An Experimental and Modeling Study of the Adsorption Equilibrium

Article pubs.acs.org/IECR

An Experimental and Modeling Study of the Adsorption Equilibrium and Dynamics of Water Vapor on Activated Carbon Max Hefti, Lisa Joss, Dorian Marx, and Marco Mazzotti* Institute of Process Engineering, ETH Zürich, Sonneggstrasse 3, CH-8092 Zürich, Switzerland S Supporting Information *

ABSTRACT: In this work, the adsorption of water vapor on a commercial activated carbon is studied by means of static and dynamic measurements. To this end, two customized setups are used, which are able to deal with the challenges associated with adsorption measurements under humid conditions. In the first part, the equilibrium of water vapor on activated carbon during adsorption and desorption at 45 °C is characterized. The equilibrium adsorbed amount of water vapor exhibits a pronounced hysteresis loop, requiring the use of an isotherm model with hysteresis to describe the data. In the second part, fixed-bed experiments for both adsorption and desorption conditions at three feed velocities are presented. These dynamic experiments are described by a nonisothermal detailed column model, which considers the linear driving force model for mass transfer and axial dispersion. Heat and mass transfer coefficients are estimated so as to describe the fixed-bed experiments. The results from the static and dynamic measurements are shown to be consistent with each other for both adsorption and desorption conditions, provided the hysteretic behavior of the adsorption equilibrium is considered. Finally, it is shown that the use of an average value for the mass transfer coefficient results in good agreement between experiment and simulation, and the improvement due to a more complex model is minimal.

1. INTRODUCTION Frequently, exhaust streams that are treated in gas adsorption processes contain water vapor, for example, carbon capture processes such as post- or pre-combustion CO2 capture. Merel et al.1 showed that a CO2 purity and recovery surpassing 80% is achievable with a cyclic temperature swing adsorption (TSA) process using zeolite 13X as sorbent material for postcombustion capture. Schell et al.2 reported a pressure swing adsorption (PSA) process to separate CO2 and H2 in the context of pre-combustion capture using activated carbon (AC) as sorbent material reaching similar purity and recovery. These studies, including many others,3−6 consider a feed stream where water vapor is absent, even though this does not necessarily reflect real conditions. The flue gas of gas- and coal-fired power plants may contain about 6% and 15% water vapor,7 respectively, while in pre-combustion capture, the feed stream to the CO2 separation PSA unit is usually saturated in water vapor at the exit temperature of the sulfur removal step.8 It is unlikely that water vapor could be co-fed into an adsorption process without a separate cycle to dry the flue gas in the case of very hydrophilic sorbents such as zeolite 13X while still reaching a reasonable energy consumption.9 Nevertheless, there is potential to avoid a separate drying step in processes using a sorbent that is less hydrophilic, for example, activated carbon (AC), because of the relatively low affinity toward water vapor at low relative humidity (RH). It is noteworthy that water vapor adsorption has not been studied more thoroughly, keeping in mind that it is a prominent impurity in these processes, usually interacting strongly with other components, in particular with CO2. From our point of view, there are mainly two reasons responsible: (i) detailed equilibrium data are either of insufficient quality or absent altogether, implying a lack of the adsorption isotherm needed © XXXX American Chemical Society

in process simulations; and (ii) the competitive behavior with respect to the other species cannot be described using standard models, for example, using ideal adsorbed solution theory.10 The objective of this work is to address the first challenge: An extensive and detailed experimental and modeling study of the behavior of water vapor on AC is presented covering both adsorption equilibrium and kinetic related aspects. Thus, this work should enable others to make use of an experimentally validated set of isotherm parameters and mass transfer coefficients in adsorption-based process simulations involving water vapor and AC. 1.1. Literature Overview. Adsorption equilibrium of water vapor on AC has been studied by a number of researchers,11−21 unanimously showing that water vapor follows an S-shaped type IV or V isotherm. In addition, a hysteretic behavior is typically observed upon desorption.11,15 Fewer works report experimental data on the adsorption dynamics of water vapor on ACs, possibly due to the experimental challenges faced during the measurements. Foley et al.,22 Harding et al.,15 and Cossarutto et al.23 used gravimetric analyzers supplied by Hiden Analytical, UK, to determine sorption kinetics. Their results show that the adsorption and the desorption kinetics of water vapor on AC follow Glueckauf’s linear driving force (LDF) mass transfer rate law. Further, they report mass transfer rates varying over orders of magnitude and observe a hysteretic behavior also in the desorption kinetics. Very few studies have used fixed-bed experiments to gain insight into the adsorption dynamics of Received: September 15, 2015 Revised: November 10, 2015 Accepted: November 12, 2015

A

DOI: 10.1021/acs.iecr.5b03445 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

for the fixed-bed experiments (diameter 300 μm). The sorbent was regenerated under vacuum (static measurements) or under helium (He) flow (fixed-bed experiments) at 150 °C prior to the experiments. As reported in Schell et al.,33 such temperature is sufficient for drying and regeneration of the sorbent. The carrier gas used in this study was obtained from Pangas, Switzerland, at a purity of 99.996% for He. Deionized and purified water (Millipore) was used as a source of water vapor. 2.2. Static Measurements. The static experiments were performed in a custom-built setup.34 At its core is a Rubotherm magnetic suspension balance (MSB) (Rubotherm, Germany), which is located for the sake of measurement accuracy in a circulation loop, as shown schematically in Figure 1. The pump

water vapor and AC. Qi et al.24 measured breakthrough curves of water vapor on AC at one feed velocity under adsorption conditions, and they were able to describe them by using an empirical adsorption loading-dependent expression for the mass transfer coefficient within the LDF model. Ribeiro et al.25 reported adsorption breakthrough curves of water vapor on AC at one feed velocity assuming isothermal behavior; they, too, used a loading-dependent mass transfer coefficient for the LDF model. Ribeiro et al.26 investigated the dynamics of water vapor on carbon molecular sieves; they presented fixed-bed experiments under adsorption conditions and a TSA process investigating thermal and electrical regeneration conditions. They used a temperature-dependent expression for the mass transfer coefficient within the LDF model. Narayan et al.27 performed measurements of the adsorption kinetics of water vapor in AC beds by observing the mass change of the bed at different values of RH; unfortunately, very little detail concerning their measurement protocol is available. A compilation of available literature on the dynamics of water vapor on AC is provided in Table 1. Table 1. List of References in Which the Dynamics of Water Vapor Adsorption on Activated Carbon Is Investigateda reference

experimental method

mass transfer model

Deitz30 Lin and Nazaroff32 Foley et al.22 Harding et al.15 Cossarutto et al.23 Narayan et al.27 Qi et al.24 Ribeiro et al.25

uptake meas uptake meas uptake meas uptake meas uptake meas uptake meas fixed-bed fixed-bed

Damköhler31 Lin and Nazaroff32 LDF LDF LDF LDF (MTC constant) LDF (MTC loading dependent) LDF (MTC loading dependent)

Figure 1. Schematic of the static setup. All of the piping and the valves are wrapped with heating wire and insulated. The gray-shaded areas indicate the locations of the thermostats. Abbreviations: rH-o, capacitive relative humidity sensor; TI, temperature indicator (thermocouple); rH-n, chilled mirror dew point sensor; PI-L, pressure indicator for pressures up to 3 bar; PI-H, PI for pressures up to 300 bar; MSB, magnetic suspension balance.

a

Abbreviations: meas = measurement; LDF = linear driving force; MTC = mass transfer coefficient.

(built in house at ETH Zürich) circulates the gas through a water tank, the temperature of which is controlled by a thermostat (Julabo, Germany). Adjusting this temperature allows one to change the water partial pressure in the gas phase, and thus the desired adsorption or desorption conditions can be attained. The water content of the gas phase is measured with a chilled mirror dew point sensor (Michell Instruments, France), operable up to a pressure of 20 bar and with an accuracy of 0.2 °C in dew point temperature. The uptake of water vapor on the AC is measured using the MSB with an accuracy of the measurement of 10 μg. The temperature is controlled with a heating jacket surrounding the measuring cell. Moreover, the temperature is measured inside the chamber of the balance using a thermocouple with an accuracy of 0.1 °C.35 When the relative change in the weight of the sample becomes small over an extended period of time, typically more than 1 h, the water tank is circumvented and the gas is circulated in the inner loop, as indicated in Figure 1. A data point is taken when both weight and dew point temperature are constant. Critical for a meaningful measurement is the avoidance of condensation. For this purpose, the entire piping and all valves were wrapped with flexible heating wire and insulated. The circulation pump is immersed in a water bath (Huber Kältemaschinenbau, Germany) that is held at sufficiently high temperature. 2.3. Fixed-Bed Experiments. Fixed-bed experiments were performed using the in-house built setup shown in Figure 2. It

In summary, literature on fixed-bed experiments of water vapor on AC under adsorption conditions is scarce, and, to the best of our knowledge no such experiments for the desorption of water vapor on AC exhibiting a large hysteresis loop have been reported. This is surprising because the loading behavior of water vapor on AC is typically of hysteretic nature; that is, the adsorbent loading and regeneration follow different paths in the space with the adsorbed phase concentration and the water vapor partial pressure as coordinates. 1.2. Outline. This article is organized as follows: Equilibrium data of both adsorption and desorption measured in a customized setup are presented and modeled using a sorption isotherm with hysteresis. Next, fixed-bed experiments at different feed velocities are reported. A detailed columnmodel developed in previous works28,29 is used to describe quantitatively the experiments, allowing the estimation of heat and mass transfer parameters. Finally, the effect of mass transfer models on the quality of the description of the experiments using the column-model is investigated.

2. EXPERIMENTAL METHODS 2.1. Materials. Commercial activated carbon (AC) AP 3-60 from Chemviron Carbon (Beverungen, Germany) is used as sorbent material in this study. The AC particles were used as supplied (diameter 3 mm; cylindrical) in the static measurements, while they had to be crushed to pack the column used B


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Figure 2. Flowsheet of the experimental fixed-bed setup. Abbreviations used: MFC, mass flow controller; LFM, liquid flow meter; CEM, controlled evaporative mixing; BT, buffer tank; TI, temperature indicator (thermocouple); PI, pressure indicator; BPR, back pressure regulator; RHI, relative humidity sensor; MS, mass spectrometer.

has been described in a previous work36 when used to perform step response experiments under dry conditions. Optionally, the feeding system is operated so that the inlet flow is humidified, which is achieved through a liquid flow meter (Bronkhorst, Switzerland) operating in the range of 90−1800 mg/h. This draws liquid water from a pressurized water tank (6 bar) and delivers the desired amount to a Controlled Evaporation Mixing (CEM) system (Bronkhorst, Switzerland), where the liquid is dispersed, mixed with the carrier gas, and vaporized. The gas stream is controlled via a mass flow controller (MFC) (Bronkhorst, Switzerland) operating in the range of 5−250 N mL/min. A heated buffer tank (750 mL) is placed at the exit of the CEM to damp any variations in water content and ensure a constant RH. The pressure is measured (Keller, Germany) upstream of the column and is adjusted via a back pressure regulator (EL-LF1, Equilibar, U.S.). The stainless steel adsorption column filled with AC is located in a furnace (Memmert UNE-200, Germany) operable between 25 and 300 °C, thus allowing for full regeneration of the sorbent inside the column before each experiment. The piping up- and downstream of the adsorption column is heated electrically (Horst, Germany) to avoid condensation. The temperature of the feed is measured by a first thermocouple (Moser TMT, Switzerland) upstream of the column, and by a second thermocouple located along the axis of the adsorption column and in the middle of it. The moisture content of the outlet stream is measured using a RH sensor (Rotronic, Switzerland), which is kept at a temperature of roughly 5 °C above the column temperature via an electric heating wire. Additionally, the gas can be analyzed by a mass spectrometer (MS) (OmniStar, Pfeiffer Vacuum, Switzerland). 2.4. Experimental Uncertainty. To assess the accuracy of the measured and calculated quantities, it is important to estimate their uncertainties. This is done by taking into account the error in each measurement taken, and how it propagates to influence the uncertainty of the quantity of interest. The uncertainties of the directly measurable quantities for both the static and the dynamic experiments are listed in Table S1 of the Supporting Information. The errors were approximated through the first-order variance approximation also known as the error propagation law for uncorrelated measurables.37

3. MODELING 3.1. Isotherm Model. To model the sorption equilibrium of water vapor on AC during adsorption and desorption, a sorption isotherm model with hysteresis has to be used. The independent variable is the RH, called x in the model equations and defined between 0 and 1 (x = 1 corresponds to 100% RH). Such a model consists of an adsorption branch, labeled with the subscript “A”, and a desorption branch, labeled with the subscript “D”. The hysteresis loop is delimited by the lower and the upper closure points, which define the range of validity of the desorption branch. At the lower closure point, the adsorbed amount is nL at the relative humidity xL, while at the upper closure point, the adsorbed amount is nU at the relative humdity xU. The general definition of the isotherm model is therefore given by adsorption:

n(x) = nA (x)

0≤x≤1

⎧ 0 ≤ x < x L or x U ≤ x ≤ 1 ⎪ nA (x) desorption: n(x) = ⎨ ⎪ xL ≤ x ≤ xU ⎩ nD(x) with

nD(x L) = nA (x L) = nL nD(x U) = nA (x U) = nU (1)

We refer to a previous study29 and to the work by Štěpánek et al.38 for a more detailed description on how to model hysteresis-dependent isotherms. It is assumed that the temperature dependence of the isotherm can be described through the variation of the vapor pressure with temperature, thus implying that the heat of adsorption equals the heat of condensation.26,39,40 This allows one to write the adsorption model in terms of the RH only, and not explicitly as a function of temperature. The adsorption isotherm consists of two contributions, one term that describes the uptake of water vapor by the functional groups and the successive clustering of water molecules around these sites, ns(x), and a second term describing the uptake in the capillary condensation region, nμ(x), that is, at medium to high RH. Closely based upon the development of the isotherm model presented by Do and Do,41 we use a similar expression for the adsorption isotherm: C


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where Nexp, Nv, and Np are the number of experiments, number of observed variables, and number of observations y, respectively. The superscript “max” indicates the maximum value of the vector y. The hat symbol indicates the estimated outputs using the parameter estimate θ. In our case, the observed variables are the mole fraction at the column exit and the temperature at midlength of the column in the case of the fixed-bed experiment and the adsorbed amount in case of the equilibrium measurements. Minimization of Φ was carried out using the Matlab-based routine “fminsearchbnd” (Copyright 2006, John D’Errico). The fitted parameters for the fixed-bed experiments were the mass transfer coefficient, kH2O, and the heat transfer coefficient from the wall to the ambient heat reservoir (oven), hW. To obtain significant transport parameters, it is important that the fixed-bed times are described with sufficient accuracy. It was demonstrated in previous works28,43 that the feed velocity had to be regarded as a model parameter to be estimated along with the transport parameters, due to the magnitude of the unavoidable uncertainty associated with the mass flow controller. To this aim, the feed velocity for each experiment was estimated, although the estimated value had to stay within the range of experimental uncertainty, which was determined according to the methodology described in section 2.4.

nA (x) = ns(x) + nμ(x) = nμ∞,ama Kμ ,ax ma ns∞K sx + (1 − Kcx)(1 + (K s − Kc)x) 1 + Kμ ,ax ma

(2)

∞ where n∞ s and nμ,a are the capacities associated with the functional groups and the pores, respectively, ma is the average number of molecules comprising a cluster, and Ks, Kc, and Kμ,a are equilibrium constants. To describe desorption in the hysteresis region, the following expression is proposed for nD:

nD(x) = ns(x) +

nμ∞,dmd Kμ ,dx md 1 + Kμ ,dx md

(3)

where n∞ μ,d, md, and Kμ,d are parameters specific for desorption, while ns(x) is the same term as used in the expression for the adsorption branch, thus implying that the same parameters n∞ s , Ks, and Kc are used. Overall the model depends on nine parameters; this is reasonable considering that (i) the shape of the isotherm is rather complex; (ii) both adsorption and desorption branches are described; and (iii) no additional parameters to describe the temperature dependence are required. It is worth noting that the functional form in eq 3 is slightly modified as compared to our previous modeling study,29 because in the meantime we have been able to obtain a much better description of the desorption branch for the real system considered in this work. 3.2. Column Model. The one-dimensional column model consisting of mass, energy, and momentum balances was described in detail in previous works.28,29 A summary of the equations is reported in Table S2 of the Supporting Information. The system of partial differential equations (PDEs) is discretized along the space coordinate using the finite volume technique and the VanLeer flux limiter, yielding a system of ordinary differential equations (ODEs). Note that with reference to the equations shown in Table S2 of the Supporting Information, the number of components considered in this work is N = 2, component 1 and 2 representing water vapor and He, respectively. Note that the relative humidity, x, used in eq 1 is equal to x = y1P/Pvap(T), where Pvap corresponds to the vapor pressure of water. As an important difference to previous works, the resulting system of ODEs was solved using the OPACK package developed by Hindmarsh42 at the Lawrence Livermore National Laboratory (U.S.); we noticed a significant improvement regarding computation time as compared to using the IVPAG solver from the IMSL library (RogueWave, U.S.). The column was simulated using 50 grid points for adsorbing conditions, while, due to the sharper fronts, 120 points were used for desorbing conditions. There are numerous parameters that need to be specified to fully describe the system; their values or the way they are determined as well as their origin are summarized in Table S3 of the Supporting Information. 3.3. Parameter Estimation. Model parameters were estimated by finding the maximum likelihood estimate (MLE):37 ⎛N ⎛ ⎞2 ⎞ ⎜ p ⎜ yijk − yijk̂ (θ ) ⎟ ⎟ 1 Φ(θ ) = ∑ ∑ ln⎜∑ ⎟ ⎟⎟ Nexp i = 1 j = 1 ⎜ k = 1 ⎜ y̲ max ⎠⎠ ij ⎝ ⎝

4. EQUILIBRIUM THEORY MODEL OF ADSORPTION 4.1. Background. Equilibrium theory (ET) is a modeling approach to describe and predict the dynamics of transitions in composition and velocity44,45 encountered in an adsorption column. ET is the de facto standard model used in liquid chromatography, and it is a valuable tool to better understand the dynamics in gas adsorption processes as well.46−48 Before presenting the main results of this work, it is useful to first introduce ET, give the governing equations, and then provide the ET solution for the system considered here, that is, water vapor on AC based on the isotherm model presented in section 3.1. It is worth noting that contrary to many studies where ET is applied, in this work the ET with nonconstant velocity as reported in Ortner et al.45 is solved, thus allowing the computation not only of the composition profiles, but also of the velocity profiles. 4.2. Governing Equations. The assumptions of ET are thermodynamic equilibrium between the solid and fluid phases, negligible dispersive effects, negligible pressure drop, and isothermal conditions. Applying this set of assumptions to the detailed column model, that is, the equations given in Table S2 of the Supporting Information, the component mass balances for water vapor (component 1) and helium (component 2) and the overall mass balance are obtained: ∂yi ∂t

+

∂(vyi ) ∂z

+

ρb ∂ni* =0 cεt ∂t

ρ ∂n * ∂v + b 1 =0 cεt ∂t ∂z

i = 1, 2

(5)

where v is the interstitial fluid velocity and c is the total concentration, that is, c = c1 + c2. Because water vapor is the only adsorbing component, n2* = 0, and due to the assumption of adsorption equilibrium, the time derivative of the adsorbed amount of water can be expressed as

Nexp Nv

(4) D


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Figure 3. Comparison of the equilibrium theory solution (solid lines) and the simulations using the detailed model under isothermal conditions (red dotted lines) and nonisothermal conditions (blue dashed lines) for the mole fraction of water vapor (A) and the normalized velocity, v/vfeed (B). The adsorption isotherm is shown as an inset, and the initial, intermediate state, and feed state are indicated with I, H, and F, respectively.

dn * ∂y ∂n1* = 1 1 dy1 ∂t ∂t

Figure 4. Comparison of the equilibrium theory solution (solid lines) and the simulations using the detailed model under isothermal conditions (red dotted lines) and nonisothermal conditions (blue dashed lines) for the mole fraction of water vapor (A) and the normalized velocity, v/vfeed (B). The desorption isotherm is shown as an inset, and the initial, intermediate states, and feed state are indicated with I, H1, H2, and F, respectively.

omitted. The reader is referred to Ortner et al.45 and Rhee et al.49 for details on the method of characteristics. The solutions for y1 and v using the isotherm model proposed in section 3.1 are calculated for adsorption and desorption conditions. The compositions and velocity profiles at the column exit for ET (solid lines) at one feed flow rate are shown for adsorption conditions in Figure 3 (0.067 m/s), while for desorption conditions they are shown in Figure 4 (0.061 m/ s). Along with the ET solutions, the profiles obtained by simulating the detailed model under isothermal conditions using a high mass transfer coefficient and zero dispersion are shown (red dotted lines); this set of conditions (isothermal/ high mass transfer coefficient/zero dispersion) is abbreviated “isothermal”. The profiles obtained from the detailed model under the true experimental conditions, which will be discussed in detail in section 5, are also shown (blue dashed lines); such conditions are abbreviated “nonisothermal”. Finally, the isotherm is shown as an inset to provide guidance in determining the transitions exhibited by the water vapor profile during adsorption (Figure 3) and during desorption (Figure 4). 4.3. Discussion. The ET solution and the results of the detailed model under isothermal conditions are fully consistent. It can readily be observed that the evolution of both the molar fraction of water vapor and the velocity at the column exit is accurately predicted by the ET solution (Figures 3 and 4). There are very slight deviations between the two simulations, which are due to the necessarily finite mass transfer rate in the

(6)

Substitution of eq 6 into eq 5 yields the two fundamental equations in the unknowns y1 and v: ⎡ ⎤ ∂y ∂y ρ dn * ⎢1 + b 1 (1 − y )⎥ 1 + v 1 = 0 1 ⎥ ⎢⎣ ∂z cεt dy1 ⎦ ∂t ρb dn1* ∂y1 ∂v + =0 cεt dy1 ∂t ∂z

(7)

The two fundamental equations given in eq 7 form a set of two reducible first-order PDEs subject to the isotherm model introduced in section 3.1. The initial state I and the feed state F are constant for all cases considered in this work; thus the solution of eq 7 is the solution of a Riemann problem, which can be obtained using the method of characteristics.49 The solution is characterized by a a single transition (in both y1 and v) from I to F (with respect to the time coordinate), and for the experimental conditions considered in this work the two states are connected not through a single front, but due to the presence of inflection points, by a combination of fronts, socalled simple waves and shocks. A simple wave is a continuous front between two constant states, while a shock is a discontinuous front connecting two constant states.50 For the sake of brevity, a description of how the solution is obtained is E


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Industrial & Engineering Chemistry Research detailed model, whereas in the scope of ET there is equilibrium between the adsorbed and the gas phase. Under adsorption conditions, the initial state I and the feed state F are connected through a leading simple wave and a trailing shock; such a combination of fronts has been called semishock.50 The simple wave emanates from the feed state and proceeds continuously to the intermediate state H (Figure 3). The simple wave and the trailing shock share this intermediate state H; that is, the concentration at state H is at the same time the end concentration reached by the simple wave and the concentration from which the shock emanates. State H is determined by the point in the isotherm for which a straight line (the so-called shock chord) tangent to the isotherm at state H can be drawn. The shock results in a discontinuous front (“jump”) in both mole fraction and velocity. Under desorption conditions, the initial state I and the feed state F are swapped with respect to the corresponding adsorption experiment; that is, I lies above F in the concentration−time plane. The transition from I to F proceeds through two discontinuous fronts that bracket a continuous one; the system exhibits a shock−wave−shock transition. As a result, a shock (labeled shock 2 in Figure 4) connects the initial state I and the intermediate state H2, and a first jump in both concentration and velocity results. The simple wave then emanates from state H2 and proceeds to a second intermediate state H1. Finally, the second shock (labeled shock 1 in Figure 4) leads from state H1 to the feed state F, and a second jump is observed in concentration and velocity. It is worth noting that the evolution of concentration and velocity is closely connected. Indeed, it is apparent in Figures 3 and 4 that the transition from the initial state I to the feed state F is achieved through exactly the same sequence of fronts in concentration and velocity. The velocity at the column exit increases when the concentration of water vapor in the gas phase increases, and, vice versa, the velocity decreases whenever the concentration of water vapor in the adsorbed phase increases.

Figure 5. Adsorption (filled symbols) and desorption (empty symbols) data obtained at 45 °C in the static setup along with the sorption isotherm model fits for adsorption and desorption outside of the hysteresis loop (solid lines) and within the hysteresis loop (dashed line).

Such behavior agrees well with studies reported in the literature.11,15,22,23 While this particular shape of the isotherm is observed frequently, there is a large variety in the adsorption capacity reported, and it depends mainly on the pore volume and the degree of oxidation of the specific AC, which determines the concentration of the functional groups on its surface. We obtained a value of 22.5 mol/kg at RH = 90%, which lies well within the range of values reported in the literature.11,15,22,23 The isotherm model allows for a good description of the data, during both wetting and drying. The set of isotherm parameters including the values of the RH and the adsorbed amount at the closure points are reported in Table 2. Note that these parameters are used in the column model.

5. RESULTS 5.1. Sorption Equilibrium. The water vapor data for adsorption (filled symbols) and desorption (empty symbols) at 45 °C are reported in Figure 5. The uncertainty in the relative humidity (horizontal error bars) is much larger than that in the adsorbed amount. In fact, the uncertainty associated with the latter quantity is several orders of magnitude lower as compared to its values, and thus it is not shown in Figure 5. Also shown are the isotherm model fits for adsorption (solid lines) and desorption (dashed line). Reproducibility of the data was verified in a further measurement, and the results are reported in Figure S1 of the Supporting Information. The characteristic features of water vapor sorption on AC are reflected in the equilibrium data. At low RH the functional groups are saturated;22 the rise in loading is almost linear up to RH ≈ 40%. Thereafter, the pores are slowly being filled with clusters of adsorbed water molecules that formed around the functional groups,22 eventually leading to the onset of capillary condensation41 at RH ≈ 55%. The pore filling extends over a wide range of humidity suggesting a broad pore size distribution, which is typical for ACs. As a consequence of capillary condensation, a wide hysteresis loop is observed during desorption.

Table 2. Isotherm Parameters Estimate and Closure Points adsorption n∞ s Ks Kc n∞ μ,a Kμ,na ma xL xU

[mol/kg] [−] [−] [mol/kg] [−] [−] [−] [−]

desorption 10.791 0.258 0.222 2.227 n∞ μ,d 28.579 Kμ,d 8.80 md closure points 0.497 0.920

nL nU

− − − [mol/kg] [−] [−] [mol/kg] [mol/kg]

1.02 24715 18.243 1.986 21.718

5.2. Adsorption Dynamics. 5.2.1. Experiments. The water vapor concentration profiles at the column exit as well as the evolution of the temperature in the middle of the column in the six experiments performed are plotted in Figures 6 and 7. The experimental measurements are plotted as a continuous (dark) line surrounded by a shaded area, representing the uncertainty band in terms of mole fraction. Adsorption and desorption experiments are illustrated in Figures 6 and 7, respectively. Feed streams entered the column at 45 °C in all cases. The relative humidity of the feed was 95% ± 1.3% for the adsorption experiments, while a dry He-stream was used in the desorption F


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Figure 6. Composition profiles of water vapor on activated carbon at the column exit (A) and corresponding temperature and velocity profiles (B) for three experiments with feed velocities of 0.140 m/s (black), 0.067 m/s (blue), and 0.045 m/s (red) under adsorption conditions. The experimental results are shown as continuous lines within their band of uncertainty, which is shown as the shaded region. The simulations obtained with the detailed model are shown as dashed lines. Note that there are no experimental values for the velocity.

Figure 7. Composition profiles of water vapor on activated carbon at the column exit (A) and corresponding temperature and velocity profiles (B) for three experiments with feed velocities of 0.127 m/s (black), 0.061 m/s (blue), and 0.041 m/s (red) under desorption conditions. The experimental results are shown as continuous lines within their band of uncertainty, which is shown as the shaded region. The simulations obtained with the detailed model are shown as dashed lines. Note that there are no experimental values for the velocity.

experiments. Three different superficial velocities of the feed have been considered. For adsorption conditions, the experimental feed velocities were 0.045, 0.067, and 0.140 m/ s, while for desorption they were 0.041, 0.061, and 0.127 m/s. Reproducibility of the data was verified by repetition of the experiment at feed velocity 0.067 m/s for adsorption conditions and feed velocity 0.061 m/s for desorption conditions (see Figures S2 and S3 of the Supporting Information). Considering the experimental profiles in Figures 6 and 7, the fronts observed in the mole fraction of water vapor predicted by the ET solution are recognizable (see also Figures 3 and 4) at all feed velocities considered. In the adsorption experiments, the composition and velocity profiles at the column exit are characterized by a leading simple wave and a trailing shock, while in the desorption experiments two shocks bracketing a simple wave are discernible. As compared to the profiles computed with ET and shown in Figures 3 and 4, the fronts observed in the experimental profiles are significantly more disperse. This is due to a combination of limitations in mass transfer, which is discussed in section 6.3, and thermal effects. Even though the agreement between ET and experiments is not quantitative, ET allows one to rationalize the complex shape of the exit profiles measured in the dynamic experiments. Under adsorption conditions, the temperature profiles shown in Figure 6B in the middle of the column are disperse, showing only a moderate amplitude. At the highest velocity, the maximum increase in temperature is 3 °C, while at the lowest

one it is roughly 1 °C. Because of the limitation in mass transfer, the temperature wave extends over an amount of time in which the major part of the heat generated is dissipated through the column wall and subsequently to the surrounding heat reservoir (oven). On the other hand, the temperature profiles observed during the desorption experiments shown in Figure 7B exhibit a relatively sharp peak for all feed velocities investigated. 5.2.2. Simulations. The detailed simulation results under the experimental conditions are plotted as dashed lines in Figures 6 and 7. The adsorption experiments are well described by the column model for most of the range of concentration as shown in Figure 6. The shock positions are described satisfactorily for all experiments, but the column model overestimates the composition from which the simple wave emanates (state H in Figure 3). The corresponding temperature profiles exhibit a small peak shortly after the beginning of the experiments, and it is slightly higher for the simulations than in the experiments, that is, an effect present at all velocities. The subsequent description of the evolution of temperature by the model is in quantitative agreement with the experiments. The experimental desorption profiles are described with reasonable accuracy by the column model. While there is a slight deviation of the mole fraction in model and experiment during the simple wave, the position of both shocks is described rather well. The corresponding temperature profiles are in good agreement with the experiments. The position of the sharp G


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the highest two flow rate levels, the estimated value is close to the lower limit of the experimental uncertainty.

drop in temperature is well described by the model, but the magnitude is somewhat overestimated, because the axial dispersion of temperature is possibly underestimated in the column model. Finally, the simulated velocity profiles at the column exit are shown as dashed lines for adsorption conditions in Figure 6B and desorption conditions in Figure 7B. As expected from the ET model used in section 4, the same fronts are observed in velocity profiles as in the composition profiles. Also here, it is evident that the fronts are significantly more disperse than predicted by ET, as expected. 5.2.3. Parameter Estimation. Not only does water vapor on AC exhibit hysteresis in the equilibrium adsorbed amounts during adsorption and desorption (see Figure 5), but also in the mass transfer kinetics, which is different during adsorption and desorption.15,23 Therefore, two mass transfer coefficients, one for adsorption, kH2O,A, and correspondingly one for desorption, kH2O,D, were estimated. The resulting values along with the coefficient for the heat-transfer from the column wall to ambient, hW, are reported in Table 3. A slightly higher value was

6. DISCUSSION 6.1. Adsorption Equilibrium and Dynamics. It is well documented28,43 that the quality of the description of fixed-bed experiments by a column model is highly sensitive to the used sorption isotherm. The agreement between the experimental profiles and their simulations in this work is rather good within the operating conditions investigated. We consider this as a satisfactory result keeping in mind that (i) no adjustments whatsoever were made to the sorption isotherms, both adsorption and desorption, after measuring them in a completely independent setup, (ii) the shape of the particular isotherm is non-Langmuirian and contains two inflection points, and (iii) there exists a wide hysteresis loop requiring a sorption isotherm with hysteresis. Such agreement confirms both the significance and the accuracy of the adsorption equilibrium data, the isotherm model along with the corresponding parameter estimates, and finally the column model. 6.2. Hysteresis. The necessity of considering the sorption hysteresis in the isotherm model is illustrated in Figure S4 of the Supporting Information, where a desorption curve is compared to simulations based on the adsorption branch of the isotherm, instead of the (real) desorption branch. Clearly, there is no agreement between experiment and simulation in this case. Indeed, the initial shock is absent in the simulation where hysteresis is not considered, and the breakthrough time of the shock connecting to the feed state is underestimated by roughly 15%. Note that we investigated only the outermost branches enveloping the entire hysteresis region in this work, but not the branches that evolve from within the hysteresis region, so-called scanning curves. Instead, we refer the interested reader to our previous modeling study29 where the effect of scanning curves on the exit profiles was investigated in detail. In a cyclic adsorption process it is likely that, provided the process contains steps operated in a comparable range of composition, neglecting hysteresis would lead to erroneous estimates of the process performance. Indeed, Štěpánek et al.38 showed convincingly by means of a PSA process targeted at air drying, that differences as high as an order of magnitude can exist between the product purity achieved in the PSA process accounting for sorption isotherms with or without hysteresis. 6.3. Mass Transfer. Existing works where the dynamics of water vapor on AC were investigated are listed in Table 1; they show by means of uptake measurements that the mass transfer rate can vary over up to 2 orders of magnitude with the sorbent loading.15,22 Motivated by this observation, and to obtain reasonable agreement between experiments and simulations, in some of the few works24,25 that are based on fixed-bed measurements, loading-dependent expressions for the mass transfer coefficient (MTC) within the linear driving force (LDF) law were used. In contrast, however, satisfactory agreement between experiments and simulations was achieved in this work simply by using a constant value for the MTC. Therefore, we have decided to investigate the role of the loading dependence of the MTC within the LDF law when simulating the fixed-bed experiments by comparing three MTC models. The first possibility (approach I) is of course to assume that the MTC is loading independent.

Table 3. Transport Parameters Estimate heat transfer coefficient wall-ambient mass transfer coefficient: adsorption

hW kH2O,A

15.2 0.013

mass transfer coefficient: desorption

kH2O,D

0.008

J (m2 s)−1 m s−1 m s−1

obtained for kH2O,A as compared to kH2O,D, consistent with experiments reported in the literature,15,22 where it was shown that mass transfer during adsorption is on average faster than that during desorption. Ribeiro et al.51 simulated a PSA process aimed at the purification of hydrogen from a multicomponent mixture, which is saturated in water vapor using AC as sorbent material. Their value for kH2O,A depends on the particle shape, 0.03 s−1 (spheres) and 0.016 s−1 (cylinders). In our case, we have estimated a value kH2O,A = 0.013 s−1. It is worth noting that before packing the column used in this work, cylindrical AC particles were crushed and sieved. Therefore, a value between those for spheres and cylinders as used by Ribeiro et al.51 was to be expected. The value of hW is clearly system specific. Nonetheless, the value obtained here compares well with literature.51 Finally, the measured and estimated feed velocities are summarized in Table 4. At the lower four flow rate levels, the agreement between estimated and calculated ones is very good, while at Table 4. Overview of the Superficial Feed Velocities for the Fixed-Bed Experimentsa experiment A1 D1 A2 D2 A3 D3

umeas [m/s]

ufit [m/s]

|umeas − ufit| [m/s]

± ± ± ± ± ±

0.046 0.042 0.069 0.062 0.135 0.123

0.0012 0.0004 0.0016 0.0013 0.0046 0.0039

0.045 0.041 0.067 0.061 0.140 0.127

0.0049 0.0049 0.0048 0.0048 0.0046 0.0047

umeas and ufit refer to the measured and fitted superficial velocity, respectively. The adsorption and the corresponding desorption experiments are numbered with increasing umeas. a

H


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Industrial & Engineering Chemistry Research Table 5. Comparison of the Mass Transfer Models Φ

parameters

adsorption

I

constant

−22.60

kH2O,A

0.013 s−1

desorption

I

constant

−20.96

kH2O,D

0.008 s−1

adsorption desorption adsorption desorption

II II III III

eq 8 not applicablea eq 9 eq 9

−22.48 − −22.62 −21.04

α − β1 − β5 β1 − β5

mode

a

approach

expression

8.0 × 10−6 mol cm2(s kg)−1 − [488.9; 9.52; 1316.9; 871.0; 2.82] [1606.6; 6.4; 800.5; 1347.9; 20.7]

Not applicable under desorption conditions because of the discontinuity in the derivative of the isotherm model presented in section 3.1.

The second one (approach II) is motivated by the work of Ribeiro et al.25 The dependence on the water sorption loading is included by assuming that the MTC is inversely proportional to the derivative of the equilibrium sorption isotherm with respect to relative humidity (x) at the prevailing relative humidity level. Approach II contains one adjustable parameter (α), and the corresponding expression is given by k H 2O =

60α d p2(dn/dx)

(8)

The third approach (approach III) is empirical and is able to mimic the main features of the evolution of the MTC with the sorbent loading that was observed in uptake measurements:23 ⎛ ⎞ β β n β5 k H2O = k H2O,0⎜⎜β1 exp( −β2 n ) + 3 4 β + 1⎟⎟ 1 + β4 n 5 ⎝ ⎠

(9) Figure 8. Comparison of the mass transfer coefficients for adsorption conditions within the LDF model. n denotes the actual adsorbed amount (relevant for approach III), while n* denotes the equilibrium adsorbed amount (relevant for approach II).

kH2O,0 was set to 10−4 s−1, corresponding approximately to the lowest value measured.23 Approach III contains five adjustable parameters (β1−β5), and it is comparable to the empirical expression used in Qi et al.24 Approaches I−III were compared in terms of their capability to describe the experimental composition profiles, which is quantified by the objective function Φ defined in eq 4. To this end, the parameter(s) of the MTC expression, that is, kH2O for approach I, α for approach II, and β1−β5 for approach III, were estimated while the heat transfer coefficient and the estimated feed velocities were fixed at the values reported in Tables 3 and 4, respectively. The resulting parameter estimates along with the objective function values are summarized in Table 5, and the corresponding dependence of the adsorption MTC on the loading is illustrated in Figure 8 (the corresponding figure for desorption is reported in the Figure S5 of the Supporting Information). The sensitivity of the objective function with respect to the different approaches to describe the MTC is small; the values of Φ vary in a relatively narrow range. The most complex expression, approach III, gives the best description of the experimental adsorption profiles, but the improvement as compared to approach I is minimal. The same conclusions can be drawn for desorption (see Table 5 and Figure S5 of the Supporting Information). 6.4. Experimental Challenges. Two customized setups are described in this work that are able to cope with the presence of water. We deem it useful for the readers to share some of the main challenges we faced during the development of these setups on the one hand, and on the other to convey the main (heuristic) lessons we learned from addressing and finally mastering these challenges. For the sake of brevity, we term the

setup to measure the adsorption equilibrium “setup-E” (Figure 1), while the setup for the fixed-bed experiments is abbreviated “setup-B” (Figure 2). Even though the experimental setups rely on different modes of operation, common features can be identified: (i) generation of a stream with a uniform moisture level; (ii) reliable measurement of the moisture content of the gas phase; (iii) avoidance of condensation. It is rather clear that the discussion is based on the experience gathered in our group. We believe that these features are to some degree of a general character; that is, they could certainly apply to similar experimental systems aimed at measuring water vapor adsorption. 6.4.1. Stream with Uniform Moisture Level. The first feature is the generation of a stream with a uniform moisture level. In setup-E, the carrier gas is humidified by circulating it through a water tank, and the desired moisture level is adjusted by changing the temperature of the water tank via a thermostat. This method has proved to work well for setup-E. For fixed-bed experiments involving water vapor, it is important to be able to set and control the moisture level of the feed stream. To this end, a feeding system consisting of a liquid-flow meter in combination with a controlled evaporative mixing chamber (CEM) was used. Such a configuration did not result in a feed stream with a constant moisture level, but significant oscillations were observed. The reason for such I


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Table 6. Heuristics for Building and Operating Experimental Setups To Measure Adsorption Equilibrium and/or Dynamics of Water Vapor feature i: stream with uniform moisture level

• two possible methods to humidify a stream are to use a bubbler or a controlled evaporative mixing system • if a carrier gas is mixed with water vapor, sufficient residence time must be provided to obtain a constant level of moisture in the resulting feed stream • the moisture content in the feed-stream of fixed-bed experiments should be measured by an independent measurement • for obvious reasons, equilibrium water vapor sorption measurements are significantly easier to perform at ambient pressure using a carrier gas, e.g., helium

feature ii: measurement of moisture content

• a suitable detector for measuring the moisture level of the gas phase should be chosen; for equilibrium measurements, a relatively accurate dew point sensor seems promising because of its high accuracy, while for fixed-bed experiments capacitive sensors seem promising due to their short response time • detectors for measuring the moisture have limited accuracy; it is important to quantify and indicate the uncertainty in the results

feature iii: avoidance of condensation

• condensation must be avoided at all cost; the presence of a cold spot will likely lead to failure of the measurement • the influence of a heating system on the temperature indicators within the experimental system should be assessed carefully; it can contribute significantly to the uncertainty in temperature

Instruments, France) with 0.2 °C uncertainty in dew point temperature, a capacitive model from the same manufacturer with an accuracy of ±2% RH in the range 5−95% RH at room temperature had been used (a comparison of the uncertainty in the relative humidity is shown in the Supporting Information). Outside of this range and at different temperature, the uncertainty of the RH indicated was larger than 2%. Indeed, we faced reproducibility issues in repeated measurements due to the large uncertainty and because there existed a strong correlation between the temperature at which the sensor was kept (by the heating wire) and the indicated value of the RH, changing up to 10% (abs) upon a variation in temperature of the heating wire of ±5 °C. A figure where the resulting experimental uncertainties are compared is reported in the Supporting Information. On the other hand, capacitive sensors have a shorter response time upon a change in the RH as compared to chilled mirror sensors, thus being more suitable for fixed-bed experiments, where high temporal resolution for recording the exit composition is required due to the presence of shock fronts, that is, sudden changes in the composition. Thus, in setup-B, the reasonable trade-off was to use a capacitive humidity sensor (Rotronic, Switzerland) with relatively high accuracy (±1.3% (abs) over the entire range of humidity). Using the experience gained from setup-E, attention was paid to keep it at constant temperature by controlling it via a dedicated thermocouple. 6.4.4. Avoidance of Condensation. The most obvious and omnipresent challenge when handling water vapor experimentally at ambient conditions is, of course, that it could potentially condense at cold spots, that is, a location within the setup where the temperature is lower than the desired operating temperature. To avoid such cold spots, in both of our setups, electric heating wire was used to keep elements of the setup, in particular piping and valves, that are not thermostat-controlled (MSB chamber in setup-E) or located in an oven (column in setup-B), at sufficiently high temperature. While this measure has been shown to be effective, it has been observed in setup-E that the temperature of the thermostated chamber within which the MSB is located has been influenced by the heating wire due to the heat conductivity of the stainless steel piping. To minimize this influence, we kept the difference between the temperature of the heating wire and that of the heating jacket of the chamber small, and increased it slightly when the relative humidity in the system approached unity. Nevertheless, we

oscillations was found to be nonuniform mixing of the water vapor and the carrier gas. The issue could only be resolved after the addition of a relatively large buffer tank downstream of the CEM, that is, a heated chamber acting as a reservoir in which the water vapor and the carrier gas reside sufficiently long to reach uniform mixing. It is worth emphasizing that it is critical to verify the expected moisture level in the feed stream by an independent measurement, for example, by a relative humidity sensor. This point is discussed in the following section. 6.4.2. Measurement of Moisture Content. The second feature is the measurement of the moisture content of the gas phase. To this end, in setup-E the moisture level was quantified by means of a chilled mirror dew point sensor (Michell Instruments, France), while in setup-B a capacitive relative humidity sensor (Rotronic, Switzerland) was used. To discuss this aspect, we would like to briefly describe a previous generation of setup-E (a schematic is shown in the Supporting Information). In that configuration, the MSB was connected directly to a water bath through an intermediate valve. In addition, no circulation loop was present; thus reaching a uniform gas phase was solely diffusion-controlled. The operating conditions were rather different as compared to the setup shown in Figure 1: the gas phase consisted of water vapor only, implying that the measurements were performed at low pressure, that is, less than the vapor pressure of water at given temperature. Without going into too much detail, the main issue encountered while using the old setup was to maintain the low pressure levels over an extended amount of time. It should be kept in mind that the setup was a closed system; thus any leakage led to accumulation of impurities. In addition, water vapor sorption experiments last for an extended period of time because of the slow adsorption dynamics. As an example, at 25 °C the water vapor partial pressure has to be maintained below 32 mbar over about 5 days. If both adsorption and desorption data are gathered, this issue becomes even more relevant. To overcome this, it was decided (i) to perform the measurements at ambient pressure in a flow-through configuration using a carrier gas and (ii) to add a dew point sensor to determine the moisture content of the gas phase. The result of these two measures is the setup shown in Figure 1 (the operating principle is explained in section 2.2). 6.4.3. Humidity Sensors. Finally, it is worth pointing out that not every humidity sensor is suitable for this application. Before employing the chilled mirror dew point sensor (Michell J



■

estimated conservatively an uncertainty in temperature of the sample of 0.5 °C. This value was used in the quantification of the experimental uncertainty of the RH (see Figure 5), and the uncertainty in this temperature contributes approximately 90% to it. 6.4.5. Heuristics. To summarize, we would like to give some heuristics concerning the handling of water vapor within these setups and similar ones. These heuristics are listed in Table 6.

AUTHOR INFORMATION

Corresponding Author

*Phone: +41 44 632 2456. Fax: +41 44 632 11 41. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has received funding from the Swiss National Science Foundation under grant NF 200021-130186.

7. CONCLUSIONS In the first part of this work, a detailed experimental and modeling study of the adsorption equilibrium of water vapor on AC is presented. To this end, a customized setup equipped with a chilled mirror dew point sensor and a magnetic suspension balance is used to measure the adsorption equilibrium during wetting and drying. This configuration combines the accurate measurement of the dew point of the gas phase and the established accuracy of a Rubotherm balance. A sorption isotherm model with hysteresis model was successfully employed to describe the equilibrium data. The second part of this work focuses on the dynamic behavior of the same sorbate−sorbent system: fixed-bed experiments at the same temperature used for the adsorption equilibrium measurements at three feed velocities are presented, both for adsorption and for desorption. To the best of our knowledge, these are the first fixed-bed experiments presented for the desorption of water vapor on AC exhibiting a large hysteresis loop. These experiments were used to estimate mass- and heat-transfer parameters. We found that the use of a single average value for the mass transfer coefficient yields a good description of the fixed-bed experiments, which stands in contrast to comparable works by Qi et al.24 and Ribeiro et al.25 A case study comparing three different approaches for the description of the mass transfer coefficient within the LDF model revealed that the improvement due to a more complicated model is minimal (approach III) or nonexistent (approach II) for the operating range investigated in this work. Finally, it was shown by simulations that ignoring the hysteretic behavior of the adsorption equilibrium leads to an erroneous description of the desorption profiles. The experimental setups along with the isotherm model and the corresponding parameters will be used in future works to investigate the behavior of water vapor in the presence of other gases, for example, CO2 or CH4, while the sorption isotherm along with its parameters and mass transfer coefficients will be used in process simulations, for example, of pre-combustion capture processes under humid conditions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b03445. Experimental uncertainties, figures of reproduced measurements, system of equations used for the detailed model and model parameters, comparison of a simulated desorption curve following the adsorption and desorption branch, estimated mass transfer coefficients for desorption conditions, and more extensive information regarding experimental challenges (PDF) K


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An Experimental and Modeling Study of the Adsorption Equilibrium

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