Supporting Information
Investigating CO2 removal by Ca- and Mg-based sorbents with application to indoor air treatment
Elliott T. Gall1,2,3, Cem Sonat2, William W Nazaroff3,4, Cise Unluer2
1Mechanical and Materials Engineering, Portland State University, Portland, OR 97201, USA
2Civil and Environmental Engineering, Nanyang Technological University, Singapore
3Berkeley Education Alliance for Research in Singapore, 1 Create Way, 138602, Singapore
4Civil and Environmental Engineering Department, University of California, Berkeley, CA
Number of pages: 8
Number of figures: 5
Additional model description
Laboratory experiments to parameterize uptake to sorbents
Kinetic parameters were determined from laboratory measurements of carbon dioxide upstream and downstream of sorbents placed in a reactor, either in dry form, or as slurries, in which sorbents were mixed with 100 cm3 of deionized water. Sorbents were then subjected to an air flow containing a known, stable concentration of carbon dioxide. Kinetic parameters were determined using coupled material balance equations describing the concentration of carbon dioxide in the reactor and the concentration of the unreacted sorbent in the reactor as shown in equations S1 and S2:
VfdCfdt=QfCin-QfCf-ykMCfVf / (S1)dMdt=-kMCf / (S2)
Here, Vf is the volume of the reactor (m3), Cf is the concentration of CO2 within and exiting the well-mixed reactor (mol CO2/m3), t is time (s), Qf is the volumetric flow rate through the reactor (m3/s), Cin is the constant concentration of CO2 entering the reactor (mol CO2/m3), y is the molar yield of the carbonation reaction (mol CO2/mol sorbent), k (m3 (mol CO2)-1 s-1) is the reaction rate constant, and [M] is the concentration of unreacted sorbent (mol unreacted sorbent/m3). Initial conditions were taken for equation S1 as Cf = 0 at t = 0 and for equation S2 as [M] = [M]i at t = 0, where [M]i is the measured moles of fresh sorbent placed in the reactor per unit reactor volume. The initial value of sorbent concentration was determined from the weighed mass of sorbent placed in the reactor. In the case of soda lime, only the mass of Ca(OH)2 was used in calculations. The value of Ca(OH)2 present in soda lime was determined from manufacturer-provided information specifying that Ca(OH)2 comprises 85% of soda lime, with the balance being NaOH, KOH, and H2O.
Equations S1 and S2 were discretized in time, as shown in equations S3 and S4, and solved simultaneously in explicit form using a time step of 0.01 seconds:
Cft+∆t=QfVfCint-QfVfCft-ykMCft∆t+Cft / (S3)Mt+∆t=-kMCft∆t+Mt / (S4)
Carbonation yields, y, were determined from the time-integrated difference between inlet and outlet CO2 monitors across the duration of an experiment to determine the total moles of CO2 removed. The yield was calculated as the total moles of CO2 removed, divided by the initial moles of sorbent placed in the reactor. Values of rate constants, k, were estimated by minimizing the function describing the sum of squared errors between measured and modeled values of Cf across physically meaningful values of k (minimized over a bound of seven orders of magnitude). The value of k reported is the value with the smallest sum of squared errors (SSE), determined from equation S5:
SSE=t=1t, finalCft,measured-Cft,modeled2 / (S5)An example of the model-measurement comparison is shown in Figure S1 for an experiment measuring carbonation rate of Ca(OH)2 under slurry conditions, with flow rate of 2.7 L/min and an inlet CO2 level of 2200 ppm.
Figure S1. Example experiment illustrating the minimization of errors procedure that resulted in an estimate of carbonation rate for Ca(OH)2. This experiment was conducted under slurry conditions, with an airflow rate of 2.7 L/min and an inlet CO2 concentration of 2200 ppm. The resulting rate constant determined for this experiment was 2.4 m3 mol CO2-1 h-1.
Application of parameterizations to hypothetical full-scale environments
Kinetic parameters were applied in modeling room-scale conditions using the kinetic and yield parameterizations determined in the laboratory experiments. Due to the larger masses of sorbents modeled (on the order of kilograms in the applied models compared to grams in the laboratory experiments), the packed beds were modeled as a series of coupled, well-mixed control volumes. Specifically, packed beds were modeled as a series of twenty well-mixed finite elements to approximate breakthrough-type conditions as carbon dioxide moves through the sorbent bed. Twenty discretized spatial elements were chosen based on preliminary sensitivity analyses that informed the compromise between computational efficiency and accuracy. Specifically, we observed a nearly unchanging solution with respect to the temporal profile of outlet CO2 when additional elements beyond twenty were used to represent the packed bed. Examples of coupled equations describing the concentrations of CO2 and masses of unreacted sorbent through the packed bed are provided in equations S6-S9:
Vf,1dCf,1dt=QfCroom-QfCf,1-ykM1Cf,1Vf,1 / (S6)dM1dt=-kM1Cf,1 / (S7)
Vf,i+1dCf,i+1dt=QfCf,i-QfCf,i+1-ykMi+1Cf,i+1Vf,i+1 / (S8)
dMi+1dt=-kMi+1Cf,i+1 / (S9)
In these equations, the index i ranges from 1 to 19, Vf,i is the volume of reactor element i, Cf,i is the concentration of CO2 in the well-mixed reactor element i, Mi is the mass of unreacted sorbent in element i, Croom is the concentration of CO2 in the room as it enters the reactor, and other terms are as described previously.
The equations describing the concentrations of CO2 entering (element at node 1) and exiting the air cleaner (element node 20) are coupled to a material balance describing carbon dioxide in the room, Croom (mol CO2/m3), as shown in equation S10:
VroomdCroomdt=QCa-QCroom-QfCroom+QfCf,20+E / (S10)Here, Vroom is the room volume (m3), Q is the outdoor air ventilation rate through the room (m3/s), Ca is the concentration of CO2 in outdoor air (moles CO2/m3), and E is the total CO2 emission rate from occupants in the room (moles/s). Similar to the procedure described for determining parameterizations of uptake from laboratory experimental data, the resulting 41 equations describing concentrations of CO2 in the twenty elements of the reactor, the as-yet-unreacted sorbent in the twenty elements of the reactor, and the CO2 concentration in the room in which the air cleaner is placed are discretized with respect to time and solved simultaneously in explicit form. Initial conditions for equations S6-S9 are similar to those described for the laboratory experiments. Initial conditions for equation S10 is such that at t = 0, Croom = 0.0163 moles CO2/m3 (or 400 ppm CO2).
Particle size distributions in sorbent materials
Figure S2. Normalized, volume-based particle size distributions of Mg(OH)2, Ca(OH)2 and MgO as determined by the particle size analyzer.
Additional modeling of indoor CO2 concentrations
Additional modeling was conducted to assess indoor CO2 concentrations for longer-term operation than reported in the primary article. Periods of 16 h, 40 h, and 40 h of continuous operation are reported in Figure S1 for the shelter-in-place (SIP), bedroom, and classroom, respectively. The additional run-time cases were modeled to estimate filter lifespan. Note that this estimate is potentially conservative with respect to CO2 loading in scrubber inlet air, as the selected time frames are longer than a typical single occupancy event, especially for the bedroom and classroom environments. It is likely that air exchange would reduce the time-averaged CO2 concentration entering the air cleaner under a scenario of intermittent occupancy (i.e., in a bedroom, 8 h of occupancy at night followed by 16 h of no occupancy rather than a continuous period of 40 h of occupancy).
As with the model results shown for the 8-h cases, Ca(OH)2 appears to be ineffective as a sorbent under the conditions modeled for SIP, the bedroom, and the classroom. Conversely, soda lime appears to be effective, especially under SIP and bedroom conditions, with more modest but still meaningful reductions of CO2 levels in classrooms until approximately 25 h of operation. There appears to be an inflection point in CO2 concentrations after approximately 9, 25, and 21 hours of operation in the SIP, bedroom, and classroom, respectively. These inflection points relate to a decreasing scrubber effectiveness, further explored in the next section of the Supporting Information, which reports modeled concentrations of Ca(OH)2 present in soda lime as a function of air cleaner run-time.
Figure S3. Modeled indoor CO2 concentrations for three hypothetical indoor environments: a shelter-in-place facility, a bedroom, and a classroom with and without the presence of an air cleaner that includes a CO2 scrubbing bed. Relevant built environment and air cleaner parameters for each of the three indoor environments are provided in Table 1 of the primary article. ‘LowQf’ refers to the low air cleaner flow rate condition; ‘highQf’ refers to the high air cleaner flow rate condition.
Modeling Ca(OH)2 concentrations in an air cleaner containing soda lime
The concentration of unreacted sorbent was modeled in hypothetical air cleaners. Packed beds of sorbents were discretized through twenty spatial nodes in the model that provides a time-series of sorbent concentrations at each node. For clarity, only the first, tenth, and twentieth nodes are reported here for an air cleaner containing soda lime and operating at high flow rate for the three indoor settings of SIP, bedroom, and classroom in Figure S2, S3, and S4, respectively. These results support the previously noted “inflection point” in modeled room CO2 concentrations; the concentration of available Ca(OH)2 in soda lime is exhausted shortly after the observed inflection point in CO2 concentrations.
Figure S4. Modeled Ca(OH)2 concentrations present in soda-lime media under the shelter-in-place scenario for continuous 16 h of operation under the high flow rate condition. The scrubber bed is modeled by discretizing to twenty nodes; only unreacted Ca(OH)2 in the first, middle, and final nodes are displayed to illustrate the conversion of Ca(OH)2 to CaCO3 in three locations of the packed bed.
Figure S5. Modeled Ca(OH)2 concentrations present in soda lime media under the bedroom scenario for continuous 40 h of operation for the high flow rate condition. See Figure S2 caption for additional information.
Figure S6. Modeled Ca(OH)2 concentrations present in soda lime media under the classroom scenario for continuous 40 h of operation for the high flow rate condition. See Figure S2 caption for additional information.
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