Getting started

Getting started

This is a very short introduction to thermopack. Once you've gotten started, we recommend a look at the Examples in the GitHub repo.

Initialising an equation of state

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 wiki. 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 

The cubic equations of state are all interfaced through the cubic class. Available cubic EoS's can are SRK, PR, VdW, SW, PT and tcPR. More information on the individual cubics, mixing rules, etc. can be found in the wiki. The specific cubic EoS to initialize is specified with a string as

from thermopack.cubic import cubic
srk = cubic('NH3,C2', 'SRK') # SRK EoS for ammonia/ethane mixture
pr = cubic('IC4,NC10', 'PR') # PR EoS for isobutane/decane mixture
vdw = cubic('C1,C2,C3,N2,O2', 'VdW') # VdW EoS for methane/ethane/propane/nitrogen/oxygen mixture
sw = cubic('R11,R12', 'SW') # Schmidt-Wensel EoS for FCl3C/F2Cl2C mixture
pt = cubic('PRLN', 'PT') # Patel-Teja EoS for pure propylene
tcpr = cubic('F6S,SO2', 'tcPR') # Translated-Consistent PR EoS for SF6/SO2 mixture

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

from thermopack.cpa import cpa
srk_cpa = cpa('H2O,ETOH,PROP1OL', 'SRK') # SRK-CPA EoS for water/ethanol/propanol mixture
pr_cpa = cpa('ACETONE,HEX1OL,CYCLOHEX') # PR-CPA EoS for acetone/hexanol/cyclohexane 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 CO2
mbwr16 = multiparam('C1', 'MBWR16') # MBWR16 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 wiki.

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 docstrings in the thermopack class, found in /addon/pycThermopack/thermopack/thermo.py. 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,NC12') # Hexane/dodecane 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. If we want volume differentials, we use the same method:

# Continued 
vg, dvdT = eos.specific_volume(T, p, x, eos.VAPPH, dvdp=True) # Vapour phase molar volume and pressure differential
vl, dvdp = 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

Similarly, 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).

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 are the docstrings in thermo.py. 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(). They are used as

from thermopack.saftvrqmie import saftvrqmie
eos = saftvrqmie('H2,HE,NE') # Helium/Neon mixture
T = 35 # Kelvin
p = 10e5 # Pascal (10 bar)
x = [0.1, 0.25, 0.65] # Molar composition
x, y, vapfrac, liqfrac, phasekey = eos.two_phase_tpflash(T, p, x) # x and y are vapour and liquid composition respectively

Note that some of the methods also output other information, such as the temperature of the flash, see the docstrings of the thermo class in thermo.py for more details.

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

To compute pxy-type phase envelopes, we use the get_binary_pxy() method as

import matplotlib.pyplot as plt
from thermopack.cpa import cpa

eos = cpa('NC12,H2O', 'SRK')  # CPA eos for Dodecane/water mixture
T = 350  # kelvin
LLE, L1VE, L2VE = eos.get_binary_pxy(T)  # Returns three tuples containing three arrays each

# Liquid-liquid phase boundaries
plt.plot(LLE[0], LLE[2], label='Liquid 1 composition')
plt.plot(LLE[1], LLE[2], label='Liquid 2 composition')

# Liquid 1-vapour phase boundaries
plt.plot(L1VE[0], L1VE[2], label='Liquid 1 bubble line')
plt.plot(L1VE[1], L1VE[2], label='Liquid 1 dew line')

# Liquid 2-vapour phase boundaries
plt.plot(L2VE[0], L2VE[2], label='Liquid 2 bubble line')
plt.plot(L2VE[1], L2VE[2], label='Liquid 2 dew line')

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

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,CH4', 'SRK')
x = [0.5, 0.5] # Total composition of the mixture
p_dew, y_dew = eos.dew_pressure(273, x) # Calculates dew pressure and dew composition at 273 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(273, x) # Calculates bubble pressure and bubble composition at 273 K
T_bub, x_bub = eos.bubble_temperature(1e5, x) # Calculates bubble temperature and bubble composition at 1 bar

Isopleths

Various isopleths 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.

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, pc, Vc = 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).