Simulation of the Mono-Thermal Ammonia Hydrogen Chemical

Sep 2, 2006 - The preliminary isotope exchange unit (PIEU) of the mono-thermal ... The model predicts an equal influence of mass transfer and reaction...
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Ind. Eng. Chem. Res. 2006, 45, 6745-6757

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Simulation of the Mono-Thermal Ammonia Hydrogen Chemical Exchange Tower as a Reactive Absorption System M. R. Sawant, A. W. Patwardhan, and V. G. Gaikar* Institute of Chemical Technology, UniVersity of Mumbai, Matunga, Mumbai 400019, India

M. Bhaskaran HeaVy Water Board, Vikram Sarabhai BhaVan, Anushakti Nagar, Mumbai 400094, India

The preliminary isotope exchange unit (PIEU) of the mono-thermal ammonia hydrogen chemical exchange process has been modeled as a reactive absorption system based on a rate-based approach. The model parameters are estimated using the operating plant data. The developed model is utilized to quantify the effects of the operating variables such as temperature, pressure, catalyst concentration, and gas load on deuterium extraction. The model predicts an equal influence of mass transfer and reaction kinetics on the rate of deuterium extraction. Therefore, a higher operation temperature of the PIEU and higher catalyst concentration increases the extraction of deuterium substantially due to improved kinetics. Introduction The NH3-H2 chemical exchange process has been used for large scale production of heavy water. The term “chemical exchange” denotes an isotopic redistribution between the exchanging substances without altering their chemical nature. The chemical exchange process can be classified depending upon the method employed for providing reflux, namely, monothermal and bi-thermal. In the mono-thermal flowsheet reflux is obtained by chemical conversion whereas in the bi-thermal process the reversibility of the exchange reaction is exploited.1 The NH3-H2 mono-thermal chemical exchange process is operated at low temperatures (∼250 K) and high pressures of typically 20-25 MPa. The process requires a large amount of ammonia and hydrogen; thus, the synthesis gas from a fertilizer plant is usually utilized in this process. The NH3-H2 chemical exchange process is based on the deuterium exchange between liquid ammonia and gaseous hydrogen as follows:

NH3(l) + HD(g) T NH2D(l) + H2(g)

(1)

A multi-stage plate column, used as the chemical exchange tower, is at the heart of the process where absorption of HD from the gaseous phase into liquid ammonia is accompanied by the liquid chemical exchange reaction given by eq 1. As the liquid ammonia phase flows downward countercurrent to the synthesis gas mixture in the tower, a continuous contact is established between the two phases. The heavier isotope accumulates in the liquid phase as NH2D and flows down the tower. Earlier attempts to model the NH3-H2 chemical exchange reaction were based on the thermodynamic equilibrium of the isotopic exchange reactions with no effort toward incorporating the chemical kinetics.2 The aim of the present analysis is, therefore, to develop a mathematical model for the exchange tower, taking into account the kinetics of the isotopic exchange reaction along with the mass transfer aspects to evaluate the performance of the exchange tower. Such a model is essential to determine the operating window and to optimize the production of heavy water. * To whom correspondence should be addressed. Fax: 91-2224145616. E-mail: [email protected].

The reaction between NH3 and HD in the liquid phase does not proceed rapidly in the absence of a catalyst. Clayes et al.3 showed that KNH2 is an efficient homogeneous catalyst for this exchange reaction. Other reported catalysts for the process are sodium amide, rubidium amide, and cesium amide.2 At the same temperature and catalyst concentration, the reaction rate constant for the amides of sodium, potassium, rubidium, and cesium are roughly in the ratio 0.3:1:1.3:1.5.2 Thus potassium amide is preferred over sodium on the account of its higher catalytic activity, whereas rubidium and cesium are too expensive to be employed on an industrial scale. The exchange process is usually called as chemical exchange distillation.4 But considering that the major components of the gas feed, that is, nitrogen and hydrogen, are well above their critical conditions, the tower should be treated as a gas absorption column. It is obvious that the relative rates of the mass transfer of HD from the gas phase into the liquid ammonia phase and the chemical reaction of deuterium exchange between different species together would decide the efficiency of the column. Any performance improvement exercise for the exchange tower would require a detailed analysis of these two steps for identification of the rate controlling parameters. The analysis of the exchange process needs investigation of the effect of operating variables, namely, temperature, pressure, catalyst concentration, gas load, and their combinations, on the overall performance of the process. The NH3-H2 chemical exchange process consists of the following reactions between the participating species: NH3, NH2D, NHD2, ND3, H2, HD, and D2 in the presence of KNH2 as a catalyst. K1

NH3(l) + HD(l) 798 NH2D(l) + H2(l) K2

NH3(l) + NHD2(l) 798 2NH2D(l) K3

NH2D(l) + ND3(l) 798 2NHD2(l) K4

H2(g) + D2(g) 798 2HD(g)

(2) (3) (4) (5)

where K represent the equilibrium constant of the exchange reaction. Figure 1 compares the equilibrium constants for the

10.1021/ie060039y CCC: $33.50 © 2006 American Chemical Society Published on Web 09/02/2006

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Scheme 1. PIEU along with Cracker and Ammonia Synthesis

isotopic exchange reactions, which clearly shows that the reaction represented by eq 2 is favored thermodynamically over the other reactions.2 Moreover, the corresponding trend of the equilibrium constant for eq 2 suggests that a possible hightemperature operation (273 K as compared to the existing 250 K) can be further explored to gain the advantage of improved kinetics. The distribution of the deuterated species between the gas and the liquid phases is conventionally represented by a separation factor (β) which is defined as the ratio of the deuterium atom fraction in the liquid phase to that in the gas phase.2

D ( D + H) β) (D +D H)

l

(6)

g

where D/(D + H) is defined as the atom fraction of deuterium. This β is related to the equilibrium constants of the exchange

reactions, vapor pressures of ammonia isotopes, and solubility of the hydrogen isotopes in liquid ammonia.2 The tower efficiency is estimated knowing β and the overall liquid-to-gas ratio in the tower. The separation factor approach has been routinely used for the H2S-H2O exchange and the CH3NH2H2 systems.5 This approach does not consider the kinetics of the chemical exchange reaction in the analysis, and the role of catalyst and temperature of the operation are, therefore, not considered rigorously in the performance evaluation. The exchange rates for deuterium are low despite the presence of catalyst, and, therefore, a special type of ejector contactors has to be employed to achieve intimate gas-liquid contacting. The column volumes required for processing 31.5 ton/h of gas at a constant extraction duty in a bubble column and packed tower are reported as 133 m3 and 1584 m3, respectively,6 as against a column volume of 71 m3 required for processing 48 ton/h of gas in an ejector tray column.7 Thus, the ejector tray configuration is favored over the conventional contactors for the mono-thermal chemical exchange process.

Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6747 Scheme 2. Typical Representation of an Ejector Tray

Figure 1. Equilibrium constants for the isotopic exchange reactions 2. (solid line) K1, (long dashed line) K2, (dotted-dashed line) K3, (short dashed line) K4.

Process Description The mono-thermal ammonia hydrogen chemical exchange process uses naturally occurring deuterium (principally HD) in the ammonia synthesis gas (i.e., N2 + 3H2) mixture. The ammonia synthesis gas is first compressed to compensate for the pressure lost due to routing the gas through the heavy water plant. The gas is then treated to remove all trace impurities which can have a detrimental effect on the catalyst, KNH2, and then cooled to the operating temperature of the exchange tower. The gas mixture further passes through the preliminary isotope exchange unit (PIEU) as shown in Scheme 1, where deuterium is extracted from the gas stream into the liquid phase. The PIEU consists of an extraction tower, T1, and an enrichment tower, T2. In the tower T1, deuterium from the synthesis gas stream gets transferred to a counter-flowing stream of liquid ammonia which carries dissolved potassium amide as the catalyst. There is, therefore, a net downward transport of deuterium in the column. The liquid stream leaving the tower T1 gets enriched in deuterium by approximately five times the deuterium concentration in the feed gas mixture. The deuterium depleted gas from the top of the tower T1 is fed to an ammonia synthesis unit to provide an ammonia reflux stream to tower T1.5 The deuterium-rich liquid ammonia from the bottom of the tower T1 is taken to the enrichment tower T2 where it again flows countercurrent to another stream of deuterium-rich gas. Thus, the liquid ammonia stream gets further enriched in its deuterium content. The deuterium-rich liquid stream leaving tower T2 is stripped of its catalyst content before routing through a cracker unit, where it is cracked to the synthesis gas mixture but with increased deuterium content. A part of this deuteriumrich gas stream is taken out for further purification (in the final enrichment unit) while the remainder stream provides a gas phase reflux to the tower T2. The highly enriched liquid ammonia leaving the final enrichment unit is cracked, and a portion of it is burnt with dry air to produce nuclear grade heavy water.5 The PIEU is the heart of the entire process because the deuterium extracted from the fresh synthesis gas feed stream in this section determines the concentration profile of the deuterium-rich liquid ammonia in the remaining sections of the process. The stage efficiencies of the conventional contacting equipments are of the order of 1-2% as a result of low interfacial areas (250-800 m2/m3), necessitating the use of

hundreds of trays to achieve significant extraction.4 However, in the ejector tube a high energy input generates highly turbulent fluid motion that results in large interfacial areas (∼4000 m2/ m3).4 Scheme 2 shows the gas and liquid flows inside the ejector tube. Each ejector tray carries a number of convergent nozzles, through which the gas enters the tray. This high velocity gas entrains into the tubes the liquid ammonia from the liquid holdup on the tray. The highly turbulent gas jet breaks the entrained liquid into minute drops within the tube and thus provides a large gas-liquid interfacial area inside the ejector tube for the mass transfer of exchanging species. The gas-liquid mixture passes tangentially into a separator from where the gas-liquid dispersion separates. The liquid falls back on the tray while the gas rises to the next tray. During its passage through the ejector nozzles the gas suffers a high-pressure drop on every tray. In the tower T1, the gas mixture gets washed on the top tray with liquid ammonia coming from the ammonia synthesis unit which is lean in deuterium. The potassium amide solution in ammonia is fed separately on the exchange tray immediately below this washing tray. The deuterium enriched liquid leaving the tower T1 is heated through a heat exchanger network before it enters the enrichment tower T2 containing another set of exchange trays and a washing tray. At the top tray, ammonia is condensed out, so that the gas leaving the top tray gets washed of its amide carryover. This gas combines with the dry synthesis gas from the fertilizer plant and is cooled and humidified with ammonia before being fed to the tower T1. Model Development A mathematical model of the PIEU of the ammonia hydrogen chemical exchange process includes a total of six components, namely, the four bulk components N2, H2, NH3, and KNH2 and two deuterated species HD and NH2D. The other deuterated species exist in negligible quantities and can safely be ignored at low concentrations of overall D/(D + H) normally achieved in the PIEU.8 The mathematical model is developed at two concentric levels, namely, (A) the equilibrium mass and energy balances for the bulk species N2, H2, and NH3 where these components are assumed to reach the gas-liquid-phase equilibrium while leaving each stage and (B) the reaction enhanced mass transfer rates of HD into liquid ammonia.

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The following assumptions are made with respect to the bulk species: i. The liquid and gas streams leaving a particular tray are in thermal and physical equilibria. ii. The isotopic species (HD and NH2D) are lumped into their bulk counterparts (H2 and NH3, respectively), because they exist in parts per million concentrations, for the overall balance. iii. Heat effects associated with solvation and mixing are negligible because of very low concentrations of the reacting species. iv. The pressure variation for the gas flow along the length of the tower based on the Bernoulli’s equation follows the relation

( ) Pin

ln

Scheme 3. (a) Equilibrium Tray and (b) Driving Force for HD Transfer at the Gas-Liquid Interface, for a Differential Element of Length Dx in the Ejector Tube

no.of trays

)σ

Pout

∑ n)1

Qg,n2

(7)

Scheme 3a shows a typical representation of the jth tray, and the corresponding balance equations for the bulk components, that is, N2, H2, and NH3, are given below.

Component mass balance: Li,j-1 + Gi,j+1 - Gi,j - Li,j ) 0

i ) 1 ... 3

(8)

Phase equilibrium relation: Gi,j 3

) Ki,ph

Gi,j ∑ i)1

Li,j

i ) 1 ... 3

3

(9)

Li,j ∑ i)1

Energy balance: 3

∑ i)1

3

G Gi,j+1hi,j+1 +

∑ i)1

3

L Li,j-1hi,j-1 -

∑ i)1

3

G Gi,jhi,j -

L Li,jhi,j )0 ∑ i)1

(10)

Phase equilibria constants:9 Ki,ph )

Hiγi for H2 and N2 Pφi

(11)

Psatγ for NH3 Pφ

(12)

Ki,ph )

The estimation of the phase equilibria of the ternary system N2-H2-NH3, at the operating conditions of the exchange towers, assumes significance while calculating the tray compositions. Because ammonia exhibits self-association in the vapor phase, especially at low temperatures and high pressures, the phase equilibrium relation for ammonia must include the association phenomena and its consequent effect on the vapor phase fugacity of ammonia. A recently developed phase equilibria model for the ternary system N2-H2-NH3 is used in the present work.9 For the bulk mass and energy balances over a tray, a system of three components yields a total of eight equations (namely, three mass balances, eq 8; three phase equilibria relations, eq 9; overall energy balance, eq 10; and equation for pressure drop, eq 7) against a total of 18 variables (12 molar flows, 3 temperatures, and 3 pressures of three stages involved in the balance equations) required to fully characterize a tray. A typical set of operating data consists of temperature, pressure, catalyst concentration, D/(D + H), and flows at the entry and exit points of both the exchange towers, T1 and T2. Therefore, a top-down

approach was followed for the tray calculations wherein the gas stream leaving the tower and the liquid stream entering at the top are specified from the plant data. The equilibrium bulk compositions, temperature, and pressure are then calculated from the top tray downward until the last tray by assuming a value of σ in eq 7. The temperature and pressure at the last tray are compared with the values available from plant data, and the procedure is repeated until the corresponding values match with the plant data. Rate-Based Analysis of the Exchange Reaction in a Single Ejector Tube. The chemical exchange reaction between HD and NH3 is exothermic (18.448 kJ/mol at 253 K). However, at low concentrations of deuterium the net heat of reaction is negligible as compared to the bulk energy terms.2 The equilibrium constant for the chemical exchange reaction eq 1 taking place in the liquid phase is defined as

K′ )

CH2CNH2D CHDCNH3

(13)

The equilibrium constant for the exchange reaction and its variation with temperature are available in the literature.10 The exchange reaction rates during HD absorption in liquid ammonia at different catalyst concentrations up to saturation were studied by Bourke and Lee11 in a bubble column through the temperature range 233-293 K. This work showed that the reaction can be represented by a pseudo-first-order reversible reaction:

HD(l) T NH2D(l)

(14)

The equilibrium constant K for this reaction is defined as

K)

CNH2D CHD

(15)

and is related to the equilibrium constant K′ for the reaction represented by eq 13 as follows

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K)

K′CNH3

(16)

CH2

Bourke and Lee11 have also reported the pseudo-first-order reaction rate constants at various concentrations of the catalyst (4.5-36 kg KNH2/m3) and at different temperatures (233-293 K).11 The above-reported data were fitted to quantitatively estimate the pseudo first-order reaction rate constant, with an average error of (7.5% as a function of temperature and catalyst concentration. The dependence of the rate constant on these parameters (eq 17) is shown in Figure 2.

at 231.4 K),12 the major resistance to the mass transfer is on the liquid side (typical values being kL ) 1.57 × 10-4 m/s and kG ) 0.2 m/s). The gas-liquid interface is assumed to be in equilibrium with HD partial pressure in the bulk gas phase. The reaction in the liquid phase proceeds rapidly in the presence of catalyst (KNH2), and almost all of the HD which gets absorbed into the liquid reacts with NH3 to form NH2D. The mass transfer flux at the interface for the reacting species HD over a differential element of thickness dx inside the ejector tube can be written as

Qe -3856 kr ) 1.0246 × 10 exp ccat1.5 T 6

(

)

(

(17)

The gas entering into the ejector tube with high nozzle velocity (∼50 m/s) entrains the liquid from the tray, creating fine gas/liquid dispersion inside the ejector tube which develops high interfacial area for intimate contact between the two phases. HD from the gas-phase gets absorbed into the liquid ammonia phase and reacts with NH3 to form NH2D. The overall mechanism is that of absorption of HD followed by its chemical reaction with NH3. The following assumptions were made for developing a rate-based model for this process: (i) Inside the ejector tube, the gas and the liquid flow vertically in a co-current plug flow manner. (ii) The liquid on the tray is assumed to be completely mixed. (iii) NH2D in the gas-phase leaving a tray is assumed to be in phase equilibrium with the NH2D in the liquid on the tray, with the phase equilibrium constant equal to that of ammonia. (iv) The liquid stream remains saturated with hydrogen, and, hence, the hydrogen formed due to the chemical exchange escapes into the gas phase. Because the amount of HD extracted into the liquid phase is very small as compared to the total amount of gas phase, this exchange has no substantial effect on the gas-phase properties. The reaction enhanced mass transfer of HD in the ejector tube is shown in Scheme 3b. Because the solubility of HD in liquid ammonia is very low (1.73 × 10-11 mol STP/m3.KN/m2

)

dCg,HD Cg,HD Cl,NH2D ) kL*aAc dx ek K

(18)

Equation 18 is integrated by the fourth order Runge-Kutta method over the entire length of the ejector tube on the individual tray. The cross-sectional area of the ejector tube is not constant; the diameter varies with height. These variations have been accounted for while integrating eq 18 along the height of the ejector tube. Based on the HD balance, the isotopic species (HD and NH2D) are de-lumped from the bulk quantities determined earlier, with subsequent changes in the hydrogen and liquid ammonia balance over the tray on account of the exchange reaction. The solution procedure based on lumping and de-lumping of isotopic species is shown in Scheme 4. The term kL* in eq 18 is the enhanced mass transfer coefficient due to the pseudo-first-order reversible reaction represented in eq 14 and is given as follows:13

DNH2D 1+K DHD kL* ) kL DNH2D tanh(Rδ) 1+K DHD Rδ

(19)

where

R)

x (

kr 1 DHD 1+ DHD K DNH2D

)

(20)

and the film thickness

∂)

DHD kL

(21)

The diffusivities for HD and NH2D in the liquid NH3 phase were evaluated using the Wilke-Chang correlation.14 The Henry’s constant of HD in liquid ammonia was evaluated from the solubility data by Bar-Eli and Klein12 and is represented as a function of temperature (eq 22) as shown below:

(

HHD ) 0.101325 exp 3.3473 +

Figure 2. Fitted curve and experimental points for the rate constant of the chemical exchange reaction. (9) Experimental data (ref 9), (solid line) fitted curve for 36 kg KNH2/m3, (dashed line) fitted curve for 18 kg KNH2/m3, (dotted-dashed line) fitted curve for 9 kg KNH2/ m3, (0) predicted point at 4.5 kg KNH2/m3.

1639.3 T

)

(22)

where the temperature T is in K. The mass transfer coefficient “kL” and interfacial area “a” of the ejector tube are the key process parameters which represent the extent of turbulence and the contact area inside the ejector tube. The “kL” and “a” values of an ejector tube were available from independent experiments15 as a function of power dissipated per unit volume (P/V) required to generate two-phase flow in the ejector tube for an air-water system within a relative error of (10% each. Similar correlations had been developed

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Scheme 4. Calculation Procedure for Exchange Tower Based on Lumping-Delumping of the Isotopic Species

() (

kL ) 3.7 × 10-5 a ) 781

0.288

P V

Dair-water

() ( ) ( ) P V

0.41

σ H2 O

)

DSyngas-NH3

0.6

σNH3

FNH3

0.5

(23)

0.2

FH2O

(24)

The typical values of kL and a at the actual operating conditions of the heavy water plant are 1.57 × 10-4 m/s and 3990 m2/m3, respectively. Based on the values of kL, kr, and DHD, the dimensionless quantity xM, for the simultaneous absorption and chemical reaction of HD, is defined as13

xM )

xDHDkr kL

(25)

Figure 3 shows the xM values estimated for the HD-NH3 chemical exchange system using the kL, DHD-NH3, and kr evaluated above. At catalyst concentrations corresponding to the operating regime of the plant the xM values range from 1 to 3, suggesting a moderately fast reaction regime of the theory of mass transfer with chemical reaction.13 For example, at T ) 252 K,

DHD-NH3 ) 8.44 × 10-9 m2 s-1 krxn ) 15.7 s-1 kL ) 1.48 × 10-4 m s-1

xM )

xDHD-NH kr ) 2.46 3

0

kL

The process is characterized by almost similar values of characteristic times for reaction and mass transfer. The reaction thus can have a significant effect on the mass transfer rates.

earlier for the interfacial area for a variety of gas-liquid contactors by Nagel et al.16 Another study by Schugerl et al.17 resulted in a similar kind of relation for the volumetric mass transfer coefficient “kLa” for a bubble column cascade in terms of P/V. More recently, Cramers et al.18,19 have developed similar correlations for “kLa” in terms of P/V for loop-venturi reactors, whereas Dirix et al.20 represented it as a function of the volumetric L/G ratios inside the loop reactor. The two-phase pressure drop is obtained by deducting the pressure drop at the nozzle from the total pressure drop over the entire ejector tray assembly. The interfacial area of the ejector tube for the air-water system needs to be corrected for the synthesis gas-ammonia system based on the difference in density and surface tension of the dispersing fluid. Ammonia with a lower density and lower surface tension provides high gas-liquid interfacial area as compared to water. Similarly, the mass transfer coefficient is corrected with respect to the diffusivity of syngas (N2 + 3H2) in ammonia and that of air in water.

Figure 3. xM plot for the HD-NH3 chemical exchange system.

Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6751 Scheme 5. Calculation Procedure for the Entrainment Ratio (L/G) inside Ejector Tube [21]

Table 1. Range of Operating Data Used for Model Validation operating variables

range in plant data

temperature pressure catalyst concentration gas load

249-258 K 17.75-24 MPa 11-25 kg KNH2/m3 45-61 ton/h

carryover ratio (e) in eq 27 is defined as moles of liquid carried per mole of gas over to the next tray. This ratio is represented as a fraction of the total liquid entrainment ratio (L/G) in the ejector tube. The ejector tube geometries for both towers T1 and T2 are the same except for their lengths (ejector length in tower T1 ) 1.42 times the ejector length in tower T2). The L/G ratio calculated from the hydrodynamic calculations over the ejector tray in tower T2 was found to be 6-7 times that in tower T1. Although the total gas load in tower T2 is approximately one-fifth of that in tower T1, the gas velocities are only half of that in tower T1 (∼70 m/s in tower T1 and 38 m/s in tower T2), resulting in comparable pressure drops per tray (i.e., 0.122 MPa for tower T1 and 0.109 MPa for tower T2) and, therefore, higher entrainment ratio in ejector tubes of tower T2. This results in higher turbulence and finer drop size of the dispersed phase, consequently leading to a greater chance of a physical carryover of the liquid phase in the ejector trays of tower T2 as compared to that in tower T1. Model Validation and Parameter Estimation Using Operating Plant Data

The ejector tube configuration on an exchange tray represents a highly turbulent system where the entrainment mass ratios (L/G) generated inside the ejector tube are significant (10 for the exchange tower T1 and 58 for the exchange tower T2). The calculation procedure for the entrainment ratios generated inside the ejector tube is shown in Scheme 5. The overall pressure drop for a single tray is further differentiated into nozzle and two-phase pressure drop. Next, a value of the L/G ratio is assumed, and the theoretical two-phase pressure drop is calculated inside the ejector tube using the Lockhart-Martinelli correlation21 and compared with the actual two-phase pressure drop. The ejector tubes have a built-in cyclone separator to separate the high velocity gas liquid mixtures leaving the ejector tube. However, the high entrainment ratios and very fine dispersions (∼20 µm), increase the possibility of liquid carryover to the next tray along with the gas stream. This carryover can affect the performance of the ejector tube and reduce the separation efficiency of the tower. The effect of liquid carryover on the deuterium extraction is included in the model using an apparent efficiency ηapp defined as follows:22

ηapp )

η 1+

e η 1-e

e %e ) L/G

(26)

The model was validated with 20 sets of operating plant data collected from a heavy water plant. This set of data was selected so as to cover the operating range (shown in Table 1), for all the process variables at the heavy water plant over a period of 730 days. The model consists of two unknown parameters σ (eq 7) and %e (eq 27) which were determined from the operating plant data. The former directly affects the pressure drop, temperature profiles, and consequently the deuterium extraction along the tower height, whereas the latter affects the extraction efficiency of an ejector tray. For a particular set of plant data the unknown parameters σ and %e were evaluated simultaneously by minimizing the SSR (sum of square of residuals) over the pressure drop and D/(D + H), respectively. The parameter σ in the pressure drop relation obtained from operating plant data is further related empirically to the gas load, and entering gas temperature for the predictive purpose,

σ∝

( )( ) 1 Gdesign T G

The proposed relation gives a satisfactory fit with a relative error of approximately (2% for tower T1 and (2.6% for tower T2 (Figure 4a,b). The proportionality constants in eq 28, obtained from the operating plant data, are 2.452 × 10-6 K-1 and 2.448 × 10-5 K-1 for T1 and T2, respectively. Colburn22 has suggested that the carryover in sieve trays can be related to the gas velocity by a power-law relation. In a similar way the percentage carryover (%e) in the exchange tower T2 was related to the volumetric gas flow over the tray as follows (eq 29):

%e ∝ Qt2 (27)

Apparent tray efficiencies due to liquid entrainment based on a similar approach have been evaluated recently.23,24 The

(28)

(29)

The % carryover in tower T2 showed a quadratic dependence on the total volumetric gas flow with a relative error of (3.5% as shown in Figure 5. The proportionality constant in eq 29 was evaluated from the operating plant data and is 192.6 s2/m6.

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Figure 5. %e in T2 related to the volumetric flow rate. (O) From plant data. (solid line) Fitted.

Figure 4. σ as a function of gas load and operating temperature. (a) for T1 and (b) for T2. (O) From plant data. (solid line) Fitted.

The model predicted no liquid carryover in tower T1, as opposed to tower T2 which showed an average of a 1.5% liquid carryover. This can be attributed to the smaller length of the ejector tubes and higher entrainment ratios in tower T2 as compared to those in tower T1 as discussed above. The parity plot of the predicted exit gas D/(D + H) concentrations using these values of σ and %e with the plant data are shown in Figure 6a,b for towers T1 and T2, respectively. The model satisfactorily predicts the performance of the exchange towers T1 and T2 with a relative error of 5.3% for T1 and 2.2% for T2. The validated model is further used to predict the optimal region of operability for the maximum deuterium extraction. Solution Scheme The systematic procedure for tower simulation is shown in Scheme 6. A top-down approach is followed for both the towers.

Figure 6. Parity plot for the exit gas D/(D + H) for exchange towers (a) T1 and (b) T2.

The input parameters required for simulation are classified as “constant” and “variable”. Except for the operating conditions of tower T1 (viz., temperature, pressure, and catalyst concentration) the rest of the parameters are kept constant. As shown the solution scheme starts by assuming gas flow, HD, and NH2D from tower T2 and then simulating tower T1. This generates an output file which is used as the input for tower T2 simulation. The simulation of exchange tower T2 generates an output file

Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6753 Scheme 6. Flow Scheme for Simultaneous Simulation of Exchange Towers T1 and T2

Figure 7. Simulated temperature and deuterium profile in the exchange tower T1.

which modifies the assumed input (from T2 at the start of the iteration procedure) for simulating T1. The procedure is repeated until the respective D/(D + H), temperature, pressure, and flow rates of the exchange towers T1 and T2 converge to a constant value. Optimization of Exchange Tower T1 with Respect to the Process Variables. The extraction of deuterium from the synthesis gas stream coming from the fertilizer plant in the stripping tower T1 forms the crux of the PIEU. A detailed analysis of the extraction tower T1 was, therefore, performed using the above model. The effect of the individual process variables, namely, operating temperature, pressure, catalyst concentration, and gas load on the performance of tower T1 is studied in detail in the present study. The work lays emphasis on the analysis of exchange tower T1 where the extraction of deuterium from fresh syngas takes place. On the other hand, the extraction tower T2 functions as an enrichment tower. Therefore, the exchange tower T1 is simulated by maintaining the operating conditions for tower T2 constant. All the simulations (except those where gas load is varied) are performed on a total gas load of 61 ton/h and 107 ppm feed D/(D + H), while maintaining the exchange tower T2 at a constant operating condition of 10.5 MPa and 281 K. Figure 7 shows a typical temperature and D/(D + H) profiles for the exchange tower T1. The exchange tower is almost isothermal for the first 13 trays, after which the temperature rises steadily due to addition of the relatively hot (∼270 K as compared to the operating temperature of tower T1) pure ammonia stream from the ammonia converter on the 16th tray and the catalyst laden liquid ammonia stream from the catalyst

Figure 8. Simulated temperature and deuterium profile in the exchange tower T2.

stripping unit (at ∼273 K) on the 15th tray. A similar profile for the exchange tower T2 is shown in Figure 8. The temperature profile in tower T2 also depends on the temperature at which the liquid ammonia stream leaving T1 enters the 9th tray (after being preheated in the heat exchanger network between T1 and T2), which in this case is higher than the average operating temperature of tower T2. Thus, the temperature rises steadily at the top trays. The tower L/G (kg/kg) ratio for T2 is approximately 1. This coupled with the closer approach temperatures of the gas and liquid streams causes a hump in the

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Figure 9. Effect of T1 operating temperature (at 21.67 MPa and 61 ton/h) on the exit gas D/(D + H) at different catalyst concentrations for (a) tower T1 and (b) tower T2. (thick dashed line) 33.5 kg KNH2/m3, (dashed-dotted-dotted line) 26.8 kg KNH2/m3, (dashed-dotted line) 20.1 kg KNH2/m3, (thin dashed line) 13.4 kg KNH2/m3, (long dashed line) 6.7 kg KNH2/m3, (solid line) 3.4 kg KNH2/m3.

Figure 10. Effect of the T1 operating pressure (at catalyst concentration of 33.5 kg KNH2/m3 NH3 and 61 ton/h) on the exit gas D/(D + H) of tower T1. (thin line) 248 K, (thick line) 268 K, (dashed line) 283 K.

Figure 11. Effect of catalyst concentration (at 20.7 MPa and 61 ton/h) on the exit gas D/(D + H) of exchange tower T1. (solid line) 248 K, (dashed line) 283 K.

temperature profile. The 10th tray constitutes an ammonia condenser to knock out ammonia from the saturated gas stream leaving the 9th tray, so as to wash the rising gas of any amide carryover; this explains the sudden drop in the temperature at the top tray. Effect of Temperature. Because the absorption is accompanied by a simultaneous chemical reaction and both kinetics and mass transfer processes are important, temperature of operation is expected to have considerable influence on the rate of HD extraction. An increase in the operating temperature

increases the extraction of HD due to improved kinetics. However, at still higher temperatures, due to increased reversibility of the reaction, this effect is nullified. The effect of the operating temperature (at 21.67 MPa and 61 ton/h) on the exit deuterium atom fraction of the exchange tower T1 is shown in Figure 9a for different catalyst concentrations. An increase in temperature increases the pseudo-first-order reaction rate constant for the exchange reaction by an order of magnitude (16.3 s-1 at 248 K to 111.6 s-1 at 283 K for 20.1 kg KNH2/m3 NH3) and increases the solubility (eq 22) of hydrogen deuteride

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Figure 12. Effect of gas load on the exit gas D/(D + H) and deuterium throughput of tower T1.

(0.34% at 248 K to 0.81% at 283 K). However, an increase in temperature also reduces the reaction equilibrium constant K′ (10.09 at 248 K to 7.42 at 283 K), thereby increasing the reversibility of the exchange reaction. Thus, for a particular operating pressure and catalyst concentration there is an optimum temperature beyond which the reversibility of the reaction limits the extraction of deuterium. At high catalyst concentrations the rates of forward reaction are high (47.75 s-1 at 253 and 33.5 kg KNH2/m3) as compared to low catalyst concentrations (1.54 s-1 at 253 and 3.4 kg KNH2/ m3). Therefore, the optimum operating temperature at high catalyst concentration is the lowest (270.2 K at 33.5 kg KNH2/ m3) and shows an increasing trend (inset Figure 9a) as the catalyst concentration is lowered (316.8 K at 3.4 kg KNH2/ m3). The variation of the exit gas D/(D + H) for the exchange tower T2 corresponding to the operating conditions in tower T1 is shown in Figure 9b. Because the operating conditions for the exchange tower T2 are kept constant, the concentration of NH2D in the liquid stream leaving tower T1 (which is the feed stream to tower T2) determines the exit gas D/(D + H) from

tower T2. For a constant separation duty of the enrichment tower T2 (determined by the constant operating conditions) and constant efficiency of the ammonia cracker which feeds the ammonia + syngas mixture to tower T2, a higher D/(D + H) in the liquid stream entering tower T2 results in an enriched liquid stream leaving tower T2. Thus the amount of HD in the gas entering the tower T2 is more, and, therefore, for a constant extraction duty, the HD in the exit gas D/(D + H) of tower T2 is higher. Moreover, a high concentration of NH2D in the liquid stream entering tower T2 results in an increased vaporization of NH2D. Thus, for a particular catalyst concentration, as the deuterium extraction in the tower T1 increases (with increasing temperature of tower T1) the corresponding deuterium concentration in the exchange tower T2 also rises. Effect of Pressure. An increase in the operating pressure of the tower T1 reduces the volumetric gas flow rate substantially. Therefore, the nozzle velocities and subsequent liquid entrainment in the ejector tube goes down. The power dissipated per unit volume and the interfacial area available for mass transfer consequently decreases adversely affecting the mass transfer process. Increasing the operating pressure, however, increases the molar gas density thus increasing the molar concentration of HD at the interface and thus the solubility of HD in liquid ammonia. This results in a corresponding increase in the transfer rate of HD according to eq 18. The residence time also increases on account of reduced volumetric gas flow rate. Hence, for a particular set of operating conditions, namely, temperature, gas load, and catalyst concentration, an optimum pressure is obtained. A typical effect of operating pressure on the exit gas deuterium fractions (D/(D + H)) of tower T1 (at catalyst concentration of 33.5 kg KNH2/m3 NH3 and 61 ton/h) for three different temperatures is shown in Figure 10. The optimum pressure increases with temperature, because at a particular operating pressure an increase in temperature increases the volumetric gas flow rate (hence the interfacial area in the tubes) and also the reaction rate constant kr (35.1 s-1 at 248 K to 240.2 s-1 at 283 K for 33.5 kg KNH2/m3 NH3). This shifts the optimum pressure to higher values, at which the opposing tendencies, namely, increase in HD concentration, increase in residence time, and decrease in power dissipation in the ejector, balance each other.

Figure 13. Surface plot for the exit gas D/(D + H) (at the T1 operating pressure of 23.6 MPa) with respect to the tower T1 operating temperature and catalyst concentration (a) for tower T1 and (b) for tower T2.

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Effect of Catalyst Concentration. An increase in the catalyst concentration increases the rate of the chemical exchange reaction (eq 17) resulting in a corresponding improvement in the enhanced mass transfer coefficient kL*. Figure 11 shows the effect of the catalyst concentration (at 20.7 MPa and 61 ton/h) on the exit gas D/(D + H) fraction of tower T1 at the operating temperatures of 248 K and 283 K. As expected, the high-temperature curve plateaus off at a low catalyst concentration (∼15 kg KNH2/m3) as compared to that at 248 K because of increased reversibility of the reaction at high temperature (283 K). Because a change in the catalyst concentration also affects the operation of the exchange tower T2, the corresponding exit gas D/(D + H) in tower T2 also decreases due to an increased extraction of HD (See Figure 13b). The relative increase in the HD extraction is maximum at low catalyst concentration which decreases as the catalyst concentration is increased and gradually plateaus off. Effect of Gas Load. The effect of gas load on the performance of the extraction tower T1 is shown in Figure 12. The residence time increases as the gas load is decreased thereby improving the extraction efficiency. However, a reduction in gas load reduces the throughput that is, the total moles of HD processed per unit time in the exchange towers. Figure 12a,b shows the combined effect of the operating temperature and catalyst concentration as the surface plot for the exit gas D/(D + H) from tower T1 and T2 respectively, at the tower T1 operating pressure of 23.6 MPa. These plots help to determine the region of optimum operability of the exchange towers to achieve maximum deuterium extraction. The study suggests that the optimum temperature of operation for the tower T1 is in the range of 268-278 K (depending upon the catalyst concentration and operating pressure). Lefrancois25 had suggested higher operating temperatures for the same process, but the detailed analysis has not been reported. An increase in the catalyst concentration beyond ∼27 kg/m3 has no significant effect on the overall deuterium extraction in T1. The study suggests a higher temperature of operation of tower T1 and high catalyst concentration for maximum deuterium extraction. However, a higher temperature of operation results in an increased concentration of ammonia in the gas stream leaving tower T1. This ammonia-laden syngas constitutes the feed to the ammonia converter which provides the liquid ammonia reflux to tower T1 by chemically converting syngas to ammonia (N2 + 3H2 T NH3). Thus, an increase in the operating temperature of tower T1 directly affects the performance of the ammonia converter (due to increased concentration of ammonia by vaporization) thereby reducing the conversion of syngas in the converter and consequently the tower L/G ratio. A reduction in the reflux ammonia flow finally affects the overall throughput of NH2D from tower T2. Hence, an overall analysis of the exchange towers (T1 and T2) in conjunction with the ammonia converter, ammonia cracker, and the catalyst stripping unit (CSU) is essential to determine the optimum operating temperature.

operability for maximizing the extraction of deuterium in the exchange tower T1. Acknowledgment The authors acknowledge the financial support extended by the Department of Atomic Energy, Govt. of India. Notation Ac ) cross-sectional area of ejector tube a ) interfacial area, m2/m3 C ) concentration, kmol/m3 c ) concentration, kg/m3 CSU ) catalyst stripping unit D ) diffusivity, m2/s D/(D + H) ) atom fraction of deuterium, defined as ppm e ) ratio of carryover, kmol/kmol ek ) phase equilibrium constant for HD at gas-liquid interface based on Cg,HD ) ekCL,HD G ) molar flow rate of gas stream, kmol/h H ) Henry’s constant, MPa h ) enthalpy, kJ/kmol K ) equilibrium constant for pseudo-first-order reaction, eq 14 K′ ) equilibrium constant for entire exchange reaction, eq 1 Kph ) phase equilibrium constant kL ) mass transfer coefficient, m/s kLa ) volumetric mass transfer coefficient, s-1 kr ) pseudo-first-order reaction rate constant, s-1 L ) molar flow rate of liquid stream, kmol/h L/G ) entrainment ratio, kg/kg xM ) dimensionless parameter P ) pressure, MPa P/V ) power dissipated per unit volume, kW/m3 Q ) volumetric gas flow rate, m3/s T ) temperature, K x ) differential length of a volume element of ejector tube β ) gas liquid separation factor ∂ ) interfacial film thickness, m γ ) activity coefficient η ) efficiency of the ejector tube σ ) fitting parameter φ ) fugacity coefficient Subscripts and Superscripts l, L ) liquid phase g, G ) gas phase i ) chemical species ph ) phase equilibrium cat ) catalyst t ) tray e ) ejector tube * ) enhancement due to reaction Literature Cited

Conclusion The PIEU of the mono-thermal ammonia hydrogen chemical exchange process is modeled from first principles taking into account the hydrodynamic and mass transfer aspects of ejector trays and the kinetics of homogeneous catalyzed isotopic exchange reaction. The model is validated using the operating plant data of one of the heavy water plants and is utilized further to gain insights into the chemical engineering aspects of the exchange process. The model provides an optimal region of

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ReceiVed for reView January 10, 2006 ReVised manuscript receiVed July 8, 2006 Accepted July 20, 2006 IE060039Y