Schematic of phase diagrams for a pure gas hydrate system of methane (CH$_4$), carbon dioxide (CO$_2$), hydrogen sulphide (H$_2$S) and nitrogen (N$_2$) between the lower and upper quadruple points are shown in the figure. Arrowheads indicate the stable hydrate region for a particular gas hydrate system. Match the phase diagram with the corresponding pure gas hydrate. 
Schematic of phase diagrams for a pure gas hydrate system of methane (CH$_4$), carbon dioxide (CO$_2$), hydrogen sulphide (H$_2$S) and nitrogen (N$_2$) between the lower and upper quadruple points are shown in the figure. Arrowheads indicate the stable hydrate region for a particular gas hydrate system. Match the phase diagram with the corresponding pure gas hydrate.
Show Hint
- I – CH$_4$; II – N$_2$; III – CO$_2$; IV – H$_2$S
- I – H$_2$S; II – CH$_4$; III – CO$_2$; IV – N$_2$
- I – N$_2$; II – CH$_4$; III – H$_2$S; IV – CO$_2$
- I – N$_2$; II – CH$_4$; III – CO$_2$; IV – H$_2$S
The Correct Option is D
Solution and Explanation
- Nitrogen (N$_2$) forms hydrates under the least stable conditions (requires highest pressure at a given temperature), hence its stability curve lies farthest to the left (I).
- Methane (CH$_4$) is more stable than N$_2$ but less than CO$_2$ and H$_2$S, hence curve (II).
- Carbon dioxide (CO$_2$) hydrates are more stable than methane, hence curve (III).
- Hydrogen sulphide (H$_2$S) hydrates are the most stable (form at the lowest pressure for a given temperature), hence curve (IV).
Therefore, the correct matching is (D).
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Questions Asked in GATE PE exam
Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
Statement:
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts, and inimical local lords—all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
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\[ \begin{aligned} N & = \text{Initial (original) oil in place, stb} \\ G & = \text{Initial volume of gas cap, scf} \\ m & = \text{Ratio of initial volume of gas cap to volume of oil initial in place, rb/rb} \\ S_{wi} & = \text{Initial water saturation} \\ S_{oi} & = \text{Initial oil saturation} \\ B_{oi} & = \text{Initial oil formation volume factor, rb/stb} \\ B_{gi} & = \text{Initial gas formation volume factor, rb/scf} \end{aligned} \]
The total pore volume (in rb) of the reservoir is:
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