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A Multiple-Compartment Ion-Transport-Membrane Reactive Oxygen Separator N. D. Mancini, S. Gunasekaran, and A. Mitsos* Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue (MIT 3-158), Cambridge, Massachusetts 02139, United States ABSTRACT: Oxy-combustion using an integrated oxygen ion-transport membrane (ITM) could substantially improve the thermodynamic performance of power plants with carbon capture and sequestration (CCS). In a reactive ITM, fuel is burned inside the unit to enhance the oxygen partial pressure driving force, thus reducing the reactor membrane material required, compared to nonreactive ITM applications. The multiple-compartment reactive ion-transport membrane (MCRI) concept proposed herein mitigates key drawbacks of the reactive ITM and improves the performance by dividing the overall ITM into stages with individual input streams in a serial arrangement. This arrangement enables more-effective thermal management of the ITM and, thus, higher average oxygen permeation flux. Consequently, the pressure drop and size (volume/surface area) are significantly reduced, compared to conventional reactive ITM designs. The MCRI is modeled and simulated in ASPEN Plus, using multiple instances of an intermediate-fidelity ITM model that captures all relevant physical processes. The simulation results indicate that a power cycle using an integrated MCRI could significantly improve the economic viability of oxycombustion CCS power plants.

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INTRODUCTION Oxy-combustion and Ion-Transport Membrane (ITM) Technology. Carbon capture and sequestration (CCS) could enable the continued use of fossil fuels by mitigating the harmful impact of greenhouse gases on the environment. There are many CCS power generation systems, each with distinct CO2 separation processes, engineering challenges, cost, and drawbacks.1 However, the economic and thermodynamic penalties associated with CCS are relatively high, and research and development is being conducted to make CCS more viable.2 Oxy-combustion is a particular type of CCS technology where a fuel is oxidized in a nitrogen-free environment in order to facilitate simplified, low-penalty CO2 separation downstream via water condensation. Oxy-combustion could significantly reduce the thermodynamic penalty and costs associated with CCS,2−4 but unfortunately requires costly air separation units with large electrical work inputs.3,5 Currently, only cryogenic air separation units with relatively low Second Law of Thermodynamics efficiencies (in the order of 25%) are available at the power plant scale.3,5 The thermodynamic and economic penalties associated with conventional cryogenic systems have prompted many researchers to investigate alternative air separation methods. Based on current research, ceramic-membrane-based oxygen separation processes offer many potential advantages, compared with the conventional cryogenic method. Extensive research has been conducted to explore the relationship between material composition and oxygen permeation.6−11 Consequently, numerical modeling tools and empirical correlations have been developed to assist with process flow and systems-level analyses for large-scale oxygen separation applications.5,12−22 These ceramic membranes, typically known as ion-transport membranes (ITMs), are composed of mixedconducting (ionic and electronic) inorganic materials that © 2012 American Chemical Society

separate oxygen from air at high temperature, because of a difference in the oxygen chemical potential.23 In an alternative ITM configuration known as the reactive ITM, fuel is oxidized inside of the unit simultaneously with oxygen separation in order to enhance the oxygen flux by maintaining a low oxygen partial pressure (virtually zero) on the fuel side. ITM technology could eventually replace conventional cryogenic air separation systems for large-scale power generation applications.12,24 However, many numerical, experimental, and systems-level analyses are required prior to large-scale commercialization. In particular, the reactive ITM is the least characterized of all ITM configurations; there are many advantages,20 as well as design challenges,19 associated with reactive ITMs that must be investigated further. Motivation and Drawbacks of Reactive ITMs. Reactive ITMs offer large oxygen partial pressure driving forces, because of the presence of relatively fast oxygen-consuming chemical reactions on the permeate side.18 Thus, the reactive ITM could reduce the amount of membrane material required, relative to nonreactive or separation-only ITM applications, and hence enhance the economic attractiveness of oxy-combustion CCS systems. However, the assumption is that the thermodynamic penalty associated with implementing reactive ITMs is, at most, equal to (but ideally lower than) the separation-only ITM. In addition, challenging ITM operational requirements must be met, and suitable materials must be developed that can withstand prolonged use in a reactive environment. Previous work20 showed that it is unlikely that the reactive ITM can surpass the separation-only ITM, in terms of low pressure drop Received: Revised: Accepted: Published: 7988

October 22, 2011 April 28, 2012 May 24, 2012 May 24, 2012 dx.doi.org/10.1021/ie202433g | Ind. Eng. Chem. Res. 2012, 51, 7988−7997

Industrial & Engineering Chemistry Research

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or thermodynamic penalty. Moreover, the results indicate that reactive ITMs have many design and operation issues and may not be viable without significant modifications to the reactor design.19 Nevertheless, the potential impact on the size or costeffectiveness of ITM air separation technology substantiates the pursuit of new reactive ITM designs. There are many underlying physical processes unique to the reactive ITM that must be addressed. ITM simulation and analysis19 demonstrated that the relatively small temperature operation range and the large pressure losses associated with reactive ITMs are the most-significant problems. A particularly stringent requirement for a reactive ITM application is to oxidize a large amount of fuel with a temperature rise of less than ∼200 K without incurring a large pressure drop. The estimated temperature rise limit is the difference between the maximum operating temperature allowed for a given membrane material and the minimum operating temperature at which the oxygen flux is still large enough to render the overall system economically or thermodynamically feasible. The maximum allowable temperature for a particular membrane varies between 700 °C and 1000 °C for the most common membrane materials, e.g., La1−xSrCo1−yFeyO3−δ (LSCF),6 La2NiO4+δ (LNO),25 BSCF,10 SCF10,26 and LSGF-BSCF.27 Generally, the maximal temperature limit represents the highest temperature at which the membrane material still retains the phase structure necessary for oxygen ions to diffuse through the lattice. The reader is referred to more-comprehensive works on the specifics of ITM materials.6−11 Clearly, this definition of temperature rise is dependent specifically on the material under consideration and has a large impact on the design and performance of reactive ITMs.19 The small temperature rise limit implies an excessive diluent flow rate, compared to conventional combustion systems for the same heat rate, and thus exacerbates the pressure drop problem.18 In general, the maximal ITM operating temperature is much lower than a conventional gas turbine inlet temperature.28 Thus, as a consequence of the Second Law of Thermodynamics, a power cycle utilizing a reactive ITM as the primary chemical to thermal energy conversion device has a lower maximum-achievable First Law of Thermodynamics efficiency, compared with conventional, and possibly separation-only ITM-based, power cycles. However, there are many concepts proposed, including the work herein, that could mitigate the main problems associated with reactive ITMs. The multiplecompartment reactive ion-transport membrane (MCRI), the use of low-activation-energy materials,19 or the implementation of hybridized reactive and separation only power cycles20 all address the temperature-related problems in a different way. Furthermore, each concept indirectly reduces the pressure drop and improves the economic viability by reducing the ITM size. Motivation and Physics of the MCRI. The results presented by Mancini and Mitsos19 demonstrate that the local membrane temperature is the controlling factor for oxygen separation when it is significantly lower than the maximal operation temperature allowed for a given material. That is, the Arrhenius dependence of oxygen permeation on the local membrane temperature drastically limits the performance of an ITM separation unit for relatively low operating temperatures. The MCRI concept, shown in Figure 1, mitigates the penalties associated with reactive applications by splitting the incoming feed, permeate, and fuel streams in such a way that the average stream-wise membrane temperature is higher,

Figure 1. Schematic of the multiple-compartment reactive ion transport membranes (MCRI) concept proposed herein. Air streams are denoted as “feed”, and the sweep gas is comprised of a mixture of CO2 and H2O.

and pressure drop is significantly lower, compared to the original configuration. The outlet temperature from each stage can be controlled to be essentially equal to the maximal allowed, and so the inlet temperature to the next stage is generally higher than it would have been in the base configuration. The stage inlet temperatures are dependent on the choice of feed, diluent, and fuel distribution to each stage. Higher average membrane temperatures increase oxygen flux significantly and accelerate chemical fuel conversion. Thus, the total volume required is reduced, and, consequently, the pressure drop is lower. Since the chemical reactions are exothermic and increase the membrane temperature, the effect of initially higher oxygen flux in “cold” operational regimes is greater than if the chemical reactions were neutral or endothermic. This latter point motivates the use of interstage duct burners discussed in upcoming sections. Furthermore, since only a fraction of the total mass flow rate goes through the initial MCRI stages, the pressure drop is further reduced. Thus, for the same inlet and outlet conditions, the MCRI concept can separate the same oxygen for a lower pressure drop using a smaller ITM, compared to a single-stage ITM reactor. In principle, the operational degrees of freedom include the feed, permeate, and fuel flow rates for each stage, as well as the excess oxygen separated from each stage, or, equivalently, the fuel burned between stages. The total inlet pressures of the feed and permeate streams could also be optimized, but are considered fixed herein to enable direct comparison with existing reactive ITM power cycles.20 However, as will be shown in the upcoming sections, operational requirements remove many of these degrees of freedom. First, the membrane temperature at any point inside the reactor must always be less than the maximum allowable. Second, the MCRI must oxidize a specified amount of fuel among all stages, e.g., a fixed thermal energy input to the power cycle. Third, the permeate stream (oxy-combustion products mixed with fuel) cannot be diluted without limit; otherwise, the fuel concentration will be too low in the free stream, and the reactions will be fuel-transportlimited, as demonstrated previously.19 Specifically, if the sweep stream containing the fuel is too dilute (e.g., the ratio of water vapor and carbon dioxide to fuel is too high), convective mass transfer of fuel to the reaction zone near the membrane surface (calculated by the ITM model) might be insufficient and could limit the overall conversion process. Fuel transport limiting conditions essentially cancel the benefits of the reactive ITM 7989

dx.doi.org/10.1021/ie202433g | Ind. Eng. Chem. Res. 2012, 51, 7988−7997


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investigated. Furthermore, the impact of low activation energy materials on the MCRI system is obtained, and significant diminishing returns are noted for this combined concept. Finally, an assessment of the potential of this novel reactive ITM design to reduce both the penalty and size associated with ITM air separation technology is conducted. ITM Intermediate Fidelity Modeling and Simulation. In order to analyze the MCRI, a physics-based ITM model is required for each individual stage. ITM air separation units, particularly reactive ITMs, exhibit a variety of physically diverse and coupled phenomena. The dependence of ITM performance on the MCRI operating conditions and flowsheet configuration must be captured in order to analyze the performance. The intermediate fidelity ITM model developed by Mancini and Mitsos18,19 is used to simulate each compartment of the MCRI. This ITM model can be used to explore the impact of geometric structure, flow configuration, operating conditions, membrane material properties on the performance (e.g., the pressure drop incurred for required oxygen separation). Furthermore, the model provides the amount of ITM material required for a specified oxygen separation, and thus can be used to conduct economic comparisons. Finally, the model has sufficient detail such that it can provide key operational constraints such as maximum internal membrane temperature, or the occurrence of fueltransport-limited reactions.18 Although the ITM model implemented herein is comprehensive, certain key assumptions are made, regarding the physics of the oxygen separation process in the presence of fuelconsuming chemical reactions and are documented in previous work.18 The most important assumption is that the oxygen permeation mechanism is not altered by the combustion process near the membrane surface; the influence of combustion on the permeation rate is to reduce the local oxygen partial pressure on the permeate side to a small value (approaching zero) and increase the local membrane temperature. The particular membrane material La1−xSrCo1−yFeyO3−δ (LSCF)6 is assumed with the following oxygen permeation mechanism, which is dependent on the local membrane temperature (TM), the local feed oxygen partial pressure (PO′ 2), and the local permeate partial pressure (PO″ 2) (set to a low value, e.g., 10 Pa):

because oxygen will accumulate on the permeate side, just as in the separation-only configuration. The implementation of many additional stages increases the system complexity and, potentially, the cost. It is expected that the addition of a small number of stages will not significantly increase the cost and yet still offer large performance gains, relative to a single stage. Furthermore, the additional manifolds introduced between each stage should not significantly contribute to the pressure drop. Finally, since the heat-transfer coefficients are lower in the initial stages due to a lower Reynolds number Re (the heat-transfer coefficient increases by an order of magnitude as the flow transitions from laminar to turbulent), the potential to overheat is larger. However, the ITM stage geometry could be optimized, e.g., the channel width could be modified as a function of the stage number to obtain optimal heat and mass transfer without large pressure losses. For example, it may be advantageous from a cost perspective to increase the surface area to volume ratio in the initial stages by decreasing the channel width where the flow rates and the corresponding pressure drops are low. Potential Impact of Low-Activation-Energy Materials. Another potential way to address the deleterious effects of low membrane temperatures is to modify the membrane material properties. This aspect is discussed and explored in detail in previous ITM simulation case studies.19 In particular, a lower effective activation energy of the electrochemical reactions allows significant oxygen flux at lower initial temperatures. This, in turn, allows a better system integration by permitting lower ITM inlet temperatures. For a fixed outlet temperature (typically the maximum allowable) and fuel consumption or heat rate, a reduced inlet temperature implies a lower diluent flow rate (from the First Law of Thermodynamics). A lower diluent flow rate leads directly to a lower pressure drop within the ITM. Finally, for the same inlet temperature, an ITM reactor with enhanced activation energy materials requires a lower residence time to oxidize the fuel. Higher oxygen flux near the inlet accelerates exothermic fuel oxidation and increases the local temperature of the membrane more rapidly than with conventional membrane materials; consequently, the average oxygen flux increases and reduces the total required membrane surface area. Undoubtedly, low-activation-energy materials will improve the performance of both reactive and separation-only ITMs. However, low activation energy (LAE) essentially shifts the dependence of oxygen flux primarily on membrane temperature to predominant dependence on the oxygen partial pressure driving force. Thus, this method would actually favor reactive ITMs and close the gap between separation-only and reactive applications. The results presented by Mancini and Mitsos19 indicated that an ∼50% reduction in the effective activation energy was enough to make the separation-only ITMs and reactive perform comparably, in terms of pressure drop and volume required for a fixed oxygen separation. In the upcoming sections, the effect of low-activation-energy materials on the MCRI concept is explored. MCRI Simulation and Analysis. Modeling and simulation provide many insights and reveal potential designs that further improve the performance of the MCRI. First, various fuel distribution profiles are used to identify candidate solutions as initial guesses for an optimization study. Next, the effect of number of stages in the MCRI on the pressure drop and size is explored. The effects of producing excess oxygen from each stage and burning some fuel between stages are also

⎛ B ⎞ JO = A exp⎜ − ⎟⎡⎣(PO′ 2)n − (PO″2)n ⎤⎦ 2 ⎝ TM ⎠

The parameters A, B, and n represent material properties and are obtained from curve fits of experimental data.18 Convective and porous mass transport correlations are used to determine the local feed oxygen partial pressure at the membrane surface.18 It should be stressed that, as new permeation mechanisms emerge, particularly those that account for the presence of combustion reactions, the MCRI concept can simply be resimulated to evaluate the impact of a particular material on the overall system performance. Finally, it is assumed that fouling or coking due to solid graphitic carbon formation (e.g., Boudart’s reaction for coking) is not present. As shown in a previous work,18 recirculation results in relative large ratios of steam to fuel which prevents this reaction from occurring. ASPEN Plus was used to evaluate the potential for solid carbon formation using equilibrium models based on the minimization of the Gibbs free energy. The results indicate that for sweep gas (equimolar mixture of steam and carbon 7990



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Figure 2. Multi-compartment reactive ITM (MCRI) implemented in ASPEN Plus using multiple instantiations of ITM models in JACOBIAN.29

neously. These simultaneous design specifications significantly increase the computational time and require a robust ITM reactor model. The degrees of freedom are Nstg − 1 fuel flow rates and Nstg ITM volumes with the condition that all fuel must be consumed, where Nstg is the number of MCRI stages. The sum of all fuel flow rates (including the duct burner fuel) must sum to a specified value that is dependent on the particular power cycle efficiency and target electrical power output. Simulations are performed to explore these remaining degrees of freedom and their corresponding impact on the MCRI performance. Five-Stage MCRI Reactor Profiles. In order to visualize the MCRI concept, reactor-state variable profiles such as the local membrane temperature as a function of reactor volume are presented; these illustrate how the MCRI concept works and provide some insight for optimizing its operation. The results are compared against a base-case reactive ITM from Mancini and Mitsos19 to assess the improvement in performance. For Figures 3−6, the sweep gas is considered to be an equimolar mixture of CO2 and H2O, to compare our results with the base case. The following profiles are obtained for a fixed excess oxygen separation of 150 mol/s from each stage. The fuel distribution is chosen as 100 mol/s CH4 for the first three stages and 200 mol/s from the last two stages. The distribution is chosen based on the tradeoffs obtained in previous analyses.19 Specifically, less fuel in the initial stages and more fuel in the latter stages ought to perform better than the opposite case. The remaining 300 mol/s of fuel must be distributed equally among the interstage duct burners in this particular case, e.g., 75 mol/s in each duct burner, to match the specified excess oxygen of separation of 150 mol/s from each stage. The appropriation of 30% of the total fuel to the duct burners was chosen in order to further boost ITM stage inlet temperatures closer to their maximal values. That is, although the streams leave any particular stage close to the maximal temperature, they mix with fresh, cooler streams prior to entering the next stage. Thus, if the exiting stream can be heated further in a duct burner before mixing with the cool stream (although this generates entropy), the performance may be enhanced, because of the dominant dependence of ITM size (and thus pressure drop) on inlet temperature. This aspect is

dioxide)-to-fuel ratios of >3:1, no solid carbon will form (usually sweep gas has a greater mole fraction of water); all results herein meet or exceed this minimum diluent ratio. MCRI Modeling and Simulation. The MCRI is a reactor network comprised of many reactive ITM stages connected in series with interstage mixing and, in some cases, interstage combustion. MCRI modeling and simulation must piece together each stage along with additional unit operation models as needed. Simulation of the MCRI is performed using multiple instantiations of the JACOBIAN29-based intermediate-fidelity ITM model18 via ASPEN Plus “USER2” blocks for each stage of the MCRI. ASPEN Plus manages the overall flowsheet convergence and input of each individual compartment; JACOBIAN provides the outputs of each ITM compartment in addition to internal simulation results such as the maximum membrane temperature. A detailed explanation of the ASPEN Plus-JACOBIAN interface used herein is provided by Mancini and Mitsos.20 Figure 2 displays a five-stage multiple-compartment ion transport membrane (MCRI) with interstage duct burners in ASPEN Plus using the interface described above. The total feed, fuel, and sweep streams are split and enter each stage separately, and additional fuel is added to the duct burners for designs with excess oxygen. Products exiting the ith stage mix with fresh streams and enter the (i+1)th stage. After a duct burner, the air-residual stream is mixed with fresh, cooler air and enters the next stage. Similarly, cool recycled products mix with the products of the duct burner and enter the permeate side of the next stage. The requirements for each stage include the maximum membrane temperature limit, the fuel transport limit on sweep diluent, and the requirement to burn the fuel provided to the stage. The maximum membrane temperature is controlled by changing the feed flow rate, using a design specification control loop. A calculator block is used to specify the recyled-products flow rate based on the fuel flow rate; this ratio of recyled products to fuel, the sweep ratio, is a key reactor parameter. Sweep ratios ranging from 15:1 to 40:1 (recycled products to fuel) are explored herein; a fuel transport limit flag is raised if the dilution level is too high. Finally, another design specification varies the ITM stage volume until the amount of excess oxygen specified is obtained. Broyden’s method is used to converge the multiple design specifications simulta7991



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coefficient is an order of magnitude lower than the last-stage heat-transfer coefficient or, more importantly, lower than the base-case ITM inlet region. On the other hand, low heattransfer coefficients may be problematic for the temperature overshoot, and so a careful choice of design conditions is required to balance these competing effects. Clearly, if an ITM designer were able to control the heattransfer coefficient at any point along the reactor, tremendous gains in reactive ITM performance could be obtained. That is, if the local membrane temperature could always be maintained near the maximal limit, regardless of the bulk temperature, the oxygen flux would be maximized. For example, variable ITM geometry as a function of the axial coordinate could be utilized, e.g., the channel width (or hydraulic diameter for nonsquare passages). Since the MCRI is modular, implementation of a different geometry for each stage should be more cost-effective and straightforward, from a design standpoint, compared to a single-stage ITM with variable geometry. The membrane temperature profiles confirm the positive effect of splitting the stream (and thus lowering the heat capacity), and suggest that the first stage should have a low flow rate in order increase in temperature quickly, and to take advantage of low heat-transfer coefficients and high local membrane temperatures, despite low bulk stream temperatures. These results demonstrate the relationship between MCRI performance and thermal management; the MCRI enables more-effective thermal management, compared to the singlestage reactive ITM. The oxygen flux distribution shown in Figure 4 clearly demonstrates the consequence of high average membrane inlet

explored in later sections where the impact of fuel distribution is analyzed. The local membrane temperature is the most important state variable for ITM oxygen separation. Figure 3 shows the local

Figure 3. MCRI simulation results: temperature profiles and base comparison using the hot-wall estimate (reactions occur directly on membrane surface). “Volume” serves as both an indication of size and of the streamwise reactor coordinate.

membrane temperature as a function of the total MCRI volume or axial “length” coordinate compared to the base temperature profile (single-stage). The MCRI profiles indicate significantly higher average membrane temperatures, compared to the base profile. The higher inlet temperatures to the (i+1)th stages further increase the flux and accelerate the fuel conversion process. The slope of the MCRI temperature profile is larger than the base case, because the heat capacity rate is much lower, because of the splitting of the overall stream, but the reaction rateand, hence, heat releaseis greater than the base case, because the oxygen flux is higher. The discontinuities in the MCRI temperature profile denote interstage mixing and fuel consumption in the interstage duct burners. Next, the magnitude of the temperature rise in each stage decreases in this case, because the the heat capacity increases with each stage more quickly than the fuel is added and because the inlet temperatures approach the maximal temperature allowed with each additional stage. It should be noted that the maximal temperature allowed is the same for both the base and the MCRI, but because of non-zero residuals of the design specification control loop in ASPEN Plus, the MCRI temperature profile shows slight overshoot for some of the stages. Another interesting result is the higher membrane temperature at the beginning of stage 1. This is due to the lower heattransfer coefficient, compared to the base case, because the flow rate is significantly lower and hence the Reynolds number (Re) is small and the flow is laminar. Consequently, the MCRI concept appears to give low heat-transfer coefficients when this characteristic is desirable (i.e., to assist the first-stage chemical reactions quickly), and high heat-transfer coefficients in the latter stages. That is, low heat-transfer coefficients maintain a relatively hot membrane, even if the streams are cool, because the heat release is likely close to or directly on the membrane surface and is removed via heat convection. This conclusion is further supported by the fact that the convective heat transfer transitions from laminar to turbulent as more diluent and fuel are added in each stage. Thus, the first-stage heat-transfer

Figure 4. MCRI simulation results: oxygen flux profiles and base comparison using the cold-wall temperature (reactions occur in the bulk stream).

temperatures. It should be noted that, in order to provide a conservative estimate, the “cold-wall membrane temperature”18 is used in the flux expression within the ITM model. The coldwall estimate provides the lower bound on the membrane temperature by assuming that all chemical reactions occur in the bulk, where heat-transfer correlations are used to determine the membrane temperature.18 In contrast, the hot-wall membrane temperature estimate shown in Figure 3 assumes that all chemical reactions occur at the membrane surface; the convective heat transfer away from the surface determines the local membrane temperature.18 In reality, the actual membrane temperature will be somewhere between these two estimates, which do not differ significantly for the base case, but might for 7992



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the MCRI, because of the lower heat-transfer coefficients in the initial stages. CFD and experimental analyses will be extremely helpful, because they will indicate the location of the reaction zone and provide the appropriate combination of the hot-wall and cold-wall temperature estimates. Regardless of which assumption is used, the effect of splitting the streams increases the membrane temperature much more rapidly than in the base case, and the resulting oxygen flux profile is, thus, higher on average. Furthermore, the actual MCRI is expected to provide slightly better performance results, as a consequence of using the conservative cold-wall temperature assumption. In addition, since the temperature constraint for the ITM is based on the hot-wall temperature estimate, a safety margin is automatically included in the design. The fuel and oxygen flow rate profiles shown in Figure 5 display the behavior of reactive ITMs generally, as well as the

Figure 6. MCRI simulation results: total pressure profiles and base comparison.

stream (ΔPTot), the amount of fuel provided to each stage as a percentage of the total fuel after accounting for the duct burners, and other useful results. The amount of fuel entering the ith stage (ṅFuel,i) is calculated by the following expression, where γi is a specified fraction between zero and one, ṅFuel,cycle is the input fuel to the power cycle (or, here, taken to be equal to 1 kmol/s), and ∑iṅFuel,DB,i is the total fuel consumed in the interstage duct burners. nFuel, − ΣinFuel,DB, ̇ i = γi × (nFuel,cycle ̇ ̇ i)

Thus, the term “% ṅf,tot” in Table 1 refers to the fuel consumed strictly within the ITM stages (or, in this particular section, 0.9 kmol/s). The excess oxygen is held fixed for stages 1−4, where 2.5% of the total fuel is consumed in each duct burner and the last stage provides no excess oxygen. The volume of each ITM stage is obtained using a design specification control loop that varies the volume (keeping the aspect ratio the same) until the specified excess oxygen in the outlet permeate stream is achieved. The effect of increasing the interstage duct burner utilization is explored later. For Tables 1−5, sweep gas is considered to be a mixture of CO2 and H2O in a molar ratio of 1:2, which represents recycling without any separation. The total volume and total pressure drop are impacted differently by the choice of the fuel distribution profile. The profiles listed in Table 1 are chosen such that the fuel is increasingly distributed more asymmetrically toward the latter stages of the MCRI with each subsequent profile. The first profile, “uniform”, simply divides the fuel equally among the stages; the pressure drop is reduced significantly (from 2.9 bar to 0.558 bar) and the size is reduced by over a factor of 2. The “linearly increasing” profile exhibits the best composite performance, in terms of volume and pressure drop. Thus, the MCRI seems to perform better (pressure drop and volume required) when the fuel distribution increases with the stage index, as expected, based on the aforementioned discussion of the benefits of low heat capacity and heat transfer in the initial stages. However, the opposite strategy, where the fuel is essentially all consumed in the last stage and the initial stages only provide some small preheating, is not the most advantageous choice for either volume or pressure drop. The “feed-last” profile has a higher pressure drop and volume, compared to the “step” and “backload” profiles. Generally, the minimum pressure drop and size appear to coincide for low excess oxygen or duct burning.

Figure 5. MCRI simulation results: permeate fuel and oxygen flow rate profiles and base comparison.

MCRI. In particular, when a significant amount of fuel is present on the permeate side, the oxygen partial pressure is virtually zero, and the fuel conversion proceeds in stoichiometric proportion to the oxygen flux. The logistical function is used to smooth the transition between reactive mode and separation-only mode as the fuel is consumed.18 The fuel and oxygen profiles illustrate that, similar to the base case, the MCRI still incurs a large residence time penalty, bceause of the low inlet temperature. However, since the flow rate is low in this stage, the pressure drop is small. Thus, the design goal is to reduce the initial residence time by carefully choosing the fuel flow rates to each stage, as well as the excess oxygen burned between each stage. Figure 6 shows the total pressure of the feed stream for both the MCRI and the base case. These profiles confirm the effect of low mass flow rates in the initial stages, because the slope or pressure gradient for the MCRI is much lower than that in the base case. The kinks in the pressure gradient, although difficult to identify in Figure 6, because of small changes in flow rate for the first three stages, indicate interstage mixing. Effect of Fuel Distribution. The fuel distribution determines how much of the total fuel is consumed in each stage and has a significant effect on the performance of the MCRI. Various fuel distribution profiles are considered for the MCRI, and the simulation results are given in Figure 1. The simulation results provide the total volume of the MCRI (VTot), the sum of the pressure drop of both the feed and permeate 7993



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example, the “linear” case has a volume and pressure drop of 539 m3 and 1.086 bar, respectively, at a sweep ratio of 15:1; at a sweep ratio of 40:1, the volume and pressure drop are reduced to 387 m3 and 0.47 bar, respectively. Fuel transport limitations generally become important with sweep ratios above 25:1 and, thus, could render the improvements with sweep ratio impractical. Although the fuel distributions above span the major design configurations, optimization could improve the overall performance. The fuel distribution profiles are provided as initial guesses to ASPEN’s SQP optimizer to determine the potential for improvement. The optimizer is set to minimize the reversible compression work required to repressurize the exiting streams up to their inlet pressures by varying the fuel flow rate to the first four stages. The last fuel flow rate is determined with a calculator block to meet the total fuel consumption constraint of 1 kmol/s. Table 2 indicates that the

Table 1. MCRI Simulation Results: Effect of Fuel Distribution Profiles on System Performance and Operating Conditionsa

VTot (m3) LTot (m) ΔPTot (bar) Ẇ Rev (MW) overall recovery ratio (%) ṅFuel,1 (% ṅf,tot) ṅFuel,2 (% ṅf,tot) ṅFuel,3 (% ṅf,tot) ṅFuel,4 (% ṅf,tot) ṅFuel,5 (% ṅf,tot) ṅAir,1 (kmol/s) ṅAir,2 (kmol/s) ṅAir,3 (kmol/s) ṅAir,4 (kmol/s) ṅAir,5 (kmol/s) ṅSweep,1 (kmol/s) ṅSweep,2 (kmol/s) ṅSweep,3 (kmol/s) ṅSweep,4 (kmol/s) ṅSweep,5 (kmol/s) avg sweep ITM inlet temp (K)

uniform

linearly increasing

step

backload

feed-last

initial guess

438 19.5 0.558 36.9 11.6

412 18.3 0.588 38.8 11.7

414 18.4 0.608 40.3 11.7

427 19 0.715 47 11.9

445 19.8 0.821 66.6 12.0

415 18.4 0.626 42 11.6

20

10

10

10

10

10

20

15

10

10

10

13.4

20

20

20

10

10

18.1

20

25

30

20

10

22.5

20

30

30

50

60

36

15.73

7.62

7.6

7.62

7.62

8.62

16.93

16

12.8

12.6

12.9

14.9

14.59

15.4

15.7

10.9

10.9

14.2

13.55

17

19.7

14.7

9.9

15.4

12.74

17

17.2

25.8

30

20.9

4.44

2.22

2.22

2.22

2.22

2.5

4.44

3.33

2.22

2.22

2.22

2.92

4.44

4.44

4.44

2.22

2.22

3.82

4.44

5.55

6.67

4.44

2.22

5

4.44

6.67

6.67

11.11

13.337

8.23

1144

1135

1140

1145

1150

1138

Table 2. MCRI Simulation Results: Fuel Distribution Optimization Results for Various Initial Guessesa

VTot (m3) ΔPTot (bar) Ẇ Rev (MW) ṅFuel,1 (% ṅf,tot) ṅFuel,2 (% ṅf,tot) ṅFuel,3 (% ṅf,tot) ṅFuel,4 (% ṅf,tot) ṅFuel,5 (% ṅf,tot)

uniform

linearly increasing

step

backload

feedlast

initial guess

437 0.559

431 0.582

415 0.586

425 0.712

433 0.629

413 0.615

36.9

38.8

38.2

46.9

41.43

40.7

17.67

9.56

9.78

10.05

9.39

11.1

24.78

25.67

17.59

10.05

15.15

12.84

18.73

28.27

16.75

10.05

37.5

16.9

25.88

17.27

28.11

20.11

9.39

21.45

12.94

19.2

27.76

49.72

28.55

37.69

a

Additional conditions: total fuel = 0.9 kmol/s, frontal area = 22.5 m2 for all cases, and sweep ratio = 25.

optimizer generally improves upon the assumed fuel distribution profiles, but not by more than 10% in most cases. However, the “feed-last” profile showed a large reduction in the compression work; the fuel was shifted toward the middle of the MCRI, which is consistent with earlier observations. The optimization analysis is also attempted with additional degrees of freedom, i.e., the excess oxygen from each stage. However, the optimizer fails to converge for a variety of initial guesses. Effect of Number of Stages. The number of individual stages or compartments is another important degree of freedom for the MCRI concept. The addition of stages increases the system complexity and should be balanced against the corresponding reduction in the pressure drop (compression work) and ITM size. The number of stages also represents the resolution or accuracy of approximating a continuous optimal fuel distribution profile with a discrete fuel distribution profile. Thus, in order to assess the dependence of pressure drop and total volume on the number of stages, simulations are performed in ASPEN Plus, ranging from a single stage to five stages. The “step” fuel distribution profile is used for five stages with a fixed total excess oxygen of 10%. That is, as the number of stages decreases, 100 mol/s of CH4 is still consumed among the remaining duct burners. Fuel distribution profiles for less than five stages are determined based on the original profile

a

Additional conditions: total fuel = 0.9 kmol/s, frontal area = 22.5 m2 for all cases, and sweep ratio = 25.

The fuel distribution simulation results are quite helpful for the design and operation of the MCRI. They demonstrate the importance of optimization, or at least parametric analysis with a good model, because the pressure drop and corresponding compression work vary significantly, depending on the choice of fuel distribution. Asymmetric profiles appear to be best, where a majority of the fuel is consumed in the latter stages. The “linearly increasing” and “feed-last” profiles demonstrate the balance between adding too much fuel initially (and paying the pressure drop penalty for large flow rates) and adding the fuel too late (low inlet temperatures and high flow rates in the last stage leads to large volumes and pressure drops). The results suggest that, generally, splitting the streams reduces the size or volume and this reduction is a weak function of the distribution profile, whereas the compression work or pressure drop shows a stronger dependence on the particular fuel distribution profile. Alternative sweep ratios of 15:1, 30:1, and 40:1 were analyzed and the trend among the distribution profiles remained unchanged. However, an increasing sweep ratio reduces the pressure drop and volume for each case. For 7994



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Table 3. MCRI Simulation Results: Effect of Number of Stages on ΔPTot and VTot for the Step Profile and Sweep Ratio = 25 stage

ΔPTot (bar)

VTot (m3)

ṅFuel,1 (% ṅf,tot)





1 2 3 4 5

2.63 0.812 0.665 0.65 0.61

903 570 481 434 414

100 40.6 20.8 12.5 10

59.4 33.3 18.75 10

45.9 31.25 20

37.5 30

30

Table 4. MCRI Simulation Results: Effect of Excess Oxygen from All Stages on ΔPTot and VTot (Frontal Area = 22.5 m2 for All Cases and Sweep Ratio = 25) excess oxygen (% total stoichiometry)

ΔPTot (bar)

VTot (m3)

ṅFuel,1 (mol/s)

ṅFuel,2 (mol/s)

ṅFuel,3 (mol/s)

ṅFuel,4 (mol/s)

ṅFuel,5 (mol/s)

0 10 20 30 40

0.580 0.602 0.638 0.610 0.587

422 414 421 431 475

100 90 80 70 60

100 90 80 70 60

200 180 160 140 120

300 270 240 210 180

300 270 240 210 180

Table 5. MCRI Simulation Results: Effect of Low-Activation-Energy (LAE) Materials on ΔPTot and VTot (Frontal Area = 22.5 m2 for All Cases and Sweep Ratio = 40) activation energy reduction (%)

ΔPTot (bar)

VTot (m3)

ṅFuel,1 (mol/s)

ṅFuel,2 (mol/s)

ṅFuel,3 (mol/s)

ṅFuel,4 (mol/s)

ṅFuel,5 (mol/s)

0 25 50 75

0.397 0.3878 0.358 0.346

372 346 310 274

90 90 90 90

90 90 90 90

90 90 90 90

180 180 180 180

450 450 450 450

(“step” in this case) using the following expression, where j is the total number of stages in the MCRI, Nstg is set as the maximum number of stages (five in this case), and i is the particular stage in the MCRI: nFuel, ̇ i,j =

nFuel, ̇ i + 1, j + 1 + nFuel, ̇ i,j+1 2

×

membrane temperature for the MCRI separation-only segments is unlikely to exceed the nominal counter-current separation-only case. Nevertheless, because of the Arhennius dependence of oxygen flux on the local membrane temperature, interstage fuel consumption fed by excess oxygen still improves the MCRI performance. Simulation results given in Table 4 give the total pressure drop and MCRI volume, as a function of the total excess oxygen. The fuel distribution among the stages for each case follows the “step” profile, based on the remaining fuel (e.g., the fuel not consumed in the duct burners). For example, 20% of the total stoichiometric oxygen required means that 200 mol/s of fuel is consumed amongst the duct burners, and the remaining 800 mol/s is consumed within the reactive ITM stages. Equivalently, this means that the excess oxygen from all stages sums to 400 mol/s in this particular example. The fuel distribution amongst the duct burners is uniform; hence, the excess oxygen separation from each stage is the same. However, this is not a constraint, and future analyses could investigate the impact of non-uniform duct burner fuel distribution profiles. The results show a tradeoff between too little and too much excess oxygen. For the step profile, it appears that ∼10% excess oxygen total, or 2.5% from each of the first four stages, is superior, both in terms of the pressure drop and volume. Interestingly, it appears that the optimal excess oxygen, in terms of pressure drop, is generally also optimal for the volume and no tradeoff is observed between VTot and ΔPTot. These results are similar to the previous fuel distribution analyses where the reactor size is generally not dependent on how the fuel is distributed nor how excess oxygen is introduced. Overall, interstage duct burning is a second-order effect, compared to the number of stages. Effect of Low-Activation-Energy (LAE) Materials. Since the use of low-activation-energy (LAE) materials increases the performance of the reactive ITM independently of the MCRI concept, it is important to quantify how it might improve the

j+1 j

i = 1 , ..., j , j = 2 , ..., Nstg − 1

The results of Table 3 indicate large improvements initially and significant diminishing returns as the number of stages approaches five. Only three stages are required to achieve a pressure drop that is comparable to the AZEP100/85 separation-only ITMs,20 and the pressure drop quickly levels off with additional stages. Reductions in the total volume also fall off rapidly as Nstg increases beyond three. Thus, a maximum of five stages is analyzed herein in order to minimize computation expense; the results do not warrant any further increase in system complexity and cost. The most important conclusion from an economic and engineering perspective is that a modest number of stages is required to achieve large improvements in reactive ITM performance. Effect of Excess Oxygen from MCRI Stages. Another key degree of freedom is the excess oxygen separation in each stage. The excess oxygen is consumed in the duct burners and increases the inlet temperature to the next stage. However, previous results19 demonstrated that co-current separation-only ITMs do not exhibit superior performance, in terms of pressure drop and size. Thus, a tradeoff between higher inlet temperatures and oversized reactor stage volumes is expected. Small values of excess oxygen separation may not be taking full advantage of the potential for high inlet temperatures to successive stages. However, large values of excess oxygen separation rely on co-current separation-only ITMs at less than the maximal temperature allowed. That is, the average 7995



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Moreover, the parametric analyses provide near-optimal operating and design configurations that can be used as initial guesses to advanced optimization analyses. Overall, the MCRI could potentially make oxy-combustion CCS systems more viable by improving their economic viability while maintaining relatively high thermodynamic performance.

MCRI. In many ways, these two concepts both address the low average membrane temperature problem that hinders the reactive ITM. Thus, there are diminishing returns present when combining the two concepts. The impact of using LAE materials on the MCRI is given in Table 5, where the “backload” fuel distribution profile with a total excess oxygen of 10% of the stoichiometric is specified. The “backload” profile was chosen in an attempt to achieve the smallest possible ITM using the combined LAE and MCRI concepts. A sweep ratio of 40:1 was chosen to enable simulations with large reductions in the activation energy. The temperature overshoot is so large for a sweep ratio of 25:1 that excessive diluent dominates the overall performance and hinders a fair assessment of such cases. A decrease in the effective activation energy leads to modest reductions in the pressure drop or thermodynamic penalty, compared to the base case. This result is not surprising, considering that the LAE concept essentially influences the first two stages of the MCRI the most, where the flow rateand, hence, the pressure dropis small. In contrast to the pressure drop, significant reductions in the MCRI total volume are achieved. Generally speaking, reductions in activation energy have an impact when the membrane temperature is relatively low. The MCRI exhibits a high average membrane temperature; therefore, the reductions in activation energy only assist a small fraction of the MCRI. However, since the ITM is extremely sensitive to membrane temperature, even a small boost in the oxygen fluxand, hence, fuel conversion rategreatly improves the performance. Again, the results show how the thermodynamic penalty (pressure drop) and the total volume are related, but are impacted differently by changes in the ITM design and operation. Overall, the use of LAE materials seems to be justified, provided that the increase in cost due to the use of these materials is less than the reduction in cost, because of the need for less materials. Optimization studies that consider the cost of both aspects, along with the thermodynamic penalty, will provide a more definitive answer, based on the particular performance aspects of a given MCRI design, using a given ITM material.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: (617)-324-6768. Fax: (617)-258-5802. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors would like to thank the King Fahd University of Petroleum and Minerals in Dhahran, Saudi Arabia, for funding the research reported in this article, through the Center for Clean Water and Clean Energy at MIT and KFUPM (under Project No. R2-CE-08).

■

NOMENCLATURE

Abbreviations

AZEPXX = AZEP cycle with XX% CO2 capture CCS = carbon capture and sequestration DB = interstage duct burner ITM = ion-transport membrane LAE = low activation energy MCRI = multiple compartment reactive ion-transport membrane SQP = sequential quadratic programming USER2 = unit operation block in ASPEN Plus Variables

Ṅ i,j = molar flow rate of stream j entering MCRI stage i [mol/s] Nstg = number of MCRI stages [−] Vi = volume of stage i [m3] VTot = volume of the MCRI reactor network [m3]

Greek Letters

■

■

CONCLUSIONS The results of the multiple-compartment reactive ion-transport membrane (MCRI) simulation and analysis presented herein has provided many valuable tools for the advancement of oxycombustion carbon capture and sequestration (CCS) power generation systems. First, the results reveal the complex coupling between the physical processes governing the performance of reactive ion-transport membranes (ITMs) and demonstrate how relatively small changes in the reactor design can lead to dramatic improvements in both thermodynamic and economic metrics. The MCRI proposed herein can significantly reduce the cost of oxy-combustion CCS systems by decreasing the amount of membrane material required to separate the requisite oxygen. Based on the results for hybrid reactive separation-only AZEP concept,20 a power cycle with an integrated MCRI could match the efficiency of the best oxycombustion power cycles using 10%−30% less membrane materials. The particular simulation results presented herein elucidate the underlying physics of both ITM and MCRI air separation systems, and provide essential design guidelines to assist with the integration of the MCRI with power cycles.

ΔPTot = total pressure drop across MCRI [bar] γi = fraction of fuel entering MCRI stage i [−]

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