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@CodingBobby
Last active April 23, 2020 20:09
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Calculation of enthaply flash happening in a distillation column
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import math"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook, an enthalpy flash will be calculated.\n",
"To introduce the used methods, the required data for the final calculation is being shown in multiple plots first.\n",
"\n",
"Bob Walter, April 2020"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Antoine coefficients and function that can find the pressure of a boiling liquid at a given temperature or vise versa."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"antoine_A = {\n",
" 'Ethanol': 23.8048,\n",
" 'Water': 23.1965\n",
"}\n",
"\n",
"antoine_B = {\n",
" 'Ethanol': 3803.98,\n",
" 'Water': 3816.44\n",
"}\n",
"\n",
"antoine_C = {\n",
" 'Ethanol': -41.68,\n",
" 'Water': -46.13\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def antoine_p(name, T):\n",
" A = antoine_A[name]\n",
" B = antoine_B[name]\n",
" C = antoine_C[name]\n",
" \n",
" return math.exp(A - B/(273.15 + C + T))\n",
"\n",
"\n",
"def antoine_T(name, p):\n",
" A = antoine_A[name]\n",
" B = antoine_B[name]\n",
" C = antoine_C[name]\n",
" \n",
" return B/(A - math.log(p)) - C - 273.15"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Van Laar activity coefficients and function."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"van_laar = {\n",
" 'EthanolWater': 1.6798,\n",
" 'WaterEthanol': 0.9227\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def act_gamma(name1, name2, X1):\n",
" A12 = van_laar[name1 + name2]\n",
" A21 = van_laar[name2 + name1]\n",
" \n",
" X2 = 1 - X1\n",
" denom = A12*X1 + A21*X2\n",
" \n",
" return [\n",
" math.exp(A12 * (A21 * X2/denom)**2),\n",
" math.exp(A21 * (A12 * X1/denom)**2)\n",
" ]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Function for finding the pressure of a boiling mixture at given temperature and composition and vise versa.\n",
"The latter utilizes an iterative method as the pressure function cannot be solved for the temperature."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def mix_pressure(name1, name2, X1, T):\n",
" [gamma1, gamma2] = act_gamma(name1, name2, X1)\n",
" \n",
" pv1 = antoine_p(name1, T)\n",
" pv2 = antoine_p(name2, T)\n",
" \n",
" return X1*gamma1*pv1 + (1 - X1)*gamma2*pv2"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def find_boiling_temp(name1, name2, X1, pu):\n",
" T1 = antoine_T(name1, pu)\n",
" T2 = antoine_T(name2, pu)\n",
" \n",
" Ta = T1 - (T1 - T2)/3\n",
" Tb = T1 - (T1 - T2)*2/3\n",
" \n",
" pa = mix_pressure(name1, name2, X1, Ta)\n",
" pb = mix_pressure(name1, name2, X1, Tb)\n",
" pn = 0\n",
" Tn = 0\n",
" \n",
" eps = .0000001\n",
" \n",
" while abs(pn - pu) > eps*pu:\n",
" Tn = Ta + (Tb - Ta) * (pu - pa)/(pb - pa)\n",
" pn = mix_pressure(name1, name2, X1, Tn)\n",
" \n",
" if abs(pa - pu) < abs(pb - pu):\n",
" pb = pn\n",
" Tb = Tn\n",
" else:\n",
" pa = pn\n",
" Ta = Tn\n",
" \n",
" return Tn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Composition of vapour phase."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def vapour_comp(name1, name2, X1, T, pu):\n",
" pv1 = antoine_p(name1, T)\n",
" phi1 = pv1/pu\n",
" \n",
" [gamma1, gamma2] = act_gamma(name1, name2, X1)\n",
" K1 = phi1*gamma1\n",
" \n",
" return K1*X1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Enthalpy of liquid and vapor phase."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"cp_L = { # kJ/kg/K\n",
" 'Ethanol': 2.92,\n",
" 'Water': 4.201\n",
"}\n",
"\n",
"cp_V = { # kJ/kg/K\n",
" 'Ethanol': 1.61,\n",
" 'Water': 1.86\n",
"}\n",
"\n",
"dh_V = { # kJ/kg\n",
" 'Ethanol': 821,\n",
" 'Water': 2285\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"h_L = lambda name, T : cp_L[name] * T\n",
"h_V = lambda name, T : cp_V[name] * T"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def h_L_mix(name1, name2, X1, T):\n",
" h_L1 = h_L(name1, T)\n",
" h_L2 = h_L(name2, T)\n",
" \n",
" return X1*h_L1 + (1 - X1)*h_L2\n",
"\n",
"\n",
"def h_V_mix(name1, name2, X1, T, T0):\n",
" h_L1 = h_L(name1, T)\n",
" h_L2 = h_L(name2, T)\n",
" \n",
" h_V1 = h_L1 + dh_V[name1] + h_V(name1, T0-T)\n",
" h_V2 = h_L2 + dh_V[name2] + h_V(name2, T0-T)\n",
" \n",
" return X1*h_V1 + (1 - X1)*h_V2"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def isotherm(T, x1):\n",
" h1 = h_L_mix(comp1, comp2, x1, T)\n",
" \n",
" x2 = vapour_comp(comp1, comp2, x1, T, press)\n",
" h2 = h_V_mix(comp1, comp2, x2, T, find_boiling_temp(comp1, comp2, 0, press))\n",
" \n",
" return [[x1, x2], [h1, h2]]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def isotherm_func(T, x1, x):\n",
" [[x1, x2], [h1, h2]] = isotherm(T, x1)\n",
" \n",
" # extra epsilon as x2-x1 could result in 0 which cannot be divided into\n",
" m = (h2 - h1)/(x2 - x1 + (0.00000001 if x2-x1 == 0 else 0))\n",
" b = (x2*h1 - x1*h2)/(x2 - x1 + (0.00000001 if x2-x1 == 0 else 0))\n",
" \n",
" return m*x + b"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Mathematical tools"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# this can solve two functions for one variable where all the other values are constant\n",
"# the two functions will be iterativey brought closer together until they are only epsilon apart\n",
"def iterate_to_equal(func1, func2, start, limit, debug=False):\n",
" f1 = func1(start)\n",
" f2 = func2(start)\n",
"\n",
" x_curr = start\n",
" \n",
" eps = 1e-10\n",
" it = 200\n",
" off = abs(limit[1]-limit[0])/50\n",
" tmp = 0\n",
" pre = 0\n",
" \n",
" while abs(f1 - f2) > eps and it >= 0:\n",
" if debug is True:\n",
" print('∆({}) = {}'.format(x_curr, abs(f1-f2)))\n",
" \n",
" xn = x_curr-off if x_curr-off >= limit[0] else limit[0]\n",
" xp = x_curr+off if x_curr+off <= limit[1] else limit[1]\n",
" \n",
" f1n = func1(xn)\n",
" f2n = func2(xn)\n",
" \n",
" f1p = func1(xp)\n",
" f2p = func2(xp)\n",
" \n",
" if abs(f1n - f2n) < abs(f1p - f2p):\n",
" tmp = -1\n",
" x_curr = xn\n",
" [f1, f2] = [f1n, f2n]\n",
" else:\n",
" tmp = 1\n",
" x_curr = xp\n",
" [f1, f2] = [f1p, f2p]\n",
" \n",
" if tmp != pre and pre != 0:\n",
" off = off/2\n",
" \n",
" pre = tmp\n",
" it = it - 1\n",
" \n",
" return x_curr"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"### Example Calculations and Plots"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# Mixture properties, used in all following calculations\n",
"comp1 = 'Ethanol'\n",
"comp2 = 'Water'\n",
"press = 101325 # Pa\n",
"T_mix = 90 # °C\n",
"mole_fraction = 0.15 # mol/mol"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Temperatures and vapour content of a mixture in thermal equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 792x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.linspace(0, 1, 100)\n",
"T = [find_boiling_temp(comp1, comp2, x, press) for x in X]\n",
"Y = [vapour_comp(comp1, comp2, X[i], T[i], press) for i in range(len(X))]\n",
"\n",
"fig, [ax1, ax2] = plt.subplots(1, 2, figsize=(11, 5))\n",
"\n",
"\n",
"####\n",
"ax1.set_title('Mole Faction – Temperature')\n",
"\n",
"ax1.set_xlabel('X ({})'.format(comp1))\n",
"ax1.set_ylabel('Temperature')\n",
"\n",
"ax1.plot(Y, T, 'b-', label='dew line')\n",
"ax1.plot(X, T, 'r-', label='bubble line')\n",
"\n",
"ax1.set_xlim(min(X), max(X))\n",
"ax1.set_ylim(min(T), max(T))\n",
"ax1.set_aspect((max(X)-min(X))/(max(T)-min(T)))\n",
"ax1.legend()\n",
"\n",
"\n",
"####\n",
"ax2.set_title('Vapour-Liquid – Equilibrium')\n",
"\n",
"ax2.set_xlabel('X ({})'.format(comp1))\n",
"ax2.set_ylabel('Y ({})'.format(comp1))\n",
"\n",
"ax2.plot(X, Y, 'g-', label='equilibrium')\n",
"ax2.plot([0, 1], [0, 1], 'k-', linewidth=0.75)\n",
"\n",
"ax2.set_xlim(min(X), max(X))\n",
"ax2.set_ylim(min(Y), max(Y))\n",
"ax2.set_aspect('equal')\n",
"ax2.legend()\n",
"\n",
"\n",
"####\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Enthalpy of the mixture at different compositions"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"T_0 = find_boiling_temp(comp1, comp2, 0, press)\n",
"\n",
"H_bubble = [h_L_mix(comp1, comp2, X[i], T[i]) for i in range(len(X))]\n",
"H_dew = [h_V_mix(comp1, comp2, X[i], T[i], T_0) for i in range(len(X))]\n",
"\n",
"T_aux = [find_boiling_temp(comp1, comp2, x, press) for x in X]\n",
"Y_aux = [vapour_comp(comp1, comp2, X[i], T_aux[i], press) for i in range(len(X))]\n",
"H_aux = [h_V_mix(comp1, comp2, Y_aux[i], T_aux[i], T_0) for i in range(len(X))]\n",
"\n",
"X_iso_start = [0.01, 0.02, 0.04, 0.08, 0.14, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.88, 0.95, 0.99]\n",
"\n",
"iso_x = [isotherm(find_boiling_temp(comp1, comp2, x, press), x)[0] for x in X_iso_start]\n",
"iso_h = [isotherm(find_boiling_temp(comp1, comp2, x, press), x)[1] for x in X_iso_start]\n",
"\n",
"\n",
"fig, ax = plt.subplots(1, 1, figsize=(8, 5))\n",
"\n",
"\n",
"####\n",
"ax.set_title('Mole Fraction – Enthalpy')\n",
"\n",
"ax.set_xlabel('X ({})'.format(comp1))\n",
"ax.set_ylabel('Enthalpy')\n",
"\n",
"ax.plot(X, H_dew, 'b-', label='dew line')\n",
"ax.plot(X, H_bubble, 'r-', label='bubble line')\n",
"\n",
"ax.plot(X, H_aux, 'k-', label='auxiliary line')\n",
"\n",
"[ax.plot(iso_x[i], iso_h[i], 'k-') for i in range(len(iso_x))]\n",
"\n",
"ax.set_xlim(min(X), max(X))\n",
"ax.set_ylim(0)\n",
"ax.legend()\n",
"\n",
"\n",
"####\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculation of enthalpy flash"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"# find mole fraction of the boiling line at the mixture temperature\n",
"temp = lambda x : find_boiling_temp(comp1, comp2, x, press)\n",
"mix = lambda x : T_mix\n",
"\n",
"X_at_T = iterate_to_equal(temp, mix, 0.5, [0, 1])\n",
"\n",
"# enthalpy at boiling line\n",
"H_L_at_X = h_L_mix(comp1, comp2, X_at_T, T_mix)\n",
"# enthalpy at dew line\n",
"H_V_at_X = h_V_mix(comp1, comp2, X_at_T, T_mix, temp(0))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"bubble point concentration: 0.05227707661222667 mol/mol\n",
"dew point concentration: 0.33077883163190863 mol/mol\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# find boiling line mole fraction which' isotherm crosses given enthalpy at start mole fraction\n",
"x_start = mole_fraction\n",
"h_end = lambda x : 1000\n",
"\n",
"# the newly iterated x is where the isotherm starts from,\n",
"# x_start is the constant to be crossed.\n",
"h_iso = lambda x : isotherm_func(find_boiling_temp(comp1, comp2, x, press), x, x_start)\n",
"\n",
"x_end = iterate_to_equal(h_iso, h_end, x_start, [0, 1])\n",
"\n",
"found_iso = isotherm(find_boiling_temp(comp1, comp2, x_end, press), x_end)\n",
"\n",
"print('bubble point concentration: {} mol/mol'.format(found_iso[0][0]))\n",
"print('dew point concentration: {} mol/mol'.format(found_iso[0][1]))\n",
"\n",
"\n",
"# plot lines\n",
"T_0 = find_boiling_temp(comp1, comp2, 0, press)\n",
"\n",
"H_bubble = [h_L_mix(comp1, comp2, X[i], T[i]) for i in range(len(X))]\n",
"H_dew = [h_V_mix(comp1, comp2, X[i], T[i], T_0) for i in range(len(X))]\n",
"\n",
"T_aux = [find_boiling_temp(comp1, comp2, x, press) for x in X]\n",
"Y_aux = [vapour_comp(comp1, comp2, X[i], T_aux[i], press) for i in range(len(X))]\n",
"H_aux = [h_V_mix(comp1, comp2, Y_aux[i], T_aux[i], T_0) for i in range(len(X))]\n",
"\n",
"\n",
"fig, ax = plt.subplots(1, 1, figsize=(8, 5))\n",
"\n",
"\n",
"####\n",
"ax.set_title('Mole Fraction – Enthalpy')\n",
"\n",
"ax.set_xlabel('X ({})'.format(comp1))\n",
"ax.set_ylabel('Enthalpy')\n",
"\n",
"ax.plot(X, H_dew, 'b-', label='dew line')\n",
"ax.plot(X, H_bubble, 'r-', label='bubble line')\n",
"\n",
"ax.plot(X, H_aux, 'k-', label='auxiliary line')\n",
"\n",
"\n",
"ax.plot(0, 0, 'g-', label='enthalpy flash')\n",
"plt.annotate('', xytext=(x_start, 0), xy=(x_start, h_end(0)),\n",
" arrowprops=dict(arrowstyle='-|>', color='green', linewidth=1.5))\n",
"plt.annotate('', xytext=(x_start, h_end(0)), xy=(found_iso[0][0], found_iso[1][0]),\n",
" arrowprops=dict(arrowstyle='-|>', color='green', linewidth=1.5))\n",
"plt.annotate('', xytext=(x_start, h_end(0)), xy=(found_iso[0][1], found_iso[1][1]),\n",
" arrowprops=dict(arrowstyle='-|>', color='green', linewidth=1.5))\n",
"\n",
"\n",
"ax.set_xlim(min(X), max(X))\n",
"ax.set_ylim(0)\n",
"ax.legend()\n",
"\n",
"\n",
"####\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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