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	   "source": [
       "# Chapter 8: Multiphase Reactors"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.1: Gas_absorption_coefficient_and_fraction_of_overall_resistance.sce"
		   ]
		  },
  {
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"//Harriot P., 2003, Chemical Reactor Design (I-Edition), Marcel Dekker, Inc., USA, pp 436.\n",
"//Chapter-8 Ex8.1 Pg No. 323\n",
"//Title:Gas absorption coefficient and fraction of overall resistance\n",
"//============================================================================================================\n",
"clear\n",
"clc\n",
"//INPUT\n",
"rho_oil=0.8;//Density of oil (g/cm3)\n",
"IV_init=130;//Iodine Value initial\n",
"IV_final=80;//Iodine Value final\n",
"P=45;//Pressure of system (psig)\n",
"T_C=204;// Temperature of system (°C)\n",
"t_run=[26 17];//Time required for hydrogenation run 2;\n",
"frac_Ni=[0.005 0.0125]//Fraction of Nickel used for different run\n",
"\n",
"//CALCULATION\n",
"r_ave=((IV_init -IV_final))*(0.039*rho_oil)*(1/60).*(t_run.^(-1));//Relationship between Iodine value and Hydrogen consumption (mol- H2/ L sec)\n",
"H_H2= 4*10^(-3);//Solubility of H2 from Fig8.4 Pg No.322\n",
"P_H2=(P/14.7)+1;//Absolute Pressure in (atm)\n",
"C_H2=P_H2 *H_H2;\n",
"Ci_by_r=C_H2.*(r_ave.^(-1));\n",
"Coeff_R_cat=frac_Ni.^(-1);\n",
"equation=[ones(1,2);Coeff_R_cat]//Simultaneous Equation\n",
"Resistance= Ci_by_r*inv(equation);\n",
"Gas_abs_resistance=(Resistance(1)*100 ).*(Ci_by_r.^(-1));\n",
"Gas_abs_coefficient=(1/Resistance(1));\n",
"\n",
"//OUTPUT\n",
"mprintf('\nThe Gas absorption coefficient is %f sec-1',Gas_abs_coefficient);\n",
"mprintf('\n The Fraction of overall resistance due to gas absorption\n  Run 1 %0.0f%% \n  Run 2 %0.0f%%',Gas_abs_resistance(1),Gas_abs_resistance(2));\n",
"\n",
"//FILE OUTPUT\n",
"fid= mopen('.\Chapter8-Ex1-Output.txt','w');\n",
"mfprintf(fid,'\nThe Gas absorption coefficient is %f sec-1',Gas_abs_coefficient);\n",
"mfprintf(fid,'\n The Fraction of overall resistance due to gas absorption\n  Run 1 %0.0f%% \n  Run 2 %0.0f%%',Gas_abs_resistance(1),Gas_abs_resistance(2));\n",
"mclose(fid);\n",
"//=======================================================END OF PROGRAM================================================="
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: External_Mass_Transfer_resistance.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"//Harriot P., 2003, Chemical Reactor Design (I-Edition), Marcel Dekker, Inc., USA, pp 436.\n",
"//Chapter-8 Ex8.2 Pg No. 329\n",
"//Title:External Mass Transfer resistance\n",
"//===========================================================================================================\n",
"\n",
"clear\n",
"clc\n",
"//INPUT\n",
"Chi=1.9;\n",
"M_A=2;//Molecular weight of Hydrogen\n",
"M_B=32;//Molecular weight of methanol\n",
"rho=0.79;//Density of methanol\n",
"myu=0.52;//Viscosity of methanol (cP)\n",
"V_A=14.3//Molar volume H2\n",
"T_C=30;//Operating Temperature(°C)\n",
"T_K=273+T_C//Temperature (K)\n",
"Epsilon=0.4;//Porosity\n",
"rho_cat_dry=1.2;//Density of dry catalyst (g/cm3)\n",
"rho_s=2;//Solid density\n",
"g=9.8// Acceleration due to gravity(m/s2)\n",
"d_p=10^(-3);//Size of catalyst (cm)\n",
"lambda=1.3;//From equation 8.4 Pg. No. 317\n",
"r_vol=2.4;//Measured rate (L/min)\n",
"V_mol=22.4;//(L/mol) assuming ideal gas\n",
"C_H2=4.1*10^(-3);//From Figure 8.3 (mol/L)  Pg. No. 321\n",
"\n",
"\n",
"//CALCULATION\n",
"//Assume D_H2 is three times the value given by the Wilke–Chang Equation\n",
"D_H2=3*(7.4*(10^(-8))*(Chi*M_B)^(0.5)*T_K)/(myu*(V_A)^0.6)\n",
"Sc=myu*10^-2/(rho*D_H2);\n",
"rho_cat_methanol=(1-Epsilon)*rho_s+Epsilon*rho;\n",
"delta_rho=rho_cat_methanol-rho;\n",
"v_t=(g*10*(d_p)^2*delta_rho)/(18*myu*10^-2);// From Stoke's Law\n",
"Re=rho*v_t*d_p/(myu*10^-2);\n",
"Sh_star=2+0.6*(Re)^(0.5)*(Sc^(1/3));//Refer equation 8.9  Pg.No.325\n",
"kc_star=Sh_star*D_H2/d_p;\n",
"kc=2*kc_star;//With vigorous agitation\n",
"a_c=6*lambda/(d_p*rho_cat_dry);//From Equation 8.4 Pg. No. 317 \n",
"r_mol=r_vol/(22.4*60);//\n",
"delta_C_ext=r_mol*10^3/(kc*a_c);\n",
"percent_ext_resistance=(delta_C_ext/C_H2)*100;\n",
"\n",
"//OUTPUT\n",
"mprintf('\nThe external mass transfer resistance is about %0.0f%% of overall resistance',percent_ext_resistance);\n",
"mprintf('\n The external mass transfer resistance is barely significant');\n",
"\n",
"//FILE OUTPUT\n",
"fid= mopen('.\Chapter8-Ex2-Output.txt','w');\n",
"mfprintf(fid,'\nThe external mass transfer resistance is about %0.0f%% of overall resistance',percent_ext_resistance);\n",
"mfprintf(fid,'\n The external mass transfer resistance is barely significant');\n",
"mclose(fid);\n",
"//=====================================================END OF PROGRAM=========================================\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
""
   ]
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: Apparent_rate_constant_and_consistency.sce"
		   ]
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"//Harriot P., 2003, Chemical Reactor Design (I-Edition), Marcel Dekker, Inc., USA, pp 436.\n",
"//Chapter-8 Ex8.3 Pg No.\n",
"//Title:Apparent rate constant and consistency\n",
"//===========================================================================================================\n",
"\n",
"clear\n",
"clc\n",
"// COMMON INPUT\n",
"LHSV_inv=[0.75 1.39];//Refer table 8.2 Test Results (Liquid Hourly Space Velocity)\n",
"X_S=[0.77 0.83];//Refer table 8.2 Percentage Sulphur removal\n",
"T_C=365;//Operating Temperature (°C)\n",
"rho=0.64;//Density of Sulphur Compounds (g/cm3)\n",
"myu=0.5;//Viscosity(cP)\n",
"T_K=273+T_C;//Temperature (K)\n",
"M_B=374;//For CHS compounds(Refer table8.1)\n",
"V_A=M_B/0.6;//Molar volume\n",
"Chi=1;\n",
"Epsilon_by_tau=0.1;\n",
"D_pore_by_D_bulk=0.5;//Hinderance due to large molecules\n",
"epsilon_holdup=0.6;// Assuming bed consists 60% catalyst\n",
"k_app_rhob=1.96//Refer Ex8.3.a Run 1\n",
"eta=0.74;\n",
"R=0.095;//Size of particle\n",
"C_H2_incorrect=0.48;//Solubility of H2 at 56 atm\n",
"P_incorrect=56;//Incorrect Pressure\n",
"P_correct=65;//Correct Pressure\n",
"m_feed=640;// Concentration of Feed (g/L);\n",
"percent_S=2.04;//Percentage of Sulphur\n",
"MW_S=32;//Molecular weight of Sulphur\n",
"N_H2=1.5;//Moles of H2\n",
"V_H2=14.3;//Solubility of Hydrogen\n",
"\n",
"//CALCULATION (Ex8.3.a)\n",
"for i=1:2\n",
"    kapp_rhob(i)=log((1/(1-X_S(i))))*(1/LHSV_inv(i));//Refer Equation 8.21\n",
"    \n",
"end\n",
"L=LHSV_inv(2)/LHSV_inv(1);\n",
"kapp_ratio=kapp_rhob(1)/kapp_rhob(2);\n",
"n=log10(kapp_ratio)/log10(L);\n",
"\n",
"//CALCULATION (Ex8.3.b)\n",
"//FOR SULPHUR\n",
"D_CHS=(7.4*(10^(-8))*(Chi*M_B)^(0.5)*T_K)/(myu*(V_A)^0.6);\n",
"D_e_S=Epsilon_by_tau*D_pore_by_D_bulk*D_CHS;\n",
"epsilon_holdup=0.6;// Assuming bed consists 60% catalyst\n",
"k_app_S=k_app_rhob/(3600*epsilon_holdup);//Refer Ex8.3.a\n",
"phi_app_S=R*(k_app_S/D_e_S)^(0.5);\n",
"//FOR H2\n",
"C_H2_corrected=C_H2_incorrect*(P_correct/P_incorrect);\n",
"C_S_initial=m_feed*percent_S*10^(-2)/MW_S;\n",
"Initial_rate=k_app_rhob*C_S_initial;\n",
"k_app_H2=N_H2*Initial_rate/(3600*epsilon_holdup*C_H2_corrected);\n",
"//Assume D_H2 is three times the value given by the Wilke–Chang Equation\n",
"D_H2=3*(7.4*(10^(-8))*(Chi*M_B)^(0.5)*T_K)/(myu*(V_H2)^0.6);\n",
"D_e_H2=Epsilon_by_tau*D_H2;\n",
"phi_app_H2=R*(k_app_H2/D_e_H2)^(0.5);\n",
"\n",
"//OUTPUT (Ex8.3.a)\n",
"mprintf('\n OUTPUT Ex8.3.a');\n",
"mprintf('\n==========================================================');\n",
"mprintf('\n\tThe Apparent rate constants are \n\t Run1 %0.2f hr-1 \n\t Run2 %0.2f hr-1  ',kapp_rhob(1),kapp_rhob(2))\n",
"mprintf('\n\tThe exponent value = %0.1f hence the difference is not consistent with repect to equations (8.23) and (8.24) for the  apparent rate constants obtained',n);   \n",
"mprintf('\n\tThe error may be due to error in assuming a first order reaction');\n",
"\n",
"//OUTPUT (Ex8.3.b)\n",
"mprintf('\n\n\n OUTPUT Ex8.3.b');\n",
"mprintf('\n==========================================================');\n",
"mprintf('\n\tThe internal effectiveness factor based on Sulphur and Hydrogen diffusion are %0.2f and %0.2f respectively',phi_app_S,phi_app_H2);\n",
"mprintf('\n\tThe internal effectiveness factor based on Hydrogen is negligible');\n",
"\n",
"//FILE OUTPUT\n",
"fid= mopen('.\Chapter8-Ex3-Output.txt','w');\n",
"mfprintf(fid,'\n OUTPUT Ex8.3.a');\n",
"mfprintf(fid,'\n==========================================================');\n",
"mfprintf(fid,'\n\tThe Apparent rate constants are \n\t Run1 %0.2f hr-1 \n\t Run2 %0.2f hr-1  ',kapp_rhob(1),kapp_rhob(2))\n",
"mfprintf(fid,'\n\tThe exponent value = %0.1f hence the difference is not consistent with repect to equations (8.23) and (8.24)for the  apparent rate constants obtained',n);   \n",
"mfprintf(fid,'\n\tThe error may be due to error in assuming a first order reaction');\n",
"mfprintf(fid,'\n\n\n OUTPUT Ex8.3.b');\n",
"mfprintf(fid,'\n==========================================================');\n",
"mfprintf(fid,'\n\tThe internal effectiveness factor based on Sulphur and Hydrogen diffusion are %0.2f and %0.2f respectively',phi_app_S,phi_app_H2);\n",
"mfprintf(fid,'\n\tThe internal effectiveness factor based on Hydrogen is negligible');\n",
"mclose(fid);\n",
"//============================================END OF PROGRAM=================================================\n",
""
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