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Getting started - Python

This is a short introduction to thermopack. Once you’ve gotten started, we recommend a look at the Examples in the GitHub repo. Comprehensive documentation for the methods available through the python interface can also be found in the doc page for the thermo class.. For more advanced users, a look at the more advanced page may also be useful.

Note: This guide applies to the most recent version of ThermoPack og GitHub. For guides applicable to versions found on PyPI, find the appropriate version in the sidebar on the ThermoPack homepage.

Equations of State (EoS’s) in ThermoPack are classes. To do calculations for a given mixture an EoS object must first be initialized for that mixture, as demonstrated in the Initializing an EoS section. Then, a wide variety of thermodynamic computations can be done, as demonstrated in the remaining sections.

Contents

Initialising an equation of state

An overview of available equations of state can be found here.

An EoS is initialized by passing in the fluid identifiers of the mixture, for example

from thermopack.saftvrmie import saftvrmie
eos = saftvrmie('C1,CO2')

will initialize a SAFT-VR Mie EoS for a mixture of methane and CO2. The complete list of component identifiers is in the Fluid identifiers list. PC-SAFT, SAFT-VRQ Mie and Lee-Kesler EoS are initialized in the same way, as

from thermopack import saftvrmie, saftvrqmie, pcsaft, lee_kesler
svrm = saftvrmie.saftvrmie('AR,KR') # SAFT-VR Mie EoS for Ar/Kr mixture
svrqm = saftvrqmie.saftvrqmie('HE') # SAFT-VRQ Mie EoS for pure He
pcs = pcsaft.pcsaft('BENZENE,NC6,NC12') # PC-SAFT EoS for ternary benzene/hexane/dodecane mixture
lk = lee_kesler.lee_kesler('N2,O2') # Lee-Kesler EoS for nitrogen/oxygen mixture

For PC-SAFT, both the simplified PC-SAFT (SPC-SAFT) and Polar PC-SAFT (PCP-SAFT) are available

from thermopack.pcsaft import SPC_SAFT, PCP_SAFT
spcs = SPC_SAFT('NC6,NC12') # Simplified PC-SAFT
pcps = PCP_SAFT('H2O,MEOH') # Polar PC-SAFT

The cubic equations of state are found in the cubic module. Available cubic EoS’s and more information on the individual cubics, mixing rules, etc. can be found on the cubic page.

from thermopack.cubic import SoaveRedlichKwong, RedlichKwong, PengRobinson, PengRobinson78
from thermopack.cubic import SchmidtWensel, PatelTeja, VanDerWaals
srk = SoaveRedlichKwong('NH3,C2') # SRK EoS for ammonia/ethane mixture
rk = RedlichKwong('NC6,CO2,NC12') # Redlich-Kwong EoS
pr = PengRobinson('IC4,NC10') # PR EoS for isobutane/decane mixture
pr78 = PengRobinson78('N2,O2,CO2') # # PR-78 EoS for isobutane/decane mixture
vdw = VanDerWaals('C1,C2,C3,N2,O2') # VdW EoS for methane/ethane/propane/nitrogen/oxygen mixture
sw = SchmidtWensel('R11,R12') # Schmidt-Wensel EoS for FCl3C/F2Cl2C mixture
pt = PatelTeja('PRLN') # Patel-Teja EoS for pure propylene

In addition to these, the Translated-Consisten Peng-Robinson is available as

from thermopack.tcPR import tcPR
tcpr = tcPR('F6S,SO2') # Translated-Consistent PR EoS for SF6/SO2 mixture

For more fine-tuned control of the cubic EoS, the parent class cubic can be initialised directly, to explicitly set mixing rules, alpha-correlation etc.

Cubic-plus association EoS’s are available for the SRK and PR EoS through the cpa module as

from thermopack.cpa import SRK_CPA, PR_CPA
srk_cpa = SRK_CPA('H2O,ETOH,PROP1OL') # SRK-CPA EoS for water/ethanol/propanol mixture

Several multiparameter EoS’s can interfaced through the multiparameter.multiparam class. The available multiparameter EoS’s are NIST-MEOS, MBWR16 and MBWR32. These are initialized as

from thermopack.multiparameter import multiparam
nist = multiparam('C3', 'NIST_MEOS') # NIST-MEOS EoS for propane
mbwr19 = multiparam('C1', 'MBWR19') # MBWR19 EoS for methane
mbwr32 = multiparam('C2', 'MBWR32') # MBWR32 EoS for ethane

please note that not all fluids are supported for multiparameter equations of state, depending on what parameters are available in the fluid database.

Finally, the Extended-corresponding state EoS is available through the extended_csp.ext_csp class as

from thermopack.extended_csp import ext_csp
eos = ext_csp('C1,C2,C3,NC4', sh_eos='SRK', sh_alpha='Classic',
              sh_mixing='vdW', ref_eos='NIST_MEOS', ref_comp='C3')

For more information on the extended-csp EoS please see the Examples and the memo.

Doing calculations

Now that we have an EoS initialized we can start computing stuff. The primary source on how to use individual methods in thermopack are the specific documentation of the thermo class. Here, a small subset of the functionality is demonstrated.

Note that all input is in SI units (moles/kelvin/pascal/cubic meters/joule)

pVT-properties

Specific volume, given temperature, pressure and composition is computed as

from thermopack.saftvrmie import saftvrmie
eos = saftvrmie('NC6,NC10') # Hexane/decane mixture
T = 300 # Kelvin
p = 1e5 # Pascal
x = [0.2, 0.8] # Molar composition
vg, = eos.specific_volume(T, p, x, eos.VAPPH) # Molar volume of gas phase (NB: Notice the comma)
vl, = eos.specific_volume(T, p, x, eos.LIQPH) # Molar volume of liquid phase (NB: Notice the comma)

where eos.VAPPH and eos.LIQPH are phase flags used to identify different phases. The commas are necessary because all output from thermopack methods are as tuples.

Similarly, pressure, internal energy, enthalpy, entropy, etc. and associated differentials can be computed via the methods chemical_potential_tv(T, V, n), internal_energy_tv(T, V, n), enthalpy_tv(T, V, n), helmholtz_tv(T, V, n), entropy_tv(T, V, n). For a full overview of the available property calculations see the TV-property interfaces and the Tp-property interfaces of the thermo class

Differentials

If we want volume differentials, we use the same method, but set the flags to calculate differentials to True:

# Continued 
vg, dvdp = eos.specific_volume(T, p, x, eos.VAPPH, dvdp=True) # Vapour phase molar volume and pressure differential
vl, dvdT = eos.specific_volume(T, p, x, eos.LIQPH, dvdt=True) # Liquid phase molar volume and temperature differential
_, dvdn = eos.specific_volume(T, p, x, eos.LIQPH, dvdn=True) # Liquid phase partial molar volumes

Differentials can be computed as functions of $(T, V, n)$ or as functions of $(T, p, n)$. For an overview of the different methods, see Advanced usage: Different property interfaces. A short example is given here as:

# Continued
n_tot = 15 # Total number of moles
n = n_tot * x
H, dHdn_TV = eos.enthalpy_tv(T, vg, n, dhdn=True) # Compute enthalpy and derivative of enthalpy wrt. mole numbers at constant (T, V)
h_vap, dhvap_dn_Tp = eos.enthalpy(T, p, x, eos.VAPPH, dhdn=True) # Compute molar vapour phase enthalpy and derivative of molar vapour phase enthalpy wrt. mole numbers at constant (T, p)
h_liq, dliq_dn_Tp = eos.enthalpy(T, p, x, eos.LIQPH, dhdn=True) # Compute molar liquid phase enthalpy and derivative of molar liquid phase enthalpy wrt. mole numbers at constant (T, p)
H, dHdn_Tp = eos.enthalpy_tvp(T, vg, n, dhdn=True) # Compute enthalpy and derivative of enthalpy wrt. mole numbers at constant (T, p)

Please note that heat capacities are not available directly, but must be computed as derivatives of enthalpy and internal energy, as

from thermopack.cubic import cubic
eos = cubic('C1,C3,NC6', 'SRK') # SRK EoS for a mixture of methane, propane and n-hexane

T = 300 # Kelvin
p = 1e5 # Pascal
x = [0.2, 0.1, 0.7] # Molar composition
_, Cp_vap = eos.enthalpy(T, p, x, eos.VAPPH, dhdt=True) # Vapour phase heat capacity at constant pressure, computed as (dH/dT)_{p,n}
_, Cp_liq = eos.enthalpy(T, p, x, eos.LIQPH, dhdt=True) # Liquid phase heat capacity at constant pressure, computed as (dH/dT)_{p,n}

vg, = eos.specific_volume(T, p, x, eos.VAPPH) # Computing vapour phase specific volume
vl, = eos.specific_volume(T, p, x, eos.LIQPH) # Liquid phase specific volume

_, Cv_vap = eos.internal_energy_tv(T, vg, x, dedt=True) # Vapour phase heat capacity at constant volume, computed as (dU/dT)_{V,n}
_, Cv_liq = eos.internal_energy_tv(T, vl, x, dedt=True) # Liquid phase heat capacity at constant volume, computed as (dU/dT)_{V,n}

Phase diagrams and Equilibria

As with other calculations, the primary source on how available methods for flash- and equilibria calculations and how to use them is the documentation of the thermo class.. Here we give a short introduction, for more extensive examples see the pyExamples directory.

Flash calculations

Flash calculations of several kinds are handled by the methods twophase_tpflash(), twophase_psflash(), twophase_phflash() and twophase_uvflash().

See the Flash interfaces in the documentation of the thermo class for the specifics on the different flash routines.

An example calculation using twophase_tpflash() may be done as

from thermopack.saftvrqmie import saftvrqmie
# SAFT-VRQ Mie for Hydrogen/Helium/Neon mixture 
eos = saftvrqmie('H2,HE,NE', minimum_temperature=20) # NB: Set minimum temperature low enough when working at very low temperatures
T = 35 # Kelvin
p = 3e6 # Pascal (30 bar)
z = [0.1, 0.25, 0.65] # Molar composition
flsh = eos.two_phase_tpflash(T, p, x) # flsh is a FlashResult object
print(flsh)
### Output: ###
# FlashResult object for Tp-flash
# Containing the attributes (description, name, value):
#   	Flash type                     flash_type : Tp  
#   	Total composition              z     : [0.1, 0.25, 0.65]  
#   	Temperature [K]                T     : 35  
#   	pressure [Pa]                  p     : 3000000.0  
#   	Liquid phase composition       x     : [0.05407302 0.03859287 0.90733411]  
#   	Vapour phase composition       y     : [0.14642524 0.46370066 0.3898741 ]  
#   	Vapour fraction                betaV : 0.497302408174766  
#   	Liquid fraction                betaL : 0.5026975918252341  
#   	Phase indentifier index        phase : 0

the result of the flash is accessed from the attributes of the FlashResult object, found in utils.py, as

# Continued
x = flsh.x # Liquid composition
y = flsh.y # Vapour composition
betaL = flsh.betaL # 
# ... etc

The FlashResult object returned by the different flash routines all contain the same attributes.

Phase envelopes

ThermoPack has interfaces to trace (T,p)-, (T,v)- and (p,x,y)-phase envelopes. For the full documentation, see the docs of the thermo class. For more comprehensive examples, see the Examples.

Tp- and Tv- phase envelopes

Phase envelopes can be generated directly with the method get_envelope_twophase() as

# Continued
T, p = eos.get_envelope_twophase(1e5, x) # arrays of temperature and pressure for phase envelope, starting at 1 bar.
plt.plot(p, T) # Tp-projection of phase envelope

T, p, v = eos.get_envelope_twophase(1e5, x, calc_v=True) # Also return the specific volume at each point along the phase envelope
plt.plot(1 / v, T) # rho-T projection of the phase envelope

pxy- and txy- phase envelopes

To compute pxy-type phase envelopes, we use the get_binary_pxy() method. This method returns a XYDiagram struct, which holds the composition and pressure / temperature of each equilibrium phase.

The XYDiagram struct has the attributes lle, l1ve and l2ve, where

We get the phase diagram as

from thermopack.cpa import SRK_CPA

eos = SRK_CPA('NC6,H2O')  # CPA-SRK eos for Hexane/water mixture
T = 350
pxy = eos.get_binary_pxy(T)  # Returns a XYDiagram struct
print(pxy)
# Result:
# XYDiagram object with attributes (name : description)
# lle  : Liquid 1 - Liquid 2 Equilibrium
# 	PxyEquilibrium object with attributes (description, name, value)
# 		Type of equilibrium                   type : lle
# 		Liquid 1 mole fraction, species 1     x1   : [4.278e-07 ... 4.145e-07], len(x1) = 457
# 		Liquid 2 mole fraction, species 1     x2   : [9.969e-01 ... 9.974e-01], len(x2) = 457
# 		Pressure                              p    : [1.648e+05 ... 1.500e+07], len(p) = 457
# 	
# l1ve : Liquid 1 - Vapour Equilibrium
# 	PxyEquilibrium object with attributes (description, name, value)
# 		Type of equilibrium                   type : lve
# 		Liquid mole fraction, species 1       x    : [4.278e-07 ... 2.197e-07], len(x) = 66
# 		Vapour mole fraction, species 1       y    : [7.880e-01 ... 6.461e-01], len(y) = 66
# 		Pressure                              p    : [1.648e+05 ... 1.000e+05], len(p) = 66
# 	
# l2ve : Liquid 2 - Vapour Equilibrium 
# 	PxyEquilibrium object with attributes (description, name, value)
# 		Type of equilibrium                   type : lve
# 		Liquid mole fraction, species 1       x    : [9.969e-01 ... 1.000e+00], len(x) = 100
# 		Vapour mole fraction, species 1       y    : [7.880e-01 ... 1.000e+00], len(y) = 100
# 		Pressure                              p    : [1.648e+05 ... 1.289e+05], len(p) = 100

For ease of use, the XYDiagram struct is iterable, such that we can unpack it efficiently as

lle, l1ve, l2ve = pxy

Now, we can plot the phase diagram as

# Continued
import matplotlib.pyplot as plt

# Liquid-liquid phase boundaries
# pxy.lle holds the composition and pressure of the liquid phases
plt.plot(pxy.lle.x1, pxy.lle.p, label='Liquid 1 composition') # lle.x1 is the mole fraction of component 1 (NC12) in Liquid 1 along the phase boundary
plt.plot(pxy.lle.x2, pxy.lle.p, label='Liquid 2 composition') # lle.x2 is the mole fraction of component 1 (NC12) in Liquid 2 along the phase boundary

# Liquid 1-vapour phase boundaries
# pxy.l2ve holds composition and pressure along the Liquid 1 - Vapour phase boundary
plt.plot(pxy.l1ve.x, pxy.l1ve.p, label='Liquid 1 bubble line') # l1ve.x is the mole fraction of component 1 (NC12) in Liquid 1 along the Liquid 1 - Vapour phase boundary
plt.plot(pxy.l1ve.y, pxy.l1ve.p, label='Liquid 1 dew line') # l1ve.y is the mole fraction of component 1 (NC12) in the Vapour phase along the Liquid 1 - Vapour phase boundary

# Liquid 2-vapour phase boundaries
# L2VE[2] is the pressure along the Liquid 2 - Vapour phase boundary
plt.plot(pxy.l2ve.x, pxy.l2ve.p, label='Liquid 2 bubble line') # l2ve.x is the mole fraction of component 1 (NC12) in Liquid 2 along the Liquid 2 - Vapour phase boundary
plt.plot(pxy.l2ve.y, pxy.l2ve.p, label='Liquid 2 dew line') # l2ve.y is the mole fraction of component 1 (NC12) in the Vapour phase along the Liquid 2 - Vapour phase boundary

plt.ylabel('Pressure [Pa]') # The third element in each tuple is the pressure along the phase boundary
plt.xlabel('Molar composition')

The method get_binary_txy works in the same way, only replacing the p attribute with T, such that we can compute

p = 1e5
lle, l1ve, l2ve = eos.get_binary_txy(p) # Unpacking the XYDiagram 

# Liquid-liquid phase boundaries
# l1ve holds the composition and pressure of Liquid 1 and Vapour along the phase boundary
plt.plot(l1ve.x, l1ve.T, label='Liquid 1 composition') # l1ve.x is the mole fraction of component 1 (NC12) in Liquid 1 along the phase boundary
plt.plot(l1ve.y, l1ve.T, label='Vapour composition') # l1ve.y is the mole fraction of component 1 (NC12) in Vapour along the phase boundary

# ... etc ...

If an equilibrium is not found, for example there is only one vapour-liquid equilibria, and no liquid-liquid equilibria, the arrays corresponding to the non-existent equilibria are empty, i.e.

T = 300
pxy = get_binary_pxy(T) # Some mixture that has only one vapour - liquid equilibria at 300 K
print(len(pxy.lle.x1) == 0) # True
print(len(pxy.lle.x2) == 0) # True
print(len(pxy.lle.p) == 0) # True
print(len(pxy.l1ve.x) == 0) # False
print(len(pxy.l1ve.y) == 0) # False
print(len(pxy.l1ve.p) == 0) # False
print(len(pxy.l2ve.x) == 0) # True
print(len(pxy.l2ve.y) == 0) # True
print(len(pxy.l2ve.p) == 0) # True

Dew- and bubble points

We can also compute the bubble-temperature, pressure etc. directly using the methods bubble_temperature(p, z), bubble_pressure(T, z), dew_temperature(p, z) and dew_pressure(T, z), where z is the composition of the mixture, as

eos = cubic('CO2,C1', 'SRK')
x = [0.5, 0.5] # Total composition of the mixture
p_dew, y_dew = eos.dew_pressure(250, x) # Calculates dew pressure and dew composition at 250 K
T_dew, y_dew = eos.dew_temperature(1e5, x) # Calculates dew temperature and dew composition at 1 bar
p_bub, x_bub = eos.bubble_pressure(230, x) # Calculates bubble pressure and bubble composition at 230 K
T_bub, x_bub = eos.bubble_temperature(1e5, x) # Calculates bubble temperature and bubble composition at 1 bar

Isolines

Various isolines can be computed using the methods get_isotherm, get_isobar, get_isentrope and get_isenthalp. In the following code snippet, the default values of the keyword arguments are indicated.

from thermopack.pcsaft import pcsaft
eos = pcsaft('NC6,NC12')
x = [0.2, 0.8]

# Calculate pressure, specific volume, specific entropy and specific enthalpy along the isotherm at 300 K
# from p = minimum_pressure to p = maximum_pressure. Compute at most nmax points.
p_iso_T, v_iso_T, s_iso_T, h_iso_T = eos.get_isotherm(300, x, minimum_pressure=1e5, maximum_pressure=1.5e7, nmax=100)

# Calculate temperature, specific volume, specific entropy and specific enthalpy along the isobar at 1 bar
# from T = minimum_temperature to T = maximum_temperature. Compute at most nmax points.
T_iso_p, v_iso_p, s_iso_p, h_iso_p = eos.get_isobar(1e5, x, minimum_temperature=200, maximum_temperature=500, nmax=100)

# Calculate temperature, pressure, specific volume and specific entropy along the isenthalp at 1 kJ / mol
# Start at the upper of (minimum_pressure, minimum_temperature)
# End at the lower of (maximum_pressure, maximum_temperature)
T_iso_h, p_iso_h, v_iso_h, s_iso_h = eos.get_isenthalp(1e3, x, minimum_pressure=1e5, maximum_pressure=1.5e7,
                                                            minimum_temperature=200, maximum_temperature=500,
                                                            nmax=100)

# Calculate temperature, pressure, specific volume and specific enthalpy along the isentrope at 5 J / mol K
# Start at the upper of (minimum_pressure, minimum_temperature)
# End at the lower of (maximum_pressure, maximum_temperature)
T_iso_s, p_iso_s, v_iso_s, h_iso_s = eos.get_isentrope(5, x, minimum_pressure=1e5, maximum_pressure=1.5e7,
                                                            minimum_temperature=200, maximum_temperature=500,
                                                            nmax=100)

Critical point

Thermopack has a critical point solver, which is called as

eos = saftvrqmie('HE,NE') # Use FH-corrected Mie potentials for Helium calculations!
n = [5, 10]
Tc, Vc, pc = eos.critical(n) # Compute the critical temperature, pressure and volume given mole numbers
vc = Vc / sum(n) # Critical specific volume computed from critical volume and mole numbers.

The solver accepts initial guesses for the critical values through the kwargs temp, and v. The error tolerance can be set via the tol kwarg (default is tol=1e-7).