Submodules¶

Fluid¶

class pythermophy.fluid.Fluid(name, M, Tc, pc, acentric, cp_coeffs)¶

Bases: object

Class for representing the fluid you want to study.

Parameters:

name (str) – name of the fluid
M (float) – molar mass of the fluid (kg/mol)
Tc (float) – critical temperature of the fluid (K)
pc (float) – critical pressure of the fluid (Pa)
acentric (float) – acentric factor of the fluid (dimensionless)
cp_coeffs (list(float)) – coefficients of the ideal gas isobaric heat capacity polynomial [a,b,c,d] $c_p = a + bT + cT^2 + dT^3$ ( $c_p$ in J/mol/K)

classmethod init_from_file(filename)¶

Creates a new Fluid instance by reading parameters from an input file.

The input file must be a yaml file in the following format:

name: CO2   # Name of the fluid
molar_mass: 44.01e-3    # Molar mass [kg/mol]
T_crit: 304.25  # Critical temperature [K]
p_crit: 7.38e+6 # Critical pressure [Pa]
acentric: 0.228 # Acentric factor [dimensionless]
ideal_cp_coeffs: [22.26, 5.981e-2, -3.501e-5, 7.469e-9] # Cp = a + b*T + c*T^2 + d*T^3 [J/mol/K]

Parameters:	filename (str) – input file

is_valid()¶

Checks if the Fluid instance is valid by ensuring that all the parameters of the object are of the correct type.

Returns:	True if valid. False otherwise.
Return type:	bool

save_to_file(filename)¶

Saves the Fluid instance to a yaml file which can later be fed to init_from_file().

Parameters:	filename (str) – output file

Parent EOS¶

class pythermophy.parent_class.EOS(fluid)¶

Bases: object

The parent equation of state (EOS) class. All the other EOS classes are derived from this.

Parameters:	fluid – a `Fluid` instance
Returns:	a `EOS` instance

R = 8.3144598¶

get_Z(T, p)¶

Returns the compressibility factor of the fluid.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	compressibility factor
Return type:	float

get_adiabatic_index(T, p, **kwargs)¶

Returns the adiabatic index (ratio between isobaric and isochoric heat capacities) for a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	adiabatic index (dimensionless)
Return type:	float

get_cp(T, p, **kwargs)¶

Returns the real gas isobaric specific heat capacity ( $c_p$ ) in J/mol/K.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	isobaric specific heat capacity (J/mol/K)
Return type:	float

get_cv(T, p, **kwargs)¶

Returns the real gas isochoric specific heat capacity ( $c_v$ ) in J/mol/K.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	isochoric specific heat capacity (J/mol/K)
Return type:	float

get_departure_cp(T, p)¶

Returns the departure (difference between real gas and ideal gas) of isobaric specific heat capacity ( $c_p$ ) in J/mol/K.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	departure for isobaric specific heat capacity (J/mol/K)
Return type:	float

get_departure_cv(T, p)¶

Returns the departure (difference between real gas and ideal gas) of isochoric specific heat capacity ( $c_v$ ) in J/mol/K.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	departure for isochoric specific heat capacity (J/mol/K)
Return type:	float

get_ideal_cp(T)¶

Returns the ideal gas isobaric specific heat capacity ( $c_p^0$ ) in J/mol/K. See http://www.wiley.com/college/moran/CL_0471465704_S/user/tables/TABLE3S/table3sframe.html

Parameters:	T (float) – temperature (K)
Returns:	ideal gas isobaric specific heat capacity (J/mol/K)
Return type:	float

get_ideal_cv(T)¶

Returns the ideal gas isochoric specific heat capacity ( $c_v^0$ ) in J/mol/K.

Parameters:	T (float) – temperature (K)
Returns:	ideal gas isochoric specific heat capacity (J/mol/K)
Return type:	float

get_rho(T, p, **kwargs)¶

Returns the density of the fluid.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)

get_speed_of_sound(T, p, **kwargs)¶

Returns the speed of sound in a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	speed of sound (m/s)
Return type:	float

Ideal Gas EOS¶

class pythermophy.ideal_gas.IdealGas(fluid)¶

Bases: pythermophy.parent_class.EOS

Ideal gas equation of state.

Parameters:	fluid – a `Fluid` instance
Returns:	an equation of state (`EOS`) instance

get_isothermal_compressibility(T, p, **kwargs)¶

Returns the isothermal compressibility of an ideal gas

Parameters:	T (float) – temperature (K) [only required for consistency with the same function for other classes; not used in computation] p (float) – pressure (Pa)
Returns:	isothermal compressibility (1/Pa)
Return type:	float

Parent Cubic EOS¶

class pythermophy.cubic_parent.CubicEOS(b, c, d, e, fluid)¶

Bases: pythermophy.parent_class.EOS

Parent class from which other cubic equations of state are derived.

The equation of state is expressed as:

$p = \frac{RT}{v - b + c} - \frac{a(T)}{v^2 + dv + e}$

where $(p, v, T)$ are the pressure, specific volume, and temperature respectively. $R$ is the specific gas constant, and $(a(T), b, c, d, e)$ are the coefficients of the cubic equation of state.

Parameters:	b (float) – coefficient $b$ c (float) – coefficient $c$ d (float) – coefficient $d$ e (float) – coefficient $e$ fluid – a `Fluid` instance
Returns:	a `EOS` instance

get_A(T, p)¶

Returns the coefficient $A$ of the cubic polynomial of compressiblity factor given by $Z^3 + A Z^2 + B Z + C = 0$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	$A$
Return type:	float

get_B(T, p)¶

Returns the coefficient $B$ of the cubic polynomial of compressiblity factor given by $Z^3 + A Z^2 + B Z + C = 0$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	$B$
Return type:	float

get_C(T, p)¶

Returns the coefficient $C$ of the cubic polynomial of compressiblity factor given by $Z^3 + A Z^2 + B Z + C = 0$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	$C$
Return type:	float

get_Z(T, p)¶

Returns the compressibility factor of a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	compressibility factor
Return type:	float

get_a(T)¶

Returns the temperature dependent coefficient $a(T)$ .

Function should be redefined in the child class.

get_departure_cp(T, p, **kwargs)¶

Returns the departure (difference between real gas and ideal gas) of isobaric specific heat capacity $c_p$ (J/mol/K)

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa) Z (float) – (optional kwarg) compressibility factor at (T, p). Computed by `get_Z()` if not provided.
Returns:	departure of isobaric specific heat capacity (J/mol/K)
Return type:	float

get_departure_cv(T, p, **kwargs)¶

Returns the departure (difference between real gas and ideal gas) for isochoric specific heat capacity ( $c_v$ ) in J/mol/K.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa) Z (float) – (optional kwarg) compressibility factor at (T, p). Computed by `get_Z()` if not provided.
Returns:	departure of isochoric specific heat capacity (J/mol/K)
Return type:	float

get_diff_a_T(T)¶

Returns the derivative of coefficient $a(T)$ wrt. temperature $T$ .

Function should be redefined in the child class.

get_double_diff_a_T(T)¶

Returns the second derivative of coefficient $a(T)$ wrt. temperature $T$ .

Function should be redefined in the child class.

get_isothermal_compressibility(T, p, **kwargs)¶

Returns the isothermal compressibility of a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	isothermal compressibility (1/Pa)
Return type:	float

get_pdiff_A_T_p(T, p)¶

Returns the partial derivative of coefficient $A$ wrt. $T$ at constant $p$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_A_p_T(T, p)¶

Returns the partial derivative of coefficient $A$ wrt. $p$ at constant $T$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_B_T_p(T, p)¶

Returns the partial derivative of coefficient $B$ wrt. $T$ at constant $p$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_B_p_T(T, p)¶

Returns the partial derivative of coefficient $B$ wrt. $p$ at constant $T$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_C_T_p(T, p)¶

Returns the partial derivative of coefficient $C$ wrt. $T$ at constant $p$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_C_p_T(T, p)¶

Returns the partial derivative of coefficient $C$ wrt. $p$ at constant $T$ .

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Return type:	float

get_pdiff_Z_T_p(T, p, **kwargs)¶

Returns the partial derivative of $Z$ wrt. $T$ at constant $p$ .

Parameters:	T (float) – temperature (K) p – pressure (Pa) Z (float) – (optional kwarg) compressibility factor at (T, p). Computed by `get_Z()` if not provided.
Return type:	float

get_pdiff_Z_p_T(T, p, **kwargs)¶

Returns the partial derivative of $Z$ wrt. $p$ at constant $T$ .

Parameters:	T (float) – temperature (K) p – pressure (Pa) Z (float) – (optional kwarg) compressibility factor at (T, p). Computed by `get_Z()` if not provided.
Return type:	float

Cubic EOS¶

class pythermophy.cubic_eos.PengRobinson(fluid)¶

Bases: pythermophy.cubic_parent.CubicEOS

Peng-Robinson equation of state. For details see: https://www.e-education.psu.edu/png520/m11_p2.html

Parameters:	fluid – a `Fluid` instance
Returns:	an `EOS` instance

get_a(T)¶: Returns the temperature dependent coefficient $a(T)$ .

get_diff_a_T(T)¶: Returns the derivative of coefficient $a(T)$ wrt. temperature $T$ .

get_double_diff_a_T(T)¶: Returns the second derivative of coefficient $a(T)$ wrt. temperature $T$ .

class pythermophy.cubic_eos.RedlichKwong(fluid)¶

Bases: pythermophy.cubic_parent.CubicEOS

Redlich-Kwong equation of state. For details see https://www.e-education.psu.edu/png520/m10_p4.html

Parameters:	fluid – a `Fluid` instance
Returns:	an `EOS` instance

get_a(T)¶: Returns the temperature dependent coefficient $a(T)$ .

get_diff_a_T(T)¶: Returns the derivative of coefficient $a(T)$ wrt. temperature $T$ .

get_double_diff_a_T(T)¶: Returns the second derivative of coefficient $a(T)$ wrt. temperature $T$ .

class pythermophy.cubic_eos.SoaveRedlichKwong(fluid)¶

Bases: pythermophy.cubic_parent.CubicEOS

Soave-Redlich-Kwong equation of state. For details see: https://www.e-education.psu.edu/png520/m10_p5.html

Parameters:	fluid – a `Fluid` instance
Returns:	an `EOS` instance

get_a(T)¶: Returns the temperature dependent coefficient $a(T)$ .

get_diff_a_T(T)¶: Returns the derivative of coefficient $a(T)$ wrt. temperature $T$ .

get_double_diff_a_T(T)¶: Returns the second derivative of coefficient $a(T)$ wrt. temperature $T$ .

Lee-Kesler EOS¶

class pythermophy.lee_kesler.LeeKesler(fluid)¶

Bases: pythermophy.parent_class.EOS

Lee-Kesler equation of state.

Parameters:	fluid – a `Fluid` instance
Returns:	a `EOS` instance

acentric_r = 0.3978¶

b1 = [0.1181193, 0.2026579]¶

b2 = [0.265728, 0.331511]¶

b3 = [0.15479, 0.027655]¶

b4 = [0.030323, 0.203488]¶

beta = [0.65392, 1.226]¶

c1 = [0.0236744, 0.0313385]¶

c2 = [0.0186984, 0.0503618]¶

c3 = [0.0, 0.016901]¶

c4 = [0.042724, 0.041577]¶

d1 = [1.55488e-05, 4.8736e-05]¶

d2 = [6.23689e-05, 7.40336e-06]¶

gamma = [0.060167, 0.03754]¶

get_B(Tr, fluid)¶

Returns $B(T_r) = b_1 - b_2/T_r - b_3/T_r^2 - b_4/T_r^3$ .

Parameters:	Tr (float) – reduced temperature ( $T_r = T/T_c$ ) fluid (str) – specifies if the fluid is simple or reference
Returns:	$B(T_r)$
Return type:	float

get_C(Tr, fluid)¶

Returns $C(T_r) = c_1 - c_2/T_r + c_3/T_r^3$ .

Parameters:	Tr (float) – reduced temperature ( $T_r = T/T_c$ ) fluid (str) – specifies if the fluid is simple or reference
Returns:	$C(T_r)$
Return type:	float

get_D(Tr, fluid)¶

Returns $D(T_r) = d_1 + c_2/T_r$ .

Parameters:	Tr (float) – reduced temperature ( $T_r = T/T_c$ ) fluid (str) – specifies if the fluid is simple or reference
Returns:	$D(T_r)$
Return type:	float

get_Z(T, p, **kwargs)¶

Returns the compressibility factor of a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa) init_vol (list(float)) – (optional kwarg) initial guess for reduced volumes of ideal and reference fluids to be used in the nonlinear equation solver in `get_reduced_volume()`. Should be a list [v0, vr], where v0 is the inital guess for the simple fluid, and vr is the initial guess for the reference fluid.
Returns:	compressibility factor
Return type:	float

get_departure_cp(T, p)¶

Returns the departure (difference between real gas and ideal gas) of isobaric specific heat capacity $c_p$ (J/mol/K)

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	departure of isobaric specific heat capacity (J/mol/K)
Return type:	float

get_departure_cp_aux(Tr, pr, fluid)¶

Auxiliary function used by get_departure_cp().

Computes the departure in isobaric specific heat capacity for simple and reference fluids.

Parameters:	Tr (float) – reduced temperature pr (float) – reduced pressure fluid (str) – specifices if the fluid is simple or reference

get_departure_cv(T, p)¶

Returns the departure (difference between real gas and ideal gas) of isochoric specific heat capacity $c_v$ (J/mol/K)

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	departure of isochoric specific heat capacity (J/mol/K)
Return type:	float

get_departure_cv_aux(Tr, pr, fluid, **kwargs)¶

Auxiliary function used by get_departure_cv().

Computes the departure in isochoric specific heat capacity for simple and reference fluids.

Parameters:	Tr (float) – reduced temperature pr (float) – reduced pressure fluid (str) – specifices if the fluid is simple or reference Vr (float) – (optional kwarg) reduced volume at (Tr, pr). If not provided, `get_reduced_volume()` is used to compute it.

get_isothermal_compressibility(T, p)¶

Returns the isothermal compressibility of a real gas.

Parameters:	T (float) – temperature (K) p (float) – pressure (Pa)
Returns:	isothermal compressibility (1/Pa)
Return type:	float

get_pdiff_pr_Tr_Vr(Tr, Vr, fluid)¶

Returns the partial derivative of $p_r$ wrt. $T_r$ at constant $v_r$ .

Parameters:	Tr (float) – reduced temperature Vr (float) – reduced volume fluid (str) – specifices if the fluid is simple or reference
Return type:	float

get_pdiff_pr_Vr_Tr(Tr, Vr, fluid)¶

Returns the partial derivative of $p_r$ wrt. $V_r$ at constant $T_r$ .

Parameters:	Tr (float) – reduced temperature Vr (float) – reduced volume fluid (str) – specifices if the fluid is simple or reference
Return type:	float

get_reduced_volume(Tr, pr, fluid, **kwargs)¶

Returns the reduced volume $v_r$ .

This is done by solving the following nonlinear equation:

$\frac{p_r v_r}{T_r} = 1 + \frac{B(T_r)}{v_r} + \frac{C(T_r)}{v_r^2} + \frac{D(T_r)}{v_r^5} + \frac{c_4}{T_r^3 v_r^2} (\beta + \frac{\gamma}{v_r^2}) \exp(-\frac{\gamma}{v_r^2})$

Parameters:	Tr (float) – reduced temperature ( $T_r = T/T_c$ ) pr (float) – reduced pressure ( $p_r = p/p_c$ ) fluid (str) – specifies if the fluid is simple or reference init_vol (float) – (optional kwarg) initial guess for reduced volume to be used in the nonlinear solver
Returns:	reduced volume
Return type:	float