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SYSTEM EVALUATION EXPERIMENTS -- Continued

Modeling of Adsorption Equilibrium

According to Dubinin (1986), the physical adsorption of vapors in micropores can be described by the theory of volume filling of micropores. In general, adsorption capacity of microporous carbons can be conveniently expressed by the Dubinin-Astakhov (DA) equation (Dubinin, 1975) in the form of

where W = pore volume filled at temperature T, and relative pressure P₀/P, W₀ = total micropore volume, A = R_uT ln (P₀ / P), R_u is the universal gas constant, b, E₀, and n are characteristic parameters of the adsorbent/adsorbate. E₀ is the characteristic energy of adsorption for a reference adsorbate and b is a coefficient expressing the ratio of the characteristic adsorption energy of the adsorbate to that of the reference adsorbate. By definition, b has a value of 1 for the reference adsorbate, benzene. The exponent n reflects the width of pore energy distribution. For a variety of microporous carbons, it has been shown that n = 2 (which reduces the DA to the Dubinin Radushkevich (DR) equation).

Using data for ln(W) versus ln(P₀ / P) and a nonlinear regression method, optimum R_uT/bE₀ and n can be found for a given adsorbate and adsorbent system. A plot of lnW versus lnⁿ (P₀ / P) should provide a straight line with a slope -(R_uT/bE₀) ⁿ and an intercept ln (W₀₎).

Results of the acetone and MEK adsorption tests for ACC-5092-20 were used to determine DA and DR parameters. Results included data obtained using the ACFC fixed-bed and packed-bed for high concentrations (1,000 to 10,000 ppmv) and data from Cal (1993,1995) for lower concentration levels (50 to 1,000 ppmv). The parameters found are given in Table 4.4, and plots of experimental data versus modeled DA and DR isotherms are given in Figures 4.15 and 4.16. The DA model fits the data more closely than DR. For acetone, the DR equation underestimates the adsorption capacity for a concentration level greater than 1,500 ppmv. For MEK, the DR and DA equations provide similarly accurate results for concentration levels greater than 100 ppmv and less than 5,000 ppmv.

Figure 4.16 Modeled DA and DR isotherms for adsorption of MEK by ACC-5092-20

Modeling of Adsorption Dynamics

Numerous models with different degrees of mathematical sophistication have been introduced for adsorption dynamics in fixed-beds over the years. Usually the adsorption dynamic models predict the BTC. Then data such as stoichiometric time, breakthrough time, TPR, length of MTZ or LUB are extracted from the predicted BTC. More rigorous models use numerical schemes to solve a series of coupled partial differential equations that describe conservation laws of systems such as mass, momentum, species, and energy. In some situations, depending on the design of the adsorber, it is possible to decouple the equations and solve them separately or disregard the effect of some of them. For systems with simple hydrodynamic and NIT conditions, it may be sufficient to solve concentration equations derived from the conservation laws of mass and species. The NIT condition prevails in a situation where either heat of adsorption is small or heat transfer between fluid and solid is slow enough to cause additional broadening of the concentration front. In NIT conditions, heat transfer from adsorbent and walls of adsorber is fast enough to prevent the formation of a distinct thermal wave in the adsorber. Application of a developed model for NIT conditions is restricted to conditions with geometric and thermo-hydrodynamic similarities. In addition to the NIT assumption, further simplifying assumptions can be made to linearize equations describing gas and solid phase concentrations. For example, it is often assumed that the mass transfer film coefficient and the effective adsorbent diffusitivity are constant.

Assuming a polynomial of second order as the deriving force for mass transfer, the rate of change of adsorbate mole fraction (volume concentration) at the bed outlet can be written in the form of:

with boundary conditions: ( t = 0, C_o/C_i = 0), (t = t_s , C_o/C_i = 0.5) and lim (C_o/C_i) =

1 as t 6 4

Solution of eq. 4.6 is in the form of:

Yoon and Nelson (1984) used concepts of probability to relate the rate of mass transfer to the product of the probability for adsorption and probability for breakthrough and derived the same equation.

Using regression analysis for data range of 0.1 < C/C₀ < 0.9, optimum sets of K and t_s can be determined. This method was applied to model the BTCs for acetone and MEK. Table 4.5 provides the K and t_s values for each set of experiments. Figures 4.17-18 show the modeled BTCs. Very good agreement exists between modeled and experimental results.

Figure 4.17 Results of modeled breakthrough curves for acetone experiments

Figure 4.18 Results of modeled breakthrough curves for MEK experiments

Electrothermal Regeneration Experiments

After completion of each breakthrough test, the saturated ACFC fixed-bed was electrothermally regenerated. In a full-scale system, the fixed-bed can be conveniently made of several separate modules placed in series. This enables regeneration of each module in a fully saturated condition. Regeneration of a saturated bed increases the thermal efficiency of the condenser as well as increasing concentration of adsorbate during regeneration. Moreover, the adsorption capacity of the bed is also fully utilized and a TPR greater than 99% can be obtained.

Regeneration of Acetone from ACFC Fixed-Bed

The experimental setup for electrothermal regeneration tests is shown in Figure 3.12. Due to the high energy rates transferred to the adsorbate in this regeneration method, supersaturated vapor streams were produced at the stages of desorption. Supersaturation caused condensation in the pipelines downstream of the adsorber and affected the concentration measurement by the GC/FID and GC/MS. This problem was solved by diluting the desorption stream to a level below the saturation level with addition of a heated UHP N₂ stream. The concentrations of the resulting diluted mixtures were measured with the GC/FID by the same

procedure as discussed before. The measured concentrations were corrected using:

(4.8)

Where C_c = concentration of the concentrated TVOC, C_d = diluted TVOC concentration, Q_N2,t = Q_N2,d + Q_N2,c = total nitrogen in the diluted stream, Q_N2,c = flow rate of nitrogen carrier gas in the fixed-bed, Q_N2,d = flow rate of dilution nitrogen added to effluent.

Regeneration tests for a saturated fixed bed of ACFC were performed to evaluate the effect of applied electrical power (Figure 4.19). N₂ gas flow rate through the bed was controlled at 1 slpm for three tests and 0.5 slpm for two tests. Electrical voltage for each test was set at select values to observe the effect of applied electrical power profile on the resulting effluent TVOC concentration and bed temperature profiles. Effluent maximum TVOC concentrations during desorption ranged from 18% to 63% by volume. TVOC concentration profile and desorption time were readily controlled by carrier gas flow rate and applied electrical power. Increasing TVOC concentration was observed with decreasing carrier gas flow rate and increasing applied power. Figure 4.20 shows the temperature profiles measured at different locations of the bed. The temperature profiles shown in Figure 4.19 display the temperature history at port D, the location of maximum temperature during regeneration. In all five tests, more than 65% of the adsorbed acetone was regenerated at a bed maximum temperature of < 50 EC and an effluent concentration of > 10% by volume. During this time, gas phase bulk temperature change was minimal (< 10EC). Low temperature changes are indicative of an efficient energy transfer.

Figure 4.19 Regeneration results for desorption of acetone from ACFC fixed-bed

Mass of acetone desorbed was calculated by numerical integration of the concentration profiles in the form of:

(4.9)

Applied energy was calculated by integration of the power from experimental data, where: v = voltage, i = current, and E_t = energy applied until time t. Note that due to assumption of ideal gas in the above equations, some inaccuracies might be introduced for high concentration values. Mass desorbed and energy supplied as functions of time are presented in Figures 4.21-22. The profiles that are marked as I, IV, and V provide supersaturated concentration. These profiles show 30-35% less mass desorption than the initial amount of adsorption. The difference between initial amount of adsorption and final amount of desorption was less than 10% for the profiles marked as II and III. The maximum concentration levels of these two profiles were less than the saturation vapor pressure. Another hypothesis for the observed mass loss might be due to dissociation of adsorbate on the surface of ACFC when high electrical power is supplied to the bed. This problem should be further investigated in the future. If these reasons are the cause of the differential mass measured, it is better to normalize the regeneration curves based on total mass desorbed at a baseline steady-state condition. Figures 4.23-24 show such curves.

As the results indicate, increasing carrier gas flow rate increases desorption rate but reduces concentration of acetone in the gas stream. Increasing electrical power increases both desorption rate and acetone concentration. Therefore, it should be possible to find an optimum set of conditions for electrical power, carrier gas flow rate, and temperature to minimize the overall energy consumption of the system.

Table 4.6 summarizes the conditions of the acetone regeneration experiments and key points derived or calculated from the experimental results.

Regeneration of MEK from ACFC Fixed-Bed

The experimental setup and dilution process was the same as those for the acetone experiments. Regeneration results for desorption of MEK from ACFC-fixed-bed are presented in Figures 4.25-28 and Table 4.7.

Figure 4.22 Normalized mass desorbed and cumulative energy consumed as a function of time for acetoneexperiments. Nitrogen flow rate = 1 slpm

Figure 4.23 Corrected normalized mass desorbed and cumulative energy consumed as a function of time for acetone experiments. Nitrogen flow rate = 0.5 slpm

 

Figure 4.24 Corrected normalized mass desorbed and cumulative energy consumed as a function of time for acetone experiments. Nitrogen flow rate = 1 slpm

Figure 4.26 Normalized mass desorbed and cumulative energy consumed as a function of time for MEK experiments

Figure 4.27 ACFC fixed-bed temperature history as a function of sampling location for desorption of MEK, profile II

The ACFC fixed-bed was regenerated with less electrical power to avoid overheating the bed. Due to higher MEK molar energy of adsorption, more electrical power was required to produce high concentration levels comparable to the ones observed for the acetone experiments. Higher supplied electrical power for profile III resulted in lower concentration levels and different shapes of concentration profile. This might be due to dissociation or polymerization of MEK on the surface of ACFC that needed further investigation.

Effect of Electrothermal Regeneration on the ACFC

Effect of electrothermal regeneration on the physical properties of the ACFC was judged by measuring specific surface area and effective micropore volume of the ACFC samples after up to 50 adsorption/desorption cycles. The measurements were done after every ten cycles. These evaluations were done on a single layer of ACFC attached to electrodes in a glass reactivation cell (Figure 4.29) developed and operated by Brett Covington of the University of Illinois.

Figure 4.29 Schematic of the setup for the cyclic adsorption/electrothermal regeneration experiments

The glass test cell was 40 cm long and 1.7 liters in volume with two opposing aluminum electrodes that act to support the cloth sample as well as provide electrical connections. A Variac, (model W10MT3), provided a potential difference across the sample and current was monitored by a Fluke 77 multimeter. The bulk temperature of the ACFC was monitored by a type K thermocouple detected by a digital multimeter (Omega 881C). Laboratory grade N₂ (99.95 % pure) was used to purge air and contaminants from the test cell.

The ACFC layer was saturated with the TVOC and then regenerated electrothermally. During the regeneration, N₂ flow was set at 0.5 lpm and the sample was heated at a bulk sample temperature of 140 " 10°C for 20 min. This required a voltage between 8 and 12 volts and a current between 0.7 and 1.1 amperes for a typical sample of 100 to 150 mg. This procedure was repeated up to 50 cycles. The samples were analyzed using the Micromeritics ASAP 2400 surface area analyzer to determine the specific surface areas and micropore volumes after the completion of 10, 20, 30, and 50 cycles. The baseline for surface areas and pore volumes were determined by analyzing the ACFC samples prior to the start of adsorption/desorption cycles. The measured N₂ isotherms were converted into specific surface area and effective micropore volume by use of the BET (Brunauer et al., 1938), DR (Dubinin, 1989), and Harkins Jura (HJ) (Harkins and Jura, 1943, Lowell and Shields, 1984) equations.

Acetone and benzene were used for these experiments. For the benzene tests, the changes in the adsorption properties of the ACC-5092-20 were 2.2 % increase for BET specific surface area and 2.4 % increase for HJ effective micropore volume for the 12 hour electrothermaly regenerated sample, 2.6 % increase for BET specific surface area and 3.1 % increase for HJ effective micropore volume for 50 cycles. For the acetone tests, the changes in the adsorption properties of the ACC-5092-20 were 3.9 % increase for BET specific surface area and 3.8 % for single point effective micropore volume for 50 cycles. All of these values were within the experimental error of 5.5% for BET specific surface area and 8.4 % for HJ effective micropore volume. For benzene tests, the largest changes were an increase in the BET specific surface area by 7.7 % and the HJ effective micropore volume by 8.49 %. Likewise the cycles of acetone saturation with electrothermal regeneration showed similar results with surface area increase of 3.9 % and single point effective micropore volume increase of 3.8 %. These variations can be considered negligible when compared to error values of more than 10 % reported by Dubinin (1989).

Cryogenic Condensation Modeling

The Wagner equation (equation 3.2) provides a method to determine the TVOC saturation concentration based on a given temperature assuming vapor/liquid equilibrium. In order to apply the Wagner equation, temperature needs to be determined and sufficient condenser surface area must exist for the TVOC vapor to reach equilibrium with its liquid condensate. Fundamental numerical modeling provides a method to determine condenser temperature and equilibrium conditions based solely on gas stream, refrigerant and condenser characteristics.

Two levels of modeling are considered: 1) thermodynamic coupled with the Wagner equation (Appendix C) and 2) mass transfer (Appendix D). Thermodynamic modeling provides outlet TVOC vapor concentration, required refrigerant flow rate and final condenser temperature assuming no heat or mass transfer resistance and equilibrium conditions. Mass transfer modeling incorporates mass transfer resistances into the thermodynamic model. However, such an approach assumes no heat transfer resistance. The condenser surface area required to reach a desired outlet TVOC concentration equilibrium can be obtained with this technique. The minimum TVOC gas phase concentration occurs at a condenser surface area in which equilibrium between the liquid condensate and the vapor is achieved.

Thermodynamic Model

Thermodynamic modeling coupled with the Wagner equation provides a predictive method to determine outlet TVOC concentrations, required refrigerant flow rates and final condenser temperature. This model is based on equilibrium and assumes no heat loss. This model does not provide condenser sizing information (e.g., condenser surface area). The model balances the latent and sensible heat gained by the LN₂ refrigerant with the latent heat of condensation lost by the organic vapor, the sensible heat lost by the vapor laden gas stream and the sensible heat lost by the condensate film.

The thermodynamic model is developed for condensation of VOCs in a non-condensable carrier gas. The following assumptions are made in the development of the model:

1) Thermodynamic equilibrium between the refrigerant and challenge gas stream is achieved,

2) no mass or heat transfer resistance, and

3) no system heat loss except from condensate wash-out.

The energy balance equation can be obtained from the first law of thermodynamics. The energy gained by the refrigerant equals the energy lost by the challenge gas stream. One benefit of cryogenic condensation is that the latent heat of vaporization for LN₂, as well as the specific heat change of the gaseous N₂, is an available heat sink (Figure 4.30). The first law of thermodynamics can be stated in words for this system as:

where,

m_LN2 = mass flow rate of liquid nitrogen

Dh_LN2 = enthalpy of vaporization for LN₂

m_GN2 = mass flow rate of gaseous N₂

C_p,N2 = specific heat of carrier gas

m_LA = mass flow rate of condensed VOC

Dh_A = enthalpy of condensation for VOC

m_A-N2 = mass flow rate of carrier gas and TVOC gas stream

C_p,A-N2 = combined specific heat of carrier gas and TVOC vapor

C_p,LA = specific heat of TVOC liquid condensate

T1 = temperature of LN₂ (77.4 K)

T2 = final temperature of the LN₂ refrigerant and carrier gas and TVOC gas stream

T3 = initial temperature of the challenge gas stream.

Condenser surface area based on heat transfer can be estimated from (USEPA^b, 1991):

where,

A_con = condenser surface area

H_load = heat load determined from the enthalpy loss of the vapor and carrier gas

U = assumed overall transfer coefficient, 20 BTU/hr ft² EF (from USEPA^b, 1991)

DT_LM = log-mean temperature difference between coolant, vapor and equilibrium temperatures

Figure 4.30 Schematic of thermodynamic model element

 

The thermodynamic model is coupled with the Wagner equation (eq. 3.2) to provide the saturation concentration at the equilibrium temperature. The complete model including mass and flow conservation is listed in Appendix C and was written in EES version 3.7. The model is written for LN₂ refrigerant and acetone in N₂ challenge gas stream. To analyze other VOCs or carrier gas streams, only the gas and liquid material properties need to be changed. A wide variety of material properties for many gases and liquids can be found in Reid et al. (1977).

Results of the thermodynamic model are presented with experimental data in this section. For design purposes, the model can be used to estimate LN₂ requirements, removal efficiency, outlet TVOC concentrations and outlet gas temperature. The typical input data required are inlet temperature, inlet gas flow rate, inlet concentration and inlet gas temperature. However, a wide variety of variables can be evaluated. For instance, a required removal efficiency may be input to determine the required LN₂ refrigerant flow rate.

 

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