Dynamic Study of the Pressure Swing Adsorption Process for Biogas

Article pubs.acs.org/IECR

Dynamic Study of the Pressure Swing Adsorption Process for Biogas Upgrading and Its Responses to Feed Disturbances Mónica P. S. Santos,† Carlos A. Grande,‡ and Alírio E. Rodrigues*,† †

Laboratory of Separation and Reaction Engineering (LSRE), Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal ‡ SINTEF Materials and Chemistry, Forskningsveien 1, 0373 Oslo, Norway ABSTRACT: Pressure swing adsorption (PSA) is one of the industrial separation processes for biogas upgrading to produce biomethane. Biogas generated from biological feedstocks can have strong variations in composition and flow rate. To tackle these variations while maximizing the performance of a PSA process, an advanced control strategy should be developed. In order to develop an advanced control system that maximizes performance of the biogas upgrading PSA under the presence of severe feed disturbances, a perturbation analysis has been performed. Zeolite 13X was used as selective adsorbent for CH4−CO2 separation and binary breakthrough curves, and single-column PSA experiments were performed. Step-function perturbations of 5% in inlet flow rate and CO2 composition were introduced in the PSA. The PSA experiments have demonstrated that a change in flow rate or in CO2 composition leads to a variation less than 2% in the temperature at the top of the column. The gas composition, at the column outlet, in the adsorption step, increases as the position of the CO2 concentration front propagates further. This work shows that temperature variations inside the column can be used as observers to monitor the location of the CO2 concentration wave and, therefore, to be able to take decisions on the PSA step times. These observers (thermocouples) should be implemented in the top of column where the variation is more pronounced. and desorption.6,7 This process is termed as a continuous periodic (cyclic) process due to the cyclic repetition of the sequence of steps, which normally have strong transient behavior.8 Therefore, the control of PSA,9−13 whose main purpose is to maximize the yield of the products separation maintaining the required product purity or to make a continuous operation feasible,14,15 is more difficult than that of the steady state processes. Another purpose of the PSA control is to avoid the multiplicity of the steady state,16−21 once the steady state of a PSA process depends on the initial conditions; this means that one objective of PSA control is to prevent the existence of products with different purities, for example. A predictive model based control for both tracking and disturbance rejection was successfully applied to an industrial scale: in this case study, to the oxygen vacuum swing adsorption process.22 The nonstationary behavior associated with disturbances on feed concentration, flow rate, pressure, or temperature make the control of these periodic processes a challenge. Taking into account that the wastewater treatment plants are subject to large diurnal fluctuations in the flow rate and compositions of the feed stream,23 the biogas production is subjected to variations too. For that reason and to improve the continuous process, the process disturbances should be detected in a timely manner and correcting actions in the PSA process should be performed. In most cases, some state variables are not physical quantities or accurate sensors may not be available or may be too expensive for measuring them. In such cases, an alternative solution is to use

1. INTRODUCTION Biogas is a gas mixture originated from the decomposition of organic matter in an anaerobic digestion process containing methane, CH4 (50−75%), and carbon dioxide, CO2 (25−45%); nitrogen, N2, oxygen, O2, water, H2O, ammonia, NH3, hydrogen sulphide, H2S, and other trace gases (e.g., hydrogen, siloxanes, etc.) may also be present in the gas mixture, depending on its natural sources.1 Biogas can be generated from commercial composting, animal farm manure anaerobic fermentation, agro food industry sludge anaerobic fermentation, and landfill and wastewater sludge anaerobic fermentation.2 These two last sources are the main sources of methane emissions in several countries.3 The waste composition and aging of the landfil4 as well as the sludge and the operation conditions of the digestion process affect the biogas composition from landfill and anaerobic digestion units of wastewater treatment plants (WWTPs), respectively. The commercial value of biogas has increased for two reasons: its release into the atmosphere contributes largely to greenhouse gas concentration (GHG) and consequently increased global warming5 and the methane can also be used for energy or fuel production, having similar properties of a fossil fuel. To obtain a high quality biomethane (+98% of methane), biogas should be purified for the removal of minor contaminants, followed by an upgrading process to carry out the bulk CH4/CO2 separation. This mixture can be separated by amine scrubbing, membranebased processes, physical absorption with water, chemical absorption with polyglycol ether, and pressure swing adsorption (PSA). The PSA process operates cyclically employing one or more fixed bed adsorbers, and each cycle comprises a sequence of steps of pressurization, adsorption, pressure equalization, blowdown, © 2013 American Chemical Society

Received: Revised: Accepted: Published: 5445

December 27, 2012 March 4, 2013 March 13, 2013 April 3, 2013 dx.doi.org/10.1021/ie303606v | Ind. Eng. Chem. Res. 2013, 52, 5445−5454

Industrial & Engineering Chemistry Research

Article

Figure 1. Breakthrough curve of CO2−CH4 (33% CO2), at ambient temperature, on Zeolite 13X and with a total flow rate of 1.84 SLPM. The adsorption was performed at 5 bar and desorption at 0.15 bar. (a and b) Molar flow rate of each gas exiting the column in the adsorption and desorption steps: ◆, ■, experimental points; solid lines, simulated curves. (c and d) Temperature profiles inside the column, in the adsorption and desorption steps, at ▲, 0.04 m; ■, 0.15 m; ◆, 0.26 m from feed inlet; solid lines, simulated curves.

five steps: feed, co-current intermediate depressurization, counter-current blowdown, counter-current purge, and cocurrent feed pressurization. A square perturbation was introduced in cycle number 11 and maintained during 10 cycles, in order to observe the gas flow rate and temperature responses. The disturbance experiments allow us to gain enough insight into the response of the process to feed variations in order to proceed to observer design for an advanced control strategy.

an observer or state estimator.24−26 The observer is a physical sensor that detects variations of one variable that is correlated to the response of the system to a perturbation. The selection of observers that can be used to monitor the variations of the state variables can be done having a physical insight and knowing the dynamic behavior of the process, given by an accurate mathematical model. Some works were already published27−30 where the cycle time varies along a swing adsorption process to adjust the changes in the feed gas composition. For example, flow rate, temperatures, and pressures are measured and therefore the purge flow rate is calculated and the regeneration time adjusted.27 The maximum feed pressure as well as the minimum regeneration pressure is monitored, and the step times are altered within a cycle to maintain constant the pressure ratio.28 The bed regeneration is based on the measure of the feed gas parameters.29 The temperature profile along the adsorbent bed is monitored to control the PSA cycle steps.30 In this work, we were focused on the effects of process disturbances on the final properties of the product, which are needed for the design of a control strategy of PSA units. The adsorption of carbon dioxide and methane on Zeolite 13X packed in a fixed bed was studied. A breakthrough of CH4/CO2 experiment was performed to validate and to find the fitting parameters of the model, the overall heat transfer coefficient, and the wall heat transfer coefficient. These parameters were estimated by fitting experimental data to the mathematical model. The knowledge of the dynamic fixed-bed behavior is an elemental tool to validate the model used to describe the PSA performance. The influence of feed disturbances (CO2 composition and flow rate), in the PSA performance, was studied in an experimental setup composed by one column and comprising

2. EXPERIMENTAL SECTION Binary CH4/CO2 breakthrough and PSA experiments were performed in a column that operates under unsteady state conditions, simulating the real operation of a single column in a multicolumn PSA process. The experimental setup can operate with gas mixtures with two or three components where each mass flow controller (Alicat Scientific) was used to control each gas flow rate. This unit is composed of one stainless steel column packed with zeolite 13X, surrounded by on−off valves (Asco) to open and close at regular time intervals, switching the position of inlet and outlet gases and regulating feed and regeneration times. The flow rate of the gas coming out the column is measured by a mass flow meter (Alicat Scientific). The pressure of the column during feed is maintained by a back pressure regulator (Bronkhorst High-Tech); the vacuum-promoted regeneration was carried out using a vacuum pump (Ilmvac) and a needle valve to control the flow. A pressure transducer was used to measure the pressure in the regeneration steps. The unit is operated automatically via an interface developed in LabView 2010 (National Instruments); data acquisition (DAQ) devices were connected to a computer that runs the control of the system (valves, pumps, and flow meters). The molar flow rates of gases exiting the column, shown in Figure 1a,b, were measured by a 5446

dx.doi.org/10.1021/ie303606v | Ind. Eng. Chem. Res. 2013, 52, 5445−5454


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Table 1. Description of the Breakthrough Experiment, the Operating Conditions, and the Column Properties mixture feed

Pfeed (bar)

yCO2

Qfeed (SLPM)

Qpurge (SLPM)

column length (m)

thermocouples distance from feed inlet (m)

column porosity

column density (kg m−3)

CO2/CH4

5

0.33

1.84

0.2

0.306

0.04−0.15−0.26

0.395

683.65

All gases used in this work were provided by Air Liquide and used as received: carbon dioxide N24, methane N35, and helium N50 (purities greater than 99.4%, 99.95%, and 99.999%, respectively).

portable and multifunction gas analyzer (LMSxi G4.18, Gas Data). The complete equipment setup was reported elsewhere.31 Each breakthrough curve and PSA experiment was started with an activated bed. Initial activation of the sample, Zeolite 13X extrudates (Siliporite G5, CECA, France), was carried out at 593 K overnight. The heating rate to reach this temperature was 1 K/ min and under a continuous flow rate of helium. The temperature profiles along the column, measured by three thermocouples at three different positions from the feed inlet, are represented in Figure 1c,d. These temperature values as well as the pressures and flow rates were recorded automatically on an interface computer. Binary breakthrough and PSA experiments were started with the column pressurized, at 5 bar, with helium. The adsorbent regeneration in the blowdown and purge steps was carried out in vacuum, at 0.15 bar. The breakthrough was performed at ambient temperature (∼296 K) using a total pressure of 5 bar with feed composition of 33% CO2 balanced with 67% of CH4, using a feed flow rate of 1.84 SLPM (liters per minute under the standard conditions of 298 K and 1 atm). The operating conditions of breakthrough, as the column properties, are presented in Table 1. The physical properties of adsorbent are shown in Table 2.

3. MODELING AND SIMULATIONS On the basis of the adsorption equilibrium and kinetic parameters of methane and carbon dioxide adsorption in Zeolite 13X already reported32,33 and shown in Table 3, the simulations of the experiments were performed. The simulation of the PSA process was carried out using a mathematical model for a fixed bed with oscillating boundary conditions to describe the different steps of the PSA process. The assumptions of this model are34 • The gas phase behaves as an ideal gas; • Mass, heat, and momentum variations in the radial direction are negligible; • The mass transfer rate is represented by a bilinear driving force (bi-LDF) model; • A film mass transfer in the layer surrounding the extrudates is considered; • The pressure drop in the column is described by the Ergun equation; • The bed porosity is considered constant along the bed. The equations of the model proposed are detailed in Table 4, and mass and heat transport parameters, necessary to solve this model, were estimated according to correlations existing in the literature.14,35−37 These correlations are detailed in Table 5. The parameters U and hw were estimated by fitting the experimental breakthrough results. The schematic representation for the PSA cycle employed in one column PSA experiments is given in Figure 2a). The five steps are 1. co-current feed, where the CO2 is selectively adsorbed in the column and therefore the CH4 is collected as product; 2. co-current intermediate depressurization, where the column is partially depressurized until intermediate pressure (2.5 bar); 3. counter-current blowdown, where the pressure is reduced to the lower pressure of the cycle (0.15 bar); 4. counter-current purge with product to displace CO2 from the product-end of the column; 5. co-current pressurization with feed, where the column pressure is increased from the blowdown pressure to the feed pressure (5 bar). The PSA process performance was evaluated according to the purity of the CH4 rich stream, product recovery, and CH4 productivity; taking into account the main aim to obtain a final

Table 2. Column Characteristics, Physical Properties of the Adsorbents, and Operating Conditions Employed in the PSA Experiments and Simulationsa

a

property

value

column radius (m) column wall specific heat (W m−1 K−1) column wall density (kg m−3) column wall thermal conductivity (W m K−1) feed pressure (bar) feed temperature (K) pellet density (kg m−3) pellet porosity pellet radius (m) mean pore radius (A) specific heat (J kg−1 K−1) wall heat transfer coefficient (W m−2 K−1) heat transfer coefficient (W m−2 K−1)

0.01075 8238 500 16 5.0 296 1130 0.54 0.0008 1610 920 85 12

The tortuosity was assumed constant and equal to 2.2.

The PSA experiments were performed using the same operating conditions of the breakthrough experiment. A square positive perturbation of 5% in the feed flow rate and the feed composition was introduced in the cycle number 11 and kept during 10 cycles; this means that in cycle 21 the flow rate or composition was again set back to the initial value.

Table 3. Adsorption Equilibrium and Kinetic Parameters of Methane and Carbon Dioxide Adsorption in Zeolite 13X32,33 gas

qi,max (mol·kg−1)

Ki0 (MPa−1) −8

−ΔH (kJ·mol−1)

ai (−)

CO2

17.901

3.20 × 10

54.729

13.120

CH4

28.871

4.34 × 10−4

15.675

8.136

5447

Dp,i/Rp2 (s−1)

Du,i (m2·s−1)

−2

3.92 × 10−15(301 K) 5.35 × 10−15(323 K) 3.00 × 10−8 (301 K) 3.30 × 10−8 (323 K)

1.23 × 10 (301 K) 1.35 × 10−2 (323 K) 1.47 × 10−2 (301 K) 1.64 × 10−2 (323 K)



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Table 4. Mathematical Model Used in the PSA Cycle Simulations for the Binary Mixture CO2/CH4 parameter

expression

(1 − εc)a pk f ∂C ⎞ ∂C ∂⎛ ∂ ⎜εcDax i ⎟ − (uiCi) = εc i + (Ci − ⟨Cp, i⟩) ⎝ ⎠ ∂z ∂z ∂z ∂t R p(1 + Bii)

component mass balance in the gas phase

∂⟨Cp, i⟩

mass balance in the solid phase, macropores

∂t

∂⟨qi̅ ⟩

mass balance in the solid phase, micropores

∂t

=

=

ΩMDp, iBii 2

R p (1 + Bii)

15Dc, i rc 2

∂⟨qi̅ ⟩ ρp ∂t εp

(qi* − ⟨qi̅ ⟩) = K u, i(qi* − ⟨qi̅ ⟩)

⎡ ⎛ q* ⎞ ⎜ i ⎟ = K Py ⎢1 − i ⎜q ⎟ i⎢ ⎝ i ,max ⎠ ⎣ adsorption equilibrium: multisite Langmuir model

(Ci − ⟨Cp, i⟩) −

a ⎛ q * ⎞⎤ i i ⎟⎥ ⎜ ∑⎜ ⎟⎥ q i ⎝ i ,max ⎠⎦

with

⎛ ΔH ⎞ i⎟ K i = K i0 exp⎜⎜− ⎟ ⎝ R gT ⎠ −

momentum balance

1.75(1 − εc)ρg 150μ(1 − εc)2 ∂P = u0 + |u0|u0 ∂z d p2εc 3 d pεc 3

εcC TCṽ energy balance in the gas phase

∂Tg ∂t

∂Tg ∂C ∂ ⎛ ∂Tg ⎞ + εcR gTg T ⎟ − u0C TCp̃ ⎜λ ∂z ⎝ ∂z ⎠ ∂z ∂t

=

− (1 − εc)hf a p(Tg − Ts) − n

2hw (Tg − Tw) Rw

n

̃ ̃ (1 − εc)[εp ∑ ⟨Cp, i⟩Cṽ i + ρp ∑ ⟨qi̅ ⟩Cv,ads, i + ρp C p ] i=1

energy balance in the solid phase

s

i=1

= (1 − εc)εpR gTs

∂⟨Cp, i⟩ ∂t

n

+ ρb ∑ (−ΔHads, i) i=1

∂Ts ∂t

∂⟨qi̅ ⟩ ∂t

+ (1 − εc)hf a p(Tg − Ts) ̃ ρw Cpw with

energy balance for column wall

αw =

expressions used

axial mass dispersion (Ruthven et al.14)

εcDax = (20 + 0.5ScRe); Dm

axial heat dispersion (Wakao and Funazkri35)

λ = (7.0 + 0.5PrRe); kg

Re =

Pr =

ρg ud p μg

;

Sc =

μg ρg Dm

Cp̂ g μg

Dm, i

⎛ y⎞ = (1 − yi )/ ∑ ⎜⎜ i ⎟⎟ j = 1 ⎝ Dij ⎠ J≠i

Knudsen diffusion (Ruthven et al.14) film mass transfer (Wakao and Funazkri35) film heat transfer (Wasch and Froment36)

D k, i = 9700rp

Tg Mw

Sh = 2.0 + 1.1Re 0.6Sc1/3; Nu = 2.0 + 1.1Re 0.6Pr1/3;

Sh =

kf dp

Nu =

αwl =

(d we − d wi)/ln(d we/d wi) e(d wi + e)

4. RESULTS 4.1. Breakthrough Curves. The breakthrough curve experiment was performed to validate the mathematical model that will be used in the simulations of the PSA experiments. This experiment was also performed to determine the energy transfer parameters of the mathematical model: the global external heat coefficient (U) and the heat transfer coefficient to the wall (hw). The temperature variation inside the column can be described with the following parameters: hw = 85 W m−2 K−1 and U = 12 W m−2 K−1. Once the global heat transfer coefficient, U, is smaller than the internal convective heat transfer coefficient between gas and the wall column, hw, we can conclude that external convective heat transfer exists between the column and the gas surrounding, as well as the contribution of conductivity of the column. The results for the binary breakthrough CO2/CH4 carried out with a total pressure in the column of 5 bar at ambient

kg

n

molecular diffusion (Bird et al.37)

d wi ; e(d wi + e)

The model described in Table 4 was implemented in the gPROMS environment (version 3.1.5, PSE Enterprise, U.K.) and numerically solved using the centered finite difference method (CFDM), with 200 discretization intervals and second order approximation for partial derivatives and integrals. The solvers employed in the simulations used a value of 1 × 10−5 for absolute tolerance.

Table 5. Correlations Used for Estimation of Mass and Heat Transfer Parameters parameter

∂Tw ∂ 2T = αwhw (Tg − Tw) − αwlU (Tw − T∞) + λ w 2w ∂t ∂z

Dm hf d p kg

product purity of 98% and to maximize the product recovery. The performance parameters are defined in Table 6. 5448



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Figure 2. (a) PSA cycle sequence for five steps of one-column PSA experiments. Steps are (1) feed, (2) co-current intermediate depressurization, (3) counter-current blowdown, (4) counter-current purge, and (5) co-current feed pressurization; (b) square perturbation of 5% performed in the feed flow rate.

were estimated from the experiments. This model was used for simulations of the PSA process for biogas upgrading. 4.2. Pressure Swing Adsorption. In order to analyze the relation between the feed disturbances and the temperature and gas composition responses of a PSA process, three PSA experiments were carried out. The different steps of the PSA cycle used are represented in Figure 2a and comprise feed, cocurrent depressurization, blowdown, purge, and co-current pressurization with feed. The performance of the one-column PSA process experiment was evaluated according to the parameters shown in Table 6. A square disturbance of 5% in the feed composition, described in Figure 2b, or flow rate was applied. The PSA experiments were performed at total feed pressure of 5 and regeneration pressure of 0.15 bar with a mixture containing 33% carbon dioxide balanced by methane. One should note that this study was performed with a mixture of CH4−CO2, but it may be applied to other cases of CO2/CH4 separations (e.g., natural gas streams containing CO2, CH4, and N2). The total feed flow rate was 1.84 SLPM. For the experimental conditions of 296 K and 5 bar, we have experimentally measured that, operating at feed flow rate, the pressurization time (tpress) must be at least 86 s. Step times as well as PSA performance results are shown in Table 7, which correspond to the cyclic steady state. Figure 3 shows the molar flow rate and temperature responses to a disturbance in the feed flow rate (experiment 2 described in Table 7) in the cycle immediately before the disturbance (cycle 10) and three cycles during the disturbance. While Figure 3a shows the CO2 and CH4 molar flow rate exiting the column in the PSA experiments, the Figure 3b presents the temperature profiles measured at three points, 0.04, 0.15, and 0.26 m from feed inlet. The temperatures inside the column are recorded by Labview 2010 software, and the molar flow rate is measured by a portable gas analyzer. In Figure 3a,b, few cycles are represented for better visualization (cycles 10−13). Solid lines in Figure 3 represent the prediction of the mathematical model described in Table 4 while the points represent the experimental data. The

Table 6. Three Parameters Used To Evaluate the Process Performance: CH4 Purity, Recovery, and Productivitya parameter purity

recovery

productivity a

expression

∫0 ∫0 ∫0

t feed t feed

∫0

t feed

CCH4u|Z = Lc dt

CCH4u|Z = Lc dt + ∫ 0

t feed

CCH4u|Z = Lc dt − ∫ 0

t feed

CCO2u|Z = Lc dt

t purge

CCH4u|Z = 0 dt + ∫ 0

t press

CCH4u|Z = Lc dt CCH4u|Z = 0 dt

yfeed,CH n feed ̇ Recovery 4

t totalwads

Cycle scheme is shown in Figure 2.

temperature and using a flow rate of 1.84 SLPM are shown in Figure 1. The molar flow rate of each gas exiting the column in the adsorption and desorption steps is represented in Figure 1a,b, respectively. The temperature profiles measured in the bottom, middle, and top of the column (0.04, 0.15, and 0.26 m from feed inlet), in the adsorption and desorption steps, are shown in Figure 1c,d. The points correspond to the experimental data and the lines to the prediction of the mathematical model. It is noticed in Figure 1a that methane is the first gas to break through the column, which is expected taking into account that it is only lightly adsorbed. Also seen in this figure is the roll-up of methane, once that carbon dioxide is the most adsorbed gas and leads to its displacement. As can be seen in Figure 1c, a large amount of heat is released during carbon dioxide adsorption in Zeolite 13X, increasing the temperature inside the column around 70 K. The first peak of temperature, visible at the middle and the top of the column but not possible to see in detail in Figure 1c, corresponds to the methane adsorption. This peak is lower than the temperature peak produced by the carbon dioxide adsorption due to its lower heat of adsorption. The mathematical model based on pure component equilibrium and kinetic data could describe the experimental binary breakthrough curve results once that thermal parameters

Table 7. Step Times and PSA Performance Results Obtained at the Cyclic Steady State exp

perturbation type

tpress (s)

tfeed (s)

teq (s)

tblow (s)

tpurge (s)

Pfeed (bar)

Plow (bar)

CH4 purity (%)

CH4 recovery (%)

CH4 productivity (mol/(kg·h))

1 2 3

feed flow rate feed flow rate feed composition

86 86 86

84 100 100

10 10 10

150 110 110

100 100 100

5 5 5

0.15 0.15 0.15

97.1 96.6 96.6

64.0 69.5 69.7

8.3 10.3 10.4

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Figure 3. PSA for CH4−CO2 separation using Zeolite 13X and for feed flow rate perturbation. Cycle scheme is shown in Figure 2 and operating conditions in Table 7 (Experiment 2). (a) Molar Flow rate of each gas exiting the column in the cycle before the disturbance and three cycles during the disturbance. Temperature histories at different positions (0.04, 0.15, and 0.26 m) from feed inlet: (b) in the cycle before disturbance and three cycles during disturbance; (c) along the PSA experiment. Experimental data (symbols); simulation (lines).

Figure 4. Evolution of (a and c) CO2 gas phase concentration and (b and d) gas temperature profiles at the end of the feed step with the cycle number. Experimental data (symbols) simulation (lines).

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Figure 5. PSA for CH4−CO2 separation using Zeolite 13X. Temperature profile in the top of the column for a simulation without and with a feed disturbance in cycle 11: (a) flow rate perturbation and (b) feed composition perturbation. Cycle scheme is shown in Figure 2 and operating conditions in Table 7.

(cycle 10 to cycle 11). It is also possible to see that more CO2 breaks the column during this step. The CO2 concentration front is accompanied by an advance in the peak of the temperature; while in cycle 10 the maximum temperature is located in the axial position 0.242 m, in cycle 11 the temperature reaches a maximum at 0.249 m. For that reason, an observer (thermocouple) should be implemented in this bed zone; that is, the thermocouple should be positioned inside the column in the range 0.249−0.280 m with respect to its inlet, corresponding to the position where the first derivative is a maximum. However, in an industrial PSA process, this strategy (in-bed thermocouple) will be useful and will work better since the adsorption bed presents nearly adiabatic behavior. This can be explained by the fact that if the column operates adiabatically, the adsorption heat released is accumulated in the bed and, therefore, the temperature peaks are higher and consequently more easily detected by the thermocouples. Although the feed suffers a disturbance of 5% in the feed flow rate, the temperature variation is less than 2%, in the first cycle of perturbation (cycle 11). The perturbation effects are more pronounced in the first cycle after the perturbation (cycle 11), which allows the development of a control strategy with a very fast response to changes. After this cycle, the CO2 gas phase and the temperature tend to the cyclic steady state; the disturbance slowly spreads along the experiment. In order to better understand the temperature and flow rate responses to two different perturbations, the first one in the feed flow rate and the second in the feed composition, the simulation results of experiments 2 and 3 (the operating conditions are shown in Table 7) were compared with those obtained without any disturbance. Figure 5 shows the temperature profiles obtained for the simulations of experiments 2 and 3 (a square disturbance of 5% in the feed flow rate and feed composition is introduced in cycle 11 and during 10 cycles, respectively) and the same simulations but without perturbation. The dashed line and the solid line correspond to the simulation performed without and with perturbation, respectively. As we can see in this figure, the temperature in the top of the column is slightly higher when a perturbation is introduced to the feed, either in the flow rate or composition. To understand the influence of time in the disturbance introduction, two simulations were performed under the conditions of experiment 2, but the flow rate perturbation was instead introduced in cycle 6 and in cycle 26. The temperature profiles in the column top, at the initial of perturbation, are represented in Figure 6a,b. As well as in the

results from Figure 3 show that the mathematical model can predict the PSA experiment, even under the presence of a feed perturbation. It can be observed in Figure 3a that the molar flow rate of methane increases during the perturbation, as well as the molar flow rate of carbon dioxide that breaks the column. The CO2 flow rate desorbed in the intermediate depressurization step also increases. Figure 3b also shows that the flow rate disturbance does induce a visible change in the temperature of the top of column due to the available adsorbent, once the carbon dioxide is fed to the column in the bottom and moves along the bed. When the molar fraction of CO2 in the feed stream increases, more CO2 is observed in the methane-rich product, decreasing its purity. The temperature in the top of the column slightly increases but enough to be detected by the thermocouple. Furthermore, the temperature profiles along the experiment, represented in Figure 3c, show that the top temperature reaches a maximum at the beginning of disturbance (around 4000 s). Note that the profiles are represented only until 6000 s. In these figures it is possible to see that, after the feed disturbance, the top temperature continually decreases until the steady state. Also, in this figure, a temperature increase of 60−70 K is visible in the first cycles in the bottom and in the middle of the column. This temperature peak is much smaller, around 20 K, during the cyclic steady state, due to the smaller amount of CO2 adsorbed. In Figure 4 the internal CO2 concentration profiles at the end of the feed step are displayed together with the temperature along the bed for different cycle numbers (three cycles before the disturbance (8−10) and along this (cycles 11−20). The lines correspond to the simulation results, and the points correspond to the temperatures monitored, at the end of the feed step, in three different locations (0.04, 0.15, and 0.26 m) during the disturbance. The temperature and concentration profiles are represented in more detail in Figures 4c,d. The mathematical model can satisfactorily predict the temperature profiles: however, the simulated temperature profiles in the bottom and middle of the column are 5 and 3 °C higher than the experimental ones, respectively. Cyclic steady state (CSS) in this unit was reached after 24 cycles. The temperature variations in the top thermocouple between cycles 15 and 24 was lower than 2% as can be seen in Figure 4 by the CO2 gas phase and the temperature profiles. The disturbance does not induce noticeable changes in these variables in the initial and middle of the bed. However, in the top of the column it is possible to see that the CO2 concentration front is slightly moving along the column 5451



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Figure 6. PSA for CH4−CO2 separation using Zeolite 13X. (a and c) Temperature profile in the top of the column and CO2 molar flow rate (zoomed) for a simulation without and with a feed flow rate disturbance: in cycles 6−11. (b and d) Temperature profile in the top of the column and CO2 molar flow rate (zoomed) for a simulation without and with a feed flow rate disturbance: in cycles 26−30. Cycle scheme is shown in Figure 2 and operating conditions in Table 7.

systems with higher thermal effects. In separations systems that present a behavior nearly isothermal, as well as the methanenitrogen adsorption in carbon molecular sieve (CMS),38 this technique will present some limitations.

previous case (see Figure 5a), the temperature variations can only be sensed at the top of the column, a reason why the temperature profiles in the bottom and in the middle are not shown. As can be seen in Figures 5a and 6, the temperature increase is higher when the disturbance occurs early due to the higher fresh adsorbent to the adsorption, and consequently more CO2 is adsorbed. This increase in the temperature can be explained by the increase of CO2 fed to the column and therefore more CO2 is adsorbed and releases heat, increasing the temperature, which is visible in Figure 6. In Figure 6c,d, the CO2 gas exiting the column is represented in the initial cycles of disturbance (4/5 cycles), and we can see that only after three cycles the CO2 flow rate exiting the column suffers an increase. It is shown in Table 7 that this PSA process can produce methane with purity higher than 97% and a recovery of 64% with a unit productivity of around 8.3 mol CH4/(kg·h). However, this product recovery can be increased by using an equalization step in a two-column process, once the gas exiting the intermediate depressurization is not considered as product. It is clearly shown that a small increase in the feed time from 84 to 100 s and a decrease in the blowdown time, from 150 to 110 s, leads to a product with a purity less than 97% and an increase in product recovery and thus unit productivity. It was successfully verified that the technique of using observers can be used for detections of feed perturbations for the separation of CH4−CO2 mixtures. However, in principle, this technique is not linked to the necessity of having the concentration and temperature waves moving at the same velocity (e.g., gas drying). It should be mentioned that this strategy will not be universal; indeed it is particularly useful for

4. CONCLUSIONS This work is focused on the response of a PSA process for biogas upgrading to perturbations in the feed stream. A binary breakthrough experiment of CO2 /CH4 was performed using a fixed bed with Zeolite 13X as selective adsorbent. The results were used to validate the mathematical model employed in the PSA simulations. PSA experiments were carried out to separate a stream of 67% CH4 and 33% CO2 in order to obtain CH4 as product. A cycle sequence comprising feed, intermediate depressurization, counter-current blowdown, counter-current purge, and cocurrent pressurization was employed in the PSA experiments. A square disturbance in the feed composition and feed flow rate was applied for 10 cycles. It was shown the responses of temperature inside the column and gas composition exiting it, to feed composition and flow rate changes. It was verified that an increase of 5% in the flow rate or CO2 composition in the feed leads to an increase in the top temperature and in the carbon dioxide that breaks the column in the feed step, which indirectly gives information about the product specifications. It was also verified that the CO2 concentration front changes when a disturbance is imposed to the feed; such change is more noticeable in the first cycle of the disturbance. 5452



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equilibrium constant at the limit T → ∞ of component i, (MPa−1) Ku,i micropore diffusivity of component i (m2 s−1) Mw molecular weight (kg mol−1) ṅfeed moles of biogas available per unit of time (mol s−1) Nu Nusselt number Pfeed feed pressure (bar) Plow blowdown and purge pressure (bar) Pr Prandtl number ⟨qi̅ ⟩ macropore averaged adsorbed phase concentration of component i (mol kg−1) qi* adsorbed phase in equilibrium with the average concentration in the macropores (mol kg−1) qi,max maximum adsorbed phase concentration of component i, (mol kg−1) feed flow rate (SLPM) Qfeed Qpurge purge flow rate (SLPM) rp pore radius (m) Re Reynolds number Rg universal gas constant (J mol−1 K−1) Rp particle radius (m) Rw radius of the column wall (m) Sc Schmidt number Sh Sherwood number SLPM standard liters per minute under the conditions of 298 K and 1 atm t time (s) tblow blowdown step time (s) teq co-current intermediate depressurization (s) tfeed feed step time (s) tpress pressurization step time (s) tpurge purge step time (s) Tg gas temperature (K) Ts solid phase temperature (K) Tw column wall temperature (K) T∞ ambient temperature (K) u0 superficial velocity (m s−1) U global external heat transfer coefficient (W m−2 K−1) yi molar fraction of component i yCH4,feed molar fraction of methane in the feed yCO2,feed molar fraction of carbon dioxide in the feed z axial position (m) K0i

The main advantage of this strategy is that using one sensor (thermocouple or gas analyzer) gives enough information to adapt the PSA cycle without any information about the feed properties. However, under an economic point of view the thermocouple use is more advantageous than a gas analyzer and, moreover, allows an earlier corrective behavior. With the temperature monitoring, is possible to have real-time knowledge of the location of the CO2 concentration wave inside the adsorber bed; that is, the temperature oscillations inside the column can be used as observers. These should be implemented in the top section of the column; for this specific case, the thermocouples should be placed in the range of 0.249−0.280 m from the feed inlet.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +351-22-5081671. Fax: +351-22-5081674. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are gratefully to Fundaçaõ para a Ciência e Tecnologia (FCT)−Portugal for providing financial support for the Project PDTC/EQU-EQU/65541/2006.

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NOTATION ai number of neighboring sites occupied by component ap particle specific area (m−1) Bii mass Biot number of component i Ci gas phase concentration of component i (mol m−3) CT total gas phase concentration (mol m−3) ̃ Cp molar constant pressure specific heat of the gas mixture (J mol−1 K−1) C̃ ps constant volumetric specific heat of component i (J kg−1 K−1) ⟨Cp,i⟩ macropore averaged concentration of component i (mol m−3) C̃ pw constant pressure specific heat of the column wall (J kg−1 K−1) ̃ Cvi molar constant volumetric specific heat of component i (J mol−1 K−1) C̃ v,ads,i molar constant volumetric specific heat of component i adsorbed (J mol−1 K−1) dp particle diameter (m) dwi wall internal diameter (m) dwe wall external diameter (m) Dax axial dispersion coefficient (m2 s−1) Dk,i Knudsen diffusivity of component i (m2 s−1) Dm,i molecular diffusivity of component i (m2 s−1) Dp,i macropore diffusivity of component i (m2 s−1) 0 Dp,i macropore diffusivity of component i at infinite temperature (m2 s−1) Dμ,i micropore diffusivity of component i, (m2 s−1) e wall thickness (m) hf film heat transfer coefficient between the gas and the solid phase (W m−2 K−1) hw wall heat transfer coefficient between the gas and the column wall (W m−2 K−1) kf film mass transfer coefficient (m s−1) kg gas thermal conductivity (W m−1 K−1)

Greek Letters

αw αwl εc εp λ λw ΔHads,i μ ρb ρg ρp ρw

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ratio of the internal surface area to the volume of the column wall (m−1) ratio of the logarithmic mean surface area of the column shell to the volume of the column wall (m−1) bed porosity particle porosity heat axial dispersion coefficient (W m−2 K−1) thermal conductivity of the column wall (W m−2 K−1) heat of adsorption of component i (J mol−1) gas viscosity (Pa s) bulk density (kg m−3) gas density (kg m−3) particle density (kg m−3) column wall density (kg m−3)

REFERENCES

(1) University of Florida. Biogas as a renewable biofuel. http://biogas. ifas.ufl.edu/biogasdefs.asp (accessed Oct. 2012). (2) Abatzoglou, N.; Boivin, S. A review of biogas purification processes. Biofuels Bioprod. Bioref. 2009, 3, 42−71.

5453



Article

(3) GHG Data. United Nations Framework Convention on Climate Change. http://unfccc.int/ghg_data/ghg_data_unfccc/items/4146. php (accessed Sept. 2012). (4) Shin, H.-C.; Park, J.-W.; Song, H.-C. Removal characteristics of trace compounds of landfill gas by activated carbon adsorption. Environ. Pollut. 2002, 119, 227−236. (5) Pritchard, C. L. Chasing the Dragon’s Tail: Life Cycle Carbon Analysis Applied to CO2 Sequestration. Presented at the 7th International Conference on Greenhouse Gas Control Technologies, Vancouver, Canada, Sept. 5−9, 2004. (6) Nikolic, D.; Giovanoglou, A.; Georgiadis, M. C.; Kikkinides, E. S. Generic Modeling Framework for Gas Separations Using Multibed Pressure Swing Adsorption Processes. Ind. Eng. Chem. Res. 2008, 47, 3156−3169. (7) Nikolic, D.; Kikkinides, E. S.; Georgiadis, M. C. Optimization of Multibed Pressure Swing Adsorption Processes. Ind. Eng. Chem. Res. 2009, 48, 5388−5398. (8) Pan, Y.; Lee, J. H. Identification and Control of Processes with Periodic Operations or Disturbances. Ind. Eng. Chem. Res. 2003, 42, 1938−1947. (9) Bitzer, M. Model-based nonlinear tracking control of pressure swing adsorption plants. In Control and Observer Design, for Nonlinear Finite and Infinite Dimensional Systems; Lecture Notes in Control and Information Sciences; Meurer, T., Graichen, K., Ernst-Dieter, G., Eds.; Springer: 2005; Vol. 322, pp 403−418. (10) Torre, V. D. L.; Fox, V. G.; Bandoni, J. A.; Biegler, L. T. Model predictive controller for periodic adsorption processes. Presented at ENPROMER, 2nd Mercosur Congress on Chemical Engineering, 2005. (11) Mulholland, M.; Latifi, M. A. Predictive control of pressure swing adsorption. Presented at 17th International Conference on Process Control, Štrbské Pleso, Slovakia, June 9−12, 2009. (12) Khajuria, H.; Pistikopoulos, E. N. Dynamic modelling and explicit/multi-parametric control MPC control of pressure swing adsorption systems. J. Process Control 2011, 21, 151−163. (13) Khajuria, H.; Pistikopoulos, E. N. Optimization and Control of Pressure Swing Adsorption Processes Under Uncertainty. AIChE J. 2013, 59, 120−131. (14) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH Publishers: New York, 1994. (15) Wu, D. J.; Xie, Y.; Ma, Z.; Wang, N.-H. L. Design of SMB chromatography for amino acid separations. Ind. Eng. Chem. Res. 1998, 37, 4023−4035. (16) Croft, D. T.; LeVan, M. D. Periodic states of adsorption cycles: I. Direct determination and stability. Chem. Eng. Sci. 1994, 49, 1821. (17) Croft, D. T.; LeVan, M. D. Periodic states of adsorption cycles: II. Solution spaces and multiplicity. Chem. Eng. Sci. 1994, 49, 1831. (18) Kikkinides, E. S.; Sikavitsas, V. I.; Yang, R. T. Natural gas desulfurization by adsorption: Feasibility and multiplicity of cyclic steady states. Ind. Eng. Chem. Res. 1995, 34, 255. (19) Rege, S. U.; Padin, J.; Yang, R. T. Olefin/paraffin separations by adsorption: complexation vs. kinetic separation. AIChE J. 1998, 44, 799. (20) Hofmann, U.; Loehr, M.; Straub, M. Sensitivity analysis of PSA processes supported by numerical simulation. Presented at the 1999 Annual AIChE Meeting, Dallas, TX, 1999. (21) Rege, S. U.; Yang, R. T. Propane/propylene separation by pressure swing adsorption: sorbent comparison and multiplicity of cyclic steady states. Chem. Eng. Sci. 2002, 57, 1139−1149. (22) Purity Predictive Model-based Control of Oxygen Vacuum Swing Adsorption Process. Presented at the 18th Mediterranean Conference on Control & Automation Congress, Palace Hotel, Marrakech, Morocco, June 23−25, 2010. (23) Butler, D.; Friedler, E.; Gatt, K. Characterizing the quantity and quality of domestic wastewater inflows. Water Sci. Technol. 1995, 31 (7), 13−24. (24) Tewari, A. Modern Control Design; John Wiley & Sons, Ltd.: New York, 2002. (25) Bitzer, M.; Zeitz, M. Design of a nonlinear distributed parameter observer for a pressure swing adsorption plant. J. Process Control 2002, 12, 533−543.

(26) Won, W.; Lee, K. S. Nonlinear observer with adaptive grid allocation for a fixed-bed adsorption process. Comput. Chem. Eng. 2012, 46, 69−77. (27) White, D. H., Jr.; Verrando, M. G.; Picek, C. R. Heatless adsorbent fractionators with microprocessor cycle control and process. U.S. Patent 4,197,095, Apr. 8, 1980. (28) Neu, B. T.; Smolarek, J.; Rogan, M. K. Low pressure ratio VPSA plant tuning and balancing system. U.S. Patent 6,277,174, Aug. 21, 2001. (29) Kalbassi, M. A.; Malik, N. H. Process for treating a feed gas. U.S. Patent 6,599,347, July 29, 2003. (30) Matz, M. J.; Knaebel, K. S. Temperature front sensing for feed step control in pressure swing adsorption. Ind. Eng. Chem. Res. 1987, 26, 1638−1645. (31) Lopes, F. V. S.; Grande, C. A.; Rodrigues, A. E. Activated carbon for hydrogen purification by pressure swing adsorption: Multicomponent breakthrough curves and PSA performance. Chem. Eng. Sci. 2011, 66, 303−317. (32) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Adsorption Equilibrium of Methane, Carbon Dioxide, and Nitrogen on Zeolite 13X at High Pressures. J. Chem. Eng. Data 2004, 49, 1095−1101. (33) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Separation of CH4/ CO2/N2 mixtures by layered pressure swing adsorption for upgrade of natural gas. Chem. Eng. Sci. 2006, 61, 3893−3906. (34) Da Silva, F. A.; Silva, J. A.; Rodrigues, A. E. A General Package for the Simulation of Cyclic Adsorption Processes. Adsorption 1999, 5, 229−244. (35) Wakao, N.; Funazkri, T. Effect of fluid dispersion coefficients on particle-to fluid mass transfer coefficients in packed beds. Chem. Eng. Sci. 1978, 33, 1375−1384. (36) Wasch, A. P. D.; Froment, G. F. Heat transfer in packed beds. Chem. Eng. Sci. 1972, 27, 567−576. (37) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; Wiley International: Singapore, 2002. (38) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Separation of Methane and Nitrogen by Adsorption on Carbon Molecular Sieve. Sep. Sci. Technol. 2005, 40, 2721−2743.

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Dynamic Study of the Pressure Swing Adsorption Process for Biogas

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