Following

Yes you can have SI/SII transition for some fluids depending on T and P, for example the fluid below has a SII/SI transition at about 16°C.

Methane 80.463%

Ethane 1.421%

Propane 0.223%

i-Butane 0.041%

n-Butane 0.071%

i-Pentane 0.030%

Carbon dioxide 8.475%

Nitrogen 7.236%

Hydrogen sulphide 1.959%

n-Pentane 0.030%

n-Hexane 0.051%

SOme other examples given in Article Development of a multiphase flash in presence of hydrates: E...

I am aware of S I/ S II transition. It is also observed in case of cyclopropane hydrates at 0.6 bara.

what I am asking is that it is theoretically possible to have equilibrium conditions of both S I and S II hydrates satisfied together for water containing inhibitors at ice point though equilibrium conditions are not satisfied for either of the type of hydrates just below the ice point. This is because of discontinuity in the ln (Xw) term at ice point for water containing inhibitors. Is such a condition observed by other researchers also and for what mixture and what inhibitors?

For my example, you have one T and P where both sI and Sii are stable.

If you have inhibitor depending on the concentration, then it does not really matter if you are below 0°C. I am not sure I understand the discontinuity.

In Van der waal and Platteu model, the chemical potential depends on ln(activity of water). If we are calculating hydrate formation temperature at a given pressure then activity of water below ice point is 1 whereas it is a slightly less than 1 just above the ice point for water without inhibitors because of some soluble components. This term, ln(activity of water), is same in calculation of chemical potential of both type of hydrates. For water with inhibitors, activity of water just above ice point can be significantly less than 1 making the term ln(activily of water) significantly less than 0. This will increase the chemical potential of both types of hydrates suddenly as we cross the ice point as this negative term is subtracted from the chemical potential of both types of hydrates. Is it not possible that this sudden increase in chemical potential of both types of hydrates may satisfy the equilibrium conditions for hydrate formation at ice point for this pressure value and many pressure values above this pressure value? In such a case instead of having one pressure value for transition of type of hydrates, we will have a range of pressure over which this transition of type of hydrates will take place.

Nope, thermodynamic says that a system can have only one structure type that is in "equilibrium" and this is defined by the guest gas or gas mixture (not water itself). It is true though that in real systems a coexistence of sI and sII is know to exist. It is related to the tiny difference in free energy between both structures and thus rather slow equilibration. Especially at low temperatures. If the formation is rapid many structures/odd cage arrangements complete with each other but at the end only one is stable. All odd cages or oder regular structures will turn into stable one over time.

Thanks for your answer, Dr Falenty.

In case we are forming hydrates out of a mixture of hydrate formers at a temperature lower than the equilibrium hydrate formation temperature at same pressure, then as a small amount of hydrates will be formed, some amount of hydrate formers will convert to hydrates. The composition of hydrate formers in hydrate phase will be different from composition of hydrate formers in gas or liquid phase resulting in change in composition of hydrate formers in gas or liquid phase after small amount of hydrates are formed. This new composition will require lower hydrate equilibrium temperature to form hydrates and will result in formation of hydrates of different properties like density, hydration number etc. Even the type of hydrate can be different for hydrates formed out of different composition of hydrate formers at decreasing temperature. Therefore for a temperature lower than equilibrium hydrate forming temperature for a mixture of hydrate formers, can't wel have hydrates of different properties (and types) coexisting with each other? I have tried to simulate this condition using my software and the results of one such condition are attached. The results tabulate the hydrate forming temperature and their properties as more and more hydrates are formed. You can notice that at some points there is also a change of type of hydrates formed.

What is wrong in this simulation and what should I do to correct it?

Dear Amit, this what you write is very commonly seen effect, during the formation of binary or more complex hydrates. There is no surprise there. During the formation and some time afterwards various compositions and different structures can coexist in one environment.

In your main question though you have asked about " the hydrate equilibrium conditions for both S I and S II hydrates are satisfied together ".

The situation you described has nevertheless noting to do with the equilibrium. The whole system in such state is completely out of the equilibrium. Some parts of hydrates that are in imbalance with the surrounding guest formers will start exchanging trapped guest molecules. This will cause a feedback loop of changing the composition of the surrounding guest and triggering another imbalance in hydrates. This goes on and on and on.

In realistic scenarios guest composition in gas hydrates will approach asymptotically the guest composition in the surrounding medium. This what chemists call an equilibrium state is likely to be never reached by real gas hydrate systems.

Thanks for your answer, Dr Falenty.

The two questions are different.

sorry for that.

Is the explanation given by you in the third and fourth paragraph of your answer for the main question? Do you mean that the kind of system described in the main question is never in equilibrium? Does the kind of system described in the main question exist?

amit