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Design of packed towers for selective chemical absorption
ChemicaI Engineering Science, Printed in Great Britain.
DESIGN
Vol. 42, No. 3, pp. 425433.
1987. 0
OF PACKED
TOWERS FOR ABSORPTION
SELECTIVE
“OO9-2509/87 $3.00 t 0.00 1987 F’ergamon Journals Ltd.
CHEMICAL
WEI-CHUNG YU and GIANNI ASTARITAT Department of Chemical Engineering, University of Delaware, Newark, DE 19711, U.S.A. (Received 18 February
1985; accepted July 1985)
Abstract-The selectivity obtained in industrial processes of gas treating with chemical solvents is of kinetic nature, and accurate procedures for designing the required packed height are therefore needed. A procedure for packed towers is presented here, which is based on the model of simultaneous absorption presented in a previous paper. The procedure takes into account the absorption of two gases, heat transfer and water evaporation.
INTRODUCTION
Selective removal of H,S from gases containing CO2 is an important industrial process, which is needed whenever the H2S/C02 ratio in the gas to be treated is less than - l/7. In fact, for such a gas, if both H,S and CO2 are removed almost completely, the concentration of H2S in the gas exiting from the regenerator would be too low for the gas to be sent economically to a Claus plant for conversion of H2S to elemental sulphur. For a review of this whole area see Astarita and Yu (1985). Selective removal of achieved commercially by use of chemical solvents, and in particular with aqueous solutions of methyldiethanolamine (MDEA) (Goar, 1980). The selectivity achieved in industrial operation is larger than the thermodynamic one (Astarita and Savage, 1983), and is thus to be ascribed to kinetic phenomena. More specifically, the selectivity is obtained by making use of the fact that HIS reacts with MDEA much faster than CO2 does. The fact that the selectivity is of a kinetic nature makes it important to be able to design accurately the absorber height: underdesign would lead to failure of meeting the H,S specifications on the treated gas, but overdesign would lead to an approach to the unfavourable thermodynamic selectivity. A design procedure for trayed towers has recently been proposed by Blauwhoff et al. (1987), which is based on the assumption that each tray can be regarded as a CSTR for both the gas and liquid phases. In this paper, we present a design procedure for countercurrent packed absorbers. We consider in particular the case of an aqueous solution of MDEA, for which we have recently presented an approximate analytical solution to the simultaneous mass transfer equations (Yu and Astarita, 1987) used in the following. For systems other than aqueous MDEA, the same procedure could be applied as well, provided enough information is available on the equilibrium and kinetics of the chemical reactions involved, and a suitable
‘Present address: Chemical Engineering University of Naples, Naples, Italy.
Department, 425
modification of the solution to the mass transfer equations given by Astarita and Yu (1985) has been developed on that basis. ISOTHERMAL
ABSORBER
We first develop the procedure for the case of an isothermal absorber. As will be seen in the following, the assumption of isothermal behaviour is not an acceptable one; however, the isothermal calculation turns out to be a useful preliminary to the more realistic adiabatic calculation. Also, discussion of the simpler isothermal case presents in an easier way the essential features of the procedure. In all the discussion that follows, plug flow has been assumed for both phases. Of course, this may not be entirely appropriate in realistic cases; however, the same assumption is typically made in the design procedure for physical absorption towers, and we see no reason to change it for the case of chemical absorption. FIowsheet
logic
The input data for the calculation are the liquidphase composition, the gas feed composition and flowrate, the pressure P in the absorber (which is assumed to be constant), and the temperature. The calculations which are presented here are for a pressure of 10 atm, gas f-eed consisting of 89 %N,, 10 y0 Co2, and 1 o/0H2S, a temperature of 40-C, and a liquid feed containing 3.0 mol dm- 3 of MDEA, 1 o/0converted to bicarbonate and 1 y0 to hydrosulphide. We use the subscripts T and B to identify conditions at the top of the counter-current absorber (lean end), and at the bottom (rich end); ’ and V identify H,S and COz, respectively, y is the fractional saturation, and p the partial pressures: the calculations presented are for y; = y’; = 0.01, p; = 0.1 atm, and p’;, = 1 atm. The first thing to be assigned is the H2S specification on the treated gas, i.e. the value of pi. This cannot simply be chosen as slightly larger than the equilibrium value corresponding to the composition of the feed liquid, because of the film effect which was discussed in our previous paper. However, at the start the magnitude of the film effect at the lean end cannot be
426
WEI-CHUNG
Yu and GIANNI
calculated, since the CO2 partial pressure at the top, &, is not known. However, the film effect cannot be larger than that corresponding to the partial pressure of CO2 in the feed gas, pi, and this is used to estimate the film effect at the top (as will be seen, the COz partial pressure changes only by about 10% over the whole absorber, so this is not a bad estimate). Thus the equilibrium partial pressure of H2S corresponding to the interface composition of the feed liquid is estimated. This value, increased by 25 O/&is chosen as the specification pk. Once p; has been assigned, the total amount of HzS absorbed can be calculated, and from this one obtains (via an H,S overall balance) the value of the H2S fractional saturation in the exit liquid, y;. Should the problem considered be one where only one gas is being absorbed, at this stage one could calculate the minimum liquid flowrate from the requirement that the liquid at the rich end be in equilibrium with the feed gas. However, this is not so for simultaneous absorption, where the equilibrium equations for H2S and CO2 are coupled, and one still needs to know the value of & in order to calculate the minimum liquid flowrate. This can only be obtained from a mass balance on COz if the value of p’; is guessed: what the actual value of p’; will be depends on what height of absorber is needed to meet the H2S specification. Once the guess on p; has been made, the minimum liquid flowrate is calculated from the requirement that p;3and yk are in equilibrium with each other at the calculated value of yg . The actual liquid flowrate is then taken as 30% larger than the minimum one. At this stage, to within the one guess which has been made, the gas and liquid molar flowrates per unit crosssectional area, G, and L, are known, as well as the compositions of the liquid and gas phases at the lean and rich end. We have assumed the liquid phase to have the physical properties of water (this is not a very realistic assumption, but it is irrelevant to the development of the procedure). One can now calculate the values of the mass transfer coefficients in the gas phase, k& and k&, of the liquid-side mass transfer coefficients which would prevail in the absence of chemical reactions, kz and kr and of the interface area per unit volume, a; we have used the well-tested correlations of Onda et al. (1968) in order to do so. In our calculations, we have considered a packing of 2-in. Fall rings. The procedure described up to now will be termed in the following the preliminary calculation (PC). The next step is the actual integration of the transport equations along the absorber axis, the details of which are discussed in the next subsection. We have chosen to start the calculation from the rich end, since that turns out to result in faster convergence of the procedure. The calculation should proceed upwards through the absorber until p’ reaches the value of pk. However, should the initial guess on pq have been an overestimate, the value of yg would be underestimated, and somewhere along the absorber height y” could become negative. Although one could stop the calculation at such a point and readjust the guess on p;, the
ASTARITA
convergence criterion would be somewhat harder to establish. Therefore, it is best to choose the initial guess on p; as a sure underestimate, so that the integration of the transport equations proceeds until p’ reaches the value pk. The calculation described in this paragraph will be referred to in the following as the main calculation (MC). The last step to be performed in a convergence procedure (CP). As the MC is finished, the value of p(f obtained will in general be larger than the initially guessed one (or from the one guessed in the previous iteration) by an amount bp”, and a new guess needs to be made, which, for the reasons discussed above, should again be an underestimate. We have chosen a convergence procedure given by: P’;” = P’;, _ 1 + B6P”
(1)
in which the second subscript on p’; indicates the iteration number. With fl = 1, this would be a repeated substitution CP, which could lead to overestimates of p’; at some iteration. We have found that a p of 0.6 never leads to an overestimate, and ensures rapid convergence. The number of iterations required of course depends on the precision required, i.e. on how small a value of 6p”/pG one chooses to regard as acceptable. It is perhaps obvious that one needs a rather strict criterion for 6p”/p;, since the corresponding GyG/yi; is significantly larger. The calculations presented here are for a maximum Gyi;/yi; of 2 %. The logic flowsheet discussed above is sketched in Fig. 1. The calculation time required is 6.03 s on a DEC-10 computer.
Main calculation The analytical interactive solution of the mass transfer equations which has been discussed by Yu and Astarita (1987) can be summarized as follows. First, a preliminary estimate of the H,S mass transfer flux per unit volume is obtained from the following system of equations: J’p = kGa(p’ - pip)
(2)
which is the gas-phase transport equation, with the subsript P indicating that it is a preliminary estimate, I identifying conditions at the interface. The liquid-side mass transport equation is: J; = k~a(a;,
- a!;)
(3)
with the subscript 0 identifying conditions in the bulk of the liquid, and a being the total concentration of dissolved gas, both in the physically dissolved form and the chemically combined one, i.e. a; = rny;r + pi/H'.
(41
The value of y; is determined by the condition that chemical equilibrium should prevail at the interface, say: &
= (fH’m/UyL
[the nomenclature
(Y;, + YM~
- Y& - .vbl
(5)
of Astarita and Yu (1987) is used].
Design of packed towers for selective chemical absorption and finally an adjusted obtained as:
Preliminary calculation t
427
mass transfer rate of H,S
J’ = k&(p’-p;)
Guess p;
J’ = F’(p’, p”, y;.
A correction factor f depends on ionic strength, and hence on y; and yb:, and therefore a solution of eq. (5) is obtained by repeated substituion on a quadratic. The system of eqs (2)-(5) is equivalent to an equation of the following form: = P’(P’,
Yb, YZ).
(6)
Once this preliminary estimate of J’ has been obtained, the mass transfer equations for COZ are: J” = @(p”-pp;)
= J’
(17)
d(Gp”/P)/dx
= J”
(18)
where the apparent kinetic constant composition, k,, is given by: k, = km(l -y;,,
(8) at the interface (9)
-y;;)
with k the true bimolecular kinetic constant of the CO,-MDEA reaction. The value of &*, the CO1 partial pressure corresponding to equilibrium with the bulk-liquid composition, is given by: (Yb + Y;;)/(l
- Yb - Y’d).
As discussed in our previous preliminary estimate of J’ has been correction is performed as follows. ment factor for COr mass transfer,
(11)
paper, once this made, a film effect First, an enhanceI”, is calculated as:
1 + Dk,/kf”‘).
With this, an excess bicarbonate interface, 6, is calculated as: 6 = (I”-
(10)
is equivalent to an equation
J” = F”(p’, p”. yb, yb:).
I” = j(
(12)
concentration
l)(p;-ppb:*)/H”.
at the (13)
The interface-composition value of the equilibrium partial pressure of HIS is now recalculated as: p; = (fH’mlK’)y;,(Y;,
= J
+ Yb: + a/t1
-Yip
(19)
= J”
(20)
a = my + p*/H.
- Yb: - 6)
(14)
(21)
In eqs (17) and (IS), G is the local molar gas flowrate, which is related to p’ and p” by an elementary mass balance. The system of eqs (17)-(20) is a system of four differential equations for four unknowns 7i, i=l,..., 4, of the following general form: drJdx
= gi(rr ,
_ ,
subject to the following
(7)
J” = (l/H”)(p;--p’d*)aJ~k~“z+Dk,)
The system of eqs (7t(lO) of the following form:
(16)
where c is the molar density of the liquid phase, and x is distance measured from the rich end. The CISare related to the ys by:
Fig. 1. Flowsheet logic, isothermal.
= (fH”mlK”)Yb:
yb’).
to an
d(Gp’/P)/dx
d (Lu”/a),‘dx
Convcr ence proce Lfure
p;;*
equivalent
Equations (11) and (16) are to be coupled with local mass balances as follows:
d(La’/a)/dx
4
(15)
the system of eqs (12t(lS) being equation of the following form:
t MC until p’ = p’T
is
x = 0, x = L,
boundary
p’=pb,
P’ = P;,
i = 1,
74),
_ ,4
conditions:
p”=p;; u’ = ct;,
(22)
(23) & = a;.
(24)
Notice that the existence of the fifth boundary condition also determines the absorber height L. The problem as stated above is a two-boundary value problem, and since it cannot be solved analytically and a numerical technique such as the Runge-Kutta method needs to be used, which requires oneboundary conditions to be imposed, it needs to be transformed accordingly. As discussed before, two of the x = L conditions can be transformed to x = 0 ones, but the third one cannot, and therefore a guess is needed on one of the variables; we have chosen to guess the value of p;. When applying the Runge-Kutta method, a strategy for determining the grid size 6x needs to be established. We have chosen to have a small 6x (1 cm) near the rich end, where most of the H,S absorption takes place, and steep concentration gradients are established in both phases. As the H,S partial pressure drops to l/10 of its initial value, the 6x value is changed to 10 cm. Finally, as one approaches the lean end, the 6x is changed again, getting smaller and smaller as the percentage approach of p’ to the value p; is decreasing. This leads, for some of the cases which have been calculated, to a total number of steps for the MC as large as 150. With the CP occasionally requiring up to 10 iterations, the mass transfer equations have to be solved as many as 1500 times for a complete calculation.
428
WEI-CHUNG
Yu
and GIANNI
ASTARITA
Results
The axial distribution of pb*, the H2S equilibrium partial pressure corresponding to the composition of the bulk liquid, spans a few orders of magnitude from the rich end to the lean end, and so do all other relevant partial pressures. These would thus need to be plotted in a semilog plot, where differences between partial pressures would hardly be noticeable. Therefore, the complete results for II,!3 are presented in the form of Fig. 2, where three curves are plotted, each one being a partial pressure divided by the local value of pb*. The leftmost curve labelled 1 is the interface partial pressure of H2S calculated without the film effect correction, i.e. the value of pip. A value of unity for the ratio p;,/p’a indicates that the H2S mass transfer is entirely gas-phase controlled. This is indeed almost the case in the top half of the absorber, as can also be seen from Fig. 3, where the ratio of gas-side to liquid-side mass transfer resistances for H,S is plotted. The middle curve labelled 3 is the interface partial pressure of H,S calculated including the fiIm effect correction, i.e. the value of pi. In the bottom part of the absorber, curves 1 and 3 almost coincide, showing that the film effect is negligible. This is, however, not true for the top part of the absorber, where the difference between the two curves is of the order of 10 %. Notice that the film effect can be predicted only by an interactive solution to the mass transfer equations. The rightmost curve labelled 2 is the partial pressure of HZS in the gas phase. The difference between lines 2 and 3 is a measure of the driving force in the gas phase; the difference between the values read on curve 1 and unity is a measure of the driving force in the liquid phase. Finally, the difference between lines 1 and 3 is a measure of the fraction of total driving force which is lost to the film effect.
R
Fig.
3. Ratio
R of gas-side to liquid-side mass transfer resistance for H2S, isothermal.
Figure 4 presents the partial pressure distribution of CO2 along the absorber axis. For C02, the mass transport is always liquid-side controlled, with the gasphase resistance amounting to no more than 0.1 y0 of the total throughout the absorber. Two observations are in order concerning Fig. 4. First, in the bottom 40cm of absorber p” slightly increases with distance from the rich end. This is on the threshold of a situation where CO2 is actually desorbed back to the gas phase; it is not quite so, because in the bottom part of the absorber most of the H,S is being absorbed, and therefore the partial pressures of COz and N, increase simply because that of H,S decreases. However, the important point is that in this region the H,S mass
1 .o
Fig.
2. pip/&*
(I),
(3) and isothermal.
pi/&*
p’,pb*
distributions,
p”(bar)
Fig. 4. p” distribution,
isothermal.
Design of packed towers for selective chemical absorption
429
transport is controlled by the liquid phase, and therefore the liquid interface is significantly more acidic than the bulk, which results in an almost zero rate of COZ absorption. This result is again one which could only be predicted by an interactive solution to the mass transfer equations. The second observation is that only about 3 o/0of the entering CO2 is being absorbed; since practically all the H,S is absorbed, the selectivity for this case is about 30. This is a large number, larger than values reported for industrial operation, but in fact, as will be seen later, it is an artifact of the isothermal approximation. The L/G, ratio obtained for the case shown in Figs 2-4 is 0.47.
ADIABATIC
ABSORBER
Thermal effects in absorbers where a chemical solvent is used may be quite conspicuous, because liquid flowrates are comparatively low (due to the large capacity of chemical solvents) and the heat released is that of a chemical reaction and may be quite significant. Only a few recent works address the question of predicting temperature distributions in absorbers employing chemical solvents (Blauwhoff et al., 1987; Gartner et al., 1979; Hegner and Molzahn, 1977; Pandya 1987). Thermal effects are connected with three phenomena: the release of the heat of chemical reactions, direct heat transfer between gas and liquid phases, and water evaporation or condensation. As will be seen in the following, all three are important, and need to be included in the calculation scheme. Heat
transfer
As the gas phase moves upwards through the absorber, the only mechanism allowing for its temperature to change is direct heat transfer to or from the liquid phase, since both the heat of chemical reactions and of water condensation are released in the liquid phase. It follows that dT,/dx can be negative only if the gas is hotter than the liquid, and vice versa. Heat transfer is obviously controlled by the gas-phase resistance, and therefore the number of transfer units for heat transfer is of the same order of magnitude as the number of transfer units for H,S mass transfer, since, as was seen before, the latter is gas-phase controlled over a large fraction of the absorber (we are here implicitly making use of the Colburn analogy). Since the partial pressure of H2S changes by a few orders of magnitude over the absorber height, the number of transfer units is large, and over most of the absorber the gas and liquid temperatures are expected to be very close, see Fig. 5. In the top part of the absorber, the liquid is expected to heat up, i.e. dT,/dx is expected to be negative, and therefore so is dTJdx expected to be. This implies that in the top part of the absorber the gas is expected to be hotter than the liquid, albeit only marginally. However, in the bottom part of the absorber the gas may well be cooler than the liquid, and indeed it is for the case presented here; hence, a section of the absorber must exist where the
Temperature (K)
Fig. 5. Temperature distributions
two temperature profiles cross each other. This is possible because water evaporation may cool down the liquid phase to a temperature lower than that of the gas phase, the lower bound being the wet-bulb temperature. The considerations above show that heat transfer and water evaporation need to be taken simultaneously into account; indeed, some preliminary calculations which we had performed neglecting water evaporation gave paradoxical results. Notice that, even if the gas feed is saturated with water vapour at the partial pressure corresponding to the exit liquid temperature and composition, so that neither evaporation nor condensation takes place at the rich end, it will take place elsewhere in the absorber where the temperature and composition of the liquid phase are different. The question of the Colburn analogy is worth discussing in more detail. The heights of a transfer unit for gas-phase controlled mass transfer and heat transfer, H,, and H,,, are given by: H GM = G/k,aP
(25)
H GH = Gcp/ha
(26)
where cp is the gas molar specific heat at constant pressure, and h is the gas-phase heat transfer coefficient. Therefore, their ratio is given by: H,,IHo, The Colburn
analogy h/c,
= h/c&%.
(27)
thus gives: Pk,
= Le213.
(28)
In eq. (28), Le is the Lewis number, i.e. the ratio of the Prandtl number to the Schmidt number: in the gas phase, the Lewis number’s value is very close to unity. logic The input data for an adiabatic absorber are, in addition to the ones for an isothermal absorber, the temperatures of the gas and liquid feeds, and the Flowsheet
430
WEI-CHUNG Yu and
partial pressure of water vapour in the gas feed, &. The calculations presented here are for a temperature of both feed streams of 4O”C, i.e. the same temperature which WdS used in the isothermal calculation, and for a dry feed gas, i.e. pBw - 0. All other input variables have the same values as the ones used for the isothermal calculation, so that the comparison of the results obtained in the two cases is a fair one. In fact, the isothermal calculation is used as a first step of the whole procedure, and its results are used as guidelines for the guesses to be made at the beginning of the adiabatic calculation procedure. The value of pk is calculated in the same way as in the isothermal case, using the temperature of the feed Iiquid. Again a value of p; is guessed, and therefore CL~ and ai are calculated from mass balances on H,S and COz. However, in this case this is not enough information to allow the calculation of the minimum L/G, ratio, since the temperature of the liquid phase at the rich end, T,,, is not known. A first guess for TLB is calculated by assuming that all the heat of reaction is still in the liquid phase at the bottom, with none having been given back to the gas phase through heat transfer and evaporation. Of course, the actual value of T,, cannot exceed this guessed value; indeed, even if the highest TL is somewhere within the absorber rather than at the rich end (as indeed turns out to be the case, see Fig. S), that highest value cannot exceed the guessed value of T,,. In our calculation, we have assumed that the total amount of water evaporated is negligible as compared to the liquid flowrate, so that the latter is still regarded as constant. It follows that no additional guess is required, and the actual integration of the transport equations can be started from the rich end. The details of this calculation are discussed in the next subsection. Again, the calculation is performed by systematically underestimating p;, for the reasons discussed before. The last step is a convergence procedure, which now involves two variables (p; and TLa), and therefore a shooting method has been used. Of course, in the adiabatic calculation the values of the physical parameters, and in particular of equilibrium and kinetic constants, changes along the tower axis because temperature is changing; this has been taken into account. The temperature of the liquid phase has been assumed to be uniform over every cross-section (while it is changing along the axis), consistent with the assumption that the resistance to heat transfer is entirely in the gas phase. The logic flowsheet discussed above is sketched in Fig. 6.
Main calculation Equations (2j( 16) are used again for the calculation of the fluxes of H2S and C02, only that in this case the parameters appearing in them depend on the local temperatures of the two phases. In addition to these, transport equations for heat and for water vapour are written as follows:
GIANNI
ASTARITA
isothermal calculation t Guess
p’+, TtB t
MC until p” = p;
Yes
p” = p’i 7 TL = T,?
11 Print results
Fig. 6. Flowsheet logic, adiabatic.
JH = ha(T,Jw = kga
TL)
(29)
@” -py)
(30)
where pw is the partial pressure of water vapour in the gas phase, and p,w is its value at the interface, which is determined by temperature and composition of the liquid phase as the corresponding equilibrium vapour pressure of water. Equations (29) and (30) are of course based on the assumption that the transport of heat and of water vapour is entirely gas-phase controlled. Equations (1 l), (16), (29) and (30) are to be coupled to the mass balances (17j(20), to which the following three have to be added:
Lc,dT,/dx
d(c,GT,)/dx
= JH
(31)
d(Gpw/P)/dx
= JH
(32)
= JH+JW(QW
+cLTL)
+ J’(Q’+cpTG)+J”(Q”+cpTG). (33) In eq. (33), QW is the heat of condensation of water, Q’ is the heat of formation of the hydrosulphide, Q” is the heat of formation of the bicarbonate, and c,_ is the liquid molar specific heat. The system of eqs (17j(20), (3 1j(33) is again of the form of eq. (22), with the index i now running from 1 to 7, since there are three additional variables (T,, TG and pw)_ The boundary conditions are again eqs (23) and (24), and in addition the values of pr, T,, and TLT are assigned, for a total of eight boundary conditions which again also determine the absorber height L. Four of the boundary conditions are assigned at x = L, and only two can be transformed by a direct balance to conditions at x = 0, so that in this case two guesses are needed. The grid size is again assigned as in the isothermal case. Since the convergence is in this case on two variables, the number of iterations is on occasion larger than 10, and a preliminary isothermal calculation is needed for entering the design procedure: this brings
431
Design of packed towers for selectivechemical absorption the number of times the transport equations have to be solved to as much as 5000 on some occasions. Results Figure 5 presents the temperature distribution in both phases. The two temperatures are almost equal along most of the absorber, except in a thin region near the lean end. A section indeed exists, about 50 cm above the rich end, where the two temperature profiles cross each other: this is of course due to the wet-bulb temperature effect. A quite significant temperature bulge is observed: the exit liquid is only about 10°C hotter than the liquid feed, but the highest liquid temperature is 20°C larger than the liquid feed temperature. Also notice that the absorber height is almost 10 m, which is quite significantly larger than the 4 m which are obtained from the isothermal calculation. Figure 7 presents the distribution of water vapour partial pressures in the gas phase. It turns out that, except again a thin region near the lean end, the gas is essentially saturated with water vapour, and the pw distribution is simply related to the temperature and composition distribution of the liquid phase. Since both the temperature and the water partial pressures in the gas phase at the lean end are essentially at equilibrium with the liquid phase, the total amount of heat released from the liquid to the gas phase can be calculated directly, which helps with the convergence procedure after the first iteration. Figure 8 presents the three relevant H2S partial pressures, in the same format as in Fig. 2. The qualitative behaviour is very similar to that obtained for the isothermal case, though the film effect appears to be less important. This is related to the higher liquid flowrate which results in a larger value of /$“, and hence in a lower value of I”. Figure 9 presents the ratio of gas-side to liquid-side mass transfer resistances for H2S, and Fig. 10 presents
Fig. 8. Same as Fig. 3, adiabatic.
0
I
1
4
8
R 800
Fig. 9. Same as Fig. 4, adiabatic.
t
0
L
0.1
pw(bar) Fig. 7. pw distribution.
the COZ partial pressure distribution. Again the interaction between the two reactions shows up conspicuously: in the region where the HZS mass transport is liquid-side controlled, the CO2 absorption rate essentially drops to zero. A comparison between the isothermal and the adiabatic calculations shows that there are three major differences. First, the required height of absorber is significantly larger when calculated for the adiabatic case. Second, the selectivity is significantly less: 8.7 for the adiabatic case (a number in good agreement with available information on industrial performance), vs 30 for the isothermal case. Finally, the L/G, ratio for the adiabatic case (0.9085) is significantly larger than one
WEI-CHUNG
432
Yu and
GIANNI
ASTARITA
Acknowl&gcmfz~0-We are grateful to Professor Westerterp for providing the Blauwhoff rt ul. (1987) paper prior to publication. 800 -
NOTATIOY
interface area per unit volume, cm-’ liquid, heat of specific molar
a CL
gmol molar
G
h H H GH H GM I
1.o
1.1
p”(bar) Fig. 10. Same as Fig. 5, adiabatic.
J k kF kG kl
would predict from the isothermal calculation. It is interesting to observe that, if one performs the isothermal calculation for the L/G, ratio of 0.9085, one obtains for the absorber height 10.2 m (vs 9.8 M from the adiabatic calculation), and for the selectivity 8.4. In other words, the only real reason for performing the more complicated adiabatic calculation is that one needs to determine the appropriate liquid-gas flowrate ratio, which is grossly underestimated by the isothermal calculation; however, once this is done, one could as well use the simpler isothermal procedure for actual design. The relevant differences encountered between the adiabatic and isothermal calculations are to attributed to the fact that, in the former, a significantly larger height of tower is calculated. This of course implies that much more CO2 is absorbed than one would calculate for the isothermal case, and hence a significantly lower selectivity is obtained. In other words, the temperature rise in the liquid phase has the main effect of decreasing the H,S absorption rate, and hence ultimately to decrease the attainable selectivity. CONCLUSIONS A design procedure for the height of packing required in selective absorption of H2S from gases containing CO2 has been presented, which is based on the analytical interactive solution to the mass transfer equations presented in our previous paper Yu and Astarita (1987). The procedure requires very little computer time, and predicts the essential interactive effects. The procedure could easily be extended to other systems, provided enough physico-chemical information is available. All details of the procedure, as well as a complete listing of the computer program, are available in a recent Ph.D. thesis (Yu, 1985).
Le m P 2 Q’ 42” T X Y
Greek ; 6 bp” =i c
letters total concentration, gmolcm-3 coefficient of convergence procedure, bicarbonate concentration difference, gmol cm 3 HIS pressure difference due to film effect, atm variables appearing in differential equations, molar density of liquid phase, gmol cm- 3
Superscripts for W H for for I, for Subscripts B G I L 0 P T
cal
specific heat of gas, calgmol- ’ "C- ’ CO2 diffusivity in liquid, cm’s_ 1 gas molar flowrate per unit area, gmol cm ‘s-l heat transfer coefficient, cal cm- ’ s- ’ “C ’ Henry’s law constant, atm cm 3 gmol- ’ height of a transfer unit for heat, cm height of a transfer unit for mass, cm enhancement factor for mass transfer mass flux per unit volume, gmol cm- ’ s- 1 reaction, kinetic constant of CO2 cm3gmol-‘s-’ liquid-side mass transfer coefficient, cm s - 1 mass transfer coefficient, gas-side gmolatm-‘cm-2s-’ apparent kinetic constant at interface, s- ’ Lewis number total amine concentration, gmol cm - 3 partial pressure, atm total pressure, atm latent heat of water evaporation, cal gmol- 1 hydrosulfide ion formation, heat of cal gmol- 1 bicarbonate ion formation, heat of cal cm01 - ’ temperature, “C vertical distance from bottom of absorber cm fractional conversion of amine
CP D
0
- L0c-l
water heat
H2S CO2
at bottom of absorber for the gas at the interface for the liquid in the bulk of the liquid preliminary estimate at top of absorber
Design of packed towers for selective chemical absorption REFERENCES Astarita, G. and Savage, D. W., 1983, Ado. Transport Process. 3, 340. Astarita, G. and Yu, W. C., 1985, Proc. 8th International Symposium on Chemical Reaction Engineering, Edinburgh, 1984. Blauwhoff, P. M. M., Kampuis, B., Van Swaij, W. P. M. and Westerterp, R., 1987, Absorber design in sour natural gas treating plants. Impact of process variables on operation and economics. To be published. Gartner, D., Hegner, B., Molzahn, M. and Schmidt, R., 1979, Germ. Chem. Engng 2, 312.
433
Goar, B. G., 1980, Proc. Gas Conditioning Conference, Norman, Oklahoma. Hegner, B. and Molzahn, M., 1977, Inst. Chem. Symp. Ser. 56, 4.2/81. Onda, K., Takeuchi, M. and Okumoto, Y., 2968, J. Chem. Engng Japan 1,56. Pandya, J. D., 1987, Chew Engng. Commun., in press. Yu, W. C., 1985, Ph.D. thesis, University of Delaware. Yu, W. C. and Astarita, G., 1987, Chem. Engng Sci., 42, 419424.
DESIGN
Vol. 42, No. 3, pp. 425433.
1987. 0
OF PACKED
TOWERS FOR ABSORPTION
SELECTIVE
“OO9-2509/87 $3.00 t 0.00 1987 F’ergamon Journals Ltd.
CHEMICAL
WEI-CHUNG YU and GIANNI ASTARITAT Department of Chemical Engineering, University of Delaware, Newark, DE 19711, U.S.A. (Received 18 February
1985; accepted July 1985)
Abstract-The selectivity obtained in industrial processes of gas treating with chemical solvents is of kinetic nature, and accurate procedures for designing the required packed height are therefore needed. A procedure for packed towers is presented here, which is based on the model of simultaneous absorption presented in a previous paper. The procedure takes into account the absorption of two gases, heat transfer and water evaporation.
INTRODUCTION
Selective removal of H,S from gases containing CO2 is an important industrial process, which is needed whenever the H2S/C02 ratio in the gas to be treated is less than - l/7. In fact, for such a gas, if both H,S and CO2 are removed almost completely, the concentration of H2S in the gas exiting from the regenerator would be too low for the gas to be sent economically to a Claus plant for conversion of H2S to elemental sulphur. For a review of this whole area see Astarita and Yu (1985). Selective removal of achieved commercially by use of chemical solvents, and in particular with aqueous solutions of methyldiethanolamine (MDEA) (Goar, 1980). The selectivity achieved in industrial operation is larger than the thermodynamic one (Astarita and Savage, 1983), and is thus to be ascribed to kinetic phenomena. More specifically, the selectivity is obtained by making use of the fact that HIS reacts with MDEA much faster than CO2 does. The fact that the selectivity is of a kinetic nature makes it important to be able to design accurately the absorber height: underdesign would lead to failure of meeting the H,S specifications on the treated gas, but overdesign would lead to an approach to the unfavourable thermodynamic selectivity. A design procedure for trayed towers has recently been proposed by Blauwhoff et al. (1987), which is based on the assumption that each tray can be regarded as a CSTR for both the gas and liquid phases. In this paper, we present a design procedure for countercurrent packed absorbers. We consider in particular the case of an aqueous solution of MDEA, for which we have recently presented an approximate analytical solution to the simultaneous mass transfer equations (Yu and Astarita, 1987) used in the following. For systems other than aqueous MDEA, the same procedure could be applied as well, provided enough information is available on the equilibrium and kinetics of the chemical reactions involved, and a suitable
‘Present address: Chemical Engineering University of Naples, Naples, Italy.
Department, 425
modification of the solution to the mass transfer equations given by Astarita and Yu (1985) has been developed on that basis. ISOTHERMAL
ABSORBER
We first develop the procedure for the case of an isothermal absorber. As will be seen in the following, the assumption of isothermal behaviour is not an acceptable one; however, the isothermal calculation turns out to be a useful preliminary to the more realistic adiabatic calculation. Also, discussion of the simpler isothermal case presents in an easier way the essential features of the procedure. In all the discussion that follows, plug flow has been assumed for both phases. Of course, this may not be entirely appropriate in realistic cases; however, the same assumption is typically made in the design procedure for physical absorption towers, and we see no reason to change it for the case of chemical absorption. FIowsheet
logic
The input data for the calculation are the liquidphase composition, the gas feed composition and flowrate, the pressure P in the absorber (which is assumed to be constant), and the temperature. The calculations which are presented here are for a pressure of 10 atm, gas f-eed consisting of 89 %N,, 10 y0 Co2, and 1 o/0H2S, a temperature of 40-C, and a liquid feed containing 3.0 mol dm- 3 of MDEA, 1 o/0converted to bicarbonate and 1 y0 to hydrosulphide. We use the subscripts T and B to identify conditions at the top of the counter-current absorber (lean end), and at the bottom (rich end); ’ and V identify H,S and COz, respectively, y is the fractional saturation, and p the partial pressures: the calculations presented are for y; = y’; = 0.01, p; = 0.1 atm, and p’;, = 1 atm. The first thing to be assigned is the H2S specification on the treated gas, i.e. the value of pi. This cannot simply be chosen as slightly larger than the equilibrium value corresponding to the composition of the feed liquid, because of the film effect which was discussed in our previous paper. However, at the start the magnitude of the film effect at the lean end cannot be
426
WEI-CHUNG
Yu and GIANNI
calculated, since the CO2 partial pressure at the top, &, is not known. However, the film effect cannot be larger than that corresponding to the partial pressure of CO2 in the feed gas, pi, and this is used to estimate the film effect at the top (as will be seen, the COz partial pressure changes only by about 10% over the whole absorber, so this is not a bad estimate). Thus the equilibrium partial pressure of H2S corresponding to the interface composition of the feed liquid is estimated. This value, increased by 25 O/&is chosen as the specification pk. Once p; has been assigned, the total amount of HzS absorbed can be calculated, and from this one obtains (via an H,S overall balance) the value of the H2S fractional saturation in the exit liquid, y;. Should the problem considered be one where only one gas is being absorbed, at this stage one could calculate the minimum liquid flowrate from the requirement that the liquid at the rich end be in equilibrium with the feed gas. However, this is not so for simultaneous absorption, where the equilibrium equations for H2S and CO2 are coupled, and one still needs to know the value of & in order to calculate the minimum liquid flowrate. This can only be obtained from a mass balance on COz if the value of p’; is guessed: what the actual value of p’; will be depends on what height of absorber is needed to meet the H2S specification. Once the guess on p; has been made, the minimum liquid flowrate is calculated from the requirement that p;3and yk are in equilibrium with each other at the calculated value of yg . The actual liquid flowrate is then taken as 30% larger than the minimum one. At this stage, to within the one guess which has been made, the gas and liquid molar flowrates per unit crosssectional area, G, and L, are known, as well as the compositions of the liquid and gas phases at the lean and rich end. We have assumed the liquid phase to have the physical properties of water (this is not a very realistic assumption, but it is irrelevant to the development of the procedure). One can now calculate the values of the mass transfer coefficients in the gas phase, k& and k&, of the liquid-side mass transfer coefficients which would prevail in the absence of chemical reactions, kz and kr and of the interface area per unit volume, a; we have used the well-tested correlations of Onda et al. (1968) in order to do so. In our calculations, we have considered a packing of 2-in. Fall rings. The procedure described up to now will be termed in the following the preliminary calculation (PC). The next step is the actual integration of the transport equations along the absorber axis, the details of which are discussed in the next subsection. We have chosen to start the calculation from the rich end, since that turns out to result in faster convergence of the procedure. The calculation should proceed upwards through the absorber until p’ reaches the value of pk. However, should the initial guess on pq have been an overestimate, the value of yg would be underestimated, and somewhere along the absorber height y” could become negative. Although one could stop the calculation at such a point and readjust the guess on p;, the
ASTARITA
convergence criterion would be somewhat harder to establish. Therefore, it is best to choose the initial guess on p; as a sure underestimate, so that the integration of the transport equations proceeds until p’ reaches the value pk. The calculation described in this paragraph will be referred to in the following as the main calculation (MC). The last step to be performed in a convergence procedure (CP). As the MC is finished, the value of p(f obtained will in general be larger than the initially guessed one (or from the one guessed in the previous iteration) by an amount bp”, and a new guess needs to be made, which, for the reasons discussed above, should again be an underestimate. We have chosen a convergence procedure given by: P’;” = P’;, _ 1 + B6P”
(1)
in which the second subscript on p’; indicates the iteration number. With fl = 1, this would be a repeated substitution CP, which could lead to overestimates of p’; at some iteration. We have found that a p of 0.6 never leads to an overestimate, and ensures rapid convergence. The number of iterations required of course depends on the precision required, i.e. on how small a value of 6p”/pG one chooses to regard as acceptable. It is perhaps obvious that one needs a rather strict criterion for 6p”/p;, since the corresponding GyG/yi; is significantly larger. The calculations presented here are for a maximum Gyi;/yi; of 2 %. The logic flowsheet discussed above is sketched in Fig. 1. The calculation time required is 6.03 s on a DEC-10 computer.
Main calculation The analytical interactive solution of the mass transfer equations which has been discussed by Yu and Astarita (1987) can be summarized as follows. First, a preliminary estimate of the H,S mass transfer flux per unit volume is obtained from the following system of equations: J’p = kGa(p’ - pip)
(2)
which is the gas-phase transport equation, with the subsript P indicating that it is a preliminary estimate, I identifying conditions at the interface. The liquid-side mass transport equation is: J; = k~a(a;,
- a!;)
(3)
with the subscript 0 identifying conditions in the bulk of the liquid, and a being the total concentration of dissolved gas, both in the physically dissolved form and the chemically combined one, i.e. a; = rny;r + pi/H'.
(41
The value of y; is determined by the condition that chemical equilibrium should prevail at the interface, say: &
= (fH’m/UyL
[the nomenclature
(Y;, + YM~
- Y& - .vbl
(5)
of Astarita and Yu (1987) is used].
Design of packed towers for selective chemical absorption and finally an adjusted obtained as:
Preliminary calculation t
427
mass transfer rate of H,S
J’ = k&(p’-p;)
Guess p;
J’ = F’(p’, p”, y;.
A correction factor f depends on ionic strength, and hence on y; and yb:, and therefore a solution of eq. (5) is obtained by repeated substituion on a quadratic. The system of eqs (2)-(5) is equivalent to an equation of the following form: = P’(P’,
Yb, YZ).
(6)
Once this preliminary estimate of J’ has been obtained, the mass transfer equations for COZ are: J” = @(p”-pp;)
= J’
(17)
d(Gp”/P)/dx
= J”
(18)
where the apparent kinetic constant composition, k,, is given by: k, = km(l -y;,,
(8) at the interface (9)
-y;;)
with k the true bimolecular kinetic constant of the CO,-MDEA reaction. The value of &*, the CO1 partial pressure corresponding to equilibrium with the bulk-liquid composition, is given by: (Yb + Y;;)/(l
- Yb - Y’d).
As discussed in our previous preliminary estimate of J’ has been correction is performed as follows. ment factor for COr mass transfer,
(11)
paper, once this made, a film effect First, an enhanceI”, is calculated as:
1 + Dk,/kf”‘).
With this, an excess bicarbonate interface, 6, is calculated as: 6 = (I”-
(10)
is equivalent to an equation
J” = F”(p’, p”. yb, yb:).
I” = j(
(12)
concentration
l)(p;-ppb:*)/H”.
at the (13)
The interface-composition value of the equilibrium partial pressure of HIS is now recalculated as: p; = (fH’mlK’)y;,(Y;,
= J
+ Yb: + a/t1
-Yip
(19)
= J”
(20)
a = my + p*/H.
- Yb: - 6)
(14)
(21)
In eqs (17) and (IS), G is the local molar gas flowrate, which is related to p’ and p” by an elementary mass balance. The system of eqs (17)-(20) is a system of four differential equations for four unknowns 7i, i=l,..., 4, of the following general form: drJdx
= gi(rr ,
_ ,
subject to the following
(7)
J” = (l/H”)(p;--p’d*)aJ~k~“z+Dk,)
The system of eqs (7t(lO) of the following form:
(16)
where c is the molar density of the liquid phase, and x is distance measured from the rich end. The CISare related to the ys by:
Fig. 1. Flowsheet logic, isothermal.
= (fH”mlK”)Yb:
yb’).
to an
d(Gp’/P)/dx
d (Lu”/a),‘dx
Convcr ence proce Lfure
p;;*
equivalent
Equations (11) and (16) are to be coupled with local mass balances as follows:
d(La’/a)/dx
4
(15)
the system of eqs (12t(lS) being equation of the following form:
t MC until p’ = p’T
is
x = 0, x = L,
boundary
p’=pb,
P’ = P;,
i = 1,
74),
_ ,4
conditions:
p”=p;; u’ = ct;,
(22)
(23) & = a;.
(24)
Notice that the existence of the fifth boundary condition also determines the absorber height L. The problem as stated above is a two-boundary value problem, and since it cannot be solved analytically and a numerical technique such as the Runge-Kutta method needs to be used, which requires oneboundary conditions to be imposed, it needs to be transformed accordingly. As discussed before, two of the x = L conditions can be transformed to x = 0 ones, but the third one cannot, and therefore a guess is needed on one of the variables; we have chosen to guess the value of p;. When applying the Runge-Kutta method, a strategy for determining the grid size 6x needs to be established. We have chosen to have a small 6x (1 cm) near the rich end, where most of the H,S absorption takes place, and steep concentration gradients are established in both phases. As the H,S partial pressure drops to l/10 of its initial value, the 6x value is changed to 10 cm. Finally, as one approaches the lean end, the 6x is changed again, getting smaller and smaller as the percentage approach of p’ to the value p; is decreasing. This leads, for some of the cases which have been calculated, to a total number of steps for the MC as large as 150. With the CP occasionally requiring up to 10 iterations, the mass transfer equations have to be solved as many as 1500 times for a complete calculation.
428
WEI-CHUNG
Yu
and GIANNI
ASTARITA
Results
The axial distribution of pb*, the H2S equilibrium partial pressure corresponding to the composition of the bulk liquid, spans a few orders of magnitude from the rich end to the lean end, and so do all other relevant partial pressures. These would thus need to be plotted in a semilog plot, where differences between partial pressures would hardly be noticeable. Therefore, the complete results for II,!3 are presented in the form of Fig. 2, where three curves are plotted, each one being a partial pressure divided by the local value of pb*. The leftmost curve labelled 1 is the interface partial pressure of H2S calculated without the film effect correction, i.e. the value of pip. A value of unity for the ratio p;,/p’a indicates that the H2S mass transfer is entirely gas-phase controlled. This is indeed almost the case in the top half of the absorber, as can also be seen from Fig. 3, where the ratio of gas-side to liquid-side mass transfer resistances for H,S is plotted. The middle curve labelled 3 is the interface partial pressure of H,S calculated including the fiIm effect correction, i.e. the value of pi. In the bottom part of the absorber, curves 1 and 3 almost coincide, showing that the film effect is negligible. This is, however, not true for the top part of the absorber, where the difference between the two curves is of the order of 10 %. Notice that the film effect can be predicted only by an interactive solution to the mass transfer equations. The rightmost curve labelled 2 is the partial pressure of HZS in the gas phase. The difference between lines 2 and 3 is a measure of the driving force in the gas phase; the difference between the values read on curve 1 and unity is a measure of the driving force in the liquid phase. Finally, the difference between lines 1 and 3 is a measure of the fraction of total driving force which is lost to the film effect.
R
Fig.
3. Ratio
R of gas-side to liquid-side mass transfer resistance for H2S, isothermal.
Figure 4 presents the partial pressure distribution of CO2 along the absorber axis. For C02, the mass transport is always liquid-side controlled, with the gasphase resistance amounting to no more than 0.1 y0 of the total throughout the absorber. Two observations are in order concerning Fig. 4. First, in the bottom 40cm of absorber p” slightly increases with distance from the rich end. This is on the threshold of a situation where CO2 is actually desorbed back to the gas phase; it is not quite so, because in the bottom part of the absorber most of the H,S is being absorbed, and therefore the partial pressures of COz and N, increase simply because that of H,S decreases. However, the important point is that in this region the H,S mass
1 .o
Fig.
2. pip/&*
(I),
(3) and isothermal.
pi/&*
p’,pb*
distributions,
p”(bar)
Fig. 4. p” distribution,
isothermal.
Design of packed towers for selective chemical absorption
429
transport is controlled by the liquid phase, and therefore the liquid interface is significantly more acidic than the bulk, which results in an almost zero rate of COZ absorption. This result is again one which could only be predicted by an interactive solution to the mass transfer equations. The second observation is that only about 3 o/0of the entering CO2 is being absorbed; since practically all the H,S is absorbed, the selectivity for this case is about 30. This is a large number, larger than values reported for industrial operation, but in fact, as will be seen later, it is an artifact of the isothermal approximation. The L/G, ratio obtained for the case shown in Figs 2-4 is 0.47.
ADIABATIC
ABSORBER
Thermal effects in absorbers where a chemical solvent is used may be quite conspicuous, because liquid flowrates are comparatively low (due to the large capacity of chemical solvents) and the heat released is that of a chemical reaction and may be quite significant. Only a few recent works address the question of predicting temperature distributions in absorbers employing chemical solvents (Blauwhoff et al., 1987; Gartner et al., 1979; Hegner and Molzahn, 1977; Pandya 1987). Thermal effects are connected with three phenomena: the release of the heat of chemical reactions, direct heat transfer between gas and liquid phases, and water evaporation or condensation. As will be seen in the following, all three are important, and need to be included in the calculation scheme. Heat
transfer
As the gas phase moves upwards through the absorber, the only mechanism allowing for its temperature to change is direct heat transfer to or from the liquid phase, since both the heat of chemical reactions and of water condensation are released in the liquid phase. It follows that dT,/dx can be negative only if the gas is hotter than the liquid, and vice versa. Heat transfer is obviously controlled by the gas-phase resistance, and therefore the number of transfer units for heat transfer is of the same order of magnitude as the number of transfer units for H,S mass transfer, since, as was seen before, the latter is gas-phase controlled over a large fraction of the absorber (we are here implicitly making use of the Colburn analogy). Since the partial pressure of H2S changes by a few orders of magnitude over the absorber height, the number of transfer units is large, and over most of the absorber the gas and liquid temperatures are expected to be very close, see Fig. 5. In the top part of the absorber, the liquid is expected to heat up, i.e. dT,/dx is expected to be negative, and therefore so is dTJdx expected to be. This implies that in the top part of the absorber the gas is expected to be hotter than the liquid, albeit only marginally. However, in the bottom part of the absorber the gas may well be cooler than the liquid, and indeed it is for the case presented here; hence, a section of the absorber must exist where the
Temperature (K)
Fig. 5. Temperature distributions
two temperature profiles cross each other. This is possible because water evaporation may cool down the liquid phase to a temperature lower than that of the gas phase, the lower bound being the wet-bulb temperature. The considerations above show that heat transfer and water evaporation need to be taken simultaneously into account; indeed, some preliminary calculations which we had performed neglecting water evaporation gave paradoxical results. Notice that, even if the gas feed is saturated with water vapour at the partial pressure corresponding to the exit liquid temperature and composition, so that neither evaporation nor condensation takes place at the rich end, it will take place elsewhere in the absorber where the temperature and composition of the liquid phase are different. The question of the Colburn analogy is worth discussing in more detail. The heights of a transfer unit for gas-phase controlled mass transfer and heat transfer, H,, and H,,, are given by: H GM = G/k,aP
(25)
H GH = Gcp/ha
(26)
where cp is the gas molar specific heat at constant pressure, and h is the gas-phase heat transfer coefficient. Therefore, their ratio is given by: H,,IHo, The Colburn
analogy h/c,
= h/c&%.
(27)
thus gives: Pk,
= Le213.
(28)
In eq. (28), Le is the Lewis number, i.e. the ratio of the Prandtl number to the Schmidt number: in the gas phase, the Lewis number’s value is very close to unity. logic The input data for an adiabatic absorber are, in addition to the ones for an isothermal absorber, the temperatures of the gas and liquid feeds, and the Flowsheet
430
WEI-CHUNG Yu and
partial pressure of water vapour in the gas feed, &. The calculations presented here are for a temperature of both feed streams of 4O”C, i.e. the same temperature which WdS used in the isothermal calculation, and for a dry feed gas, i.e. pBw - 0. All other input variables have the same values as the ones used for the isothermal calculation, so that the comparison of the results obtained in the two cases is a fair one. In fact, the isothermal calculation is used as a first step of the whole procedure, and its results are used as guidelines for the guesses to be made at the beginning of the adiabatic calculation procedure. The value of pk is calculated in the same way as in the isothermal case, using the temperature of the feed Iiquid. Again a value of p; is guessed, and therefore CL~ and ai are calculated from mass balances on H,S and COz. However, in this case this is not enough information to allow the calculation of the minimum L/G, ratio, since the temperature of the liquid phase at the rich end, T,,, is not known. A first guess for TLB is calculated by assuming that all the heat of reaction is still in the liquid phase at the bottom, with none having been given back to the gas phase through heat transfer and evaporation. Of course, the actual value of T,, cannot exceed this guessed value; indeed, even if the highest TL is somewhere within the absorber rather than at the rich end (as indeed turns out to be the case, see Fig. S), that highest value cannot exceed the guessed value of T,,. In our calculation, we have assumed that the total amount of water evaporated is negligible as compared to the liquid flowrate, so that the latter is still regarded as constant. It follows that no additional guess is required, and the actual integration of the transport equations can be started from the rich end. The details of this calculation are discussed in the next subsection. Again, the calculation is performed by systematically underestimating p;, for the reasons discussed before. The last step is a convergence procedure, which now involves two variables (p; and TLa), and therefore a shooting method has been used. Of course, in the adiabatic calculation the values of the physical parameters, and in particular of equilibrium and kinetic constants, changes along the tower axis because temperature is changing; this has been taken into account. The temperature of the liquid phase has been assumed to be uniform over every cross-section (while it is changing along the axis), consistent with the assumption that the resistance to heat transfer is entirely in the gas phase. The logic flowsheet discussed above is sketched in Fig. 6.
Main calculation Equations (2j( 16) are used again for the calculation of the fluxes of H2S and C02, only that in this case the parameters appearing in them depend on the local temperatures of the two phases. In addition to these, transport equations for heat and for water vapour are written as follows:
GIANNI
ASTARITA
isothermal calculation t Guess
p’+, TtB t
MC until p” = p;
Yes
p” = p’i 7 TL = T,?
11 Print results
Fig. 6. Flowsheet logic, adiabatic.
JH = ha(T,Jw = kga
TL)
(29)
@” -py)
(30)
where pw is the partial pressure of water vapour in the gas phase, and p,w is its value at the interface, which is determined by temperature and composition of the liquid phase as the corresponding equilibrium vapour pressure of water. Equations (29) and (30) are of course based on the assumption that the transport of heat and of water vapour is entirely gas-phase controlled. Equations (1 l), (16), (29) and (30) are to be coupled to the mass balances (17j(20), to which the following three have to be added:
Lc,dT,/dx
d(c,GT,)/dx
= JH
(31)
d(Gpw/P)/dx
= JH
(32)
= JH+JW(QW
+cLTL)
+ J’(Q’+cpTG)+J”(Q”+cpTG). (33) In eq. (33), QW is the heat of condensation of water, Q’ is the heat of formation of the hydrosulphide, Q” is the heat of formation of the bicarbonate, and c,_ is the liquid molar specific heat. The system of eqs (17j(20), (3 1j(33) is again of the form of eq. (22), with the index i now running from 1 to 7, since there are three additional variables (T,, TG and pw)_ The boundary conditions are again eqs (23) and (24), and in addition the values of pr, T,, and TLT are assigned, for a total of eight boundary conditions which again also determine the absorber height L. Four of the boundary conditions are assigned at x = L, and only two can be transformed by a direct balance to conditions at x = 0, so that in this case two guesses are needed. The grid size is again assigned as in the isothermal case. Since the convergence is in this case on two variables, the number of iterations is on occasion larger than 10, and a preliminary isothermal calculation is needed for entering the design procedure: this brings
431
Design of packed towers for selectivechemical absorption the number of times the transport equations have to be solved to as much as 5000 on some occasions. Results Figure 5 presents the temperature distribution in both phases. The two temperatures are almost equal along most of the absorber, except in a thin region near the lean end. A section indeed exists, about 50 cm above the rich end, where the two temperature profiles cross each other: this is of course due to the wet-bulb temperature effect. A quite significant temperature bulge is observed: the exit liquid is only about 10°C hotter than the liquid feed, but the highest liquid temperature is 20°C larger than the liquid feed temperature. Also notice that the absorber height is almost 10 m, which is quite significantly larger than the 4 m which are obtained from the isothermal calculation. Figure 7 presents the distribution of water vapour partial pressures in the gas phase. It turns out that, except again a thin region near the lean end, the gas is essentially saturated with water vapour, and the pw distribution is simply related to the temperature and composition distribution of the liquid phase. Since both the temperature and the water partial pressures in the gas phase at the lean end are essentially at equilibrium with the liquid phase, the total amount of heat released from the liquid to the gas phase can be calculated directly, which helps with the convergence procedure after the first iteration. Figure 8 presents the three relevant H2S partial pressures, in the same format as in Fig. 2. The qualitative behaviour is very similar to that obtained for the isothermal case, though the film effect appears to be less important. This is related to the higher liquid flowrate which results in a larger value of /$“, and hence in a lower value of I”. Figure 9 presents the ratio of gas-side to liquid-side mass transfer resistances for H2S, and Fig. 10 presents
Fig. 8. Same as Fig. 3, adiabatic.
0
I
1
4
8
R 800
Fig. 9. Same as Fig. 4, adiabatic.
t
0
L
0.1
pw(bar) Fig. 7. pw distribution.
the COZ partial pressure distribution. Again the interaction between the two reactions shows up conspicuously: in the region where the HZS mass transport is liquid-side controlled, the CO2 absorption rate essentially drops to zero. A comparison between the isothermal and the adiabatic calculations shows that there are three major differences. First, the required height of absorber is significantly larger when calculated for the adiabatic case. Second, the selectivity is significantly less: 8.7 for the adiabatic case (a number in good agreement with available information on industrial performance), vs 30 for the isothermal case. Finally, the L/G, ratio for the adiabatic case (0.9085) is significantly larger than one
WEI-CHUNG
432
Yu and
GIANNI
ASTARITA
Acknowl&gcmfz~0-We are grateful to Professor Westerterp for providing the Blauwhoff rt ul. (1987) paper prior to publication. 800 -
NOTATIOY
interface area per unit volume, cm-’ liquid, heat of specific molar
a CL
gmol molar
G
h H H GH H GM I
1.o
1.1
p”(bar) Fig. 10. Same as Fig. 5, adiabatic.
J k kF kG kl
would predict from the isothermal calculation. It is interesting to observe that, if one performs the isothermal calculation for the L/G, ratio of 0.9085, one obtains for the absorber height 10.2 m (vs 9.8 M from the adiabatic calculation), and for the selectivity 8.4. In other words, the only real reason for performing the more complicated adiabatic calculation is that one needs to determine the appropriate liquid-gas flowrate ratio, which is grossly underestimated by the isothermal calculation; however, once this is done, one could as well use the simpler isothermal procedure for actual design. The relevant differences encountered between the adiabatic and isothermal calculations are to attributed to the fact that, in the former, a significantly larger height of tower is calculated. This of course implies that much more CO2 is absorbed than one would calculate for the isothermal case, and hence a significantly lower selectivity is obtained. In other words, the temperature rise in the liquid phase has the main effect of decreasing the H,S absorption rate, and hence ultimately to decrease the attainable selectivity. CONCLUSIONS A design procedure for the height of packing required in selective absorption of H2S from gases containing CO2 has been presented, which is based on the analytical interactive solution to the mass transfer equations presented in our previous paper Yu and Astarita (1987). The procedure requires very little computer time, and predicts the essential interactive effects. The procedure could easily be extended to other systems, provided enough physico-chemical information is available. All details of the procedure, as well as a complete listing of the computer program, are available in a recent Ph.D. thesis (Yu, 1985).
Le m P 2 Q’ 42” T X Y
Greek ; 6 bp” =i c
letters total concentration, gmolcm-3 coefficient of convergence procedure, bicarbonate concentration difference, gmol cm 3 HIS pressure difference due to film effect, atm variables appearing in differential equations, molar density of liquid phase, gmol cm- 3
Superscripts for W H for for I, for Subscripts B G I L 0 P T
cal
specific heat of gas, calgmol- ’ "C- ’ CO2 diffusivity in liquid, cm’s_ 1 gas molar flowrate per unit area, gmol cm ‘s-l heat transfer coefficient, cal cm- ’ s- ’ “C ’ Henry’s law constant, atm cm 3 gmol- ’ height of a transfer unit for heat, cm height of a transfer unit for mass, cm enhancement factor for mass transfer mass flux per unit volume, gmol cm- ’ s- 1 reaction, kinetic constant of CO2 cm3gmol-‘s-’ liquid-side mass transfer coefficient, cm s - 1 mass transfer coefficient, gas-side gmolatm-‘cm-2s-’ apparent kinetic constant at interface, s- ’ Lewis number total amine concentration, gmol cm - 3 partial pressure, atm total pressure, atm latent heat of water evaporation, cal gmol- 1 hydrosulfide ion formation, heat of cal gmol- 1 bicarbonate ion formation, heat of cal cm01 - ’ temperature, “C vertical distance from bottom of absorber cm fractional conversion of amine
CP D
0
- L0c-l
water heat
H2S CO2
at bottom of absorber for the gas at the interface for the liquid in the bulk of the liquid preliminary estimate at top of absorber
Design of packed towers for selective chemical absorption REFERENCES Astarita, G. and Savage, D. W., 1983, Ado. Transport Process. 3, 340. Astarita, G. and Yu, W. C., 1985, Proc. 8th International Symposium on Chemical Reaction Engineering, Edinburgh, 1984. Blauwhoff, P. M. M., Kampuis, B., Van Swaij, W. P. M. and Westerterp, R., 1987, Absorber design in sour natural gas treating plants. Impact of process variables on operation and economics. To be published. Gartner, D., Hegner, B., Molzahn, M. and Schmidt, R., 1979, Germ. Chem. Engng 2, 312.
433
Goar, B. G., 1980, Proc. Gas Conditioning Conference, Norman, Oklahoma. Hegner, B. and Molzahn, M., 1977, Inst. Chem. Symp. Ser. 56, 4.2/81. Onda, K., Takeuchi, M. and Okumoto, Y., 2968, J. Chem. Engng Japan 1,56. Pandya, J. D., 1987, Chew Engng. Commun., in press. Yu, W. C., 1985, Ph.D. thesis, University of Delaware. Yu, W. C. and Astarita, G., 1987, Chem. Engng Sci., 42, 419424.