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Heat Capacity

class scithermo.cp.CpIdealGas(dippr_no: str = None, compound_name: str = None, cas_number: str = None, T_min_fit: float = None, T_max_fit: float = None, n_points_fit: int = 1000, poly_order: int = 2, T_units='K', Cp_units='J/mol/K')

Heat Capacity \(C_{\mathrm{p}}^{\mathrm{IG}}\) [J/mol/K] at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions [RWO+07]

(1)\[C_{\mathrm{p}}^{\mathrm{IG}} = C_1 + C_2\left[\frac{C_3/T}{\sinh{(C_3/T)}}\right] + C_4 \left[\frac{C_5/T}{\cosh{(C_5/T)}}\right]^2\]

where \(C_{\mathrm{p}}^{\mathrm{IG}}\) is in J/mol/K and \(T\) is in K.

Computing integrals of Equation (1) is challenging. Instead, the function is fit to a polynomial within a range of interest so that it can be integrated by using an antiderivative that is a polynomial.

Parameters

• dippr_no (str, optional) – dippr_no of compound by DIPPR table, defaults to None

• compound_name (str, optional) – name of chemical compound, defaults to None

• cas_number (str, optional) – CAS registry number for chemical compound, defaults to None

• MW (float, derived from input) – molecular weight in g/mol

• T_min (float, derived from input) – minimum temperature of validity for relationship [K]

• T_max (float, derived from input) – maximum temperature of validity [K]

• T_min_fit – minimum temperature for fitting, defaults to Tmin

• T_max_fit – maximum temperature for fitting, defaults to Tmax

• C1 (float, derived from input) – parameter in Equation (1)

• C2 (float, derived from input) – parameter in Equation (1)

• C3 (float, derived from input) – parameter in Equation (1)

• C4 (float, derived from input) – parameter in Equation (1)

• C5 (float, derived from input) – parameter in Equation (1)

• Cp_units (str, optional) – units for \(C_{\mathrm{p}}^{\mathrm{IG}}\), defaults to J/mol/K

• T_units (str, optional) – units for \(T\), defaults to K

• n_points_fit (int, optional) – number of points for fitting polynomial and plotting, defaults to 1000

• poly_order (int, optional) – order of polynomial for fitting, defaults to 2

cp_integral(T_a, T_b)

(2)\[\int_{T_a}^{T_b}C_{\mathrm{p}}^{\mathrm{IG}}(T^\prime) \mathrm{d}T^\prime\]

Parameters

• T_a – start temperature in K

• T_b – finish temperature in K

Returns

integral

eval(T, f_sinh=<ufunc 'sinh'>, f_cosh=<ufunc 'cosh'>)

Parameters

• T – temperature in K

• f_sinh (callable) – function for hyperbolic sine, defaults to np.sinh

• f_cosh (callable) – function for hyperbolic cosine, defaults to np.cosh

Returns

\(C_{\mathrm{p}}^{\mathrm{IG}}\) J/mol/K (see equation (1))

get_numerical_percent_difference()

Calculate the percent difference with numerical integration obtained by scipy

numerical_integration(T_a, T_b) → tuple

Numerical integration using scipy

class scithermo.cp.CpStar(T_ref: float, **kwargs)

Dimensionless Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions [RWO+07]

The dimensionless form is obtained by introducing the following variables

\[\begin{split}\begin{align} C_{\mathrm{p}}^\star &= \frac{C_\mathrm{p}^\mathrm{IG}}{\text{R}} \\ T^\star &= \frac{T}{T_\text{ref}} \end{align}\end{split}\]

where R is the gas constant in units of J/mol/K, and \(T_\text{ref}\) is a reference temperature [K] input by the user (see T_ref)

The heat capacity in dimensionless form becomes

(3)\[C_{\mathrm{p}}^\star = C_1^\star + C_2^\star \left[\frac{C_3^\star/T^\star}{\sinh{(C_3^\star/T^\star)}}\right] + C_4^\star \left[\frac{C_5^\star/T^\star}{\cosh{(C_5^\star/T^\star)}}\right]^2\]

where

\[\begin{split}\begin{align} C_1^\star &= \frac{C_1}{\text{R}} \\ C_2^\star &= \frac{C_2}{\text{R}} \\ C_3^\star &= \frac{C_3}{T_\text{ref}} \\ C_4^\star &= \frac{C_4}{\text{R}} \\ C_5^\star &= \frac{C_5}{T_\text{ref}} \end{align}\end{split}\]

Parameters

T_ref (float) – reference temperature [K] for dimensionless computations

eval(T, f_sinh=<ufunc 'sinh'>, f_cosh=<ufunc 'cosh'>)

Parameters

• T – temperature in K

• f_sinh (callable) – function for hyperbolic sine, defaults to np.sinh

• f_cosh (callable) – function for hyperbolic cosine, defaults to np.cosh

Returns

\(C_{\mathrm{p}}^{\star}\) [dimensionless] (see equation (3))

class scithermo.cp.CpRawData(T_raw: list, Cp_raw: list, T_min_fit: float = None, T_max_fit: float = None, poly_order: int = 2, T_units='K', Cp_units='J/mol/K')

From raw data for Cp(T) * fit to polynomial of temperature * fit polynomial to antiderivative

Parameters

• T_min_fit (float, optional) – minimum temperature for fitting function [K]

• T_max_fit (float, optional) – maximum temperature for fitting function [K]

• poly_order (int, optional) – order of polynomial for fitting, defaults to 2

• T_raw (list) – raw temperatures in K

• Cp_raw (list) – raw heat capacities in J/K/mol

• Cp_units (str, optional) – units for \(C_{\mathrm{p}}\), defaults to J/mol/K

• T_units (str, optional) – units for \(T\), defaults to K

get_max_percent_difference()

Get largest percent difference

Critical Properties

class scithermo.critical_constants.CriticalConstants(dippr_no: str = None, compound_name: str = None, cas_number: str = None, **kwargs)

Get critical constants of a compound

If critical constants are not passed in, reads from DIPPR table

Parameters

• dippr_no (str, optional) – dippr_no of compound by DIPPR table, defaults to None

• compound_name (str, optional) – name of chemical compound, defaults to None

• cas_number (str, optional) – CAS registry number for chemical compound, defaults to None

• MW (float, derived from input) – molecular weight in g/mol

• T_c (float, derived from input) – critical temperature [K]

• P_c (float, derived from input) – critical pressure [Pa]

• V_c (float, derived from input) – critical molar volume [m^3/mol]

• Z_c (float, derived from input) – critical compressibility factor [dimensionless]

• w (float, derived from input) – accentric factor [dimensionless]

• tol (float, hard-coded) – tolerance for percent difference in Zc calulcated and tabulated, set to 0.5

Z_c_percent_difference()

calculate percent difference between Z_c calculated and tabulated

calc_Z_c()

Calculate critical compressibility, for comparison to tabulated value

class scithermo.critical_constants.CriticalConstants(dippr_no: str = None, compound_name: str = None, cas_number: str = None, **kwargs)

Get critical constants of a compound

If critical constants are not passed in, reads from DIPPR table

Parameters

• dippr_no (str, optional) – dippr_no of compound by DIPPR table, defaults to None

• compound_name (str, optional) – name of chemical compound, defaults to None

• cas_number (str, optional) – CAS registry number for chemical compound, defaults to None

• MW (float, derived from input) – molecular weight in g/mol

• T_c (float, derived from input) – critical temperature [K]

• P_c (float, derived from input) – critical pressure [Pa]

• V_c (float, derived from input) – critical molar volume [m^3/mol]

• Z_c (float, derived from input) – critical compressibility factor [dimensionless]

• w (float, derived from input) – accentric factor [dimensionless]

• tol (float, hard-coded) – tolerance for percent difference in Zc calulcated and tabulated, set to 0.5

Z_c_percent_difference()

calculate percent difference between Z_c calculated and tabulated

calc_Z_c()

Calculate critical compressibility, for comparison to tabulated value

Virial Equation of State

class scithermo.eos.virial.Virial(pow: callable = <ufunc 'power'>, exp: callable = <ufunc 'exp'>)

Parameters

• R (float, hard-coded) – gas constant, set to SI units

• pow (callable, optional) – function for computing power, defaults to numpy.power

• exp (callable, optional) – function for computing logarithm, defaults to numpy.exp

d_B0_d_Tr_expr(T_r)

\[\frac{\mathrm{d} B^0}{\mathrm{d}T_\mathrm{r}}\]

d_B1_d_Tr_expr(T_r)

\[\frac{\mathrm{d} B^1}{\mathrm{d}T_\mathrm{r}}\]

hat_phi_i_expr(*args)

expression for fugacity coefficient

class scithermo.eos.virial.SecondVirial(dippr_no: str = None, compound_name: str = None, cas_number: str = None, pow: callable = <ufunc 'power'>, **kwargs)

Virial equation of state for one component. See [GP07][SVanNessA05]

G_R_RT_expr(P, T)

Dimensionless residual gibbs

\[\frac{G^\mathrm{R}}{RT} = (B^0 + \omega B^1)\frac{P_\mathrm{r}}{T_\mathrm{r}}\]

Returns

Expression for residual gibbs free (divided by RT) – dimensionless

H_R_RT_expr(P, T)

Dimensionless residual enthalpy

\[\frac{H^\mathrm{R}}{RT} = P_\mathrm{r}\left[ \frac{B^0}{T_\mathrm{r}} - \frac{\mathrm{d} B^0}{\mathrm{d}T_\mathrm{r}} + \omega\left(\frac{B^1}{T_\mathrm{r}} - \frac{\mathrm{d}B^1}{\mathrm{d}T_\mathrm{r}}\right) \right]\]

Returns

Expression for residual enthalpy (divided by RT) – dimensionless

S_R_R_expr(P, T)

Dimensionless residual entropy

\[\frac{S^\mathrm{R}}{R} = -P_\mathrm{r}\left( \frac{\mathrm{d} B^0}{\mathrm{d}T_\mathrm{r}} + \omega\frac{\mathrm{d}B^1}{\mathrm{d}T_\mathrm{r}} \right)\]

Returns

Expression for residual entropy (divided by R) – dimensionless

ln_hat_phi_i_expr(P, T)

logarithm of fugacity coefficient

Note

single-component version

\[\ln\hat{\phi}_i = \frac{PB}{RT}\]

Parameters

• P (float) – pressure in Pa

• T (float) – temperature in K

plot_Z_vs_P(T, P_min, P_max, symbol='o', ax=None, **kwargs)

Plot compressibility as a function of pressure

Parameters

• T (float) – temperature [K]

• P_min (float) – minimum pressure for plotting [Pa]

• P_max (float) – maximum pressure for plotting [Pa]

• phase (str) – phase type (liquid or vapor), defaults to vapor

• symbol (str) – marker symbol, defaults to ‘o’

• ax (plt.axis) – matplotlib axes for plotting, defaults to None

• kwargs – keyword arguments for plotting

class scithermo.eos.virial.BinarySecondVirial(i_kwargs=None, j_kwargs=None, k_ij=0.0, pow: callable = <ufunc 'power'>, exp: callable = <ufunc 'exp'>)

Second virial with combining rules from [PLdeAzevedo86]

\[\begin{split}\begin{align} w_{ij} &= \frac{w_i + w_j}{2} \\ T_{\mathrm{c},ij} &= \sqrt{T_{\mathrm{c},i}T_{\mathrm{c},j}}(1-k_{ij}) :label:eq_Tcij\\ P_{\mathrm{c},ij} &= \frac{Z_{\mathrm{c},ij}RT_{\mathrm{c},ij}}{V_{\mathrm{c},ij}} \\ \end{align}\end{split}\]

where

\[\begin{split}\begin{align} Z_{\mathrm{c},ij} &= \frac{Z_{\mathrm{c},i} + Z_{\mathrm{c},j}}{2} \\\ V_{\mathrm{c},ij} &= \left(\frac{V_{\mathrm{c},i}^{1/3} + V_{\mathrm{c},j}^{1/3}}{2}\right)^{3} \end{align}\end{split}\]

Parameters

• k_ij (float) – equation of state mixing rule in calculation of critical temperautre, see Equation eq_Tcij. When \(i=j\) and for chemical similar species, \(k_{ij}=0\). Otherwise, it is a small (usually) positive number evaluated from minimal \(PVT\) data or, in the absence of data, set equal to zero.

• cas_pairs (list(tuple(str))) – pairs of cas registry numbers, derived from cas_numbers calculated

• other_cas (dict) – map from one cas number to other

B_ij_expr(cas_1, cas_2, T)

Returns \(B_{ij}\) considering that i=j or i!=j

If i=j, find the component \(k\) for which k=i=j (all cas no’s equal). Then return \(B_{kk}\) where

\[B_{kk}=\frac{RT_{\mathrm{c},k}}{P_{\mathrm{c},k}}\left[ B^0\left(\frac{T}{T_{\mathrm{c},k}}\right) + \omega_k\left(\frac{T}{T_{\mathrm{c},k}}\right) \right]\]

Otherwise, if i!=j, return \(B_{ij}\), where

\[B_{ij}=\frac{RT_{\mathrm{c},ij}}{P_{\mathrm{c},ij}}\left[ B^0\left(\frac{T}{T_{\mathrm{c},ij}}\right) + \omega_{ij}\left(\frac{T}{T_{\mathrm{c},ij}}\right) \right]\]

This is implemented in a simplified fashion usintg BinarySecondVirial.get_w_Tc_Pc() and then calling the generic expression for \(B\)

Parameters

• cas_1 (str) – cas number of first component

• cas_2 (str) – cas number of second component

• T – temperature [K]

B_mix_expr(y_k, T)

Parameters

• y_k (dict[cas_numbers, float]) – mole fractions of each component \(k\)

• T – temperature in K

Returns

\(B\) [m^3/mol], where \(Z = 1 + BP/R/T\)

G_R_RT(*args)

Residual free energy of mixture \(G^\mathrm{R}\)

H_R_RT(*args)

Residual enthalpy of mixture \(H^\mathrm{R}\)

S_R_R(*args)

Residual entropy of mixture \(S^\mathrm{R}\)

Tstar_d_lnphi_dTstar(cas_i, y_i, P, T)

Returns

\[\begin{split}\begin{align} T^\star \frac{\partial \ln{\hat{\phi}_i}}{\partial T^\star} &= \frac{T T_\text{ref}}{T_\text{ref}}\frac{\partial \ln{\hat{\phi}_i}}{\partial T} = \frac{T}{T_\text{c}}\frac{\partial \ln{\hat{\phi}_i}}{\partial T_\text{r}} \\ &= \frac{T}{T_\text{c}}\left[ \frac{P}{RT}\left( \frac{\partial B_{ii}}{\partial T_r} + (1-y_i)^2\frac{\partial \delta_{ij}}{\partial T_r} \right) - \frac{T_c\ln\hat{\phi}_i}{T} \right] \\ &= \frac{P}{R T_\text{c}}\left( \frac{\partial B_{ii}}{\partial T_r} + (1-y_i)^2\frac{\partial \delta_{ij}}{\partial T_r} \right) - \ln\hat{\phi}_i \\ &= -\frac{\bar{H}_i^\text{R}}{RT} \end{align}\end{split}\]

where \(\frac{\partial \delta_{ij}}{\partial T_r}\) is given by (3)

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

X_R_dimensionless(method: callable, cas_i: str, y_i: float, P: float, T: float)

Residual property of \(X\) for mixture.

Parameters

method (callable) – function to compute partial molar property of compound

bar_GiR_RT(*args)

Dimensionless residual partial molar free energy of component \(i\)

(1)\[\frac{\bar{G}^\mathrm{R}_i}{RT} = \ln\hat{\phi}_i\]

bar_HiR_RT(cas_i, y_i, P, T)

Dimensionless residual partial molar enthalpy of component \(i\)

\[\begin{split}\begin{align} \frac{\bar{H}^\mathrm{R}_i}{RT} &= -T \left(\frac{\partial \ln\hat{\phi}_i}{\partial T}\right)_{P,y} \\ &= - \frac{T}{T_c} \left(\frac{\partial \ln\hat{\phi}_i}{\partial T_r}\right)_{P,y} \\ &= - \frac{T}{T_c}\left( \frac{P}{RT}\left[ \frac{\partial B_{ii}}{\partial T_r} + (1-y_i)^2\frac{\partial \delta_{ij}}{\partial T_r} \right] - \frac{T_c\ln\hat{\phi}_i}{T} \right) \end{align}\end{split}\]

where \(\frac{\partial \delta_{ij}}{\partial T_r}\) is given by (3) so that we obtain

(2)\[\frac{\bar{H}^\mathrm{R}_i}{RT} = -\frac{P}{RT_c}\left[ \frac{\partial B_{ii}}{\partial T_r} + (1-y_i)^2\frac{\partial \delta_{ij}}{\partial T_r} \right] + \ln\hat{\phi}_i\]

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

bar_SiR_R(cas_i, y_i, P, T)

Dimensionless residual partial molar entropy of component \(i\)

Since

\[G^\mathrm{R} = H^\mathrm{R} - T S^\mathrm{R}\]

In terms of partial molar properties, then

\[\begin{split}\begin{align} \bar{S}_i^\mathrm{R} &= \frac{\bar{H}_i^\mathrm{R} - \bar{G}_i^\mathrm{R}}{T} \\ \frac{\bar{S}_i^\mathrm{R}}{R} &= \frac{\bar{H}_i^\mathrm{R}}{RT} - \frac{\bar{G}_i^\mathrm{R}}{RT} \\ \end{align}\end{split}\]

By comparing Equation (1) and (2) it is observed that

\[\frac{\bar{S}_i^\mathrm{R}}{R} = -\frac{P}{RT_c}\left[ \frac{\partial B_{ii}}{\partial T_r} + (1-y_i)^2\frac{\partial \delta_{ij}}{\partial T_r} \right]\]

where \(\frac{\partial \delta_{ij}}{\partial T_r}\) is given by (3)

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

bar_ViR_RT(cas_i, y_i, P, T)

residual Partial molar volume for component i

\[\begin{split}\begin{align} \frac{\bar{V}_i^\mathrm{R}}{RT} &= \left(\frac{\partial \ln\hat{\phi}_i}{\partial P}\right)_{T,y}\\ &= \frac{B_{ii} + (1-y_i)^2\delta_{ij}}{RT} \end{align}\end{split}\]

Note

This expression does not depend on \(P\)

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

Returns

\(\bar{V}_i^\mathrm{R}/R/T\)

calc_Z(y_k, P, T)

Parameters

• y_k (dict) – mole fractions of each component \(k\)

• P – pressure in Pa

• T – temperature in K

Returns

\(Z\) [mol/m^3], where \(Z = 1 + BP/R/T\)

d_dij_d_Tr(T)

(3)\[\frac{\partial \delta_{ij}}{\partial T_r} = 2\frac{\partial B_{ij}}{\partial T_r}-\frac{\partial B_{ii}}{\partial T_r}-\frac{\partial B_{jj}}{\partial T_r}\]

Parameters

T – temperature [K]

d_ij_expr(T)

(4)\[\delta_{ij} = 2B_{ij} - B_{ii} - B_{jj}\]

Parameters

T – temperature [K]

Returns

\(\delta_{ij}\) [m**3/mol]

fugacity_i_expr(cas_i, y_i, P, T)

Fugacity of component i in mixture \(f_i=\hat{\phi}_i y_i P\)

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

get_w_Tc_Pc(cas_i, cas_j=None)

Returns critical constants for calculation based off of whetner i = j or not

Returns

(\(w\), \(T_c\), \(P_c\))

Return type

tuple

ln_hat_phi_i_expr(cas_i, y_i, P, T)

logarithm of fugacity coefficient

\[\ln\hat{\phi}_i = \frac{P}{RT}\left[B_{ii} + (1-y_i)^2\delta_{ij}\right]\]

Parameters

• cas_i (str) – cas number for component of interest

• y_i (float) – mole fraction of component of interest

• P (float) – pressure in Pa

• T (float) – temperature in K

where \(\delta_{ij}\) is given by Equation (4)

Cubic Equation of State

class scithermo.eos.cubic.Cubic(sigma: float, epsilon: float, Omega: float, Psi: float, dippr_no: str = None, compound_name: str = None, cas_number: str = None, **kwargs)

Generic Cubic Equation of State Defined as in [GP07]

\[P = \frac{RT}{V - b} - \frac{a(T)}{(V + \epsilon b)(V + \sigma b)}\]

where \(\epsilon\) and \(\sigma\) are pure numbers–the same for all substances. \(a(T)\) and \(b\) are substance-dependent.

Parameters

• R (float, hard-coded) – gas constant, set to SI units

• sigma (float) – Parameter defined by specific equation of state, \(\sigma\)

• epsilon (float) – Parameter defined by specific equation of state, \(\epsilon\)

• Omega (float) – Parameter defined by specific equation of state, \(\Omega\)

• Psi (float) – Parameter defined by specific equation of state, \(\Psi\)

• tol (float) – tolerance for percent difference between compressilibity factor calculated iteratively, set to 0.01

G_R_RT_expr(P, V, T, log=None)

Dimensionless residual gibbs

\[\frac{G^\mathrm{R}}{RT} = Z - 1 + \ln(Z-\beta) - qI\]

Returns

Expression for residual gibbs free (divided by RT) – dimensionless

H_R_RT_expr(P, V, T, log=None)

Dimensionless residual enthalpy

\[\frac{H^\mathrm{R}}{RT} = Z - 1 + \left[\frac{\mathrm{d} \ln \alpha(T_\mathrm{r})}{\mathrm{d} \ln T_\mathrm{r}} - 1\right]qI\]

Returns

Expression for residual enthalpy (divided by RT) – dimensionless

H_expr(P, V, T, T_ref, val_ref=0.0, log=None)

Expression for fluid enthalpy

Parameters

• P – pressure in Pa

• V – molar volume [m**3/mol]

• T – temperautre in K

• T_ref – reference temperature in K

• val_ref – value at reference temperature [J/mol/K]

• log – function used for logarithm

Returns

\(H\) [J/mol/K]

I_expr(P, V, T, log=None)

\[I = \frac{1}{\sigma - \epsilon}\ln{\left( \frac{Z + \sigma \beta}{Z + \epsilon \beta} \right)}\]

Parameters

log (callable, optional) – function to be used for natural logarithm, defaults to np.log

S_R_R_expr(P, V, T, log=None)

Dimensionless residual entropy

\[\frac{S^\mathrm{R}}{R} = \ln(Z-\beta) + \frac{\mathrm{d} \ln \alpha(T_\mathrm{r})}{\mathrm{d} \ln T_\mathrm{r}} qI\]

Returns

Expression for residual entropy (divided by R) – dimensionless

Z_liquid_RHS(Z, beta, q)

Compressibility of vapor [GP07]

(1)\[\beta + (Z + \epsilon\beta)(Z + \sigma\beta)\left(\frac{1 + \beta - Z}{q\beta}\right)\]

Z_vapor_RHS(Z, beta, q)

Compressibility of vapor [GP07]

(2)\[1 + \beta - \frac{q\beta (Z - \beta)}{(Z + \epsilon\beta)(Z + \sigma\beta)}\]

Returns

a_expr(T)

\[a(T) = \Psi \frac{\alpha(T_r)R^2T_{\mathrm{c}}^2}{P_{\mathrm{c}}}\]

Parameters

T – temperautre in K

alpha_expr(T_r)

An empirical expression, specific to a particular form of the equation of state

Parameters

T_r – reduced temperature (T/Tc), dimensionless

Returns

\(\alpha (T_r)\)

beta_expr(T, P)

\[\beta = \Omega\frac{P_\mathrm{r}}{T_\mathrm{r}}\]

Parameters

• T – temperature in K

• P – pressure in Pa

Returns

\(\beta\)

cardano_constants(T, P)

Parameters

• T – temperature [T]

• P – pressure [Pa]

Returns

cardano constants p, q

Return type

tuple

coefficients(T, P)

Polynomial oefficients for cubic equation of state

\[Z^3 c_0 + Z^2c_1 + Z*c_2 + c_3 = 0\]

Returns

(c_0, c_1, c_2, c_3)

d_ln_alpha_d_ln_Tr(T_r)

Parameters

T_r – reduced temperature [dimensionless]

Returns

Expression for \(\frac{\mathrm{d} \ln \alpha(T_\mathrm{r})}{\mathrm{d} \ln T_\mathrm{r}}\)

iterate_to_solve_Z(T, P, phase) → float

Parameters

• T – temperature in K

• P – pressure in Pa

• phase (str) – phase [vapor or liquid]

Returns

compressibility factor

num_roots(T, P)

Find number of roots

See [ML12][Dei02]

Parameters

• T – temperature in K

• P – pressure in Pa

Returns

number of roots

plot_Z_vs_P(T, P_min, P_max, phase='vapor', symbol='o', ax=None, **kwargs)

Plot compressibility as a function of pressure

Parameters

• T (float) – temperature [K]

• P_min (float) – minimum pressure for plotting [Pa]

• P_max (float) – maximum pressure for plotting [Pa]

• phase (str) – phase type (liquid or vapor), defaults to vapor

• symbol (str) – marker symbol, defaults to ‘o’

• ax (plt.axis) – matplotlib axes for plotting, defaults to None

• kwargs – keyword arguments for plotting

print_roots(T, P)

Check to see if all conditions have one root

q_expr(T)

\[q = \frac{\Psi \alpha(T_\mathrm{r})}{\Omega T_\mathrm{r}}\]

Parameters

T – temperautre in K

residual(P, V, T)

Parameters

• P – pressure in Pa

• V – volume in [mol/m**3]

• T – temperature in K

Returns

residual for cubic equation of state

class scithermo.eos.cubic.RedlichKwong(**kwargs)

Redlich-Kwong Equation of State [RK49]

alpha_expr(T_r)

An empirical expression, specific to a particular form of the equation of state

Parameters

T_r – reduced temperature (T/Tc), dimensionless

Returns

\(\alpha (T_r)\)

d_ln_alpha_d_ln_Tr(T_r)

Parameters

T_r – reduced temperature [dimensionless]

Returns

Expression for \(\frac{\mathrm{d} \ln \alpha(T_\mathrm{r})}{\mathrm{d} \ln T_\mathrm{r}}\)

class scithermo.eos.cubic.SoaveRedlichKwong(**kwargs)

Soave Redlich-Kwong Equation of State [Soa72]

Parameters

f_w (float, derived) – empirical expression used in \(\alpha\) [dimensionless?]

alpha_expr(T_r)

An empirical expression, specific to a particular form of the equation of state

Parameters

T_r – reduced temperature (T/Tc), dimensionless

Returns

\(\alpha (T_r)\)

d_ln_alpha_d_ln_Tr(T_r)

Parameters

T_r – reduced temperature [dimensionless]

Returns

Expression for \(\frac{\mathrm{d} \ln \alpha(T_\mathrm{r})}{\mathrm{d} \ln T_\mathrm{r}}\)

class scithermo.eos.cubic.PengRobinson(**kwargs)

Peng-Robinson Equation of State [PR76]

Parameters

f_w (float, derived) – empirical expression used in \(\alpha\) [dimensionless?]

Vapor Thermal Conductivity

Vapor Viscosity

References

Dei02

U K Deiters. Calculation of Densities from Cubic Equations of State. AIChE J., 48:882–886, 2002.

GP07

D W Green and R H Perry. Perry’s Chemical Engineers’ Handbook. McGraw-Hill Professional Publishing, 8th edition, 2007.

ML12

R Monroy-Loperena. A Note on the Analytical Solution of Cubic Equations of State in Process Simulation. Ind. Eng. Chem. Res., 51:6972–6976, 2012. doi:10.1021/ie2023004.

PR76

D-Y Peng and D B Robinson. A New Two-Constant Equation of State. Ind. Eng. Chem., Fundam., 15:59–64, 1976.

PLdeAzevedo86

J Prausnitz, R N Lichtenthaler, and E G de Azevedo. Molecular Thermodynamics of Fluid-Phase Equilibria, pages 132,162. Prentice-Hall, Englewood Cliffs, NJ, 2nd edition, 1986.

RK49

O Redlich and J N S Kwong. On the Thermodynamics of Solutions. V: An Equation of State. Fugacities of Gaseous Solutions. Chem. Rev., 44:233–244, 1949.

RWO+07

R L Rowley, W V Wilding, J L Oscarson, Y Yang, N A Zundel, T E Daubert, and R P Danner. DIPPR$^\mathrm ®$ Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties. In Design Institute for Physical Properties of the American Institute of Chemical Engineers. AIChE, New York, 2007.

SVanNessA05

J M Smith, H C Van Ness, and M M Abbott. Introduction to Chemical Engineering Thermodynamics. McGraw-Hill, 7th edition, 2005.

Soa72

G Soave. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci., 27:1197–1203, 1972.

Indices and tables

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