On the Limita+ons of Breakthrough Curve Analysis in Fixed- Bed Adsorp+on Jim Knox Knox, J. C.; Ebner, A. D.; LeVan, M. D.; Coker, R. F.; Ri:er, J. A., Limita<ons of Breakthrough Curve Analysis in Fixed- Bed Adsorp<on. Ind Eng Chem Res.
Introduc+on Fixed Beds used for Separa<on via Gas Adsorp<on in Numerous Applica<ons, for example: Chemical processing industry (petrochemicals, foods, medicines, etc.) Thermochemical energy storage DOE funded efforts to develop affordable flue gas CO capture systems Atmospheric control in habitable volumes Generally mul<ple bed cyclic processes such as pressure swing adsorp<on (PSA) or temperature swing adsorp<on (TSA) Direct simula<on of the highly random sorbent par<cle packing and small- scale features of the flow between par<cles in a fixed- bed is CPU intensive To achieve cyclic steady- state in a process simula<on, as required for process design, - D models are u<lized //
Fluid flow in a packed bed studies in catalyst reactor design Dixon AG, Nijemeisland M, S<: EH. Packed Tubular Reactor Modeling and Catalyst Design using Computa<onal Fluid Dynamics. In: Guy BM, ed. Advances in Chemical Engineering. Vol Volume 3: Academic Press; :37-39. Behnam M, Dixon AG, Nijemeisland M, S<: EH. A New Approach to Fixed Bed Radial Heat Transfer Modeling Using Velocity Fields from Computa<onal Fluid Dynamics Simula<ons. Ind Eng Chem Res. 3// 3;5():5-5 // 3
Principle Equa+ons in - D Model c t + ε ε q t D c L x = υ c i x q t = k n (q* q) T T T εa ρ c εa k εa ρ υc a a h T T Ph T T t x x f f f f f pf f eff = f f i pf + f s s s f + i i w f ( ε)ρ s c ps T s t = a f a s h s ( T f T s ) ( ε)a f λ q t ( ) ( ) Pe = D ε υr p + = ReSc + Pe =.73ε ReSc + + 3.73ε ReSc c p = a o + a T f + a T f + a 3 T f 3.377 < R p <.7 cm h i = k f Nu with Nu =.3Re. exp R p R i Sh = +.Sc 3 Re. h s = ShD R p R i a w ρ w c pw T w t T a w k w w x = p h T i i ( f T w ) + P o h o ( T a T w ) k e = k f k s k f n k with n =..757log ε.57log s k f n = ap + (bp) t ; b = b exp(e / T ); a = a exp(e / T ); t = t + c / T /t k k eff = k e f +.75PrRe k f where Pr = c pµ ρ f k f All variables in Mass and Heat Balance Equa<ons are determined except D L, k n, and h o //
Virtual Adsorp+on Test Suite Matlab/COMSOL Component: Inputs engineering data from actual or proposed test (breakthrough or cyclic) Based on inlet condi<ons, calculates gas proper<es required for heat and mass transfer correla<ons Builds requested PDE- based model with specified grid spacing, <me steps, cycles etc. Hands off model to COMSOL Mul<physics (used as PDE Solver) for execu<on and retrieves results when complete Has been used with NASA X- TOOLSS (gene<c algorithms) for parameter op<miza<on Allows for mul<- variable parametric runs, and compares SSR of results vs. test data for parameter op<miza<on Generates paper- ready plots including plot over of test data Mathcad Component: Provides independent verifica<on of all calcula<ons in Matlab component Provides sensi<vity analysis of correla<ons to temperature and concentra<on changes expected during a simula<on // 5
Virtual Adsorp+on Test Suite Interface //
Experimental Results for H O on 5A AA 5 cm. cm.7 cm.7 cm. cm T S, T S, T S, T T (a) AA R. 5. cm Thermocouple Probe View AA Sampling Tube (b) How to independently derive free parameters? // 7
Step : Wall to Ambient Heat Transfer Coefficient 39 3. 37 Sum of Square Residuals..........3..5..7. CanAmbH, W/(m K) 3 35 3 33 Inlet Mid 3 3 3 Exit 3% 5% 9% 9......... h o is empirically derived via a Thermal Characteriza<on Test //
Gas Concentration (mol/m 3 ).3.5..5..5 Step : Linear Driving Force Mass Transfer Coefficient SSE.5.3..9.7.5.3. -..5.7.9..3.5.7 LDF (/s).5.5.5 Axial Disperson per E-R Axial Disperson per W-F Gas Concentration (mol/m 3 ).3.5..5..5 Diamonds: experimental data; dashed lines: simulations with the Edwards and Richardson correlation for axial dispersion and corresponding k n values; dotted lines: simulations with the Wakao and Funazkri correlation for axial dispersion and corresponding k n values..7.75..5.9.95..5. Fits of the -D axial dispersed plug flow model to the 97.5% location (diamonds) experimental centerline gas-phase concentration breakthrough curves for CO (left) and HO vapor (right) on zeolite 5A, and corresponding predictions from the model of the.5% (circles) and 5% (squares) locations. The saturation term in the CO-zeolite 5A isotherm was increased by 5%. The saturation term in the H O vaporzeolite 5A isotherm was decreased by 3%. The void fraction was reduced to.33 based on the Cheng distribution (Cheng et al., 99) with C =. and N = 5, as recommended by Nield and Bejan (99) k n is empirically derived via fijng to centerline concentra<on breakthough curve. For this step, dispersion is taken to // result from pellet effects only (no wall effects). Choice of dispersion correla<on has a small impact on k n 9 Sum of Squared Errors.35.3.5..5..5 E-R LDF Fit W-F LDF Fit LDF coefficient (/s)
Step 3: Axial Dispersion Coefficient (CO Case) Gas Concentration (mol/m 3 ).3.5..5..5.5.5..35.3.5..5.5.7.9..3.5.7.9. Axial Dispersion.5.5.5 Slope of Gas Concentration (mol/m 3 /s) 3 -.5.5 9.5.5 CO on zeolite 5A: Fit of the -D axial dispersed plug flow model to the outside bed (triangles) experimental breakthrough curve using a value of D L 7 times greater than that from the Wakao and Funazkri correlation and the fitted LDF k n =.3 s - (left panel). The reported saturation term for the CO -zeolite 5A isotherm was used, along with the reported void fraction of.35. Predictions from the model (lines) of the gas-phase concentration breakthrough curves at,,,,, 9, 9 and % locations in the bed are also shown in the left panel, along with the.5% (circles), 5% (squares) and 97.5% location (diamonds) experimental center line gas-phase concentration breakthrough curves (left panel). The corresponding derivative (or slope) of the predicted gas-phase concentration breakthrough curves in the bed are shown in the middle panel. Predictions from the model (lines) of the.5% (circles), 5% (squares) and 97.5% location (diamonds) experimental center line temperature profile histories are shown in the right panel. D L term is fit to mixed gas concentra<on (far downstream), but requires value 7 <mes the correla<on value to compensate for wall channeling. Fit is specific to the size of the column; for a much larger column wall channeling may be neglected and correlated values of D L used (but not for fixed beds with a tube to pellet ra<o of as in this case, or less ) // 3 3 3 3 3 3 9
Step 3: Axial Dispersion Coefficient (H O Case) Gas Concentration (mol/m 3 ).3.5..5..5 Sum of Squared Errors 5 3.5..5..5 DL coefficient (m/s ) 35 3 35 3 H O vapor on zeolite 5A: Predictions from the -D axial dispersed plug flow model of the outside the bed (triangles) experimental breakthrough curve when varying the value of D L. D L = (dotted lines), 3 (dashed lines), 5 (solid lines) and 7 (dash-dot lines) times greater than Wakao and Funazkri correlation with the LDF k n =.3 s - (left panel). The reported saturation term for the H O-zeolite 5A isotherm was used, along with the reported void fraction of.35. The corresponding predictions from the model (lines) of the.5% (circles), 5% (squares) and 97.5% location (diamonds) experimental center line temperature profile histories are shown in the right panel. D L term is fit to mixed gas concentra<on (far downstream), but requires value 5(!) <mes the correla<on value to compensate for wall channeling. However the temperature profiles deviate increasingly from the test data with increasing D L indica<ng a breakdown of the axial dispersed plug flow model. // 95
Breakthrough Sharpening and Breakdown of Constant PaXern Behavior Increasing DL. Run ID = W-F.35 void DL at 3X, Model Name = PDE, Solver = FC Increasing DL. Run ID = W-F.35 void DL at X, Model Name = PDE, Solver = FC. X.5.. 95..5. 7X.5 7 5 3 3 35 3 95 3X 3.5 3.5.5 9.5..5. 5X 3 35 3 95.5 9 Increasing DL. Run ID = W-F.35 void DL at 5X, Model Name = PDE, Solver = FC Time (hours).3.5. 35-5 (d) 35.5 5.5 3 Slope of Gas Concentration (mol/m 3 /s) Gas Concentration (mol/m3 ).5..5. 9 Increasing DL. Run ID = W-F.35 void Time DL at 7X, Model Name = PDE, Solver = FC (hours).3 3. -5 (b) 35 Gas Concentration (mol/m3 ) 3 3.5..5 Slope of Gas Concentration (mol/m 3 /s)...3 Slope of Gas Concentration (mol/m 3 /s).5 (c) 35. Gas Concentration (mol/m3 ) Slope of Gas Concentration (mol/m 3 /s) Gas Concentration (mol/m3 ).3 (a) -5 3 3 35 3.5 -. 3.5.5 3 35 3 95.5 9 Input= Values: Ads Initial TempCS = 3.35[degC]; Ads Inlet Temp =.35[degC]; Ads Initial Conc =.[mol/m^3]; Ads Initial Load = [mol/m^3]; Free Flow Area = 7.[cm Input Values: Ads Initial Temp = 3.35[degC]; Ads Inlet Temp =.35[degC]; Ads Initial Conc =.[mol/m^3]; Ads Initial Load = [mol/m^3]; Free Flow Area 7.[cm^]; Canister Area =.5[cm^]; Can Time TimeWall (hours) (hours) Time (hours) TimeWall (hours) Inner Perimeter =.9[cm]; Can Outer Perimeter Void Fraction = ; Can Cond =.[W/(m*K)]; Can Q Ca Inner Perimeter =.9[cm]; Can Outer(hours) Perimeter = 5.9[cm]; Bed Length =.5[m]; Void Fraction =.35; Void Fraction = ; Can Cond =.[W/(m*K)]; Can Q Capac =Time 75[J/(kg*K)]; Can Density == 5.9[cm]; Bed Length =.5[m]; Void Fraction =.35; 733[kg/m^3]; Ambient Temp =.[degc]; Can-Amb H =.5[W/(m^*K)]; Part Density = [kg/m^3]; Mass Trans Coeff =.3[/s]; Sorb Q Cond =.[W/(m* 733[kg/m^3]; Ambient Temp =.[degc]; Can-Amb H =.5[W/(m^*K)]; Part Density = [kg/m^3]; Mass Trans Coeff =.3[/s]; Sorb Q Cond =.[W/(m*K)]; Sorb Q Capac =.7[J/(kg*K)]; Heat of Ads = -5.[kJ/mol]; Length[s] = 3; Heat of Ads = -5.[kJ/mol]; Half-Cycle Length[s] = 3; Time Step[s] = 3; Node Sep Max =.[m]; Node Sep Init =.[m]; Ads Concentrat =.375[mol/m^3]; Gas Q Cap =Half-Cycle.[kJ/(kg*K)]; Axial Cond Time Step[s] = 3; Node Sep Max =.[m]; Node Sep Init =.[m]; Ads Concentrat =.375[mol/m^3]; G =.95[W/(m*K)]; Cap =.97[kJ/(kg*K)]; Sorb-Gas H =.3335[W/(m^*K)]; Gas-Can H = 9.97[W/(m^*K)]; Ads Axial Disp =.75[m^/s]; Ads T =.95[W/(m*K)]; Sorbate Q Cap =.97[kJ/(kg*K)]; Sorb-Gas H =.3335[W/(m^*K)]; Gas-Can H = 9.97[W/(m^*K)]; Ads Axial Disp =.5[m^/s]; Ads TotalSorbate Press = Q.5[kPa]; Ads Gas.[kg/m^3]; Ads Superfic VelE==.[m/s]; Dens =.[kg/m^3]; Ads Superfic Vel =.[m/s]; Equiv Pellet Dia =.3[mm]; Area to Vol ratio =.7[/m]; Toth a =.e-[mol/kg/kpa];=toth b =.7e-[/kPa]; Toth 9955[K]; TothEquiv to = Pellet Dia =.3[mm]; Area to Vol ratio =.7[/m]; Toth a =.e-[mol/kg/kpa]; Toth b =.7e-[ L L.35; Toth c = -5.[K];.35; Toth c = -5.[K]; HO vapor on zeolite 5A: Predictions from the model (lines) shown in Figure 9 of the gas-phase concentration breakthrough curves at,,,,, 9, 9 and % locations in the bed (left panels). The.5% (circles), 5% (squares) and 97.5% location (diamonds) experimental centerline gas-phase concentration breakthrough curves are also shown for comparison in the left panels. The corresponding derivatives (or slopes) of the gas-phase concentration breakthrough curves in the bed are shown in the right panels. (a) D = Wakao-Funazkri correlation, and (b) D = 7, (c) 3 and (d) 5 times greater than Wakao and Funazkri correlation. At 7X, internal concentra<on history slope matches mixed concentra<on just as for CO case. This indicates that same dispersive mechanism occurs regardless of sorbate. To overcome non- physical breakthrough sharpening, DL // must be increased by 5X to decrease breakthrough slope. Expected CPB is lost en<rely for this condi<on.
Conclusions thus far: Breakthrough tests with tube diameter to pellet diameter ra<os of around (or less), are subject to wall channeling, an mechanism not captured in standard dispersive correla<ons. Breakthrough tests are generally subscale to conserve sorbent materials and gas flow equipment costs and thus frequently in this range. The typical breakthrough measurement is taken far downstream, aker mixing. FiAng the mass transfer coefficient to this measurement will provide erroneous results for a larger (or smaller) diameter column due to the influence of channeling. A method has been demonstrated where a centerline measurement is used to derive a mass transfer coefficient that captures physics free of wall effects and thus appropriate for scale- up to large diameter columns. Using the mass transfer coefficient derived above, this method uses the mixed concentra<on data for fijng of a dispersion coefficient D L specific to the tube diameter, as needed for processes that u<lize small diameter tubes. However fijng D L blindly to the breakthrough curve (as apparent in many published breakthrough analyses) can, in specific cases, result in a complete breakdown of the axially dispersed plug flow model, and result in fi:ed coefficients that are incorrect. Thus it is important to map the set of condi7ons where significant breakthrough sharpening occurs, and which will lead to a breakdown of the expected constant pa@ern behavior. This work is a topic for future discussion! // 3