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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10 : Vapor Liquid Equilibrium VLE at High Pressures"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.1 Page: 260"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Variables\n",
"P = 100. #[psia] Bubble point pressure\n",
"x_ethane = 0.10 # Mole fraction of ethane in liquid phase\n",
"x_hepmath_tane = (1-x_ethane)\n",
"\n",
"# a) From figure 10.7( page 260 ) given in the book\n",
"# We read the chart to get the bubble-point temperature\n",
"# The dew point curve for 100 psia crosses the 10 mol% ethane line at about temperature \n",
"T1 = 165. #[C]\n",
"# Now, we horizontally from that intersection point to the dew-point curve, finding the vapor phase composition of ethane \n",
"y1_e = 0.92\n",
"y1_h = (1- y1_e)\n",
"\n",
"# b) By Raoult's law, we use a trial and error procedureon the temperature\n",
"# Antoine equation consmath.tants for ethanol are given \n",
"A_e = 6.80267\n",
"B_e = 656.4028\n",
"C_e = 255.99\n",
"\n",
"# and that for n-hepmath_tane are\n",
"A_h = 6.9024\n",
"B_h = 1268.115\n",
"C_h = 216.9\n",
"\n",
"# Antoine equation is given by\n",
"# (math.log10p) = (A - B/(T+C))\n",
"T = 50. #[C]\n",
"err = 1.\n",
" \n",
"# Calculations\n",
"while err > 10**(-4):\n",
" p1_e = (10**(A_e - B_e/(C_e + T)))*(14.7/760)\n",
" p1_h = (10**(A_h - B_h/(C_h + T)))*(14.7/760)\n",
" y2_e = p1_e*x_ethane/P\n",
" y2_h = p1_h*x_hepmath_tane/P\n",
" err = abs((y2_e + y2_h) - 1)\n",
" T = T + 0.0001\n",
"\n",
"# Changing the temperature in deg F \n",
"T2 = T*9./5 + 32 #[F] Bubble-point temperature\n",
"\n",
"# c) In this method, we use L-R rule, instead of simple Raoult's law\n",
"# So,\n",
"# y_i = (x_i*p_i)/(v_i*P)\n",
"# Where calculated values of v_i from EOS are given in the table 10.A and are \n",
"v_e = 0.950 # For ethane\n",
"v_h = 0.459 # For n-hepmath_tane\n",
"\n",
"# We again use trial and error on the temperature\n",
"# Let us assume the initial temperature \n",
"Ti = 50. #[C]\n",
"err = 1\n",
" \n",
"while err > 10**(-4):\n",
" p2_e = (10**(A_e - B_e/(C_e + Ti)))*(14.7/760)\n",
" p2_h = (10**(A_h - B_h/(C_h + Ti)))*(14.7/760)\n",
" y3_e = p2_e*x_ethane/(P*v_e)\n",
" y3_h = p2_h*x_hepmath_tane/(P*v_h)\n",
" err = abs((y3_e + y3_h) - 1)\n",
" Ti = Ti + 0.0001\n",
"\n",
"# Changing the temperature in deg F \n",
"T3 = Ti*9./5 + 32 #[F] Bubble-point temperature\n",
"\n",
"# Results\n",
"print \" The results are summarized in the following table:\"\n",
"print \" Variable \\t Values calculated from\\t Values calculated from \\t Values calculated \"\n",
"print \" \\t from figure 10.7 \\t Raoult''s law \\t\\t\\t from L-R rule\"\n",
"print \" Tdeg F) \\t %f \\t\\t %f \\t\\t\\t %f\"%(T1,T2,T3)\n",
"print \" y_ethane \\t %f \\t\\t %f \\t\\t\\t %f\"%(y1_e,y2_e,y3_e)\n",
"print \" y_heptane \\t %f \\t\\t %f \\t\\t\\t %f\"%(y1_h,y2_h,y3_h)\n",
"print \"\\nWhere T is boiling point temperature\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The results are summarized in the following table:\n",
" Variable \t Values calculated from\t Values calculated from \t Values calculated \n",
" \t from figure 10.7 \t Raoult''s law \t\t\t from L-R rule\n",
" Tdeg F) \t 165.000000 \t\t 133.014380 \t\t\t 124.179620\n",
" y_ethane \t 0.920000 \t\t 0.968397 \t\t\t 0.943469\n",
" y_heptane \t 0.080000 \t\t 0.031504 \t\t\t 0.056431\n",
"\n",
"Where T is boiling point temperature\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
" Example 10.2 Page: 262\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"import math \n",
"\n",
"# Variables\n",
"P = 800. #[psia] Bubble point pressure\n",
"x_ethane = 0.60 # Mole fraction of ethane in liquid phase\n",
"x_hepmath_tane = (1-x_ethane)\n",
"\n",
"# a) From figure 10.7( page 260 ) given in the book\n",
"# We read the chart to get the bubble-point temperature\n",
"# The dew point curve for 800 psia crosses the 60 mol% ethane line at about temperature \n",
"# T1 = 165\n",
"# Now, we horizontally from that intersection point to the dew-point curve, finding the vapor phase composition of ethane \n",
"# y1_e = 0.95\n",
"# But, by linear interpolation in the experimental data on which Figure 10.7 is based we make a slightly more reliable estimate and get \n",
"T1 = 209. #[F]\n",
"y1_e = 0.945\n",
"y1_h = (1- y1_e)\n",
"\n",
"# b) By Raoult's law, we use a trial and error procedureon the temperature\n",
"# Antoine equation consmath.tants for ethanol are given \n",
"A_e = 6.80267\n",
"B_e = 656.4028\n",
"C_e = 255.99\n",
"\n",
"# and that for n-hepmath_tane are\n",
"A_h = 6.9024\n",
"B_h = 1268.115\n",
"C_h = 216.9\n",
"\n",
"# Antoine equation is given by\n",
"# (math.log10p) = (A - B/(T+C))\n",
"T = 50. #[C]\n",
"err = 1.\n",
" \n",
"# Calculations\n",
"while err > 10**(-4):\n",
" p1_e = (10**(A_e - B_e/(C_e + T)))*(14.7/760)\n",
" p1_h = (10**(A_h - B_h/(C_h + T)))*(14.7/760)\n",
" y2_e = p1_e*x_ethane/P\n",
" y2_h = p1_h*x_hepmath_tane/P\n",
" err = abs((y2_e + y2_h) - 1)\n",
" T = T + 0.0001\n",
"\n",
"# Changing the temperature in deg F \n",
"T2 = T*9./5 + 32 #[F] Bubble-point temperature\n",
"\n",
"# c) In this method, we use L-R rule, instead of simple Raoult's law\n",
"# So,\n",
"# y_i = (x_i*p_i)/(v_i*P)\n",
"# Where calculated values of v_i from EOS are given \n",
"v_e = 0.6290642 # For ethane\n",
"v_h = 0.0010113 # For n-hepmath_tane\n",
"\n",
"# We again use trial and error on the temperature\n",
"# Let us assume the initial temperature \n",
"Ti = 10. #[C]\n",
"err = 1.\n",
" \n",
"while err > 10**(-4):\n",
" p2_e = (10**(A_e - B_e/(C_e + Ti)))*(14.7/760)\n",
" p2_h = (10**(A_h - B_h/(C_h + Ti)))*(14.7/760)\n",
" y3_e = p2_e*x_ethane/(P*v_e)\n",
" y3_h = p2_h*x_hepmath_tane/(P*v_h)\n",
" err = abs((y3_e + y3_h) - 1)\n",
" Ti = Ti + 0.0001\n",
"\n",
"# Changing the temperature in deg F \n",
"T3 = Ti*9./5 + 32 #[F] Bubble-point temperature\n",
"\n",
"# Results\n",
"print \" The results are summarized in the following table:\"\n",
"print \" \\t Variable \\t\\t Values calculated from\\t Values calculated from Values calculated\"\n",
"print \" \\t\\t\\t\\t from figure 10.7 \\t Raoult''s law \\t\\t from L-R rule\"\n",
"print \" \\n\\t Tdeg F \\t\\t %f \\t\\t %f \\t\\t %f\"%(T1,T2,T3)\n",
"print \" \\t y_ethane \\t\\t %f \\t\\t %f \\t\\t %f\"%(y1_e,y2_e,y3_e)\n",
"print \" \\t y_heptane \\t\\t %f \\t\\t %f \\t\\t %f\"%(y1_h,y2_h,y3_h)\n",
"print \"\\nWhere T is boiling point temperature\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The results are summarized in the following table:\n",
" \t Variable \t\t Values calculated from\t Values calculated from Values calculated\n",
" \t\t\t\t from figure 10.7 \t Raoult''s law \t\t from L-R rule\n",
" \n",
"\t Tdeg F \t\t 209.000000 \t\t 172.210640 \t\t 70.854980\n",
" \t y_ethane \t\t 0.945000 \t\t 0.996044 \t\t 0.632080\n",
" \t y_heptane \t\t 0.055000 \t\t 0.003856 \t\t 0.367822\n",
"\n",
"Where T is boiling point temperature\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
" Example 10.3 Page: 262\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"\n",
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"# Variables\n",
"# The initial data for this example is same as that of example 10.2, i.e.\n",
"P = 800. #[psia] Bubble point pressure\n",
"x_e = 0.60 # Mole fraction of ethane in liquid phase\n",
"x_h = (1-x_e) # Mole fraction of n-hepmath.tane in the liquid phase\n",
"R = 0.08314 #( L*bar/(mol*K)) Universal gas consmath.tant \n",
"\n",
"# Changing the pressure in bar\n",
"Pb = (800/14.7)*(1.01325) #[bar]\n",
"\n",
"# In this problem we will denote ethane by 'e' and that to n-hepmath.tane by 'h'\n",
"# From table A.1 ( page 417 ) given in the book, critical temperatures of ethane and hepmath.tane are \n",
"T_c_e = 305.3 #[K]\n",
"T_c_h = 540.2 #[K]\n",
"\n",
"# and critical pressures are\n",
"P_c_e = 48.72 #[bar]\n",
"P_c_h = 27.40 #[bar]\n",
"\n",
"# also the accentric facors are \n",
"w_e = 0.1\n",
"w_h = 0.35\n",
"\n",
"# Thus we have\n",
"P_r_e = Pb/P_c_e\n",
"P_r_h = Pb/P_c_h\n",
"\n",
"# Now from equations (F.13) and (F.14) ( page 459 ) given in the book we have\n",
"# A_e = 0.42747 + ( 1 + (0.480 + 1.574*w_e - 0.17*w_e**(2))*( 1 - T_r_e**(0.5)))**(2)*(P_r_e/T_r_e**(2))\n",
"# A_h = 0.42747 + ( 1 + (0.480 + 1.574*w_h - 0.17*w_h**(2))*( 1 - T_r_h**(0.5)))**(2)*(P_r_h/T_r_h**(2))\n",
"# and\n",
"# B_e = 0.08664*(P_r_e/T_r_e)\n",
"# B_h = 0.08664*(P_r_h/T_r_h)\n",
"\n",
"# We will take the help trial and error method both on Temperature and the vapor phase composition of ethane\n",
"# Let us assume the starting temperature 200 deg F. Changing this temperature in K\n",
"T = (200-32)*5./9 + 273.15 #[K]\n",
"err = 1\n",
"\n",
"# Calculations\n",
"while err > 10**(-4):\n",
" T_r_e = T/T_c_e\n",
" T_r_h = T/T_c_h\n",
" A_e = 0.42747*( 1 + (0.480 + 1.574*w_e - 0.17*w_e**(2))*( 1 - T_r_e**(0.5)))**(2)*(P_r_e/T_r_e**(2))\n",
" A_h = 0.42747*( 1 + (0.480 + 1.574*w_h - 0.17*w_h**(2))*( 1 - T_r_h**(0.5)))**(2)*(P_r_h/T_r_h**(2))\n",
" \n",
" B_e = 0.08664*(P_r_e/T_r_e)\n",
" B_h = 0.08664*(P_r_h/T_r_h)\n",
" \n",
" # Now we will take the starting value of vapor phase composition of ethane as \n",
" y_e = 0.9\n",
" err1 = 1\n",
" \n",
" while err1 > 10**(-6):\n",
" # Now value of A_mix and B_mix for both liquid and vapor phase are calculated as\n",
" \n",
" A_mix_l = (x_e*math.sqrt(A_e) + x_h*math.sqrt(A_h))**(2) # For liquid phase\n",
" A_mix_v = (y_e*math.sqrt(A_e) + (1 - y_e)*math.sqrt(A_h))**(2) # For vapor phase\n",
" B_mix_l = (x_e*B_e + x_h*B_h) # For liquid \n",
" B_mix_v = (y_e*B_e + (1 - y_e)*B_h) # For liquid \n",
"\n",
" def f(z1): \n",
" return z1**(3) - z1**(2) + z1*(A_mix_l - B_mix_l - B_mix_l**(2)) - A_mix_l*B_mix_l\n",
" z_l = fsolve(f,0.2)\n",
" # and\n",
" def g(z2): \n",
" return z2**(3) - z2**(2) + z2*(A_mix_v - B_mix_v - B_mix_v**(2)) - A_mix_v*B_mix_v\n",
" z_v = fsolve(g,0.3)\n",
" # Now\n",
" phi_el = B_e/B_mix_l*( z_l - 1) - math.log(z_l - B_mix_l) - (A_mix_l/B_mix_l)*(2*math.sqrt(A_e/A_mix_l)-B_e/B_mix_l)*math.log(1-B_mix_l/z_l)\n",
" phi_hl = B_h/B_mix_l*( z_l - 1) - math.log(z_l - B_mix_l) - (A_mix_l/B_mix_l)*(2*math.sqrt(A_h/A_mix_l)-B_h/B_mix_l)*math.log(1-B_mix_l/z_l)\n",
" phi_ev = B_e/B_mix_v*( z_v - 1) - math.log(z_v - B_mix_v) - (A_mix_v/B_mix_v)*(2*math.sqrt(A_e/A_mix_v)-B_e/B_mix_v)*math.log(1-B_mix_v/z_v)\n",
" phi_hv = B_h/B_mix_v*( z_v - 1) - math.log(z_v - B_mix_v) - (A_mix_v/B_mix_v)*(2*math.sqrt(A_h/A_mix_v)-B_h/B_mix_v)*math.log(1-B_mix_v/z_v)\n",
" K_e = phi_el/phi_ev\n",
" K_h = phi_hl/phi_hv\n",
" y_e1 = K_e*x_e\n",
" y_h1 = K_h*x_h\n",
" err1 =abs((y_e1 - y_e))\n",
" y_e = y_e1\n",
"\n",
" err = abs((y_e1 + y_h1) -1)\n",
" T = T + 0.1\n",
"\n",
"\n",
"# Changing the temperature in deg F, we have \n",
"Tf = ( T - 273.15)*9./5 + 32 #[F]\n",
"\n",
"# Results\n",
"print \" Bubble point of the given ethanol and n-hepmath.tane mixture at 800 psia is %f deg F\"%(Tf)\n",
"print \" Amount of ethanol in the vapour phase of the mixture at the given condition is %f \"%(y_e1)\n",
"print \" Amount of n-heptane in the vapour phase of the mixture at the given condition is %f \"%(y_h1)\n",
"\n",
"# Answers may vary because of rounding error."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Bubble point of the given ethanol and n-hepmath.tane mixture at 800 psia is 200.180000 deg F\n",
" Amount of ethanol in the vapour phase of the mixture at the given condition is 0.599997 \n",
" Amount of n-heptane in the vapour phase of the mixture at the given condition is 0.399997 \n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:227: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
" improvement from the last five Jacobian evaluations.\n",
" warnings.warn(msg, RuntimeWarning)\n",
"/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:227: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
" improvement from the last ten iterations.\n",
" warnings.warn(msg, RuntimeWarning)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
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