polykin.thermo.flash

flash2_PT

flash2_PT(
    F: float,
    z: FloatVector,
    P: float,
    T: float,
    Kcalc: Callable[
        [float, float, FloatVector, FloatVector],
        FloatVector,
    ],
    *,
    beta0: float | None = None,
    maxiter: int = 50,
    atol_inner: float = 1e-09,
    rtol_outer: float = 1e-06,
    alpha_outer: float = 1.0
) -> FlashResult

Solve a 2-phase flash problem at given pressure and temperature.

References

• M.L. Michelsen and J. Mollerup, "Thermodynamic models: Fundamentals and computational aspects", Tie-Line publications, 2nd edition, 2007.

PARAMETER	DESCRIPTION
F	Feed mole flowrate (mol/s). TYPE: float
z	Feed mole fractions (mol/mol). TYPE: FloatVector
T	Temperature (K). TYPE: float
P	Pressure (Pa). TYPE: float
Kcalc	Function to calculate K-values, with signature Kcalc(T, P, x, y). TYPE: Callable[[float, float, FloatVector, FloatVector], FloatVector]
beta0	Initial guess for vapor phase fraction. TYPE: float | None DEFAULT: None
maxiter	Maximum number of iterations. TYPE: int DEFAULT: 50
atol_inner	Absolute tolerance for the inner beta-loop. TYPE: float DEFAULT: 1e-09
rtol_outer	Relative tolerance for the outer K-values loop. TYPE: float DEFAULT: 1e-06
alpha_outer	Relaxation factor for the outer K-values loop. TYPE: float DEFAULT: 1.0

RETURNS	DESCRIPTION
FlashResult	Flash result.

Source code in src/polykin/thermo/flash/vle.py

def flash2_PT(
    F: float,
    z: FloatVector,
    P: float,
    T: float,
    Kcalc: Callable[[float, float, FloatVector, FloatVector], FloatVector],
    *,
    beta0: float | None = None,
    maxiter: int = 50,
    atol_inner: float = 1e-9,
    rtol_outer: float = 1e-6,
    alpha_outer: float = 1.0,
) -> FlashResult:
    r"""Solve a 2-phase flash problem at given pressure and temperature.

    **References**

    *  M.L. Michelsen and J. Mollerup, "Thermodynamic models: Fundamentals and
       computational aspects", Tie-Line publications, 2nd edition, 2007.

    Parameters
    ----------
    F : float
        Feed mole flowrate (mol/s).
    z : FloatVector
        Feed mole fractions (mol/mol).
    T : float
        Temperature (K).
    P : float
        Pressure (Pa).
    Kcalc : Callable[[float, float, FloatVector, FloatVector], FloatVector]
        Function to calculate K-values, with signature `Kcalc(T, P, x, y)`.
    beta0 : float | None
        Initial guess for vapor phase fraction.
    maxiter : int
        Maximum number of iterations.    
    atol_inner : float
        Absolute tolerance for the inner beta-loop.
    rtol_outer : float
        Relative tolerance for the outer K-values loop.
    alpha_outer : float
        Relaxation factor for the outer K-values loop.

    Returns
    -------
    FlashResult
        Flash result.
    """

    method = "2-Phase PT Flash"
    message = ""
    success = False

    # Initial guesses
    z = z/z.sum()
    x = z
    y = z
    beta = np.nan
    K = Kcalc(T, P, z, z)

    for _ in range(maxiter):

        # Find beta
        sol = solve_Rachford_Rice(K, z, beta0, maxiter, atol_inner)
        beta = sol.beta
        if not sol.success:
            message = f"Inner Rachford-Rice loop did not converge after {maxiter} iterations. Solution: {sol}."
            break

        # Compute x, y
        x = z/(1 + beta*(K - 1))
        y = K*x
        x /= x.sum()
        y /= y.sum()

        # Update K
        K_old = K.copy()
        K_new = Kcalc(T, P, x, y)

        # Check convergence
        k0 = min(k for k in K_new if k > 0)
        if np.allclose(K_new, K_old, atol=k0*rtol_outer):
            success = True
            message = "Outer loop converged within specified tolerance."
            break
        else:
            K = exp(alpha_outer*log(K_new) + (1 - alpha_outer)*log(K_old))
            beta0 = beta

    else:
        message = f"Outer loop did not converge after {maxiter} iterations."

    # Overall balance
    V = F*beta
    L = F - V

    return FlashResult(method, success, message, T, P, F, L, V, beta, z, x, y, K)