Article Cite This: Energy Fuels XXXX, XXX, XXX−XXX
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Separation of Landfill Gas CH4 from N2 Using Pressure Vacuum Swing Adsorption Cycles with Heavy Reflux Lutfi Erden, Armin D. Ebner, and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208, United States S Supporting Information *
ABSTRACT: Simulations were carried out to study the purification of CH4 from pretreated landfill gas containing 88 vol % CH4 and 12 vol % N2 using BPL activated carbon and three different four-bed four-step pressure vacuum swing adsorption (PVSA) cycles. All three PVSA cycle schedules included feed (F), heavy reflux (HR), countercurrent depressurization (CnD), and light product pressurization (LPP) steps. The light-end heavy-reflux plus recycle (LEHR−Rec) cycle had a HR step fed to the light end of a bed by a partial reflux of the product from the CnD step and a full recycle of the product from the HR step blended back with the feed. The heavy-end HR plus recycle (HEHR−Rec) cycle was the same as the LEHR−Rec cycle except the HR step was fed to the heavy end of a bed. The heavy-end HR (HEHR) cycle was the same as the HEHR−Rec cycle, except that it did not have Rec, so the product from the HR step was taken as light product. For all three PVSA cycles, increases in either the feed throughput or the HR reflux ratio caused the CH4 recovery to decrease or the CH4 purity to increase, and concomitantly, the feed throughput did not have any effect on the vacuum pump/compressor energy penalty, while increasing the HR reflux ratio caused the energy penalty to increase. The energy penalty was essentially the same for all three PVSA cycles. Recycle-to-feed from the HR step was also more important than whether the HR step was carried out cocurrently or countercurrently, but the cocurrent approach was generally better. Overall, pipeline-quality CH4 with a purity greater than 98 vol % could be produced with both the HEHR−Rec and LEHR−Rec at feed throughputs as high as 500 L(STP) h−1 kg−1, with the HEHR−Rec generally exhibiting the better performance and the HEHR cycle exhibiting the worst performance. The best performance exhibited by the HEHR−Rec had a CH4 purity of 99.4 vol %, a CH4 recovery of 99.2%, a feed throughput of 500 L(STP) h−1 kg−1, and an energy penalty of 27.0 kJ mol−1 CH4 produced.
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INTRODUCTION Landfill gas (LFG) is produced from the anaerobic bacterial decomposition of organic material contained in municipal solid waste. 1 It contains primarily CH 4 and CO 2 in bulk concentrations, but it also contains several other gases at lower concentrations and many other gases at trace levels. The CH4 in LFG can be extracted from landfills in two ways.2 The first (passive) method simply allows the LFG to percolate to the surface of the landfill, where it is collected for processing. However, this passive method results in low CH4 recoveries and low CH4 productivities. In contrast, the second (active) method applies a vacuum to the landfill to significantly increase the amount of LFG brought to the surface. However, the resulting negative pressures within the landfill cause air to leak in, thereby adding appreciable amounts of O2 and N2 to the extracted LFG, which adds complications to the subsequent CH4 purification steps. These complications are more than offset by the fact that this active method significantly increases the CH4 recoveries and CH4 productivities compared to the passive method, making CH4 recovery from landfills potentially profitable. The goal is to produce a saleable CH4 stream as an energy source or pipeline town gas. The recovery and purification of CH4 from LFG can be accomplished in several ways.3,4 They all require many unit operations operating in series, including both separators and reactors, to remove trace contaminants, H2O vapor, CO2, O2, and N2. The last step in this series of unit operations is typically © XXXX American Chemical Society
the separation of CH4 from N2, a separation that is well-known to be challenging. Among the methods that can separate CH4 from N2, which include adsorption, membranes, and cryogenic distillation, several different pressure swing adsorption (PSA) processes have been studied for this purpose and even commercialized, with PSA emerging as one of the preferred methods for this separation.4−16 A nonexhaustive review of the PSA literature on the separation of CH4 from N2 is provided in Table 1, wherein only the best performance results based on CH4 purity are presented from each study. Note that this table also includes some of the results from this study that are discussed later in this paper. These PSA processes use a variety of different adsorbents that facilitate either an equilibrium- or kinetic-based separation, a variety of different PSA cycle steps including lightreflux (LR), heavy-reflux (HR), and dual-reflux (LR and HR) steps, and a variety of different process conditions, including PSA, vacuum swing adsorption (VSA), and pressure vacuum swing adsorption (PVSA) conditions. These differences produce a range of PSA process performances, with CH4 purities, CH4 recoveries, and feed throughputs varying widely, depending on many factors. In general, however, the cycle schedules incorporating a HR step tend to outperform the ones Received: November 13, 2017 Revised: February 6, 2018 Published: February 7, 2018 A
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
B
F+Rec−HEHR−CnD−LPP
F−CnD−LR−FP F−CnD−LR−I−LPP
4-bed 4-step
2-bed 4-step 3-bed 4-step
exp exp
mod
mod
mod mod
mod
mod mod
exp exp mod mod mod mod mod mod mod mod mod mod exp exp mod exp exp exp
mod or exp
equ/kin equ/kin
equilibrium
equilibrium
kinetic equilibrium
kinetic
kinetic kinetic
kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic kinetic equilibrium equilibrium equilibrium equilibrium equilibrium
separation mechanism
13X/CMS 13X/CMS
Calgon BPL AC
Calgon BPL AC
CMS CMS ETS-Ba400 ETS-Sr190 ETS-Sr270 CMS-BF CMS-T CMS-T CMS-T clinoptilolite Mg−clinoptilolite ETS-4 CTS-1 Norit RB3 AC silicalite AC AC Takeda G2 X7/12 AC ETS-4 purified clinoptilolite Mg/Na (50/50) clinoptilolite Ce−clinoptilolite Calgon BPL AC
adsorbent
26.9 27.9
26.9
26.9
21.9 26.9
21.9
21.9 21.9
amb amb 26.9 26.9 26.9 26.9 26.9 amb amb 21.9 21.9 21.9 26.7 amb 24.9 amb amb 4.9
T (oC)
1.2 2.5
7.9
7.9
7.0 7.9
7.0
7.0 7.0
3.0 3.0 9.0 9.0 9.0 9.0 9.0 11.5 13.0 7.0 7.0 7.0 27.2 5.0 6.9 3.4 3.7 3.0
PH (atm)
d
c
12.0 25.0
16.0
16.0
17.5 16.0
17.5
17.5 17.5
3.0 3.0 18.0 18.0 18.0 18.0 18.0 35.0 27.0 17.5 17.5 17.5 80.0 3.6 23.3 92.3 54.0 12.0
70/10/0/20 60/20/0/20
88/12/0/0
88/12/0/0
80/20/0/0 88/12/0/0
80/20/0/0
80/20/0/0 80/20/0/0
60/40/0/0 92/8/0/0 90/10/0/0 90/10/0/0 90/10/0/0 90/10/0/0 90/10/0/0 85/15/0/0 85/15/0/0 85/15/0/0 85/15/0/0 85/15/0/0 75/25/0/0 50/50/0/0 85/15/0/0 70/30/0/0 74/23/3/0 55/36/9/0
yF (vol %) PH/PL CH4/N2/O2/CO2
92.5 86.0
99.4
99.1
96.0 98.6
96.0
96.0 96.0
75.3 96.2 98.2 98.0 95.5 92.6 93.5 95.0 95.0 95.4 93.3 97.3 96.0 72.5 96.1 98.0 95.0 96.2
yCH4,P (vol %)
54.5 52.6
99.2
97.3
92.6 89.6
93.7
96.2 95.5
NA NA 90.0 56.0 65.0 90.0 92.0 94.0 94.0 73.1 41.6 53.2 80.0 98.0 98.1 95.0 99.9 90.4
RCH4,P (%)
299.5 264.7
500.0
500.0
131.0 500.0
119.4
73.4 79.0
30.4 25.5 367.9 525.5 495.2 285.1 278.9 242.4 333.2 252.5 297.1 250.9 315.7 91.1 163.0 152.9 344.7 758.9
θF [L(STP)/h/kg] ref
14 this work this work this work 15 16
14
14 14
5 5 6 6 6 6 6 7 7 8 8 8 9 10 11 12 4 13
e
e
e
e
e
e
d
b,c
c
c
c
b
b
b
b
b
a
a
note
Mass fed during FP not considered. Assumed bulk density of ETS and CMS adsorbents of 550 and 690 g/L, respectively. Assumed a four-bed system based on cycle time and feed times given. Assumed feed pressurization part of the feed. eAssumed two beds for each train.
F+Rec−LEHR−CnD−LPP
4-bed 4-step
b
F-CoD-CnD−LR−FP/F−CoD−CnD−LR−FP F−HEHR−CnD−LPP
2-train 2-bed 5-step 4-bed 4-step
a
F−CoD−CnD−LR−FP/F−CoD−CnD−LR−FP
2-train 2-bed-5 step
F−CnD−LR−FP F−CnD−LR−FP F−CnD−LR−FP F−CnD−LR−FP F−CnD−LR−FP F−CnD−LR−FP F−CnD−LR−FP F−Eq−CnD 1−CnD2−Eq−FP F−I−Eq−CoD−CnDI−Eq−FP F−CoD−CnD1−CnD2−FP F−CoD−CnD1−CnD2−FP F−CoD−CnD1−CnD2−FP F−Eq1−Eq2−CoD−CnD−LR−I−Eq2−Eq1−LPI F/LR/HR−HPP−CnD F−HEHR−Eq1−eq2−I−CnD−Eq2−I−Eq1−FP F+Rec−HEHR−CnD1−CnD2−LPP−RFP F+Rec−I−LEHR−I−CnD1−CnD2−LR−LPP F+Rec−I−LEHR−I−CnD−LPP−FP
F−CoD−CnD−LR−FP/F−CoD−CnD−LR−FP F−CoD−CnD−LR−FP/F−CoD−CnD−LR−FP
4-step 4-step 4-step 4-step 4-step 4-step 4-step 6-step 8-step 5-step 5-step 5-step 9-step 5-step 10-step 6-step 8-step 7-step
cycle step sequence
2-train 2-bed 5-step 2-train 2-bed 5-step
2-bed 2-bed 2-bed 2-bed 2-bed 2-bed 2-bed 2-bed 6-bed 4-bed 4-bed 4-bed 4-bed 2-bed 3-bed 4-bed 4-bed 3-bed
continuous feed cycle configuration
Table 1. Review of Published PSA Cycles Developed for the Separation of CH4 from N2
Energy & Fuels Article
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels that do not. This observation is based on achieving a saleable CH4 purity (e.g., >95 vol %) while also achieving high CH4 recovery (e.g., >90%) and feed throughput [e.g., >150 L(STP)/ h/kg] using feed streams containing relatively low levels of CH4 (e.g., ≤88 vol %). According to the literature studies in Table 1, the HR step can be incorporated into a cycle schedule in at least three ways. One of the cycle schedules utilizes a unique but unconventional enriching PSA approach in a two-bed configuration,10 while the other two utilize the more conventional stripping PSA approach in three-bed11,13 and four-bed configurations.4,12 The stripping PSA approach is the only approach of interest to this work (the difference between stripping and enriching PSA cycles is explained elsewhere17). In the stripping PSA approach, the HR gas can be supplied to a bed either cocurrently11,12 or countercurrently4,13 relative to the feed step, and the respective light or heavy product from this HR step may4,12,13 or may not11 be recycled to the feed. However, no one has ever compared these seemingly similar cocurrent versus countercurrent HR approaches directly against each other. Therefore, the objective of this work was to study via simulation these two different stripping PSA HR approaches. For this purpose, three different four-bed four-step HR PVSA cycle schedules were formulated and studied for the separation of 88 vol % CH4 from 12 vol % N2 using BPL activated carbon. The effects of the feed throughput and HR reflux ratio on the CH 4 recovery, CH 4 purity, and energy penalty were investigated. The goal was to produce pipeline-quality CH4 at purities greater than 97 vol %, recoveries greater than 90%, high-feed throughputs, and low vacuum pump/compressor energy penalties, while revealing the subtle features of these three seemingly similar HR PVSA cycles. HR PVSA Cycle Schedule Descriptions. The three PVSA cycle schedules along with the interbed connections are shown in Figure 1. They all utilize feed (F), heavy reflux (HR), countercurrent depressurization (CnD), and light product pressurization (LPP) steps; they do not incorporate the very common light reflux (LR) step like so many of them do, as shown in Table 1. These three PVSA cycle schedules differ only in how the HR step is carried out. In the first cycle schedule in Figure 1a, the HR gas is obtained from a partial reflux of the heavy product from a bed undergoing the CnD step. This gas is fed to the heavy end of a bed undergoing the HR step, where the light product from the HR step is blended with the light product from the F step. This cycle is called heavy-end HR (HEHR) and is similar to but simpler than that of Delgado et al.11 The second cycle schedule in Figure 1b is the same as the one in Figure 1a, except that now the light product from the HR step is blended back with the feed gas as a recycle stream. This cycle is called HEHR plus recycle-to-feed (HEHR−Rec) and is similar to but simpler than that of Reinhold et al.12 The third cycle schedule in Figure 1c is the same as that in Figure 1b, except that now the HR gas is fed to the light end of a bed undergoing the HR step, where the heavy product from the HR step is blended back with the feed gas as a recycle stream. This cycle is called light-end HR plus recycle-to-feed (LEHR−Rec) and is similar to but simpler than those of Knaebel4 or Olajossy et al.13 It is worth pointing out that these are all four-bed four-step cycle schedules, with equal step times. In fact, the cycle schedules for the HEHR−Rec and LEHR−Rec cycles are identical and differ from the HEHR cycle schedule only by having F+Rec instead of just F in the feed step boxes. Although
Figure 1. Schematic diagrams showing interbed connections (left) and cycle step schedules (right) for the three heavy reflux (HR) pressure vacuum swing adsorption (PVSA) cycles: (a) heavy-end HR (HEHR), (b) HEHR plus recycle (HEHR−Rec), and (c) light-end HR plus Rec (LEHR−Rec). The black circle indicates the location of the vacuum pump/compressor.
similar but more complex variations of these cycle schedules were studied by Delgado et al.,11 Reinhold et al.,12 Knaebel,4 and Olajossy et al.,13 there is no way to compare their performances because they were all carried out under different conditions. Thus, these simpler versions are formulated in such a way that their performances can be readily compared to each other in a more systematic and fair manner, mainly to discern the effectiveness of HE versus LE HR and the effectiveness of recycle-to-feed. Mathematical Model. The performance of each PSA cycle was determined via simulation using a dynamic adsorption process simulator (DAPS).18 DAPS is written in FORTRAN and uses finite differences along with the time adaptive DAE solver, called DASPK.19 The assumptions used in DAPS, the DAPS equations, and the corresponding boundary conditions for each of the PVSA cycles are provided in the Supporting Information (SI). PVSA Process Performance Indicators. The process performance indicators of these PVSA cycles are evaluated in terms of the CH4 purity in the heavy product (HP), the CH4 recovery in the HP, and the feed throughput, respectively defined as yCH ,HP = 4
moles of not recycled CH4 product produced during CnD total moles of not recycled product produced during CnD (1) C
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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Table 2. Bed, Adsorbent, and Process Characteristics
R CH4,HP = moles of not recycled CH4 product produced during CnD moles of CH4 fed to the bed during F
Bed Characteristics bed radius (m) bed length (m) bed porosity bulk bed density (kg m−3) heat transfer coefficient (kW m−2 K−1) Adsorbent Characteristics
(2)
⎛ L(STP) ⎞ θ⎜ ⎟ ⎝ h kg ⎠ gas fed to one bed during F in one cycle = mass of adsorbent in one bed × total cycle time
adsorbent pellet radius (m) pellet density (kg m−3) pellet porosity pellet heat capacity (J kg−1 K−1) Process Characteristics
(3)
In addition to CH4 recovery, CH4 purity, and feed throughput, the energy (E) required by the vacuum pump/compressor during the CnD step was calculated using the following equation: ⎛ ⎞ kJ E⎜ ⎟ ⎝ moles CH4 produced ⎠ ⎤1 ⎡ P γ − 1/ γ t − 1⎥ δ n(̇ t ) dt ∫t = 0 CnD γ −γ 1 RT ⎢ PHL ⎦ ⎣ = moles of CH4 produced
feed flow rate [L(STP) min−1] feed throughput [L(STP) kg−1 h−1] step time (s) cycle time (s) feed mole fractions of CH4, N2 feed temperature (K) wall temperature (K) high pressure (kPa) low pressure (kPa)
( ) ( )
(4)
where tCnD is the duration of the CnD step, γ is the isentropic constant (equal to 1.4), ṅ(t) is the molar flow rate leaving a bed at time t, δ is the vacuum pump/compressor efficiency (assumed to be 85%), PH is the F or HR step pressure (i.e., 800 kPa) and also the pump discharge pressure, and PL is the suction pressure of the pump and lowest pressure of the cycle (i.e., 50 kPa). Although this integral equation accounts for the fact that the suction pressure of the pump (PL) may vary with time in a PSA process, like it did for Mohammadi et al.,18 in this work, both PH and PL were constants. The other process parameter of interest was the HR reflux ratio (RR). RR is defined as the ratio of the number of moles fed to a bed undergoing the HR step to the total number of moles leaving a bed undergoing the CnD step. This means 1 − RR is the fraction taken as heavy product. Bed, Adsorbent, and Process Characteristics. The bed, adsorbent, and process characteristics used in DAPS are listed in Table 2. The bed size was chosen to be more like a pilotscale facility. In this way, a relatively small value was chosen for the heat transfer coefficient, so the bed operated closer to the adiabatic condition. Equilibrium adsorption isotherms for CH4 and N2 adsorbed by BPL activated carbon were measured in-house,20 with the results fitted in this work to the dual-process Langmuir (DPL) model (eqs S6−S8, SI) simultaneously at all three of the available temperatures.21,22 The resulting DPL model parameters are given in Table 3. The corresponding experimental data and DPL model fits are shown in Figure 2. Details about the experiments and fitting procedure are given elsewhere.20 The DPL model inherently has an isosteric heat of adsorption that depends on the adsorbed phase loading.22 Because the version of DAPS used in this work does not account for a loading-dependent isosteric heat of adsorption, ΔHi in eq S9 (SI) was obtained from the Toth equilibrium adsorption isotherm model according to qi* = qis
BPL activated carbon 0.0025 800 0.50 1.05
50 265.5, 60 318.5, 70 371.6, 80 424.8 500, 600, 700, 800 50 200 0.88, 0.12 300 300 800 50
Table 3. Equilibrium and Kinetic Parameters parameters B1,i (K) B2,i (K) bo1,i (k Pa−1) bo2,i (k Pa−1) qs1,i (mol kg−1) qs2,i (mol kg−1) Bi (K) boi (k Pa−1) qsi (mol kg−1) ti ΔHi (kJ mol‑1) ki (s−1)
⎛ ΔHi ⎞ ⎟ bi = bio exp⎜ − ⎝ RT ⎠
CH4 DPL Model 3040.38 1901.02 6.726 × 10−7 2.021 × 10−6 0.5431 5.0925 Toth Equation 2062.472 1.865 × 10−6 8.131 0.5812 −17.147 LDF Model 0.61
N2 2011.96 1312.38 2.355 × 10−6 1.421 × 10−6 1.1513 8.3399 1663.930 3.051 × 10−6 3.966 0.8652 −13.834 0.70
(6)
The same equilibrium adsorption isotherm data provided elsewhere20 were fitted to eqs 5 and 6 simultaneously at all three of the available temperatures to obtain ΔHi. The Toth model parameters are also given in Table 3. The LDF mass transfer coefficients in eq S3 (SI) were obtained from the literature for CH4 and N2 on BPL activated carbon.23 Only the single-component mass transfer information was used from that work. The LDF mass transfer coefficients are also listed in Table 3.
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RESULTS AND DISCUSSION The goal of this work was to study the separation of CH4 from N2 with BPL activated carbon using the three different HR PVSA cycle configurations shown in Figure 1, while discerning the effectiveness of HEHR versus LEHR and the effectiveness of recycle-to-feed. In these equilibrium-based PVSA cycle
biPyi [1 + (bjPyj )ti ]1/ ti
0.5 4.00 0.40 480 0.01
(5) D
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 2. CH4 and N2 equilibrium adsorption isotherms on BPL activated carbon at three temperatures20 in linear−linear and log−log scales: experimental data (symbols) and DPL model (lines).
schedules, the high-purity CH4 was recovered in the heavy product (HP). In all cases for these four-bed four-step equal step time cycle schedules, PH = 800 kPa, PL = 50 kPa, T = 300 K, ts = 50 s, tc = 200 s, and the feed mole fractions of CH4 and N2 were 0.88 and 0.12, respectively. Recall that during the CnD step the discharge pressure of the vacuum pump/compressor was fixed at PH and the suction pressure of the vacuum pump/ compressor was fixed at PL. A HP CH4 purity >97 vol % and a HP CH4 recovery >90% were sought, while varying the feed throughput [θF = 500, 600, 700, and 800 L(STP) h−1 kg−1] and HR reflux ratio (RR = 50, 0.55, 0.60, and 0.65), with the above conditions fixed. The results from 18 DAPS runs (6 for each PVSA cycle configuration) are provided in Figures 3−6. The component material balance errors for all runs were quite low and on average only 0.12% for CH4 and 0.98% for N2. The effect of the feed throughput on the process performance in terms of CH4 purity versus CH4 recovery is shown in Figure 3a for all three PVSA cycle schedules. In all cases, the CH4 recovery decreased with increasing feed throughput, ranging from nearly 100% for HEHR−Rec to less than 70% for LEHR−Rec. HEHR was always in between those values, thus showing the least effect. In contrast, there was essentially no effect of the feed throughput on the CH4 purity for the HEHR−Rec, the value always being about 99.4 vol %. Similar values for CH4 purity also resulted for the other two HR cycles, but only at the higher two feed throughputs. At the lowest feed throughput, the CH4 purity decreased to 99.1 and 98.6, respectively, for LEHR−Rec and HEHR. For this set of conditions, the most robust HR cycle was HEHR−Rec, because it exhibited the highest CH4 purity and CH4 recovery in the
Figure 3. Performances of the three HR PVSA cycles at (a) feed throughputs of 500, 600, and 700 L(STP) kg−1 h−1 and a fixed HR reflux ratio of 0.55, and (b) a fixed feed throughput of 500 L(STP) kg−1 h−1 and HR reflux ratios of 0.50, 0.55, 0.60 and 0.65.
target zone, followed by LEHR−Rec, with HEHR just missing the target values. It is clear from these results that increasing the feed throughput caused more breakthrough of CH4 into the light product (LP), thereby resulting in substantial decreases in the E
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 4. Initial (i) and final (f) specific molar profiles (total or sum in the gas and adsorbed phases, ni) of CH4 (left) and N2 (right) in the bed for the three HR PVSA cycles during the HR step for HR reflux ratios of 0.50, 0.55, 0.60 and 0.65 and a fixed feed throughput of 500 L(STP) kg−1 h−1.
saturated with CH4 (bed profiles are shown and discussed later). This resulted in high-purity CH4 for all three HEHR− Rec runs. This was clearly not the case at the lowest feed throughput for the other two cycles, wherein the CH4 purity decreased when changing from cocurrent HR (HEHR−Rec) to countercurrent HR (LEHR−Rec), and then it decreased even
CH4 recovery for all three HR PVSA cycles. This was the case whether there was recycle-to-feed or not. In contrast, the effect of the feed throughput on the CH4 purity depended much more on the HR cycle configuration. For HEHR−Rec, the CH4 purity was independent of the feed throughput, indicating that even at the lowest feed throughput, the bed was nearly F
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 5. Initial (i) and final (f) specific molar profiles (total or sum in the gas and adsorbed phases, ni) of CH4 (left) and N2 (right) in the bed for the three HR PVSA cycles during the CnD step for HR reflux ratios of 0.50, 0.55, 0.60 and 0.65 and a fixed feed throughput of 500 L(STP) kg−1 h−1.
further when eliminating recycle-to-feed (HEHR), even though
from the HR step was more important than whether the HR step was carried out cocurrently or countercurrently. The effect of the heavy reflux ratio (RR) on the process performance in terms of CH4 purity versus CH4 recovery is shown in Figure 3b for all three PVSA cycle schedules. In all cases the CH4 recovery decreased with increasing RR, ranging from nearly 100% for both HEHR−Rec and LEHR−Rec to less
HR was in the cocurrent configuration. This indicated that the level of CH4 saturation in the bed depended very strongly on the way the HR step was carried out, with the most robust HR cycle being HEHR−Rec, but only slightly better than LEHR− Rec. These results also suggested so far that recycle-to-feed G
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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the HR step was more important than whether the HR step was carried out cocurrently or countercurrently. To understand the underlying characteristics of each individual HR PVSA cycle that produced the trends observed in Figure 3, the initial and final periodic state specific molar profiles in the bed during the HR and CnD steps for CH4 and N2 were utilized. These specific molar profiles represent the total or sum of the specific moles in the gas and adsorbed phases ni according to ni = qi +
(εb + (1 − εb)εp) (1 − εb)ρp
yC i T
(7)
Figure 4 shows these profiles for the HR step and Figure 5 shows them for the CnD step. Note that the final profiles in Figure 4 are the initial profiles in Figure 5. The same conditions used in Figure 3b were chosen, i.e., θF = 500 L(STP) h−1 kg−1 and RR = 50, 0.55, 0.60 and 0.65, because the three HR PVSA cycles exhibited more marked differences in performance. In general, the profiles in Figure 4 show that for all three HR PVSA cycles, the HR step was very effective at displacing N2 from the bed, especially as RR increased. Similarly, the profiles in Figure 5 show that for all three HR PVSA cycles, the CnD step was very effective at removing essentially all the N2 from the bed, and more so with increasing RR. However, at the end of the CnD step, a significant amount of CH4 remained in the bed, no matter the RR or HR PVSA cycle. This CH4 heel was inconsequential, as the CH4 purity and recovery in each case were still quite high for all three HR PVSA cycles, as shown in Figure 3. Figure 4 also shows that the N2 profiles in the bed at the beginning (initial) and end (final) of the HR step were unique to each HR PVSA cycle. This was especially true for the initial profiles. For HEHR, there was a more gradual displacement of the N2 front toward the light end of the bed with increasing RR, compared to those for both HEHR−Rec and LEHR−Rec with both exhibiting more abrupt displacements. In fact, only HEHR−Rec at RR = 0.50 showed a significant amount of N2 in the bed, the value being even larger than that associated with any of the HEHR profiles. For all other RR the amount of N2 in the bed for both HEHR−Rec and LEHR−Rec was significantly smaller than that for HEHR to the extent that there was very little N2 remaining in the bed at the end of the HR step. Similarly, the CH4 profiles were also unique to each HR PVSA cycle, but more so for HEHR, just like with the N2 profiles. At the beginning of the HR step, the CH4 profiles did not penetrate as far into the bed for HEHR compared to the other cycles with recycle-to-feed steps, except for HEHR−Rec at RR = 0.50. Nevertheless, by the end of the HR step CH4 filled essentially the entire bed in all three HR PVSA cycles. Figure 5 exhibits somewhat similar CH4 and N2 profiles in all cases except for LEHR−Rec. It is clearer in this figure but also noticed in Figure 4 that N2 was more prominent for LEHR− Rec at the heavy end of the bed at the beginning of the CnD step, i.e., at the end of the HR step. This was due to operating the HR step countercurrently to the feed step into the light end of the bed. This resulted in a significantly lower CH4 purity, especially at the lowest RR = 0.50, as shown in Figure 3. The trends in Figures 4 and 5 were consistent with the trends observed in Figure 3. They revealed the sensitivity of the performance to variations in RR for the HR PVSA cycles utilizing a recycle-to-feed step, i.e., HEHR−Rec and LEHR− Rec. They revealed that the proximity of N2 near the heavy end
Figure 6. Vacuum pump/compressor energy requirements of the three HR PVSA cycles (a) at feed throughputs of 500, 600, and 700 L(STP) kg−1 h−1 and a fixed HR reflux ratio of 0.55 and (b) a fixed feed throughput of 500 L(STP) kg−1 h−1 and HR reflux ratios of 0.50, 0.55, 0.60 and 0.65.
than 75% for HEHR. HEHR again showed the least effect. The effect of RR on the CH4 purity was also quite marked, with LEHR−Rec exhibiting the largest spread from 94.8 to 99.8 vol %. The increases in CH4 purity for both HEHR−Rec and LEHR−Rec were also quite substantial in going from RR = 0.50 to 0.55, with HEHR exhibiting more gradual increases and the least effect over this range of RR. Nevertheless, for this set of conditions, the most robust HR cycle was once again HEHR− Rec, because it exhibited the highest CH4 purity and CH4 recovery in the target zone, followed by LEHR−Rec, with HEHR now at least meeting the target values at the lowest RR. It is clear from these results that increasing RR caused more breakthrough of CH4 into the light product (LP), thereby resulting in substantial decreases in the CH4 recovery for all three HR cycles. Again, this was the case whether there was recycle-to-feed or not. In contrast, the effect of RR on the CH4 purity again depended much more on the HR cycle configuration. For both HEHR−Rec and LEHR−Rec, the CH4 purity was nearly independent of RR for the three highest values, indicating that the bed was nearly saturated with CH4 under these conditions. However, for these two cycles at the lowest RR, the CH4 purity decreased substantially and more so for LEHR−Rec, indicating there was not enough reflux to saturate the bed with CH4, which was why the CH4 recoveries were nearly 100%. In contrast, HEHR exhibited less extreme changes in performance but also less desirable performances, indicating that recycle-to-feed played a significant but interesting role in dictating the performance of these HR cycles. These results again suggested that recycle-to-feed from H
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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CONCLUSIONS Simulations of three different four-bed four-step equal step time pressure vacuum swing adsorption (PVSA) cycles were carried out with the dynamic adsorption process simulator (DAPS). These three PVSA cycle schedules all included feed (F), heavy reflux (HR), countercurrent depressurization (CnD), and light product pressurization (LPP) steps; they did not include the very common light reflux (LR) step. These three PVSA cycles differed only in how the heavy reflux (HR) step was carried out. The light-end heavy-reflux plus recycle (LEHR−Rec) cycle had a HR step fed to the light end of a bed by a partial reflux of the product from the CnD step and a full recycle of the product from the HR step blended back with the feed. The heavy-end HR plus recycle (HEHR−Rec) cycle was the same as the LEHR−Rec cycle, except that the HR step was fed to the heavy end of a bed. The heavy-end HR (HEHR) cycle was the same as the HEHR−Rec cycle, except that it did not have Rec, so the product from the HR step was taken as light product. Overall, the results showed that it was indeed possible to produce pipeline-quality CH4 at high recovery and feed throughput from a feed containing 88 vol % landfill gas CH4 and 12 vol % N2 using BPL activated carbon. A CH4 purity >98 vol % could be produced with both the HEHR−Rec and LEHR−Rec PVSA cycles at feed throughputs as high as 500 L(STP) h−1 kg−1. The HEHR−Rec generally exhibited the better performance, and the HEHR cycle exhibited the worst performance, with performance judged in terms of CH4 purity, CH4 recovery, feed throughput, and vacuum pump/compressor energy penalty. The best performance exhibited by the HEHR−Rec PVSA cycle had a CH4 purity of 99.4 vol %, a CH4 recovery of 99.2%, a feed throughput of 500 L(STP) h−1 kg−1, and an energy penalty of 27.0 kJ mol−1 CH4 produced. For all three PVSA cycles, increases in either the feed throughput or the HR reflux ratio caused the CH4 recovery to decrease or the CH4 purity to increase; concomitantly, the feed throughput did not have any effect on the energy penalty, while increasing the HR reflux ratio caused the energy penalty to increase. The energy penalty was essentially the same for these three PVSA cycle configurations, indicating that the CH4 purity and CH4 recovery in the heavy product were the important process performance indicators. This study also showed that recycle-to-feed from the HR step was more important than whether the HR step was carried out cocurrently or countercurrently, but the cocurrent approach was generally better.
of the bed was the reason why LEHR−Rec did not perform as effectively as HEHR−Rec. Finally, they revealed that the HR step was more effective at removing N2 from the bed and filling the bed with CH4 when the HR PVSA cycle included a recycleto-feed step. The effects of the feed throughput (θ) and heavy reflux ratio (RR) on the energy penalty are respectively shown in Figure 6a,b for all three PVSA cycle schedules. Recall that this energy penalty stemmed from the use of a PVSA cycle and was solely due to the cost of operating the vacuum pump/compressor during the CnD step. In all cases, the energy consumption was independent of the feed throughput, with all three HR PVSA cycles exhibiting essentially the same energy consumptions, but with LEHR−Rec noticeably always being the highest. These energy penalties for the lowest RR ranged from 27.0 to 27.5 kJ/ mol of CH4 produced. In contrast, the energy consumption increased significantly and nearly linearly in all cases with an increase in RR. Again, the energy consumptions associated with all three cycles basically overlapped, but with LEHR−Rec always being the highest. These energy penalties for the lowest θ ranged from 25.5 to 34.5 kJ/mol of CH4 produced. This was nearly a 50% increase in energy consumption for only a 30% increase in RR. It was clear from these results that from an energy perspective for these HR PVSA cycle configurations, it did not matter how much feed was fed to the bed, but it did matter markedly how much heavy reflux was sent to the bed undergoing the HR step from the bed undergoing the CnD step It was not entirely clear why LEHR−Rec always required slightly more energy to operate than either HEHR−Rec or HEHR, which essentially required the same energy. Equation 4 shows that the energy of the vacuum pump/compressor is proportional to the ratio of the discharge to suction pressure (PH/PL) and the molar flow rate (ṅ) through the pump. How these two quantities changed over time during the CnD step essentially dictated the required energy. Nevertheless, plots of these quantities over time during the CnD step for these three different HR PVSA cycles were inconclusive, so they are not shown. Instead, the total energy required during the CnD step, the moles of CH4 produced during the cycle, and their quotient were calculated for one case corresponding to RR = 0.55 and θF = 500 L(STP) h−1 kg−1. HEHR, HEHR−Rec, and LEHR−Rec respectively required 40.4, 44.0, and 44.0 MJ per cycle, showing that HEHR without recycle-to-feed was indeed the least energy intensive. HEHR, HEHR−Rec, and LEHR−Rec respectively produced 1.47, 1.63, and 1.60 kmol of CH4 during the cycle, showing that HEHR without recycle-to-feed also produced the least CH4, while HEHR−Rec produced the most CH4 but only slightly more than LEHR−Rec. The quotient of these numbers provided the energy numbers in Figure 3 for this particular case, i.e., E = 27.3, 27.0, and 27.5 kJ/mol CH4 produced for HEHR, HEHR−Rec, and LEHR−Rec, respectively. This analysis indicated that LEHR−Rec was slightly more energy intensive than HEHR−Rec, because although it required the same energy during the CnD step, it produced a bit less CH4 during the cycle, making it slightly more energy intensive than the other two cycles. These results further indicated that just from an energy perspective the choice of the HR PVSA cycle configuration was immaterial and that CH4 purity and CH4 recovery were the important process performance indicators for these three HR PVSA cycle configurations.
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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.energyfuels.7b03534. A discussion of the mathematical model used and tables summarizing initial and boundary conditions (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
James A. Ritter: 0000-0003-2656-9812 Notes
The authors declare no competing financial interest. I
DOI: 10.1021/acs.energyfuels.7b03534 Energy Fuels XXXX, XXX, XXX−XXX
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ti = Toth model parameter for component i in eq 5 ts = step time, s T = temperature, K T0 = ambient temperature, K v = interstitial velocity, m s−1 yi = mole fraction of component i yCH4 = mole fraction of CH4 in the heavy product defined in eq 1 z = column axial coordinate, m
ACKNOWLEDGMENTS
Continued financial support provided over many years by both the NASA Marshall Space Flight Center and the Separations Research Program at UTAustin is greatly appreciated.
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NOMENCLATURE bi = Toth model parameter for component i in eq 5, kPa−1 boi = Toth model parameter for component i in eq 6, kPa−1 B 1,i = dual-process Langmuir model parameter for component i in eq S7 (SI), K−1 B 2,i = dual-process Langmuir model parameter for component i in eq S8 (SI), K−1 b 1,i = dual-process Langmuir model parameter for component i in eq S6 (SI), kPa−1 b 2,i = dual-process Langmuir model parameter for component i in eq S6 (SI), kPa−1 0 b 1,i = dual-process Langmuir model parameter for component i in eq S7 (SI), kPa−1 0 b 2,i = dual-process Langmuir model parameter for component i in eq S8 (SI), kPa−1 Cpg,i = gas-phase heat capacity of component i, kJ mol−1 K−1 Cpa,i = adsorbed-phase heat capacity of component i, kJ mol−1 K−1 Cpg = gas-phase heat capacity, kJ mol−1 K−1 Cpp = adsorbent particle heat capacity, kJ mol−1 K−1 CT = total molar concentration, mol m−3 cv = valve coefficient, dimensionless E = energy defined in eq 4, kJ/mol CH4 Ḟ = molar flow rate through the valve, L(STP)/min hw = overall heat transfer coefficient, kW m−2 K−1 ΔHi = isosteric heat of adsorption of component i from eq 6, kJ mol−1 ki = mass transfer coefficient of component i in eq S5 (SI), s−1 Mg = gas-phase average molecular weight, kg mol−1 L = column length, m ṅ = molar flow rate, mol s−1 ni = total moles in the gas and adsorbed phases defined in eq 7 , mol kg−1 N = number of components P = pressure, kPa PH = highest feed or HR step pressure, and vacuum pump/ compressor discharge pressure, kPa PL = lowest CnD step pressure, kPa qi = adsorbed phase loading of component i, mol kg−1 q*i = adsorbed phase equilibrium loading of component i, mol kg−1 qsi = Toth model parameter for component i in eq 5, mol kg−1 s q 1,i = dual-process Langmuir model parameter for component i in eq S6 (SI), mol kg−1 s q 2,i = dual-process Langmuir model parameter for component i in eq S6 (SI), mol kg−1 R = universal gas constant, kPa m3 mol−1 K−1 RCH4 = recovery of CH4 in the heavy product defined in eq 2 RR = heavy reflux recycle ratio rb,i = column internal radius, m rp = adsorbent particle radius, m Sg = molecular weight ratio between gas and air at 1 atm and 21.45 °C t = time, s tc = cycle time, s
Greek Symbols
γ = isentropic constant in eq 4 δ = vacuum pump/compressor efficiency in eq 4 εb = column porosity εp = adsorbent particle porosity ρp = adsorbent particle density, kg m−3 μg = gas-phase viscosity, Pa s θF = feed throughput defined in eq 3, L(STP) h−1 kg−1
Cycle Step Acronyms
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CnD = countercurrent depressurization CoD = cocurrent depressurization Eq = equalization EqD = equalization down EqU = equalization up F = feed FP = feed pressurization HE = heavy end HEHR = heavy end heavy reflux HR = heavy reflux HP = heavy product HPP = heavy product pressurization I = idle LE = light end LEHR = light end heavy reflux LP = light product LPP = light product pressurization LR = light reflux Rec = recycle RFP = recycle feed pressurization
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