RACHFORD_RICE

This function computes vapor fraction and phase compositions by solving the classical Rachford-Rice objective for specified overall mole fractions and K-values.

The equation is:

\sum_i \frac{z_i(K_i-1)}{1 + VF(K_i-1)} = 0

Optional derivative flags allow secant, Newton, or Halley-style updates.

Excel Usage

=RACHFORD_RICE(zs, ks, use_first_derivative, use_second_derivative, guess)
  • zs (list[list], required): Overall mole fractions as a selected range (-).
  • ks (list[list], required): Equilibrium K-values as a selected range (-).
  • use_first_derivative (bool, optional, default: false): Use first derivative in solve step (Newton-Raphson).
  • use_second_derivative (bool, optional, default: false): Use second derivative in solve step (Halley method).
  • guess (float, optional, default: null): Initial vapor-fraction guess (-).

Returns (list[list]): 2D array containing vapor fraction and phase compositions.

Example 1: Classical Rachford-Rice solve

Inputs:

zs ks
0.5 0.3 0.2 1.685 0.742 0.532

Excel formula:

=RACHFORD_RICE({0.5,0.3,0.2}, {1.685,0.742,0.532})

Expected output:

Property Value
VF 0.69073
xs [0.33940869696634357, 0.3650560590371706, 0.2955352439964858]
ys [0.5719036543882889, 0.27087159580558057, 0.15722474980613044]
Example 2: Newton-Raphson variant

Inputs:

zs ks use_first_derivative
0.5 0.3 0.2 1.685 0.742 0.532 true

Excel formula:

=RACHFORD_RICE({0.5,0.3,0.2}, {1.685,0.742,0.532}, TRUE)

Expected output:

Property Value
VF 0.69073
xs [0.33940869696634357, 0.3650560590371706, 0.2955352439964858]
ys [0.5719036543882889, 0.27087159580558057, 0.15722474980613044]
Example 3: Halley variant

Inputs:

zs ks use_first_derivative use_second_derivative
0.5 0.3 0.2 1.685 0.742 0.532 true true

Excel formula:

=RACHFORD_RICE({0.5,0.3,0.2}, {1.685,0.742,0.532}, TRUE, TRUE)

Expected output:

Property Value
VF 0.69073
xs [0.33940869696634357, 0.3650560590371706, 0.2955352439964858]
ys [0.5719036543882889, 0.27087159580558057, 0.15722474980613044]
Example 4: Custom initial guess

Inputs:

zs ks guess
0.4 0.4 0.2 2 0.8 0.4 0.5

Excel formula:

=RACHFORD_RICE({0.4,0.4,0.2}, {2,0.8,0.4}, 0.5)

Expected output:

Property Value
VF 0.518417
xs [0.26343228527928286, 0.4462708596090614, 0.2902968548930794]
ys [0.5268645705585657, 0.35701668768724915, 0.11611874195723176]

Python Code

Show Code 
from chemicals.rachford_rice import Rachford_Rice_solution as chemicals_rachford_rice_solution

def rachford_rice(zs, ks, use_first_derivative=False, use_second_derivative=False, guess=None):
    """
    Solve the classical Rachford-Rice flash equation.

    See: https://chemicals.readthedocs.io/chemicals.rachford_rice.html#chemicals.rachford_rice.Rachford_Rice_solution

    This example function is provided as-is without any representation of accuracy.

    Args:
        zs (list[list]): Overall mole fractions as a selected range (-).
        ks (list[list]): Equilibrium K-values as a selected range (-).
        use_first_derivative (bool, optional): Use first derivative in solve step (Newton-Raphson). Default is False.
        use_second_derivative (bool, optional): Use second derivative in solve step (Halley method). Default is False.
        guess (float, optional): Initial vapor-fraction guess (-). Default is None.

    Returns:
        list[list]: 2D array containing vapor fraction and phase compositions.
    """
    try:
        def to_list(x):
            if isinstance(x, list):
                out = []
                for row in x:
                    if isinstance(row, list):
                        for val in row:
                            if val is not None and val != "":
                                out.append(float(val))
                    elif row is not None and row != "":
                        out.append(float(row))
                return out
            if x is None or x == "":
                return []
            return [float(x)]

        z_vals = to_list(zs)
        k_vals = to_list(ks)
        if len(z_vals) == 0 or len(z_vals) != len(k_vals):
            return "Error: zs and ks must be non-empty and have the same length"

        vf, xs, ys = chemicals_rachford_rice_solution(zs=z_vals, Ks=k_vals, fprime=use_first_derivative, fprime2=use_second_derivative, guess=guess)
        return [["Property", "Value"], ["VF", vf], ["xs", str(xs)], ["ys", str(ys)]]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Overall mole fractions as a selected range (-).
Equilibrium K-values as a selected range (-).
Use first derivative in solve step (Newton-Raphson).
Use second derivative in solve step (Halley method).
Initial vapor-fraction guess (-).