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dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-14T21:18:54","documenter_version":"1.8.0"}}
+{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-16T22:46:04","documenter_version":"1.8.0"}}

dev/tutorials/getting_started/index.html

@@ -10,13 +10,13 @@
 plot(P, l_at_300, size = (500, 250), label = "300K")
 plot!(P, l_at_350, label = "350K")
 xlabel!("P (Pa)")
-ylabel!(&quot;l (mol/kg)&quot;)</code></pre><img src="1c3bcc98.svg" alt="Example block output"/><p>You can also estimate other properties from the isotherm such as the henry coefficient at a given temperature by calling <code>henry_coefficient(model::IsothermModel, T)</code>. The henry coefficient should correspond to the slope of the isotherm when <span>$P \rightarrow 0.0$</span>. In Langmuir.jl, this is obtained using automatic differentiation and introduces no numerical error in the estimate. You can see in the example below how to visualize the tangent line built from the henry coefficient at <span>$300K$</span>.</p><pre><code class="language-julia hljs">P_ = P[1:3]
+ylabel!(&quot;l (mol/kg)&quot;)</code></pre><img src="a05b382b.svg" alt="Example block output"/><p>You can also estimate other properties from the isotherm such as the henry coefficient at a given temperature by calling <code>henry_coefficient(model::IsothermModel, T)</code>. The henry coefficient should correspond to the slope of the isotherm when <span>$P \rightarrow 0.0$</span>. In Langmuir.jl, this is obtained using automatic differentiation and introduces no numerical error in the estimate. You can see in the example below how to visualize the tangent line built from the henry coefficient at <span>$300K$</span>.</p><pre><code class="language-julia hljs">P_ = P[1:3]
 plot(P_, l_at_300[1:3], size = (500, 250), label = &quot;300K&quot;)
 H = henry_coefficient(isotherm, 300.0)
-plot!(P_, H*P_, label = &quot;Tangent line&quot;)</code></pre><img src="2723c661.svg" alt="Example block output"/><p>To finish this section for single component adsorption, one can also estimate the isosteric heat of adsorption by calling <code>isosteric_heat(model, Vg, p, T)</code> where Vg is the molar volume of the gas phase, <code>p</code> the pressure in Pascal and <code>T</code> the temperature in Kelvin. For the Langmuir model, the isosteric heat should be constant and equal to the energy parameter <code>E</code>. You can plot the isosteric heat either as a function of the pressure or loading.</p><p>Below it is assumed that the ideal gas law is a good approximation to describe the molar volume of the gas phase.</p><pre><code class="language-julia hljs">import Langmuir: Rgas
+plot!(P_, H*P_, label = &quot;Tangent line&quot;)</code></pre><img src="b7854eb2.svg" alt="Example block output"/><p>To finish this section for single component adsorption, one can also estimate the isosteric heat of adsorption by calling <code>isosteric_heat(model, Vg, p, T)</code> where Vg is the molar volume of the gas phase, <code>p</code> the pressure in Pascal and <code>T</code> the temperature in Kelvin. For the Langmuir model, the isosteric heat should be constant and equal to the energy parameter <code>E</code>. You can plot the isosteric heat either as a function of the pressure or loading.</p><p>Below it is assumed that the ideal gas law is a good approximation to describe the molar volume of the gas phase.</p><pre><code class="language-julia hljs">import Langmuir: Rgas
 ΔH = map(P -&gt; isosteric_heat(isotherm, P, 300.), P[2:end]) |&gt; x -&gt; round.(x, digits = 7)
 scatter(l_at_300[2:end], ΔH, size = (500, 250),  ylabel = &quot;Isosteric heat (J/mol)&quot;, xlabel = &quot;loading (mol/kg)&quot;, label = &quot;Estimated isosteric heat with AD&quot;)
-plot!([first(l_at_300), last(l_at_300)], [E, E], label = &quot;Expected value&quot;)</code></pre><img src="eba137e5.svg" alt="Example block output"/><h2 id="Estimating-properties-in-multicomponent-adsorption."><a class="docs-heading-anchor" href="#Estimating-properties-in-multicomponent-adsorption.">Estimating properties in multicomponent adsorption.</a><a id="Estimating-properties-in-multicomponent-adsorption.-1"></a><a class="docs-heading-anchor-permalink" href="#Estimating-properties-in-multicomponent-adsorption." title="Permalink"></a></h2><p>When it comes to estimating properties in multicomponent adsorption, the Ideal Adsorption Solution Theory (IAST) has been proven accurate for a number of systems. It allows one to estimate multicomponent adsorption behavior from single component isotherms.</p><p>When formulated, estimating the loading with IAST becomes a nonlinear solve problem which can be solved in different ways. Here, we support the <strong>Nested Loop</strong> and <strong>FastIAS</strong> methods. To know more about the two and which one to choose, refer to this paper: 10.1002/aic.14684.</p><p>It can be shown analytically that IAST estimation of multicomponent loading is the same as the extendend Langmuir method when the parameter <span>$M_i$</span> (saturation loading) are the same for all components, i.e., <span>$M_1 = M_2 = ... = M_{N_c}$</span>. The extended langmuir has the form <span>$n_i = \frac{M_i \times K_{i,0} \exp{\frac{\Delta H}{RT}}}{1 + \sum_i K_i \times P_i}$</span>. Below you can see a numerical verification of IAST for that condition.</p><pre><code class="language-julia hljs">using Langmuir
+plot!([first(l_at_300), last(l_at_300)], [E, E], label = &quot;Expected value&quot;)</code></pre><img src="3707db7d.svg" alt="Example block output"/><h2 id="Estimating-properties-in-multicomponent-adsorption."><a class="docs-heading-anchor" href="#Estimating-properties-in-multicomponent-adsorption.">Estimating properties in multicomponent adsorption.</a><a id="Estimating-properties-in-multicomponent-adsorption.-1"></a><a class="docs-heading-anchor-permalink" href="#Estimating-properties-in-multicomponent-adsorption." title="Permalink"></a></h2><p>When it comes to estimating properties in multicomponent adsorption, the Ideal Adsorption Solution Theory (IAST) has been proven accurate for a number of systems. It allows one to estimate multicomponent adsorption behavior from single component isotherms.</p><p>When formulated, estimating the loading with IAST becomes a nonlinear solve problem which can be solved in different ways. Here, we support the <strong>Nested Loop</strong> and <strong>FastIAS</strong> methods. To know more about the two and which one to choose, refer to this paper: 10.1002/aic.14684.</p><p>It can be shown analytically that IAST estimation of multicomponent loading is the same as the extendend Langmuir method when the parameter <span>$M_i$</span> (saturation loading) are the same for all components, i.e., <span>$M_1 = M_2 = ... = M_{N_c}$</span>. The extended langmuir has the form <span>$n_i = \frac{M_i \times K_{i,0} \exp{\frac{\Delta H}{RT}}}{1 + \sum_i K_i \times P_i}$</span>. Below you can see a numerical verification of IAST for that condition.</p><pre><code class="language-julia hljs">using Langmuir
 import Langmuir: Rgas
 isotherm_1 = LangmuirS1(1.913, 6.82e-10, -21_976.40)
 isotherm_2 = LangmuirS1(1.913, 1.801e-9, -16_925.01)
@@ -34,4 +34,4 @@
 
 println(&quot;IAST estimated loading for component 1 is: &quot;, round(loading_1, digits = 4))
 println(&quot;Extende langmuir estimated loading for component 1 is: &quot;, round(loading_1_expected, digits = 4))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">IAST estimated loading for component 1 is: 0.3377
-Extende langmuir estimated loading for component 1 is: 0.3377</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../background/">« Background</a><a class="docs-footer-nextpage" href="../tutorial/">A typical workflow with Langmuir.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 14 November 2024 21:18">Thursday 14 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Extende langmuir estimated loading for component 1 is: 0.3377</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../background/">« Background</a><a class="docs-footer-nextpage" href="../tutorial/">A typical workflow with Langmuir.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Saturday 16 November 2024 22:46">Saturday 16 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>