ć. Formed crystal nu-
cleus induced the nearby region and the new hydrate was
formed as shown in fig. 3(a). After 2 s, the crystal grew
along the interface and continually induced other region.
The crystal growth is shown in fig. 3(b) and (c). After 11 s,
formed hydrate covered the whole liquid HFC-134a sur-
face. Finally, the hydrate stopped forming because the
contact between water and HFC-134a was cut off. The
final morphology of hydrate formation is shown in fig.
3(d). The HFC-134a hydrate formation appears like ar-
borization. The branch grows from the trunk and forms
another trunk. The branch and trunk grow continually. The
whole formation process takes on the self-similarity and
has fractal growth characteristics.
at 0.5ć and is larger than that of water. Thus, the main
amount of HFC-134a liquid was under the water, while a
thin layer of HFC-134a was formed on the upper surface
of the water due to viscosity and surface tension of the
liquid. The initial situation is shown as in fig. 2(a). It can
be seen that there are two interfaces between liquid water
and liquid HFC-134a formed at upper and bottom of the
water, respectively. Water vapor and HFC-134a vapor are
mixed in the top of the reactor. In condition of supercool-
ing, the hydrates are formed after about 1-h inducement
time. The reaction first takes place at the top interface
between water and HFC-134a. The crystal nucleus were
firstly formed at the reactor’s wall and then induced to the
nearby region.
2
Photo processing
The nucleation process continued and extended to
the whole interface. A layer of hydrate was finally formed
on the upper interface of HFC-134a and water. At the
same time, the hydrate was also formed in the mixed va-
por region. Later, the hydrate was formed at the bottom
interface between water and HFC-134a. The hydrate
crystals then continually grew into the water because
HFC-134a diffused into the water through the two hydrate
layers. The processes are shown from fig. 2(b) to (h).
(ο) HFC-134a hydrate microscopic formation pho-
tos. Mori[9] put a drop of HFC-134a liquid into the water
and observed the surface reaction through glass lens. The
microscopic formation photos by magnified 10 times are
shown in fig. 3.
(ν) Photo transforming. The final morphology of
hydrate in fig. 3(d) is a gray photo. The gray photo was
first transformed to black/white 2-level photo. The black
represents hydrate. According to the continuity of hydrate
formation, some unclear parts in the photo were refined to
form continuous branches and trunks as shown in fig. 4.
3
RIN model
(ν) Particle system. Particle system has been con-
sidered as one of most successful methods for generating
a simulation pattern of irregular blurry object[12,15]. This
method is quite different from other pattern generation
systems but very effective for scenery drawing. The scen-
ery is generated by thousands of irregular random-distri-
bution particles which have certain life cycles and various
The hydrate layer was formed at the interface be-
Chinese Science Bulletin Vol. 46 No. 1 January 2001
1427

NOTES
moving patterns. The particles in the system are moving
constantly in random behavior and can disappear when
new particles join into the system. The parameters for
every movement of the particle are controlled by a ran-
dom process to keep good randomicity. The particle sys-
tem is adopted to simulate the model of crystal formation
process of HFC-134a gas hydrate.
goes by, the second, third, fourth seed will appear soon.
Each nucleus grows following the same rule. If two
branches meet with each other, they will stop growing.
The simulation results are shown in fig. 5. The boundary
for this simulation is semicircular. In the program, the
initial variables were set before performing the main pro-
cedure. Whether the node will grow up is decided by the
initial set. If the node can grow, the length of the branch
will depend on a random value. The first branch from this
node will be regarded as the main stem. The main stem
may have a left, a right, both or none branches. This also
depends on a random value. With the random angle and
the certain length r, the location of the next node can be
calculated. A queue is set up in the program for placing
the node which will grow next time. The nodes in the
queue will grow one by one. The first node in the queue
grows first. After the queue finishes from the beginning to
the end, the queue will be restarted and repeated until the
growth is ended. The node not satisfying the growing
condition will disappear in the queue automatically.
Fig. 4. Black/white schematic (from fig. 3(d)).
(ξ) Mechanisms of HFC-134a gas hydrate forma-
tion. According to the macroscopic and microscopic
formation photos of HFC-134a hydrate, the characteristics
of hydrate formation have been detected as in the follow-
ing:
(1) Gas hydrate can be formed when water and
HFC-134a contact in supercooling condition.
(2) Crystal nucleus can occur randomly on the sub-
strate. There appear four seeds of crystal nucleus in fig.
3(b).
(3) Nearby hydrate can be formed by seed stimula-
tion. New hydrate nucleus can be formed and located
randomly, but it can be survived only nearby. Because the
crystal heat prevents new crystal generation, the new
crystallization will be formed away from existing crystal
(π) Dimension calculation. The dimensions for
scenery presented in fig. 4 and fig. 5(d) are determined
with the box counting method. In the program, the number
(N) of the black pixel (hydrate) is counted with a circle
which has a radius r. Dual logarithm graphics according
to r and N are built up. The value of the line slope in the
dual logarithm graphics represents the dimension of the
scenery. The results are shown in fig. 6. The difference
between the two dimension values of the two graphics is
very small. Since the real growth of hydrate and the
simulation of the growth process are both random proc-
esses, the two dimensions will not be exactly the same. It
can be seen that the growth dimension varies between
1.69 and 1.85 and the average is 1.78, which is little less
than the real growth dimension. Since the growing angles
of main stem and branches are random in the simulation,
and the earlier contact of adjacent branches and main stem
will prevent the part of growth from going on. It can be
seen from the simulated graphics that the whole growth is
not very even and there are some empty places, which
reduce the dimension of simulation.
as far as possibleˈso branches appear. There are two or
three branches in fig. 3.
(4) All the seeds will grow up according to the same
rule. The nucleus will stimulate and generate the newer
continually.
(5) When different branches meet with each other,
new nucleus generation will stop.
The growth dimension is synthetically embodied as
the structure of hydrate, the speed of growth of hydrate
nucleus and the density of hydrate. It is closely related
with the outside conditions of the growing process. The
parameters used in the program is to meet the outside
condition.
(6) Finally, the whole surface of the refrigerant liquid
droplet is covered by hydrate and stop further growing.
The shape of grown crystals has a dendrite pattern.
(ο) RIN Model. The whole hydrate growth proc-
ess is simulated by the particle system, in which every
nucleus is regarded as a particle. The first seed of nucleus
is regarded as the seed particle. The seed particle induce
the next particle to grow with a certain initial angle and
distance. When the second particle is generated, branches
will appear randomly near this particle. Then the next
branch will be simulated to grow with the same distance
and the process goes on generation by generation. The
angle has also a random value in a certain range. As time
(ρ) Influence of parameters to dimension
(1) Influence of step of main stem or branch. In the
simulation, the step is first defined as the number of pixels
between one particle and the next. It is the stimulated dis-
tance between particles. Under the same outside condi-
tions, the stimulated distance of main stem or branches
should be the same. The results of the simulation display
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Chinese Science Bulletin Vol. 46 No. 1 January 2001

Fig. 5. Schematic of RIN simulation model.
Fig. 6. Dual logarithm graphics for determination of fractal dimension. (a) For scenery of fig. 4; (b) for scenery of fig. 5(d).
that the dimension first increases and then reduces while
the step decreases. The increase of the dimension might be
due to the dense hydrate branches. Because the number of
particles for simulation is limited, when the step is less
further, the particles will be exhausted. This results in a
large empty space among branches, and the dimension
turns small.
(2) Influence of branch increment. In the program,
the branch increment for every step in the procedure is
specified. The larger this increment is, the faster the
branches appear, and the simulated graphics becomes
denser. The simulation results show that the more the in-
crement is, the bigger the dimension will be.
(3) Influence of branch angle. The branch angle
specified in the program is the upper limitation for varia-
tion of the angle between main stem and branches. The
angle varing between zero and the branch angle will de-
termine the birth location of the next branch. From the
simulation results, it can be seen that the bigger the angle
is, the less the dimension is. If the angle is very small, the
branches of hydrate will tend to grow in one direction and
the hydrate growth becomes denser. When the branch an-
gle is S/4, hydrate will grow in all directions and appear in
disorder.
Chinese Science Bulletin Vol. 46 No. 1 January 2001
1429

NOTES
Well books, 1997.
4
Conclusions
HFC-134a gas hydrate macroscopic formation pho-
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The mechanism of hydrate formation is analyzed.
The formation of gas hydrate can be considered as the
inducement of nucleation generated in supercooling con-
dition.
A random inducement nucleation model is proposed
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formation pattern and the simulated pattern are compared.
The parameters influencing the growth dimension are also
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Acknowledgements This work was supported by the National Natural
Science Foundation of China (Grant Nos. 59836230 and 59706001) and
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