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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Equations, units, and PALEO variable name conventions · PALEOsediment Documentation</title><meta name="title" content="Equations, units, and PALEO variable name conventions · PALEOsediment Documentation"/><meta property="og:title" content="Equations, units, and PALEO variable name conventions · PALEOsediment Documentation"/><meta property="twitter:title" content="Equations, units, and PALEO variable name conventions · PALEOsediment Documentation"/><meta name="description" content="Documentation for PALEOsediment Documentation."/><meta property="og:description" content="Documentation for PALEOsediment Documentation."/><meta property="twitter:description" content="Documentation for PALEOsediment Documentation."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">PALEOsediment Documentation</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">PALEOsediment.jl documentation</a></li><li><span class="tocitem">Examples and Tutorials</span><ul><li><input class="collapse-toggle" id="menuitem-2-1" type="checkbox"/><label class="tocitem" for="menuitem-2-1"><span class="docs-label">boudreau1996</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../collated_examples/boudreau1996/README/">Sediment Boudreau (1996) test cases</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-2-2" type="checkbox"/><label class="tocitem" for="menuitem-2-2"><span class="docs-label">transport_tests</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../collated_examples/transport_tests/README/">Sediment transport test cases</a></li></ul></li></ul></li><li><span class="tocitem">Design</span><ul><li class="is-active"><a class="tocitem" href>Equations, units, and PALEO variable name conventions</a><ul class="internal"><li><a class="tocitem" href="#Reservoir-configuration"><span>Reservoir configuration</span></a></li><li><a class="tocitem" href="#Rate-laws-for-reactions"><span>Rate laws for reactions</span></a></li><li><a class="tocitem" href="#Unit-conversions-for-rate-laws"><span>Unit conversions for rate laws</span></a></li></ul></li></ul></li><li><span class="tocitem">Reference</span><ul><li><a class="tocitem" href="../PALEOsediment_Reactions/">PALEOsediment Reactions</a></li></ul></li><li><a class="tocitem" href="../References/">References</a></li><li><a class="tocitem" href="../indexpage/">Index</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Design</a></li><li class="is-active"><a href>Equations, units, and PALEO variable name conventions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Equations, units, and PALEO variable name conventions</a></li></ul></nav><div class="docs-right"><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Equations,-units,-and-PALEO-variable-name-conventions"><a class="docs-heading-anchor" href="#Equations,-units,-and-PALEO-variable-name-conventions">Equations, units, and PALEO variable name conventions</a><a id="Equations,-units,-and-PALEO-variable-name-conventions-1"></a><a class="docs-heading-anchor-permalink" href="#Equations,-units,-and-PALEO-variable-name-conventions" title="Permalink"></a></h1><p>Conservation equations for a species <code>C</code> in PALEO are defined in terms of moles of <code>C</code> per cell, where a cell <code>volume (m^3)</code> is partitioned into solute volume <code>volume_solute = volume * phi (m^3)</code> and a solid volume <code>volume_solid = volume * phi_solid (m^3)</code> where <code>phi</code> is the porosity and <code>phi_solid = 1 - phi</code>.</p><p>The conservation equation for a species <code>C</code> is then:</p><pre><code class="nohighlight hljs">dC/dt = C_sms (mol yr-1)</code></pre><p>A solute concentration is defined as moles per m^3 of solute:</p><pre><code class="nohighlight hljs">C_conc = C / volume_solute (mol m-3)</code></pre><p>and a solid concentration as moles per m^3 of solid:</p><pre><code class="nohighlight hljs">C_conc = C / volume_solid (mol m-3)</code></pre><h2 id="Reservoir-configuration"><a class="docs-heading-anchor" href="#Reservoir-configuration">Reservoir configuration</a><a id="Reservoir-configuration-1"></a><a class="docs-heading-anchor-permalink" href="#Reservoir-configuration" title="Permalink"></a></h2><p>For the usual case where <code>C</code> is defined by a <code>ReactionReservoir</code> or <code>ReactionReservoirTotal</code>, the yaml file configuration for a solute reservoir should include:</p><pre><code class="nohighlight hljs"> variable_links:
volume: volume_solute # relink volume so C_conc is solute concentration
variable_attributes:
R_conc:vphase: VP_Solute # label phase for transport etc</code></pre><p>and the yaml file for a solid reservoir should include:</p><pre><code class="nohighlight hljs"> variable_links:
volume: volume_solid # relink volume so C_conc is solid-phase concentration
variable_attributes:
R_conc:vphase: VP_Solid # label phase for transport etc</code></pre><h2 id="Rate-laws-for-reactions"><a class="docs-heading-anchor" href="#Rate-laws-for-reactions">Rate laws for reactions</a><a id="Rate-laws-for-reactions-1"></a><a class="docs-heading-anchor-permalink" href="#Rate-laws-for-reactions" title="Permalink"></a></h2><p>PALEO units for rate constants for both solute and solid-phase first-order rate constants are <code>(mol m-3)-1 yr-1</code>. This follows the convention in (<a href="../References/#VanCappellen1996a">Van Cappellen and Wang, 1996</a>) (see Table 3 and equations 72 and 76).</p><h4 id="Reactions-between-solute-species"><a class="docs-heading-anchor" href="#Reactions-between-solute-species">Reactions between solute species</a><a id="Reactions-between-solute-species-1"></a><a class="docs-heading-anchor-permalink" href="#Reactions-between-solute-species" title="Permalink"></a></h4><p>For a hypothetical reaction between solutes A, B, C</p><pre><code class="nohighlight hljs">A + B -&gt; C</code></pre><p>with first-order kinetics hence reaction rate</p><pre><code class="nohighlight hljs">R_abc = k_abc * A_conc * B_conc (mol (m^3 solute)-1 yr-1)</code></pre><p><code>k_abc</code> has units <code>(mol m-3)-1 yr-1</code>, where concentration units are <code>mol (m^3 solute)-1</code>. <code>A_sms</code> and similar contributions to tracer conservation equations are then:</p><pre><code class="nohighlight hljs">A_sms = - R_abc * volume_solute (mol yr-1)</code></pre><p>and similar for <code>B_sms</code>, <code>C_sms</code>.</p><p>This means that PALEO Reactions implementing eg secondary redox between solute species usually will require the yaml configuration to include:</p><pre><code class="nohighlight hljs"> variable_links:
volume: volume_solute # relink volume so volume refers to solute volume</code></pre><h4 id="Reactions-between-a-solid-phase-species-and-solute-phase-species"><a class="docs-heading-anchor" href="#Reactions-between-a-solid-phase-species-and-solute-phase-species">Reactions between a solid phase species and solute phase species</a><a id="Reactions-between-a-solid-phase-species-and-solute-phase-species-1"></a><a class="docs-heading-anchor-permalink" href="#Reactions-between-a-solid-phase-species-and-solute-phase-species" title="Permalink"></a></h4><p>For a hypothetical reaction between solid-phase species <code>D</code> and solute <code>B</code></p><pre><code class="nohighlight hljs">D + B -&gt; C</code></pre><p>with first-order kinetics hence reaction rate</p><pre><code class="nohighlight hljs">R_dbc = k_dbc * D_conc * B_conc (mol (m^3 solid)-1 yr-1)</code></pre><p><code>k_dbc</code> (still) has units <code>(mol m-3)-1 yr-1</code>, where concentration units for <code>D</code> are <code>mol (m^3 solid)-1</code> and for B are <code>mol (m^3 solute)-1</code>. <code>D_sms</code> and similar contributions to tracer conservation equations are then:</p><pre><code class="nohighlight hljs">D_sms = - R_dbc * volume_solid (mol yr-1)</code></pre><p>and similar for <code>B_sms</code>, <code>C_sms</code>.</p><p>This means that PALEO Reactions implementing eg secondary redox between a solid and solute species usually will require the yaml configuration to include:</p><pre><code class="nohighlight hljs"> variable_links:
volume: volume_solid # relink volume so volume refers to solid phase volume</code></pre><h2 id="Unit-conversions-for-rate-laws"><a class="docs-heading-anchor" href="#Unit-conversions-for-rate-laws">Unit conversions for rate laws</a><a id="Unit-conversions-for-rate-laws-1"></a><a class="docs-heading-anchor-permalink" href="#Unit-conversions-for-rate-laws" title="Permalink"></a></h2><pre><code class="nohighlight hljs">[mol/l]-1 [yr-1] = [mol m-3] [yr-1]
1 M-1 yr-1 = 1e-3 (mol m-3)-1 yr-1
1 M-0.5 yr-1 = 3.16e-2 (mol m-3)^-0.5 yr-1

1 M-1 h-1 = 8.766 (mol m-3)-1 yr-1
1 M-0.5 h-1 = 277.2 (mol m-3)^-0.5 yr-1</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../collated_examples/transport_tests/README/">« Sediment transport test cases</a><a class="docs-footer-nextpage" href="../PALEOsediment_Reactions/">PALEOsediment Reactions »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 28 February 2024 20:14">Wednesday 28 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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