Measurement of CO2 Diffusivity in Phase-Changing Aminosilicone

May 4, 2018 - John McDermott,. †. Robert Enick,*,⊥ and Deepak Tapriyal. ⊥,∥. †. GE Global Research, 1 Research Circle, Niskayuna, New York 1...
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Cite This: Energy Fuels XXXX, XXX, XXX−XXX

Measurement of CO2 Diffusivity in Phase-Changing Aminosilicone CO2 Capture Solvent Tiffany Westendorf,† Rachel Farnum,‡ Gosia Rubinsztajn,† Benjamin Wood,§ Robert Perry,† John McDermott,† Robert Enick,*,⊥ and Deepak Tapriyal⊥,∥ †

GE Global Research, 1 Research Circle, Niskayuna, New York 12309, United States Envirospec Engineering, PLLC, 349 Northern Boulevard, Suite 3, Albany, New York 12204, United States § MECS, Incorporated, 14522 South Outer Forty Road, Chesterfield, Missouri 63017, United States ⊥ Department of Chemical and Petroleum Engineering, University of Pittsburgh, 1249 Benedum Hall, 3700 O’Hara Street, Pittsburgh, Pennsylvania 15261, United States ∥ National Energy Technology Laboratory (NETL), 626 Cochran Mill Road, Pittsburgh, Pennsylvania 15236, United States ‡

ABSTRACT: The mass transfer performance of a phase-changing aminosilicone CO2 post-combustion capture absorbent has been characterized. The aminosilicone, 1,3-bis(3-aminopropyl)-1,1,3,3-tetramethyldisiloxane (GAP-0), rapidly transforms from a low-viscosity liquid into a friable solid upon exposure to gaseous CO2. Mass transfer performance of this absorbent was studied to inform design and scaleup of a CO2 capture process. The long-term mass transfer rate of CO2 gas through a solid GAP-0 carbamate salt layer into a quiescent pool of liquid GAP-0 was characterized using pressurized thermogravimetric analysis. This experiment led to an estimate of the CO2 permeability of the carbamate salt solid of 1.46 × 10−9 mol of CO2 m−1 s−1 atm−1. Given literature-reported values of CO2 solubility in silicone polymers, the CO2 diffusivity through GAP-0 carbamate salt was inferred to be approximately 4.39 × 10−11 m2/s. In parallel, the CO2 absorption rate into a spray of GAP-0 droplets was studied in a laboratory spray reactor. While the rate of CO2 absorption was anticipated to be limited by the rate of CO2 diffusion through a solid carbamate salt layer on the surface of a droplet, experimental results suggest that the GAP-0 droplets behave more like a liquid during spray absorption. The effective diffusivity of CO2 through these droplets was estimated to be approximately 6 × 10−9 m2/s.

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INTRODUCTION We recently reported on the use of phase-changing aminosilicone CO2 capture sorbents and preliminary development of a process relying on these novel materials.1 In this process, the liquid sorbent is contacted with flue gas in a spray absorber, and particles of solid carbamate salt are formed. These particles are disengaged from the scrubbed flue gas and are transported to a pressurized desorption vessel, wherein the salt is heated. A pressurized CO2 stream is generated, and the regenerated liquid sorbent is recycled to the spray chamber. Each element of this process has been studied at the laboratory scale to demonstrate feasibility and to generate the data required to scale up the process. Solids formation at the laboratory scale has been accomplished using a small spray reactor, in which neat 1,3bis(3-aminopropyl)-1,1,3,3-tetramethyldisiloxane (i.e., GAP-0), a low-viscosity (4.4 mPa s at 20 °C) liquid aminosilicone is atomized into a co-current stream of simulated flue gas (16.4 mol % CO2 in N2). The rate of CO2 absorption at the temperature and partial pressure of CO2 in the absorber is needed to design and scale up the spray absorber. Previous experiments investigated the rate of absorption of CO2 into a GAP-0/triethylene glycol (TEG) solution.2,3 Because GAP-0 and GAP-0 carbamate are both soluble in TEG, the formation of solid carbamate was inhibited in those experiments, which allowed for the study of GAP-0/CO2 reaction kinetics in the absence of the mass transfer limitations caused by solidification. © XXXX American Chemical Society

In the spray absorber, the mass transfer limitations caused by the liquid-to-solid phase change that occurs when neat GAP-0 reacts with CO2 (Figure 1) to form the carbamate particles are unavoidable. As GAP-0 droplets begin to react with CO2 and form solid carbamate, the rate of absorption is anticipated to be limited by the rate of mass transfer of CO2 through that solid. This mass transfer rate is governed by the diffusivity of CO2 through GAP-0 carbamate, which must be characterized to design the spray absorber. The first objective of this study is to determine the long-term mass transfer rate of CO2 from the gas phase through a relatively large solid GAP-0 carbamate salt layer of known area and thickness into a quiescent pool of underlying liquid GAP-0. This analysis will yield the CO2 permeability of the carbamate salt solid and, given an estimate of the solubility of CO2 in the carbamate salt layer, an estimate of the diffusivity of CO2 in the solid carbamate salt. The second objective is to demonstrate absorption in a spray reactor system, through which the mass transfer rate in a representative system can be estimated. Through these experiments, insight into the rate-limiting step governing CO2 absorption by the atomized liquid and the effect Received: March 11, 2018 Revised: May 4, 2018

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DOI: 10.1021/acs.energyfuels.8b00836 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Reaction of GAP-0 (liquid) with CO2 (gas) leads to the formation of GAP-0 carbamate (solid).

Figure 2. Conceptual illustration of the long-term reaction of CO2 with GAP-0 (liquid) retained in an open cylindrical glass vial involving diffusion of CO2 through a layer of the GAP-0 carbamate (solid). The change in the mass of the container (reflecting the amount of CO2 that has formed carbamate) and the change in the thickness of the GAP-0 carbamate layer are monitored for ∼1100 h.

Figure 3. Schematic of the laboratory spray reactor.4 mol, 0.893 g/cm3] was obtained from Gelest or Momentive Performance Materials and used as received. TGA. Because GAP-0 solidifies upon reaction with CO 2 , experimental techniques that are typically employed to measure the diffusivity of gases in liquids are inappropriate. Instead, an experiment leveraging long-term TGA was conducted, as shown in Figure 2. A small, cylindrical glass sample holder was filled with GAP-0 and exposed to pure CO2 at ambient temperature and 1.0 atm pressure for an extended period. It was anticipated that rapid reaction of CO2 with GAP-0 would occur, leading to the formation of a thin layer of solid

of the phase change on the CO2 absorption rate will be obtained.

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EXPERIMENTAL SECTION

Materials. Cylinders of liquid CO2 (99.9%, Butler Gas), regulated to ∼0.1 psig were used to establish the slowly flowing CO2 atmosphere in thermogravimetric analysis (TGA). 1,3-Bis(3-aminopropyl)-1,1,3,3tetramethyldisiloxane [95+%, molecular weight (MW) of 248.52 g/ B

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Energy & Fuels carbamate. It was further anticipated that over time, the thickness of this layer would increase as CO2 diffused through carbamate and reacted with liquid GAP-0. The diffusivity of CO2 through the solid carbamate layer would then be inferred from the rate of increase in the layer thickness and the increase of the mass of the small container that held the GAP-0 and GAP-0 carbamate. Evaporative losses of both the GAP-0 and GAP-0 carbamate were assumed to be negligible. Because 1 mol of CO2 (MW of 44.01 g/mol) reacts with 1 mol of GAP-0 (MW of 248.52 g/mol) to form 1 mol of GAP-0 carbamate (MW of 292.53 g/mol), the largest possible increase in mass for complete conversion of all GAP-0 would be 17.7% relative to the initial amount of GAP-0. These experiments were performed using a Thermo Scientific TGA VersaTherm thermogravimetric analyzer. It records the change in mass of the sample kept at 25 °C while exposed to a slowly flowing gas stream of pure CO2 at 1 atm. The glass sample cylinder was approximately 0.020 m tall and had an inner diameter of 0.0100 m, corresponding to a cross-sectional area of 7.85 × 10−5 m2. A 0.515 g sample (0.577 cm3) of GAP-0 was placed into the cylinder and exposed to 1 atm of slowly flowing CO2 at 25 °C for ∼1100 h. The mass of the sample was monitored continuously. The sample was removed from TGA and visually inspected for ∼5 min at ∼80 h intervals. CO2 continued to flow in TGA while the sample was being inspected. Laboratory Spray Dryer. Because GAP-0 solidifies upon reaction with CO2, a conventional packed absorption column is inappropriate for a process to effect CO2 absorption with GAP-0. Instead, the process is envisioned to use a spray absorber, wherein liquid solvent is atomized into a CO2-rich gas stream, the droplets solidify upon reaction with CO2, and the resulting solid particles are separated from the CO2-lean gas stream. Solids formation at the laboratory scale has been accomplished using a small spray reactor, in which liquid GAP-0 aminosilicone was sprayed cocurrently with 16.4 mol % CO2 in N2 using a gas atomizing nozzle. The gas effluent concentration was monitored by mass spectrometry (MS); these data were used to infer the steady-state CO2 conversion in the reactor. Experiments were conducted for a range of liquid and gas flow rates, which generated a range of droplet sizes and average gas residence times. A Yamato ADL-311S laboratory spray dryer4 was modified for use as a spray reactor to evaluate CO2 absorption by phase-changing liquid aminosilicone sorbents. The unit is shown in schematic form in Figure 3 and consists of the following: (1) heater, (2) inlet temperature sensor, (3) distributor, (4) reactor, (5) cap, (6) outlet temperature sensor, (7) cyclone, (8) product collection jar, (9) solids trap, (10) solenoid valve, (11) three-way solenoid valve, (12) needle valve, (13) pressure gauge, (14) spray nozzle, (15) liquid peristaltic pump, (16) mass spectrometer, (17) gas flow meter, and (18) gas flow controller. The spray nozzle employed in this unit is a twin-fluid nozzle that relies on pressurized gas flowing in the annular portion of the nozzle around the tube in the nozzle (14) carrying the liquid GAP-0. The pressurized gas and liquid GAP-0 combine at the nozzle tip [i.e., the bottom of the spray nozzle (14) in Figure 3] to form the atomized GAP-0. For this type of nozzle, the spray droplet size is dependent upon the atomizing gas pressure (as will be subsequently demonstrated in Table 2 of the results). Gases are supplied from cylinders and are fed through mass flow controllers to enable accurate measurement of the gas feed rate to the reactor. Typically, simulated flue gas was used for both the atomizing and bulk gases, and most of the gas was fed to the reactor through the atomizing nozzle. While the bulk gas feed rate was controlled directly, using a mass flow controller, the desired atomizing gas flow rate was attained by adjusting the atomizing gas pressure in the nozzle. As shown in Figure 4, the atomizing gas pressure and flow rate are linearly dependent upon each other. Most of the solids that are generated during a spray reaction collect within the reactor. Fine particles that are carried out of the reactor are disengaged from the gas stream in the cyclone. The bulk of the gas effluent is vented to the laboratory fume hood exhaust, and a slipstream of this gas is fed to a MKS Cirrus mass spectrometer (MS) for gas composition analysis. A solids trap is mounted upstream of the MS to ensure that any solids that may escape from the cyclone are not

Figure 4. Atomizing gas pressure varies linearly with the gas flow rate.

carried into the instrument. Gas composition is used to quantify CO2 captured by the aminosilicone in an experiment and is compared to compositional analysis of the solids product. In a typical spray reactor experiment, GAP-0 is sprayed into the reactor, in which a controlled flow rate of CO2/N2 has been established. At the end of the spray period, the gas flow is shut off as quickly as possible to minimize exposure of the carbamate solids in the reactor to CO2 after the spray. Typically, the liquid spray period is long enough that steady-state CO2 capture is achieved. CO2 capture is quantified via the CO2 concentration in the reactor feed and effluent gases as measured by MS. Spray droplet size was measured within the laboratory spray reactor using a Malvern Spraytec laser diffraction instrument5 for a range of GAP-0 flow rates and atomizing gas pressures. Given the refractive index of the droplets, the instrument infers the droplet size distribution from the diffraction of light by the spray. The instrument is capable of measuring droplets between 0.1 and 900 μm in diameter and reports droplet size distribution as well as parameters such as the Sauter mean diameter6 (D32). An acrylic box with quartz windows was constructed to interface with the laboratory spray reactor to allow for in situ droplet size measurement, because the instrument requires that the laser pass through flat surfaces of optically clear material (quartz).

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MODELING Permeability Model of TGA Data. A solution-diffusion mechanism of CO2 transport through the carbamate salt layer, coupled with instantaneous reaction of CO2 and GAP-0 on the permeate side of the layer, allowed the permeability of CO2 through the GAP-0 carbamate layer to be calculated in a manner similar to that used to calculate gas permeability in dense, highly CO2-permeable polymeric membranes.7 Equation 1 presents the solution-diffusion permeability model in the case where the thickness of the carbamate salt layer, which is acting as a CO2-permeable membrane, is constant (L) NCO2L P = DS = (1) ΔP where P is the CO2 permeability through the carbamate salt layer (mol m−1 s−1 atm−1), D is the diffusivity of CO2 through the carbamate salt layer (m2/s), S is the solubility of CO2 in the carbamate salt layer (mol m−3 atm−1), NCO2 is the CO2 flux through the carbamate salt layer (mol s−1 m−2), L is the thickness of the carbamate salt layer (m), and ΔP is the CO2 partial pressure drop across the carbamate salt layer (atm). C

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Figure 5. Droplet-level mass transfer model, in which the initially liquid droplet of GAP-0 is exposed to CO2 (left), leading to the formation of a GAP-0 carbamate skin that grows (center), until the entire droplet is a solid GAP-0 carbamate salt spherical particle (right).

is calculated using the equation for CO2 flux assuming that bulk mass transfer is the rate-limiting step, where the gas-side mass transfer coefficient is derived from the Sherwood number, the Schmidt number, and the Reynolds number.9 This calculation is performed for a GAP-0 droplet falling at terminal velocity, which is dependent upon the droplet diameter. The equation for CO2 flux assuming that bulk mass transfer is the ratelimiting step is provided in eq 3

The rate of mass increase of the sample shown in Figure 2 corresponds to the rate of CO2 passing through the carbamate layer. Using this value, the molar flux of CO2 is calculated as follows in eq 2: NCO2 =

dm dt πd 2 M w,CO2 4

(2)

NCO2 = kg(C bulk − Csurface‐gas)

where dm/dt is the rate of mass increase of the GAP-0 sample (g/s), d is the inside diameter of the sample holder and the carbamate layer (m), and Mw,CO2 is the molecular weight of CO2. Because permeability is the product of solubility and diffusivity (eq 1), the diffusivity of CO2 through the carbamate layer can be estimated given an estimate of CO2 solubility in carbamate. Mass Transfer Model of Spray Absorption. A dropletlevel mass transfer model was developed that allowed insight into the rate-limiting steps of the absorption process. It is believed that mass transfer limitations dominate the reaction rate of CO2 with GAP-0 because of the change in phase (liquid to solid) that occurs upon reaction. This model, illustrated in Figure 5, calculates the CO2 flux (absorption rate) into a single droplet of GAP-0 falling at terminal velocity through simulated flue gas under three limiting scenarios related to mass transfer: (1) bulk mass transfer, in which the CO2 absorption rate is limited by the diffusion of CO2 from the bulk gas through the gas boundary layer surrounding the GAP-0 droplet to the gas-side surface of the droplet, and (2) droplet-side mass transfer, in which the CO2 absorption rate is limited by the diffusion of CO2 from the droplet-side surface of the droplet into the center of the droplet, assuming that (a) the droplet behaves as a liquid throughout absorption and (b) the droplet behaves as a solid throughout absorption. A comparison of the CO2 flux calculated for these limiting cases to the actual CO2 absorption rate observed in the laboratory spray reactor suggests which regime dominates in the laboratory reactor and allows for inference of effective CO2 diffusivity through the droplet and effective CO2 reaction rate. The model development is similar to that described in the literature.8 In scenario 1, the rate of CO2 absorption is assumed to be limited by the mass transfer of CO2 in the gas phase from the bulk to the surface of a GAP-0 droplet. This mass transfer rate

(3)

where NCO2 is the CO2 flux (mol m−2 s−1) into the droplet per unit droplet surface area, kg is the gas-side mass transfer coefficient (m/s), Cbulk is the CO2 concentration in the bulk gas (mol/m3), and Csurface‑gas is the droplet surface concentration of CO2 on the gas side (mol/m3). It is also of note that the gas-side droplet surface concentration of CO2 in this scenario is assumed to be zero. The assumption that the overall CO2 absorption rate is limited by the bulk mass transfer rate implies that the chemical reaction rate is instantaneous relative to the bulk mass transfer rate, which means that the CO2 concentration on the gas side of the droplet surface is effectively zero. In scenario 2, the rate of CO2 absorption is assumed to be limited by the mass transfer of CO2 through the droplet and is calculated using eq 4, which is Danckwerts’ penetration theory model of reactive diffusion for a pseudo-first-order, irreversible reaction at steady state.10 For a single droplet, GAP-0 is present as a pure component and, thus, is assumed to be present in excess. In this case, the droplet-side surface CO2 concentration is estimated using literature correlations for the solubility of CO2 in silicone polymers,12 which is approximately 33.3 mol of CO2 m−3 atm−1. Because the effective diffusivity is unknown for our system, the calculation was performed using two assumptions: (2a) the diffusivity is similar to that of CO2 through liquids,11 i.e., ignoring the effect of the phase change upon reaction, and (2b) the diffusivity is similar to that of CO2 through solid clathrate hydrates.14 Thus, the sensitivity of the result to diffusivity can be assessed. The penetration theory equation for CO2 flux assuming that droplet-side mass transfer is the rate-limiting step is found in eq 4 NCO2 = Csurface‐drop Deff ka[GAP‐0]

(4)

where NCO2 is the CO2 flux (mol m−2 s−1) into the droplet per unit droplet surface area, Csurface‑drop is the droplet surface D

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Energy & Fuels concentration of CO2 on the droplet side (mol/m3), Deff is the effective diffusivity of CO2 in the droplet (m2/s), ka is the absorption rate constant (m3 mol−1 s−1), and [GAP-0] is the GAP-0 concentration in the droplet (mol/m3).

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RESULTS Experimental TGA Results. Figure 6 shows the sample mass increase with time. The increase is expressed as the ratio of the combined mass of GAP-0 and GAP-0 carbamate to the initial mass of GAP-0 charged to the apparatus. A constant rapid increase in the mass, 1.86 × 10−6 g of CO2/s, occurred during the first hour, when the solid “skin” of GAP-0 carbamate would be first forming and expected to have its least significance on mass transport. It was not possible to detect or measure the thickness of this skin during this hour. The initial flux during this initial 1 h was determined to be 5.4 mol of CO2 m−2 s−1 based on the initial rate of mass increase and the cross-sectional area of the open cylindrical container based on its inside diameter, as shown in eq 5.

Figure 6. Rate of CO2 uptake by GAP-0 aminosilicone at 1 atm CO2 at 25 °C; a period of the most rapid initial mass increase (0−1 h) tapers off, followed by a period of constant rate of mass gain at prolonged times (450−1100 h). The small discontinuity at approximately 500 h was due to a CO2 cylinder change. The colors correspond to the duration of the experiment between periodic visual inspections of the sample.

⎛ g of CO2 absorbed ⎞ ⎜1.86 × 10−6 ⎟ ÷ (7.85 × 10−5 m 2) s ⎝ ⎠ ⎛ g of CO2 ⎞ ÷ ⎜44 ⎟ ⎝ mol of CO2 ⎠ mol of CO2 = 5.4 × 10−4 m2 s

previous work with CO2 absorption by neat GAP-0, significant mass transfer limitations consistent with viscosity build/ solidification were observed at 60−80% of the theoretical maximum CO2 loading.1 It was not possible to obtain detailed measurements of the number, size, or growth rate of the crystallites during this interval because the vials were removed from TGA every 80 h for only 5 min to take a photograph of the vial. We were able to affirm the thickness of the film from these photographs but could not derive the kinetics of the crystallite formation or growth. Permeability Modeling of TGA Results. The solutiondiffusion mass transfer model (eq 1) was used to calculate the CO2 permeability through a layer of solid GAP-0 carbamate using the TGA data. The thickness of this layer was measured after approximately 243 h of exposure and was found to be 1.0 mm, as shown in Figure 7. The analysis was conducted on the absorption rates measured in the pseudo-steady-state portion of the experiment (120−450 h), at which time the carbamate salt layer was believed to have been fully developed and prior to the formation of crystallites below the film, and on the 450−1100-h interval, during which the rate of mass increase remained constant. In this analysis, the GAP-0 carbamate salt layer was modeled as a gas-permeable polymeric membrane having no porosity or pinhole defects. The gas side of the layer was treated as the retentate, and the liquid side of the layer was treated as the permeate. The chemical reaction kinetics were believed to be very fast relative to the rate of CO2 transport through the carbamate salt layer, as evidenced by the very initial rapid rate of mass increase as the carbamate skin was starting to form compared to the relatively slow rate later in the experiment when the 1.0 mm thick skin was fully developed (Figure 6). Therefore, the CO2 concentration in the liquid GAP-0 on the permeate side of the carbamate layer was assumed to be zero. Thus, the mass transfer driving force across the carbamate salt layer was assumed to remain constant during the experiment and equal to the partial pressure of CO2 in the retentate, which was maintained at 1 atm throughout the experiment.

(5)

Between 1 and 120 h of this long-term test, the rate of mass increase diminished significantly. Between 120 and 450 h, the rate of mass increase decreased slightly with time, averaging 8.80 × 10−9 g of CO2/s. This was followed by a long period (450−1100 h), during which there was a constant rate of mass increase of 5.05 × 10−9 g of CO2/s. The CO2 exposure experiment ended after 1100 h, at which time the combined mass of the unreacted GAP-0 and GAP-0 carbamate was 1.11 times that of the initial charge of GAP-0, which represents 62% conversion of GAP-0 to GAP-0 carbamate. Periodic visual inspection of the sample during this time showed that the fastest rate of mass increase was occurring at the beginning of the experiment, while the GAP-0 carbamate film at the CO2−GAP-0 interface was being established. This film, which started with a thickness of 0 mm at the start of the experiment, grew to a thickness of 0.7 mm at 80 h and 0.9 mm after 161 h. By the third inspection, which occurred at 243 h, the film had attained a thickness of 1.0 mm. The film thickness remained at 1.0 mm until the test was completed at 1100 h. Between 50 and 450 h, the transparent pool of liquid GAP-0 under the GAP-0 carbamate layer appeared to gel. Eventually, after ∼450 h, small spherical crystalline domains were formed in the GAP-0 liquid beneath the GAP-0 carbamate film, as shown in Figure 7. This behavior was attributed to thermal convection within the unreacted portion of the sample. As CO2 diffused through the carbamate layer and reacted exothermically with the bulk GAP-0, the temperature gradient caused recirculation of the fluid GAP-0, which dispersed the newly formed carbamate throughout the liquid portion of the sample. As this process continued, the carbamate content in this fluid increased, which caused an increase in fluid viscosity. At some critical carbamate content, crystalline domains were formed. Crystallites were observed in the sample after approximately 500 h of exposure, which corresponds to 9 wt % CO2 loading or approximately 50% of the theoretical maximum loading. In E

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Figure 7. Visual appearance of the GAP-0 sample during long-term exposure to CO2, showing development of crystalline carbamate domains; from left to right, the duration of exposure to CO2 was 72, 243, 520, and 930 h.

The fastest rate of mass transport occurred during the first hour of the experiment, when the mass of the sample increased by 1.86 × 10−6 g of CO2/s, corresponding to CO2 flux of 5.4 × 10−4 mol of CO2 m−2 s−1, as shown in eq 5. During this time, the solution-diffusion model was not applied because it was not possible to detect a distinct continuous carbamate salt layer. As shown in Figure 6, the rate of CO2 transport through the carbamate skin, dm/dt, during the 120−450 h interval averaged 8.800 × 10−9 g of CO2/s. During the 450−1100 h interval, the rate of CO2 permeating through the carbamate skin was 5.054 × 10−9 g of CO2/s. On the basis of eq 2, the corresponding flux values are 2.55 × 10−6 and 1.46 × 10−6 mol of CO2 m−2 s−1, respectively, as shown in Table 1. Because the thickness of the

similar to that in silicone polymers. CO2 solubility in silicone polymers at 25 °C is reported in the literature11 to be on the order of 33.3 mol of CO2 m−3 atm−1. Given this value as an approximation for the solubility of CO2 in the carbamate salt film, CO2 diffusivity is estimated to be roughly 4.39 × 10−11 m2/s (4.39 × 10−7 cm2/s) during the 450−1100 h period. This diffusivity value is on the same order of magnitude as reported for values of gas diffusivity through solids (10−10−10−14 m2/ s),12 for CO2 diffusion through clathrate hydrates (10−12 m2/ s),13 and for CO2 diffusion through polymeric materials [from 10−10 to 10−14 m2/s for poly(methyl methacrylate), poly(chlorotrifluoroethylene), cross-linked poly(dimethylsilane), poly(vinyl acetate), and polystyrene].14,15

Table 1. CO2 Flux, Permeability, and Diffusivity Calculations from TGA Experiments in the 450−1100 h Interval

EXPERIMENTAL SPRAY DRYER RESULTS Spray Droplet Size Measurement. The droplet size was measured for GAP-0 sprayed using atomizing gas comprised of 16.4 mol % CO2 in N2, as typical of spray absorption experiments. Because the refractive index of GAP-0 carbamate was unknown, the sensitivity of the measured droplet size to this refractive index was assessed within the range of 1.4−1.6, as typical for silicone polymers.16 The mean droplet size was found to vary by approximately 5% within this range. The droplet sizes reported herein were derived using the refractive index of liquid GAP-0, which is 1.447. Absorption experiments were conducted for a wide range of spray conditions, with multiple repeats (3−5) performed at each GAP-0 flow rate (20−40 mL/min) and gas pressure (0.05−0.3 MPa). However, only those runs that yielded reliable results are reported in Table 2. Numerous trials resulted in a spray too dense for the Malvern to detect or formed droplet sizes that approached the measurement limits of the instrument or particles that adhered to the side of the chamber, blocking the light source. The conditions shown in Table 2 cover the full range of operable atomizing gas pressures and reflect GAP-0/ CO2 molar stoichiometries ranging from 0.45 to 0.90; because the stoichiometric ratio of GAP-0/CO2 is 1:1, as shown in Figure 1, the 0.45−0.90 molar ratios represent 122−11% excess CO2. For this process, the GAP-0/CO2 molar feed ratio must favor excess CO2 (i.e., be less than 1) to ensure that solids are produced. As atomizing gas pressure was increased at a given liquid flow rate, the degree to which the spray scattered the laser light (obscuration) increased to a point where the instrument could not measure the droplet size distribution. The laser beam is scattered by individual spray droplets; as the size of those droplets decreases, the degree to which the light is scattered increases. Also, for a given liquid flow rate, the

time (h) dm/dt (g of CO2/s) cross-sectional area (m2) MW of CO2 NCO2 (mol of CO2 m−2 s−1)

450 − 1100 5.05 × 10−9 7.85 × 10−5 44 1.46 × 10−6

L (m) ΔP (atm) permeability (mol CO2 m−1 s−1 atm−1) permeability (barrer) solubility estimate (mol of CO2 m−3 atm−1) diffusivity (m2/s) diffusivity (cm2/s)

0.001 1 1.46 × 10−9 432 33.3 4.39 × 10−11 4.39 × 10−7

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carbamate salt layer (0.0010 m), the CO2 concentration gradient across the carbamate salt layer (1 atm), and the flux of CO2 through the carbamate skin all remained constant during the 450−1100 h interval, the permeability of the carbamate salt layer was determined from the data in this interval. Equation 1 was used to determine the permeability of the carbamate salt layer to be 1.46 × 10−9 mol of CO2 m−1 s−1 atm−1. In terms of barrers [defined as 1 × 10−10 cm3 standard temperature and pressure (STP) cm−1 s−1 cm−1 of Hg], this CO2 permeability value is 430 barrers, which is comparable to several polymeric materials considered to be reasonably CO2permeable.7 Because permeability is the product of diffusivity and solubility, CO2 diffusivity through the carbamate salt layer can be calculated as the ratio of CO2 permeability to CO2 solubility in the salt. Because the core of the GAP-0 molecule is a silicone linkage, CO2 solubility in GAP-0 was assumed to be F

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value for diffusivity (liquid droplet versus solid droplet). A comparison of these calculated values to the absorption rate, as measured in the laboratory spray absorber, suggests that the CO2 absorption rate in the phase-changing process is dropletside mass-transfer-limited and that the diffusivity of CO2 in the droplets is consistent with values that are typical for gas diffusivity in liquids. The spray absorber experimental data shown in Figure 8 was calculated using CO2 and GAP-0 flow rates to the absorber during the experiment, observed CO2 capture percentage, and estimates of the droplet residence time in the spray absorber. This calculation is shown in eq 6 for the CO2 absorption rate observed in spray absorber experiments (volume basis) during run 6 of Table 2. This value is then used in eq 4 to infer diffusivity, which is summarized in Table 3

Table 2. Summary of Droplet Size Measurements for 16.4 mol % CO2 in N2 Atomizing Gas absorption run ID

GAP-0 flow rate (mL/min)

atomizing gas pressure (MPa)

Sauter mean droplet diameter, D32 (μm)

1 2 3

20 20 20

0.05 0.10 0.13

66.3 8.6 95% obscuration during spray

NCO2 =

number density of droplets in the spray increases as the droplet size decreases, which increases the light obscuration by the spray.17 Finally, as the mean droplet size approaches the lower detection limits of the instrument, measurement of the droplet size distribution becomes impossible. Despite these limitations on the measurement range of the instrument relative to the spray operating range of interest (atomizing gas pressure in the range of 0.05−0.3 MPa), the measurements obtained by this method yield useful insight into the droplet sizes produced in the laboratory spray reactor during absorption experiments. At a constant atomizing gas pressure, droplet size decreases with a decreasing liquid flow rate (for example, run 4 versus run 6 or run 2 versus run 5); this is rational, because the same volume of gas should atomize a smaller liquid stream more efficiently than a larger liquid stream. Overall, we can conclude with confidence that, for most of the spray conditions studied, the mean droplet size was most typically 9−15 μm and may possibly have been up to 70 μm for conditions having a low atomizing gas pressure. Absorption Results. The results of limiting-case calculations of the CO2 absorption rate as a function of the droplet diameter are shown in Figure 8 in terms of moles of CO2 absorbed per volume of GAP-0 per second. The droplet-side mass transfer rate is much lower than that in the bulk, and the droplet-side mass transfer is highly sensitive to the assumed

nCO2χ vGAP‐0τ

=

mol of CO2 min

(0.18

)(0.64)

3 −5 m GAP‐0 min

(4.2 × 10

)(14.9 s)

mol of CO2

= 184.1

m3 s

(6)

Table 3. Summary of Spray Absorption Experiments, Including Droplet Size Measurements and Inferred Effective Diffusivity Values

absorption run ID

Sauter mean droplet diameter, D32 (μm)

1 2 3 4 6 7

66.3 8.6