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Electrochemical CO2 capture thermodynamics
International Journal of Greenhouse Gas Control 95 (2020) 102878
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Electrochemical CO2 capture thermodynamics Ryan A. Shaw, T. Alan Hatton*
T
Massachusetts Institute of Technology, Department of Chemical Engineering, Cambridge, MA 02139, United States
ARTICLE INFO
ABSTRACT
Keywords: Carbon capture Electrochemical Complexation separation Competitive complexation separation
We analyze four general architectures for electrochemically mediated carbon dioxide capture systems, in each of which the electrophilicity of a redox active absorbent or absorbent blocking species is manipulated to influence the system's affinity for CO2. It is shown that the open circuit potentials of these architectures converge given the appropriate reference - namely a state in which no CO2 is present in the stream. The resulting difference between the open circuit potential of a stream and of that same stream lacking CO2 is referred to as the deviation potential. In the context of this deviation potential, four system process configurations are analyzed. The most efficient process configuration for all four electrochemical architectures is one that employs both a cathodic absorption taking place simultaneously with the reduction process and an anodic desorption that occurs along with the oxidation of the redox active species; decoupled electrochemical reactions and absorption/desorption steps incur significant energetic penalties.
1. Introduction Anthropogenic carbon dioxide emissions have resulted in a 40% increase in atmospheric CO2 concentration since the industrial revolution, half of which has come in the last 50 years (Marcott et al., 2013). Carbon dioxide, a greenhouse gas, absorbs infrared radiation reflected from the earth's surface which would otherwise be sent to space (Solomon et al., 2009). As such, there is strong agreement within the scientific community that these greenhouse gas emissions are causing climate change (Oreskes, 2004). The result is a sharp increase in global temperature anomalies over the same 50 year time period. An average global temperature increase of 0.8 ∘C since 1900 is one of many symptoms of this change which also include rising and more acidic oceans, significant loss of arctic sea ice, and a myriad of related climate events. Mitigation of climate change, whose primary cause is anthropogenic CO2 production, is therefore one of the most important issues the scientific community currently faces (National Academy of Sciences, 2014). To avoid the 2 ∘C global warming limit target established by the Paris agreement, stop gap measures like carbon capture and storage (CCS) will need to be employed (Rogelj et al., 2016; UNFCCC, 2015). While many CO2 capture processes utilize thermal or pressure cycles to manipulate an absorbent's affinity for CO2 (Wilcox, 2012), a promising approach is to instead apply an electrochemical cycle (Stern et al., 2013; Rheinhardt et al., 2017). Electrochemical cells have the advantage that they can be readily integrated as plug-and-play processes
⁎
that do not require external sources of steam or high pressures or vacuum for their operation. A number of redox active materials have been explored for carbon capture, including direct complexation species such as quinones (Apaydin et al., 2014; Gurkan et al., 2015; Scovazzo et al., 2003), bipyridines (Ishida et al., 1994; Ranjan et al., 2015), and disulfides (Singh et al., 2017) as well as competitive complexation species such as in copper/amine systems (Stern et al., 2013). Table 1 summarizes the underlying electrochemical processes driving these different systems. An appropriate thermodynamic framework is necessary to enable comparative analyses of the energetic demands of different processes and process configurations; this is the goal of this report. 2. Electrochemical architectures for CO2 capture systems Stern describes two architectures for electrochemically mediated carbon dioxide capture: electrochemically mediated complexation separation (EMCS) and electrochemically mediated competitive complexation separation (EMCCS) (Stern, 2014). In EMCS a redox active absorbent is activated for CO2 capture at the cathode and deactivated at the anode to release the captured CO2. In EMCCS a redox active blocker species whose electrophilicity may be manipulated serves to displace CO2 bound to an electrochemically inert absorbent. Since this blocker species becomes a stronger electrophile upon oxidation, the absorbent is deactivated for CO2 binding at the anode. Both of these architectures, which are summarized in Fig. 1, could employ a dormant electrochemically active species either in solution or as a solid bound to the
Corresponding author. E-mail address: [email protected] (T.A. Hatton).
https://doi.org/10.1016/j.ijggc.2019.102878 Received 15 June 2019; Received in revised form 21 September 2019; Accepted 21 October 2019 1750-5836/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Table 1 Electrochemical carbon dioxide capture chemistries. Architecture
System/species
Reaction(s) of interest
Ref.
EMCS
Quinones (Q)
Q+e Q• + e Q2 Q2 + CO2 Q2 [CO2] Q2 [CO2] + CO2 Q2 [CO2]2
(Apaydin et al., 2014; Gurkan et al., 2015; Scovazzo et al., 2003; Mizen and Wrighton, 1989; Watkins et al., 2015; Appel et al., 2005)
EMCS
Bipyridine (B)
(Ishida et al., 1994; Ranjan et al., 2015)
EMCS
Disulfides
B+e B + CO2
EMCCS
Metals (Cu for example)
Q•
RSSR + 2e 2RS + 2CO2
B BCO2
(Singh et al., 2017)
2RS 2RSCO2
(Stern et al., 2013; Stern and Hatton, 2014)
Cu2 + + 2e Cu Am + CO2 AmCO2 2Am + Cu2 +
Cu(Am)22 +
Fig. 1. Two possible architectures exist for both EMCS and EMCCS systems: (a, c) the dormant electrochemically active species remains in solution, (b, d) only the active electrochemically active species is in solution.
electrodes. The thermodynamics of each of these systems is described below. Four possible process configurations are considered. The first is a twostage system, in which carrier activation and CO2 absorption occur simultaneously at the cathode and carrier deactivation and CO2 desorption occur at the anode. The second is a four-stage system where absorbent activation and deactivation, which occur at the cathode and anode respectively, are decoupled from absorption and desorption. Two possible three-stage systems are created by incorporating either a cathodic absorption or anodic desorption in an otherwise four-stage system. Practical examples of two of these different architectures are
shown in Fig. 2a and b. 2.1. EMCS: an electrochemically active absorbent The simplest EMCS cycle involves a concerted m electron electrochemical reaction and a homogeneous binding of an activated absorbent, Am−, to m CO2 molecules. Therefore, for every electron passed through the EMCS cycle a single CO2 molecule is captured at perfect Faradaic efficiency. Examples of this include: Scovazzo et al.'s one electron bipyridine system (Scovazzo et al., 2003), Gurkan et al.'s two electron quinone process (Gurkan et al., 2015), or Buttry et al.'s two
2
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Fig. 2. Example EMCS and EMCCS architectures. (a) Quinone molecules activated at the cathode complex with CO2 before transferring to the anode, where they are deactivated and release CO2. (b) The amine-CO2 complex from the absorption column is introduced to the anode chamber where cupric ions are released and complex with the amines, releasing the CO2. The amines are regenerated on reduction of the copper in the cathode chamber.
electron benzyldisulfide system (Singh et al., 2017). The open circuit potential, the potential at which there is no current, for this reaction establishes total work of separation for an EMCS cycle (Bard and Faulkner, 2001). It will be shown that the strength of binding of CO2 to an activated sorbent molecule, defined by binding constant K CO2 , has a strong effect on this open circuit potential. The EMCS architecture requires that an activated carrier molecule be in solution in order to transport bound carbon dioxide to the anode for release. However, an inactive or dormant absorbent may be either in solution or in a solid state, which will affect the open circuit potential. As shown in Fig. 1a and b, respectively, a dormant absorber in solution may be used in a continuous cycle, whereas a solid dormant absorbent will be shuttled from cathode to anode when in the activated solution state.
Electrochemical
Homogeneous
A(aq) + me
Am
(a)
RT C m E=E ln A mF CA (aq) + mCO2 (g) A(CO2)m m (aq) K CO2 =
Overall
Am (aq)
CA (CO2 )m m C Am
A(aq) + me + mCO2 (g)
P0 PCO2
(b)
m
A(CO2)m m (aq) (c)
(1)
The open circuit potential for such a system, as described by the Nernst Equation, is given in Eq. (1)a. Here Ci is the concentration of component i, PCO2 is the partial pressure of CO2, and P0 is the reference pressure (1 bar). For convenience, we define total absorbent concentration and absorbent activation in the following manner:
A0 = CA + C Am + CA (CO2 )m m 2.1.1. EMCS dormant absorbent in solution Consider first an EMCS cycle with a dormant absorbent in solution, like that employed by Scovazzo et al. (2003). The relevant reactions are
xA =
3
C Am + CA (CO2 )m m A0
(2) (3)
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
The state of charge (SOC) is directly related to the total absorbent concentration and the activated fraction through the equation
oxidation of a copper anode. As in the EMCS cycle one electron releases one CO2 molecule. Similar to the EMCS system, EMCCS may utilize a dormant redox active species which is either in solution or in the solid state. As shown in Fig. 1c and d respectively, a dormant blocker in solution may be used in a continuous cycle, whereas a solid dormant blocker will be shuttled from anode to cathode.
(4)
SOC = m (C Am + CA (CO2 )m ) = mA0 x A m
The state of charge as well as the open circuit potential, given by Eq. (1)a, define the total work of capture for an EMCS cycle. An approach similar to that taken by Gurkan et al. may be employed to arrive at a relationship between the open circuit potential and the parameters above, which define the state of the system (Gurkan et al., 2015). Thus
E=E +
RT 1 xA m [ln( ) + ln 1 + K CO2 P˜CO2 ] mF xA
(
)
2.2.1. EMCCS dormant blocker in solution A similar approach to that taken for the thermodynamics of an EMCS system may be employed for an EMCCS system. Consider first a dormant blocker, B, which remains in solution. The open circuit potential for such a system, as described by the Nernst Equation, is given in Eq. (10)a.
(5)
where P˜CO2 = PCO2/ P0 . It is of note that while the open circuit potential is not an explicit function of total absorbent concentration for the activated absorbent architecture, this will not be the case for other architectures described.
Electrochemical Bn + (aq) + ne B(aq) (a) RT CB E=E ln( ) nF C Bn + Homogeneous A(aq) + mCO2 (g) A(CO2)m (aq) (b) CA (CO2)m P0 m K CO2 = ( ) CA PCO2 n + Homogeneous A(aq) + Bn + (aq) B(A)nn/m (aq) (c) m n / m CB (A)nn +/m C0 = CAn/ m C Bn +
2.1.2. EMCS solid dormant absorbent For an EMCS system with a solid state dormant absorbent, assuming unit activity for the solid species, the relevant reactions with their thermodynamic equilibria are
Electrochemical
A(s) + me
Am (aq)
RT C ln A mF C0 (aq) + mCO2 (g) A(CO2)m m (aq) E=E
Homogeneous
Am
K CO2 = Overall
(a)
m
CA (CO2 )m m
P0 PCO2
C Am
A(CO2)m m
A(s) + me + mCO2 (g)
(b)
(aq) (c)
A0 = CA + CA (CO2 )m +
(7)
(
)
,
(11)
CB + CB (A)nn +/ m
(12)
We further define the total activated blocker fraction as
(8)
RT C m [ln( 0 ) + ln 1 + K CO2 P˜CO2 ] mF A0
n CB (A)nn +/ m m
B0 = CB + C Bn + + CB (A)nn +/m
As before we may establish a relationship between the open circuit potential of a stream and its state as
E=E +
(10)
we also describe total blocker concentration as
Since the dormant absorbent is solid in this scenario, the state of charge is a function only of the amount of absorbent that has become activated and entered solution, as given by
SOC = m (C Am + CA (CO2 )m ) = mA0 m
(d)
In addition to describing total absorbent concentration as in the EMCS case,
(6)
Here C0 is the reference concentration (1 M). The total absorbent concentration in solution is
A0 = C Am + CA (CO2 )m m
+ B(A)nn/m (aq) + ne + nCO2 (g) n B(aq) + A(CO2)m (aq) m
Overall
m
xB =
nCB (A)nn+/ m
(13)
mA0
This analysis assumes the binding of the blocker to the absorbent is quite strong, i.e. β ≫ 1 in Eq. (10)c. The result is that any activated blocker will be bound to an absorber as long as any absorbent remains. Note then that the state of charge (SOC) is directly related to the total activated blocker fraction via
(9)
Note that while the open circuit potential relationship varies for the dormant absorbent in solution versus that for the solid dormant absorbent systems – as given by Eqs. (5) and (9), respectively – it will be shown that given appropriate reference states these two may be treated identically.
SOC = n (C Bn + + CB (A)nn+/ m )
nCB (A)nn +/m = mxB A0
(14)
The relationship between the open circuit potential of a stream and its state can then be shown to be
2.2. EMCCS: an electrochemically active blocker
RT C [ln( 0 ) ln((1 mF A0 m + ln 1 + K CO2 P˜CO2 ]
An EMCCS cycle differs from an EMCS cycle in the role played by the redox active material. For an EMCCS cycle the redox active material is activated to block a non-redox active absorbent. The simplest EMCCS cycle involves a concerted n electron electrochemical reaction that oxidizes a blocker molecule, B, enabling the blocking of absorbent A and release of captured CO2. A homogeneous reaction between free absorbent and m CO2 molecules may occur in the absence of a blocker. An example of such a system is given by Stern et al. (2013), where CO2 bound to an amine (m = 1) is displaced during the bidentate complexation of two amines with divalent cupric ions (n = 2) released on
E=E +
(
)
xB )( [
nB0 mxB A0
1])m / n) (15)
2.2.2. EMCCS solid dormant blocker The EMAR system originally described by Stern (see Fig. 2b) employs cupric ions as the redox active blocker for amine absorbents (Stern et al., 2013). As such, it utilizes a solid inactive blocker as shown schematically in Fig. 1d. In general
4
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Bn + (aq) + ne
Electrochemical
A(aq) + mCO2 (g) K CO2 =
E dev =
A(CO2 )m (aq)
CA (CO2 )m P0 CA PCO2
m
We consider four general operational strategies for flow systems in electrochemically modulated CO2 capture processes, each with its own particular characteristics. In a two-stage process, as shown in Fig. 3a for the EMCS system, the CO2 is absorbed and complexed with the redoxactive absorbent as soon as it is activated by reduction at the cathode. By the same token, the complex is broken and the CO2 removed as it is released on oxidation of the absorbent at the anode. A similar process can be used in an EMCCS system, except that now it is the deactivation of the blocker molecule at the cathode and breaking of the blockerabsorbent complex that frees up the absorbent to capture CO2. The activation of the blocker at the anode then leads to release of the CO2 which can be removed directly. At the other end of the spectrum, we can use a four-stage process in which each of the steps progresses independently, as illustrated for the EMCCS system in Fig. 3b. Here, the absorbent molecule is freed up through the deactivation of the blocker molecule, and only later is it contacted with the feed gas stream from which the CO2 is absorbed. The complex is then introduced to the anode chamber where the blocker is activated, and the displaced CO2 is retained as a dissolved species that is only removed from solution in the fourth step in a sweep stream. A similar sequence of steps can be used in the EMCS system, too. Combinations of elements of the two- and four-stage strategies can also be used to generate a three-stage process, such as, for instance, simultaneous absorbent activation and CO2 complexation in the cathode chamber in a single step (termed cathodic absorption) while the breaking of the complex in the anode chamber and the subsequent removal by desorption of the CO2 occur in two sequential steps. A different three-stage process would entail activation of the absorbent prior to its contact with the feed gas in a separate stage, followed by the simultaneous release and removal of the CO2 in a single step in the anode chamber (termed anodic desorption).
(16)
A0 = CA + CA (CO2 )m +
n CB (A)nn +/ m m
(17)
B0 = C Bn + + CB (A)nn+/ m
CB (A)nn+/ m
(18)
For convenience, the blocker loading can be defined as
nB0 mA0
mA0
(19)
Note that the state of charge (SOC) is directly related to the total activated blocker in solution by (20)
SOC = nB0 = mxB A0
The relationship between the open circuit potential of a stream and its state, for all systems with sufficiently large β, is then given by
RT C [ln( 0 ) ln((1 mF A0 m + ln 1 + K CO2 P˜CO2 ]
E=E +
(
xB )(
)
nC0 m / n ) ) mxB A 0 (21)
4.1. Thermodynamic paths
3. Deviation potential
Three simple thermodynamic pathways exist for the different stages in the EMCS and EMCCS systems. They are:
The open circuit potentials for each of the four molecular architectures show one striking similarly, in all cases with increasing m K CO2 P˜CO2 the open circuit potential increases by the same magnitude. We can use this feature to select appropriate reference conditions for each architecture to ensure that all of the open circuit potential relationships converge. We define E0 as the open circuit potential of a stream with no CO2 (PCO2 = 0 ), which is only a function of the state of charge. Then the deviation potential, Edev, the open circuit potential deviation from E0, can be defined for all molecular architectures described above, as
Constant state of charge: The non-electrochemical steps of absorption from the feed gas and desorption to a sweep stream both occur under a constant state of charge while the CO2 partial pressure and total concentration in the liquid vary. Constant total CO2concentration: When the electrochemical reactions occur with no simultaneous uptake or release of CO2, the total CO2 concentration in solution remains constant, while the actual distribution of CO2 between its physically dissolved state (as reflected in the partial pressure) and its complexed state changes in response to changes in the state of charge. Constant CO2partial pressure: Under cathodic absorption or anodic desorption, a constant CO2 partial pressure is maintained, even as the state of charge changes. Under these conditions, the total CO2 concentration changes are reflected in changes in the CO2 complexed with the activated or deactivated absorbent.
E dev
(
)
E0 x A
EMCS Inactive Absorbent
(
)
E0 (A 0 )
in Solution EMCS Solid Dormant
E PCO2,x A E PCO2,A0 =
( )
(
E PCO2,A0 , B0, xB
(
E PCO2,A0 , xB
)
)
(22)
4. System configurations
(c)
+ B(A)nn/m (aq) + ne + nCO2 (g) B(s) (d) n + A(CO2)m (aq) m
nCB (A)nn+/ m
(
for all architectures, from which it is evident that E is a function of only CO2 partial pressure, not state of charge or total absorbent concentration.
(b)
The Nernst equation given in (16)a for this electrochemical reaction assumes that the reduced form of the blocking molecule, B, is solid and has an activity of 1. As in the previous case, the assumption is made that β ≫ 1. The total absorbent and blocker concentrations are given by A0 and B0 respectively:
xB =
RT m ln 1 + K CO2 P˜CO2 ) mF dev
n + A(aq) + Bn+ (aq) B(A)nn/m (aq) m n m / CB (A)nn +/ m C0 = CAn/ m C Bn +
Homogeneous
Overall
(a)
RT C0 ln nF C B n+
E=E Homogeneous
B(s)
Absorbent E0 (A0 , B0, xB ) EMCCS Dormant Blocker
E0 (A0 , xB )
A relationship between the open circuit potential and the state of charge of EMCS and EMCCS systems established for constant CO2 partial pressure paths is given by Eq. (22). In order to resolve the other two paths listed above, it is necessary to establish a relationship between the state of charge, CO2 partial pressure, and total CO2
in Solution EMCCS Solid Dormant Blocker
It can readily be shown that 5
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Fig. 3. Flow geometries for both EMCS and EMCCS systems may employ either two, three, or four-stage geometries. (a) CO2 is captured during activation of the sorbent, and released as it is deactivated. (b) The CO2 is absorbed in a separate stage from the sorbent activation, and desorbed only once the solution has been fully deactivated.
concentration in the liquid. We define the total carbon dioxide concentration as
decreases. Fig. 4a gives the base case against which the others are compared. In Fig. 4b, the physical solubility for the CO2 in free solution is doubled relative to that in the base case. A lower partial pressure is needed to attain the same level of dissolved CO2 in the solution at a given state of charge, and thus the deviation potential is lowered relative to the base case. This effect is very pronounced at high partial pressures, but diminishes with increasing state of charge or at low partial pressures where the solution is dominated by the bound CO2 and the impact of the free solution concentration is negligible. The effect of a doubling of the binding affinity K CO2 is indicated in Fig. 4c. The deviation potential increases for a given partial pressure. Eq. (25) indicates that the state of charge needed to attain a given overall CO2 concentration, with the same distribution between solution and bound states, must decrease with an increase in K CO2 ; the lower state of charge is associated with an increase in deviation potential, and thus the curves are shifted upwards relative to those in the base case. Similarly, a doubling of the absorbent affinity for CO2 leads to an increase in Edev for any given partial pressure, i.e., the constant partial pressure lines also move upwards on the Edev - α plot. When both the binding affinity and the physical solubility are doubled relative to their base case values, their effects on the constant concentration curves counteract each other (when m = 1) and the curves in Fig. 4d are the same as for the base case. The impact of partial pressure on the deviation potential is governed by the effects of the binding affinity on this potential, and thus the constant partial pressure curves are shifted upwards relative to the base case, as in Fig. 4c. Fig. 5 gives examples of the paths followed for the four different strategies, two-, four-, and two three-stage systems, for k˜CO2 = 0.05 and K CO2 = 500 , as described below. The total work of separation for an electrochemical cycle, defined by the path integral of the open circuit potential, E, as it changes with state of charge, Q, is
(23)
CO2,0 = CCO2 + mCA (CO2 )m
The dissolved CO2 concentration, CCO2 , is related to the partial pressure PCO2 by the Henry's law constant, kh,CO2 , according to (24)
CCO2 = PCO2 kh,CO2 kh,CO2 P0
CO2,0
For convenience, we define k˜h,CO2 = mA and x CO2,0 = mA for all 0 0 systems where the total absorbent concentration is unchanged. For systems in which the absorbent concentration changes, i.e. EMCS with kh,CO P0 CO solid dormant absorbent, we define k˜h,CO2 = mC2 and x CO2,0 = mC2,0 . 0 0 It can be shown that the relationship between state of charge, CO2 partial pressure, and total CO2 concentration is given by m
x CO2,0 =
K CO2 P˜CO2 + k˜h,CO2 P˜CO2 m 1 + K CO2 P˜CO2
(25)
where the α parameter, given in Table 2, indicates the system state of charge. Fig. 4 shows the Edev - α thermodynamic diagram for different combinations of absorbent affinity (K CO2 ) and CO2 solubility (k˜H,CO2 ). The deviation potential increases with increasing partial pressure, but is unaffected by the state-of-charge in the system under a given partial pressure, in accord with Eq. (22), i.e., the constant PCO2 lines are horizontal. The constant concentration lines, on the other hand, are strongly curved, with high deviation potentials at low state of charge and high partial pressure, decreasing to low potentials at high state of charge and low partial pressures, reflecting the fact that with a greater fraction of the CO2 bound to the activated absorbent with higher state of charge, the fraction of free CO2 in solution, or the partial pressure, Table 2 Parameters for carbon dioxide balance given in Eq. (25).
ECMS with dormant absorbent in solution ECMS with solid dormant absorbent ECCMS with dormant blocker in solution ECCMS with solid dormant blocker
W=
x CO2,0
α
k˜h,CO2
CO2,0
xA
kh,CO2 P 0
mA0 CO2,0 mC0 CO2,0 mA0 CO2,0 mA0
A0 C0
1 − xB 1 − xB
E dQ =
E dev dQ
(26)
which is proportional to the shaded area shown in each of the panels of Fig. 5. In all cases, the absorption begins at a feed partial pressure of 0.15 bar and state of charge of 0.25, and continues until the state of charge is 0.75 (i.e. a swing in the state of charge of 0.5) and is removed as a pure CO2 stream at 1 bar. The other conditions along the path depend on the system geometry employed. In the four-stage system shown in Fig. 5a, the solution introduced to the cathode consists of inactivated absorbent solution in equilibrium
mA0 kh,CO2 P 0 mC0 kh,CO2 P 0 mA0 kh,CO2 P 0 mA0
6
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Fig. 4. Effect of absorbent affinity, K CO2 , and CO2 solubility, k˜H,CO2 on the deviation potential when m = 1. Solid lines show deviations from the base case. Blue lines are for constant partial pressure, and red lines denote constant total concentration (bound and free) in solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
with the 1 bar product gas stream. As the absorbent is activated (1), i.e., the state of charge increases, the total CO2 concentration remains constant, and the path follows the corresponding constant concentration curve, but the free amount in solution (the partial pressure) decreases and the complexed amount increases. In the next stage (2), the activated absorbent is contacted with the feed gas, and the uptake of the CO2 traces a vertical path at constant state of charge, traversing the total CO2 concentration and partial pressure lines until the partial pressure of the feed gas is reached. In the anodic chamber (3), where the absorbent is deactivated as the state of charge decreases, the total CO2 concentration remains constant, but the partial pressure increases as the balance shifts from the complexed to the free CO2 in solution. Provided the pressure in the anodic chamber is greater than about 10 bar, the free CO2 in solution is not saturated and, at the end of this cycle, is at a partial pressure of 10 bar. In the final step (4), the CO2 is removed by desorption as a gas in the flash tank at a pressure of 1 bar; the state of charge remains constant in this case, but the total CO2 concentration in solution decreases. The final solution is then returned to the cathodic chamber to begin the cycle again. In the three-stage system with coupled anodic deactivation and direct removal of the CO2, in Fig. 5b, the cathodic activation (1) and absorption steps (2) are the same as for the four-stage scenario, but now the deactivation step follows a different path. During the initial stages of decreasing state of charge, the free CO2 is below the saturation limit, (i.e., partial pressure is below the system pressure) and the path follows
the constant CO2 curve (3a). Once the partial pressure reaches its saturation value of 1 bar, all the subsequent CO2 is released at this constant pressure as the state of charge decreases (3b). In the three-stage system with coupled cathodic activation and simultaneous capture of CO2 (Fig. 5c), as outlined in a recent patent application (Hatton et al., 2019), the activation process initially traces the constant concentration curve 1(a) as the free CO2 in solution complexes with the activated absorbent and the partial pressure decreases until it reaches the partial pressure of the feed gas stream (0.15 bar in this example) at which point CO2 capture begins. At this point, the path breaks away from the constant concentration curve and moves horizontally, or almost horizontally, to the final state of charge (1b). If the feed stream is in significant excess, a constant partial pressure curve will be taken; otherwise, the partial pressure will drop as absorption occurs and the feed stream becomes leaner. The separate deactivation/ desorption and CO2 gas disengagement steps (3) and (4) are the same as in the four-stage system. Finally, the two-stage system combines features of both three-stage processes, as shown in Fig. 5d, with the path now tracing the (1a)–(1b)–(3a)–(3b) curves. It is evident from the four scenarios given in Fig. 5 that the work required for the four-stage system is significantly larger than that for either of the three-stage processes, which themselves require more work than the two-stage system. The reason for this is that those processes in which the CO2 in the gas phase is constantly in equilibrium 7
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Fig. 5. Thermodynamic paths for four system geometries: (a) four-stage system employing: (1) cathodic activation, (2) absorption to 0.15 bar, (3) anodic deactivation, (4) desorption to 1 bar; (b) three-stage system employing: (1) cathodic activation, (2) absorption to 0.15 bar, (3) anodic desorption to 1 bar; (c) three-stage system employing: (1) cathodic absorption from 0.15 bar to 0.075 bar, (3) anodic deactivation (4) desorption to 1 bar; (d) two-stage system employing: (1) cathodic absorption from 0.15 bar to 0.075 bar, (3) anodic desorption to 1 bar. k˜CO2 = 0.05 and K CO2 = 500 .
with the solution phase are thermodynamically reversible, whereas the multistep activation and absorption, or deactivation and desorption, processes are not. These results are summarized succinctly in Fig. 6, where the penalty for non-cathodic absorption is shown in red, and that for non-anodic desorption in blue. The total energy penalty for a fourstage process is the sum of the penalties for the two three-stage processes.
solution, since the higher the solubility, the greater the drive to transfer from the gas to the liquid phase, and hence the lower the work required to effect the separation. For the three-stage process with anodic desorption, on the other hand, the separation work required depends strongly on the binding energy, reflecting the increasing energy penalty associated with the breaking of the bonds between the CO2 and the absorbent with increasing K CO2 . The weak dependence on physical solubility is because the CO2 is removed from solution as it is released by the deactivated absorbent. The four-stage process, on the other hand, exhibits features of both three-stage systems as illustrated in Fig. 5, with a functional dependency on K CO2 and k˜H,CO2 being a combination of the dependencies observed for the cathodic absorption and anodic desorption cases, respectively.
4.2. Sensitivity to K CO2 and k˜H,CO2 The ideal work required to capture CO2 from a feed gas at 0.15 bar and release it as a pure CO2 gas at 1 bar is shown in Fig. 7 as a function of the binding constant K CO2 for different values of the Henry's law constant k˜H,CO2 under the four different operating strategies discussed here. It is remarkable that the work for the two-stage system tracks the thermodynamic minimum work for this process, attributed as above to the fact that the absorption and desorption both follow fully reversible paths. The work for CO2 capture in the three-stage process with cathodic absorption is unaffected by the strength of complexation of CO2 with the absorbent, since any CO2 absorbed by the solution immediately complexes with the absorbent; it does, however, depend almost logarithmically on the physical solubility of the gas in the
5. Conclusions The analysis given in this report provides a coherent, unified picture of the thermodynamics of two different electrochemically based approaches, ECMS and ECCMS, for the capture of CO2 from a feed gas at low partial pressure and its release in pure form at a higher pressure. The results obtained are independent of molecular architecture and are guided by a single deviation potential for all modes of operation that depends on the strength of binding in the complexation reactions, the 8
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
reactions at the electrodes was recognized as well as the fact that to follow the activation and deactivation curves closely, as required for an energetically efficient operation, a spatially dependent deviation potential would be necessary – this can be accounted for by use of segmented electrodes, each of which could be addressed individually, as discussed by Wang et al. (2018) The thermodynamic framework established in this paper can be the basis for future studies on the energetics of electrochemically mediated separation processes, not only for gas separations, but also for a range of other Faradaically driven applications such as, e.g., in water treatment for removal of trace organic contaminants (Achilleos and Hatton, 2016; Su and Hatton, 2017; Mao et al., 2018; Ren et al., 2018). Conflict of interest The authors declare that they have no conflict of interest. References Achilleos, D.S., Hatton, T.A., 2016. Selective molecularly mediated pseudocapacitive separation of ionic species in solution. ACS Appl. Mater. Interfaces 8 (48), 32743–32753. https://doi.org/10.1021/acsami.6b07605. Apaydin, D.H., Głowacki, E.D., Portenkirchner, E., Sariciftci, N.S., 2014. Direct electrochemical capture and release of carbon dioxide using an industrial organic pigment: quinacridone. Angew. Chem. Int. Ed. 53 (26), 6819–6822. https://doi.org/10.1002/ anie.201403618. Appel, A.M., Newell, R., DuBois, D.L., Rakowski DuBois, M., 2005. Concentration of carbon dioxide by electrochemically modulated complexation with a binuclear copper complex. Inorg. Chem. 44 (9), 3046–3056. https://doi.org/10.1021/ ic050023k. Bard, A.J., Faulkner, L.R., 2001. Electrochemical Methods: Fundamentals and Applications, 2nd edition. Wiley, New York. Gurkan, B., Simeon, F., Hatton, T.A., 2015. Quinone reduction in ionic liquids for electrochemical CO2 separation. ACS Sustain. Chem. Eng. 3 (7), 1394–1405. https://doi. org/10.1021/acssuschemeng.5b00116. Hatton, T.A., Shaw, R.A., Wang, M., Voskian, S., 2019. Methods and Systems for Removing CO2 from a Feed Gas. Ishida, H., Ohba, T., Yamaguchi, T., Ohkubo, K., 1994. Interaction between CO2 and electrochemically reduced species of N-propyl-4,4′-bipyridinium cation. Chem. Lett. 23 (5), 905–908. https://doi.org/10.1246/cl.1994.905. Mao, X., Tian, W., Ren, Y., Chen, D., Curtis, S.E., Buss, M.T., Rutledge, G.C., Hatton, T.A., 2018. Energetically efficient electrochemically tunable affinity separation using multicomponent polymeric nanostructures for water treatment. Energy Environ. Sci. 11 (10), 2954–2963. https://doi.org/10.1039/C8EE02000K. Marcott, S.A., Shakun, J.D., Clark, P.U., Mix, A.C., 2013. A reconstruction of regional and global temperature for the past 11,300 years. Science 339 (6124), 1198–1201. https://doi.org/10.1126/science.1228026. Mizen, M.B., Wrighton, M.S., 1989. Reductive addition of CO2 to 9,10-phenanthrenequinone. J. Electrochem. Soc. 136 (4), 941–946. https://doi.org/10.1149/1. 2096891. National Academy of Sciences, 2014. Climate Change: Evidence and Causes. https://doi. org/10.17226/18730. Oreskes, N., 2004. The scientific consensus on climate change. Science 306 (5702), 1686. https://doi.org/10.1126/science.1103618. Ranjan, R., Olson, J., Singh, P., Lorance, E.D., Buttry, D.A., Gould, I.R., 2015. Reversible electrochemical trapping of carbon dioxide using 4,4′-bipyridine that does not require thermal activation. J. Phys. Chem. Lett. 6 (24), 4943–4946. https://doi.org/10. 1021/acs.jpclett.5b02220. Ren, Y., Lin, Z., Mao, X., Tian, W., Van Voorhis, T., Hatton, T.A., 2018. Superhydrophobic, surfactant-doped, conducting polymers for electrochemically reversible adsorption of organic contaminants. Adv. Funct. Mater. 28 (32), 1801466. https://doi.org/10.1002/adfm.201801466. Rheinhardt, J.H., Singh, P., Tarakeshwar, P., Buttry, D.A., 2017. Electrochemical capture and release of carbon dioxide. ACS Energy Lett. 2 (2), 454–461. https://doi.org/10. 1021/acsenergylett.6b00608. Rogelj, J., den Elzen, M., Höhne, N., Fransen, T., Fekete, H., Winkler, H., Schaeffer, R., Sha, F., Riahi, K., Meinshausen, M., 2016. Paris Agreement climate proposals need a boost to keep warming well below 2°C. Nature 534 (7609), 631–639. https://doi.org/ 10.1038/nature18307. Scovazzo, P., Poshusta, J., DuBois, D., Koval, C., Noble, R., 2003. Electrochemical nitrogen. J. Electrochem. Soc. 150 (5), D91–D98. https://doi.org/10.1149/1.1566962. Singh, P., Rheinhardt, J.H., Olson, J.Z., Tarakeshwar, P., Mujica, V., Buttry, D.A., 2017. Electrochemical capture and release of carbon dioxide using a disulfide–thiocarbonate redox cycle. J. Am. Chem. Soc. 139 (3), 1033–1036. https://doi. org/10.1021/jacs.6b10806. Solomon, S., Plattner, G.-K., Knutti, R., Friedlingstein, P., 2009. Irreversible climate change due to carbon dioxide emissions. PNAS 106 (6), 1704–1709. https://doi.org/ 10.1073/pnas.0812721106. Stern, M.C., Hatton, T.A., 2014. Bench-scale demonstration of CO2 capture with electrochemically-mediated amine regeneration. RSC Adv. 4 (12), 5906–5914. https://
Fig. 6. A thermodynamic penalty exists for decoupling electrochemical steps and absorption/desorption. The penalty for a non-cathodic absorption (passing through 2) is given in red, whereas the penalty for a non-anodic desorption (passing through 4) is given in blue. The intersection of these two regions, as delineated by the solid lines, gives the energetics for an ideal two-stage system. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Total work of capture, W (in kJ/mol CO2 captured), as a function of sorbent binding affinity, K CO2 , and CO2 solubility, k˜H,CO2 for each system geometry: 4-stage, 3-stage with anodic desorption (3a), 3-stage with cathodic absorption (3c), and 2-stage. Case considered: 50% capture of a 15 mol% CO2 stream at 323 K, with desorption at 1 bar, m = 1, and a state of charge shift between α = 0.25 and α = 0.75.
partial pressure of CO2 (or its physical solubility) in solution, and the state of charge of the redox active species. The total work required to attain a given degree of separation depends on the operating strategy adopted, the most efficient being when the absorption and desorption of the gas are coupled directly and occur simultaneously with the activation and de-activation of the absorbent, respectively. The least efficient operation is when the activation, absorption, deactivation and desorption processes are fully decoupled and operate sequentially. Only thermodynamically ideal operations were included in this study, and a more rigorous assessment of the energy requirements in electrochemically modulated CO2 capture and release operations can use this framework as a basis upon which the solution non-idealities can be imposed. Wang et al. used a more specific formulation of this analysis for the EMCCS case with a solid dormant blocker, namely for the electrochemically mediated amine regeneration (EMAR) process developed in our laboratories (Wang et al., 2018). The need for the application of overpotentials to ensure sufficiently rapid Faradaic 9
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R.A. Shaw and T.A. Hatton doi.org/10.1039/C3RA46774K. Stern, M.C., Simeon, F., Herzog, H., Hatton, T.A., 2013. Post-combustion carbon dioxide capture using electrochemically mediated amine regeneration. Energy Environ. Sci. 6 (8), 2505–2517. https://doi.org/10.1039/C3EE41165F. Stern, M.C., 2014. Electrochemically-Mediated Amine Regeneration for Carbon Dioxide Separations (Ph.D. thesis). Massachusetts Institute of Technology. Su, X., Hatton, T.A., 2017. Electrosorption at functional interfaces: from molecular-level interactions to electrochemical cell design. Phys. Chem. Chem. Phys. 19 (35), 23570–23584. https://doi.org/10.1039/C7CP02822A.
UNFCCC, 2015. Adoption of the Paris Agreement. Tech. Rep. FCCC/CP/2015/L.9/Rev.1. Wang, M., Hariharan, S., Shaw, R.A., Hatton, T.A., 2019. Energetics of electrochemically mediated amine regeneration process for flue gas CO2 capture. Int. J. Greenh. Gas Control 82, 48–58. https://doi.org/10.1016/j.ijggc.2018.12.028. Watkins, J.D., Siefert, N.S., Zhou, X., Myers, C.R., Kitchin, J.R., Hopkinson, D.P., Nulwala, H.B., 2015. Redox-mediated separation of carbon dioxide from flue gas. Energy Fuels 29 (11), 7508–7515. https://doi.org/10.1021/acs.energyfuels.5b01807. Wilcox, J., 2012. Carbon Capture. Springer, New York.
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Contents lists available at ScienceDirect
International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc
Electrochemical CO2 capture thermodynamics Ryan A. Shaw, T. Alan Hatton*
T
Massachusetts Institute of Technology, Department of Chemical Engineering, Cambridge, MA 02139, United States
ARTICLE INFO
ABSTRACT
Keywords: Carbon capture Electrochemical Complexation separation Competitive complexation separation
We analyze four general architectures for electrochemically mediated carbon dioxide capture systems, in each of which the electrophilicity of a redox active absorbent or absorbent blocking species is manipulated to influence the system's affinity for CO2. It is shown that the open circuit potentials of these architectures converge given the appropriate reference - namely a state in which no CO2 is present in the stream. The resulting difference between the open circuit potential of a stream and of that same stream lacking CO2 is referred to as the deviation potential. In the context of this deviation potential, four system process configurations are analyzed. The most efficient process configuration for all four electrochemical architectures is one that employs both a cathodic absorption taking place simultaneously with the reduction process and an anodic desorption that occurs along with the oxidation of the redox active species; decoupled electrochemical reactions and absorption/desorption steps incur significant energetic penalties.
1. Introduction Anthropogenic carbon dioxide emissions have resulted in a 40% increase in atmospheric CO2 concentration since the industrial revolution, half of which has come in the last 50 years (Marcott et al., 2013). Carbon dioxide, a greenhouse gas, absorbs infrared radiation reflected from the earth's surface which would otherwise be sent to space (Solomon et al., 2009). As such, there is strong agreement within the scientific community that these greenhouse gas emissions are causing climate change (Oreskes, 2004). The result is a sharp increase in global temperature anomalies over the same 50 year time period. An average global temperature increase of 0.8 ∘C since 1900 is one of many symptoms of this change which also include rising and more acidic oceans, significant loss of arctic sea ice, and a myriad of related climate events. Mitigation of climate change, whose primary cause is anthropogenic CO2 production, is therefore one of the most important issues the scientific community currently faces (National Academy of Sciences, 2014). To avoid the 2 ∘C global warming limit target established by the Paris agreement, stop gap measures like carbon capture and storage (CCS) will need to be employed (Rogelj et al., 2016; UNFCCC, 2015). While many CO2 capture processes utilize thermal or pressure cycles to manipulate an absorbent's affinity for CO2 (Wilcox, 2012), a promising approach is to instead apply an electrochemical cycle (Stern et al., 2013; Rheinhardt et al., 2017). Electrochemical cells have the advantage that they can be readily integrated as plug-and-play processes
⁎
that do not require external sources of steam or high pressures or vacuum for their operation. A number of redox active materials have been explored for carbon capture, including direct complexation species such as quinones (Apaydin et al., 2014; Gurkan et al., 2015; Scovazzo et al., 2003), bipyridines (Ishida et al., 1994; Ranjan et al., 2015), and disulfides (Singh et al., 2017) as well as competitive complexation species such as in copper/amine systems (Stern et al., 2013). Table 1 summarizes the underlying electrochemical processes driving these different systems. An appropriate thermodynamic framework is necessary to enable comparative analyses of the energetic demands of different processes and process configurations; this is the goal of this report. 2. Electrochemical architectures for CO2 capture systems Stern describes two architectures for electrochemically mediated carbon dioxide capture: electrochemically mediated complexation separation (EMCS) and electrochemically mediated competitive complexation separation (EMCCS) (Stern, 2014). In EMCS a redox active absorbent is activated for CO2 capture at the cathode and deactivated at the anode to release the captured CO2. In EMCCS a redox active blocker species whose electrophilicity may be manipulated serves to displace CO2 bound to an electrochemically inert absorbent. Since this blocker species becomes a stronger electrophile upon oxidation, the absorbent is deactivated for CO2 binding at the anode. Both of these architectures, which are summarized in Fig. 1, could employ a dormant electrochemically active species either in solution or as a solid bound to the
Corresponding author. E-mail address: [email protected] (T.A. Hatton).
https://doi.org/10.1016/j.ijggc.2019.102878 Received 15 June 2019; Received in revised form 21 September 2019; Accepted 21 October 2019 1750-5836/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Greenhouse Gas Control 95 (2020) 102878
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Table 1 Electrochemical carbon dioxide capture chemistries. Architecture
System/species
Reaction(s) of interest
Ref.
EMCS
Quinones (Q)
Q+e Q• + e Q2 Q2 + CO2 Q2 [CO2] Q2 [CO2] + CO2 Q2 [CO2]2
(Apaydin et al., 2014; Gurkan et al., 2015; Scovazzo et al., 2003; Mizen and Wrighton, 1989; Watkins et al., 2015; Appel et al., 2005)
EMCS
Bipyridine (B)
(Ishida et al., 1994; Ranjan et al., 2015)
EMCS
Disulfides
B+e B + CO2
EMCCS
Metals (Cu for example)
Q•
RSSR + 2e 2RS + 2CO2
B BCO2
(Singh et al., 2017)
2RS 2RSCO2
(Stern et al., 2013; Stern and Hatton, 2014)
Cu2 + + 2e Cu Am + CO2 AmCO2 2Am + Cu2 +
Cu(Am)22 +
Fig. 1. Two possible architectures exist for both EMCS and EMCCS systems: (a, c) the dormant electrochemically active species remains in solution, (b, d) only the active electrochemically active species is in solution.
electrodes. The thermodynamics of each of these systems is described below. Four possible process configurations are considered. The first is a twostage system, in which carrier activation and CO2 absorption occur simultaneously at the cathode and carrier deactivation and CO2 desorption occur at the anode. The second is a four-stage system where absorbent activation and deactivation, which occur at the cathode and anode respectively, are decoupled from absorption and desorption. Two possible three-stage systems are created by incorporating either a cathodic absorption or anodic desorption in an otherwise four-stage system. Practical examples of two of these different architectures are
shown in Fig. 2a and b. 2.1. EMCS: an electrochemically active absorbent The simplest EMCS cycle involves a concerted m electron electrochemical reaction and a homogeneous binding of an activated absorbent, Am−, to m CO2 molecules. Therefore, for every electron passed through the EMCS cycle a single CO2 molecule is captured at perfect Faradaic efficiency. Examples of this include: Scovazzo et al.'s one electron bipyridine system (Scovazzo et al., 2003), Gurkan et al.'s two electron quinone process (Gurkan et al., 2015), or Buttry et al.'s two
2
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Fig. 2. Example EMCS and EMCCS architectures. (a) Quinone molecules activated at the cathode complex with CO2 before transferring to the anode, where they are deactivated and release CO2. (b) The amine-CO2 complex from the absorption column is introduced to the anode chamber where cupric ions are released and complex with the amines, releasing the CO2. The amines are regenerated on reduction of the copper in the cathode chamber.
electron benzyldisulfide system (Singh et al., 2017). The open circuit potential, the potential at which there is no current, for this reaction establishes total work of separation for an EMCS cycle (Bard and Faulkner, 2001). It will be shown that the strength of binding of CO2 to an activated sorbent molecule, defined by binding constant K CO2 , has a strong effect on this open circuit potential. The EMCS architecture requires that an activated carrier molecule be in solution in order to transport bound carbon dioxide to the anode for release. However, an inactive or dormant absorbent may be either in solution or in a solid state, which will affect the open circuit potential. As shown in Fig. 1a and b, respectively, a dormant absorber in solution may be used in a continuous cycle, whereas a solid dormant absorbent will be shuttled from cathode to anode when in the activated solution state.
Electrochemical
Homogeneous
A(aq) + me
Am
(a)
RT C m E=E ln A mF CA (aq) + mCO2 (g) A(CO2)m m (aq) K CO2 =
Overall
Am (aq)
CA (CO2 )m m C Am
A(aq) + me + mCO2 (g)
P0 PCO2
(b)
m
A(CO2)m m (aq) (c)
(1)
The open circuit potential for such a system, as described by the Nernst Equation, is given in Eq. (1)a. Here Ci is the concentration of component i, PCO2 is the partial pressure of CO2, and P0 is the reference pressure (1 bar). For convenience, we define total absorbent concentration and absorbent activation in the following manner:
A0 = CA + C Am + CA (CO2 )m m 2.1.1. EMCS dormant absorbent in solution Consider first an EMCS cycle with a dormant absorbent in solution, like that employed by Scovazzo et al. (2003). The relevant reactions are
xA =
3
C Am + CA (CO2 )m m A0
(2) (3)
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
The state of charge (SOC) is directly related to the total absorbent concentration and the activated fraction through the equation
oxidation of a copper anode. As in the EMCS cycle one electron releases one CO2 molecule. Similar to the EMCS system, EMCCS may utilize a dormant redox active species which is either in solution or in the solid state. As shown in Fig. 1c and d respectively, a dormant blocker in solution may be used in a continuous cycle, whereas a solid dormant blocker will be shuttled from anode to cathode.
(4)
SOC = m (C Am + CA (CO2 )m ) = mA0 x A m
The state of charge as well as the open circuit potential, given by Eq. (1)a, define the total work of capture for an EMCS cycle. An approach similar to that taken by Gurkan et al. may be employed to arrive at a relationship between the open circuit potential and the parameters above, which define the state of the system (Gurkan et al., 2015). Thus
E=E +
RT 1 xA m [ln( ) + ln 1 + K CO2 P˜CO2 ] mF xA
(
)
2.2.1. EMCCS dormant blocker in solution A similar approach to that taken for the thermodynamics of an EMCS system may be employed for an EMCCS system. Consider first a dormant blocker, B, which remains in solution. The open circuit potential for such a system, as described by the Nernst Equation, is given in Eq. (10)a.
(5)
where P˜CO2 = PCO2/ P0 . It is of note that while the open circuit potential is not an explicit function of total absorbent concentration for the activated absorbent architecture, this will not be the case for other architectures described.
Electrochemical Bn + (aq) + ne B(aq) (a) RT CB E=E ln( ) nF C Bn + Homogeneous A(aq) + mCO2 (g) A(CO2)m (aq) (b) CA (CO2)m P0 m K CO2 = ( ) CA PCO2 n + Homogeneous A(aq) + Bn + (aq) B(A)nn/m (aq) (c) m n / m CB (A)nn +/m C0 = CAn/ m C Bn +
2.1.2. EMCS solid dormant absorbent For an EMCS system with a solid state dormant absorbent, assuming unit activity for the solid species, the relevant reactions with their thermodynamic equilibria are
Electrochemical
A(s) + me
Am (aq)
RT C ln A mF C0 (aq) + mCO2 (g) A(CO2)m m (aq) E=E
Homogeneous
Am
K CO2 = Overall
(a)
m
CA (CO2 )m m
P0 PCO2
C Am
A(CO2)m m
A(s) + me + mCO2 (g)
(b)
(aq) (c)
A0 = CA + CA (CO2 )m +
(7)
(
)
,
(11)
CB + CB (A)nn +/ m
(12)
We further define the total activated blocker fraction as
(8)
RT C m [ln( 0 ) + ln 1 + K CO2 P˜CO2 ] mF A0
n CB (A)nn +/ m m
B0 = CB + C Bn + + CB (A)nn +/m
As before we may establish a relationship between the open circuit potential of a stream and its state as
E=E +
(10)
we also describe total blocker concentration as
Since the dormant absorbent is solid in this scenario, the state of charge is a function only of the amount of absorbent that has become activated and entered solution, as given by
SOC = m (C Am + CA (CO2 )m ) = mA0 m
(d)
In addition to describing total absorbent concentration as in the EMCS case,
(6)
Here C0 is the reference concentration (1 M). The total absorbent concentration in solution is
A0 = C Am + CA (CO2 )m m
+ B(A)nn/m (aq) + ne + nCO2 (g) n B(aq) + A(CO2)m (aq) m
Overall
m
xB =
nCB (A)nn+/ m
(13)
mA0
This analysis assumes the binding of the blocker to the absorbent is quite strong, i.e. β ≫ 1 in Eq. (10)c. The result is that any activated blocker will be bound to an absorber as long as any absorbent remains. Note then that the state of charge (SOC) is directly related to the total activated blocker fraction via
(9)
Note that while the open circuit potential relationship varies for the dormant absorbent in solution versus that for the solid dormant absorbent systems – as given by Eqs. (5) and (9), respectively – it will be shown that given appropriate reference states these two may be treated identically.
SOC = n (C Bn + + CB (A)nn+/ m )
nCB (A)nn +/m = mxB A0
(14)
The relationship between the open circuit potential of a stream and its state can then be shown to be
2.2. EMCCS: an electrochemically active blocker
RT C [ln( 0 ) ln((1 mF A0 m + ln 1 + K CO2 P˜CO2 ]
An EMCCS cycle differs from an EMCS cycle in the role played by the redox active material. For an EMCCS cycle the redox active material is activated to block a non-redox active absorbent. The simplest EMCCS cycle involves a concerted n electron electrochemical reaction that oxidizes a blocker molecule, B, enabling the blocking of absorbent A and release of captured CO2. A homogeneous reaction between free absorbent and m CO2 molecules may occur in the absence of a blocker. An example of such a system is given by Stern et al. (2013), where CO2 bound to an amine (m = 1) is displaced during the bidentate complexation of two amines with divalent cupric ions (n = 2) released on
E=E +
(
)
xB )( [
nB0 mxB A0
1])m / n) (15)
2.2.2. EMCCS solid dormant blocker The EMAR system originally described by Stern (see Fig. 2b) employs cupric ions as the redox active blocker for amine absorbents (Stern et al., 2013). As such, it utilizes a solid inactive blocker as shown schematically in Fig. 1d. In general
4
International Journal of Greenhouse Gas Control 95 (2020) 102878
R.A. Shaw and T.A. Hatton
Bn + (aq) + ne
Electrochemical
A(aq) + mCO2 (g) K CO2 =
E dev =
A(CO2 )m (aq)
CA (CO2 )m P0 CA PCO2
m
We consider four general operational strategies for flow systems in electrochemically modulated CO2 capture processes, each with its own particular characteristics. In a two-stage process, as shown in Fig. 3a for the EMCS system, the CO2 is absorbed and complexed with the redoxactive absorbent as soon as it is activated by reduction at the cathode. By the same token, the complex is broken and the CO2 removed as it is released on oxidation of the absorbent at the anode. A similar process can be used in an EMCCS system, except that now it is the deactivation of the blocker molecule at the cathode and breaking of the blockerabsorbent complex that frees up the absorbent to capture CO2. The activation of the blocker at the anode then leads to release of the CO2 which can be removed directly. At the other end of the spectrum, we can use a four-stage process in which each of the steps progresses independently, as illustrated for the EMCCS system in Fig. 3b. Here, the absorbent molecule is freed up through the deactivation of the blocker molecule, and only later is it contacted with the feed gas stream from which the CO2 is absorbed. The complex is then introduced to the anode chamber where the blocker is activated, and the displaced CO2 is retained as a dissolved species that is only removed from solution in the fourth step in a sweep stream. A similar sequence of steps can be used in the EMCS system, too. Combinations of elements of the two- and four-stage strategies can also be used to generate a three-stage process, such as, for instance, simultaneous absorbent activation and CO2 complexation in the cathode chamber in a single step (termed cathodic absorption) while the breaking of the complex in the anode chamber and the subsequent removal by desorption of the CO2 occur in two sequential steps. A different three-stage process would entail activation of the absorbent prior to its contact with the feed gas in a separate stage, followed by the simultaneous release and removal of the CO2 in a single step in the anode chamber (termed anodic desorption).
(16)
A0 = CA + CA (CO2 )m +
n CB (A)nn +/ m m
(17)
B0 = C Bn + + CB (A)nn+/ m
CB (A)nn+/ m
(18)
For convenience, the blocker loading can be defined as
nB0 mA0
mA0
(19)
Note that the state of charge (SOC) is directly related to the total activated blocker in solution by (20)
SOC = nB0 = mxB A0
The relationship between the open circuit potential of a stream and its state, for all systems with sufficiently large β, is then given by
RT C [ln( 0 ) ln((1 mF A0 m + ln 1 + K CO2 P˜CO2 ]
E=E +
(
xB )(
)
nC0 m / n ) ) mxB A 0 (21)
4.1. Thermodynamic paths
3. Deviation potential
Three simple thermodynamic pathways exist for the different stages in the EMCS and EMCCS systems. They are:
The open circuit potentials for each of the four molecular architectures show one striking similarly, in all cases with increasing m K CO2 P˜CO2 the open circuit potential increases by the same magnitude. We can use this feature to select appropriate reference conditions for each architecture to ensure that all of the open circuit potential relationships converge. We define E0 as the open circuit potential of a stream with no CO2 (PCO2 = 0 ), which is only a function of the state of charge. Then the deviation potential, Edev, the open circuit potential deviation from E0, can be defined for all molecular architectures described above, as
Constant state of charge: The non-electrochemical steps of absorption from the feed gas and desorption to a sweep stream both occur under a constant state of charge while the CO2 partial pressure and total concentration in the liquid vary. Constant total CO2concentration: When the electrochemical reactions occur with no simultaneous uptake or release of CO2, the total CO2 concentration in solution remains constant, while the actual distribution of CO2 between its physically dissolved state (as reflected in the partial pressure) and its complexed state changes in response to changes in the state of charge. Constant CO2partial pressure: Under cathodic absorption or anodic desorption, a constant CO2 partial pressure is maintained, even as the state of charge changes. Under these conditions, the total CO2 concentration changes are reflected in changes in the CO2 complexed with the activated or deactivated absorbent.
E dev
(
)
E0 x A
EMCS Inactive Absorbent
(
)
E0 (A 0 )
in Solution EMCS Solid Dormant
E PCO2,x A E PCO2,A0 =
( )
(
E PCO2,A0 , B0, xB
(
E PCO2,A0 , xB
)
)
(22)
4. System configurations
(c)
+ B(A)nn/m (aq) + ne + nCO2 (g) B(s) (d) n + A(CO2)m (aq) m
nCB (A)nn+/ m
(
for all architectures, from which it is evident that E is a function of only CO2 partial pressure, not state of charge or total absorbent concentration.
(b)
The Nernst equation given in (16)a for this electrochemical reaction assumes that the reduced form of the blocking molecule, B, is solid and has an activity of 1. As in the previous case, the assumption is made that β ≫ 1. The total absorbent and blocker concentrations are given by A0 and B0 respectively:
xB =
RT m ln 1 + K CO2 P˜CO2 ) mF dev
n + A(aq) + Bn+ (aq) B(A)nn/m (aq) m n m / CB (A)nn +/ m C0 = CAn/ m C Bn +
Homogeneous
Overall
(a)
RT C0 ln nF C B n+
E=E Homogeneous
B(s)
Absorbent E0 (A0 , B0, xB ) EMCCS Dormant Blocker
E0 (A0 , xB )
A relationship between the open circuit potential and the state of charge of EMCS and EMCCS systems established for constant CO2 partial pressure paths is given by Eq. (22). In order to resolve the other two paths listed above, it is necessary to establish a relationship between the state of charge, CO2 partial pressure, and total CO2
in Solution EMCCS Solid Dormant Blocker
It can readily be shown that 5
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Fig. 3. Flow geometries for both EMCS and EMCCS systems may employ either two, three, or four-stage geometries. (a) CO2 is captured during activation of the sorbent, and released as it is deactivated. (b) The CO2 is absorbed in a separate stage from the sorbent activation, and desorbed only once the solution has been fully deactivated.
concentration in the liquid. We define the total carbon dioxide concentration as
decreases. Fig. 4a gives the base case against which the others are compared. In Fig. 4b, the physical solubility for the CO2 in free solution is doubled relative to that in the base case. A lower partial pressure is needed to attain the same level of dissolved CO2 in the solution at a given state of charge, and thus the deviation potential is lowered relative to the base case. This effect is very pronounced at high partial pressures, but diminishes with increasing state of charge or at low partial pressures where the solution is dominated by the bound CO2 and the impact of the free solution concentration is negligible. The effect of a doubling of the binding affinity K CO2 is indicated in Fig. 4c. The deviation potential increases for a given partial pressure. Eq. (25) indicates that the state of charge needed to attain a given overall CO2 concentration, with the same distribution between solution and bound states, must decrease with an increase in K CO2 ; the lower state of charge is associated with an increase in deviation potential, and thus the curves are shifted upwards relative to those in the base case. Similarly, a doubling of the absorbent affinity for CO2 leads to an increase in Edev for any given partial pressure, i.e., the constant partial pressure lines also move upwards on the Edev - α plot. When both the binding affinity and the physical solubility are doubled relative to their base case values, their effects on the constant concentration curves counteract each other (when m = 1) and the curves in Fig. 4d are the same as for the base case. The impact of partial pressure on the deviation potential is governed by the effects of the binding affinity on this potential, and thus the constant partial pressure curves are shifted upwards relative to the base case, as in Fig. 4c. Fig. 5 gives examples of the paths followed for the four different strategies, two-, four-, and two three-stage systems, for k˜CO2 = 0.05 and K CO2 = 500 , as described below. The total work of separation for an electrochemical cycle, defined by the path integral of the open circuit potential, E, as it changes with state of charge, Q, is
(23)
CO2,0 = CCO2 + mCA (CO2 )m
The dissolved CO2 concentration, CCO2 , is related to the partial pressure PCO2 by the Henry's law constant, kh,CO2 , according to (24)
CCO2 = PCO2 kh,CO2 kh,CO2 P0
CO2,0
For convenience, we define k˜h,CO2 = mA and x CO2,0 = mA for all 0 0 systems where the total absorbent concentration is unchanged. For systems in which the absorbent concentration changes, i.e. EMCS with kh,CO P0 CO solid dormant absorbent, we define k˜h,CO2 = mC2 and x CO2,0 = mC2,0 . 0 0 It can be shown that the relationship between state of charge, CO2 partial pressure, and total CO2 concentration is given by m
x CO2,0 =
K CO2 P˜CO2 + k˜h,CO2 P˜CO2 m 1 + K CO2 P˜CO2
(25)
where the α parameter, given in Table 2, indicates the system state of charge. Fig. 4 shows the Edev - α thermodynamic diagram for different combinations of absorbent affinity (K CO2 ) and CO2 solubility (k˜H,CO2 ). The deviation potential increases with increasing partial pressure, but is unaffected by the state-of-charge in the system under a given partial pressure, in accord with Eq. (22), i.e., the constant PCO2 lines are horizontal. The constant concentration lines, on the other hand, are strongly curved, with high deviation potentials at low state of charge and high partial pressure, decreasing to low potentials at high state of charge and low partial pressures, reflecting the fact that with a greater fraction of the CO2 bound to the activated absorbent with higher state of charge, the fraction of free CO2 in solution, or the partial pressure, Table 2 Parameters for carbon dioxide balance given in Eq. (25).
ECMS with dormant absorbent in solution ECMS with solid dormant absorbent ECCMS with dormant blocker in solution ECCMS with solid dormant blocker
W=
x CO2,0
α
k˜h,CO2
CO2,0
xA
kh,CO2 P 0
mA0 CO2,0 mC0 CO2,0 mA0 CO2,0 mA0
A0 C0
1 − xB 1 − xB
E dQ =
E dev dQ
(26)
which is proportional to the shaded area shown in each of the panels of Fig. 5. In all cases, the absorption begins at a feed partial pressure of 0.15 bar and state of charge of 0.25, and continues until the state of charge is 0.75 (i.e. a swing in the state of charge of 0.5) and is removed as a pure CO2 stream at 1 bar. The other conditions along the path depend on the system geometry employed. In the four-stage system shown in Fig. 5a, the solution introduced to the cathode consists of inactivated absorbent solution in equilibrium
mA0 kh,CO2 P 0 mC0 kh,CO2 P 0 mA0 kh,CO2 P 0 mA0
6
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Fig. 4. Effect of absorbent affinity, K CO2 , and CO2 solubility, k˜H,CO2 on the deviation potential when m = 1. Solid lines show deviations from the base case. Blue lines are for constant partial pressure, and red lines denote constant total concentration (bound and free) in solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
with the 1 bar product gas stream. As the absorbent is activated (1), i.e., the state of charge increases, the total CO2 concentration remains constant, and the path follows the corresponding constant concentration curve, but the free amount in solution (the partial pressure) decreases and the complexed amount increases. In the next stage (2), the activated absorbent is contacted with the feed gas, and the uptake of the CO2 traces a vertical path at constant state of charge, traversing the total CO2 concentration and partial pressure lines until the partial pressure of the feed gas is reached. In the anodic chamber (3), where the absorbent is deactivated as the state of charge decreases, the total CO2 concentration remains constant, but the partial pressure increases as the balance shifts from the complexed to the free CO2 in solution. Provided the pressure in the anodic chamber is greater than about 10 bar, the free CO2 in solution is not saturated and, at the end of this cycle, is at a partial pressure of 10 bar. In the final step (4), the CO2 is removed by desorption as a gas in the flash tank at a pressure of 1 bar; the state of charge remains constant in this case, but the total CO2 concentration in solution decreases. The final solution is then returned to the cathodic chamber to begin the cycle again. In the three-stage system with coupled anodic deactivation and direct removal of the CO2, in Fig. 5b, the cathodic activation (1) and absorption steps (2) are the same as for the four-stage scenario, but now the deactivation step follows a different path. During the initial stages of decreasing state of charge, the free CO2 is below the saturation limit, (i.e., partial pressure is below the system pressure) and the path follows
the constant CO2 curve (3a). Once the partial pressure reaches its saturation value of 1 bar, all the subsequent CO2 is released at this constant pressure as the state of charge decreases (3b). In the three-stage system with coupled cathodic activation and simultaneous capture of CO2 (Fig. 5c), as outlined in a recent patent application (Hatton et al., 2019), the activation process initially traces the constant concentration curve 1(a) as the free CO2 in solution complexes with the activated absorbent and the partial pressure decreases until it reaches the partial pressure of the feed gas stream (0.15 bar in this example) at which point CO2 capture begins. At this point, the path breaks away from the constant concentration curve and moves horizontally, or almost horizontally, to the final state of charge (1b). If the feed stream is in significant excess, a constant partial pressure curve will be taken; otherwise, the partial pressure will drop as absorption occurs and the feed stream becomes leaner. The separate deactivation/ desorption and CO2 gas disengagement steps (3) and (4) are the same as in the four-stage system. Finally, the two-stage system combines features of both three-stage processes, as shown in Fig. 5d, with the path now tracing the (1a)–(1b)–(3a)–(3b) curves. It is evident from the four scenarios given in Fig. 5 that the work required for the four-stage system is significantly larger than that for either of the three-stage processes, which themselves require more work than the two-stage system. The reason for this is that those processes in which the CO2 in the gas phase is constantly in equilibrium 7
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Fig. 5. Thermodynamic paths for four system geometries: (a) four-stage system employing: (1) cathodic activation, (2) absorption to 0.15 bar, (3) anodic deactivation, (4) desorption to 1 bar; (b) three-stage system employing: (1) cathodic activation, (2) absorption to 0.15 bar, (3) anodic desorption to 1 bar; (c) three-stage system employing: (1) cathodic absorption from 0.15 bar to 0.075 bar, (3) anodic deactivation (4) desorption to 1 bar; (d) two-stage system employing: (1) cathodic absorption from 0.15 bar to 0.075 bar, (3) anodic desorption to 1 bar. k˜CO2 = 0.05 and K CO2 = 500 .
with the solution phase are thermodynamically reversible, whereas the multistep activation and absorption, or deactivation and desorption, processes are not. These results are summarized succinctly in Fig. 6, where the penalty for non-cathodic absorption is shown in red, and that for non-anodic desorption in blue. The total energy penalty for a fourstage process is the sum of the penalties for the two three-stage processes.
solution, since the higher the solubility, the greater the drive to transfer from the gas to the liquid phase, and hence the lower the work required to effect the separation. For the three-stage process with anodic desorption, on the other hand, the separation work required depends strongly on the binding energy, reflecting the increasing energy penalty associated with the breaking of the bonds between the CO2 and the absorbent with increasing K CO2 . The weak dependence on physical solubility is because the CO2 is removed from solution as it is released by the deactivated absorbent. The four-stage process, on the other hand, exhibits features of both three-stage systems as illustrated in Fig. 5, with a functional dependency on K CO2 and k˜H,CO2 being a combination of the dependencies observed for the cathodic absorption and anodic desorption cases, respectively.
4.2. Sensitivity to K CO2 and k˜H,CO2 The ideal work required to capture CO2 from a feed gas at 0.15 bar and release it as a pure CO2 gas at 1 bar is shown in Fig. 7 as a function of the binding constant K CO2 for different values of the Henry's law constant k˜H,CO2 under the four different operating strategies discussed here. It is remarkable that the work for the two-stage system tracks the thermodynamic minimum work for this process, attributed as above to the fact that the absorption and desorption both follow fully reversible paths. The work for CO2 capture in the three-stage process with cathodic absorption is unaffected by the strength of complexation of CO2 with the absorbent, since any CO2 absorbed by the solution immediately complexes with the absorbent; it does, however, depend almost logarithmically on the physical solubility of the gas in the
5. Conclusions The analysis given in this report provides a coherent, unified picture of the thermodynamics of two different electrochemically based approaches, ECMS and ECCMS, for the capture of CO2 from a feed gas at low partial pressure and its release in pure form at a higher pressure. The results obtained are independent of molecular architecture and are guided by a single deviation potential for all modes of operation that depends on the strength of binding in the complexation reactions, the 8
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reactions at the electrodes was recognized as well as the fact that to follow the activation and deactivation curves closely, as required for an energetically efficient operation, a spatially dependent deviation potential would be necessary – this can be accounted for by use of segmented electrodes, each of which could be addressed individually, as discussed by Wang et al. (2018) The thermodynamic framework established in this paper can be the basis for future studies on the energetics of electrochemically mediated separation processes, not only for gas separations, but also for a range of other Faradaically driven applications such as, e.g., in water treatment for removal of trace organic contaminants (Achilleos and Hatton, 2016; Su and Hatton, 2017; Mao et al., 2018; Ren et al., 2018). Conflict of interest The authors declare that they have no conflict of interest. References Achilleos, D.S., Hatton, T.A., 2016. 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Fig. 6. A thermodynamic penalty exists for decoupling electrochemical steps and absorption/desorption. The penalty for a non-cathodic absorption (passing through 2) is given in red, whereas the penalty for a non-anodic desorption (passing through 4) is given in blue. The intersection of these two regions, as delineated by the solid lines, gives the energetics for an ideal two-stage system. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Total work of capture, W (in kJ/mol CO2 captured), as a function of sorbent binding affinity, K CO2 , and CO2 solubility, k˜H,CO2 for each system geometry: 4-stage, 3-stage with anodic desorption (3a), 3-stage with cathodic absorption (3c), and 2-stage. Case considered: 50% capture of a 15 mol% CO2 stream at 323 K, with desorption at 1 bar, m = 1, and a state of charge shift between α = 0.25 and α = 0.75.
partial pressure of CO2 (or its physical solubility) in solution, and the state of charge of the redox active species. The total work required to attain a given degree of separation depends on the operating strategy adopted, the most efficient being when the absorption and desorption of the gas are coupled directly and occur simultaneously with the activation and de-activation of the absorbent, respectively. The least efficient operation is when the activation, absorption, deactivation and desorption processes are fully decoupled and operate sequentially. Only thermodynamically ideal operations were included in this study, and a more rigorous assessment of the energy requirements in electrochemically modulated CO2 capture and release operations can use this framework as a basis upon which the solution non-idealities can be imposed. Wang et al. used a more specific formulation of this analysis for the EMCCS case with a solid dormant blocker, namely for the electrochemically mediated amine regeneration (EMAR) process developed in our laboratories (Wang et al., 2018). The need for the application of overpotentials to ensure sufficiently rapid Faradaic 9
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