Urethane - Revision history

RobertLampel: /* Parameters */

2024-11-13T09:07:03Z

Parameters

← Older revision		Revision as of 09:07, 13 November 2024
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	== Parameters ==		== Parameters ==

	<table border="1.5">		<table style="border-collapse:collapse" border="1.5">
	<tr>		<tr>
	<td colspan=2 style="text-align: center; padding:5pt">Intial Values</td>		<td colspan=2 style="text-align: center; padding:5pt">Intial Values</td>
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	<table border="1.5">		<table style="border-collapse:collapse" border="1.5">
	<tr>		<tr>
	<td colspan=3 style="text-align: center; padding:5pt">Constants</td>		<td colspan=3 style="text-align: center; padding:5pt">Constants</td>

RobertLampel: /* Chemical background */

2024-11-13T09:02:38Z

Chemical background

← Older revision		Revision as of 09:02, 13 November 2024
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	<tr style="border-bottom: 2pt solid black">		<tr style="border-bottom: 2pt solid black">
	<th style="border-right:2pt solid black; padding:2pt">Letter</th>		<th style="border-right:2pt solid black; padding:2pt">Letter</th>
	<th>Substance</th>		<th style="padding:2pt">Substance</th>
	</tr>		</tr>
	<tr>		<tr>

RobertLampel: /* Chemical background */

2024-11-13T09:02:01Z

Chemical background

← Older revision		Revision as of 09:02, 13 November 2024
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	</p>		</p>
	For ease of notation the chemical substances use the abbreviations		For ease of notation the chemical substances use the abbreviations
	<table border="1">		<table style="border-collapse:collapse;" border="1">
	<tr>		<tr style="border-bottom: 2pt solid black">
	<th>Letter</th>		<th style="border-right:2pt solid black; padding:2pt">Letter</th>
	<th>Substance</th>		<th>Substance</th>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>A</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>A</math></td>
	<td>Phenyl Isocyanate</td>		<td style="padding:2pt">Phenyl Isocyanate</td>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>B</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>B</math></td>
	<td>Butanol</td>		<td style="padding:2pt">Butanol</td>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>C</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>C</math></td>
	<td>Urethane <i>(Main Product)</i></td>		<td style="padding:2pt">Urethane <i>(Main Product)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>D</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>D</math></td>
	<td>Allophanate <i>(Secondary Product)</i></td>		<td style="padding:2pt">Allophanate <i>(Secondary Product)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>E</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>E</math></td>
	<td>Isocyanurate <i>(Byproduct)</i></td>		<td style="padding:2pt">Isocyanurate <i>(Byproduct)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td><math>L</math></td>		<td style="border-right:2pt solid black; text-align: center; padding:2pt"><math>L</math></td>
	<td>Dimethyl Sulfoxide</td>		<td style="padding:2pt">Dimethyl Sulfoxide</td>
	</tr>		</tr>
	</table>		</table>

RobertLampel: /* Optimal Experimental Design Problem */

2024-11-12T15:20:52Z

Optimal Experimental Design Problem

← Older revision		Revision as of 15:20, 12 November 2024
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	== Optimal Experimental Design Problem ==		== Optimal Experimental Design Problem ==
	<!--<span style="color:red">To specify</span~~>--~~>		<!--<span style="color:red">To specify</span>
	In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means		In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means
	<p>		<p>
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	</math>		</math>
	</p>		</p>
			-->
	Now we formulate the OED problem as described in [[#OEDUDE \| [3]]].		Now we formulate the OED problem as described in [[#OEDUDE \| [3]]].
	<p>		<p>

RobertLampel: /* Optimal Experimental Design Problem */

2024-11-12T15:19:56Z

Optimal Experimental Design Problem

← Older revision		Revision as of 15:19, 12 November 2024
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	== Optimal Experimental Design Problem ==		== Optimal Experimental Design Problem ==
	<span style="color:red">To specify</span>		<!--<span style="color:red">To specify</span>-->
	In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means		In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means
	<p>		<p>

RobertLampel: /* Mathematical formulation */

2024-11-12T15:16:50Z

Mathematical formulation

← Older revision		Revision as of 15:16, 12 November 2024
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	</math>		</math>
	</p>		</p>
	Each experiment lasts 80 h. The beginning is Monday, 8 pm, the end Thursday, 4 pm. During the		Each experiment lasts 80 hours. The beginning is Monday, 8 pm, the end Thursday, 4 pm. During the
	nights, the feed rates and the heating=cooling rate have to be zero due to safety rules.		nights, the feed rates and the heating=cooling rate have to be zero due to safety rules.
	Further control variables for experimental design are		Further control variables for experimental design are

RobertLampel: /* Mathematical formulation */

2024-11-12T15:07:12Z

Mathematical formulation

← Older revision		Revision as of 15:07, 12 November 2024
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	<math>		<math>
	\begin{align}		\begin{align}
	MV_1 &= \frac{n_{a2}+n_{a2eb}}{n_{a1} + n_{a1ea}}, \~~quad~~ && g_a &= \frac{n_{a1} \cdot M_1 + n_{a2} \cdot M_2}{n_{a1} \cdot M_1 + n_{a2} \cdot M_2 + n_{a6} \cdot M_6}, \\		MV_1 &= \frac{n_{a2}+n_{a2eb}}{n_{a1} + n_{a1ea}}, \qquad && g_a &&= \frac{n_{a1} \cdot M_1 + n_{a2} \cdot M_2}{n_{a1} \cdot M_1 + n_{a2} \cdot M_2 + n_{a6} \cdot M_6}, \\
	MV_2 &= \frac{n_{a1ea}}{n_{a1}}, && g_{aea} &= \frac{n_{a1ea} \cdot M_1}{n_{a1ea} \cdot M_1 + n_{a6ea} \cdot M_6}, \\		MV_2 &= \frac{n_{a1ea}}{n_{a1}}, && g_{aea} &&= \frac{n_{a1ea} \cdot M_1}{n_{a1ea} \cdot M_1 + n_{a6ea} \cdot M_6}, \\
	MV_3 &= \frac{n_{a2eb}}{n_{a1}}, \quad && g_{aeb} &= \frac{n_{a2eb} \cdot M_2}{n_{a2eb} \cdot M_2 + n_{a6eb} \cdot M_6}, \\		MV_3 &= \frac{n_{a2eb}}{n_{a1}}, \quad && g_{aeb} &&= \frac{n_{a2eb} \cdot M_2}{n_{a2eb} \cdot M_2 + n_{a6eb} \cdot M_6}, \\
	& && V_a &= \frac{n_{a1}}{\rho_1} \cdot M_1 + \frac{n_{a2}}{\rho_2} \cdot M_2 + \frac{n_{a6}}{\rho_6} \cdot M_6		& && V_a &&= \frac{n_{a1}}{\rho_1} \cdot M_1 + \frac{n_{a2}}{\rho_2} \cdot M_2 + \frac{n_{a6}}{\rho_6} \cdot M_6
	\end{align}		\end{align}
	</math>		</math>

RobertLampel: /* Optimal Experimental Design Problem */

2024-11-12T13:22:23Z

Optimal Experimental Design Problem

← Older revision		Revision as of 13:22, 12 November 2024
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	== Optimal Experimental Design Problem ==		== Optimal Experimental Design Problem ==
			<span style="color:red">To specify</span>
	In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means		In this approach, we add the so-called sensitivities <math>G=dy/d\theta</math>. For the differential equations this means
	<p>		<p>

RobertLampel: /* Chemical background */

2024-11-12T12:49:24Z

Chemical background

← Older revision		Revision as of 12:49, 12 November 2024
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	</tr>		</tr>
	<tr>		<tr>
	<td>A</td>		<td><math>A</math></td>
	<td>Phenyl Isocyanate</td>		<td>Phenyl Isocyanate</td>
	</tr>		</tr>
	<tr>		<tr>
	<td>B</td>		<td><math>B</math></td>
	<td>Butanol</td>		<td>Butanol</td>
	</tr>		</tr>
	<tr>		<tr>
	<td>C</td>		<td><math>C</math></td>
	<td>Urethane <i>(Main Product)</i></td>		<td>Urethane <i>(Main Product)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td>D</td>		<td><math>D</math></td>
	<td>Allophanate <i>(Secondary Product)</i></td>		<td>Allophanate <i>(Secondary Product)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td>E</td>		<td><math>E</math></td>
	<td>Isocyanurate <i>(Byproduct)</i></td>		<td>Isocyanurate <i>(Byproduct)</i></td>
	</tr>		</tr>
	<tr>		<tr>
	<td>L</td>		<td><math>L</math></td>
	<td>Dimethyl Sulfoxide</td>		<td>Dimethyl Sulfoxide</td>
	</tr>		</tr>

RobertLampel: /* Mathematical formulation */

2024-11-12T12:48:02Z

Mathematical formulation

← Older revision		Revision as of 12:48, 12 November 2024
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	== Mathematical formulation ==		== Mathematical formulation ==
	We can ~~model~~ this process using a nonlinear DAE model		We can describe this process using a nonlinear DAE model
	<p>		<p>
	<math>		<math>