<p fontName="Arial"></p>

b6cb0ca3-5ec2-47ec-8904-21d084a6264c 36 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Example 7: Universal Fixed Bed Reactor (steady state)

]]>

Partial oxidation of methanol to formaldehyde

]]>

CH3OH + 1/2 O2 ----> CH2O + H2O R1

]]>

CH2O + 1/2 O2 ------> CO + H2O R2

]]>

This example shares most of the physical and reaction properties used in Example 5. A tubular reactor cooled at the wall is simulated in this example, but

the program can also be used to simulate an adiabatic reactor.

A section has been added to predict the parameters for heat transfer at the wall and radial dispersion coefficients. This section can be copied into other

worksheets as needed. In some cases, the parameter correlations are phase specific, i.e. for liquid or gas. Therefore, the user designates the fluid type in

the section that describes the reactor.

Finally, although the program may appear complicated, once written, it can be easily used to simulate other reaction systems by merely changing the

physical properties and the reaction sections. The numerical program was written because the PDE solvers in Mathcad currently do not support the solution of vector problems as required

for this model.

The integration program can be duplicated in most high level computer languages. The key feature required is the function capability. Some "in-line"

Fortran compilers used in process simulation packages do not include that feature although it is included in full Fortran compilers. The vectorization and

other matrix operations can be readily programmed with simple loops.

The portions of the program that are unchanged from Example 5 are hidden to reduce printing. Areas that have been added are highlighted in yellow. A

blue highlight indicates a changed value.

]]>

mc_AOpen 1

select the formaldehyde database

stream 1 :

stream mc_edS #

NC 6 :

i_1 NC range :

ccode i_el stream i_mc_getCC :

the component codes are obtained from stream 6

name i_el ccode i_el mc_CompN :

ccode 104713121631596884126461 mat

name METHANOL OXYGEN WATER CARBON MONOXIDE FORMALDEHYDE NITROGEN 61 mat

molecular weights

]]>

molecular formulas

Mw i_el ccode i_el mc_CompMw g mol / * :

C H O N

]]>

Atom 14100020021010101210000264 mat :

name METHANOL OXYGEN WATER CARBON MONOXIDE FORMALDEHYDE NITROGEN 61 mat

Mw 0.032 kg mol / * 0.032 kg mol / * 0.018 kg mol / * 0.028 kg mol / * 0.03 kg mol / * 0.028 kg mol / * 61 mat

Thermophysical properties

]]>

heats of formation

]]>

free energies

]]>

ΔHf i_el ccode i_el mc_CompHf kJ kg / * Mw i_el * :

]]>

ΔFf i_el ccode i_el mc_CompGf kJ kg / * Mw i_el * :

ΔHf kJ mol / 200.99 - 0 241.816 - 110.53 - 108.6 - 061 mat

ΔFf kJ mol / 162.31 - 0 228.77 - 137.16 - 109.9 - 061 mat

Feed conditions

T.0 525 K * :

feed temperature

Tw 525 K * :

wall temperature

Ptot 5 atm * :

moles or mole fractions in feed

G 0.8 g cm 2^s * / * : 8 s Pa * m / *

mass flux

molf 1 1.1 0.1467 0.0563 0.0065 8.7905 61 mat :

molf molf molf sum / : 0.0901 0.0991 0.0132 0.0051 0.0006 0.7919 61 mat

normalized mole fractions

M.f molf Mw * : 0.0286 kg mol / *

molecular weight of feed mixture

dimensionless feed conditions

ω.0 molf Mw * vectorize M.f / : 0.1008 0.1107 0.0083 0.005 0.0006 0.7746 61 mat

convert to mass fractions

θ.0 1 :

temperature

p.0 1 :

pressure

Reactor geometry and type

L 1 m * :

reactor length

fluid gas :

fluid is "gas" or "liquid"

D.t 2.0574 cm * :

tube I.D

adiabatic yes :

adiabatic is "yes" or "no"

Ri D.t 2 / :

reactor radius

Catalyst properties

d.p 2.5 mm * :

equivalent particle diameter

Cp.c 0.25 cal g K * / * :

catalyst heat capacity

ε 0.496 :

bed void fraction

shape cylinder :

catalyst shape, "cylinder" or "sphere"

ρ.c 53 lb ft 3^/ * :

catalyst bulk density

smooth yes :

catalyst surface is smooth, "yes" or "no"

k.s 2 BTU hr ft * °Ra * / * :

solid conductivity

The hidden are below contains the following sections: Gas and Liquid Properties Stoichiometry Equilibria Reaction rate expressions Net mass and heat production rates

Gas Properties

The properties for nitrogen, the dominate component, will be used for the gas properties.

σ 3.798 Å * :

Lennard-Jones parameter for nitrogen

gas viscosity

T μ 2.67 105 -^* Mw NC el T K / * g mol / / sqrt * σ Å / (2^/ g cm s * / * :

Bird et al(2002), eq 1.4-14

900 K * μ poise 0.0003

molar heat capacities computed in the area below

Curve fit PPP enthalpies to obtain a cubic polynomial heat capacity formula

]]>

generate data

]]>

npts 30 :

number of data points

t1 500 K * :

t2 1000 K * :

temperature range

npts 30 :

M trans nr M rows : nc M cols : j 1 nc range k 1 nr range MT j k el M k j el : for for MT 41 line :

transpose function because the SMath version had problems with one of the matricies below

t phase Ccode ii Cp phase is a string, either Vapor of Liquid Mw ii el Ccode ii el mc_CompMw g mol / * : phase Liquid ≡ cp Ccode ii el t K / t 1 Δ°C * + K / mc_CompHL Mw ii el * kJ kg K * / * : 11 sys cp Ccode ii el t K / t 1 Δ°C * + K / mc_CompHG Mw ii el * kJ kg K * / * : 11 sys if cp 41 line :

compute heat capaciitiy of one compound at temperature "t"

t1 t2 phase Ccode npts Matcp k 1 npts range X k el t1 k t2 t1 - npts / (* + : for k 1 npts range ii 1 Ccode rows range Mcp k ii el X k el phase Ccode ii Cp : for for Mcp X 12 mat 31 line :

compute heat capacity matrix for all compounds of interest

phase Vapor :

T CTf 1 T K / T K / (2^T K / (3^41 mat :

cubic temperature function

MCP X 12 mat t1 t2 phase ccode npts Matcp :

compute cubic polynomial coefficients

]]>

data X cubic npts data rows : nc data cols : x Φ 1 x x 2^x 3^41 mat : c 1 nc range j 1 x Φ rows range ii 1 npts range M ii j el X ii el Φ j el : for for Y data c col : b c el M transpose M * (1 -^M transpose Y * (* : 31 line for coeff b 1 el : nc 1 > c 2 nc range coeff coeff b c el augment : for do nothing if B coeff trans : B 81 line :

data X cubic2 npts data rows : nc data cols : x Φ 1 x x 2^x 3^41 mat : c 1 nc range j 1 x Φ rows range ii 1 npts range M ii j el X ii el Φ j el : for for Y data c col : b c el M transpose M * (1 -^M transpose Y * (* : 31 line for coeff b 1 el : nc 1 > c 2 nc range coeff coeff b c el augment : for do nothing if B coeff transpose : B 81 line :

cp MCP kJ kmol K * / / X K / cubic kJ kmol K * / * :

cp2 MCP kJ kmol K * / / X K / cubic2 kJ kmol K * / * : #

The only change to cubic2 was the transpose of coeff at the end

cp kJ kmol K * / 9.1933 0.1289 6.0755 105 -^* - 1.2132 108 -^* 23.1606 0.0211 1.1622 105 -^* - 2.2532 109 -^* 30.9402 0.0059 6.3247 106 -^* 1.8992 109 -^* - 28.9621 0.0054 - 1.8204 105 -^* 8.5985 109 -^* - 16.4602 0.0618 1.2419 105 -^* - 3.8139 109 -^* - 30.1377 0.0095 - 2.1354 105 -^* 9.2552 109 -^* - 64 mat

each row contains the coefficients for one compound

cp transpose kJ kmol K * / 9.1933 23.1606 30.9402 28.9621 0.1289 0.0211 0.0059 0.0054 - 6.0755 105 -^* - 1.1622 105 -^* - 6.3247 106 -^* 1.8204 105 -^* 1.2132 108 -^* 2.2532 109 -^* 1.8992 109 -^* - 8.5985 109 -^* - 44 mat

the transpose function works outside the function environment on the cp matrix produced by cubic

num div vectdiv ii 1 num rows range res ii el num ii el div ii el / : for res 21 line :

The vectorize function doesn't work as expected in SMath. Thus, this function is used below.

ω.0 Mw vectdiv 3.1456 mol kg / * 3.4601 mol kg / * 0.4615 mol kg / * 0.1771 mol kg / * 0.0204 mol kg / * 27.651 mol kg / * 61 mat

ω.0 Mw / (vectorize 31.2088 mol kg / * 31.2512 mol kg / * 55.5085 mol kg / * 35.701 mol kg / * 33.3041 mol kg / * 35.6971 mol kg / * 61 mat

correct

wrong

ω θ Cpm cp θ T.0 * CTf * (transpose ω Mw vectdiv * :

heat capacitiy of stream on a mass basis as a function of the state variables

ω.0 θ.0 Cpm J kg K * / 1146.2154 11 mat

ω Mwt 1 ω ii el Mw ii el / ii 1 NC sum / :

molecular weight of mixture

ω θ p ρ.f p Ptot * ω Mwt * R.m T.0 * θ * / :

density