Skiadas C.H., Dimotikalis I. (editors) Chaotic Systems: Theory and Applications
Подождите немного. Документ загружается.
388 F Zaknoun et al.
The pump syringe was filled with 50 mL
of
4.3 M H
2
S0
4
,
which were
delivered at the rate
of
1.0
mL
per hour, through a piece
of
teflon tubing
fitted into the tiny orifice.
As
this type
of
rock is weak and brittle, it was
neccessm'y that a small orifice, 3 mm diameter and 1 cm depth, be cm'efully
drilled in a way to allow the insertion
of
the
il~jection
tube. With this setup, a
well-controlled flow is attained. The pump syringe is refilled as soon as the
acid is · consumed. Figure 4 shows pictures
of
the treated rock at various
stages
of
the infiltration-acidization evolution.
Figure 4. Ferruginous limestone rock acidized with H
2
S0
4
through the teflon tube
shown. Time evolution
of
the rock treatment showing the gradual formation
of
the
deposits. The numbers indicate the time in days.
2.2. Preliminary Tests
A number
of
simple preliminary chemical tests are carried out to guide our
analysis, while the final rock composition
in
various band domains is
confirmed by X-ray analysis.
1.
A zone rich in
CaC0
3
is indicated by an effervescence upon treatment
with 6M HCI, due
to
the reaction:
CaC0
3
(.I')
+ 2HCI (aq)
~
Ca
2
+ (aq) + 2Cl- (aq) + CO
2
(g) + H
2
0 (l)
2. A zone predominantly consisting
of
CaS0
4 would show no fizzing upon
treatment with HCl.
3.
An inter-band zone void
of
CaS04 showing no reaction upon addition
of
HCl is
an
indication
of
the depletion
of
the bare rock medium
of
any
carbonate, due to prior consumption by the originally infiltrating acid
(H
2
S0
4
),
This would leave only the other minerals supporting the bare
rock medium.
Simulation
of
Geochemical Se(f-O';r;anization 389
4. A small sample
of
white salt from a CaS04 ring dissolved in HCI, yields
a yellow solution, attributed
to
the presence of ferric ions originating
from the rock medium (ferruginous limestone). The presence
of
Fe
3
+ is
confirmed by testing with
KSCN solution. Upon addition
of
a few drops
of
SCN-, the solution turned blood-red indicating the formation
of
the
FeSCN
2
+ complex.
5. Flame atomic absorption analysis
of
the precipitate (done on a Thermo-
elemental
Solaar atomic absorption spectrophotometer), in CaS04-rich
regions (after dissolution in HCI) was carried out to determine the
elemental mass ratio
of
calcium
to
iron [14].
2.3. Composition Analysis
of
the Treated Rock
The treatment was fulfilled in a series
of
experiments, the latest
of
which was
extended over a period of about one year and eight months.
In
the latter (most
recent) expeliment, the
H
2
S0
4
infusion started on October
5,
2005 and was
stopped on May 23,
2007. The final pattern was examined to delineate the
various regions wherein
CaS04 bands may have formed. The pattern span
area
was
divided into eight main textural regions,
as
highlighted in Fig.
5.
Figure 5. Final rock pattern at
t:=
692 days. The rock was partitioned into eight
"banded" zones for differentiation by X-ray analysis.
Powder samples from each region were taken and placed· in small tubes,
which were stoppered thereafter. Each sample
was
analyzed
by
powder X-ray
diffraction. Each diffractogram was mapped onto a Library
of
standard
diffractograms for the calcite, gypsum and anhydrite minerals. Mter the
peaks for each mineral were identified, the relative mass proportions
of
each
mineral in the sample mixtures were determined
by
integrating the area under
the peaks
of
each mineral [15]. The average composition
of
every region in
each
of
the three minerals (over a representative number
of
samples) could
then be calculated.
390 F Zilknoun et al.
3. Results and Discussion
3.1. Stage I
At a first stage, the analysis
of
a treated ferruginous limestone rock was
performed in a preliminary experiment wherein the
H
2
S0
4
infiltration was
stopped at time t =
161
days.
Figure 6.
CaS04
deposition in the limetsone rock sample, infiltrated by H
2
S0
4
.
The central region is a dense
CaS04
precipitate zone. Then, beyond a brown
depleted zone, a distinct belt
of
CaS04
suggests the formation
of
a first Liesegang
ring.
TIle photo is taken on day 161. A 1 em scale is placed on the picture.
The analysis
of
the white deposits in the central region and the ring shown in
Fig. 6 confirmed the dominant presence
of
the gypsum mineral [14J.
Photomicrographs
of
the deposit areas (notably in the ring region), before
and after infiltration, depicted in Fig.
7,
show the white crystals
of
the
gypsum mineral embedded in the rock medium.
Figure 7.a. Rock texture
before the
acid injection.
Magnification
(lOx).
The
scale is indicated on the
picture.
Fig. 7.b. Rock texture
after
acid injection,
displaying the white
crystals
of
CaS04
(labeled
W)
emhedded
within the rock.
Magnification (lOx).
Figure 7.c. Rock texture
in the central region
wherein the rock is
entirely
"stuffed" with
CaS04.
Simulation
(i
Geochemical Self-Organization
391
3.2 Stage
II
The results
of
the experiment described in Sect.
2.1
(analysis procedure
described in Sect. 2.3) are now presented. Samples from each
of
the regions
shown in Fig. 5 were taken by drilling small holes in the desired area,
collecting the resulting powder in small vials and storing them for later X-ray
analysis. The diffractograms confirmed the formation
of
gypsum
(CaS04'2H20), which was quite dominant over anhydrite (CaS04,
anhydrous) as the main deposit product in reaction
2.
The central region
(domains
1,
2 and 3) consists almost entirely
of
gypsum. Then depletion
starts
in
region 4 (almost exactly like
in
a real Liesegang pattern wherein
bands start separating from a uniform zone that extends over a relatively
wide spatial domain). The % composition in gypsum (calculated for the
relative mass proportions
of
gypsum and calcite exclusively) drops to 28.4 %
(see Table
1,
and notably Fig. 8).
Region % gyps.
1 100
2 97.5
3 98.9
4 28.4
5 85.8
6 17.6
7 5.4
Table
1.
Variation
of
% gypsum over the
rock regions.
120
E
100
::I
..,
80
~
Q)
~
60
40
20
0
0
2
3 4 5 6 7 8
Region
Figure
8.
Variation
of
% gypsum over the different rock
regions.
Although some gypsum is present, it has dropped significantly in favor
of
unreacted calcite, suggesting the residence
of
an inter-band zone, relatively
depleted in the diffusing
sol-, just as predicted by the Ostwald cycle [3].
Then comes a new gypsum band (region 5; 85.8% gypsum) and so on.
Hence, the % composition in gypsum essentially alternates. The complete
depletion
of
gypsum between the bands (no 0% zones) is rendered impossible
by the complex random percolation
of
the infiltrating acid (not a simple
diffusion process), given the broad distribution
of
the pore sizes. The
unexpectedly low composition in the last point (instead
of
an
increase; see
Fig. 8) is due to the incomplete formation
of
the gypsum band at that stage.
392
F.
Zaknoun et al.
4. Fractal Reaction Front Contours
We now focus on the shape
of
the front contours in the different regions. The
shape
of
the acidization front is to a large extent governed by porosity
variations [16,17].
As
a result, irregularities emerge, and thus may give rise
to fractal structures. We analyze the front contours using Matlab and the
Image Processing Toolbox. After choosing a specific region (from domains
1-8), the RGB image is cropped, and the region
of
interest is retained. The
interface between the two corresponds to the contour
of
the chosen region.
We used color segmentation using the L*a*b color space whereby we select
the color
of
the contour to a tolerance
of
10%. The plate was then
transformed into a binary image. Morphological operations were afterwards
applied to fill any open holes. Contours
of
regions 8 (the outer front) and 4
delimited by this method are shown in Fig. 9.
Figure 9.a. Contour
of
region
8,
of
fractal dimension 1.87.
Figure 9.b. Contour
of
region 4,
of
fractal dimension 1.44.
The fractal dimension using the box count algorithm was computed and
found to be 1.87 for region 8 (frame. 9.a) and 1.44 for region 4 (frame. 9.b).
This study is under continuing investigation, wherein all the contours will be
meticulously traced and analyzed.
5. Conculsions
In this paper,
we
simulated a Liesegang banding expeirment in-situ, i.e.
inside a real rock bed. After a long treatment with acid infiltrated from a
central source, band formation was induced in a way similar to what
we
see
in a naturally banded rock. X-ray analysis revealed the alternation
of
minerals, thus resembling a 2D Liesegang pattern. The contours
of
the
acidization fronts were found to be fractal.
Simulation
of
Geochemical Self-Organization 393
Acknowledgements: This work was supported by a grant from the Lebanese
National Council for Scientific Research (LNCSR). The authors thank Dr.
Abdel-Fattah Abdel-Rahman, for his valuable and very helpful advice. All
the X-ray and AA measurements were performed in the Central Research
Science Lab (CRSL)
of
the American University
of
Beirut.
References
[1]
R.
E.
Liesegang, Chemische Fernwirkung, Lieseg. Photograph. Arch. 37: 305,
1896; continued
in
37:
331,1896.
[2] H. K. Henisch, Crystals
in
Gels
and
Liesegang Rings, Cambridge University
Press, Cambridge, 1988.
[3]
Wi. Ostwald, Lehrbuch der Allgemeinen Chemie, 2. Aufl., Band 2,
2.
Teil:
Verwandtschaftslehre, Engelmann: Leipzig, 1896-1902,
p.
778.
[4]
J.
A. Shapiro and M. Dworkin, Eds., Bacteria as Multicellular Organisms, Oxford
University
Press, New York, 1997.
[5]
V.
V. Kravchenko, A. B. Medvinskii, A.
N.
Reshetilov and
G.
R.
Ivanitskii, Dokl.
Akad. Nauk,
364: 114,1999; ibid, Dokl. Akad. Nauk" 364:
687,1999.
[6]
D. Xie,
J.
Wu, G. Xu, Q. Ouyang,
R.
D. Soloway, and T. Hu,
1.
Phys.Chem. B,
103: 8602, 1999.
[7]
R.
E. Liesegang, Geologische DijJusionen, Steinkopff, Dresden, 1913;
R.
E.
Liesegang, Die Achate, Steinkopf, Dresden-Leipsig, 1915.
[8]
T. Moxon, Educ. Chem. July issue, 105,2001.
[9]
T.
Moxon, Agate: Microstructure and Possible Origin, Terra Publications,
Doncaster, 1996.
[10]
J.
H.
Kruhl, Ed., Fractals and Dynamic Systems
in
Geoscience, Springer-Verlag,
Berlin, 1994.
[II]
P. Ortoleva, Geochemical Self-Organization, Oxford University Press, New
York, 1994.
[12] M. Ohkawa,
Y.
Yamashita, M. Inoue,
R.
Itagawa and
S.
Takeno, Mineralogy and
Petrology, 70:
15,2000.
[13] B. Jamtveit and P. Meakin (Eds.), Growth, Dissolution and Pattern Formation
in
Geosystems, Kluwer, Dordrecht, 1999.
[14] M. Msharrafieh, M. AI-Ghoul and
R.
Sultan, in Complexus Mundi: Emergent
Patterns
in
Nature, Proceedings
of
the Fractals 2006 Conference, Vienna, Austria;
M. M. Novak, Editor; World Scientific, Singapore,
2006, pp. 225-236.
394 F Zaknoun et
al.
[15] C. Suryanarayana and M. Grant Norton, X-Ray Diffraction, A Practical
Approach,
Plenum Press, New York, 1998; Experimental Module 7, Quantitative
Analysis
of
Powder Mixtures, pp. 223-236.
[16]
K.
Lund,
H.
S.
Fogler and C. C. McCune, Chern. Eng. Sci. 28: 691-700,1973.
[17]
K.
Lund and
H.
S.
Fogler, Chern. Eng. Sci. 31: 373-380, 1976.
Akkaya E. E., 93
AI-Ghoul Mazen, 385
AI-Joubeily Samia, 385
Alomari Majdi M., 1
Aniszewska Dorota, 9
AwrejcewiczJan, 17, 139
Aybar
O.
b., 93
Baehr Christophe, 27
Becerra Alonso David, 35
Boutalis Yiannis, 346
Brianzoni Serena, 43
Byrne G., 147
Chin Chou Hsin, 215
Christodoulou Manolis, 346
Commendatore
Pasquale, 59
Daniels S., 147
De Campos Cristina,
51
Dingwell Donald B.,
51
Dobrescu Loretti I., 67
Dodson
C.
T. J.,
75
Dowling D. P., 147
EI-Rassy Houssam, 385
Ertel-Ingrisch Werner,
51
Filippaki E., 377
Fraedrich Klaus,
170
Gopar Victor A.,
191
Grigoras Carmen,
85
Grigoras Victor,
85
Author Index
Hacinliyan
A.
S., 93
Haller George, 294
Iliopoulos A.
c.,
268
Jevtic N.,
101
Karakatsanis L. P., 268
Khots Boris,
111
Khots Drnitriy,
111
Kolesnikov Alexander A., 119
Kolesnikov Anatoly A., 128, 134
Konkov
L. E., 369
Krysko
V.
A., 139
Kudra Grzegorz,
17
Kut;;beyzi
t,
93
Kuzmenko Andrew A., 134
Kuznetsova
E.
S., 139
Lan Boon Leong, 165
Law
V.
J., 147
Lawrance Anthony J., 155
Liang Shiuan-Ni, 165
Lucarini Valerio,
170
Mammana Cristiana, 43
Manneville
P., 185
Mello
Pier A.,
191
Mendez-Bermudez J. A.,
191
Michetti Elisabetta, 43, 59
Mikishev Alexander B.,
207
Mitskevich S., 139
Mokalled Tharwat, 385
395
396 Author Index
Neamtu Mihaela, 67
Nepomnyashchy Alexander A.,
207
Ni David C., 215
Oommen
B.
John, 284
Opri~
Dumitru, 67
Orman Gabriel V., 224
Pannekoucke Olivier, 27
Pantelidis Leonidas, 232
Papageorgiou
C.
D.,
241
Papamarkou Theodore, 249
Patidar Vinod, 257
Pavlos
E.
G., 268
Pavlos George P., 268
Perugini Diego,
51
Pinto Antonio, 59
Poli Giampero,
51
Prants
S.
V., 369
Purohit G., 257
Qin Ke, 284
Rabih Sultan, 385
Raptis
T. E.,
241
Rybaczuk Marek, 9
Sapsis Themistoklis, 294
Schweitzer
J.
S.,
101
Skiadas Christos H., 302
Smorodin Boris L., 207
Sokolov Valentin V., 309
Soldatov V., 139
Sotiropouios Anastasios D., 320, 327
Sotiropoulos Vaggelis D., 320, 327
Srisuchinwong Baniue, 338
Sud
K. K., 257
Temizer
L,
93
Tereshko Valery, 35
Theodoridis Dimitris, 346
Tsoutsouras
V.
G., 268
Tynan 1., 147
Umut
Omiir, 362
Vitkovsky V.
0.,
369
Xapianteris
C.
L., 377
Zaknoun Farah, 385
Zhigalov M., 139
Zhu Jian Gue, 1
This page intentionally left blankThis page intentionally left blank