Beispiel 17.1: LANGMUIRsche Adsorptionsisotherme"
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"Bearbeitet von Alexander Zirn\n",
"\n",
"Dieses Beispiel befindet sich im Lehrbuch auf der Seite 234-235. Die Nummerierung der aus dem Lehrbuch verwendeten Gleichungen entspricht der Nummerierung im Lehrbuch. Gleichungen, die nur im vorliegenden Beispiel verwendet werden, sind durch einfache fortlaufende Zahlen gekennzeichnet."
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"source": [
"# 1. Reaktionsgeschwindigkeit"
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"Gemäß Beispiel 17.1 wird die Stöchiometrie der Adsorption der Komponente $\\mathrm{A}_1$ an freien Adsorptionsstellen $\\mathrm{A}^{\\star}_0$ durch Gleichung (1) beschrieben. Die Desorption der adsorbierten Komponente $\\mathrm{A}^{\\star}_1$ stellt die Rückreaktion dar.\n",
"\n",
"\\begin{align}\n",
"\\mathrm{A}_1+\\mathrm{A}^{\\star}_0\\rightleftharpoons\\mathrm{A}^{\\star}_1\\tag{1}\n",
"\\end{align}\n",
"\n",
"Die Kinetik der Ad- und Desorption wird mit den Gleichungen (2) und (3) ausgedrückt. Darin haben die verwendeten Größen folgende Einheiten: Reaktionsgeschwindigkeit $\\left[r\\right]=\\mathrm{mol\\,m^{-2}\\,s^{-1}}$, Konzentration der nicht-adsorbierten $\\left[c\\right]=\\mathrm{mol\\,m^{-3}}$ und der adsorbierten Spezies $\\left[c^{\\star}\\right]=\\mathrm{mol\\,m^{-2}}$, Geschwindigkeitskonstante der Adsorption $\\left[k_\\mathrm{ads}\\right]=\\mathrm{m^{3}\\,mol^{-1}\\,s^{-1}}$ und der Desorption $\\left[k_\\mathrm{des}\\right]=\\mathrm{s^{-1}}$.\n",
"\n",
"\\begin{align}\n",
"r_{\\mathrm{ads},1}&=k_{\\mathrm{ads},1}\\,c_1\\,c^{\\star}_0,\\tag{2}\\\\\n",
"r_{\\mathrm{des},1}&=k_{\\mathrm{des},1}\\,c^{\\star}_1.\\tag{3}\n",
"\\end{align}\n",
"\n",
"Um eine Abhängigkeit vom Bedeckungsgrad zu erhalten, werden die Gleichungen (2) und (3) jeweils durch die Gesamtkonzentration an Sorptionsstellen an der Oberfläche $c^\\star_\\mathrm{tot}$ geteilt (mit $c^\\star_\\mathrm{tot} = \\sum_i^N c^\\star_\\mathrm{i}$). Nach Umformung ergeben sich Gleichungen (4) und (5) mit $K_{\\mathrm{1}}=\\frac{k_{\\mathrm{ads},1}}{k_{\\mathrm{des},1}}$ (vgl. Gleichung 17.3b im Lehrbuch) sowie $\\theta_1=\\frac{c^{\\star}_1}{c^\\star_\\mathrm{tot}}$ (vgl. Gleichung 17.6 im Lehrbuch).\n",
"\n",
"\\begin{align}\n",
"\\frac{r_{\\mathrm{ads},1}}{c^\\star_\\mathrm{tot}}&=k_{\\mathrm{ads},1}\\,c_1\\,\\left(1-\\theta_1\\right)\\tag{4}\\\\\n",
"\\frac{r_{\\mathrm{des},1}}{c^\\star_\\mathrm{tot}}&=\\frac{k_{\\mathrm{ads},1}}{K_{\\mathrm{1}}}\\,\\theta_1\\tag{5}\n",
"\\end{align}\n",
"\n",
"Diese kinetischen Gleichungen für die Reaktionsgeschwindigkeiten der Ad- und Desorption werden in Python mittels der Funktion \"rxn\" implementiert. "
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"def rxn(t, theta_1, c_1):\n",
" \"\"\" adsorption and desorption rates\n",
"\n",
" Parameters\n",
" ----------\n",
" t : array\n",
" time in s\n",
" theta_1 : array\n",
" coverage in 1\n",
" c_1 : array\n",
" concentration of non-adsorbed species 1 in mol/m3\n",
"\n",
" Returns \n",
" -------\n",
" array of size 2\n",
" rates for adsorption and desorption \n",
" \"\"\"\n",
" \n",
" r_ads = k_1_ads * c_1 * (1 - theta_1) # adsorption rate \n",
" r_des = k_1_ads / K_1 * theta_1 # desorption rate\n",
"\n",
" return [r_ads, r_des]"
]
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"id": "3c7207b7",
"metadata": {},
"source": [
"# 2. Bilanzgleichungen"
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"## 2.1 Dynamischer Fall\n",
"Aus der Stoffmengenbilanz ergibt sich die zeitliche Änderung der adsorbierten Stoffmenge $n^\\star_{1}$ der Komponente $\\mathrm{A_1}$ aus der Differenz der Adsorptions- und Desorptionsgeschwindigkeit (Gleichung (6)). Darin ist $A_\\mathrm{s}$ die Oberfläche des Sorptionsmittels. Die Oberflächenkonzentration $c^\\star$ hat hier die Einheit $\\mathrm{mol\\,m^{-2}}$. Durch Umformung lässt sich die zeitliche Änderung des Bedeckungsgrades in Abhängigkeit der Adsorptions- und Desorptionsgeschwindigkeiten ausdrücken (Gleichung (8)). \n",
"\n",
"\\begin{align}\n",
"\\frac{\\mathrm{d}n^\\star_{1}}{\\mathrm{d}t}&=\\left. \\left(r_{\\mathrm{ads},1}-r_{\\mathrm{des},1}\\right)\\,A_\\mathrm{s}\\right|:A_\\mathrm{s}\\tag{6}\\\\\n",
"\\frac{\\mathrm{d}c^\\star_{1}}{\\mathrm{d}t}&=\\left. r_{\\mathrm{ads},1}-r_{\\mathrm{des},1}\\;\\right|:c^\\star_\\mathrm{tot}\\tag{7}\\\\\n",
"\\frac{\\mathrm{d}\\theta_1}{\\mathrm{d}t}&=\\frac{r_{\\mathrm{ads},1}-r_{\\mathrm{des},1}}{c^\\star_\\mathrm{tot}}\\tag{8}\n",
"\\end{align}\n",
"\n",
"Diese gewöhnliche Differentialgleichung wird in Python mittels der Funktion \"ode\" implementiert."
]
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"def ode(t, theta_1, c_1):\n",
" \"\"\" dynamic balance equation\n",
"\n",
" Parameters\n",
" ----------\n",
" t : array\n",
" time in s\n",
" theta_1 : array\n",
" coverage in 1\n",
" c_1 : array\n",
" concentration non-adsorbed species in mol/m3\n",
"\n",
" Returns \n",
" -------\n",
" array\n",
" time derivative of coverage in s-1\n",
" \"\"\"\n",
" \n",
" r_ads, r_des = rxn(t, theta_1, c_1) # calling adsorption and desorption rate \n",
"\n",
" dtheta_dt = (r_ads - r_des)/c_tot # material balance\n",
" \n",
" return dtheta_dt"
]
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"source": [
"## 2.2 Stationärer Fall"
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"Im stationären Zustand ändert sich der Bedeckungsgrad nicht über die Zeit, da Adsorption sowie Desorption ein dynamisches Gleichgewicht bilden. Entsprechend wird die zeitliche Ableitung des Bedeckungsgrads in der Bilanzgleichung (8) null gesetzt und es ergibt sich Gleichung (9).\n",
"\n",
"\\begin{align}\n",
"0&=r_{\\mathrm{ads},1}-r_{\\mathrm{des},1}\\tag{9}\n",
"\\end{align}\n",
"\n",
"In Realität wird das dynamische Gleichgewicht und damit der stationäre Zustand erst bei $t \\to \\infty$ erreicht (Gleichung (10)).\n",
"\n",
"\\begin{align}\n",
"\\lim \\limits_{t \\to \\infty} \\frac{\\mathrm{d}\\theta_1}{\\mathrm{d}t}=0\\tag{10}\n",
"\\end{align}\n",
"\n",
"\n",
"Die Implementierung in Python erfolgt mittels der Funktion \"ode_stat\". \"ode_stat\" ruft \"ode\" auf und setzt die zeitlichen Ableitungen des Bedeckungsgrades (linke Seite) gleich null, um den stationären Zustand abzubilden. Diese Gleichung ist nur dann korrekt, wenn auch die rechte Seite Null ist, was erst bei $t \\to \\infty$ im Gleichgewicht erreicht wird. Da der Zeitpunkt $\\infty$ nicht implementiert werden kann, wird die Differentialgleichung \"ode\" zu einem sehr späten Zeitpunkt gelöst, zu dem das Gleichgewicht praktisch erreicht ist. Im vorliegenden Beispiel wird angenommen, dass für den Zeitpunkt $t=10^{100}\\,\\mathrm{s}$ die Abweichungen zum Gleichgewicht vernachlässigt werden können.\n",
"\n",
"Der Hintergrund dieser Vorgehensweise ist, dass dieselbe Funktion (hier \"ode\") für den stationären und dynamischen Fall benutzt werden kann. Der stationäre Fall wird entsprechend als Sonderfall in einer zusätzlichen Funktion (hier \"ode_stat\") abgebildet, die auf die allgemeine Funktion zurückgreift. Dadurch wird sichergestellt, dass ein Vergleich beider Lösungsfälle auf der selben Grundlage erfolgt."
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"def ode_stat(theta_1, c_1):\n",
" \"\"\" stationary balance equation\n",
"\n",
" Parameters\n",
" ----------\n",
" theta_1 : array\n",
" coverage in 1\n",
" c_1 : array\n",
" concentration non-adsorbed species in mol/m3\n",
"\n",
" Returns \n",
" -------\n",
" array\n",
" value close to zero\n",
" \"\"\"\n",
"\n",
" zero = ode(1e100, theta_1, c_1) # mass balance\n",
" \n",
" return zero"
]
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"source": [
"# 3. Parameter und Lösen der Gleichungen"
]
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"source": [
"# IMPORT SECTION\n",
"import numpy as np # import of numpy\n",
"from scipy.integrate import solve_ivp # import of initial value problem solver\n",
"import matplotlib.pyplot as plt # import of matplotlib\n",
"from scipy.optimize import root # import of the numerical solver function"
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"## Physical properties\n",
"k_1_ads = 1 # kinetic constant adsorption\n",
"K_1 = 1 # equilibrium constant\n",
"c_tot = 1 # total concentration of surface sorption sites\n",
"\n",
"## Numerical parameters\n",
"N_disc = 101 # discretization\n",
"\n",
"## Starting conditions\n",
"theta_init = [0] # initial coverage of the catalyst surface in 1\n",
"c1_span = np.array((0, 0.2, 0.4, 0.6, 0.8, 1)) # concentration of non-adsorbed species in mol/m3\n",
"c1_high_disc = np.linspace(c1_span[0], c1_span[-1], N_disc) # span for concentration of non-adsorbed species in mol/m3\n",
"\n",
"## Integration spans\n",
"t_span = np.linspace(0, 5, N_disc) # time span in s\n",
"t_lim = [t_span[0], t_span[-1]] # lower and upper limit of time span in s"
]
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"Die stationären Lösungen werden erhalten, indem \"ode_stat\" für verschiedene Gaskonzentrationen gelöst wird. Die Funktion \"stationary_solver\" gibt für alle Gaskonzentrationen aus \"c_1_span\" den entsprechenden Bedeckungsgrad zurück, indem die Nullstellen der Funktion \"ode_stat\" für alle Gaskonzentrationen bestimmt werden. Dafür bietet \"scipy.optimize\" die Funktion \"root\" an."
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"def stationary_solver(ode_stat, c_1_span):\n",
" \"\"\" solving the stationary balance\n",
"\n",
" Parameters\n",
" ----------\n",
" ode_stat : array\n",
" stationary balance equation\n",
" c_1_span : array\n",
" concentration of non-adsorbed species in mol/m3\n",
" \n",
" Returns\n",
" ----------\n",
" array of size N_disc\n",
" solutions of steady-state balance for all gas concentrations in c_1_span\n",
" \"\"\"\n",
" \n",
" rt = np.zeros_like(c_1_span) # empty vector for solutions\n",
"\n",
" for i in np.arange(0, c_1_span.size):\n",
" rt[i] = root(ode_stat, x0 = 0, args = (c_1_span[i]), method ='lm').x # solving of the root problem\n",
" \n",
" return rt"
]
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"
\n",
"Dynamische Lösungen können erhalten werden, indem das Anfangswertproblem \"ode\" mittels des Anfangswertproblemsolvers von \"scipy.integrate\", \"solve_ivp\", gelöst wird. Um die Lösungen für verschiedene Konzentrationen zu erhalten, wird die Funktion \"dynamic_solver\" abhängig der Gaskonzentration formuliert."
]
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"execution_count": 8,
"id": "cd946573",
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"source": [
"def dynamic_solver(ode, c_1):\n",
" \"\"\" solving the dynamic balance\n",
"\n",
" Parameters\n",
" ----------\n",
" ode : array\n",
" dynamic balance equation\n",
" c_1 : array\n",
" concentration of non-adsorbed species in mol/m3\n",
"\n",
" Returns\n",
" -------\n",
" array of size N_disc\n",
" solutions for coverage over time\n",
" \"\"\"\n",
" \n",
" langmuir_isotherm = solve_ivp(ode, t_lim, theta_init, t_eval = t_span, args = ([c_1])).y # solving of initial value problem \n",
" \n",
" return langmuir_isotherm"
]
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"source": [
"# 4. Darstellung der Ergebnisse"
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"
\n",
"Die dynamischen sowie stationären Lösungen sollen im Weiteren graphisch dargestellt werden."
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"outputs": [
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Setting the figure size\n",
"colors = ['darkorange', 'red', 'blue', 'green', 'purple', 'brown'] # list of colors\n",
"\n",
"fig = plt.subplots(1, 2, figsize = (20, 10)) # fixing size of diagram\n",
"\n",
"plt.subplot(1, 2,1) \n",
"for i in np.arange(0, c1_span.size):\n",
" plt.plot(t_span, dynamic_solver(ode, c1_span[i]).T, label='$c_1 = %.1f\\,\\mathrm{mol\\,s^{-1}}$'%(c1_span[i]), color = colors[i]) # plots dynamic solutions for all concentrations of non-adsorbed species\n",
" plt.plot(t_span[-1], dynamic_solver(ode, c1_span[i]).T[-1], 'o', markersize=15, color = colors[i]) # plots solutions in the end of the time frame of the dynamic case for all concentrations of non-adsorbed species\n",
"plt.xlim(t_span[0],t_span[-1]) # sets limits for x-axis\n",
"plt.ylim(0, ) # sets limits for y-axis\n",
"plt.ylabel(r\"$\\theta_1\\,/\\,1$ \", fontsize = 18)# adds label to x-axis\n",
"plt.xlabel(\"$t\\,/\\,\\mathrm{s}$\", fontsize=18) # adds label to y-axis\n",
"plt.tick_params(labelsize=14,direction='in') # turns direction of ticks\n",
"#plt.title('(a)',fontsize=18,loc='left') # label diagrams \n",
"plt.legend(frameon=False, fontsize=14) # plots legend and removes frame\n",
"\n",
"\n",
"plt.subplot(1, 2,2)\n",
"plt.plot(c1_high_disc, stationary_solver(ode_stat, c1_high_disc), '-.') # plots steady-state solutions\n",
"for i in np.arange(0, c1_span.size):\n",
" plt.plot(c1_span[i], dynamic_solver(ode, c1_span[i]).T[-1], 'o', markersize=15, color = colors[i]) # plots solutions in the end of the time frame of the dynamic case for all concentrations of non-adsorbed species\n",
"plt.xlim(c1_span[0],c1_span[-1]) # sets limits for x-axis\n",
"plt.ylim(0, ) # sets limits for y-axis\n",
"plt.ylabel(r\"$\\theta_1\\,/\\,1$ \", fontsize = 18)# adds label to x-axis\n",
"plt.xlabel(\"$c_1\\,/\\,\\mathrm{mol\\,s^{-1}}$\", fontsize=18) # adds label to y-axis\n",
"plt.tick_params(labelsize=14,direction='in') # turns direction of ticks\n",
"#plt.title('(b)',fontsize=18,loc='left') # label diagrams \n",
"\n",
"#plt.figtext(0,0.04,r\"$\\mathbf{Abbildung\\,1:}$(a) Zeitliche Änderung des Bedeckungsgrades $\\theta_1$ für verschiedene Konzentrationen der nicht-adsorbierten Spezies $c_1$, (b) Bedeckungsgrad $\\theta_1$ im Gleichgewicht in Abhängigkeit der Konzentrationen der nicht-adsorbierten Spezies $c_1$.\", fontsize=16, horizontalalignment='left') # subtitle to the figure \n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "eda8d455",
"metadata": {},
"source": [
"Die Abbildung zeigt den zeitlichen Verlauf des Bedeckungsgrads (links) sowie den stationären Bedeckungsgrad (rechts) für verschiedene Konzentrationen der Komponente $\\mathrm{A_1}$. Die Bedeckungsgrade, die am Ende der Zeitspanne des dynamischen Falls erreicht wurden sind markiert (links) und entsprechenen denen im stationären Fall (rechts), da das Sorptionsgleichgewicht im dynamischen Fall praktisch bereits (fast) erreicht wurde.\n",
" \n",
"Die linke Abbildung zeigt, dass der Bedeckungsgrad zunächst stark ansteigt und die Adsorption dominiert. Im zeitlichen Verlauf erreicht der Bedeckungsgrad asymptotisch den stationären Wert. Bereits nach $5\\,\\mathrm{s}$ ist keine signifikante Änderung des Bedeckungsgrades mit der Zeit festzustellen und das Sorptionsgleichgewicht ist praktisch erreicht, da die Geschwindigkeiten der Adsorption und Desorption gleich sind. Für höhere Konzentrationen der Komponente $\\mathrm{A_1}$ in der fluiden Phase können höhere Gleichgewichtsbedeckungsgrade erreicht werden, da die Adsorption gegenüber der Desorption bevorzugt wird. Allerdings werden die Abstände zwischen den Gleichgewichtsbedeckungsgraden immer kleiner, was den Schluss zulässt, dass auch hier eine Sättigung erreicht wird. Dieses asymptotische Verhalten des stationären Bedeckungsgrades in Abhängigkeit der Konzentrationen von Komponente $\\mathrm{A_1}$ ist auch in der rechten Abbildung zu erkennen.\n",
"\n",
"Bemerkung: Es werden generische Werte für die Parameter $c^\\star_\\mathrm{tot} = 1\\,\\mathrm{mol\\,m^{-2}}$, $k_{\\mathrm{ads}} = 1\\,\\mathrm{m^{3}\\,mol^{-1}\\,s^{-1}}$ und $K_{\\mathrm{1}} = 1\\,\\mathrm{m^{3}\\,mol^{-1}}$ gewählt, um die prinzipiellen Verläufe darzustellen. Allerdings sind die Zahlenwerde nicht realistisch, so dass eine quantitative Interpretation der Ergebnisse im Vergleich zu Experimenten nicht sinnvoll ist. Das vorgestellte Modell ist aber geeignet, um die Parameter an eigene Messwerte anzupassen.\n"
]
}
],
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