A To calculate dew pressure of hydrocarbon mixture by PC-SAFT

AI Thread Summary
The discussion focuses on using the PC-SAFT method to calculate dew point pressures of hydrocarbon mixtures, where the bubble pressure calculations align well with experimental data, but the dew pressure calculations fail to converge. The user highlights the difference in fugacity calculations between bubble and dew pressures as a potential issue. Despite accurate bubble pressure results indicating correct internal parameters, the inability to compute dew pressure remains unresolved. The user seeks assistance and has shared code and screenshots to clarify their calculation algorithm. The thread emphasizes the complexities involved in applying the PC-SAFT method for phase envelope plotting.
yan3220
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Hello, everyone:
I'm trying to use the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) method to calculate the bubble point and dew point pressures of hydrocarbon mixtures, and subsequently plot the PT phase envelope. My calculations for bubble pressure match the experimental data very well. However, when calculating dew pressure at different temperatures, the program fails to converge. I understand that the difference between calculating bubble pressure and dew pressure lies in how the component compositions are determined through fugacity calculations. Therefore, if the bubble pressure calculations are very accurate, it indicates that the internal parameters of PC-SAFT are correct. So why can't the dew pressure be calculated at all?
I have attached the code for calculating dew pressure below.
I'm really hoping someone can offer me some help and advice. Thank you so much!



Code: 
def cal_VLE_dew_point(temperature, initial_system_pressure, component_mixture,pc_saft_para_dict,component_name,univeral_model_constant=univeral_model_constant):

    composition_liquid = component_mixture.copy()
    composition_vapor = component_mixture.copy()
    def wrapped_cal_pressure(initial_packing_fraction, temperature, component_mixture, pc_saft_para_dict, target_pressure):
        calculated_pressure = cal_pressure(initial_packing_fraction,temperature,univeral_model_constant,component_name, component_mixture, pc_saft_para_dict,boltzmann_constant = 1.3806*10**-23)
        return np.array(calculated_pressure, dtype=np.float64) - target_pressure
    iteration = 0
    error = 100
    vapor_packing_fraction = 10**-10
    liquid_packing_fraction = 0.5
    while (error > 0.00001) and iteration < 300:
        result = least_squares(wrapped_cal_pressure, liquid_packing_fraction, args=(temperature, composition_liquid, pc_saft_para_dict, initial_system_pressure), xtol=1e-12,ftol=1e-12,gtol=1e-12,max_nfev=50000) 
        liquid_packing_fraction = result.x 
        result = least_squares(wrapped_cal_pressure, vapor_packing_fraction, args=(temperature, composition_vapor, pc_saft_para_dict, initial_system_pressure), xtol=1e-12,ftol=1e-12,gtol=1e-12,max_nfev=50000) 
        vapor_packing_fraction = result.x



        fugacity_coefficient_liquid = cal_fugacity(liquid_packing_fraction, temperature, univeral_model_constant,component_name, composition_liquid, pc_saft_para_dict)
        fugacity_coefficient_vapor = cal_fugacity(vapor_packing_fraction, temperature, univeral_model_constant,component_name, composition_vapor, pc_saft_para_dict)

        update_liquid_compostion = {}
        total_composition_liquid = 0
        for i in component_name:
            update_liquid_compostion = fugacity_coefficient_vapor*composition_vapor/fugacity_coefficient_liquid
            total_composition_liquid += update_liquid_compostion
        for k,v in update_liquid_compostion.items():
            update_liquid_compostion[k] = update_liquid_compostion[k]/total_composition_liquid
        composition_liquid = update_liquid_compostion.copy()
        initial_system_pressure = total_composition_liquid * initial_system_pressure
        error = np.abs(total_composition_liquid - 1.0)
        iteration += 1
    dew_point_pressure = cal_pressure(liquid_packing_fraction,temperature, univeral_model_constant,component_name, composition_liquid, pc_saft_para_dict,boltzmann_constant = 1.3806*10**-23)

    return composition_liquid, composition_vapor, dew_point_pressure
 
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Rather than attaching the code, please provide the equations you used.
 
Thank you very much for your response. The PC-SAFT method has many formulas. Here, I have attached screenshots of my calculation algorithm in hopes that it will more clearly illustrate the problem I am encountering. Thank you.

1720785645594.png
 
can I get this report here please
 

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