Introduction
Planetary protection is a discipline concerned with preventing contamination of solar system bodies with Earth life (forward contamination) and protecting Earth from possible extraterrestrial life (backward contamination). In 1967, the United Nations Outer Space Treaty established guidelines to preserve the scientific integrity of future explorations (United Nations, 1967). Since then, the Committee on Space Research has updated the guidelines that national space agencies use as part of their mission planning (COSPAR, 2020). In compliance with the Committee on Space Research policies, the National Aeronautics and Space Administration (NASA) monitors spacecraft bioburden to prevent forward and backward contamination.
The assessment of bioburden, particularly in materials like adhesives and paints, is a complex process that often requires a combination of destructive assays and various techniques (Angelotti et al., Reference Angelotti, Maryanski, Butler, Peeler and Campbell1968; Gustan & Olsen, Reference Gustan and Olson1971; Stam et al., Reference Stam, Bruckner, Spry, Venkateswaran and La Duc2012). Due to direct sampling challenges, specification values are sometimes adopted for bioburden estimation (NASA, 2022). For example, 30 spores/cm3 is assumed for non-electronic solid materials. There is no specification value for liquids. Specification values have been shown to be conservative and not reflective of the actual microbial load (Schubert et al., Reference Schubert, Newlin, Chung and Ellyin2016). Assuming a specification value is disadvantageous as it can result in a substantial total spore value that quickly exhausts the available margin for a given mission.
Historical mission designs at JPL, including the Mars Pathfinder, Mars Exploration Rover and Mars Science Laboratory, have featured Heat Redistribution Systems (HRS) to comply with Planetary Protection standards (Birur et al., Reference Birur, Bhandari, Gram and Durkee1996; Ganapathi et al., Reference Ganapathi, Birur, Tsuyuki and Krylo2003; Bhandari et al., Reference Bhandari, Birur, Karlmann, Bame, Liu, Mastropietro and Kinter2011). The design for the Europa Clipper mission’s HRS incorporates a 2.0 µm filter, diverging from past missions due to different bioburden constraints for Europa exploration (Ochoa et al., Reference Ochoa, Hua, Mastropietro, Lee, Paris, Emis and Williams2017). Trichlorofluoromethane (CFC-11; Freon), the refrigerant used in the HRS, has been previously studied for its microbial inhibitory effects, providing a rationale for certain design decisions (Auken et al., Reference Auken, Healy and Kaufmann1974; Gunaratne & Spencer, Reference Gunaratne and Spencer1974).
A CFC-11 bioburden study was performed during the MSL mission (JPL internal document; D-72309 MSL Planetary Protection Post-Launch Report), which resulted in a bioburden density of 29.7 spores/L that was applied to the total CFC-11 volume (9294 cm3) to obtain the total spores. Had MSL applied the NASA specification of 30 spores/cm3, 55.8% of the total spore budget for the mission would be allocated to the CFC-11. The same density of 29.7 spores/L was applied to the Mars 2020 mission given the similar MGSE design. The experimental design and controls from the MSL study are poorly understood, and the calculations are difficult to trace and are not based on rigorous statistical modeling. Therefore, we mention this prior study but do not attempt to reconcile or understand similarities and differences in results between these two studies. The HRS MGSE used for MSL/Mars 2020 and Europa Clipper is markedly different, which was the driving reason for a new study.
Given a possible Mars Sample Return mission’s heightened bioburden restrictions, this study re-examines the bioburden associated with CFC-11 in the context of the HRS MGSE system used on Europa Clipper. Through a targeted study using membrane filtration (MF) and the NASA Standard Assay, no growth was observed in CFC-11 samples (NASA, 2010; Stott et al., Reference Stott, Morgan, Shearer, Steadham, Ballarotto and Hendrickson2022). These observations informed a predictive probability distribution that estimated 0.04 spores/L were transferred to the flight HRS from the Freon – significantly lower than the MSL study bioburden density. These results challenge the necessity of a 0.2 µm filter in the system, suggesting potential efficiencies in mission design without compromising on bioburden control. This model and its findings may have significant implications for future missions, such as Mars Sample Return Mars Retrieval Lander (MSR SRL) mission and their approach to meeting Planetary Protection requirements.
Materials and methods
Preparation of filter assembly
The HRS Mechanical Ground Support Equipment (MGSE) designed for the Europa Clipper spacecraft delivers CFC-11 to the spacecraft, as demonstrated in Figure 1. Notably, the system utilizes three 2 µm filters: one located on the Storage Drum (SD), one located on the Refrigerant Transfer Cylinder (RTC) and one on the Flight Fill Panel (FFP) that filters the CFC-11 before it leaves that panel via a flex hose, subsequently entering the spacecraft. This design is markedly different from the Mars 2020 or MSL missions that utilized a 0.2 µm filter to meet Planetary Protection spore requirements. Additional technical details of the testing setup are described in the Appendix A. All personnel handling CFC-11 hold federal Environmental Protection Agency (EPA) 608 Type III or Universal licenses.
HRS MGSE. The Storage Drum (SD) contains CFC-11 that is transferred to the Refrigerant Transfer Cylinder (RTC), which is used to fill the FFP (a process referred to as “charging”). The Refrigerant Recovery Cylinder (RRC) is used to support CFC-11 recovery operations and is designed to interface with the Recovery System (Refrigerant Recovery Cylinder and Recovery Machine). The FFP is used for supplying CFC-11 at controlled flow rates to the spacecraft. The system utilizes stainless-steel bellows flex hoses with stainless-steel braided jacket.
Three sterile filter assemblies (PN YY3009000, Sigma Aldrich, St. Louis, MO, USA) were used to collect CFC-11 samples from three different locations within the Europa Clipper HRS MGSE system. Each assembly consisted of a 90 mm, 0.2 µm cellulose acetate membrane (PN CA029025, Sterlitech, Auburn, WA, USA) housed in a sterilized filter holder equipped with stainless-steel fittings for compatibility with system flex hoses. Custom welded tee fittings and diaphragm valves allowed controlled flushing and isolation of the filter before sample collection. All internal surfaces of the assemblies, including filters and fittings, were sterilized by autoclaving at 121 °C and 30 psia prior to use.
NASA standard assay (NSA)
Per NASA HDBK 6022 (NASA, 2010) swab and wipe samples from surfaces are processed via the NASA Standard Assay (NSA) procedure. When surface samples are acquired using wipes, the wipes are aseptically transferred to a media bottle containing 200 mL of Planetary Protection (PP) rinse solution that is then sonicated to release any spores captured in the wipe. The 90 mm cellulose acetate filter in this study was processed in the same way, where the filter was aseptically transferred to a media bottle containing 200 mL PP rinse solution. PP rinse solution (buffered solution + Tween 80) was prepared in accordance with NASA HDBK 6022 (NASA, 2010). Samples were then vortexed and sonicated for two minutes in an aqueous bath of 0.02% v/v Tween 80, at 19–27kHz. Samples were then split into two equal fractions: for one fraction, the samples were exposed to “heat shock” at 80 °C for 15 minutes to enable the detection of aerobic, mesophilic, cultivable spores. Samples are then quickly cooled to 30 °C – 35 °C. The second fraction was not treated to heat shock, to detect all viable organisms. All samples were then processed via membrane filtration.
Membrane filtration (MF)
The MF equipment includes a 3-place Pall laboratory manifold with hose barb cap, end cap and manifold valves (PN 4889, Pall, Port Washington, NY, USA). The equipment also includes manifold standard adapters (PN 4891, Pall, Port Washington, NY, USA), 150 mL magnetic filter funnels (PN 424, Pall, Port Washington, NY, USA), 47 mm diameter Whatman 0.2 µm cellulose acetate membrane filters (PN 10404112, Cytiva, Marlborough, MA), filter forceps, Tygon tubing, vacuum trap system (PN 3022001FLS, Foxx Life Sciences, Salem, NH, USA) and vacuum pressure pump (PN DOA-P704-AA, GAST, Benton Harbor, MI).
The MF setup was assembled in a laminar flow environment or Class II, Type A2 biological cabinet as following: The Pall laboratory manifold was first connected to the pump and filtrate receptacle using Tygon tubing. The 150 mL magnetic filter funnels were placed into each of the three manifold openings via the manifold standard adapters, and subsequently, the 0.2 µm Whatman filters were placed inside the magnetic filter funnels using sterile forceps.
MF was performed according to the procedure established for PP flight implementation (Stott, et al., Reference Stott, Morgan, Shearer, Steadham, Ballarotto and Hendrickson2022). To begin MF, 5 mL of sterile 18.2 MΩ deionized water was filtered through each funnel to wet the filters. Next, the sample volume was poured into a filter funnel. To avoid results where Colony Forming Units (CFU) would be too numerous to count, the volumes from CFC-11 samples were split into 5 mL, 10 mL, 25 mL and 60 mL fractions. The volumes were filtered via vacuum and the sample allowed to drain completely. The funnels and filters were rinsed of potentially inhibitory residues with an additional ∼50 mL of sterile water followed by filtration.
Plating
For sample volumes processed with MF, the 47 mm membrane filters were aseptically removed from the funnels and placed onto sterile 100 × 15 mm Petri dishes prepared with Trypticase Soy Agar (TSA) by slowly rolling the filter onto the solidified agar to avoid trapped air bubbles underneath the filter. Plates were then incubated at 32 °C and CFU enumerated at 24, 48 and 72 hours. The 90 mm membrane filters remaining in the media bottles were additionally processed by placing them directly onto sterile 150 × 15 mm Petri dishes prepared with TSA, to recover any potential spores on the surface that did not rinse off into the PP rinse solution. Plates were then incubated at 32 °C and CFU enumerated at 24, 48 and 72 hours.
Recovery efficiency
An experiment was conducted to determine the recovery efficiency of the laboratory process for input into the modeling study. First, serial dilutions of 106 Bacillus atrophaeus spores were performed to obtain a stock dilution with the expected yield of 50 CFU on plates. Next, this stock dilution was directly plated in ten replicates (expected yield samples). Using the same stock dilution, sterile 90 mm filters were spiked and each placed in bottles containing 100 mL PP rinse. Just as with the CFC-11 samples, these samples were sonicated, heat shocked and processed with MF to enumerate CFU on the 47 mm filters, and the 90 mm filters were aseptically removed from the bottles and directly plated for CFU enumeration (observed yield samples). To calculate the recovery efficiency, the average observed yield CFU was divided by the average expected yield CFU. Then, this value was multiplied by 0.5 to account for the 50% pour fraction of the CFC-11 samples (i.e., the 200 mL fractions were split in half).
Mathematical method
A probabilistic model was developed to characterize the transfer and recovery of spores through the MGSE system during CFC-11 fill operations (Appendix B). This model incorporates experimental data from three filter assembly (FA) tests: FA1, FA2 and FA3, to estimate the likelihood of a single spore passing through each filtration stage and being recovered. Key elements considered by this model are filter efficiency and spore size. Figure 2 below shows a representative filtration efficiency curve for a 2 µm filter along with the range of spore diameters relevant to this study (from Bacillus atrophaeus).
Filter efficiency (solid curve) results from the combined effects of diffusive and electrostatic forces, which dominate at particle diameters smaller than the minimum penetrating particle size (MPPS), and impaction and interception mechanisms, which become more significant at larger diameters. This filtration efficiency curve is informed by vendor specifications, including 95% efficiency and the minimum penetrating particle size (MPPS). Overlaid in grey is the range of spore diameters relevant to this study, showing the 0.1–99.9th percentiles of B. atrophaeus using data from Carrera et al. (Reference Carrera, Zandomeni, Fitzgibbon and Sagripanti2007).
In the FA1 experiment, a known volume of CFC-11 was transferred from the Storage Drum (SD) through a 2.0 µm MGSE filter, establishing baseline measurements for filter capture efficiency and spore recovery probability. These data informed the posterior distributions of three key model parameters: the MGSE filter capture rate (λMGSE), the 0.22 µm filter capture rate (λFA) and the recovery probability (ϕ).
Subsequent experiments (FA2 and FA3) used a residual spore population from the RTC, which had been previously filled during FA1. In FA2, CFC-11 was transferred through a 2.0 µm MGSE filter and a 0.22 µm filter, while in FA3, the transfer passed through two sequential 2.0 µm MGSE filters before reaching the 0.22 µm filter. The probability that a spore was transferred and recovered through these stages was modeled as a function of filter efficiency, spore size, spore transfer volume fractions and recovery rates.
The joint likelihood for FA2 and FA3 was derived by marginalizing over the unknown spore population in the RTC, incorporating parameter posteriors from FA1. This approach refined estimates of transfer and recovery probabilities, updating the model based on spore recovery data from FA2 and FA3.
The final model was applied to predict the spore bioload introduced into the Flight HRS during launch operations, incorporating uncertainty in the initial spore concentration in the RTC, filter efficiencies and recovery probabilities. Detailed mathematical derivations of the model, including likelihood functions, marginalizations and posterior updates, are provided in Appendix B.
Results
Experimental results
The intent behind selecting three different locations on the MGSE to sample CFC-11 was to characterize the system and inform future designs. For example, depending on the resulting CFU at each location, the Planetary Protection engineer may expect future missions with stringent requirements (e.g., MSR SRL) to swap the 2.0 µm filter with a 0.2 µm filter to reduce the bioburden. In parallel, the approach of sampling different locations also provided a more representative sample. All three filter assemblies were successfully integrated with the HRS MGSE. 1 L of CFC-11 was passed through each filter assembly. CFC-11 was recovered from the downstream side of the filter, suggesting that CFC-11 did in fact flow through the filter; with the filter assembly being tightly sealed, there was no physical way the fluid could have bypassed the filter inside the filter assembly. Moreover, the change in weights from each flow process provides evidence that fluid was introduced to the downstream side of the filters.
Each filter assembly was aseptically disconnected from the HRS MGSE and returned to the Planetary Protection flight support lab for processing (Figure 3 shows the end-to-end process flow). Regarding the 90 mm filter inside the filter assembly, one option was to directly plate the filters on TSA plates and incubate with CFU counting at 24, 48 and 72 hours. However, at the risk of having too numerous to count (TNTC) results, the filters were instead treated like sampling wipes and processed using the NASA Standard Assay and MF, during which four different volume fractions were processed to avoid possible TNTC results. After the liquid from each sample was processed via MF, the 90 mm filters were aseptically retrieved from the glass media bottles, directly plated onto TSA plates and incubated, with CFU counted at 24, 48 and 72 hours, to capture any residual microorganisms on the filters after the filters were submerged in PP rinse solution.
Process flow. The filters from the Filter Assemblies were each placed into bottle containing 200 mL PP rinse solution. The sample bottles were vortexed and sonicated. The 200 mL volumes were split into two equal fractions to process with (80 °C for 15 min) and without heat shocking. The 90 mm filter resided in the bottle that underwent heat shock. Each 100 mL sample, with and without heat shock, was processed via membrane filtration by further fractioning the volumes into 60, 45, 15 and 5 mL fractions. This was to ensure CFU could be enumerated in the event the counts were high. The 45 mm membrane filtration filters were plated and incubated for CFU enumerated. After the liquid from each sample was decanted for membrane filtration, the 90 mm filters left inside the bottles were aseptically retrieved and directly plated and incubated for CFU enumeration of any CFU that had not been recovered in the PP rinse solution.
All assays, including those using the 90 mm filters directly plated, resulted in zero CFU across all CFC-11 sample and control groups, with the exception of positive controls, which demonstrated expected growth. A more detailed breakdown of the individual CFU results can be found in Appendix C. To confirm that the cellulose acetate filters did not inhibit microbial growth, an additional qualitative test was conducted with Bacillus atrophaeus, which showed growth consistent with the positive control, ruling out filter inhibition as a factor for the observed zero CFU.
The recovery efficiency study calculated an observed CFU yield of 41.4, divided by the expected CFU yield of 52.2, resulting in an efficiency of 39.66%. This was adjusted by a factor of 0.5 to account for the 50% pour fraction of the CFC-11 samples, which were split into heat-shocked and non-heat-shocked sets. This efficiency value was incorporated as a critical input in the modeling analysis.
Modeling results
Modeling results were based on inputs summarized in Table 1, with prior distributions for model parameters calibrated using experimental observations. The posterior distributions of key parameters, including spore concentration in the SD (ρ), showed significant shifts, indicating the influence of experimental data. Notably, the distribution of ρ, which initially had a broad range, narrowed to near zero, reflecting the lack of spore growth in the FA1 experiment. Other model parameters exhibited similar prior and posterior distribution trends, suggesting consistency with prior knowledge. However, further controlled experiments on filter efficiency would help validate these findings.
Summary of model inputs
The filter efficiency curves, derived from posterior distributions of the λ parameters, indicate that the MGSE filter achieves 95% efficiency at approximately 2 µm, while the FA filter achieves the same efficiency at around 0.22 µm. Sensitivity analysis revealed that model outcomes were most sensitive to changes in spore diameter and filter efficiency. Figure 4 shows the probability mass function of the predicted number of spores in CFC-11 transferred from MGSE to the flight HRS on the Europa Clipper spacecraft given the observations from experiments in this study. Notably, the model predicts an 80% probability of zero spores being transferred into the HRS during planned launch operations, with a mean spore transfer estimate of 0.29 spores and a 95% confidence interval of (0.24, 0.34).
Probability mass function for the predicted number of spores in CFC-11 transferred from the MGSE to the Europa Clipper flight Heat Reclamation System (HRS), based on experimental observations and model outputs. The MGSE filter demonstrates 95% efficiency at approximately 2 µm, while the FA filter reaches the same efficiency near 0.22 µm. Model sensitivity analysis identified spore diameter and filter efficiency as key drivers of uncertainty. The model predicts an 80% probability of zero spore transfer during nominal launch operations, with a mean estimate of 0.29 spores and a 95% confidence interval of (0.24, 0.34).
Discussion
Three different locations on the MGSE (SD, RTC and FFP) were sampled to quantify bioburden transfer via CFC-11 into the HRS. All samples resulted in 0 CFU, even after direct plating of the 90 mm filters. To verify that CFC-11 exposure did not inhibit microbial growth, the same filters were intentionally spiked with spores, which produced positive growth comparable to the control. These results confirm that the observed bioburden transferred via CFC-11 is negligible under the test conditions.
To date, for all missions, the same CFC-11 supplier was used; however, the batch of CFC-11 was different for each mission. For future investigations, batch-to-batch variations in spore concentration remain a potential concern due to differences in purity standards, storage conditions or statistical variability. The tolerance of bioburden estimates to variations in spore concentration between different batches can be readily assessed by the mathematical model in this study, if necessary. While these results are robust for Europa Clipper, future missions, such as a potential Mars Sample Return mission with stricter planetary protection thresholds, should confirm the applicability of this model and consider additional testing.
A positive control involving spiking CFC-11 with a known concentration of spores is also recommended for future studies. However, this is challenging because (1) flowing “dirty” CFC-11 through the flight hardware contacting MGSE is hardly acceptable and (2) collecting CFC-11 (in a bottle for example) and returning it to the microbiology lab for processing presents a myriad of challenges (e.g., EPA compliance, evaporation, risk of contamination, etc.). The absence of such a positive control is a limitation of this study, and the results should be viewed as a starting point for future experimental refinement.
The mathematical model integrates filtration theory, literature data, vendor specifications on spore sizes and experimental observations from MGSE testing in flight-like configurations. We found that the mean number of spores transferred with 8 L of CFC-11 into the HRS is 0.29, equivalent to 0.04 spores/L. This value is orders of magnitude below the conservative “NASA standard” spore load assumption, demonstrating that the HRS fill process contributes negligible contamination risk.
This study also recommends additional sensitivity analysis to assess driving parameters and assess future work. One recommendation is to perform dedicated experiments to study the filtration efficiency of filters used by the MGSE and filter assemblies. The filter efficiencies from the vendor used in this study can change depending on a wide variety of factors, including flow velocity, Reynolds number and pressure changes (Liu & Lee, Reference Liu and Lee1976; Spurny et al., Reference Spurny, Lodge, Frank and Sheesley1969; Kouropoulos, Reference Kouropoulos2014). While the results of this study do not point to any significant issue with the filter efficiencies elicited from vendors and the literature, dedicated experiments would provide useful validation and increase model credibility.
For purposes of Planetary Protection flight implementation and bioburden accounting, we recommend using a value of 0.04 spores/L of CFC-11 for the Europa Clipper HRS and future missions employing the same MGSE design. This result is particularly encouraging because it (1) reduces spore allocation margins and (2) supports operational efficiency by allowing the use of 2.0 µm filters instead of 0.2 µm filters without compromising contamination control. If significant design or operational changes occur, this recommendation must be revalidated.
Acknowledgments
The authors would like to acknowledge Fei Chen for reviewing and providing input into the final HRS MGSE setup and sample processing protocols and for reviewing the final manuscript. The authors would also like to acknowledge Gayane Kazarians for reviewing and providing input into the final HRS MGSE setup and sample processing protocols. Additionally, the authors would like to acknowledge Moogega Cooper, Wayne Schubert and Emily Klonicki for technical guidance. Finally, the authors would like to acknowledge Laura Newlin for technical guidance and transfer of mathematical equations from LaTex to Word.
Author contributions
KS contributed to experimental design, writing of the initial and final HRS MGSE setup and sample processing protocols, experiment completion, data interpretation and drafting of the overall manuscript. MD developed and implemented the mathematical model, contributed to the experimental design and data interpretation and drafted the mathematical modeling portion of the manuscript. CM contributed to experimental design, writing of the final HRS MGSE setup protocol, experiment completion, data interpretation and drafting of the HRS MGSE portion of the manuscript. CW contributed to experiment completion, data interpretation and review of relevant journal articles. BC contributed to experimental design, experiment completion and data interpretation. AA contributed to initial experimental design and writing of the initial HRS MGSE setup and sample processing protocols. RH contributed to experimental design, experiment completion and data interpretation. All authors contributed to reading and editing the manuscript and approved the final manuscript.
Funding statement
The research was supported by the Europa Clipper Project and the Mars Sample Return Sample Retrieval Lander Project. The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004).
Competing interests
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Appendix A: Technical details of freon sampling set up
Filter assembly 1: CFC-11 in storage drum (SD)
Setup
See Figure 5A for setup. From a chemical perspective, the CFC-11 in the SD is homogenous. In order for the HRS MGSE team to perform fill operations, the SD, which weighs over 90 kgs., is moved around extensively, thereby indirectly mixing the liquid. This is consistent with flight fill operations, thus provides a more representative sample.
Filter Assembly 1 Schematic. This schematic shows the equipment connections for the first filter assembly that is set up to take in CFC-11 from the Storage Drum (SD) (A). This schematic also summarizes the starting valve configurations for performing vacuum (B), flow-through (C) and recovery via the Refrigerant Recovery Cylinder (RRC) (D). Valves are denoted as V1, V2, etc. MGSE Swagelok filters are denoted as F1, F2, etc. Pressure Gauges are denoted as PG.
The SD was verified to have a gas ullage charge of approximately 15 psig (∼103 kPa) of certified Grade B (or better) nitrogen gas filtered through a 0.5 μm filter (PN SS-4FWS-05, Swagelok, Solon, OH, USA). The dip tube and associated outlet valves of the SD were verified to be fully primed with CFC-11 up through valve V1 and 2 μm filter F1 (PN SS-4FWS-2, Swagelok, Solon, OH, USA) to valve V2 (PN SS-DSVCR4, Swagelok, Solon, OH, USA).
On a Class 100 (ISO 5) clean bench, using sterile gloves, a clean VCR diaphragm valve (PN 6LW-DPFR4-P1, Swagelok, Solon, OH, USA) was installed to the ¼” (6.35 mm) male VCR fitting, previously installed onto the filter holder, using a sterilized non-plated VCR side-load retainer gasket (PN SS-4-VCR-2-ZC-VS, Swagelok, Solon, OH, USA), hereafter referred to as a VCR gasket. This valve was kept in the closed position. A VCR tee fitting (PN SS-4-VCR-T, Swagelok, Solon, OH, USA) was also installed at the inlet to the valve with a new VCR gasket. Finally, a sterilized VCR gasket was installed on the outlet VCR fitting of the filter assembly and capped with a sterilized VCR cap (PN SS-4-VCR-CP, Swagelok, Solon, OH) for limiting filter exposure prior to subsequent connections outside of the clean bench. The valves and flex hoses were not sterilized because there is no existing plan to autoclave such components prior to a flight system fill. The only components that were autoclaved were the filter assemblies and associated connection hardware (NPT to VCR fittings, gaskets and caps), since these would not be present in a flight system fill and therefore should not contribute to the measured bioburden of the system for a representative assessment of the mission CFC-11 spore count.
All HRS MGSE components were cleaned to at least Particulate Cleanliness Level (PCL) 100 A (International Organization for Standardization, 2003). A stainless-steel bellows flex hose was connected between valve V2 and the VCR tee at the inlet to valve V4 using two new VCR gaskets. Another stainless-steel bellows flex hose was connected from the VCR tee at the inlet to valve V4 to one of the inlet ports at V5 on the empty RRC using two new VCR gaskets. The outlet cap was carefully removed from the filter assembly and a stainless-steel bellows flex hose was installed. The other end of this flex hose was installed to the VCR inlet tee on the RRC adjacent to valve V6 and valve V7. A TriScroll 600 dry vacuum pump (PN PTS06001UNIV, Agilent, Santa Clara, CA, USA) was connected to valve V7 to prepare to pull vacuum on the system for charging (filling/pressurizing) with CFC-11.
Pulling vacuum on the system
See Figure 5B for starting valve configuration. Please note that V1 remained open for all steps and only served as a service valve to isolate the filter, F1, when it was necessary to recover the fluid between V1 and V2 to replace the filter F1. In this case, liquid CFC-11 was already primed up to the closed valve, V2. The vacuum pump was turned on to evacuate the flex lines interfacing to the system.
Valve V7 was slowly opened to allow the pump to pull vacuum on the wetted volume of the system up to valve V2. Once the vacuum level had plateaued below 100 mTorr (13.33 kPa), valve V7 was closed to isolate the vacuum pump and monitor the pressure of the system for a period of 5 minutes to ensure that there were no leaks in the system before proceeding or introducing CFC-11. When no pressure decay was observed during the 5 minutes of observation, valve V7 and V4 were opened to allow the vacuum pump to continue pulling on the system volume for a period of at least 15 minutes to extract residual moisture from the system and prepare for charging with CFC-11. A vacuum level of approximately 15 mTorr (2 kPa) was achieved for a period of 20 minutes for this step.
After the requisite evacuation period, valve V7 was closed to isolate the vacuum pump. The evacuation phase was complete, and the vacuum pump was turned off and removed from the system. As a best practice for maintaining system cleanliness, a VCR cap was installed on the outlet port of valve V7 after the vacuum flex hose was disconnected.
CFC-11 flow-through
See Figure 5C for starting valve configuration. The RRC was placed on a scale (OHAUS Defender 5000), to monitor the flow of refrigerant from the CFC-11 drum. RRC starting mass: 10.8 kgs.
Valve V2 was slowly opened to allow CFC-11 to fill the line from valve V2 up to valve V4 and V5. RRC mass after upstream line fill: 23.86 lbs.
To obtain a representative sample of the fluid that will fill the spacecraft, and to be consistent with pre-fill point-of-use sampling that will occur prior to introduction of CFC-11 into the spacecraft, a mass of 2.0 lbs. (610 mL) was flushed before introducing fluid through the filter assembly. This flush was accomplished by keeping valve V4 closed but opening valve V5 to allow the equivalent sample volume to be passed into the RRC. After this sample volume was passed into the RRC, valve V5 was closed. RRC mass post-flush: 25.86 lbs.
The target sample mass to flow through the filter assembly was 3.5 lbs., to yield a sample volume of 1.07 L at room temperature (22 °C). Therefore, the target mass for the RRC was 29.36 lbs. To start, valve V4 was slowly opened to allow CFC-11 to fill the filter assembly and downstream line volumes to valve V6. Then, valve V6 was slowly opened to allow the CFC-11 to continue flowing through the filter assembly to the RRC. The target mass was achieved, and valve V4 was closed. RRC mass after flow-through: 29.38 lbs.
CFC-11 recovery
See Figure 5D for starting valve configuration. To comply with EPA 608 regulations (EPA, 2020), all CFC-11 must be recovered to a minimum level of 25 mmHg (25 Torr; 3.33 kPa) prior to opening the system. The refrigerant recovery system (RRC and recovery machine) was connected to valve V7 and turned on while valve V7 was still closed. Once the recovery system was warmed up and ready, valve V7 was opened to start recovering the CFC-11 from the system. It is important to note that valve V4 stayed closed for this recovery process to prevent additional CFC-11 volume from being pulled through the filter assembly and skewing intended sample volume. Recovery continued until the system pressure was below 25 Torr (3.33 kPa) with the recovery machine isolated from the system.
Using sterile gloves, the connection between valve V4 and the filter assembly was opened, and a sterilized VCR cap was immediately installed. The same was done for the bottom fitting of the filter assembly immediately after removing the flex hose.
Preparation of refrigerant transfer cylinder (RTC) and filling with CFC-11
Setup
See Figure 6A for setup. The empty RTC with a tank heater installed was placed on a scale and the empty mass recorded at 27.68 lbs. to get the starting mass for the RTC. Next, the pressure ullage on the CFC-11 drum was confirmed to be in the range of 10-15 psig. Valve V1 was verified open and CFC-11 drum outlet line was verified to be primed up to outlet valve V2, by dispensing ∼50 mL of fluid sample into a glass jar, to help clear any foreign object debris that might have been present in assembly of the field joints or residual particles in the MGSE lines. This jar was appropriately labeled and stored for recovery of refrigerant. Using a stainless-steel bellows flex hose, fill valve V9 of RTC was connected to outlet valve V2 on CFC-11 SD.
Preparing Refrigerant Transfer Cylinder (RTC): This schematic shows the equipment connections for CFC-11 charging of RTC (A) and the respective starting valve configuration (B), in preparation for Filter Assembly 2 and 3 operations. Valves are denoted as V1, V2, etc. MGSE Swagelok filters are denoted as F1, F2, etc. Pressure Gauges are denoted as PG.
Evacuation; RTC charging; CFC-11 recovery
See Figure 6B for starting valve configuration. A stainless-steel bellows flex hose was connected from valve V8 to a dry scroll vacuum pump (TriScroll 600, Agilent, Santa Clara, CA, USA); it’s important to pull vacuum at valve V8 to avoid pulling gas backwards through the outlet filter, F2, of the RTC. Next, the vacuum pump was turned on. Valve V8 was slowly opened to allow the pump to pull vacuum on the RTC and flex hose up to valve V2. Once the vacuum level had plateaued below 100 mTorr (13.33 kPa), valve V8 was closed to isolate the vacuum pump and monitor the pressure of the system for a period of 5 minutes as a vacuum decay leak test. This is to ensure that there are no leaks in the system prior to proceeding or introducing CFC-11. After no pressure decay was observed during the 5 minutes of observation, valve V8 was opened to allow the vacuum pump to continue pulling on the system volume for a period of at least 15 minutes to extract residual moisture from the system and prepare for charging with CFC-11. Vacuum Achieved: 15 mTorr (2 kPa). Duration: 60 minutes. After the evacuation period, valve V8 was closed to isolate the vacuum pump. At this point the evacuation phase is over, and the vacuum pump can be turned off and removed from the system. As a best practice for maintaining system cleanliness, a VCR cap was installed on the outlet port of valve V8 immediately after the vacuum flex hose was disconnected. To begin charging the RTC, valve V9 was closed and valve V2 opened, filling connecting flex hose with CFC-11. The RTC mass was tared to monitor the fill volume of the RTC by itself. Valve V9 was slowly opened and 22.68±0.45 kg of CFC-11 was added. Valve V9 was closed. The final charging weight was 35.14 kg. (empty mass + fill mass). Finally, to recover the CFC-11, the RRC was connected to valve V10 using a stainless-steel bellows flex hose. The RRC and flex hose connecting the RRC to valve V10 was evacuated using a vacuum pump until a pressure of less than 100 mTorr (13.33 kPa) was achieved. The RRC was isolated from the vacuum pump. Valve V2 was closed, then immediately following this, valve V10 was slowly opened, and CFC-11 was recovered in the charging line to the EPA-required level of 25 Torr (3.33 kPa). The flex hose was disconnected from the system, VCR plugs installed and placed in a bag to maintained flex hose cleanliness. VCR caps were installed on all RTC and SD connections.
Filter assembly 2 and 3: CFC-11 in refrigerant transfer cylinder (RTC) and flight fill panel (FFP)
Setup
See Figure 7A for setup. On a Class 100 (ISO 5) clean bench, using sterile gloves, a sterilized VCR cap (PN SS-4-VCR-CP, Swagelok, Solon, OH, USA) was installed using a sterilized non-plated VCR side-load retaining stainless-steel gasket (PN SS-4-VCR-2-ZC-VS, Swagelok, Solon, OH, USA) for limiting filter exposure prior to subsequent connections outside of the clean bench. This was performed for all inlets and outlets of both filter assembly 2 and 3.
Filter Assembly 2 and 3 Schematic. This schematic shows the equipment connections for the second and third filter assemblies that are set up to take in CFC-11 from the Refrigerant Transfer Cylinder (RTC) and Flight Fill Panel (FFP), respectively (A). In the FFP, the only line that sees CFC-11 is the liquid line. Other lines are greyed out as they are not used in the CFC-11 charging process. This schematic also summarizes the starting valve configurations for performing vacuum (B), flow-through (C) and recovery via the Refrigerant Recovery Cylinder (RRC) (D). Valves are denoted as V1, V2, etc. MGSE Swagelok filters are denoted as F1, F2, etc. Pressure Gauges are denoted as PG.
The valves and flex hoses were not sterilized because there is not a plan to autoclave such components prior to a flight system fill. The only components that were autoclaved were the filter assemblies and associated connection hardware (NPT to VCR fittings, gaskets and caps) since these would not be present in a flight system fill and therefore should not contribute to the measured bioburden of the system for a representative assessment of the mission CFC-11 spore count. All components used in this assembly were cleaned to at least PCL 100 A (ISO14952-2). All VCR connections were made using non-plated VCR side-load retaining stainless-steel gaskets (PN SS-4-VCR-2-ZC-VS, Swagelok, Solon, OH, USA).
A VCR tee fitting (PN SS-4-VCR-T, Swagelok, Solon, OH, USA) was connected to the inlet of valve V11, outlet of valve V12 and outlet of valve V16 (PN SS-DSV51, Swagelok, Solon, OH, USA). The inlet of VCR diaphragm valves (PN 6LW-DPFR4-P1, Swagelok, Solon, OH, USA) was connected to the previously installed tees for valve V13 and valve V15. A VCR 90° Elbow fitting (PN SS-4-VCR-9, Swagelok, Solon, OH, USA) was connected to the outlet of valve V14 (PN SS-DSV51, Swagelok, Solon, OH, USA). The VCR 90° Elbow fitting from valve V14 was connected to the VCR Tee fitting at valve V16 using a stainless-steel bellows flex hose. A stainless-steel bellows flex hose was connected from the VCR tee at valve V16 to valve V6 on the RRC.
A stainless-steel bellows flex hose was connected from valve V8 to the VCR tee at valves V11/V13. A stainless-steel bellows flex hose was connected from valves V12/V15 to valve V5. The inlet cap from filter assembly 2 was removed and connected to valve V13. The inlet cap from filter assembly 3 was removed and connected to valve V15. The outlet cap from filter assembly 2 was removed and connected to valve V14. The outlet cap from filter assembly 3 was removed and connected to valve V16. The system was now fully configured and ready for evacuation.
Pulling vacuum on the system
See Figure 7B for starting valve configuration. A dry scroll vacuum pump (TriScroll 600, Agilent, Santa Clara, CA, USA) was connected to valve V7 to prepare to pull vacuum on the system for charging with CFC-11. The vacuum pump was turned on and the flex lines interfacing to the system up to valve V7 were evacuated. Valve V7 was slowly opened to allow the pump to pull vacuum on the wetted volume of the system up to valve V8 and up to the isolation valves for each filter assembly. After system vacuum level had stabilized, valves V14 and V16 were slowly opened to remove air from the filter assemblies. After vacuum levels stabilized again, valves V13 and V15 were opened. This valving order ensures that the volume of gas pulled through the filter assembly filter is minimized and that the system is pulling in the intended flow direction.
Once the vacuum level has plateaued below 100 mTorr (13.33 kPa), valve V7 was closed to isolate the vacuum pump and monitor the pressure of the system for a period of 5 minutes as a vacuum decay leak test. This was to ensure that there were no leaks in the system prior to proceeding or introducing CFC-11. When no pressure decay was observed during the 5 minutes of observation, valve V7 was opened to allow the vacuum pump to continue pulling on the system volume for a period of at least 15 minutes to extract residual moisture from the system and prepare for charging with CFC-11. Vacuum Achieved: 15 mTorr (2 kPa). Duration: 45 minutes.
After the evacuation period, valve V7 was closed to isolate the vacuum pump. The evacuation phase was complete, and the vacuum pump was turned off and removed from the system. As a best practice for maintaining system cleanliness, a VCR cap was installed on the outlet port of valve V7 after the vacuum flex hose was disconnected.
CFC-11 flow-through
See Figure 7C for starting valve configuration.
Starting mass of the RTC: 77.48 lbs. Valve V8 was slowly opened to fill the upstream supply line to the filter assemblies. New RTC mass: 76.50 lbs.
To obtain a representative sample of the fluid that will fill the spacecraft, consistent with pre-fill point-of-use sampling that will occur prior to introduction of CFC-11 into the spacecraft, a mass of 2.0 lbs. (610 mL) was flushed prior to introducing fluid through the filter. This flush is accomplished by keeping valves V13 and V15 closed but valve V5 open to allow the equivalent sample volume to be passed into the RRC. After this sample volume was passed into the RRC, valve V5 was closed. RTC mass post flush: 74.38 lbs.
The purpose of filter assembly 2 was to determine the bioburden of CFC-11 flowing through the RTC. The target sample mass to flow through the filter was 3.5 lbs, to yield a sample volume of 1.07 L at room temperature (22 °C). Therefore, the target mass for the RTC was 70.88 lbs. First, valves V13 and V14 were slowly opened to allow CFC-11 to fill the filter assembly filter and downstream line volumes to valve V6. Then, valve V6 was slowly opened to allow the CFC-11 to continue flowing through the filter to the RRC. Valve V13 was closed after the target mass was achieved. RTC mass after filter assembly 2 flow-through: 70.74 lbs.
The flow through of filter assembly 3 was to sample the CFC-11 from the FFP. The target sample mass to flow through the filter was 3.5 lbs., to yield a sample volume of 1.07 L at room temperature (22 °C). Therefore, the target mass for the RTC was 67.24 lbs. Valve V15 was slowly opened, then valve V16 opened to allow CFC-11 to start flowing through the filter to the RRC. Valve V15 was closed after the target mass was achieved. RTC mass after filter assembly 3 flow-through: 67.23 lbs.
CFC-11 recovery
See Figure 7D for starting valve configuration. To comply with EPA 608 regulations (EPA, 2020), all CFC-11 must be recovered to a minimum level of 25 mmHg (25 Torr; 3.33 kPa) prior to opening the system. The refrigerant recovery system (RRC and recovery machine) was connected to valve V7 and turned on while valve V7 was still closed.
Once the recovery system was warmed up and ready, valve V8 was closed and valve V5 was immediately opened to access the CFC-11 on the upstream side of the filter assemblies from the RRC. Then, valve V7 was slowly opened to start recovering the CFC-11 from the system. It is important to note that valve V13 and valve V15 stay closed for this recovery process to prevent additional CFC-11 volume from being pulled through the filter assembly and skewing the intended sample volumes. Recovery continued until the system pressure was below 25 Torr (3.33 kPa) with the recovery machine isolated from the system. Using sterile gloves, the connections between valves V13, V14, V15, V16 and the filter assemblies were opened one at a time, with the immediate installation of a sterilized VCR cap at each location.
Detailed construction and sterilization procedures for filter assemblies
Three filter holders (PN YY3009000, Sigma Aldrich, St. Louis, MO, USA) were used to filter the CFC-11, each from a different location. The holder uses a 90 mm filter (Figure 8). Specifically, a 0.2 µm cellulose acetate membrane filter (PN CA029025, Sterlitech, Auburn, WA, USA) was used. The filter holder was outfitted with fittings to be used with the Europa Clipper HRS MGSE system; each holder had two (top and bottom) ¼” (6.35 mm) Male Vacuum Coupling Radiation (VCR) to ¼” (6.35 mm) Male NPT fittings (PN SS-4-VCR-1-4, Swagelok, Solon, OH, USA) installed using Polytetrafluoroethylene (PTFE) tape. These VCR fittings allow stainless-steel flex hoses to be connected between the sampling source, filter and the Refrigerant Recovery Cylinder (RRC). VCR fittings were selected due to their leak-tight sealing, reliable mate/de-mate performance for MGSE connections and cleanliness standards required for HRS applications at JPL. In addition to the stainless-steel flex hoses, custom-welded VCR tee fittings and three Swagelok diaphragm valves were used to control flow through the filter versus bypass during pre-collection flushing operations. A valve was installed at the inlet and outlet of the filter holder to isolate the holder from the flush, and an additional valve was placed in parallel with the filter to allow bypass. The installed relief valve on the filter holder functioned only as a plug. The filter holders and installed fittings (henceforth referred to as the “filter assembly”) were autoclaved at 121 °C, 30 psia, to sterilize all internal surfaces including the 90 mm filter. VCR side-load retainer gaskets (PN SS-4-VCR-2-ZC-VS, Swagelok, Solon, OH, USA) and VCR caps (PN SS-4-VCR-CP, Swagelok, Solon, OH, USA) were autoclaved separately.
Filter Assembly Elements. Adapted from the user manual, this figure shows elements of the Millipore 90 mm filter holder. Grey boxes indicate specifics for this study. A 0.2 µm cellulose acetate membrane filter was used. The filter holder was outfitted with fittings to be used with the Europa Clipper HRS MGSE system, where each filter holder had two (top and bottom) ¼” (6.35 mm) Male Vacuum Coupling Radiation (VCR) to ¼” (6.35 mm) Male NPT fittings installed using Polytetrafluoroethylene (PTFE) tape. These VCR fittings allow full stainless-steel flex hoses to be connected between the sampling source, filter holder and the Refrigerant Recovery Cylinder (RRC). The installed relief valve on the filter holder functioned as a plug only. Hex keys used for assembling parts together.
Appendix B: Probalistic model
Appendix A provides detailed information regarding the experimental design, including materials, sterilization procedures and assembly configurations used for CFC-11 sample collection during Europa Clipper HRS MGSE testing. In this Appendix, we provide a detailed presentation of the probabilistic model complementing this experimental design, developed to assess the likelihood of forward contamination associated with the sampling system. The model integrates measured system parameters, observed contamination controls and failure mode assumptions to estimate the probability of contaminant transfer to Europa Clipper critical surfaces. All inputs, assumptions and calculation methods are documented herein to support transparency and reproducibility for future mission applications. The appendix also provides the prior distributions for all parameters used in the model developed in this study. All parameters are assumed to be independent of one another prior to seeing the data; hence, the product of the prior distributions is equal to the joint prior distribution of all parameters.
The mathematical modelFootnote 1 developed for this study aims to assess the number of spores transferred from the Mechanical Ground Support Equipment (MGSE) into the Heat Reclamation System (HRS) used on the Europa Clipper spacecraft during charging with CFC-11. This same system is planned to be used on the Sample Retrieval Lander for the Mars Sample Return Mission. It does so by defining a model, within a probabilistic framework, of the processes involved with generating the data observed from the CFC-11 samples obtained from the experiments in this study. Rather than assuming fixed experimental parameters such as the starting spore population, filter efficiencies and spore recovery efficiency, the model takes these parameters as probability distributions based on data collected from control experiments or publicly available literatureFootnote 2 . These distributions are then informed by observations made in experiment using Bayes’ Theorem. This reveals parameter values that make the observed data more or less likely by way of a joint probability distribution of the model parametersFootnote 3 , accounting for all uncertainties in the model. The model is then used to predict a quantity of interest; in this case, the number of spores transferred from the MGSE into the HRS during charging with CFC-11. Note that this model only evaluates the abundance of NASA-defined spores in heat-shocked samples from experiments performed for this study. Non-spore forming or vegetative microorganism abundances that may be present in non-heat-shocked samples are not evaluated by this model.
Let
${\pi _{y|x}}$
denote the probability that an individual particle (e.g., a spore) is transferred from device
$x$
to or through device
$y$
. Figure 9 summarizes how the model represents the experimental design that generates the data observed. As discussed in the subsequent subsections, the modeling starts by using FA1 experiments to estimate the spore concentration,
$\rho $
, in the CFC-11 SD, which, when filled contains
${M_1}$
particles, and the transfer probability from the SD, through the first MGSE filter, and into the RTC,
${\pi _{{\rm{RTC}}|{\rm{SD}}}}$
. This allows us to estimate the bioload in the RTC,
${\tilde n_{{\rm{RTC}}}}$
, after charging, which is the source of CFC-11 used to fill the HRS. Next, FA2 and FA3 experiments are used to understand the transfer probability from the RTC through two further MGSE filters, to the HRS, denoted by
${\pi _{{\rm{HRS}}|{\rm{RTC}}}}$
. In order to estimate these probabilities appropriately from the recovered number of spores,
${r_1}$
,
${r_2}$
and
${r_3}$
, a recovery efficiency study was performed (described in the Section titled Recovery efficiency) to understand the extraction and recovery probability of spores,
$\phi $
, collected from the filters of each filter assembly. Not shown in this figure is how filtration was modeled; this will be elaborated on in the subsection below. Recovery of CFC-11 is not included in the modeling process as it is a negligible contributor to the transfer of spores in this study given leak tests performed and careful valve controls employed during CFC-11 recovery.
Summary of the modeling process and key terms. FA1 experiments are used to estimate the spore concentration,
${\rm{\rho }}$
, of the CFC-11 Storage Drum (SD), which, when filled contains
${{\rm{M}}_1}$
particles, and the transfer probability from the SD, through the first MGSE filter and into the RTC,
${\pi _{{\rm{RTC}}|{\rm{SD}}}}$
. This allows estimation of the bioload in the RTC,
${{\rm{\tilde n}}_{{\rm{RTC}}}}$
after charging, which is the source of CFC-11 used in the HRS. Next, FA2 and FA3 experiments are used to understand the transfer probability from the RTC, through two further MGSE filters, to the Heat Reclamation System (HRS), denoted by
${\pi _{{\rm{HRS}}|{\rm{RTC}}}}$
. In order to estimate these probabilities appropriately from the recovered number of spores,
${r_1}$
,
${r_2}$
and
${r_3}$
, controls were performed to understand the extraction and recovery probability of spores,
$\phi $
, collected from the filters of each filter assembly.
Model assumptions, characterization of filter efficiency and the spore size distribution
The model developed for this study makes two overarching assumptions having to do with (1) the interaction of spores during transfer of CFC-11 through MGSE and spore recovery processes, and (2) the uniformity of the conditions during this transfer and recovery. Assumption (1) is that the transfer of one spore in the CFC-11 fluid and its recovery does not affect the probability of another spore’s transfer or recovery; that is, one spore’s transfer and recovery is treated as independent of another spore. While this needs to be validated, it is reasonable to first-order given the dry, nutrient-poor environment provided by CFC-11 that likely inhibits clumping and other microorganism interactions. Moreover, clumping of spores with one another or with inert particulates in CFC-11 would result in larger particles that are more readily filtered; thus, assuming no clumping occurs is intuitively conservative when modeling the number of spores transferred to the HRS. For this analysis, an individual spore size of approximately 1 µm was assumed. Sensitivity analysis performed with the model confirms this intuition.
Regarding assumption (2), similar media and processes are applied in each experiment and, as appropriate, are performed as they would be during launch operations. The aspects of the NSA process pertaining to spore recovery are applied consistently throughout the experiments performed for this study. Sterilization of media used in experiments, validated by controls, avoids recontamination issues. The MGSE and filter assembly valves and hoses were checked for leaks by pulling vacuum and observing pressure, then flushed to ensure consistency of CFC-11 samples and that these samples are representative of the CFC-11 used for flight. Non-biocidal media, validated by controls, was used in order to avoid inadvertent biocidal effects that could artificially lower the observed spores in experiment. Given the uniformity of these processes and precautions taken to avoid introducing disturbances into the process being tested, the model treats each individual spore as having the same probability of transfer and recovery. That said, this study was unable to quantify or control for species diversity. Further research is needed in order to quantify this diversity. For this study, all spores are assumed to be of the size of B. atrophaeus, one of the most common indicator organisms used by NASA Planetary Protection. Similar to the earlier discussion about clumping of microorganisms, if spores in CFC-11 were found to typically be smaller than B. atrophaeus, the model would show more spores being transferred to the HRS on average. Finally, this model does not assess the survival probability of a spore in CFC-11. Even though some bactericidal effects have been observed for some bacteria (e.g., Auken et al, Reference Auken, Healy and Kaufmann1975; Gunaratne & Spencer, Reference Gunaratne and Spencer1974), strong evidence could not be found in the literature that documented significant biocidal effects of CFC-11 on cleanroom microorganisms.
Characterization of Filter Efficiency. Assume that a homogenous fluid flow containing particles of diameter δ moves through a filter with a given pore size. Fundamental filtration theory (Liu & Lee, Reference Liu and Lee1976; Lee & Liu, Reference Lee and Liu1980; Spurny et al., Reference Spurny, Lodge, Frank and Sheesley1969; Purchas & Sutherland, Reference Purchas and Sutherland2002; Ripperger et al., Reference Ripperger, G¨osele and Alt2012) describes two modes of filtration behavior: (I) diffusion and electrostatics (primarily diffusion), that tend to be extremely efficient at filtering very small particles (<0.1 µm) but rapidly diminish in efficiency as the particle size moves into larger regimes; and (II) interception and impaction, which become the dominant filtration mechanisms for larger particles (>1 µm). Let
${\lambda _{\rm{I}}}$
denote the filtration efficiency rate due to diffusive forces, and let
${\lambda _{{\rm{II}}}}$
denote the filtration efficiency rate due to interception and impaction, both with respect to particle diameter.
The literature expresses an exponential relationship between efficiency rate and the filter’s efficiency. This study interprets the filter efficiency as a probability that a particle of a certain size,
$\delta $
, is filtered. Hence, the probability that an individual particle is filtered by diffusive or electrostatic forces is taken to be
${e^{ - {\lambda _{\rm{I}}}\delta }}$
. Similarly, the probability that an individual particle is filtered by way of interception or impaction is
$1 - {e^{ - {\lambda _{{\rm{II}}}}\delta }}$
. Figure 10 illustrates the behavior when these two types of forces are brought together to model the filter’s efficiency. Assuming these forces do not interact, the event that an individual particle is filtered by way of type (I) forces is independent of the event it is filtered by way of type (II) forces. Therefore, the probability that an individual particle is filtered by a single MGSE filter is equal to
$$\begin{align}{p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right) &= \;{e^{ - {\lambda _{{\rm{I}},{\rm{MGSE}}}}\delta }}\; + \;\left( {1 - {e^{{\lambda _{{\rm{II}},{\rm{MGSE}}}}\delta }}} \right)\; - \;{e^{ - {\lambda _{{\rm{I}},{\rm{MGSE}}}}\delta }}\; \times \;\left( {1\; - \;{e^{ - {\lambda _{{\rm{II}},{\rm{MGSE}}}}\delta }}} \right) \\&= 1 - \;{e^{ - {\lambda _{{\rm{II}},{\rm{MGSE}}}}\delta }} + \;{e^{ - \left( {{\lambda _{{\rm{I}},{\rm{MGSE}}}} + {\lambda _{{\rm{II}},{\rm{MGSE}}}}} \right)\delta }}\end{align}$$
Filter efficiency is a result of diffusive and electrostatic forces as well as impaction and interception of particles. Diffusive and electrostatic forces taper off for larger diameter particles at a rate of
${\lambda _{\rm{I}}}$
, while impaction and interception of particles become more dominate at a rate of
${\lambda _{{\rm{II}}}}$
. The sum of these forces produces the total efficiency curve (solid curve). Appropriate ranges for the
$\lambda $
parameters are estimated by the 95% efficiency specification from the vendor together with the minimum penetrating particle size (MPPS).
Similarly, the probability that an individual particle is filtered by a single filter on a filter assembly is equal to
$${p_{{\rm{FA}}}}\left( {U\;{\rm{|}}\;\delta } \right) = 1 - \;{e^{ - {\lambda _{{\rm{II}},{\rm{FA}}}}\delta }} + \;{e^{ - \left( {{\lambda _{{\rm{I}},{\rm{FA}}}} + \;{\lambda _{{\rm{II}},{\rm{FA}}}}} \right)\delta }}$$
In these equations, the type of filter has been added to the subscript on the efficiency rates. MGSE filters are the MGSE Swagelok filters having a nominal pore size of 2 µm, whereas FA filters are the Sterlitech 90 mm filters having a nominal pore size of 0.22 µm. Initial ranges on
${\lambda _{{\rm{I}},{\rm{MGSE}}}}$
,
${\lambda _{{\rm{II}},{\rm{MGSE}}}}$
,
${\lambda _{{\rm{I}},{\rm{FA}}}}$
and
${\lambda _{{\rm{II}},{\rm{FA}}}}$
are obtained from vendor specifications of the filters’ efficiency at their nominal pore sizes (Swagelok catalog, 2022; Sterlitech catalog, 2016, respectively) and filtration studies available in the literature (Lee & Liu, Reference Lee and Liu1980) to estimate the most penetrating particle size (MPPS). Since the flow characteristics (e.g., velocity, pressure) of this study are within filter specifications, this study has not undertaken controlled experiments of its own to test the efficiency of filters used in the experiments. In what follows, efficiency rates for each filter type will be written as
${\lambda _{{\rm{MGSE}}}}\; = \;\left( {{\lambda _{{\rm{I}},{\rm{MGSE}}}},{\lambda _{{\rm{II}},{\rm{MGSE}}}}} \right)$
and
${\lambda _{{\rm{FA}}}}\; = \;\left( {{\lambda _{{\rm{I}},{\rm{FA}}}},{\lambda _{{\rm{II}},{\rm{FA}}}}} \right)$
. Prior distributions associated with
${\lambda _{{\rm{MGSE}}}}$
and
${\lambda _{{\rm{FA}}}}$
used in the statistical analysis can be found in sections of this appendix titled Prior distributions.
The spore size distribution. The particles of interest to be removed from the fluid are spores. This study uses the results from Carrera (2007) for B. atrophaeus to assign a normal probability density function to the spore diameter,
$\delta $
,
$$p\left( \delta \right) = \;{1 \over {{\sigma _\delta }\sqrt {2\pi } }}\;{e^{ - {1 \over 2}{{\left( {{{\delta - \;{\mu _\delta }} \over {{\sigma _\delta }}}} \right)}^2}}}$$
and pictured in Figure 11. Values for
${\mu _\delta }$
and
${\sigma _\delta }$
are summarized in Table 1. It is feasible that spores could clump together or attach to other particulates in the CFC-11 fluid, thereby leading to spore-hosting particles larger in size than this distribution would likely allow for. While the model can be refined to consider these other types of particles, sensitivity analysis showed that the model allows more spores to transfer through MGSE as the overall particle size becomes smaller (as expected), resulting in higher spore counts transferring through MGSE to the HRS. This conservatism was accepted by the model rather than adding further model complexity for the other spore-particle configurations. Therefore, this study assumes all particles of interest to be removed from the fluid are particles consisting of a single spore only, based on the distribution given by Equation (3).
Spore diameter probability density function,
$p\left( \delta \right)$
, used for this study, based on B. atrophaeus data from Carrera et al. (Reference Carrera, Zandomeni, Fitzgibbon and Sagripanti2007).
In what follows, Equations (1), (2) and (3) will serve as the basic building blocks to construct probabilities that a spore is transferred through various filter configurations used throughout the experiments performed for this study and those expected during launch operations to fill the flight HRS. Note that this implicitly assumes, when the filter efficiencies and particle size are known, that a particle that penetrates one filter does not provide any additional information to calculate the probability that this same particle penetrates a subsequent filter used in this study. More concisely, a particle penetrating a filter is independent of whether or not it penetrated any other filters when filter efficiencies and the particle size are known.
Filter assembly 1: estimating the CFC-11 spore concentration in the storage drum (SD)
Suppose an initial volume of
${V_1}$
is contained in the SD and is composed of
${M_1}$
particles. For this study, it is assumed that the volume is dominated by CFC-11 particles due to purity regulations followed by the vendor from whom the CFC-11 is procured. Due to the lack of information available in the literature or from the CFC-11 vendor describing the spore concentration,
$\rho $
, in CFC-11, or, mathematically speaking, the probability that an individual particle in the SD is a spore, a Jeffreys prior distribution (see the first section below titled Prior distribution) is initially placed on
$\rho $
in order to allow the data to have the most influence on this parameter.
Following the experiment described in Appendix A, a volume
${v_1}$
is transferred from the SD, through MGSE on the RTC, then through the FA1 filter. A total of
${r_1}$
spores are then recovered from FA1 using the MF protocol. Let the probability that an individual spore is transferred from the SD to FA1 be denoted by
${\pi _{{\rm{FA}}1|{\rm{SD}}}}$
. This probability can be calculated by considering a spore of a given diameter
$\delta $
and the event it penetrates the MGSE filter on the SD but is filtered by the FA1 filter. Using Equations (1) and (2), the probability of this event is
$\left[ {1 - \;{p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right)} \right]\; \times \;{p_{{\rm{FA}}}}\left( {U\;{\rm{|}}\;\delta } \right)$
. Integrating over all possible spore diameters, the probability that an individual spore is transferred from the SD to FA1 is
$${\pi _{{\rm{FA}}1|{\rm{SD}}}} = \;\mathop \int \nolimits_0^\infty \left[ {1 - \;{p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right)} \right]\;{p_{{\rm{FA}}}}\left( {U\;{\rm{|}}\;\delta } \right)\;p\left( \delta \right)\;d\delta $$
Let
$\phi $
denote the probability that an individual spore is recovered after being transferred to the FA1 filter. Control experiments assessing the efficiency of the spore recovery method used in this study were performed and informed this probability (see the section titled Recovery efficiency and Appendix C). The total probability that an individual particle in the SD is a spore and is recovered by way of the FA1 experiment is
$${\theta _{{\rm{FA}}1}}\left( {{v_1},\;{V_1}} \right) = \;\rho \; \times \;{{{v_1}} \over {{V_1}}}\; \times \;{\pi _{{\rm{FA}}1|{\rm{SD}}}}\; \times \;\phi $$
The probability that
${r_1}$
spores are recovered in the FA1 experiment is therefore
$$p\left( {{r_1}{\rm{|}}{\theta _{{\rm{FA}}1}}\left( {{v_1},\;{V_1}} \right)} \right) = \;\left( {\matrix{ {{M_1}} \cr {{r_1}} \cr } } \right)\;{\left[ {{\theta _{{\rm{FA}}1}}\left( {{v_1},\;{V_1}} \right)} \right]^{{r_1}}}\;{\left[ {1 - \;{\theta _{{\rm{FA}}1}}\left( {{v_1},\;{V_1}} \right)} \right]^{{M_1} - \;{r_1}}}$$
where
${M_1} = \left[ {{V_1} \times {N_{\rm{A}}} \times {\mu ^{ - 1}} \times \kappa \times 1000} \right]$
. Here
$[ \cdot ]$
is the nearest integer function,
${N_{\rm{A}}}$
is Avogadro’s Number (≈ 6.022 × 1023 molecules mol−1), μ is the molar mass of CFC-11 (≈ 137.36 g · mol−1),
$\kappa $
is the density of CFC-11 (≈ 1.494 g · cm−3), and the factor of 1000 converts from cubic cm to liters.
Writing Equation (6) in terms of the underlying parameters of the function
$\theta $
,
$p\left( {{r_1}\;{\rm{|}}\;\rho, \;{\lambda _{{\rm{MGSE}}}},\;{\lambda _{{\rm{FA}}}},\;\phi } \right) = \;p\left( {{r_1}\;{\rm{|}}{\theta _{{\rm{FA}}1}}\left( {{v_1},\;{V_1}} \right)} \right)$
, and using Bayes’ Theorem, the joint probability distribution of the parameters given the data from the FA1 experiment is
$$p\left( {\rho, \;\;{\lambda _{{\rm{MGSE}}}},\;\;{\lambda _{{\rm{FA}}}},\;\phi \;{\rm{|}}\;{r_1}} \right)\; \propto p\left( {{r_1}\;{\rm{|}}\;\rho, \;\;{\lambda _{{\rm{MGSE}}}},\;\;{\lambda _{{\rm{FA}}}},\;\phi } \right)\; \times p\left( {\rho, \;\;{\lambda _{{\rm{MGSE}}}},\;\;{\lambda _{{\rm{FA}}}},\;\phi } \right)$$
Equation (7) will be used in the following section to estimate the bioload in the RTC. Finally, the marginal posterior distribution of
$\rho $
is given by
$$p\left( {\rho {\rm{|}}{r_1}} \right) = \;\mathop \int \nolimits_{\phi, {\lambda _{{\rm{FA}}}},{\lambda _{{\rm{MGSE}}}}}^\; p\left( {\rho, \;{\lambda _{{\rm{MGSE}}}},\;{\lambda _{{\rm{FA}}}},\;\phi {\rm{|}}{r_1}} \right)\;d{\lambda _{{\rm{MGSE}}}}\;d{\lambda _{{\rm{FA}}}}\;d\phi $$
Spore bioload in refrigerant transfer cylinder (RTC) after filling with CFC-11 from the SD
The process of transferring spores into the RTC (Appendix A) is mathematically very similar to that described above: a sample of size
$v$
with spore concentration
$\rho $
is transferred from the SD to the RTC. In order for spores to transfer to the RTC, they must penetrate the MGSE filter on the SD. Since there is no other filtering involved when filling the RTC, Equations (1) and (3) can be used to calculate the probability that an individual spore is transferred from the SD to the RTC. Therefore,
$${\pi _{{\rm{RTC}}|{\rm{SD}}}} = \;\mathop \int \nolimits_0^\infty \left[ {1 - \;{p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right)} \right]\;p\left( \delta \right)\;d\delta $$
Note that this equation is the same as Equation (4), with the FA filtering probability removed since it is not applicable to this calculation.
Suppose there is a volume
${V_{{\rm{SD}}}} \gt v$
in the SD just prior to filling the RTC (e.g., after flushing the MGSE), amounting to a total of
$M$
particles residing in the SD, where
$M = \left[ {{V_{{\rm{SD}}}} \times {N_{\rm{A}}} \times {\mu ^{ - 1}} \times \kappa \times 1000} \right]$
.
To estimate the number of spores in the RTC after being filled, an expression for the probability that a particle is a spore and is transferred to the RTC from the SD, denoted by
${\theta _{{\rm{RTC}}}}$
, is created using what has been learned about applicable model parameters from the FA1 experiment, quantified by Equation (7). Parameters applicable to predicting
${\theta _{{\rm{RTC}}}}$
are
$\rho $
and
${\lambda _{{\rm{MGSE}}}}$
, but not
${\lambda _{{\rm{FA}}}}$
or
$\phi $
since there is no filter besides the MGSE filter on the RTC and no spore recovery that takes place when the RTC is being filled. Assuming
$\rho $
and
${\lambda _{{\rm{MGSE}}}}$
parameters are known, the probability that an individual particle is a spore and is transferred from the SD to the RTC during filling of the RTC with CFC-11 is
$${\theta _{{\rm{RTC}}}}\left( {v,\;{V_{{\rm{SD}}}}} \right) = \rho \times {v \over {{V_{{\rm{SD}}}}}} \times {\pi _{{\rm{RTC}}|{\rm{SD}}}}$$
Since these particles are independent of one another during transfer, the probability that there are
${\tilde n_{{\rm{RTC}}}}$
particles that are spores and are transferred from the SD to the RTC during filling of the RTC with CFC-11 is
$$p\left( {{{\tilde n}_{{\rm{RTC}}}}{\rm{|}}\rho, \;{\lambda _{{\rm{MGSE}}}}} \right) = \left( {\matrix{ M \cr {{{\tilde n}_{{\rm{RTC}}}}} \cr } } \right){\left[ {{\theta _{{\rm{RTC}}}}\left( {v,\;{V_{{\rm{SD}}}}} \right)} \right]^{{{\tilde n}_{{\rm{RTC}}}}}}{\left[ {1 - {\theta _{{\rm{RTC}}}}\left( {v,\;{V_{{\rm{SD}}}}} \right)} \right]^{M - {{\tilde n}_{{\rm{RTC}}}}}}$$
The joint probability distribution of
$\rho $
and
${\lambda _{{\rm{MGSE}}}}$
given the data from the FA1 experiment is obtained by integrating Equation (7) over all values of
${\lambda _{{\rm{FA}}}}$
and
$\phi $
, in which case
$$p\left( {\rho, \;{\lambda _{{\rm{MGSE}}}}{\rm{|}}{r_1}} \right) = \mathop \int \nolimits_{\phi, {\lambda _{{\rm{FA}}}}}^\; p\left( {\rho, \;{\lambda _{{\rm{MGSE}}}},\;{\lambda _{{\rm{FA}}}},\;\phi {\rm{|}}{r_1}} \right)\;d{\lambda _{{\rm{FA}}}}\;d\phi $$
Finally, using Equation (11) with parameters
$\rho $
and
${\lambda _{{\rm{MGSE}}}}$
informed by Equation (12), the total probability that there are ñRTC particles that are spores transferred from the SD to the RTC during filling of the RTC with CFC-11 is
$$p\left( {{{\tilde n}_{{\rm{RTC}}}}} \right) \equiv p\left( {{{\tilde n}_{{\rm{RTC}}}}{\rm{|}}{r_1}} \right) = \mathop \int \nolimits_{{\lambda _{{\rm{MGSE}}}},\rho }^\; p\left( {{{\tilde n}_{{\rm{RTC}}}}{\rm{|}}\rho, \;{\lambda _{{\rm{MGSE}}}}} \right)\;p\left( {\rho, \;{\lambda _{{\rm{MGSE}}}}{\rm{|}}{r_1}} \right)\;d\rho \;d{\lambda _{{\rm{MGSE}}}}$$
where the integral runs over all possible spore concentrations and applicable filter efficiency rates. Figure 12 shows the probability distribution of the number of spores in the RTC, as calculated by Equation (13), when
$v = $
15.14 L from the SD total volume of
${V_{{\rm{SD}}}} = $
61 L filtered through one MGSE filter with nominal pore size equal to 2 µm, and given
${r_1} = 0$
spores are observed in the FA1 experiment. This is the scenario that is currently planned for launch operations, and is almost identical to how the RTC was charged prior to performing experiment FA2. Note that Equation (13) is a function of
$v$
and
${V_{{\rm{SD}}}}$
by way of Equation (11), although this has been suppressed in the notation of Equation (13) for readability. This allows calculation of the initial spore bioload in the RTC under various fill scenarios. Finally, this distribution closely resembles a hypergeometric distribution, which can be helpful for computational purposes and simulation.
Probability distribution of the predicted number of spores in CFC-11 transferred from the SD to the RTC prior to charging the flight Heat Reclamation System (HRS), given
${r_1} = 0$
spores are observed in the FA1 experiment. Assumes 15.14 L CFC-11 is transferred from the SD to the RTC through one 2 µm filter.
Filter assemblies 2 and 3: the probability that an individual spore is transferred through the MGSE and recovered
Mathematically, FA2 and FA3 experiments are modeled in a similar way as the FA1 experiment, except for the starting point being the RTC with an informed probability distribution of spore counts, rather than the SD with an uninformed probability distribution of spore counts, and an added filter in the FA3 experiment. As described in Appendix A, after the FA1 experiment and preparations for the FA2 experiment, there is a volume
${V_2}$
remaining in the RTC. The initial number of spores in the RTC at the start of the FA2 experiment,
${\tilde n_{{\rm{RTC}}}}$
, is given by Equation (13) with
$v = {V_2}$
. In the FA2 experiment, a volume
${v_2}$
of CFC-11 is transferred from the RTC, through a 2.0 µm MGSE filter on the RTC, then through the 0.22 µm filter on filter assembly 2. The probability that an individual spore penetrates the MGSE filter on the RTC but is filtered by filter assembly 2 is
$${\pi _{{\rm{FA}}2|{\rm{RTC}}}} = \mathop \int \nolimits_0^\infty \left[ {1 - {p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right)} \right]\;{p_{{\rm{FA}}}}\left( {U\;{\rm{|}}\;\delta } \right)\;p\left( \delta \right)\;d\delta $$
and an individual spore that has been filtered in this way is recovered as before with probability
$\phi $
. Therefore, the probability that an individual spore is transferred from the RTC and recovered by way of the FA2 experiment is
$${\theta _{{\rm{FA}}2}}\left( {{v_2},\;{V_2}} \right) = {{{v_2}} \over {{V_2}}} \times {\pi _{{\rm{FA}}2|{\rm{RTC}}}} \times \phi $$
A total of
${r_2}$
spores are then recovered from the filter assembly.
Without refilling the RTC, the FA3 experiment is performed next. A volume
${V_3}$
remains in the RTC after the FA2 experiment. In the FA3 experiment, a volume
${v_3}$
of CFC-11 is transferred from the RTC, through a 2.0 µm MGSE filter on the RTC, through another 2.0 µm MGSE filter in the FFP, then through the 0.22 µm filter on filter assembly 3. The probability that an individual spore penetrates both MGSE filters but is filtered by filter assembly 3 is
$${\pi _{{\rm{FA}}3|{\rm{RTC}}}} = \mathop \int \nolimits_0^\infty {\left[ {1 - {p_{{\rm{MGSE}}}}\left( {U{\rm{\;|\;}}\delta } \right)} \right]^2}{\rm{\;}}{p_{{\rm{FA}}}}\left( {U{\rm{\;|\;}}\delta } \right){\rm{\;}}p\left( \delta \right){\rm{\;}}d\delta $$
and an individual spore that has been filtered in this way is recovered as before with probability
$\phi $
. Therefore, the probability that an individual spore is transferred from the RTC and recovered by way of the FA3 experiment is
$${\theta _{{\rm{FA}}3}}\left( {{v_3},\;{V_3}} \right) = {{{v_3}} \over {{V_3}}} \times {\pi _{{\rm{FA}}3|{\rm{RTC}}}} \times \phi $$
Finally, a total of
${r_3}$
spores are recovered from the filter assembly.
Let
$\theta = \left( {{\theta _{{\rm{FA}}2}}\left( {{v_2},\;{V_2}} \right),{\theta _{{\rm{FA}}3}}\left( {{v_3},\;{V_3}} \right)} \right)$
. If there are initially
${\tilde n_{{\rm{RTC}}}}$
spores in the RTC at the start of the FA2 experiment, the probability that
${r_2}$
spores are recovered from the FA2 experiment and
${r_3}$
spores are recovered from the FA3 experiment (and
${\tilde n_{{\rm{RTC}}}} - {r_2} - {r_3}$
spores are not recovered in either experiment) is
$$p\left( {{r_2},{\rm{\;}}{r_3}{\rm{|}}\theta, {\rm{\;}}{{{\rm{\tilde n}}}_{{\rm{RTC}}}}} \right) = \left( {\matrix{ {{{{\rm{\tilde n}}}_{{\rm{RTC}}}}} \cr {{r_2}} \cr } } \right)\left( {\matrix{ {{{{\rm{\tilde n}}}_{{\rm{RTC}}}} - {r_2}} \cr {{r_3}} \cr } } \right)$$
$$ \times {\left[ {{\theta _{{\rm{FA}}2}}\left( {{v_2},{\rm{\;}}{V_2}} \right)} \right]^{{r_2}}} \times {\left[ {{\theta _{{\rm{FA}}3}}\left( {{v_3},{\rm{\;}}{V_3}} \right)} \right]^{{r_3}}} \times {\left[ {1 - {\theta _{{\rm{FA}}2}}\left( {{v_2},{\rm{\;}}{V_2}} \right) - {\theta _{{\rm{FA}}3}}\left( {{v_3},{\rm{\;}}{V_3}} \right)} \right]^{{{\tilde n}_{{\rm{RTC}}}} - {r_2} - {r_3}}}$$
Summing Equation (18) over all possible spore counts initially in the RTC,
$$p\left( {{r_2},{\rm{\;}}{r_3}{\rm{|}}\theta } \right) = \mathop \sum \limits_{{{\tilde n}_{{\rm{RTC}}}} = {r_2} + {r_3}}^\infty p\left( {{{\tilde n}_{{\rm{RTC}}}}} \right){\rm{\;}}p\left( {{r_2},{\rm{\;}}{r_3}{\rm{|}}\theta, {\rm{\;}}{{\tilde n}_{{\rm{RTC}}}}} \right)$$
Writing Equation (19) in terms of the underlying parameters of the function
$\theta $
,
$p\left( {{r_2},{\rm{\;}}{r_3}{\rm{\;|\;}}{\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi } \right) = p\left( {{r_2},{\rm{\;}}{r_3}{\rm{\;|\;}}\theta } \right)$
, and applying Bayes’ Theorem, the joint probability distribution of the parameters
$\left( {{\lambda _{{\rm{MGSE}}}},{\lambda _{{\rm{FA}}}},\phi } \right)$
given the data from all experiments is
$$p\left( {{\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi {\rm{\;|\;}}{r_1},{\rm{\;}}{r_2},{\rm{\;}}{r_3}} \right) \propto p\left( {{r_2},{\rm{\;}}{r_3}{\rm{\;|\;}}{\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi } \right) \times p({\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi {\rm{\;}}|{\rm{\;}}{r_1})$$
where, using Equation (7),
$p\left( {{\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi {\rm{\;|\;}}{r_1}} \right) = {\rm{\;}}\mathop \int \nolimits_\rho ^{\rm{\;}} p\left( {\rho, {\rm{\;}}{\lambda _{{\rm{MGSE}}}},{\rm{\;}}{\lambda _{{\rm{FA}}}},{\rm{\;}}\phi {\rm{\;|\;}}{r_1}} \right){\rm{\;}}d\rho $
.
Equation (20) is the joint probability distribution of all model parameters that describe the probability that an individual spore is transferred from the MGSE and recovered that now includes all information learned from FA1, FA2 and FA3 experiments. In what follows, this will be used to predict spore counts in the HRS after charging with CFC-11 during launch operations.
Predicting the spore bioload transferred through MGSE to the flight HRS
This model is now applied to the planned operations of the MGSE during launch operations when filling the HRS for flight. For this study, the experiments were performed under very similar conditions as those anticipated for filling the HRS during launch operations, the most notable difference being the length of the hose from the FFP to HRS. This is not expected to significantly change the flow dynamics (e.g., pressure change, velocity) or bioload transfer relative to the experimental setup used in this study.
Before filling the HRS, a SD containing a volume
${V_{{\rm{SD}}}}$
of CFC-11 is obtained. A volume
${v_{{\rm{RTC}}}}$
of CFC-11 is transferred from the SD through a 2 µm MGSE filter into the RTC. Using Equations (11) and (13) with
${V_{{\rm{SD}}}} = $
61.0 L and
$v = {v_{{\rm{RTC}}}} = $
15.14 L, we calculate the probability that the RTC contains
${\tilde n_{{\rm{RTC}}}}$
spores after its planned charging during launch operations,
$p({\tilde n_{{\rm{RTC}}}})$
.
With the RTC filled, a volume
${v_{{\rm{HRS}}}}$
of CFC-11 is transferred from the RTC, through two 2 µm MGSE filters (one on the RTC outlet, another in the FFP) and into the HRS. The probability that an individual spore penetrates both MGSE filters into the HRS is
$${\pi _{{\rm{HRS}}|{\rm{RTC}}}} = \mathop \int \nolimits_0^\infty {\left[ {1 - {p_{{\rm{MGSE}}}}\left( {U{\rm{\;|\;}}\delta } \right)} \right]^2}{\rm{\;}}p\left( \delta \right){\rm{\;}}d\delta $$
and the probability that an individual spore is transferred from the RTC into the HRS is
$$\theta \left( {{v_{{\rm{HRS}}}},\;{v_{{\rm{RTC}}}}} \right) = {{{v_{{\rm{HRS}}}}} \over {{v_{{\rm{RTC}}}}}} \times {\pi _{{\rm{HRS}}|{\rm{RTC}}}}$$
If there are initially
${\tilde n_{{\rm{RTC}}}}$
spores in the RTC at the start of fill operations and filter efficiency parameters are known, the probability that
${\tilde n_{{\rm{HRS}}}}$
spores transfer to the HRS is
$$p\left( {{{\tilde n}_{{\rm{HRS}}}}{\rm{\;|\;}}{{\tilde n}_{{\rm{RTC}}}},{\rm{\;}}{\lambda _{{\rm{MGSE}}}}} \right) = \left( {\matrix{ {{{\tilde n}_{{\rm{RTC}}}}} \cr {{{\tilde n}_{{\rm{HRS}}}}} \cr } } \right){\left[ {\theta \left( {{v_{{\rm{HRS}}}},{\rm{\;}}{v_{{\rm{RTC}}}}} \right)} \right]^{{{\tilde n}_{{\rm{HRS}}}}}}{\rm{\;}}{\left[ {1 - \theta \left( {{v_{{\rm{HRS}}}},{\rm{\;}}{v_{{\rm{RTC}}}}} \right)} \right]^{{{\tilde n}_{{\rm{RTC}}}} - {{\tilde n}_{{\rm{HRS}}}}}}$$
Integrating over all possible filter efficiency parameter values, the probability that
${\tilde n_{{\rm{HRS}}}}$
spores transfer to the HRS when there are initially
${\tilde n_{{\rm{RTC}}}}$
spores in the RTC at the start of fill operations is
$$p\left( {{{\tilde n}_{{\rm{HRS}}}}{\rm{\;|\;}}{{\tilde n}_{{\rm{RTC}}}},{\rm{\;}}{r_1},{\rm{\;}}{r_2},{\rm{\;}}{r_3}} \right) = \mathop \int \nolimits_{{\lambda _{{\rm{MGSE}}}}}^{\rm{\;}} p\left( {{{\tilde n}_{{\rm{HRS}}}}{\rm{\;|\;}}{{\tilde n}_{{\rm{RTC}}}},{\rm{\;}}{\lambda _{{\rm{MGSE}}}}} \right){\rm{\;}}p\left( {{\lambda _{{\rm{MGSE}}}}{\rm{\;|\;}}{r_1},{\rm{\;}}{r_2},{\rm{\;}}{r_3}} \right){\rm{\;}}d{\lambda _{{\rm{MGSE}}}}$$
where, using Equation (20),
$$p\left( {{\lambda _{{\rm{MGSE}}}}\;{\rm{|}}\;{r_1},\;{r_2},\;{r_3}} \right) = \mathop \int \nolimits_{\phi, {\lambda _{{\rm{FA}}}}}^\; p\left( {{\lambda _{{\rm{MGSE}}}},\;{\lambda _{{\rm{FA}}}},\;\;\phi \;{\rm{|}}\;{r_1},\;{r_2},\;{r_3}} \right)\;d{\lambda _{{\rm{FA}}}}\;d\phi $$
Therefore, summing over all possible spore counts in the RTC, the probability that
${\tilde n_{{\rm{HRS}}}}$
spores transfer to the HRS during fill operations is
$$p\left( {{{\tilde n}_{{\rm{HRS}}}}\;{\rm{|}}\;{r_1},\;{r_2},\;{r_3}} \right) = \mathop \sum \nolimits_{{{\tilde n}_{{\rm{RTC}}}} = 0}^\infty p\left( {{{\tilde n}_{{\rm{RTC}}}}} \right) \times p\left( {{{\tilde n}_{{\rm{HRS}}}}\;{\rm{|}}\;{{\tilde n}_{{\rm{RTC}}}},{r_1},\;{r_2},\;{r_3}} \right)$$
Equation (26) is used in what follows to predict the number of spores that transfer to the HRS by way of CFC-11 fill operations during planned launch operations. Finally, since model parameters pertain to individual filter efficiencies and the spore concentration of CFC-11, the model is somewhat flexible in terms of its ability to consider alternative MGSE filter configurations. For instance, an alternative configuration that uses a 0.22 µm filter on the SD rather than a 2 µm filter could also be assessed by the model. One would simply replace
${p_{{\rm{MGSE}}}}\left( {U\;{\rm{|}}\;\delta } \right)$
with
${p_{{\rm{FA}}}}\left( {U\;{\rm{|}}\;\delta } \right)$
in Equation (9) when calculating the probability distribution
$p\left( {{{\tilde n}_{{\rm{RTC}}}}} \right)$
from Equation (13). That said, alternative configurations are not considered by this study.
Prior distribution for
$\rho $
, the probability that an individual particle is a spore
$$\rho \sim Beta\left( {{\alpha _\rho },{\beta _\rho }} \right)$$
where
${\alpha _\rho } = $
0.5 and
${\beta _\rho } = $
0.5.
Prior distribution for
${\lambda _{I,MGSE}}$
, the efficiency rate of diffusion of an MGSE filter
$${\lambda _{{\rm{I}},{\rm{MGSE}}}}\sim Lognormal\left( {{\mu _{{\lambda _{{\rm{I}},{\rm{MGSE}}}}}},{\rm{\;}}{\sigma _{{\lambda _{{\rm{I}},{\rm{MGSE}}}}}}} \right)$$
where
${\mu _{{\lambda _{{\rm{I}},{\rm{MGSE}}}}}} = 10.0$
and
${\sigma _{{\lambda _{{\rm{I}},{\rm{MGSE}}}}}} = 0.15$
.
Prior distribution for
${\lambda _{II,MGSE}}$
, the efficiency rate of interception and impaction of an MGSE filter
$${\lambda _{{\rm{II}},{\rm{MGSE}}}}\sim Lognormal\left( {{\mu _{{\lambda _{{\rm{II}},{\rm{MGSE}}}}}},{\rm{\;}}{\sigma _{{\lambda _{{\rm{II}},{\rm{MGSE}}}}}}} \right)$$
where
${\mu _{{\lambda _{{\rm{II}},{\rm{MGSE}}}}}} = - {{{\rm{ln}}\left( {1 - {E_{2.0}}} \right)} \over {2.0}}$
and
${\sigma _{{\lambda _{{\rm{II}},{\rm{MGSE}}}}}} = 0.15$
. Here,
${E_{2.0}}$
is the vendor provided efficiency specification (2022 Swagelok catalog, 2022).
Prior distribution for
${\lambda _{I,FA}}$
, the efficiency rate of diffusion of the filter used in filter assemblies
$${\lambda _{{\rm{I}},{\rm{FA}}}}\sim Lognormal\left( {{\mu _{{\lambda _{{\rm{I}},{\rm{FA}}}}}},{\rm{\;}}{\sigma _{{\lambda _{{\rm{I}},{\rm{FA}}}}}}} \right)$$
where
${\mu _{_{{\rm{I}},{\rm{FA}}}}} = 10.0$
and
${\sigma _{{\lambda _{{\rm{I}},{\rm{FA}}}}}} = 0.15$
.
Prior distribution for
${\lambda _{II,FA}}$
, the efficiency rate of interception and impaction of the filter used in filter assemblies
$${\lambda _{{\rm{II}},{\rm{FA}}}}\sim Lognormal\left( {{\mu _{{\lambda _{{\rm{II}},{\rm{FA}}}}}},{\rm{\;}}{\sigma _{{\lambda _{{\rm{II}},{\rm{FA}}}}}}} \right)$$
where
${\mu _{{\lambda _{{\rm{II}},{\rm{FA}}}}}} = - {{{\rm{ln}}\left( {1 - {E_{0.22}}} \right)} \over {0.22}}$
and
${\sigma _{{\lambda _{{\rm{II}},{\rm{FA}}}}}} = 0.15$
. Here,
${E_{0.22}}$
is the vendor provided efficiency specification (2016 Sterlitech catalog, 2016).
Prior distribution for
$\phi $
, the probability an individual spore is extracted and recovered given transfer is completed
$$\phi \sim Beta\left( {{\alpha _\phi },{\beta _\phi }} \right)$$
where
${\alpha _\phi } = 14.54$
and
${\beta _\phi } = 21$
. These parameter values were obtained from the results of control experiments discussed in Appendix C.
Mathematical model results
Model inputs are summarized in Table 1. Filter efficiency and MPPS model inputs, together with the prior distribution assumptions in the Appendix, result in the prior distributions for each model parameter shown in Figure 13. Calibrating these prior distributions with the experimental observations
${r_1} = 0$
,
${r_2} = 0$
and
${r_3} = 0$
results in the posterior distributions of these parameters shown in Figure 14.Footnote
4
The prior and posterior distributions of the spore concentration in the SD,, are significantly different, demonstrating how much the model has been informed by the observational data for this parameter. Prior to experiment,
$\rho $
was assumed to take a wide range of values across the unit interval, with a mean value of 0.5. After observation from the experiment, the distribution of
$\rho $
is almost entirely behind 1 × 10−23. This is expected for two reasons: (1) since the prior distribution on
$\rho $
was defined in a way that maximizes the influence of the data; and (2) due to the large number of particles in the 1-liter sample from the SD that resulted in zero spores observed from the FA1 experiment. Prior and posterior distributions for all other model parameters are similar. This similarity is reassuring, to some extent, as the observations from experiment are consistent with prior knowledge. However, additional controlled experiments dedicated to studying the efficiency of the filters used in these experiments would be valuable to validate these results. Note that none of these parameters show evidence of being correlated with one another, which makes sense with an intuitive understanding of the physics and processes involved with this study. For example, non-interaction of diffusive and impaction/interception efficiency rates, and no known relationship between spore concentration in the SD and spore recovery protocols, lead to an intuitive expectation that no dependency exists between these model parameters.
Prior distributions of model parameters. Top-left:
$\rho $
, the probability that an individual particle is a spore. Top-right:
$\phi $
, the probability that an individual spore that has been transferred to the FA filter is extracted and produces an observable CFU. Other graphs, top to bottom, left to right: filter efficiency rates
$\lambda $
associated diffusion (I) and interception/impaction (II), for MGSE and FA filters.
Marginal distributions of model parameters, based on 4,000 samples from their posterior distribution. Top-left:
$\rho $
, the probability that an individual particle is a spore. Top-right:
$\phi $
, the probability that an individual spore that has been transferred to the FA filter is extracted and produces an observable CFU. Other graphs, top to bottom, left to right: filter efficiency rates
$\lambda $
associated diffusion (I) and interception/impaction (II), for MGSE and FA filters.
Recall that the
$\lambda $
parameters are used to construct filtration efficiency curves for each filter type. The posterior distribution of the efficiency curve for each filter are shown in Figure 15. The uncertainty in filter efficiency curves imply that a 95% efficiency occurs when a particle is between 1–3 µm for the MGSE filter and 0.1–0.3 µm for the FA filter. The extent to which diffusion or impaction/interception filtration mechanisms dominate varies, but, given the results of sensitivity analysis, impaction/interception appears to drive model results for the spore sizes assumed.
Filter efficiency curves for (A) an MGSE filter that is 95% efficiency at 2 µm as defined by Equation (1) and (B) an FA filter that is 95% efficiency at 0.22 µm as defined by Equation (2). Grey curves are calculated using 4,000 samples from the joint posterior distribution of
${\lambda _{{\rm{MGSE}}}}$
and
${\lambda _{{\rm{FA}}}}$
. The black curve shows the efficiency curves calculated using the posterior average values of
${\lambda _{{\rm{I}},{\rm{MGSE}}}}$
,
${\lambda _{{\rm{II}},{\rm{MGSE}}}}$
,
${\lambda _{{\rm{I}},{\rm{FA}}}}$
and
${\lambda _{{\rm{II}},{\rm{FA}}}}$
.
With the inputs in Table 1, the posterior distribution of parameters described by Equations (8) and (20) is calculated, and Equation (26) is used to calculate the predict the number of spores in the CFC-11 transferred from the MGSE to the HRS during planned launch operations,
${\tilde n_{{\rm{HRS}}}}$
, given the observations made from FA1, FA2 and FA3 experiments performed in this study. Figure 16 shows the resulting probability distribution associated
${\tilde n_{{\rm{HRS}}}}$
. Currently, the HRS is planned to be filled with 8 L of CFC-11. This study estimates an 80% probability that there are zero spores transferred into the HRS during this process; 14% probability of one spore; 3% probability of two spores; and about a 3% probability of more than two spores. The mean number of spores transferred into the HRS is 0.29, with a 95% confidence interval of (0.24, 0.34).
Probability distribution of the predicted number of spores in CFC-11 transferred from MGSE to the flight Heat Reclamation System (HRS), given zero spores were observed from all experiments (
${r_1} = {r_2} = {r_3} = 0$
). Assumes 8 L CFC-11 is transferred from the RTC to the HRS through two 2 µm filters. Mean number of spores (with 95% confidence interval) = 0.29 (0.24, 0.34).
A first-order sensitivity analysis shows that, for a fixed set of CFC-11 volume inputs assumed for the SD, RTC and HRS, the model results are sensitive to changes in the mean spore diameter,
${\mu _\delta }$
and filter efficiency inputs. Smaller (larger) diameter spores imply higher (lower) mean number of spores in the CFC-11 transferred from the MGSE to the HRS. Lower filter efficiencies for both MGSE and FA filters result in higher mean number of spores in the CFC-11 transferred from the MGSE to the HRS. Higher filter efficiency for MGSE filters also can significantly reduce the mean number of spores in the CFC-11 transferred from the MGSE to the HRS. Higher filter efficiency for FA filters and a reasonable range of MPPS values for both MGSE and FA filters do not significantly affect model results. This is because there is not much more efficiency to gain from a filter that is already 95% efficient given the spore sizes assumed in this study. The standard deviation of spore diameter is positively correlated with the mean spore diameter, and therefore varies with the mean spore diameter when performing sensitivity analysis.
Appendix C CFU results and recovery efficiency
This appendix provides a detailed breakdown of the colony-forming unit (CFU) results obtained from the various CFC-11 sample and control assays, including those using 90 mm filters directly plated. All samples, including controls, yielded zero CFU, with the exception of the positive controls, which demonstrated expected growth. Additionally, the recovery efficiency of the assays, calculated as following a beta distribution with a mean of 41% (see Prior distributions and Mathematical model results in Appendix B), is included as one of the key inputs for the modeling study. A comprehensive listing of individual CFU counts and further experimental details can be found below.
Table 2 shows the CFU results for all the freon samples and controls. All samples, including the 90 mm filters that were directly plated, resulted in 0 CFU. Filter controls and media controls also resulted in 0 CFU. The positive controls resulted in growth, as expected.
CFC-11 sample list
Cellulose acetate filters are compatible with freon (msscientific Chromatographie-Handel GmbH). Nonetheless, to ensure the 90 mm cellulose acetate filters used in our study didn’t inhibit growth, after the filters had been incubated for 72 hours and resulted in zero growth, 100 µl of 104 B. atrophaeus was added to the filters and again incubated. There was sufficient growth after 24 hours of incubation (qualitative) commensurate with the positive control, suggesting that there was no inhibition of growth that would account for the 0 observed CFU.
Table 3 shows the CFU results for recovery efficiency study. First, the average observed CFU yield (41.4) was divided by the expected CFU yield (52.2). Next, the efficiency was multiplied by 0.5 to account for the 50% pour fraction of the CFC-11 samples (i.e., the 200 mL fractions were split in half with one set heat shocked and the other non-heat shocked). Thus, the percent recovery efficiency was 39.66%. This efficiency was used to calculate one of the inputs to the modeling study.
Recovery efficiency sample list
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