def get_state(self, volume, temperature=None):
'''
Using SAFT gamma mie and automatic differentiation, return all the properties
that could be derived from the EoS: (A, P, S, G, H)
'''
Var.set_order(2)
self.volume = Var(mt.m3mol_to_nm(volume,
molecules=self.__moltol())) # nm3
if isinstance(temperature, float):
self.temp = Var(temperature)
else:
self.temp = Var(self.temp)
A = self.helmholtz() # J total for current system, Var
molcs = self.__moltol()
d1 = derivative(A, self.volume, self.temp, order=1, getvar=False)
P = -d1[0] / pow(cst.nmtom, 3) # Pa, float
S = -d1[1] / molcs # J/K per molecule, float
G = (A + P * self.volume *
pow(cst.nmtom, 3)) / molcs # (J + Pa*m3) for each molecule, Var
H = G + S * self.temp # J + J/K * K (it is already in per molecule here), Var
A = A.value / molcs
# Reset system back to floats
self.volume = self.volume.value
self.temp = self.temp.value
return (A, P, S, G.value, H.value)
def critical_point(self,
initial_t=300,
initial_v=3e-4,
v_nd=None,
get_volume=False,
get_density=False,
print_results=True,
solver=least_squares,
solver_kwargs={'bounds': (0.1, 10)},
xtol=1e-8,
print_progress=False):
tscale = initial_t
x0 = np.array([1.])
if not isinstance(solver_kwargs, dict): solver_kwargs = {}
if not isinstance(v_nd, np.ndarray): v_nd = np.logspace(-4, -2, 50)
Var.set_order(2)
crit_pt = solver(self.__crit_t,
x0,
xtol=xtol,
args=(v_nd, tscale, print_progress),
**solver_kwargs)
if print_progress: print()
if print_results: print(crit_pt)
T = crit_pt.x[0] * tscale
crit_v = solver(self.__crit_v,
np.array([initial_v]),
xtol=xtol,
args=(T, ),
bounds=(min(v_nd), max(v_nd)))
v = crit_v.x[0]
Var.set_order(1)
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
self.temp = T
A = self.helmholtz()
P = -derivative(A, self.volume, order=1) / pow(cst.nmtom, 3)
self.volume = mt.m3mol_to_nm(v, molecules=self.__moltol())
results = (P, T)
if get_volume: results += (v, )
if get_density: results += (1 / v, )
return results
def __crit_v(self, v, T):
self.temp = T
v = v[0]
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
A = self.helmholtz()
_, dpdv = derivative(A, self.volume, order=2)
dpdv = -dpdv / (pow(cst.nmtom, 6) * cst.Na) / (cst.R * T)
return dpdv
def __getp(self, x, targetP):
'''
Takes in single value to get P
'''
x = x[0]
self.volume = Var(mt.m3mol_to_nm(x, molecules=self.__moltol()))
A = self.helmholtz()
P = -derivative(A, self.volume, order=1) / pow(cst.nmtom, 3)
return P - targetP
def get_critical_point(self,
initial_guess=(3e-4, 300),
get_volume=False,
get_density=False,
print_results=True,
solver=least_squares,
solver_kwargs={'bounds': ((1e-1, 1e-1), (10, 10))},
xtol=1e-8,
print_progress=False):
scaler = initial_guess
x0 = np.array([1., 1.])
if not isinstance(solver_kwargs, dict): solver_kwargs = {}
Var.set_order(3)
crit_pt = solver(self.__critpt,
x0,
xtol=xtol,
args=(print_progress, scaler),
**solver_kwargs)
if print_progress: print()
if print_results: print(crit_pt)
vT = crit_pt.x
v = vT[0] * scaler[0]
T = vT[1] * scaler[1]
Var.set_order(1)
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
self.temp = T
A = self.helmholtz()
P = -derivative(A, self.volume, order=1) / pow(cst.nmtom, 3)
self.volume = mt.m3mol_to_nm(v, molecules=self.__moltol())
results = (P, T)
if get_volume: results += (v, )
if get_density: results += (1 / v, )
return results
def __crit_t(self, x, v_nd, scale, print_):
T = x[0] * scale
dp = np.zeros(np.size(v_nd))
for i in range(len(v_nd)):
v = v_nd[i]
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
self.temp = T
A = self.helmholtz()
_, dpdv = derivative(A, self.volume, order=2)
dp[i] = -dpdv / (pow(cst.nmtom, 6) * cst.Na) / (cst.R * T)
if print_:
print(f'Current: T = {T:7.3f}: max dP/dV = {max(dp):7.3e}',
end='\r')
return max(dp)
def vapour_pressure(self,
temperature=None,
initial_guess=(1e-4, .1),
get_volume=False,
get_gibbs=False,
print_results=True,
solver=least_squares,
solver_kwargs={'bounds': ((0.1, 1e-2), (1e2, 1e2))},
print_progress=False):
if isinstance(temperature, float) or isinstance(temperature, int):
self.temp = temperature
scaler = initial_guess
x0 = np.array([1., 1.])
if not isinstance(solver_kwargs, dict): solver_kwargs = {}
vle = solver(self.__eqpg,
x0,
args=(print_progress, scaler),
**solver_kwargs)
if print_progress: print()
if print_results:
print(
f'Scaled wrt initial guess of ({scaler[0]:7.3e},{scaler[1]:7.3e})'
)
print(vle)
vlv = (vle.x[0] * scaler[0], vle.x[1] * scaler[1])
v = vlv[1]
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
A = self.helmholtz()
P = -derivative(A, self.volume, order=1) / pow(cst.nmtom, 3)
G = (A.value +
P * self.volume.value * pow(cst.nmtom, 3)) / self.__moltol()
self.volume = mt.m3mol_to_nm(v, molecules=self.__moltol())
result = (P, )
if get_volume: result += (vlv, )
if get_gibbs: result += (G, )
return result
def __eqpg(self, x, print_, scaler):
'''
Takes in ndarray to find Pressure1 - Pressure2
'''
P = []
G = []
v_ = [x[0] * scaler[0], x[1] * scaler[1]]
for i in v_:
self.volume = Var(mt.m3mol_to_nm(i, molecules=self.__moltol()))
A = self.helmholtz()
Pi = -derivative(A, self.volume, order=1) / pow(cst.nmtom, 3)
P.append(Pi)
G.append((A.value + Pi * self.volume.value * pow(cst.nmtom, 3)) *
cst.Na)
if print_:
print(
f'Current: v\'s = {v_[0]:7.3e}, {v_[1]:7.3e}; dP = {(P[0]-P[1]):7.3e}, dG = {(G[0]-G[1]):7.3e}'
)
return np.array([(P[0] - P[1]), (G[0] - G[1])])
def __critpt(self, x, print_, scale):
'''
Takes in (v, T) to solve for dP/dV = 0 and d2P/dV2 = 0
'''
v_ = scale[0]
T_ = scale[1]
v = x[0] * v_
T = x[1] * T_
self.volume = Var(mt.m3mol_to_nm(v, molecules=self.__moltol()))
self.temp = T
A = self.helmholtz()
dP = -np.array(derivative(A, self.volume, order=3)) / pow(cst.nmtom, 3)
dP[1] = dP[1] / (pow(cst.nmtom, 3) * cst.Na) / (cst.R * T)
dP[2] = dP[2] / (pow(cst.nmtom, 6) * pow(cst.Na, 2)) / (cst.R * T)
dP[0] = dP[0] / (cst.R * T)
if print_:
print(
f'Current: v = {v:7.3e}, T = {T:7.3f}: P, dP/dV, d2P/dV2 = {dP[0]:7.3e},{dP[1]:7.3e},{dP[2]:7.3e}',
end='\r')
dP[0] = min(dP[0], 0)
return dP