def fugacity_coefficients(self, Z, zs):
        r'''Literature formula for calculating fugacity coefficients for each
        species in a mixture. Verified numerically.
        Called by `fugacities` on initialization, or by a solver routine 
        which is performing a flash calculation.
        
        .. math::
            \ln \hat \phi_i = \frac{b_i}{V-b} - \ln\left[Z\left(1
            - \frac{b}{V}\right)\right] - \frac{2\sqrt{aa_i}}{RTV}
        
        Parameters
        ----------
        Z : float
            Compressibility of the mixture for a desired phase, [-]
        zs : list[float], optional
            List of mole factions, either overall or in a specific phase, [-]
        
        Returns
        -------
        phis : float
            Fugacity coefficient for each species, [-]
                         
        References
        ----------
        .. [1] Walas, Stanley M. Phase Equilibria in Chemical Engineering. 
           Butterworth-Heinemann, 1985.
        '''
        phis = []
        V = Z*R*self.T/self.P
        for i in self.cmps:
            phi = self.bs[i]/(V-self.b) - log(Z*(1. - self.b/V)) - 2.*(self.a_alpha*self.ais[i])**0.5/(R*self.T*V)
            phis.append(exp(phi))
        return phis
def fugacity_coefficients(self, Z, zs):
        r'''Literature formula for calculating fugacity coefficients for each
        species in a mixture. Verified numerically.
        Called by `fugacities` on initialization, or by a solver routine 
        which is performing a flash calculation.
        
        .. math::
            \ln \hat \phi_i = \frac{b_i}{V-b} - \ln\left[Z\left(1
            - \frac{b}{V}\right)\right] - \frac{2\sqrt{aa_i}}{RTV}
        
        Parameters
        ----------
        Z : float
            Compressibility of the mixture for a desired phase, [-]
        zs : list[float], optional
            List of mole factions, either overall or in a specific phase, [-]
        
        Returns
        -------
        phis : float
            Fugacity coefficient for each species, [-]
                         
        References
        ----------
        .. [1] Walas, Stanley M. Phase Equilibria in Chemical Engineering. 
           Butterworth-Heinemann, 1985.
        '''
        phis = []
        V = Z*R*self.T/self.P
        for i in self.cmps:
            phi = self.bs[i]/(V-self.b) - log(Z*(1. - self.b/V)) - 2.*(self.a_alpha*self.ais[i])**0.5/(R*self.T*V)
            phis.append(exp(phi))
        return phis
def fugacity_coefficients ( self , Z , zs ) : phis = [ ] V = Z * R * self . T / self . P for i in self . cmps : phi = self . bs [ i ] / ( V - self . b ) - log ( Z * ( 1. - self . b / V ) ) - 2. * ( self . a_alpha * self . ais [ i ] ) ** 0.5 / ( R * self . T * V ) phis . append ( exp ( phi ) ) return phis
r'''Literature formula for calculating fugacity coefficients for each
        species in a mixture. Verified numerically.
        Called by `fugacities` on initialization, or by a solver routine 
        which is performing a flash calculation.
        
        .. math::
            \ln \hat \phi_i = \frac{b_i}{V-b} - \ln\left[Z\left(1
            - \frac{b}{V}\right)\right] - \frac{2\sqrt{aa_i}}{RTV}
        
        Parameters
        ----------
        Z : float
            Compressibility of the mixture for a desired phase, [-]
        zs : list[float], optional
            List of mole factions, either overall or in a specific phase, [-]
        
        Returns
        -------
        phis : float
            Fugacity coefficient for each species, [-]
                         
        References
        ----------
        .. [1] Walas, Stanley M. Phase Equilibria in Chemical Engineering. 
           Butterworth-Heinemann, 1985.
r Literature formula for calculating fugacity coefficients for each species in a mixture . Verified numerically . Called by fugacities on initialization or by a solver routine which is performing a flash calculation . .. math :: \ ln \ hat \ phi_i = \ frac { b_i } { V - b } - \ ln \ left [ Z \ left ( 1 - \ frac { b } { V } \ right ) \ right ] - \ frac { 2 \ sqrt { aa_i }} { RTV } Parameters ---------- Z : float Compressibility of the mixture for a desired phase [ - ] zs : list [ float ] optional List of mole factions either overall or in a specific phase [ - ] Returns ------- phis : float Fugacity coefficient for each species [ - ] References ---------- .. [ 1 ] Walas Stanley M . Phase Equilibria in Chemical Engineering . Butterworth - Heinemann 1985 .