New process for producing methanol from Coke Oven Gas using CO2

reforming. Comparison with conventional process

J.M. Bermúdeza, N. Ferreraa, S. Luqueb, A. Arenillasa, J.A. Menéndeza*

a
Instituto Nacional del Carbón, CSIC, Apartado 73, 33080 Oviedo, Spain
b
Department of Chemical and Environmental Engineering, University of Oviedo,
33071 Oviedo, Spain
* Corresponding author. Tel.: +34 985 118972; Fax: +34 985 297672
E-mail address: angelmd@incar.csic.es

Supplementary material

Glossary
Symbol Description Units
A Membrane area m2
Atot Overall membrane area m2
F Feed molar flowrate mol/s
i Stage i dimensionless
J Permeate flux mol(m-2·s-1)
k Component k dimensionless
l Membrane thickness m
Pk Permeability of k component (mol·m)/(m2·s·Pa)
PF Feed pressure Pa
PP Permeate pressure Pa
Pr Reduced pressure dimensionless
R Retentate molar flow rate mol/s
X H2 recovery in each stage dimensionless
Xtot Total H2 recovery dimensionless
yFk Mole fraction of the k component in the feed dimensionless
yRk Mole fraction of the k component in the retentate dimensionless
yPk Mole fraction of the k component in the permeate dimensionless
αH2/k Membrane selectivity of k component- respect to H2 dimensionless
Θ Stage-cut dimensionless
The Aspen Plus® software does not contain a simulation block for membrane
separation. To include a membrane separation unit in the simulation, it is necessary to
program it with Fortran. Here it is shown how the modelling of the unit was done and
the Fortran program that was used in the simulation of the DR-COG process.

1. Modelling of the membrane separation unit

Fig. 1 shows a scheme of the membrane gas separation unit. The feed is the stream
RECOVERI which comes from the condenser at 30 ºC and 30 bar. The products are the
retentate (the stream PURGE), under the same conditions of temperature and pressure
as the feed, and the permeate (the stream H2RECOVE) which leaves the unit at 30 ºC
and 1 bar. The objective of the unit was to achieve a H2 recovery of 40%, which would
make it possible to obtain an optimum value for the R parameter in the synthesis gas.

FIGURE 1

For modelling purposes, the unit was split into several stages and it was assumed that
the exiting streams were always perfectly mixed. Each stage was computed so that it
would result in a H2 recovery of 5% (based on the H2 fed into each stage). The overall
calculation involved an iterative loop in which the number of stages was increased until
the targeted overall recovery of the unit was 40 %. This model is shown in Fig. 2.

FIGURE 2

In order to solve each of the perfectly mixed stages (Fig. 3), another iterative procedure
(an inner loop) was set up, starting with the transport equation and the mass balances for
each stage (Equations 1, 2 and 3)
 y R H 2  Pr  y P H 2 
 PF  y R k  PP  y P k  
Pk yP H2
J  yP k    H2 / k   (Equation 1)
l yP k  y R k  Pr  y P k 
 
F  J  A R (Equation 2)
F  yF k  J  A  yP k  R  yR k (Equation 3)

FIGURE 3
The permeated fraction of the feed is then defined, the so-called stage-cut (θ, Equation
4), and the mass balance for the component j is rewritten as follows (Equation 5).

JA
 (Equation 4)
F
y F k    y P k  1     y R k (Equation 5)

Next, the recovery of the reference component, H2 (represented by X), is defined and
related to the stage-cut. This allows the mass balances of the rest of the compounds to
be rewritten on the basis of the reference substance. By rearranging the balances
Equation 8 is obtained. This equation is used in the iterative calculation to relate the
mole fraction of the i component in the retentate to its molar fraction, those of H2 in the
feed and in the permeate and the H2 recovery.

J  A  yP H2 yP H2
X   (Equation 6)
F  yF H2 yF H2

yP H2  yP H2 
yF k  X   y P k  1  X    yR k (Equation 7)
yF H2  yF H2 
 
yF k  yP H2  X  yF H2  yP k
yR k  (Equation 8)
yP H2  X  yF H2

By substituting Equation 8 into Equation 1 and rearranging, the second equation needed
for the iterative procedure (Equation 9) is obtained.

y F k  y P2 H 2
yP k 
H 2 /k     
 y P H 2  X  y F H 2  y R H 2  Pr  y P H 2  y P H 2  Pr  y P H 2  X  y F H 2  1  Pr 

(Equation 9)

The iterative procedure was as follows:

 1. The calculation is initialized by estimating a value for (yPH2)i. This initial value
is obtained from Equation 1 by assuming a maximum transport gradient, e.g.,
permeate pressure equal to 0 bar. For the subsequent iterations, this value is
updated with the outcome of the previous iteration.
2. (yRH2)i is obtained from Equation 8.
3. (yPk)i is computed from Equation 9.
4. (yRk)i is calculated from Equation 8.

checked by   y   1 and   y R k   1 .
n n
i i
5. Convergence is Pk
k 1 k 1

a. If this condition is not achieved, the value of yPH2 is updated as follows:

y     1   y  
n
i 1
 yP H2
i i
P H2 Pk (Equation 10)
 k 1 

b. If the condition is achieved, then the stage cut (θ) is calculated by means
of Equation 6, the molar flow rates of each component in the permeate
and retentate are computed from Equations 11 and 12, and the membrane
area from Equation 13.

J  Ak    F  yP k (Equation 11)

R k  F  y F k   J  A k (Equation 12)

A
 J  A
(Equation 13)
J

This procedure is repeated for as many stages as are needed in order to achieve the H2
recovery initially set as a target.

The Fortran programme was then embedded in a custom block within the Aspen Plus
simulation package.

2. Implementation of the Fortran programme in Aspen Plus ®

In Aspen Plus ®, before the Fortran programme is introduced, it is necessary to
establish which variables need to be imported from the flowsheet to the custom block
for the calculation to be performed and those that need to be exported from the Fortran
programme to the flowsheet. These variables are shown in Table 1.

TABLE 1

2. Fortran programme

C Program GS multicomponent
C Model of series of stages with perfect mix
C Calculation based on intervals of 5 per 100 of recovery
C Perm(7) are the permeabilities of the seven different components
C fy(7) are the mole fractions in the feed of each of the components
C X is the H2 recovery at each stage
C suma_J is the total permeate flux
C yf(7,100) are the molar fractions of each of the components in the feed at each
stage
C PJ(7,100) are the permeate flux per unit of membrane area at each stage
C yp(7,100) are the molar fractions of each of the components in the permeate at
each stage

Real Perm(7), fy(7), X, suma_J, yf(7,100), PJ(7,100),yp(7,100)

C i are the stages and k the components

C c and b are dummies for the iterations

Integer i, k, b, c

C yr(7,100) are the molar fractions in the retentate at each stage

C alfa(7,100) is the membrane selectivity, denominator in Equation 9
C d(100), e(100) are terms of the denominator of Equation 9
C sum_yp is the summation of the mole fractions in the permeate at each stage

Real yr(7,100), d(100), e(100), alfa(7,100), sum_yp, Error

C theta(100) are the stage-cuts

C PJA(7,100) are the permeate molar flow rates of each component at each stage
C F(100) are the feed molar flow rate at each stage
C R(7,100) are the retentate molar flow rates of each component at each stage
C A(100) is the cumulative membrane area of after each stage

Real theta(100), PJA(7,100), F(100), R(7,100), A(100)

C Rec(100) is the total recovery after each stage

C PJA_ac(7) is the cumulative flow rate of retentate of each component after each
stage
C yp_tot(7) are the final (overall) mole fractions of each component in the
permeate

Real Rec(100), PJA_ac(7), yp_tot(7)

C Values of the permeabilities in (mol·m)/(m2·s·Pa) units

Perm(1)=2*10**(-7.0)
Perm(2)=2.3*10**(-8.0)
Perm(3)=7*10**(-9.0)
Perm(4)=6.2*10**(-9.0)
Perm(5)=4*10**(-10.0)
Perm(6)=6*10**(-7.0)
Perm(7)=1.7*10**(-6.0)

C Target total recovery

XTOT=0.4

C Reduced pressure

Pr=PP/PF

C Mole fractions in the feed

fy(1)=YFH2
fy(2)=YFCO
fy(3)=YFCH4
fy(4)=YFCO2
fy(5)=YFN2
fy(6)=YFMET
fy(7)=YFH2O

C H2 recovery after each stage

X=0.05

C First stage

i=1

C Initial permeate flux set equal to 0

suma_J=0

C Feed of the first stage

 F(i)= Feed

C Mole fractions of the first stage

C Initialising the program by calculating permeate flux
C assuming maximum gradient

do k=1,7,1
yf(k,i)=fy(k)
PJ(k,i)=Perm(k)*100*3600*PF*yf(k,i)
suma_J= suma_J + PJ(k,i)
end do

C Mole fraction of H2 in the permeate assuming maximum gradient

yp(1,i)=PJ(1,i)/suma_J

C Initialising the iterative loop for the stage i

C Calculation of mole fraction of H2 of retentate using Equation 8

1 sum_yp=yp(1,i)
yr(1,i)=(yf(1,i)*yp(1,i)-X*yf(1,i)*yp(1,i))/(yp(1,i)-X*yf(1,i))
d(i)=(yp(1,i)-X*yf(1,i))*(yr(1,i)-Pr*yp(1,i))
e(i)=yp(1,i)*(Pr*yp(1,i)+X*(1-Pr)*yf(1,i))

C Calculation of mole fractions in the permeate using Equation 9

C Calculation of mole fractions of in the retentate using Equation 8

do k=2,7,1
alfa(k,i)=e(i)+d(i)*(Perm(1)/Perm(k))
yp(k,i)=yf(k,i)*yp(1,i)*yp(1,i)/alfa(k,i)
yr(k,i)=(yf(k,i)*yp(1,i)-X*yf(1,i)*yp(k,i))/(yp(1,i)-X*yf(1,i))
sum_yp= sum_yp + yp(k,i)
end do

C Convergence check: Calculate the error,

Error=abs(1-sum_yp)

C Continue or re-start the iterative loop for the stage

if (error .GT. 0.0001) then

yp(1,i)=yp(1,i)+(1-sum_yp)
go to 1
end if

C Calculation of stage-cut
 k=1
theta(i)=X*(yf(1,i)/yp(1,i))

C Calculation of permeate and retentate molar flow rates at i stage

do k=1,7,1
PJ(k,i)=Perm(k)*100*3600*(PF*yr(k,i)-PP*yp(k,i))
PJA(k,i)=theta(i)*F(i)*yp(k,i)
R(k,i)=F(i)*yf(k,i)-PJA(k,i)
end do

C Calculation of the membrane area for the i stage

A(i)=PJA(1,i)/PJ(1,i)

C Calculation of the cumulative recovery after i stage

Rec(i)=1-(R(1,i)/(Feed*fy(1)))

C Finish or re-start iterative loop at i+1 stage

if (Rec(i) .LE. XTOT) then

c=i+1
F(c)=0

do k=1,7,1
yf(k,c)=yr(k,i)
yp(1,c)=yp(1,i)
F(c)=F(c)+R(k,i)
end do

i=i+1
go to 1
end if

C Set final H2 recovery

XTOT=Rec(i)

C Calculate overall permeate flowrate and membrane area

b=1
k=1
AREA=0

do k=1,7,1
PJA_ac(k)=0
end do
 k=1

do while (b .LE. i)
A_tot=A_tot+A(b)

do k=1,7,1
PJA_ac(k)=PJA_ac(k)+PJA(k,b)
end do

b=b+1
end do

PJA_tot=0

do k=1,7,1
PJA_tot=PJA_tot+PJA_ac(k)
end do

C Calculate final permeate mole fractions

k=1
do k=1,7,1
yp_tot(k)=PJA_ac(k)/PJA_tot
end do

C Calculate final recoveries

if (YFCO .EQ. 0) then

COREC=0
else
COREC=PJA_ac(2)/(FEED*YFCO)
end if

if (YFCH4 .EQ. 0) then

CH4REC=0
else
CH4REC=PJA_ac(3)/(FEED*YFCH4)
end if

if (YFCO2 .EQ. 0) then

CO2REC=0
else
CO2REC=PJA_ac(4)/(FEED*YFCO2)
end if

if (YFN2 .EQ. 0) then

N2REC=0
else
N2REC=PJA_ac(5)/(FEED*YFN2)
end if

if (YFMET .EQ. 0) then

METREC=0
else
METREC=PJA_ac(6)/(FEED*YFMET)
end if

if (YFH2O .EQ. 0) then

H2OREC=0
else
H2OREC=PJA_ac(7)/(FEED*YFH2O)
end if
Table 1. Imported and exported variables for the Fortran Programme
Imported variables Exported variables
Fortran Fortran
Definition Definition
Acronym Acronym
Pressure of RECOVERI H2 recovery. H2 split of
PF XTOT
stream MEMSEP
Pressure of H2RECOVE CO recovery. CO split of
PP COREC
stream MEMSEP
Mole flow of RECOVERI CH4 recovery. CH4 split of
FEED CH4REC
stream MEMSEP
Molar fraction of H2 in CO2 recovery. CO2 split of
YFH2 CO2REC
RECOVERI stream MEMSEP
Molar fraction of CO in N2 recovery. N2 split of
YFCO N2REC
RECOVERI stream MEMSEP
Molar fraction of CH4 in CH3OH recovery. CH3OH
YFCH4 METREC
RECOVERI stream split of MEMSEP
Molar fraction of CO2 in H2O recovery. H2O split of
YFCO2 H2OREC
RECOVERI stream MEMSEP
Molar fraction of N2 in Membrane area
YFN2 AREA
RECOVERI stream
Molar fraction of CH3OH in
YFMET
RECOVERI stream
Molar fraction of H2O in
YFH2O
RECOVERI stream
Fig. 1. Scheme of the membrane separation unit
Fig. 2. Model consisting of a series of perfectly mixed stages for the membrane
separation unit
Fig. 3. Scheme of a perfectly mixed stage