Initial Conditions Card Options (HYDT-KE)

A summary of the seven initial condition types and the associated phase conditions are listed.

The tables indicate the specified (user input) variables and the possible resulting phase condition numbers.
For initial conditions with hydrate present, the hydrate formers in the mobile and hydrate phases can either be in equilibrium or not.
The Iterative Solved Variable(s) column indicates those variables that are solved in the flash calculation using a Newton-Raphson iteration scheme. Variables within a set of braces are solved simultaneously. Multiple braces indicate two sequential solves are required for the flash calculation.

Initial Condition #1 -- Hydrate-mobile phase non-equilibrium

Initial Condition #1 applies to Phase Condition #10.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P 2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂ or 2 of 3: z^CO₂, z^CH₄, z^N₂ W_l^f	z^CO₂, z^CH₄, z^N₂	T, P, P_V^CO₂, P_V^CH₄, P_V^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂

or 2 of 3: z^CO₂, z^CH₄, z^N₂

W_l^f

z^CO₂, z^CH₄, z^N₂

T, P, P_V^CO₂, P_V^CH₄, P_V^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

where T is temperature, P is pressure, φ_mⁱ is the mole fraction of component "i" of mobile formers (ie., of mobile CO₂, CH₄, and N₂), zⁱ is the nonaqueous (gas and NAPL) mole fraction of "i", and W_l^f is the relative saturation of dissolved hydrate formers.

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

Initial Condition #2 -- Hydrate-mobile phase non-equilibrium

Initial Condition #2 applies to Phase Conditions #21 - 23.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P S_l 2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂	z^CO₂, z^CH₄, z^N₂	T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

S_l

2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂

z^CO₂, z^CH₄, z^N₂

T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

where T is temperature, P is pressure, S_l is aqueous saturation, and φ_mⁱ is the mole fraction of component "i" of mobile formers (ie., of mobile CO₂, CH₄, and N₂).

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

Initial Condition #3 -- Hydrate-mobile phase non-equilibrium

Initial Condition #3 applies to Phase Conditions #41-43.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P 2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂ or 2 of 3: z^CO₂, z^CH₄, z^N₂ W_l^f S_h 2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂	z^CO₂, z^CH₄, z^N₂	T, P, P_V^CO₂, P_V^CH₄, P_V^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂

or 2 of 3: z^CO₂, z^CH₄, z^N₂

W_l^f

S_h

2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂

z^CO₂, z^CH₄, z^N₂

T, P, P_V^CO₂, P_V^CH₄, P_V^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

where T is temperature, P is pressure, φ_mⁱ is the mole fraction of component "i" of mobile hydrate formers (ie., of mobile CO₂, CH₄, and N₂), zⁱ is the nonaqueous (gas and NAPL) mole fraction of "i", W_l^f is the relative saturation of dissolved hydrate formers, S_h is the hydrate saturation, and φ_hⁱ is the mole fraction of component "i" of hydrate formers in hydrate (ie., of CO₂, CH₄, and N₂ hydrates).

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

Initial Condition #4 -- Hydrate-mobile phase non-equilibrium

Initial Condition #4 applies to Phase Conditions #31-39.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P S_l 2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂ S_h 2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂	z^CO₂, z^CH₄, z^N₂	T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

S_l

2 of 3: φ_m^CO₂, φ_m^CH₄, φ_m^N₂

S_h

2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂

z^CO₂, z^CH₄, z^N₂

T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

where T is temperature, P is pressure, φ_mⁱ is the mole fraction of component "i" of mobile hydrate formers (ie., of mobile CO₂, CH₄, and N₂), S_h is the hydrate saturation, and φ_hⁱ is the mole fraction of component "i" of hydrate formers in hydrate (ie., of CO₂, CH₄, and N₂ hydrates).

S_h > 0, S_g+S_n > 0, S_l+S_i < 1

Initial Condition #5 -- Hydrate-mobile phase equilibrium

Initial Condition #5 applies to Phase Conditions #31-39.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P S_l S_h 2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂	φ_h^CO₂, φ_h^CH₄, φ_h^N₂	T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

S_l

S_h

2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂

φ_h^CO₂, φ_h^CH₄, φ_h^N₂

T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, φ_h^CO₂, φ_h^CH₄, φ_h^N₂, Ψ_b^s

where T is temperature, P is pressure, S_l is aqueous saturation, S_h is the hydrate saturation, and φ_hⁱ is the mole fraction of component "i" of hydrate formers in hydrate (ie., of CO₂, CH₄, and N₂ hydrates).

S_h > 0, S_g+S_n > 0, S_l+S_i < 1

Initial Condition #6 -- Hydrate-mobile phase non-equilibrium

Initial Condition #6 applies to Phase Conditions #21-23.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P S_l 2 of 3: z^CO₂, z^CH₄, z^N₂	z^CO₂, z^CH₄, z^N₂	T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

S_l

2 of 3: z^CO₂, z^CH₄, z^N₂

z^CO₂, z^CH₄, z^N₂

T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

where T is temperature, P is pressure, S_l is the aqueous saturation, and zⁱ is the nonaqueous (gas and NAPL) mole fraction of "i".

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

Initial Condition #7 -- Hydrate-mobile phase non-equilibrium

Initial Condition #7 applies to Phase Conditions #31-39.

Specified Variables	Iteratively Solved Variables	Phase Condition Variables
T P S_l 2 of 3: z^CO₂, z^CH₄, z^N₂ S_h 2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂	φ_h^CO₂, φ_h^CH₄, φ_h^N₂	T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

Specified Variables

Iteratively Solved Variables

Phase Condition Variables

S_l

2 of 3: z^CO₂, z^CH₄, z^N₂

S_h

2 of 3: φ_h^CO₂, φ_h^CH₄, φ_h^N₂

φ_h^CO₂, φ_h^CH₄, φ_h^N₂

T, S_l+S_i, P, z^CO₂, z^CH₄, z^N₂, S_h, m_h^CO₂, m_h^CH₂, m_h^N₂, Ψ_b^s

where T is temperature, P is pressure, S_l is the aqueous saturation, zⁱ is the nonaqueous (gas and NAPL) mole fraction of "i", S_h is the hydrate saturation, and φ_hⁱ is the mole fraction of component "i" of hydrate formers in hydrate (ie., of CO₂, CH₄, and N₂ hydrates).

S_h > 0, S_g+S_n > 0, S_l+S_i < 1

Input Option Character Strings

Initial Condition Variable	Input Parameter Name
T	temperature
P	Pressure
φ_^m^CO₂	mobile CO2 mole fraction of formers
φ_m^CH₄	mobile CH4 mole fraction of formers
φ_m^N₂	mobile N2 mole fraction of formers
z^CO₂	total nonaqueous CO2 mole fraction
z^CH₄	total nonaqueous CH4 mole fraction
z^N₂	total nonaqueous N2 mole fraction
W_l^f	aqueous relative saturation of formers
φ_h^CO₂	hydrate CO2 mole fraction of formers
φ_h^CH₄	hydrate CH4 mole fraction of formers
φ_h^N₂	hydrate N2 mole fraction of formers
S_l	aqueous saturation
S_h	hydrate saturation
ρ_l^S	dissolved salt volumetric concentration
ω_l^S	dissolved salt mass fraction
x_l^S	dissolved salt relative saturation

Initial Condition Option	Input Condition Option Name
1	IC1
2	IC2
3	IC3
4	IC4
5	IC5
6	IC6
7	IC7

Initial Conditions Card Options (HYDT-KE)

Input Option Character Strings

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