Supplementary Information for:
Formation of Methane Nano-bubbles during Hydrate Decomposition and Their Effect on Hydrate
Growth
S. Alireza Bagherzadeh,1 Saman Alavi,1,2,* John Ripmeester,1,2 and Peter Englezos1,*
1
Chemical and Biological Engineering, University of British Columbia, Vancouver, V6T1Z3,
Canada
2
National Research Council of Canada, 100 Sussex Dr., K1A0R6, Ottawa, Canada
E-mail: [email protected]; [email protected]
1
FIG. S1. Protocol applied in this work. The entire system is equilibrated at hydrate equilibrium point of
302 K and 400 bar during a 500 ps NVT followed by a 500 ps NPT. Subsequently, the liquid water and
methane gas phases are warmed up to the desired temperature to stimulate hydrate decomposition.
During equilibration stages the oxygens of water molecules in the hydrate phase are position restrained.
The decomposition of hydrate is investigated in an NPT ensemble at 400 bar and temperature of interest
(320-360 K) for a few tens of nano-seconds (20-60 ns) with no constraints on the hydrate phase.
2
The potential energy of the system at different times during equilibration stages is plotted in FIG. S2. As
seen, potential energy converges during each of the three equilibration stages, namely, 500 ps NVT-eq,
500 ps NPT-eq and 250 ps simulated annealing. Depending on the temperature of interest the final
potential energy of the equilibrated system is different.
FIG. S2. Potential energy of the system during equilibration stages: NVT-eq at 302 K followed by NPTeq at 302K and 400 bar. The temperature of the liquid water and methane gas phases were increased via
a short simulated annealing to stimulate hydrate decomposition. To illustrate the common behavior of
the system, raising liquid water temperature to 320 K and 350 K are only shown.
3
The SHAKE tolerance was chosen to be very small (10-10) to produce acceptable energy
conservation. As the methane hydrate undergoes the endothermic dissociation, the potential energy
content of the total system increases, as seen in the initial behaviors in FIG. 2 and FIG. S3. If the only
process occurring after the decomposition of the hydrate is the endothermic diffusion of methane from
liquid water into the gas phase (the evaporation of methane from water), the potential energy of the
system would become more positive and increase. However, as shown in Figures 4 – 6, the picture is
complicated by nanobubble formation, growth, and then subsequent methane dissolution in water
processes. Figures 2 and S3 show that the potential energy shows a downwards drift to lower potential
energy values. As seen in FIG. S3, the downward drift in potential energy is not uniform and occurs in
steps. We attribute this downwards drift to the nanobubble-related physical processes occurring in the
simulation system and not energy drift problems related to loose tolerance in the SHAKE calculations.
4
FIG. S3. Potential energy of the system as a function of simulation time for the dissociation simulation
at 350 K. The increase in the potential energy during the first 5 ns is due to the dissociation of the
hydrate phase. The decreasing trend until ~ 50 ns is due to the dissolution of nanobubbles in the aqueous
phase. After about 50 ns the system has reached equilibrium and there is no drift in the energy.
5
FIG. S4. Projections of the configurations of the G-W-H-W-G three-phase decomposition simulation at
330 K on the yz-plane. Top: 0 ns; middle: 6 ns; bottom 30 ns. The ordered cage-like structure of hydrate
phase is evident in the middle of the simulation box. Liquid water and methane molecules are show by
red-and-white bonds and cyan spheres, respectively. The approximate location of the hydrate/water
interface is shown by yellow lines. Decomposition proceeds in a stepwise manner where dissociation of
layers of hydrate cages parallel to the interface is apparent.
6
FIG. S5. Radius and z-coordinate of the center of the bubble 1 formed during the dissociation simulation
at 350 K. The movement of the bubble along the z-direction does not show any specific trend towards or
away from the hydrate-water or water-gas interface. The bubble remains approximately at the same
location with some degrees of fluctuation. The average z-coordinate of the center of the bubble 1 is 89 Ǻ
with a standard deviation of 6.2 Ǻ.
7
Two additional simulations for the growth of hydrate in the presence of methane nanobubble are
performed. In one simulation the same configuration, shown in FIG 9(A) of the text, is taken but the
temperature is lowered 5 K more to 275 K. In the other simulation a new configuration at 3.75 ns after
dissociation simulation at 350 K, shown in figure below, is taken and the temperature is lowered to 280
K to observe the growth.
FIG. S6. Partial yz-snapshot at 3.75 ns of the partially decomposed hydrate at 350 K. Water molecules in
the hydrate and liquid phases are shown by hydrogen-bonds in red and red-and-white bonds,
respectively. Methane molecules initially in the hydrate and gas phases are shown in cyan and green
spheres, respectively. The small spherical bubble of methane is visible on the right side of the hydrate
template.
8
FIG. S7. F3 profile of the hydrate growth simulation at 275 K and 400 bar. L4 through L10 and L11
through L17 refer to the slices along the z-axis on the non-bubble side and bubble side, respectively. As
seen, on the bubble side of the hydrate template, three layers (L12, L13 and L14) show that hydrate
cages have grown whereas on the non-bubble side there are only two layers (L6 and L7) that show
hydrate growth.
9
FIG. S8. F3 profile of the hydrate growth simulation at 280 K and 400 bar. L4 through L10 and L11
through L17 refer to the slices along the z-axis on the non-bubble side and bubble side, respectively. As
seen, on the bubble side of the hydrate template (FIG. S6), three layers (L12, L13 and L14) show that
hydrate cages have grown whereas on the non-bubble side there are only two layers (L6 and L7) that
show hydrate growth. It is clearly visible that the rate of hydrate growth, i.e., the slope of decrease in F3,
is larger on the bubble side.
10