##### Question

In: Mechanical Engineering

# Cryogenic engineering. Theoretically investigate the performance of zeiner liquefaction system using inline helical and spherical tube...

Cryogenic engineering.

Theoretically investigate the performance of zeiner liquefaction system using inline helical and spherical tube arrangements...
Model the system and list all the variables related to it....Also study the efffect of varying outside conditions and inside conditions...

validate the results using scilab and Fortran 77...

please answer if u can otherwise skip it
don't waste my question quota....please

## Solutions

##### Expert Solution

"!Solving Chemical Equilibrium using the Law of Mass Action "

"Liquid octane at 300 K is reacted with 120% theoretical air also at 300 K. The reaction can be written:

C8H18 + a (O2+3.76N2) = b C02 + c CO + d H2O + e N2 + f O2 + g NO

Determine the temperature and composition of the equilibrium products which are at 5 bar.

This problem illustrates the use of the external procedure JANAF in a function and in a procedure."

procedure h&g(S$,T:h,g) "This procedure uses the JANAF external procedure to return the enthalpy and Gibbs energy of species S$ at T."
call JANAF(S$,T:cp,h,s) g:=h-T*s end h_g Function hf(S$,T)
"This function uses the JANAF external procedure to return the enthalpy of species S$at T." Call JANAF(S$,T:cp,hf,s)
end hf

"Stoichiometry for a basis of 1 kgmole of octane"
8-b-c=0            "Carbon balance"
18-2*d=0            "Hydrogen balance"
2*a-2*b-c-d-2*f-g=0       "Oxygen balance"
a*3.76*2-2*e-g=0       "Nitrogen balance"
a_stoic=8+4.5       "no excess oxygen and complete combustion"
a=a_stoic*1.2           "120% theoretical air"
P=5 [bar]            "specified pressure of productsr"
P_ref=1[bar]            "reference pressure for evaluation of standard state Gibbs energy"
R=R#             "Universal gas constant"

"Total moles of gas and mole fractions."
n_tot=(b+c+d+e+f+g)
y_CO2=b/n_tot; y_CO=c/n_tot; y_H2O=d/n_tot; y_N2=e/n_tot;; y_O2=f/n_tot; y_NO=g/n_tot

"The following equations provide the enthalpy and the specific Gibbs Free Energy for each chemical species at T and the reference pressure of 101.3 kPa. The JANAF external procedure is used in the Procedure h&g to calculate h and g at the equilibrium temperature, which is determined from an energy balance."
call h&g('CO2',T:h_CO2, g|o_CO2)
call h&g('CO',T:h_CO, g|o_CO)
call h&g('N2',T:h_N2, g|o_N2)
call h&g('O2',T:h_O2, g|o_O2)
call h&g('NO',T:h_NO, g|o_NO)
call h&g('H2O',T:h_H2O, g|o_H2O)

"Standard-state Gibbs Free Energy change for CO-CO2 and for N2-O2 reactions."
DELTAG|o_1=0.5*g|o_O2+g|o_CO-g|o_CO2
DELTAG|o_2=2*g|o_NO-g|o_O2-g|o_N2

"Law of Mass Action for reactions 1 and 2"
DELTAG|o_1=-R*T*ln(K_1)
DELTAG|o_2=-R*T*ln(K_2)

"Definition of equilibrium constant for reactions 1 and 2"
K_1=y_CO/y_CO2*(sqrt(y_O2*P/P_ref))
K_2=y_NO^2/(y_O2*y_N2)

"Find the enthalpy of the reactants- liquid octane is not in the EES or JANAF data base."
h_f_C8H18=-249952       "[kJ/kmol] enthalpy of formation of liquid octane at 300 K."
h_f_O2=hf('O2',300)       "[kJ/kmol] enthalpy of O2 at 300 K"
h_f_N2=hf('N2',300)       "[kJ/kmol] enthalpy of N2 at 300 K"
HR=h_f_C8H18+a*h_f_O2+3.76*a*h_f_N2

"Find the enthalpy of products"
HP=b*h_CO2+c*h_CO+d*h_H2O+e*h_N2+f*h_O2+g*h_NO

"Apply an adiabatic energy balance to determine the product temperature"
HR=HP

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