Ind. Eng. Chem. P r O C e S Des. Dev. 1986, 25, 899-705
899
Wi = bottom flow rate of column i, mol/h
ponents C and D are present in its feed in comparison to the feed of the second column in the simple direct sequence. Vapor rate savings on the order of 20% are typical in this tower. The third column also has a smaller vapor rate than the third column of the simple sequence, since the upper feed is richer in the light component C and the lower feed is richer in the heavy component D. Again, savings on the order of 20% are typical for the vapor rate in this column. Therefore, this new complex scheme will have lower operating costs than the corresponding simple sequence, provided that the utility used to reboil the bottoms of the side-stream column has the same cost as that used in the first column of the simple sequence; e.g., steam at the same pressure can be used. Finally, the first column will have a higher capaital cost than the corresponding simple column due to the additional trays needed in the stripping section. This capital expenditure is likely to be counterbalanced by the savings obtained for both the second and third columns (both have a reduced diameter, heat-exchanger surface areas, and utilities loads).
F = feed flow rate, mol/h
Vi = vapor internal flow rate of column i, mol/h
Ri= reflux ratio of column i S1= reboil ratio of the side-stream tower defined by S1= VI/
w1
N3 = number of theoretical trays below the side stream q = feed quality X.. = mole fraction of component i in stream j (xp)dn= minimum attainable mole fraction of component i in the side stream Greek Symbols ai = relative volatility of component i with respect to the heaviest component C$ = root of (5) lying between the key components f = largest root of Underwood’s equation for the stripping section Subscripts op = optimal value m or min = minimum value
Literature Cited
Conclusions A family of new complex distillation sequences can be generated by combining side stream with double-feed towers. We examined cases here where only the first separator is a side-stream column. This family of designs expands as we introduce alternatives where more than one column is a side stream, like the one shown in Figure 7e. In such a case, the optimal values of the intermediate flows and compositions can be found as done above for the scheme of Figure la.
ChemShare, Inc. DESIW 2000, Version 1 0 . 1 Oct ~ 1, 1985. W a s , N. P.; Luyben, W. L. Instrum. Tech/. 1978 (June), 43. Gllnos, K. Ph.D. Dissertation, Unkerslty of Massachusetts, Amherst. 1984. Gllnos, K.; Malone, M. F. Ind. Eng. Chem. Process Des. D e v . 1984, 23, 784. Gllnos, K.; Malone, M. F. Ind. Eng. Chem. Process D e s , Dev. 1985, 24, 822. Jafarey. A.; McAvoy, T. J.; Douglas, J. M. Ind. Eng. Chem. Fundem. 1979, 18, 101. King, C. J. “Separation Processes”, 2nd ed.;McOlaw-Hlli: New York, 1980. Malone, M. F.; Glinos. K.; Marquez, F. E.; Douglas, J. M. AIChE J . 1085, 31,
083. Underwood. A. J. V. J . Inst. Pet. 1848, 32, 598.
Received for review October 22, 1984 Revised manuscript received July 1, 1985 Accepted December 2, 1985
Acknowledgment We are thankful to the US Department of Energy (Grant DE-AC02-81ER10938)which supported this work.
Supplementary Material Available: Details of the rigorous design calculations for the examples shown in Tables 11-IV (4pages). Ordering information is given on any current masthead page.
Nomenclature Di= distillate flow rate of column i, mol/h P = side-stream flow rate, mol/h
Simulation of Continuous-Contact Separation Processes: Multicomponent, Adiabatic Absorption David M. HHch, Ronald W. Rousseau,’ and James K. Ferret1 Deparfment of Chemical Engineerfg, North Carollna State Univers& Raleigh, North Carolina 27695-7905
A new algorithm has been developed for the steady-state simulation of multicomponent, adiabatic absorption in packed columns. The system of differential model equations that describe the physical absorption process is reduced to algebraic equations by using a finite difference method. This system of algebraic equations is then solved by using a block-tridiagonei matrix decomposition procedure. Both the physical model and the matrix solution method are discussed in this paper. Simulation predictions are compared with experimental results and with the predictions of an earlier algorithm. The new simulation procedure was found to perform qulte well for the system studled and represents a considerable improvement over its predecessor from the standpoint of solution accuracy.
separation devices. The primary reason for this is the added complication of dealing with the rates of heat and mass transfer between phases. King (1980) effectively describes this added complication when he states that the separation in a “discretely staged equilibrium device” is
Methods for the design and/or simultion of packed columns are less well developed than for plate or staged
* To whom correspondence should be addressed. 0196-4305/86/1125-0699$01.50/0
0
1986 American Chemical Society
700
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986
determined by equilibrium conditions alone, whereas for a continuous-contact process mass-transfer rate effects are controlling. Of all the numerical solution procedures available for the design or simulation of multicomponent separation processes, by far the most rigorous and efficient algorithms are those that deal with stagewise mass-transfer operations. The methods used for the simulation and/or design of packed columns are generally deficient in one way or another. For example, the packed absorber and stripper design algorithms of Feintuch (1978), Kelly (1981), Kelly et al. (1984),and Staton (1983) are rigorous as far as their ability to handle complex multicomponent systems, yet they are also subject to numerical problems at liquid-bgas ratios approaching the minimum and as component mole fractions approach zero. All these algorithms make use of the shooting method to integrate the differential model equations. The shooting method procedure begins at the bottom of the column and moves upward, computing the temperature and concentration profiles along the way, until a desired separation of a key component is achieved. Conditions at the top of the column are compared with assumed values of outlet gas composition and temperature to test convergence. If the convergence criteria are not met, then new guesses of these outlet conditions are made, and the procedure is repeated. The stepwise convergence approach of the shooting method is generally not as computationally efficient as the newer simultaneous matrix solution procedures. Other packed column simulation procedures have been developed that emphasize computational efficiency (McDaniel and Holland, 1970; von Stockar and Wilke, 1977; von Rosenberg and Hadi, 1980; Billingsley and Chirachavala, 1981; Holland and Liapis, 1983; Srivastava and Joseph, 1984). In general, the procedures are not flexible enough to simulate more than one type of masstransfer process, or they do not have the capability to handle complex multicomponent systems in a rigorous fashion. Because of the shortcomings of the methods cited above, there is still the need for a packed column simulation that incorporates all the desirable characteristics of flexibility, the ability to handle complex systems, and computational efficiency. Toward this end, a new procedure has been developed for the steady-state simulation of multicomponent absorption in packed columns. This computer simultion, known as SIMCAL, has been tested by using experimental data obtained from the Coal Gasification/Gas Cleaning Pilot Plant facility at North Carolina State University, and the performance of the algorithm was compared with that of a previously developed design algorithm, known as MCOMP (Kelly, 1981; Kelly et al., 1984). The results of this comparison show that SIMCAL does a better job of simulating actual plant conditions than does MCOMP. Some of these results, as well as a description of the model equations and numerical methods that form a basis for this new simulation, are given below. Description of Model The initial goal of this research effort has been to develop a numerical algorithm suitable for the steady-state simulation of physical absorption in a packed column. For this reason, a very simple model of the absorption process was chosen as a starting point, thus minimizing numerical problems often encountered with more complex and highly nonlinear models. Several key conditions are imposed to reduce the difficulties in the development of this simple physical model: (1)Gas-liquid Equilibrium is described by Henry’s law. (2) Mass-and heat-transfer relationships
Table 1. Model Variables 1. nc liquid component flow rates 2. nc gas component flow rates 3. nc liquid interfacial mole fractions 4. nc gas interfacial mole fractions 5. 1 liquid phase temperature 6. 1 gas phase temperature 7. 1 interfacial temperature total number of variables = 4nc 3
li
gi Xi*
Y1*
TL TG
T*
+
are based on resistances in the series model, which implies low flux conditions and dilute solutions. (3) The column is adiabatic. (4) The pressure drop through column is negligible. (5) Gas and liquid streams are in the plug flow; Le., there are no radial temperature or concentration gradients. Although the system-specificimplications of conditions 1and 2 reduce the generality of the model, these conditions have been used successfully to describe a number of important physical absorption systems. They were made in the present case to provide a reasonably simple, linear system of equations for solution by the chosen algorithm. Conditions 3, 4, and 5 are realistic and have been shown to be valid for the column used to obtain the experimental results presented below. Condition 5 may become invalid for large, randomly packed columns; it may, however, be used appropriately in structured packings, regardless of the column diameter. The physical model described above must now be expressed in terms of a system of equations. Table I lists the variables to be found by solving the following system of model equations for steady-state, adiabatic, packed column absorption involving nc chemical components: (1)steady-state material balances -dli- - =dgi nc equations dz dz (2) mass-transfer relationships (a) liquid side dli _ dz - k d x i - xi*) nc equations (b) gas side dgi dz = k,ia(yi* - y J
nc equations
(3) equilibrium relationships yi* = Kixi* nc equations (4) steady-state, adiabatic energy balance d(LHL) d(G&) ---- 0 1 equation dz dz where nc
HG
= cyi[cGi(TGi=l
TO)+ xi1
nc
HL
= Cxi[cLi(T~- To) +
a s i 1
i=l
nc
G = Cgi i=l nc
L =
Eli
i=l
(5) heat-transfer relationships (a) liquid side nc d(LHL) -dz - h d T L - T*l - iCNiahi* =l
1 equation
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986 PACKED MSORBER
(b) gas side -I'
nc
d(GHG) -- h@[T* - TG]- CNiahi*
1 equation
i
dz i=l where Ni is the mass flux of component i across the interface and is taken to be positive for absorption, Le., transfer from the gas to the liquid phase. total number of equations = 4nc + 3 In order to solve the above system of equations, certain physical parameters must be estimated. For example, Henry's law distribution coefficients Ki was calculated by using solubility data presented by Lazalde-Crabtree et al. (1980) and Landolt-Bornstein (1976). Mass-transfer coefficients kXiand kYiand the specific interfacial area a were estimated by using correlations developed by Onda et al. (1968). Finally, heat-transfer coefficients hLand hG were determined by using the j-factor analogy (i.e., j , = j,) (Treybal, 1980), with the assumption that the same interfacial area applies for both heat and mass transfer. Heat-transfer coefficients estimated in this way are strictly valid only in the absence of mass transfer. For the gas phase, a correlation factor has been used to account for mass-transfer effects (Ackerman, 1937). No such factor exists for the liquid phase, but the magnitude of hLa is generally such that the effect of a correction for mass transfer would be negligible.
Steady-State Simulation Algorithm The numerical method chosen for the steady-state simulation uses finite difference expressions to approximate the derivatives in the differential model equations, thereby reducing the system of ODE to a coupled system of algebraic equations. A solution to this set of finite difference equations is obtained at each of a number of grid or mesh points separated by a uniform mesh size. One major drawback of the finite difference approach is that a large number of points is frequently required, which can result in an excessive time requirement on some computers. Fortunately, for absorption in a packed column, as well as many other mass-transfer operations, the system of finite difference equations, representing the physical model, can be expressed in a sparse matrix format. The system of equations studied here form a block-tridiagonal matrix, which may be solved by a mathematical procedure known as lower-upper decomposition (LUD) (Finlayson, 1980). One computer subroutine, known as BANDJ, that performs lower-upper decomposition on a block-tridiagonal matrix was developed by Newman (1973) and is used in this work. The details of the implementation of the finite difference method and a description of the matrix solution subroutine BANDJ are given below. Given a general linear system of first-order ordinary differential equations involving n-dependent variables c k as a function of the independent variable z
where i = equation number and k = variable number, through the use of Taylor series expansions, the first-order derivative terms may be expressed by the well-known forward and backward difference approximations: ck(J
701
+ 1) - c k ( J ) Az
ck(J) - ck(J - 1) Az
-~
,
k
\J
L,.,,
i
I
Figure 1. Finite difference grid.
In the above equations, the points J + 1, J , and J - 1 refer to three interior mesh points in the finite difference grid containing N J points, as shown in Figure 1. As an example of the use of finite difference expressions to approximate first-order derivatives, consider the material balance equation for mass transfer in a packed column written for component 1: dll dgl =O (4) dz dz With the application of the forward and backward difference approximations for the liquid and gas streams, respectively, this differential equation is transformed into the algebraic equation 1i(J
+ 1)- li(J)
-
g i ( J ) - gi(J - 1)
Az
Az
=0
(5)
If finite difference expressions are used to approximate all the derivatives in the model equations, then the system of linear differential equations (1)becomes a system of linear algebraic equations, which may be written in the manner
C Ai,k(J)Ck(J- 1)+ &,k(J)Ck(J)+
k=l
Di,k(J)ck(J + 1) = Gi(J)
i = 1,...,n (6)
These algebraic difference equations, along with appropriate expressions for the boundary conditions at J = 1 and J = N J may be written in matrix form as
or
MXT=Z where the elements of M (e.g., B&)) are n X n matrices and the elements of T and Z are n-dimensional vectors, n being the number of dependent variables in the system of differential equations (White, 1978). In the computer program SIMCAL, the physical model equations for packed column absorption have been expressed in finite difference form via the method described above. Initial estimates of the dependent variables Ck
702
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986
I
,
I h P U T INITIAL AND COMPOSITIOU PROFILES A \ D SET INLET FLOW RATES A h D COLUMh HEIGHT
7 -
I
---
CALL SUBROCTIhES T O C O \ l P L T E PHYSICAL AUD T R A \ S P O R T P R O P E R T Y PARAMETER \ U I F\
--
s = s R n w mi
Figure 3. Acid gas removal system. ~.______
_---
L
ISL'ERT TRI-DL4GON.X COEFFICIENT MATRIX VI.4 YELi'LLIS S LIETHOD
1
6 >'rot'
Figure 2.
SIMCAL flow
chart.
(representing liquid and gas phase flow rates, interfacial mole fractions, and temperatures) are currently generated by performing one iteration of the design algorithm MCOMP (Kelly, 1981) and then interpolating/extrapolating these values to obtain an initial profile throughout the packing section. Although it is not necessary to provide such a good ''first guess" of the ultimate solution, it has been found that SIMCAL will converge in less time than if, for example, a linear profile is assumed. Physical and transport properties are calculated by subroutines based on these initial concentration and temperature profiles. These properties are in turn used to compute the elements of the coefficient matrix M and vector Z. BANDJ is next called to decompose M and solve for an improved set of the dependent variables Ck,which become the new trial values for the next iteration. Once these variables fail to change between iterations, by more than a set convergence tolerance, execution stops and the final profiles are printed. Figure 2 is a simplified flow diagram for the computer program SIMCAL.
Experimental System The packed absorber simulation program, SIMCAL, has been tested by using data from the NCSU Coal Gasification Pilot Plant. The operation of the pilot plant and, in particular, the Acid Gas Removal System (AGRS) has been described in detail elsewhere (Kelly, 1981; Staton, 1983). Only a brief overview of the AGRS operation will be presented here. The AGRS consists, primarily, of a nominal 0.127 m (5 in.) diameter absorber and a 0.152 m (6 in.) diameter stripper, each consisting of three sections; each section is approximately 2.2 m (7.1 ft) in length and is packed with 6.25-mm (1/4-in.) ceramic Intalox saddles (see Figure 3). Solvent feed lines were constructed so that one, two, or three sections could be used in mass-transfer studies. All the data presented below were taken with just one packing section in use, both in the absorber and in the stripper. Any combination of three flash tanks may also be included
Table 11. ?'mica1 Sour Gas ComDosition compomole compomole component fraction nent fraction nent Hz CH, COS 0.2401 0.3504 CO 0.0021 CpH, HPS 0.1710 COS N, C2H6 0.0001 0.1685
mole fraction 0.0583
0.0042 0.0053
in the configuration. The system is capable of operating with either a physical or chemical solvent, but testing of the algorithm has been solely on data involving physical absorption using refrigerated methanol as a solvent. The methanol absorbs the acid gases (Le., C02, H2S, and COS) under high-pressureand low-temperature conditions in the absorption column. It may then be regenerated by any combination of several methods, including flashing to lower pressures and stripping with nitrogen or heat. The gaseous feed to the AGRS may come from one of two sources: either make-gas from the fluidized bed gasifier or a syngas of specified composition. Most of the data was obtained from the AGRS operated to condition the gas produced from coal. These data consist, essentially, of analyses of the absorber feed gas (sour gas), absorber product gas (sweet gas), flash gas from any flash tanks being used, and finally the gas released in the stripping column (acid gas). In addition, temperature profiles are monitored with thermocouples in both packed columns as well as in the flash tanks. Finally, the gas flow rates and pressures in each process vessel are observed. All the temperature, pressure, and flow rate data are compiled and recorded by a captive computerized data-acquisition system. The composition of the gasifier make-gas (sour gas) varies from run to run, but usually about nine components are present in significant concentrations. These components, as well as a typical sour gas composition, are given in Table 11.
Steady-State Simulation Results SIMCAL has been used to simulate the operation of the packed absorber for a number of pilot plant runs. One, AMI-53, which used nitrogen for stripping, was used by Kelly (1981) to test his design algorithm MCOMP. A comparison of the actual measured sweet gas composition with that predicted by both SIMCAL and MCOMP is contained in Table 111. Table IV gives a similar comparison of the results from run AMIL-14, which was selected for simulation because stripping was accomplished by using reboiled methanol. This is an important distinction because an implicit assumption used in both algorithms is that the solvent entering the top of the absorber is pure, and it has been shown (Staton, 1983) that this condition is most nearly achieved when the stripping is accomplished through reboiling. The assumption of a pure solvent en-
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986 703 0
Table 111. AMI-53 Absorber Product Gas CompositionD SIMCAL Output MCOMP Output gas analysis % % mole mole deviamole deviacomponent fraction fraction tion fraction tion 0.000 00 0.000 05 0.002 94 COP trace HZS 0.000 17 0.000 00 cos 0.000 01 0.000 00 trace 0,000 00 0.000 56 0.000 76 MEOH 2.08 0.43294 0.17 HZ 0.43222 0.441 22 co 0.22616 0.22029 2.60 0.22199 1.84 N2 0.27612 0.27711 0.36 0.27258 1.28 CH, 0.06466 0.05995 7.28 0.06469 0.04 CzH4 0.00021 0.00027 28.6 0,00123 486.0 18.2 0.00287 538.0 C2H6 0.00045 0.00055 total 1.00000 1.00000 1.00000 a Measured total flow = 1.868 lb mol/h. SIMCAL predicted total flow = 1.820 lb mol/h. % deviation = 2.58. MCOMP predicted total flow = 1.854 lb mol/h. % deviation = 0.74.
Table IV. AMIL-14 Absorber Product Gas Composition4 SIMCAL Output MCOMP Output gas analysis % % mole mole deviamole deviacomponent fraction fraction tion fraction tion COZ 0.000 00 0.000 00 0.000 40 H2S 0.000 00 0.000 00 0.000 00 cos 0.000 00 0.000 00 0.00000 MEOH 0.000 00 0.000 10 0.000 14 HZ 0.49220 0.49780 1.14 0.47364 3.77 co 0.17110 0.16570 3.16 0.16847 1.54 N2 0.28970 0.29140 0.59 0.28230 2.55 0.04690 0.04500 4.05 0.06132 30.7 CHI 0.001 40 CZH, 0.000 00 0.000 00 CzHG 0.000 00 0.00000 0.000 28 1.00000 total 1.00000 1.000 00 "Measured total flow = 1.020 lb mol/h. SIMCAL predicted for total flow = 1.047 lb mol/h. % deviation = 2.68. MCOMP predicted total flow = 1.112 lb mol/h. % deviation = 9.02.
tering the absorber was made solely because no data were available, giving the composition of this high-pressure liquid feed stream. Both algorithms, MCOMP and SIMCAL, are capable of handling any specified gas and liquid feed composition. A n examination of Table I11 shows that both SIMCAL and MCOMP did a good job of predicting the final compositions of the four major inert gases H2, CO, N2, and CHI but SIMCAL gave a much better prediction for the minor components C2H4 and CzH6and the major acid gas COP The fact that MCOMP predicted a significant amount of C02 in the sweet gas is due primarily to the nature of the algorithm. Again, MCOMP is a design algorithm which finds the height of packing required for a given separation to occur. Once this desired separation is reached, the program stops execution and is, therefore, unable to give any information as to what occurs in the upper regions of the column. The desired separation is determined by the fractional absorption of a key component, which for MCOMP happens to be C02. Therefore, the amount of COPremoved is an input variable for MCOMP, and because numerical problems are encountered when 100% absorption is specified, the outlet concentration of COZ can never be expected to go to zero. No such problem exists for SIMCAL, because the height of packing, rather than the degree of separation, is specified and there is nothing to prevent the predicted C02concentration from reaching zero, as seen in Table IV. Also, Table IV shows that the concentrations of COz, C2H4, and C2H6in the sweet gas, predicted by MCOMP, are again too high, as is that of CHI. SIMCAL, however, predicts to within 4% the outlet concentrations of each of the major
lL
x t
-- mSIWCAL e a s w e e profile Prediction i -4
1
,
L U - L L - 1 2.0
0.0
6.0
4.0
8.0
(ftl
Height
Figure 4. Comparison of measured absorber temperature profile a. SIMCAL predicted profile for run AMI-53.
LL
:
Y
I
1 .
1 1
0 0
I
I 2 0
I
I
I
Height
I 6 0
4.0
1
J 8.0
[fti
Figure 5. Comparison of measured absorber temperature profile vs. SIMCAL predicted profile for run AMIL-14.
inert gases and correctly shows that the concentrations of the acid gases, as well as C2H4,and C2H6go to zero. A final method for evaluating the accuracy of the simulation program is to compare the temperature profile in the absorber predicted by SIMCAL with the measured profile for each of the two runs mentioned above. Figure 4 is a plot of the actual absorber liquid temperature profile for AMI-53 compared with the profile predicted by SIMCAL. Likewise, Figure 5 gives the actual liquid temperature profile for AMIL-14 as well as the SIMCAL prediction. These plots reveal that SIMCAL correctly predicts the rapid increase in the liquid-phase temperature near the bottom of the column, due primarily to the heat of absorption of COz and the other acid gases. In addition, the liquid outlet temperature predicted by SIMCAL is close, within 2 or 3 O F , to that actually observed for both runs. Finally, SIMCAL may be used to generate composition profiles within the absorber column. Even though samples of the liquid and gas streams within the high-pressure environment of the absorber were unavailable, the qualitative behavior of a number of components can be compared with that expected. Some selected plots of SIMcAL-generated total flow and individual component composition profiles are included in Figures 6-10. Figure 6 gives the predicted total liquid flow rates throughout the column for both runs AMI-53 and AMIL-14. The curves are S-shaped, showing rapid absorption of some gaseous components near the bottom of the column, followed by a section where little net mass transfer is taking place, and finally there is a region near the top where a relatively small amount of further absorption occurs. The rapid absorption region near the bottom of the absorber is explained by Figures 7 and 8 which depict the individual
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986
704
0
i.?,
X
t
-
Run AMI-53 Run AMIL-14
X
+
0
-
-
.Run 4Mt-53 Run PHIL-14
I
-
0
e
0 '
OF I
01
tm
I
Y
I
I
I
I
1
I
i
L-1..
.
0.0
1 - i - L A . -1
2 0
6.0
4.0
Height
8.0
(ftl
Figure 9. CO absorber liquid concentration profiles predicted by SIMCAL for runs AMI-53 and AMIL-14. N 0
X
t
-
Run 4HI-53 Run 4HIL-14 \
W I
0 6
3
U c
O!0
-
h
I
i
_I
N
r"
5 - u 2
\
-\ 8
W 0 n
I
'L
q l
t
X
t
-
Run 4HI-53 Run AHIL-14
1
0 U
-
8 0 Height
Height
ifti
Figure 7. COz absorber liquid concentration profiles predicted by SIMCAL for runs AMI-53 and AMIL-14.
O C
x
m
Y
+
u
m
-
Run *HI-53
--1I
L U W
3
0
I D c
3
0
,-
i
Run 4HIL-I4
:\
i
ni w
_1
ffl N
I
Height
[ftl
Figure 8. HzS absorber liquid concentration profiles predicted by SIMCAL for runs AMI-53 and AMIL-14.
liquid composition profiles of two of the acid gases, C02 and H2S. These plots show that the highly soluble acid gases are almost completely absorbed by the solvent shortly after entering the column, with no detectable, at least not in the scale of the plots, mass transfer taking place above this region. The absorption near the top of the column, therefore, must be due to the presence of at least some of the other, less soluble constituents, as demonstrated by Figures 9 and 10. The figures show the individual liquid composition profiies of CO and H2 and reveal little change in the concentration near the bottom and midsection of the column but slight absorption of CO and H2 at the very top of the column. The apparently large dip in the curves is deceiving
(ftl
Figure 10. Hz absorber liquid concentration profiles predicted by SIMCAL for runs AMI-53 and AMIL-14.
because of the scale of the plots; the total amount of CO and H2 absorbed is only about 0.2 lb mol/(h ft2),which is considerably less than the approximately 4.0lb mol/(h ft2) of C 0 2 removed. The fact that these relatively insoluble gases are absorbed a t the top of the column can be explained if one considers that by the time the vapor phase reaches the uppermost section of the packing, the acid gases have been almost completely removed and the partial pressures of the inert components are at their highest values. This is coupled with the fact that the methanol a t the top is essentially pure, and since the Henry's law constants are finite for all components, some absorption must occur in this region. Another interesting aspect of these curves is an apparent, very slight desorption of the inert gases near the bottom. This is because the solvent in this region has absorbed significant amounts of the acid gases, the liquid temperature has increased to its highest value, and the partial pressures of CO and H2 in the gas phase are at their lowest values. Conclusions A new algorithm for the steady-state simulation of multicomponent, adiabatic absorption in packed columns has been presented. The algorithm represents a significant improvement over earlier algorithms, which were formulated in a design format. Implementation of the new algorithm to simulate absorption in an acid gas removal system resulted in good agreement with data against which it was tested. The algorithm correctly predicted both the outlet gas compositions and the liquid temperature profiles. In addition, the composition patterns predicted by the program are a t least qualitatively valid. Future improvements to the simulation will likely concentrate on
Ind. Eng. Chem. Process Des. Dev. 1986, 25, 705-710
computational efficiency. Thus far, even though the program has been found to converge in 2 or 3 iterations, each iteration takes about 11cpu min on a VAX 11/750 minicomputer, using 50 packing increments in the finite difference grid. Acknowledgment We gratefully acknowledge support of this research effort by the Environmental Protection Agency under Cooperative Agreement No. CR-809317. Nomenclature a = interfacial are per unit volume of packing, area/volume CGi = heat capacity of i in gas phase, energy/(time-area-degree) CLi = heat capacity of i in liquid phase, energy/(time-areadegree) gi = molar flow rate of i in gas phase, moles/(time-area) G = total molar flow rate of gas phase, moles/(time-area) hi* = partial molar enthalpy of component i in the liquid at concentration xi* and temperature T* hG‘ = gas-phase heat-transfer coefficient corrected for mass transfer, energy/ (time-area-degree) hL = liquid-phase heat-transfer coefficient, energy/ (timearea-degree) Hi* = partial molar enthalpy of component i in the gas at concentration yi* and temperature T* HG = enthalpy of the gas phase, energy/mole HL = enthalpy of the liquid phase, energy/mole AHsi = heat of solution of i, energy/mole in solution K i = Henry’s law constant kXi= mass-transfer coefficient for component i in liquid phase, moles/ (time-interfacial area) kYi = mass-transfer coefficient for component i in gas phase, moles/ (time-interfacial area) li = molar flow rate of i in liquid phase, moles/(time-area) L = total molar flow rate of liquid phase, moles/(time-area) Ni = molar flux of i across the gas/liquid interface, moles/ (time-interfacial area)
705
nc = number of components in system TG = bulk temperature of gas phase, degrees TL= bulk temperature of liquid phase, degrees To = reference temperature, degrees T* = interfacial temperature, degrees xi = mole fraction of i in liquid phase xi* = mole fraction of i in liquid-phase interface yi = mole fraction of i in gas phase yi* = mole fraction of i in gas-phase interface z = position in column, length hi = latent heat of vaporization of i, energy/mole Literature Cited Ackerman, 0. Forschungsheff 1837, 382, 1. Bllllngsley, D. S.; Chirachavala, A. AIChE J . 1981, 2 7 , 966. Felntuch, H. M.; Treybai, R. E. Ind. Eng. Chem. Process D e s . Dev. 1978, 17, 505. Finlayson, B. A. “Nonllnear Analysis in Chemical Engineering”, 1st ed.; McGraw-Hill: New York, 1980. Holland, C. D.; Lapls, A. I . ”Computer Methods for Sohrlng Dynamic Separation Problems”, 1st ed.;McGraw-Hill: New York, 1983. Kelly, R. M. Ph.D. Thesis, North Carolina State University, Raleigh, 1981. Kelly, R. M.; Rousseau. R. W.; Ferret J. K. Ind. Eng. Chem. Process D e s . Dev. 1084, 23. 102. Klng, C. J. ”Separation Processes”, 2nd ed.; McGraw-Hill: New York, 1980; pp 556-557. “Landolt-Ei5rnstein. Zahlenwarte und Funktionen 6. Auflage IV. Band Technik, 4. Teil Warmetechnik Bestandtell C1, Absorption in Flussigkelten mlt niedrigem Dampfruck”; Springer-Verlag: Berlin-Heldelberg-New York, 1976. LazabCrabtree, H.; Breedveld, 0. J. F.; Prausnitz, J. M. AIChE J . 1980, 2 6 , 462. McDaniel, R.; Holland, C. D. Chem. Eng. Sci. 1970, 25, 1283. Newman, J. S. “ElectrochemicalSystems”, 1st ed.; Prentice-Hall: Englewood Cllffs, NJ, 1973. Onda, K.; Takeuchl, H.; Okumoto, Y. J . C t ” . Eng. Jpn. 1968, 1 , 56. Srivastava, Joseph B. Comput. Chem. Eng. 1984, 8 , 43. Staton, J. S. M.S. Thesis, North Carolina State University, Raleigh, 1983. Treybal, R. D. “Mass-Transfer Operations”, 3rd ed.; McGraw-Hili: New York, 1980. Von Rosenberg, D. U.; Hadi, M. S. Chem. Eng. Commun. 1080, 4 , 313. Von Stockar, U.; Wllke, C. R. Ind. Eng. Chem. Fundam. 1977, 16, 88. White, R. E. Ind. Eng. Chem. Fundam. 1978, 17, 367.
Received for review March 22, 1985 Revised manuscript received October 30, 1985 Accepted November 15, 1985
Kinetics of Coal Liquefaction under Supercritical Conditions Glrlsh V. Deshpande, Gerald D. Holder,’ and Yatlsh 1.Shah Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 1526 1
Bruceton bituminous coal was liquefied in supercritical toluene at temperatures ranging from 647 to 698 K and at densities ranging from 0.157 to 0.601 g/cm3. The experimental results show that the fractional conversion of the coal to toluene soluble material increased not only with temperature but with density as well. The rate of conversion increased similarly. These results are explained by a kinetic model that postulates that toluene acts as a solvent for the reacting species although it is not a reactant itself. Since the degree of solubility of a solid in a supercritical fluid generally increases with temperature and density, the conversion also increases with temperature and density. The conversion products subsequently undergo condensation reactions which accounts for the maximum in conversion vs. time which is observed.
Earlier efforts aimed at understanding supercritical extraction of coal used both flow and batch reactors. However, the experimental procedure used in these studies did not allow all the variables necessary for kinetic modeling to be measured.
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all correspondence should be addressed. 0196-4305/86/1125-0705$01.50/0
In the flow reactors (Slomka and Rutkowski, 1982; Jezko et al., 1982; Kershaw, 1982; Whitehead and Williams, 1975; Penninger, 1984),coal was packed into the reactor and the supercritical fluid was passed through the bed of coal until the condensed effluent was clear. The conversion was defined as the btal weight loss of the coal due to extraction by the solvent. This type of reactor is not ideal for measuring kinetics because the absence of mixing means 0 1986 American Chemical Society
