Znd. Eng. Chem. Res. 1992,31, 2209-2215 Processes. 5. The Topology of the Boiling Temperature Surface and ita Relation to Azeotropic Distillation. Chem. Eng. Sci. 1984,
2209
Single Column. Ind. Eng. Chem. Fundam. 1985, 24, 454-463. Received for review January 30, 1991 Revised manuscript received January 28, 1992 Accepted May 25, 1992
39 (5), 883-892.
Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogeneous Azeotropic Distillation. 1. Problem Formulation for a
GENERAL RESEARCH Product Distributions in the C02-NH3-H20System from Liquid Conductivity Measurements James E. Pelkie, P. John Concannon, and David B. Manley Chemical Engineering Department, University of Missouri-Rolla, Rolla, Missouri 65401
Bruce E. Poling* Chemical Engineering Department, University of Toledo, Toledo, Ohio 43606
The objective of this work was to illustrate how liquid conductivity measurements could be used to provide information about the extent of ionization and the amounts of the various ionic products that are formed in the liquid phase in the C02-NH3-H20 system. To accomplish this, pressures and liquid-phase conductivities for the C02-NH3-H20 system were measured at 25 "C and over a range of pressures and concentrations. In order to acquire the desired information from bulk conductivity measurements, calibration curves were established from measurements with several potassium salts. These curves, in conjunction with the experimental conductivity, allowed the (approximate) determination of both the concentration of the NH4+ion and the distribution of C 0 2 between singly and doubly charged ions. Comparison to the predictions of two existing models for the C02-NH3-H20 system showed that these models underpredicted the concentration of the ammonium ion. This suggests that correct predictions of the vapor-phase compositions and pressures by a solution model do not guarantee that the description of the liquid phase is correct.
Introduction The chemical reactions that occur in COP-NH3-H20 mixtures result in dramatic reductions in the concentration of free C02 and/or NH, which in turn give dramatic reductions in the vapor-phase partial pressures. The same typea of reactions that occur in the above system also occur when COPand H2S are absorbed from vapor streams by amine solutions, and this fact has provided incentive to characterize the VLE (vapor-liquid equilibria) behavior of these systems. Traditional VLE studies in which samples of the liquid and vapor phases have been taken and analyzed have been limited because reliable samples of the two phases are difficult to obtain. Furthermore, the information obtained has been the total concentration of C02 and NH3 in each phase. But what is desired is the concentration of each species in the liquid phase after the various reaction equilibria have been established. While existing models can be used to calculate these concentrations, they have not previously been acquired experimentally, so there is no guarantee that the calculated results from the models are accurate. To verify the results of the models, different experimental information is required. Thus, we chose to develop and build equipment to simultaneously measure pressures and conductivities. The advantage of this approach is that conductivities are relatively easy to measure, and it was hoped that these measurements would provide information about the ionic products that were formed. However, techniques to deduce concentrations of individual species from bulk phase
conductivity measurements had not been established. Thus, another objective was to establish just how conductivity measurements could be used to provide the desired information.
Background When both C02 and NH, are dissolved in H20, the chemical reactions that may occur are (see p 377, Reid et al. (1987)) 3" + H20 F! NH4+ + OH(1) COP+ HzO e HC03- + H+
(2)
HC03- F? C032-+ H+
(3)
NH3 + HC03- NH2C02-+ H20 (4) HzO F! H+ + OH(5) The above reactions can be rewritten in the form below which illustrates the formation of ammonium bicarbonate, ammonium carbonate, and ammonium carbamate, all of which are commercially available solids: NH3 + COZ + H20 EZ! NH4+HC03- (ammonium bicarbonate) (6) 2NH3 + C02 + H20 s (NH4+)2C032-(ammonium carbonate) (7) 2NH3 + C02 ~t NH4+NH2C02- (ammonium carbamate) (8)
0888-5885/92/2631-22Q9~Q3.0Q/Q 0 1992 American Chemical Society
2210 Ind. Eng. Chem. Res., Vol. 31, No.9,1992
This latter repmaentation does not include the H+and the OH- ions (which in many applications cannot be ignored), but does illustrate that the same solutions could, in principle, be prepared either by mixing appropriate amounta of CO,. NH,, and HZO or by dissolving appropriate amounta of the solids in water. Also, when COz and NH, are present, one or the other is almost completely used up in the formation of the above three producta. Thus, reactions €-8 very nicely illustrate the two limiting cases of excess CO, and NH,. When excess COz is present, very little free NH, remains and the bicarbonate is formed almost exclusively. When there is excess NH,, very little free COz remains, and the amounta of both the carbonate and carbamate increase because these latter two producta are formed with a 2 to 1 ratio of NH, to COPwhile the bicarbonate is formed with a 1to 1ratio of NH, to COP The excess COz case is easier to model because the concentrations of the carbonate and carbamate are small. In the excess NH3 case, the carbonate and carbamate concentrations cannot be ignored, and must be calculated. While the equilibrium constant for carbonate formation is well established,that for the carbamate is not. The work described in this paper primarily addresses the liquidphase composition for the excess NH, case. When a mixture is prepared by adding COzand NH, to water, a carbon atom balance gives NCO; = Nco2 "coj -+ N N H K + ON ~ c % ~ (9) where Ncqo is the initial moles of COP Electroneutrnlity requires that N w , + + NW = NHC%-+ Nm,c%- + uVc,p + NOH(10) For excess NH,, Ncod the moles of free C02, in eq 9 is much smaller than the other terms. Furthermore, for the conditions in this study, NH+and NOH-in eq 10 are also small. Ignoring thee three terms and combining eqs 9 and 10 leads to: Ncos* = N w , + - Nc,' (11) or e = N m + / N c G o- 1 (12) where is N%s/N O, the fraction of the initial carbon atom that end up an%e doubly charged carbonate species. The conductivity measurementa described below can set the value of NNH,+*; the value of can then be calculated with eq 12.
Experimental Section Conductivities are most easily measured by disaolving known amounta of a salt in water, placing the solution in a constant-temperature bath, and then measuring the conductivity. Thii approach does not give reliable resulta for the C0,-NH3-Hz0 system because the three salta, ammonium carbamate, ammonium carbonate, and ammonium bicarbonate, although commercially available, decompose to NH, and COzwhen in Solution and open to the atmosphere. Furthermore, the initial purities of these three salta are not well established. An approach that avoids these problems, and the one that we used, was to add CO,, NH,, and H,O to a constant-volume cell that could be placed in a constant-temperature bath, and in which the pressure could be measured. The mass of each component was determined by weighing the cell after addition of each component. The pressure, along with the cell volume and the VLE model in ASPEN was used to perform a flash calculation to determine the amount of each of the three components in the vapor which then led
TO NITROGEN GAS
FERRITE CORE
-
I
SET NUT
001 3 1 6 5 5 TEFLON SEAL
nni
Figure 1. Cell 88 o r i g i d y designed to measure pressures.
to a corrected overall liquid-phaae composition. Thi correction is significant when COz is in excess, but insignificant when NH, is in excess. The water used was deionized, distilled in a stainless steel still, and degassed by boiling. The ammonia wan d e g d by a series of fr-thaw cycles. Carbon dioxide from Matheson Gas Products was wed without further purification. Analysis of both COz and NH, by gas chromatography with a thermal conductivitydetector indicated a purity of at least 99.99%. A diagram of the total preasure cell that had been used previously for VLE measurementa is shown in Figure 1 (Smolen et al., 1991). The cell was modified as shown in Figure 3 to measure conductivities. The probe labeled vapor phase conductivity probe in Figure 3 was not used in this study. To ethis cell, known m888e8 of the deaired gases or liquids were charged to the previously evacuated sample cavity. The lower half of the apparatus was placed in a temperature bath, and the pressure was determined by measuring the nitrogen pressure required to null the stainless steel diaphragm. The position of the diaphragm was sensed by the ferrite coretransducer arrangement. A calibration curve, shown in Figure 2, indicates that pressures could be measured to *0.01 psi with this apparatus. The pressure range was 0-500 psi. The nitrogen pressure was measured with one of three digital pressure gauges which had ranges of 0-20,0-150, and 0-2500 pig and were accurate to 0.008,0.06, and 1psia, respectively. The accuracy of the gauges had previously been checked with a Ruska dead weight gauge. The estimated uncertainties in the pressure due to uncertainties in all variables were
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 2211 150
" " 1 " " " " '
1
( " "
I " "
1 " " ~ .
-
I
-100 -150
-
a
1
-200 -0.15
-0.1
0.05 Pressure (psig)
-0.05
0
0.1
"0
0.15
Figure 2. Diaphragm response in the -0.1 to 0.1 psi range. Note sensitivity and reproducibility. 0001 3 1 6 5 5 DIAPHRAGM TEFLON
n
/
VAPOR PHASE CONDUCT1 VlTV PROBE
Figure 3. Pressure cell as modified to measure conductivities.
i0.06 p i a for P < 20 psia, i0.5 psia for P < 150 pia, and *2 psia for P > 150 psia Temperature was measured with an Azonix digital thermometer which was accurate to 0.01 OC. Total compositions were determined from the masses of the components which were measured to the nearest milligram with an estimated accuracy of 10.001 g. To determine the composition of the liquid phase from the experimental data (temperature,pressure, cell volume, and overall composition), a flash calculation was required. The equation which describes this calculation is x , = Zi/(L + K,(1 - L ) ) (13) The equilibrium ratio, K, was calculated with the weak electrolyte model in ASPEN (Chen et al., 1982;Mock et al., 1984). Ki is defied as yi/xi,where yi is the vapor-phase mole fraction, x , is the liquid-phase mole fraction, and zi is the overall mole fraction. Uncertainties in the calculated value of K i lead to uncertainties in the calculated vaporphase composition. However, for the excess NH3 points especially, the number of moles in the vapor phase is quite small due to the low pressure so that the value of x i , the overall liquid-phase mole fraction, is close to z,and has essentially the same experimental uncertainty as does zi. To measure conductivities with the pressure cell, the probe was first calibrated with solutions of potassium chloride. The result of this calibration is shown in Figure 4. Details are given by Pelkie (1990). Results The actual data consisted of the grams of C02,NH3,and H20that were loaded into the cell, the pressure, and the conductivity, all of which are listed in Table I. These data are listed in order of increasing values of the ratio of NH3 to C02,so that the first points are for excess C02,while the last points are for excess NHB. The cell volume was determined in a separate calibration to be 36.12 cm3. Analysis of Conductivity Measurements. Analysis of the Conductivity meaeurements required two steps. The
35
Figure 4. Conductivityprobe calibration against a known electrode with KCl solutions. Table I. Conductivity-Pressure Results et 25 O C for the C02-NH,-H20 System grams fed conductivity, p..p.* C02 NH3 H20 psia Zm,/Zc, mmho/cm 1.627 1.020 1.044 1.454 0.304 0.304 0.468 0.309 0.355 0.266 11 0.193 12 0.153 13 0.145 14 0.104 1
iRT
5 10 15 20 25 30 Measured Conductivity (millimho)
2 3 4 5 6 7 8 9 10
0.176 0.131 0.210 0.334 0.120 0.175 0.342 0.342 0.399 0.399 0.399 0.342 0.399 0.342
21.130 13.587 23.002 22.536 12.728 12.728 20.402 20.402 20.778 20.778 20.778 20.402 20.778 20.402
302.0 163.4 2.67 0.93 1.10 0.94 0.73 0.61 0.59 0.80 0.62 0.64
0.28 0.33 0.52 0.59 1.02 1.49 1.89 2.86 2.91 3.88 5.35 5.79 7.12 8.51
37.0 42.4 44.5 62.8 42.3 47.0 52.8 42.0 46.4 36.0 29.4 24.8 19.6 17.0
first was to establish the conductivity-concentration relationship for each pure salt in water, and the second was to relate the mixture conductivity to the pure-salt conductivities. The result of this analysis which is diecuseed below is that the conductivity depends primarily on the ammonium ion concentration. For ammonium bicarbonate, the conductivity-concentration relationship was determined experimentally. However, for ammonium carbonate and carbamate, this was not possible because when either of these latter two salts are dissolved in water, an equilibrium mixture is formed that contains all three salts. The conductivity behavior of potassium carbonate could be determined experimentally,and correlations such as those presented by Davies (1962)suggested that the conductivity-concentration relationship for both ammonium carbonate and ammonium carbamate would be the same as for the corresponding potassium salts. In his study of ion pairing, Davies (1962)proposed that "a region exists in which completely dissociated salts show a common behaviour". To support thisproposal, he showed that the conductivities of a number of halides could be correlated up to 0.1 mol/L by the following "generalized" correlation: A = &-S~(C) (14) In eq 14,A is the equivalent conductivity and is defied as the conductivity divided by the concentration in equivalenta per liter. The quantity f ( c )is a function only of concentration and the charge on the ions. In other words, a single function applies to all 1:l salts. A different function applies for 21 salts such as potassium or ammonium carbonate. S and & are not functions of concentration. S depends on the solvent, the temperature, the charge on the ions, and A., & is the limiting equivalent conductivity for the salt and is the sum of the contributions of the limiting (infinitedilution) conductivitiea of the anion and cation, Loand X+O. The important implication of eq
2212 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992 Table 11. Limiting Ionic Conductivities ion X + O or Lo K+ 73.5 NH,+ 73.5 HCOf 44.5 '/2CO3*74.0
ref 1 1 1 2
....
6o
.....
...............
....
,
(1)Robinson and Stokes, 1959. (2) Horvath, 1985. Table 111. Parameters for Eq salt NHdHCOS K2C03
("MQ
10 ih 118 147.5 147.5
S 87.4 186.5 186.5
20
0 0
,...,...,... 00
0.2 0.4 0.6
0.8
1
1.2
1.4
Concentration (miter)
Figure 5. Conductivities of KHCOs and NH,HC03 solutions and C02-NH3-H20 solutions with excess COP Note similarity of POtassium and ammonium ion behavior.
14 is that two different 1:l salts with the same & values will have the same conductivity-mncentration relationahip. Applicable values of Xo that are available in the literature are shown in Table 11, and the correspondingvalues of & and S are listed in Table 111. The Xo values for the potassium and ammonium ions are the same. All this suggests that the conductivity curves for ammonium and potassium salts with the same anion should be the same at least to 0.1 mol/L and perhaps to even higher concentrations. It was possible to test this notion experimentally for ammonium and potassium bicarbonate. The conductivity curvea for each of these two salts are shown in Figure 5, and it can be seen that the two curves very nearly coincide. The two curves in this figure show conductivity vemw concentration for these two salts as determined from our measurements for solutions of various concentrations which were open to the atmoephere and had been prepared by dissolving either potassium or ammonium bicarbonate in water. For solutions of both of these salts, the amount of reaction of the bicarbonate to either the carbonate or carbamate is small so that the concentration of the bicarbonate ion is within 99% of the concentration of the salt itself. The points that are shown in Figure 5 correspond to the first five points listed in Table I, namely those with excess C02. Figure 5 supports the idea that potassium and ammonium bicarbonate demonstrate the same conductivityconcentration behavior, at least up to 0.8 mol/L. In Figure 5, the two curves are very close to each other up to 0.6 mol/L. At higher concentrations,the curve for "4HC03 is slightly below that for KHC03 because of the slow but steady decomposition of NH4HCOBand subsequent evolution of COPand NH3 to the atmosphere. The points from the high-pressure cell are consistent with this explanation because for this closed system, in which decomposition does not occur,the conductivity is actually closer to the potassium curve than the open-beaker ammonium curve. This suggests that the curve in Figure 5 labeled
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Concentration (miter)
.
Figure 6. Conductivities of C02-NH3-H20 mixtum Pointaarefor concentrations calculated by TIDES or ASPEN and should fall between the curves. Both modela underpredict the NH,+ concentration.
KHCO, is an accurate representation of the true NH4HCO, curve at least up to 0.8 mol/L and perhaps to even higher concentrations. For the data points shown in Figure 5, the large excess of C02would favor a shift toward the bicarbonate ion if the ions were not already in this form. That the points with excess C02 demonstrate the same behavior as the curves is consistent with the notion that the negative ions in the solutions from the salts are already present as the bicarbonate ion. Thus, Figure 5 supports the validity of eq 14 and also suggests that NH4HC03is completely ionized in water with no ion-pair formation. To establish the conductivity behavior of (NH4)2C03, which could not be measured directly, conductivities of K2CO3 solutions were measured. Ae suggested by eq 14, and because the behavior of potassium and ammonium bicarbonate was the same, it was assumed that the behavior of the two carbonates was also the same. The conductivity-concentration curve for K&O3 is shown in Figure 6 along with the NH4HC03curve from Figure 6. To determine the K2CO3 curve, conductivitiesof solutions of various concentrations were measured. When K2CO9 is dissolved in water, the carbonate ion is the dominant ion and ita concentration is within 99% of the concentration of the salt (this is not the case with ammonium carbonate). The carbamate conductivity curve could also not be measured experimentally, so to establish the carbamate conductivity behavior, we used the notion that, in addition to solvent properties, the charge on the ion, the temperature, and the pressure, ho depends on the radius of the ion (p 56, Smedley (1980)). The carbamate and bicarbonate ions have nearly the same molecular weight (60and 61) and have similar structures (an -NH group appeara in the carbamate, while an oxygen appears in the bicarbonate), so we presumed the radii and thus the Xo values of these two ions would be the same. However, if the Xo values are the same, then the conductivity curves for the carbamate and bicarbonate would also be the same. In this way the conductivity behavior of the three pure salts was established. To summarize, we took the top curve
Ind. Eng. Chem. Res., Vol. 31,No. 9,1992 2213 Table IV. Limits on Ammonium Ion Concentrations (Cm,+ in mol/L) from Experimental Conductivities As Determined from Curves in Figure 6; Values Predicted by TIDES and ASPEN Are Also Listed carbonate bicarbonate curve curve TIDES ASPEN 0.468 0.449 0.468 1 0.413 0.535 0.526 0.535 2 0.483 0.517 0.557 0.517 3 0.510 0.825 0.838 0.825 4 0.747 0.519 0.517 0.524 5 0.481 0.569 0.593 0.600 6 0.543 0.567 0.681 0.620 7 0.619 0.395 0.520 0.442 8 0.477 0.443 0.584 0.502 9 0.535 0.388 0.339 10 0.400 0.435 0.289 0.254 11 0.316 0.345 0.234 0.208 0.284 12 0.260 0.195 0.218 0.222 13 0.199 0.146 0.186 0.161 14 0.169
Table V. Fraction of Initial C02Present as Carbonate Ion (a) from Conductivity Measurements As Determined from Eq 12 and Curves in Figure 6; Values Predicted by TIDES and ASPEN Are Also Listed carbonate bicarbonate curve curve TIDES ASPEN 1 0.0002 0.0002 2 0.0002 0.0001 0.0007 0.0003 3 4 0.002 O.OOO6 5 0.01 0.02 0.14 0.118 0.08 6 0.023 7 0.12 0.22 0.338 0.216 0.17 0.31 0.537 0.411 8 0.17 0.537 0.32 9 0.407 10 0.19 0.35 0.520 0.398 0.22 11 0.39 0.655 0.519 0.23 12 0.39 0.683 0.540 0.24 0.41 0.392 13 0.267 0.27 0.43 0.621 14 0.470
in Figure 6 to represent the conductivity of (NHJ2C03and the bottom curve to represent the behavior of both N&HCOg and NH4NH2C02. The simplest way to relate mixture conductivities to pure component conductivities would be to use a weighted linear average of the conductivities that the pure salts exhibit at the same total concentration (in equivalents per liter). Davies (1962)states that this “mixture rule does not apply exactly but deviations from it are small”. In fact, deviations from this rule are smallest when one of the ions is common to the various pure salts, when the conductivitiesof the pure salts are not too different, and when there is no ion pairing or complex formation. Mixtures of magnesium chloride and sodium chloride are an example of a system with ions of mixed valency for which the additivity rule is fairly accurate. For this system Van Rysselberghe et al. (1937)report a series of conductivities at an overall concentration of 1 N for which deviations from the additivity rule are less than 1%. A difference in pure component conductivities or complexing between the different salts gives rise to negative deviations,and in fact, when deviations do occur they usually are negative. MgC12-Na.#04 is an example of such a system (Smith and Gortner, 1933). For this system, conductivities can be as much as 10% below the value predicted by the additivity rule. For a deviation from the additivity rule to be positive, one of the pure salts must exist as ion pairs, so that addition of the other salt at constant total concentration d t s in a dilution effect that reduces the extent of pairing and thus increases the ion concentration. These systems are rare, and when they occur, for example in the NaC1CuS04 system, the deviations are still less than 3% (Davies, 1962). Because the mixtures in this study have a common cation, NH4+,because the three pure component Conductivities are nearly the same, because all three anions are chemically similar, and because the bicarbonate (and probably the other two salts) are completely ionized, it seems likely that the additivity rule will be obeyed within experimental uncertainty by the mixtures in this study. The above analysis places limits on the ammonium ion concentration. For each experimental conductivity listed in Table I, these limits are the values read from the two curves in Figure 6 and have been listed in Table IV for each of the points from Table I. Comparison to Literature VLE Models. Two models that can be used for VLE calculations for the C02-NH3-H20 system are TIDES, developed by Prausnitz and co-workers (Pawlikowski et al., 1982; Kawazuishi and Prausnitz, 1987),and the weak electrolyte model in ASPEN (Chen et al., 1982;Mock et al., 1984). As part of the
calculational scheme, both models solve the reaction equilibria problem in the liquid phase. In other words, both models can be used to predict the ammonium ion concentration for each of the data points listed in Table I. These predictions are listed in Table IV, along with the predictions from the conductivities. The fiit five points in Table IV are for excess C02,where essentially all the NH3is present in the form of ammonium bicarbonate. For these five points, the models necessarily give the correct value for the ammonium ion concentration, and the deviations of the “bicarbonate curve” values from the model values can be taken as a measure of the experimental uncertainty in the conductivity method. Except for point 3,these deviations are 0.02mol/L or leas. Point 3 was done early on before the experimental procedure was firmly established; the deviation for point 3 is 0.04 mol/L. Points 7-14 in Table IV are for excess NH3, and it can be seen that, for these points, the models generally underpredict the ammonium ion concentration. The CNH,+from Table IV and eq 12 can be used to calculate a, the fraction of initial C02 converted to the carbonate, and these values are listed in Table V. Except for point 13,which seems to be a bad point, it can be seen that the models predict that the carbonate ion concentration is too low and the s u m of the carbamate and bicarbonate ion concentrations is too high. To achieve agreement with the concentrations predicted by TIDES, the experimental conductivities would have to be 1-4 mmho/cm smaller. To achieve agreement between the concentrations predicted by ASPEN, the experimental conductivities would have to be 3-10 mmho/cm smaller. The disagreement between the models and the results of the conductivity measurements is also illustrated by the +,C values predicted by the pints in Figure 6 where the models are plotted versus the experimental conductivities. If the models were consistent with the results from the conductivitiea,the points would fall between the two curvea in this figure. Another way to compare the experimentalConductivities to the VLE models is to use the concentrations from the VLE models and simply calculate the conductivity, K , by K = 8 K 1 + (1- 8 ) K 2 (15) where 8 is the fraction of negative charges present aa the carbonate; 1 - 8 is the fraction present as bicarbonate or carbamate. K~ and K~ correspond to values on the curves in Figure 6 for a given total ammonium ion concentration, and eq 15 says the mixture conductivity, K , would lie between these two pure component values. The value of 8 in eq 15 is similar to,but not the same as a, defined earlier.
...
2214 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992 Table VI. Comparison of Calculated and Experimental Conductivities exptl - calcd exptl conductivity TIDES ASPEN 1 -1.7 -1.7 37 -1.0 -1.0 2 42.4 2.4 2.4 44.5 3 62.8 0.9 0.9 4 -0.1 0.1 42.3 5 -1.7 0.9 47.0 6 2.2 6.6 52.8 7 4.1 8.0 42.0 8 4.0 46.4 9.8 9 2.0 6.2 10 36.0 6.2 3.0 29.4 11 2.9 24.8 5.4 12 -1.3 19.6 1.3 13 1.0 17.0 2.9 14 Table VII. Liquid- and Vapor-Phase Compositions Predicted by TIDES and ASPEN for Point 10 in Table I" mole fraction molality (liquid) (vapor) component TIDES ASPEN TIDES ASPEN NH4+ 0.3942 0.3474 HCOC 0.0793 0.0831 co320.1032 0.0558 NHZC02- 0.1085 0.1527 3" 0.627 0.641 0.268 0.263 2.12 X 2.05 X 0.0190 0.0153 co2 0.713 0.721 HzO
Liquid concentrations are after reaction equilibria are established.
0 is calculated from model predictions of the concentrations as follows: [ ("4)2C031 e = 2[(NH4)2COJ + 2[NH,HCO3] + [NHJW2CO2] (16) The brackets denote concentration in moles per liter; molalities or mole fractions of course yield the same value of 8. Conductivities were calculated with eq 15 for the points listed in Table I for both VLE models and compared to the experimental conductivities in Table VI. For the first five points with excess C02,the calculated and experimental conductivities should agree, and the average absolute deviation of 1.2 mmho/cm for these five points is a measure of the experimental uncertainty. Some of this uncertainty results from the flash calculation which playa a more important role for these five points because of the higher pressures and corresponding larger number of molea in the vapor phase. For these reasons, the experimental uncertain@ for the last nine points in Table V is no greater than 1.2 mmho/cm. For point 6, the ratio of NH3 to C02 is 1.49, and both models agree with the experimental conductivity. For points 7-14,the NH3to C02ratio is 1.89 or greater and both models predict conductivities that are too low, ASPEN more so than TIDES. To predict higher conductivities requires that the models predict higher ammonium ion concentrations. To better understand the subtle differences in the predictions of the two VLE models, concentrations for all the species as predicted by both models are listed in Table VI1 for one of the points in the values listed in Table VI. In order to satisfy the ammonia material balance, ASPEN predicts a higher concentration of carbamate than does TIDES. The last way in which the model predictions can be compared to our experimentalresults is by comparing the predicted and experimental pressures; this is done in Table
Table VIII. Comparison of Calculated and Experimental Pressures, psia exptl ASPEN TIDES 1 302.0 301 338 2 470 564 3 199 221 4 163.4 146 170 5 2.67 6.18 4.91 0.93 6 0.99 0.84 1.10 7 0.69 0.64 0.94 0.59 8 0.58 0.73 0.61 9 0.60 10 0.61 0.63 0.62 11 0.59 0.66 0.65 12 0.80 0.66 0.63 0.68 13 0.62 0.67 14 0.64 0.66 0.65
VIII. For the most part, there is satisfactory agreement between the models and experiment. Figure 6 contains information from three different sources, namely, the experimental conductivities (the points), concentrationpredictions of the two VLE models (the two sets of points), and the conductivity behavior of the potassium salts (the two curves). As presented, the information from these three source is not consistent. The most obvious way (to us) to achieve consistency would be to modify the parameters in the VLE models, but it could certainly be ergued that one of the models is right, and that the conductivityanalysis is flawed because of the various assumptions that were made. The assumption that the lower curve in Figure 6 represents the conductivity of ammonium bicarbonate is certainly justified because this curve was established with information from three different sources, namely, conductivities of ammonium bicarbonate solutions, potassium bicarbonate solutions, and the excess C02 points from the high-pressure cell. The additivity assumption for mixtures is admittedly not rigorous, but deviations from it are likely to be lesa than the experimental uncertainty. Even if deviations from this rule are greater, it is not likely that the conductivitywould go through a maximum, which would be required for the model concentration values to give calculated conductivities as high as the experimentalvalues. The assumptions used to establish the conductivity-concentration curves for the carbonate and carbamate, while reasonable, seem the most tenuous. However, because the equivalent conductivity of the ammonium ion, which is well established, is about twice that of the anions, the equivalent conductivity of the carbamate ion, for example, would have to be more than twice as large as the value used for the bicarbonate ion in order for the calculated and model results to agree. This seems most unlikely, and in fact, it would be easier to argue that the value should be lower (because of possible ion pairing), rather than higher. Finally, the conductivity analysis used in this study ignored the effect of H+, OH-, and undissociated carbamic acid. If undissociated carbamic acid were present, the discrepancy between the models and experiment would be larger, not smaller. The equivalent conductivity of H+ is much greater than that of the other ions in solution, but the pH of the excess NH, solutions is greater than 7, so the H+ ion concentration is small enough that the contribution to the conductivity due to the H+ ion can be ignored. The equivalent conductivity of OH- is also greater than that of the other ions in solution, but the concentration of the OH- ion is also small enough that the maximum contribution to the conductivity due to the OH- ion is still no more than 0.03 mmho/cm, and so this effect too can be safely ignored.
Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992 2216 The results just described suggest that the ASPEN version used in this study predicts the liquid-phase composition less accurately than the TIDES model that was used. This certainly does not imply that ASPEN is not a good model, and in fact, it is our position that both of these models do an excellent job in dealing with a very difficult problem. Both models reproduce the experimental pressure behavior (Table VIII), and both models generally reproduce existing vapor-phase composition data. Furthermore, a variety of parameter sets have been used and/or published for both models, and it is quite possible that had a different parameter set been used for either model, consistency would have been achieved with the conductivity data. However, the purpose of this study was not to evaluate all possible parameter sets, but rather to show how conductivity data could be used to help accomplish this task. An advantage of both models is that they possess sufficient flexibility that, as new data become available, the parameters in these model can be adjusted to accommodate those data. Whether the conductivity assumptions are right or not does not change the fact that traditional VLE measurements alone do not serve to completely set the liquid-phase behavior, no matter what model is used. To establish the correct liquid-phase behavior, additional information is required. Conductivities provide some of the additional information that is required, but still do not provide a complete picture. Specifically, they do not distinguish between the singly charged bicarbonate and carbamate ions, and so they do not establish the concentration of free COzand NH3. It would be nice to couple the conductivities with pH data, which would better establish the distribution between carbonate and bicarbonate ions. Also, it would be nice to establish the concentrations of all the ions by another method, perhaps by NMR, to validate the assumptions used in the conductivity analysis. All of these things await future work. The main contribution of this work has been to show the reasoning and the behavior that must be characterized in order that conductivities lead to useful additional information for the C02-NH3-H20 system. Conclusions An experimental apparatus has been designed and constructed to measure the conductivity and pressure simultaneously and has been used to make measurements for the C02-NH3-H20 system at 25 "C. The conductivity results establish a rather narrow range in which the NH4+ ion concentration should fall. A method was presented
whereby concentrations predicted by a VLE model could be used to predict the mixture conductivity. When this was done and for points with excess NH3, neither of the two models that were evaluated predicted NH4+concentrations that fell within this range. However, because TIDES predicted a C032-concentration greater than that of ASPEN, the TIDES predictions were more nearly consistent with the conductivity measurements. TIDES also predicted a lower carbamate concentration than did ASPEN. Finally, the purpose of this article is not to suggest that TIDES is better than ASPEN or vice versa, but rather that information other than traditional VLE data is necessary to accurately establish the liquid-phase behavior of the C02-NH3-H20 system. The manner in which conductivities can help accomplish this task has been described. Acknowledgment Financial support from The National Science Foundation for this work is gratefully acknowledged. Registry No. NH3, 7664-41-7; COz, 124-38-9. Literature Cited Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. AZChE J. 1982, 28, 533. Davies, C. W. Zon Association; Butterwortha: London, 1962. Horvath, A. L. Handbook of Aqueous Electrolyte Solutions; Ellis Horwood Chichester, UK, 1985. Kawazuishi,K.; Prausnitz, J. M. Ind. Eng. Chem. Res. 1987,26,1482; 1988,27, 1958. Mock, B.; Evans, L. B.; Chen, C. C. Proc. Summer Comput. Simul. Conf. 1984, 558. Pawlikowski, E. M.; Newman, J.; Prausnitz, J. M. Znd. Eng. Chem. Process Des. Deu. 1982,21, 764. Pelkie, J. E. Vapor-LiquidEquilibria and Conductivity Data for the Carbon Dioxide, Ammonia, and Water System. M.S. Thesis, University of Missouri-Rolla, 1990. Reid, R. C.;Prausnitz, J. M.; Poling, B. E. Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Robinson, R. A.;Stokes, R. H. Electrolyte Solutions, 2nd ed.; Academic Press: New York, 1959, rev. 1965. Smedley, S. I. The Interpretation of Ionic Conductiuity in Liquids; Plenum Press: New York, 1980. Smith, A. K.; Gortner, R. A. J. Phys. Chem. 1933,37, 79. Smolen, T. M.: Manlev, D. B.: Poling, - B. E. J. Chem. En#. - Data 1991, 36, 202.
Van Rysselberghe, P.; Grinnell, S. W.; Carlson, J. M. J. Am. Chem. SOC.1937, 59, 336.
Receiued for review September 5, 1991 Revised manuscript received May 5, 1992 Accepted June 8, 1992
