mirror of https://github.com/Nonannet/pyladoc.git
rendering tests updated
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Nicolas
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import pyladoc
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import matplotlib.pyplot as plt
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import pandas as pd
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import document_validation
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import numpy as np
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VALIDATE_HTML_CODE_ONLINE = False
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WRITE_RESULT_FILES = True
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def mason_saxena_k_mixture(x_h2):
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"""
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Calculate the thermal conductivity of a H2/CO2 gas mixture using the Mason and Saxena mixing rule.
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The mixture thermal conductivity is computed as:
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k_mix = Σ_i [ X_i * k_i / (Σ_j X_j * φ_ij) ]
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with:
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φ_ij = 1/√8 * (1 + M_i/M_j)^(-0.5) * [ 1 + ( (k_i/k_j)**0.5 * (M_j/M_i)**0.25 ) ]^2
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Parameters:
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x_h2 (float or array-like): Mole fraction of H2 (from 0 to 1). The CO2 mole fraction is 1 - x_h2.
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Returns:
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float or array-like: Thermal conductivity of the mixture in W/m·K.
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"""
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# Pure gas properties (at room temperature, approx.)
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k_h2 = 0.1805 # Thermal conductivity of H2 in W/mK
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k_co2 = 0.0166 # Thermal conductivity of CO2 in W/mK
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M_h2 = 2.016 # Molar mass of H2 in g/mol
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M_co2 = 44.01 # Molar mass of CO2 in g/mol
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# Define the phi_ij function according to Mason and Saxena.
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def phi(k_i, k_j, M_i, M_j):
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return (1 / np.sqrt(8)) * (1 + M_i / M_j) ** (-0.5) * (1 + ((k_i / k_j) ** 0.5 * (M_j / M_i) ** 0.25))**2
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# Compute phi terms for the two species.
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# For i = j the phi terms should be 1.
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phi_h2_h2 = phi(k_h2, k_h2, M_h2, M_h2) # Should be 1
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phi_h2_co2 = phi(k_h2, k_co2, M_h2, M_co2)
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phi_co2_h2 = phi(k_co2, k_h2, M_co2, M_h2)
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phi_co2_co2 = phi(k_co2, k_co2, M_co2, M_co2) # Should be 1
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# Ensure we can perform vectorized operations.
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x_h2 = np.array(x_h2)
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x_co2 = 1 - x_h2
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# Use the Mason-Saxena mixing rule:
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# k_mix = X_H2 * k_H2 / (X_H2*φ_H2_H2 + X_CO2*φ_H2_CO2) +
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# X_CO2 * k_CO2 / (X_CO2*φ_CO2_CO2 + X_H2*φ_CO2_H2)
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k_mix = (x_h2 * k_h2 / (x_h2 * phi_h2_h2 + x_co2 * phi_h2_co2)) + \
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(x_co2 * k_co2 / (x_co2 * phi_co2_co2 + x_h2 * phi_co2_h2))
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return k_mix
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def make_document():
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doc = pyladoc.DocumentWriter()
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doc.add_markdown("""
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# Thermal Conductivity of Mixtures
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The determination of the thermal conductivity of gas mixtures is a central aspect of modeling
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transport phenomena, particularly in high-temperature and high-pressure processes. Among the
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most established approaches is the empirical equation introduced by Wassiljewa, which was
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subsequently refined by Mason and Saxena to improve its applicability to multicomponent systems.
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This model offers a reliable means of estimating the thermal conductivity of gas mixtures based
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on the properties of the pure components and their molar interactions.
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The thermal conductivity of a gas mixture, denoted by $$\\lambda_{\\text{mix}}$$, can expressed as
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shown in equation @eq:lambda_mixture.
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$$
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\\label{eq:lambda_mixture}
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\\lambda_{\text{mix}} = \\sum_{i=1}^{n} \\frac{x_i \\lambda_i}{\\sum_{j=1}^{n} x_j \\Phi_{ij}}
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$$
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In this equation, $$x_i$$ represents the molar fraction of component $$i$$ within the mixture,
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while $$\\lambda_i$$ denotes the thermal conductivity of the pure substance $$i$$. The denominator
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contains the interaction parameter $$\\Phi_{ij}$$, which describes the influence of component
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$$j$$ on the transport properties of component $$i$$.
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The interaction parameter $$\\Phi_{ij}$$ is given by the relation shown in equation @eq:interaction_parameter.
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$$
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\\label{eq:interaction_parameter}
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\\Phi_{ij} = \\frac{1}{\\sqrt{8}} \\left(1 + \\frac{M_i}{M_j} \\right)^{-1/2} \\left[ 1 + \\left( \\frac{\\lambda_i}{\\lambda_j} \\right)^{1/2} \\left( \\frac{M_j}{M_i} \\right)^{1/4} \\right]^2
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$$
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Here, $$M_i$$ and $$M_j$$ are the molar masses of the components $$i$$ and $$j$$, respectively.
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Molar masses and thermal conductivity of the pure substances are listed in table @table:gas_probs.
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The structure of this expression illustrates the nonlinear dependence of the interaction term on
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both the molar mass ratio and the square root of the conductivity ratio of the involved species.
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""")
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# Table
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data = {
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"Gas": ["H2", "O2", "N2", "CO2", "CH4", "Ar", "He"],
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"Molar mass in g/mol": ["2.016", "32.00", "28.02", "44.01", "16.04", "39.95", "4.0026"],
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"Thermal conductivity in W/m/K": ["0.1805", "0.0263", "0.0258", "0.0166", "0.0341", "0.0177", "0.1513"]
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}
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df = pd.DataFrame(data)
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doc.add_table(df.style.hide(axis="index"), 'Properties of some gases', 'gas_probs')
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doc.add_markdown("""
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This formulation acknowledges that the transport properties of a gas mixture are not a simple
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linear combination of the individual conductivities. Rather, they are governed by intermolecular
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interactions, which affect the energy exchange and diffusion behavior of each component. These
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interactions are particularly significant at elevated pressures or in cases where the gas components
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exhibit widely differing molecular masses or transport properties.
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The equation proposed by Wassiljewa and refined by Mason and Saxena assumes that binary interactions
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dominate the behavior of the mixture, while higher-order (three-body or more) interactions are
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neglected. It also presumes that the gases approximate ideal behavior, although in practical
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applications, moderate deviations from ideality are tolerated without significant loss of accuracy.
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In figure @fig:mixture the resulting thermal conductivity of an H2/CO2-mixture is shown.""")
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# Figure
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x_h2_values = np.linspace(0, 1, 100)
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k_mixture_values = mason_saxena_k_mixture(x_h2_values)
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fig, ax = plt.subplots()
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ax.set_xlabel("H2 molar fraction / %")
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ax.set_ylabel("Thermal Conductivity / (W/m·K)")
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ax.plot(x_h2_values * 100, k_mixture_values, color='black')
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doc.add_diagram(fig, 'Thermal Conductivity of H2/CO2 mixtures', 'mixture')
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doc.add_markdown("""
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In engineering practice, the accurate determination of $$\\lambda_{\\text{mix}}$$ is essential
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for the prediction of heat transfer in systems such as membrane modules, chemical reactors, and
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combustion chambers. In the context of membrane-based gas separation, for instance, the thermal
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conductivity of the gas mixture influences the local temperature distribution, which in turn affects
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both the permeation behavior and the structural stability of the membrane.
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It is important to note that the calculated mixture conductivity reflects only the gas phase
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behavior. In porous systems such as carbon membranes, additional effects must be considered.
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These include the solid-phase thermal conduction through the membrane matrix, radiative transport
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in pore channels at high temperatures, and transport in the Knudsen regime for narrow pores.
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To account for these complexities, models based on effective medium theory, such as those of
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Maxwell-Eucken or Bruggeman, are frequently employed. These models combine the conductivities of
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individual phases (gas and solid) with geometrical factors that reflect the morphology of the
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porous structure.
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---
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Expanded by more or less sensible AI jabbering; based on: [doi:10.14279/depositonce-7390](https://doi.org/10.14279/depositonce-7390)
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""")
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return doc
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def test_html_render():
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doc = make_document()
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html_code = doc.to_html()
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document_validation.validate_html(html_code, VALIDATE_HTML_CODE_ONLINE)
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if WRITE_RESULT_FILES:
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with open('tests/out/test_html_render1.html', 'w', encoding='utf-8') as f:
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f.write(pyladoc.inject_to_template(html_code, internal_template='templates/test_template.html'))
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def test_latex_render():
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doc = make_document()
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if WRITE_RESULT_FILES:
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with open('tests/out/test_html_render1.tex', 'w', encoding='utf-8') as f:
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f.write(doc.to_latex())
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assert doc.to_pdf('tests/out/test_latex_render1.pdf', font_family='serif')
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if __name__ == '__main__':
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test_html_render()
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test_latex_render()
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@ -8,9 +8,9 @@ WRITE_RESULT_FILES = True
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def make_document():
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dw = pyladoc.DocumentWriter()
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doc = pyladoc.DocumentWriter()
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dw.add_markdown("""
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doc.add_markdown("""
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# Special characters
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ö ä ü Ö Ä Ü ß @ ∆
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@ -20,9 +20,9 @@ def make_document():
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£ ¥ $ €
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Œ
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# Link
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This is a hyperlink: [nonan.net](https://www.nonan.net)
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# Table
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@ -42,15 +42,15 @@ def make_document():
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| 3 | KL3202 | PT100 2 Temperatureingänge (3-Leiter)
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| 1 | KL2404 | 4 Digitalausgänge
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| 2 | KL9010 | Endklemme
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---
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# Equations
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This line represents a reference to the equation @eq:test1.
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""")
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dw.add_equation(r'y = a + b * \sum_{i=0}^{\infty} a_i x^i', 'test1')
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doc.add_equation(r'y = a + b * \sum_{i=0}^{\infty} a_i x^i', 'test1')
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# Figure
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fig, ax = plt.subplots()
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@ -65,7 +65,7 @@ def make_document():
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ax.set_title('Fruit supply by kind and color')
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ax.legend(title='Fruit color')
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dw.add_diagram(fig, 'Bar chart with individual bar colors')
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doc.add_diagram(fig, 'Bar chart with individual bar colors')
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# Table
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mydataset = {
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@ -79,9 +79,9 @@ def make_document():
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}
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df = pd.DataFrame(mydataset)
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dw.add_table(df.style.hide(axis="index"), 'This is a example table', 'example1')
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doc.add_table(df.style.hide(axis="index"), 'This is a example table', 'example1')
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return dw
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return doc
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def test_html_render():
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@ -91,7 +91,7 @@ def test_html_render():
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document_validation.validate_html(html_code, VALIDATE_HTML_CODE_ONLINE)
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if WRITE_RESULT_FILES:
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with open('tests/out/test_html_render.html', 'w', encoding='utf-8') as f:
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with open('tests/out/test_html_render2.html', 'w', encoding='utf-8') as f:
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f.write(pyladoc.inject_to_template(html_code, internal_template='templates/test_template.html'))
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@ -100,7 +100,7 @@ def test_latex_render():
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# print(doc.to_latex())
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assert doc.to_pdf('tests/out/test_latex_render.pdf', font_family='serif')
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assert doc.to_pdf('tests/out/test_latex_render2.pdf', font_family='serif')
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if __name__ == '__main__':
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