{"id":4160,"date":"2023-03-18T11:34:25","date_gmt":"2023-03-18T10:34:25","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=4160"},"modified":"2023-08-22T09:53:54","modified_gmt":"2023-08-22T08:53:54","slug":"model-equation-system","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=4160","title":{"rendered":"Model: Equation system"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4160\/#Purpose\" >Purpose<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4160\/#Explanation-of-the-editor\" >Explanation of the editor<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4160\/#Workflow\" >Workflow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4160\/#Workflow-for-setting-up-a-flowsheet\" >Workflow for setting up a flowsheet<\/a><\/li><\/ul><\/nav><\/div>\n\n<p class=\"has-vivid-red-color has-text-color\"><strong>Mandatory element<\/strong><\/p>\n\n\n<p>To formulate an equation system inside MOSAICmodeling, you need at least one notation and one equation. In addition, models may consist of a collection of connected equation systems with different notations, functions, and parameter lists. They may also form whole flowsheets with ports and streams. These hierarchical levels will be explained elsewhere. Here, we assume the simplest case.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Purpose\"><\/span>Purpose<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An equation system is the combination of all your model elements, i.e., notation, equations, functions, etc. It is the element that is then further used in the simulation tab of MOSAICmodeling.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Explanation-of-the-editor\"><\/span>Explanation of the editor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Figure 1 shows the editor of the equation system. The elements of the editor are explained in Table 1. New elements can be added to an equation system by clicking on &#8220;+EQU\/EQS&#8221; at the bottom. Therefore, you can not only add single equations, but also complete equation systems to a new equation system. Thus, you can strongly modularize your equation system for readability. You could have an equation system that only contains mass balances, equilibria, summation, and energy balances; another that contains your hydrodynamic model; one that contains the thermodynamics, etc.<\/p>\n<p>When you add an element to your equation system, the small window in Figure 1 pops up. At this point, you can select the naming policy &#8211; integrate or encapsulate (see <a href=\"http:\/\/mosaic-modeling.de\/?page_id=4158\">connectors<\/a>) &#8211; you want to use for this element. In addition, you can apply a transformation on the element or you can use a connector.<\/p>\n<figure id=\"attachment_4941\" aria-describedby=\"caption-attachment-4941\" style=\"width: 1920px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4941\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem.png\" alt=\"\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem.png 1920w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-300x169.png 300w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-1024x576.png 1024w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-768x432.png 768w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-1536x864.png 1536w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-1110x624.png 1110w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_EquationSystem-528x297.png 528w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><figcaption id=\"caption-attachment-4941\" class=\"wp-caption-text\">Figure 1: The editor of the equation system lets you connect all previously defined model elements and enables you to apply transformations and connectors on them.<\/figcaption><\/figure>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Element<\/th><th class=\"has-text-align-left\" data-align=\"left\">Explanation<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">File<\/td><td class=\"has-text-align-left\" data-align=\"left\">Filename of your equation system once you have saved or loaded it<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Notation<\/td><td class=\"has-text-align-left\" data-align=\"left\">Specifies the super notation of the equation system<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Description<\/td><td class=\"has-text-align-left\" data-align=\"left\">A description of the current equation system<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Keywords<\/td><td class=\"has-text-align-left\" data-align=\"left\">Optional keywords for your equation system<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Usages<\/td><td class=\"has-text-align-left\" data-align=\"left\">Model elements, i.e., equations or functions, in which the equation system is used<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Connected Elements<\/td><td class=\"has-text-align-left\" data-align=\"left\">Contains all connected elements, i.e., equations or equation systems, that are part of the current equation system<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Functions<\/td><td class=\"has-text-align-left\" data-align=\"left\">Contains all functions connected to the current equation system<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Flowsheeting<\/td><td class=\"has-text-align-left\" data-align=\"left\">Specify the ports and streams for equation system (optional)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Preview<\/td><td class=\"has-text-align-left\" data-align=\"left\">Preview the current equation system, i.e., take a look at all included equations and functions<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Elements of the equation system.<\/figcaption><\/figure>\n\n\n<h3><span class=\"ez-toc-section\" id=\"Workflow\"><\/span>Workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The image below illustrates the workflow to set up an equation system. Below that, you can find the workflow for setting up a flowsheet within MOSAICmodeling.<\/p>\n<figure id=\"attachment_3247\" aria-describedby=\"caption-attachment-3247\" style=\"width: 1506px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3247 size-full\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2.png\" alt=\"\" width=\"1506\" height=\"1789\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2.png 1506w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2-253x300.png 253w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2-768x912.png 768w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-System-Editor-Workflow-2-862x1024.png 862w\" sizes=\"auto, (max-width: 1506px) 100vw, 1506px\" \/><\/a><figcaption id=\"caption-attachment-3247\" class=\"wp-caption-text\">Figure 2: Workflow to set up an equation system.<\/figcaption><\/figure>\n<h3><span class=\"ez-toc-section\" id=\"Workflow-for-setting-up-a-flowsheet\"><\/span>Workflow for setting up a flowsheet<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In this workflow, all required steps to set up a flowsheet are laid out. The workflow is based on MOSAICmodeling&#8217;s capabilities regarding units and streams. The steps are based on the concepts illustrated in the examples for <a href=\"http:\/\/mosaic-modeling.de\/?page_id=4741\">Connectors<\/a> and <a href=\"http:\/\/mosaic-modeling.de\/?page_id=834\">Ports and Streams<\/a>.<\/p>\n<figure id=\"attachment_3250\" aria-describedby=\"caption-attachment-3250\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3250 size-full\" title=\"drawit diagram\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/09\/drawit-diagram-4.png\" alt=\"\" width=\"600\" height=\"4484\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/09\/drawit-diagram-4.png 600w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/09\/drawit-diagram-4-40x300.png 40w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/09\/drawit-diagram-4-137x1024.png 137w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-3250\" class=\"wp-caption-text\">Figure 3: Workflow to set up a flowsheet.<\/figcaption><\/figure>","protected":false},"excerpt":{"rendered":"<p>Mandatory element To formulate an equation system inside MOSAICmodeling, you need at least one notation and one equation. In addition, models may consist of a collection of connected equation systems with different notations, functions, and parameter lists. They may also form whole flowsheets with ports and streams. These hierarchical levels will be explained elsewhere. Here, [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":4140,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4160","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/252"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4160"}],"version-history":[{"count":7,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4160\/revisions"}],"predecessor-version":[{"id":5686,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4160\/revisions\/5686"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4140"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}