LI_JOHNS_AHMADI

This function solves the Li-Johns-Ahmadi flash equation, an alternative to classical Rachford-Rice formulations, for vapor fraction and phase compositions.

It uses overall composition and K-values and can accept an optional initial guess.

Excel Usage

=LI_JOHNS_AHMADI(zs, ks, guess)
  • zs (list[list], required): Overall mole fractions as a selected range (-).
  • ks (list[list], required): Equilibrium K-values as a selected range (-).
  • guess (float, optional, default: null): Initial guess for the solution (-).

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

Example 1: Base Li-Johns-Ahmadi solve

Inputs:

zs ks
0.5 0.3 0.2 1.685 0.742 0.532

Excel formula:

=LI_JOHNS_AHMADI({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: Alternate composition and K-values

Inputs:

zs ks
0.45 0.35 0.2 1.7 0.75 0.5

Excel formula:

=LI_JOHNS_AHMADI({0.45,0.35,0.2}, {1.7,0.75,0.5})

Expected output:

Property Value
VF 0.5
xs [0.33333333333333337, 0.39999999999999997, 0.26666666666666666]
ys [0.5666666666666668, 0.3, 0.13333333333333333]
Example 3: Solve with a custom guess

Inputs:

zs ks guess
0.4 0.4 0.2 1.9 0.82 0.45 0.5

Excel formula:

=LI_JOHNS_AHMADI({0.4,0.4,0.2}, {1.9,0.82,0.45}, 0.5)

Expected output:

Property Value
VF 0.561159
xs [0.26577314719086675, 0.44494307181957643, 0.2892837809895568]
ys [0.5049689796626468, 0.36485331889205264, 0.13017770144530058]
Example 4: Three-component mixture case

Inputs:

zs ks
0.2 0.5 0.3 3 0.9 0.2

Excel formula:

=LI_JOHNS_AHMADI({0.2,0.5,0.3}, {3,0.9,0.2})

Expected output:

Property Value
VF 0.128591
xs [0.1590859595994075, 0.5065133044595129, 0.33440073594107966]
ys [0.47725787879822246, 0.45586197401356165, 0.06688014718821593]

Python Code

Show Code 
from chemicals.rachford_rice import Li_Johns_Ahmadi_solution as chemicals_li_johns_ahmadi_solution

def li_johns_ahmadi(zs, ks, guess=None):
    """
    Solve the Li-Johns-Ahmadi flash equation for vapor fraction and phase compositions.

    See: https://chemicals.readthedocs.io/chemicals.rachford_rice.html#chemicals.rachford_rice.Li_Johns_Ahmadi_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 (-).
        guess (float, optional): Initial guess for the solution (-). 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_li_johns_ahmadi_solution(zs=z_vals, Ks=k_vals, 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 (-).
Initial guess for the solution (-).