equilibrium solvers moved to separate file "_solver.py"
This commit is contained in:
Nicolas Kruse
parent
973aedf058
commit
802aa68a25
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@ -13,8 +13,8 @@ Example usage:
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"""
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from ._main import species, fluid_system, fluid, elements
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from ._operations import set_solver, get_solver, equilibrium
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from ._operations import stack, concat, carbon_activity, oxygen_partial_pressure
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from ._solver import set_solver, get_solver, equilibrium
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__all__ = [
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'species', 'fluid_system', 'fluid', 'elements',
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@ -1,48 +1,9 @@
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from typing import Literal, Any
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from math import exp
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from scipy.optimize import minimize, root
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import numpy as np
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from ._main import T, elements, fluid, fluid_system
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from .typing import NDFloat, FloatArray
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from .constants import p0, epsy, R
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def set_solver(solver: Literal['gibs minimization', 'system of equations']) -> None:
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"""
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Select a solver for chemical equilibrium.
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Solvers:
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- **system of equations** (default): Finds the root for a system of
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equations covering a minimal set of equilibrium equations and elemental balance.
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The minimal set of equilibrium equations is derived by SVD using the null_space
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implementation of scipy.
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- **gibs minimization**: Minimizes the total Gibbs Enthalpy while keeping
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the elemental composition constant using the SLSQP implementation of scipy
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Args:
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solver: Name of the solver
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"""
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global _equilibrium_solver
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if solver == 'gibs minimization':
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_equilibrium_solver = equilibrium_gmin
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elif solver == 'system of equations':
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_equilibrium_solver = equilibrium_eq
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else:
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raise ValueError('Unknown solver')
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def get_solver() -> Literal['gibs minimization', 'system of equations']:
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"""Returns the selected solver name.
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Returns:
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Solver name
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"""
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if _equilibrium_solver == equilibrium_gmin:
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return 'gibs minimization'
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else:
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assert _equilibrium_solver == equilibrium_eq
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return 'system of equations'
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from ._main import T, elements, fluid
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from .typing import FloatArray
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from .constants import p0, R
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from ._solver import equilibrium
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def stack(arrays: list[T], axis: int = 0) -> T:
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@ -81,111 +42,6 @@ def concat(arrays: list[T], axis: int = 0) -> T:
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axis=axis), a0.fs)
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def equilibrium_gmin(fs: fluid_system, element_composition: FloatArray, t: float, p: float) -> FloatArray:
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"""Calculate the equilibrium composition of a fluid based on minimizing the Gibbs free energy"""
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def element_balance(n: FloatArray, fs: fluid_system, ref: FloatArray) -> FloatArray:
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return np.dot(n, fs.array_species_elements) - ref # type: ignore
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def gibbs_rt(n: FloatArray, grt: FloatArray, p_rel: float): # type: ignore
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# Calculate G/(R*T)
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return np.sum(n * (grt + np.log(p_rel * n / np.sum(n) + epsy)))
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cons: dict[str, Any] = {'type': 'eq', 'fun': element_balance, 'args': [fs, element_composition]}
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bnds = [(0, None) for _ in fs.species]
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grt = fs.get_species_g_rt(t)
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p_rel = p / p0
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start_composition_array = np.ones_like(fs.species, dtype=float)
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sol = np.array(minimize(gibbs_rt, start_composition_array, args=(grt, p_rel), method='SLSQP',
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bounds=bnds, constraints=cons, options={'maxiter': 2000, 'ftol': 1e-12})['x'], dtype=NDFloat) # type: ignore
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return sol
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def equilibrium_eq(fs: fluid_system, element_composition: FloatArray, t: float, p: float) -> FloatArray:
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"""Calculate the equilibrium composition of a fluid based on equilibrium equations"""
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el_max = np.max(element_composition)
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element_norm = element_composition / el_max
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a = fs.array_stoichiometric_coefficients
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a_sum = np.sum(a)
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el_matrix = fs.array_species_elements.T
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# Log equilibrium constants for each reaction equation
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b = -np.sum(fs.get_species_g_rt(t) * a, axis=1)
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# Pressure corrected log equilibrium constants
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bp = b - np.sum(a * np.log(p / p0), axis=1)
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logn_start = np.ones(el_matrix.shape[1]) * 0.1
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def residuals(logn: FloatArray): # type: ignore
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n = np.exp(logn)
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n_sum = np.sum(n)
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# Residuals from equilibrium equations:
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eq_resid = np.dot(a, logn - np.log(n_sum)) - bp
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# Derivative:
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j_eq = a - a_sum * n / n_sum
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# Residuals from elemental balance:
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el_error = np.dot(el_matrix, n) - element_norm
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ab_resid = np.log1p(el_error)
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# Derivative:
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j_ab = el_matrix * n / np.expand_dims(el_error + 1, axis=1)
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return (np.hstack([eq_resid, ab_resid]), np.concatenate([j_eq, j_ab], axis=0))
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ret = root(residuals, logn_start, jac=True, tol=1e-30)
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n = np.exp(np.array(ret['x'], dtype=NDFloat))
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return n * el_max
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def equilibrium(f: fluid | elements, t: float | FloatArray, p: float = 1e5) -> fluid:
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"""Calculate the equilibrium composition of a fluid at a given temperature and pressure"
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Args:
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f: Fluid or elements object
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t: Temperature in Kelvin
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p: Pressure in Pascal
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Returns:
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A new fluid object with the equilibrium composition
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"""
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assert isinstance(f, (fluid, elements)), 'Argument f must be a fluid or elements'
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m_shape: int = f.fs.array_stoichiometric_coefficients.shape[0]
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if isinstance(f, fluid):
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if not m_shape:
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return f
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else:
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if not m_shape:
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def linalg_lstsq(array_elemental_composition: FloatArray, matrix: FloatArray) -> Any:
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# TODO: np.dot(np.linalg.pinv(a), b) is eqivalent to lstsq(a, b).
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# the constant np.linalg.pinv(a) can be precomputed for each fs.
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return np.dot(np.linalg.pinv(matrix), array_elemental_composition)
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# print('-->', f.array_elemental_composition.shape, f.fs.array_species_elements.transpose().shape)
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composition = np.apply_along_axis(linalg_lstsq, -1, f.array_elemental_composition, f.fs.array_species_elements.transpose())
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return fluid(composition, f.fs)
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assert np.min(f.array_elemental_composition) >= 0, 'Input element fractions must be 0 or positive'
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if isinstance(t, np.ndarray):
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assert f.shape == tuple(), 'Multidimensional temperature can currently only used for 0D fluids'
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t_composition = np.zeros(t.shape + (f.fs.array_species_elements.shape[0],))
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for t_index in np.ndindex(t.shape):
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t_composition[t_index] = _equilibrium_solver(f.fs, f.array_elemental_composition, float(t[t_index]), p)
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return fluid(t_composition, f.fs)
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else:
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composition = np.ones(f.shape + (len(f.fs.species),), dtype=float)
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for index in np.ndindex(f.shape):
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# print(composition.shape, index, _equilibrium(f.fs, f._element_composition[index], t, p))
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composition[index] = _equilibrium_solver(f.fs, f.array_elemental_composition[index], t, p)
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return fluid(composition, f.fs)
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def carbon_activity(f: fluid | elements, t: float, p: float) -> float:
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"""Calculate the activity of carbon in a fluid at a given temperature and pressure.
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At a value of 1 the fluid is in equilibrium with solid graphite. At a value > 1
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@ -292,6 +148,3 @@ def oxygen_partial_pressure(f: fluid | elements, t: float, p: float) -> FloatArr
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return np.apply_along_axis(get_oxygen, -1, x)
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else:
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return get_oxygen(x)
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_equilibrium_solver = equilibrium_eq
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@ -0,0 +1,152 @@
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from typing import Literal, Any
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from scipy.optimize import minimize, root
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import numpy as np
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from ._main import elements, fluid, fluid_system
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from .typing import NDFloat, FloatArray
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from .constants import p0, epsy
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def set_solver(solver: Literal['gibs minimization', 'system of equations']) -> None:
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"""
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Select a solver for chemical equilibrium.
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Solvers:
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- **system of equations** (default): Finds the root for a system of
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equations covering a minimal set of equilibrium equations and elemental balance.
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The minimal set of equilibrium equations is derived by SVD using the null_space
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implementation of scipy.
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- **gibs minimization**: Minimizes the total Gibbs Enthalpy while keeping
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the elemental composition constant using the SLSQP implementation of scipy
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Args:
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solver: Name of the solver
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"""
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global _equilibrium_solver
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if solver == 'gibs minimization':
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_equilibrium_solver = equilibrium_gmin
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elif solver == 'system of equations':
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_equilibrium_solver = equilibrium_eq
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else:
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raise ValueError('Unknown solver')
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def get_solver() -> Literal['gibs minimization', 'system of equations']:
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"""Returns the selected solver name.
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Returns:
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Solver name
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"""
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if _equilibrium_solver == equilibrium_gmin:
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return 'gibs minimization'
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else:
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assert _equilibrium_solver == equilibrium_eq
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return 'system of equations'
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def equilibrium_gmin(fs: fluid_system, element_composition: FloatArray, t: float, p: float) -> FloatArray:
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"""Calculate the equilibrium composition of a fluid based on minimizing the Gibbs free energy"""
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def element_balance(n: FloatArray, fs: fluid_system, ref: FloatArray) -> FloatArray:
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return np.dot(n, fs.array_species_elements) - ref # type: ignore
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def gibbs_rt(n: FloatArray, grt: FloatArray, p_rel: float): # type: ignore
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# Calculate G/(R*T)
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return np.sum(n * (grt + np.log(p_rel * n / np.sum(n) + epsy)))
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cons: dict[str, Any] = {'type': 'eq', 'fun': element_balance, 'args': [fs, element_composition]}
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bnds = [(0, None) for _ in fs.species]
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grt = fs.get_species_g_rt(t)
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p_rel = p / p0
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start_composition_array = np.ones_like(fs.species, dtype=float)
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sol = np.array(minimize(gibbs_rt, start_composition_array, args=(grt, p_rel), method='SLSQP',
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bounds=bnds, constraints=cons, options={'maxiter': 2000, 'ftol': 1e-12})['x'], dtype=NDFloat) # type: ignore
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return sol
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def equilibrium_eq(fs: fluid_system, element_composition: FloatArray, t: float, p: float) -> FloatArray:
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"""Calculate the equilibrium composition of a fluid based on equilibrium equations"""
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el_max = np.max(element_composition)
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element_norm = element_composition / el_max
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a = fs.array_stoichiometric_coefficients
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a_sum = np.sum(a)
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el_matrix = fs.array_species_elements.T
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# Log equilibrium constants for each reaction equation
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b = -np.sum(fs.get_species_g_rt(t) * a, axis=1)
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# Pressure corrected log equilibrium constants
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bp = b - np.sum(a * np.log(p / p0), axis=1)
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logn_start = np.ones(el_matrix.shape[1]) * 0.1
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def residuals(logn: FloatArray): # type: ignore
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n = np.exp(logn)
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n_sum = np.sum(n)
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# Residuals from equilibrium equations:
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eq_resid = np.dot(a, logn - np.log(n_sum)) - bp
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# Derivative:
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j_eq = a - a_sum * n / n_sum
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# Residuals from elemental balance:
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el_error = np.dot(el_matrix, n) - element_norm
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ab_resid = np.log1p(el_error)
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# Derivative:
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j_ab = el_matrix * n / np.expand_dims(el_error + 1, axis=1)
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return (np.hstack([eq_resid, ab_resid]), np.concatenate([j_eq, j_ab], axis=0))
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ret = root(residuals, logn_start, jac=True, tol=1e-30)
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n = np.exp(np.array(ret['x'], dtype=NDFloat))
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return n * el_max
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def equilibrium(f: fluid | elements, t: float | FloatArray, p: float = 1e5) -> fluid:
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"""Calculate the equilibrium composition of a fluid at a given temperature and pressure"
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Args:
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f: Fluid or elements object
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t: Temperature in Kelvin
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p: Pressure in Pascal
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Returns:
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A new fluid object with the equilibrium composition
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"""
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assert isinstance(f, (fluid, elements)), 'Argument f must be a fluid or elements'
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m_shape: int = f.fs.array_stoichiometric_coefficients.shape[0]
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if isinstance(f, fluid):
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if not m_shape:
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return f
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else:
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if not m_shape:
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def linalg_lstsq(array_elemental_composition: FloatArray, matrix: FloatArray) -> Any:
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# TODO: np.dot(np.linalg.pinv(a), b) is eqivalent to lstsq(a, b).
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# the constant np.linalg.pinv(a) can be precomputed for each fs.
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return np.dot(np.linalg.pinv(matrix), array_elemental_composition)
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# print('-->', f.array_elemental_composition.shape, f.fs.array_species_elements.transpose().shape)
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composition = np.apply_along_axis(linalg_lstsq, -1, f.array_elemental_composition, f.fs.array_species_elements.transpose())
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return fluid(composition, f.fs)
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assert np.min(f.array_elemental_composition) >= 0, 'Input element fractions must be 0 or positive'
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if isinstance(t, np.ndarray):
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assert f.shape == tuple(), 'Multidimensional temperature can currently only used for 0D fluids'
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t_composition = np.zeros(t.shape + (f.fs.array_species_elements.shape[0],))
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for t_index in np.ndindex(t.shape):
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t_composition[t_index] = _equilibrium_solver(f.fs, f.array_elemental_composition, float(t[t_index]), p)
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return fluid(t_composition, f.fs)
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else:
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composition = np.ones(f.shape + (len(f.fs.species),), dtype=float)
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for index in np.ndindex(f.shape):
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# print(composition.shape, index, _equilibrium(f.fs, f._element_composition[index], t, p))
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composition[index] = _equilibrium_solver(f.fs, f.array_elemental_composition[index], t, p)
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return fluid(composition, f.fs)
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_equilibrium_solver = equilibrium_eq
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