polykin.thermo.flash

flash2_TV

flash2_TV(
    F: float,
    z: FloatVector,
    T: float,
    beta: float,
    Kcalc: Callable[
        [float, float, FloatVector, FloatVector],
        FloatVector,
    ],
    *,
    P0: float = 100000.0,
    maxiter: int = 50,
    atol_inner: float = 1e-09,
    rtol_outer: float = 1e-06
) -> FlashResult

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

References

• J.F. Boston, H.I. Britt, "A radically different formulation and solution of the single-stage flash problem", Computers & Chemical Engineering, Volume 2, Issues 2-3, 1978, p. 109-122,

PARAMETER	DESCRIPTION
F	Feed mole flowrate (mol/s). TYPE: float
z	Feed mole fractions (mol/mol). TYPE: FloatVector
T	Temperature (K). TYPE: float
beta	Vapor phase fraction (mol/mol). TYPE: float
Kcalc	Function to calculate K-values, with signature Kcalc(T, P, x, y). TYPE: Callable[[float, float, FloatVector, FloatVector], FloatVector]
P0	Initial guess for pressure (Pa). TYPE: float DEFAULT: 100000.0
maxiter	Maximum number of iterations. TYPE: int DEFAULT: 50
atol_inner	Absolute tolerance for the inner R-loop. TYPE: float DEFAULT: 1e-09
rtol_outer	Relative tolerance for the outer volatility parameters loop. TYPE: float DEFAULT: 1e-06

RETURNS	DESCRIPTION
FlashResult	Flash result.

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

def flash2_TV(
    F: float,
    z: FloatVector,
    T: float,
    beta: float,
    Kcalc: Callable[[float, float, FloatVector, FloatVector], FloatVector],
    *,
    P0: float = 1e5,
    maxiter: int = 50,
    atol_inner: float = 1e-9,
    rtol_outer: float = 1e-6,
) -> FlashResult:
    r"""Solve a 2-phase flash problem at given temperature and vapor fraction.

    **References**

    *  J.F. Boston, H.I. Britt, "A radically different formulation and solution
       of the single-stage flash problem", Computers & Chemical Engineering,
       Volume 2, Issues 2-3, 1978, p. 109-122,

    Parameters
    ----------
    F : float
        Feed mole flowrate (mol/s).
    z : FloatVector
        Feed mole fractions (mol/mol).
    T : float
        Temperature (K).
    beta : float
        Vapor phase fraction (mol/mol).
    Kcalc : Callable[[float, float, FloatVector, FloatVector], FloatVector]
        Function to calculate K-values, with signature `Kcalc(T, P, x, y)`.
    P0 : float
        Initial guess for pressure (Pa).
    maxiter : int
        Maximum number of iterations.   
    atol_inner : float
        Absolute tolerance for the inner R-loop.
    rtol_outer : float
        Relative tolerance for the outer volatility parameters loop.

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

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

    # Initial guesses
    z = z/z.sum()
    P = P0
    K = Kcalc(T, P, z, z)
    x = z/(1 + beta*(K - 1))
    y = K*x
    x /= x.sum()
    y /= y.sum()

    # Initialize volatility parameters
    Pref = 1e5
    u, Kb, A, B = _parameters_TV(T, P, x, y, beta, Kcalc, Pref, all=True)
    Kb0 = Kb

    # Outer loop
    for _ in range(maxiter):

        v_old = np.concatenate((u, [A]))

        # Inner R-loop
        if abs(beta - 0) <= eps:
            R = 0.0
        elif abs(beta - 1) <= eps:
            R = 1.0
        else:
            sol = root_brent(lambda R: _Rloop(R, u, Kb0, beta, z),
                             0.0, 1.0,
                             maxiter=maxiter,
                             tolx=atol_inner,
                             tolf=atol_inner)
            R = sol.x
            if not sol.success:
                message = f"Inner R-loop did not converge after {maxiter} iterations. Solution: {sol}."
                break

        # Compute x, y
        p = z/(1 - R + Kb0*R*exp(u))
        eup = exp(u)*p
        sum_p = p.sum()
        sum_eup = eup.sum()
        x = p/sum_p
        y = eup/sum_eup

        # Compute P
        Kb = sum_p/sum_eup
        sol = root_newton(lambda P: log(Kb*P) - A - B*(P/Pref),
                          x0=exp(A)/Kb, tolx=0.0, tolf=1e-10)
        if sol.success:
            P = sol.x
        else:
            message = f"Pressure did not converge after {maxiter} iterations. Solution: {sol}."
            break

        # Update u, A, K
        u, A, K = _parameters_TV(T, P, x, y, beta, Kcalc, Pref, all=False, B=B)
        v_new = np.concatenate((u, [A]))

        # Check convergence
        v0 = min(vi for vi in v_new if vi > 0.0)
        if np.allclose(v_new, v_old, atol=v0*rtol_outer):
            success = True
            message = "Outer loop converged within specified tolerance."
            break

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

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

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