Initial Conditions Card Description (HYDT-KE)

Equation of State

Each conservation equation is solved for a single primary variable, yielding a set of nine primary variables. The constitutive equations are used to compute all secondary variables from the nine primary variables. Under pressure and temperature conditions for geologic accumulations of natural gas hydrates, there is the possibility for three mobile phases:

1) Aqueous - assumed to primarily comprise liquid water, with dissolved concentrations of hydrate formers determined using Henry’s law.

2) Nonaqueous liquid- assumed to primarily comprise the hydrate formers, with dissolved concentrations of water.

3) Gas - assumed to primarily comprise the hydrate formers, with dissolved concentrations of water.

To avoid the numerical burden of the conventional phase stability and flash calculations for determining the existence of gas and nonaqueous liquid phases and their compositions, phase envelopes were generated at 0.1 mole fraction points for the hydrate formers, over a temperature range from -50°C to the cricondentherm point and stored in tabular form. The Peng-Robinson (Peng and Robinson, 1976) cubic EOS was used to generate the phase envelopes. An interpolation scheme is then used to determine the phase state and composition of the existing phases, given the temperature, pressure, and mole fraction of hydrate formers.

Phase conditions

Phase transitions require that the primary variables that make up the set vary with phase conditions. STOMP-HYDT-KE uses a tiered primary variable switching scheme, with four principal primary variable sets and secondary alterations of the primary variables with variations in the mobile and hydrate concentration of hydrate formers (i.e., CO2, CH4, and N2) as listed below.

(1) S_h = 0, S_g+S_n = 0, S_l+S_i = 1

Phase Condition #10

Primary Variables
Energy	Water	Mobile CO2	Mobile CH4	Mobile N2	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	P_l	P_V^CO₂	P_V^CH₄	P_V^N₂	m_h^CO₂	m_h^CH₂	m_h^N₂	Ψ_b^s

(2) S_h = 0, S_g+S_n > 0, S_l+S_i < 1

Phase Condition #21

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	^_-	z^CH₄	z^N₂	m_h^CO₂	m_h^CH₂	m_h^N₂	Ψ_b^s

Phase Condition #22

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	^_-	z^N₂	m_h^CO₂	m_h^CH₂	m_h^N₂	Ψ_b^s

Phase Condition #23

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	z^CH₄	^_-	m_h^CO₂	m_h^CH₂	m_h^N₂	Ψ_b^s

(3) S_h > 0, S_g+S_n > 0, S_l+S_i < 1

Phase Condition #31

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	^_-	z^CH₄	z^N₂	S_h	^_-	φ_h^CH₂	φ_h^N₂	Ψ_b^s

Phase Condition #32

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	^_-	z^CH₄	z^N₂	S_h	φ_h^CO₂	^_-	φ_h^N₂	Ψ_b^s

expanded

Phase Condition #33

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	^_-	z^CH₄	z^N₂	S_h	φ_h^CO₂	φ_h^CH₂	^_-	Ψ_b^s

Phase Condition #34

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	-	z^N₂	S_h	^_-	φ_h^CH₂	φ_h^N₂	Ψ_b^s

Phase Condition #35

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	-	z^N₂	S_h	φ_h^CO₂	^_-	φ_h^N₂	Ψ_b^s

Phase Condition #36

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	^_-	z^N₂	S_h	φ_h^CO₂	φ_h^CH₂	^_-	Ψ_b^s

Phase Condition #37

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	z^CH₄	^_-	S_h	^_-	φ_h^CH₂	φ_h^N₂	Ψ_b^s

Phase Condition #38

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	z^CH₄	^_-	S_h	φ_h^CO₂	^_-	φ_h^N₂	Ψ_b^s

Phase Condition #39

Primary Variables
Energy	Water	Max. Mobile Mass Component	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	S_l+S_i	P	z^CO₂	z^CH₄	^_-	S_h	φ_h^CO₂	φ_h^CH₂	^_-	Ψ_b^s

(4) S_h > 0, S_g+S_n = 0, S_l+S_i < 1

Phase Condition #41

Primary Variables
Energy	Water	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	P	P_V^CO₂	P_V^CH₄	P_V^N₂	S_h	^_-	φ_h^CH₂	φ_h^N₂	Ψ_b^s

Phase Condition #42

Primary Variables
Energy	Water	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	P	P_V^CO₂	P_V^CH₄	P_V^N₂	S_h	φ_h^CO2	^_-	φ_h^N₂	Ψ_b^s

Phase Condition #43

Primary Variables
Energy	Water	Mobile CO2	Mobile CH4	Mobile N2	Max. Hydrate Mass component	Hydrate CO2	Hydrate CH4	Hydrate N2	Salt
T	P	P_V^CO₂	P_V^CH₄	P_V^N₂	S_h	φ^CO₂	φ^CH₂	^_-	Ψ_b^s

Initial Conditions Card Description (HYDT-KE)

Equation of State

Phase conditions

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