Page 271 - Handbook Of Multiphase Flow Assurance

270 10. Research methods in flow assurance

Normalized number of
polygons per molecule
0.4

0.35

0.3

0.25

0.2

0.15
0.1

0.05

0
1 2 3 4 5 6 7 8 9 10 11
Number of water molecules in hydrogen bonded polygon
FIG. 10.40 Distribution of hydrogen bonded polygons in water at 283 K (Rahman and Stillinger, 1973).

The validation part checks for the short circuits of other hydrogen bonds crossing the found
polygon. A visual explanation of short circuited polygons is presented in Fig. 10.35. If no
short circuits are found, a polygon is counted. Also this program checks for the “penetration”
polygons which go across the periodic boundary conditions implied in this search. Some of
such polygons do not close into a loop and are discarded. An example of a faulty polygon
may be a chain of hydrogen bonds going across the simulation box and crossing the periodic
boundary only once (shown in Fig. 10.41). Due to the limited number of water molecules al-
lowed to form a hydrogen bonded ring, this periodic boundary penetration effect decreases
with the size of simulation box.
The program to count the hydrogen bonded polygons has been extensively tested and
shown to be valid. A relatively short program was written in Turbo Pascal in order to help
visually verify the validity of counted polygons. This program allows to see a projection of
each 3-dimensional hydrogen bonded ring pattern separately. An example of a valid pattern
crossing the boundaries of the simulation box is shown in Fig. 10.42. The faulty polygon pat-
tern shown in Fig. 10.41 was drawn in Paintbrush for Windows, while the valid polygon is a
typical output of the visualization program.
Derivation of hydrogen bond connectivity
Data for the ring counting program was supplied from another program written in Fortran
which translates the SYBYL® simulation coordinate output file into a list of pairs of hydrogen
bonded molecules for a given time “snapshot”. Two water molecules were considered to be