A reference high-pressure CH₄ adsorption isotherm for zeolite Y: results of an interlaboratory study

As mentioned, ILS2 involved measurement of CH₄/ZY surface excess adsorption isotherms at 25 °C for pressures up to 7.5 MPa, using NIST RM 8850 as the adsorbent. This reference material is highly homogenized and characterized with reference values for elemental composition (e.g., Si/Al = 2.547 ± 0.037, Na/Al = 0.997 ± 0.018) and certain other physicochemical properties (e.g., loss-on-fusion ≈ loss-on-ignition ≈ 0.25), and information values for a range of structural properties (Turner et al. 2008). Sufficient units of this material are in stock at NIST (https://​www.​nist.​gov/​srm) to ensure availability for the foreseeable future.

In total, 20 laboratories participated in ILS2; seven of the 20 were participants in ILS1. The measurement capabilities of these laboratories included both commercial and custom-built manometric and gravimetric instruments.

The measurement protocol instructions were minimal. For CO₂/ZSM-5 measurements, the protocol and conditions developed in ILS1 were prescribed (Nguyen et al. 2018). For the CH₄/ZY, the measurement protocol specified a minimum purity of the adsorptive (≥ 99.999%), the sample pretreatment (activation at 350 °C for at least 12 h using a turbomolecular pump), the pressure range (7.5 MPa or the maximum capability of the instrument), the recommended equilibrium pressure points, the temperature (25 °C), and the number of isotherms to be measured (two isotherms each for two separate aliquots, totaling four isotherms for CH₄). It was recommended to perform a blank run (i.e., an isotherm in the absence of the adsorbent) to subtract from the isotherm measured with the adsorbent present (Nguyen et al. 2017). Each participant was provided with one unit (40 g) each of RM 8852 and RM 8850. Participants were asked to submit an experimental report, which detailed their experimental procedures and data processing steps, and to submit the isotherms as surface excess uptake in units of millimoles of adsorbed fluid per gram of activated zeolite in a provided template. For the most part, the participants followed the prescribed protocols, although there were some small deviations. Details on various experimental parameters and procedures for each dataset can be found in Table 1.

Each participant in ILS2 submitted at least one high-pressure dataset. For clarity, a CH₄/ZY dataset is composed of four adsorption isotherms from two aliquots of ZY (aliquot 1—isotherm 1, aliquot 1—isotherm 2, aliquot 2—isotherm 1, aliquot 2—isotherm 2). In general, the intralaboratory isotherms were highly reproducible (except for DS 14 and 15; see Figs. S6–S10 in the Supplemental Information). Twenty-six high-pressure CH₄/ZY datasets were submitted, for a total of 104 isotherms. In addition, two participants submitted 5 isotherms over the pressure range of 1 kPa to 100 kPa. These low-pressure data were useful in constraining the empirical reference function at low-pressure.

Labs who had not participated in ILS1 were asked to provide two CO₂/ZSM-5 isotherms (20 °C), one isotherm each from two separate sample aliquots. In general, these intralaboratory isotherms were also highly reproducible (except for DS 14, see Figs. S3–S5 in the Supplemental Information). The purpose of this exercise was to demonstrate the measurement capabilities of these laboratories. Successful replication of the CO₂/ZSM-5 isotherm was a criterion for inclusion of CH₄/ZY isotherms from these labs in determination of the reference isotherm for ILS2. The CO₂/ZSM-5 isotherms were evaluated with two metrics. First, the residuals from the reference isotherm (reference isotherm minus measured isotherm) were determined. Ideally, all residuals should be within the prediction interval of the CO₂/ZSM-5 reference isotherm (U_k=2=  ± 0.075 mmol/g). This metric provides a qualitative measure of replication of the CO₂/ZSM-5 reference isotherm. A second more quantitative metric of replication of the CO₂/ZSM 5 reference isotherm, the “goodness-of-fit” (GOF), was also computed. For this test, the reference function from ILS1, which defines the amount of gas adsorbed versus pressure, was compared to each of the CO₂/ZSM-5 datasets for new participants in ILS2. The GOF metric was based on the residuals to the reference function, using a Bayesian, Markov Chain Monte Carlo algorithm. This calculation included the uncertainty in the estimates of the reference function as well as the uncertainty of the submitted datasets. The lower the value of this test, the better the dataset replicates the CO₂/ZSM-5 reference isotherm. When this test was applied to the datasets of ILS1, the average GOF value was 0.078, with a standard deviation of 0.048. With this range as a guide, it was decided that CO₂/ZSM-5 isotherms submitted to ILS2 with a GOF value less than 0.07 would be considered to have replicated the reference isotherm, those with a value between 0.07 and 0.12 would be evaluated on a case-by-case basis, and those with a value greater than 0.12 would be considered as failing to replicate the reference isotherm and submitted CH₄/ZY isotherm data would not be included in determining the reference function for ILS2. Of course, passing the GOF test was a necessary—but not sufficient—criterion for a CH₄/ZY dataset to be included in the determination of the reference isotherm for ILS2. The GOF calculation was done using the OpenBUGS (Lunn et al. 2009) code shown in the Supplemental Information.

To clearly display a plot including datasets from all participants, the average of the isotherms for each dataset was determined. These are shown in the figures in the text. [There were two datasets (DS 14 & DS 15) for which averaging was not possible. In these cases, one representative isotherm was selected for display.] In determination of the reference isotherm, the full datasets shown in the Supplemental Information were used–not the averaged datasets shown in the figures of the body of the text. The number of each dataset is random and does not correspond to the numeric listing of authors.

The CH₄/ZY isotherms were fit collectively to the function,

[n_ex—surface excess uptake (mmol/g), P—equilibrium pressure (MPa), a, b, c, d, and e being empirical parameters shown in Table 2]. The values of a, b, c, d, and e and the associated 95% uncertainty interval to that fit were determined using a Bayesian, Markov Chain Monte Carlo method (Gelman 2013; Possolo and Toman 2007). The 95% uncertainty interval is the expanded uncertainty (U_k=2) with k = 2, or 2 times the uncertainty of the reference value, which equates to 95% coverage probability or 95% level of confidence that the true value lies within the interval (Taylor and Kuyatt 2001). The OpenBUGS code used for the fit is given in the Supplemental Information. This function was selected because it replicated the form of the measured isotherms. No physical significance should be associated with the function or its parameters, following the practice of ILS1.

In total, 17 CO₂ datasets were submitted by 12 labs, with one lab submitting four datasets, and two labs submitting two datasets (see Figs. S2–S6). The residuals of the datasets (reference isotherm minus measured data) are displayed in Fig. 1. From visual inspection two datasets (DS 4 & DS 14) are noticeably outside of the uncertainty interval of the CO₂/ZSM-5 reference function. The datasets were also evaluated for their goodness-of-fit to the CO₂/ZSM-5 reference data and placed into one of three categories based on their goodness-of-fit values: pass (GOF < 0.07), borderline (GOF between 0.07 and 0.12), and fail (GOF > 0.12). Among those participating in ILS2 who had not participated in ILS1, four (DS 1, DS 4, DS 10 & DS 14) were identified as having failed the goodness-of-fit test. Seven CO₂/ZSM-5 datasets (DS 2, DS 6, DS 7, DS 13, DS 16, DS 17 & DS 18) passed the goodness-of-fit test. Six datasets (DS 3, DS 5 DS 8, DS 9, DS 11 & DS 12) fell into the borderline category. The quality of the residuals of the datasets shown in Fig. 1 correlate well with the goodness-of-fit values (see Supplemental Information). Datasets that failed and some datasets borderline in the GOF test exhibit slightly greater variability in the intralaboratory replicate isotherms (Figs. S3–S5), although in general, intralaboratory isotherms have good reproducibility.

For the interested reader, ILS1 is a great resource providing pitfalls and recommendations for high-pressure CO₂ measurement (Nguyen et al. 2018). The participants of the failed datasets (DS 1, DS 4, DS 10, and DS 14) were unable to remeasure, reprocess, or (in one case) improve the data to identify the origin for the deviation. However, two failed datasets came from labs that each had at least one other CO₂/ZSM-5 dataset that didn’t fail the GOF test, suggesting an issue with their instrument or method rather than with the material. Evaluation of the experimental details indicated the activation protocol was not followed for one case (DS 14), which could explain the lower uptake. The importance of following the activation protocol was explicitly highlighted in ILS1(Nguyen et al. 2018), and modeling work based on the CO₂/ZSM-5 reference data underscored that varying the pretreatment temperature of ammonium ZSM-5 affects what cations are in the zeolite (Fang et al. 2020).

All participants were allowed to submit CH₄/ZY isotherms, although CH₄/ZY datasets from labs and/or instruments that failed to replicate the CO₂/ZSM 5 isotherm would automatically be excluded in the determination of the reference isotherm for ILS2. The as-submitted CH₄/ZY datasets, excluding DS 14, which did not follow the prescribed activation protocol, were plotted together and Eq. (1) was fitted to them. This process identified ten datasets that were statistical outliers (DS 1, DS 4, DS 9, DS 10, DS 11, DS 12, DS 14, DS 15, DS 16 & DS 27), with datapoints lying outside the 95% uncertainty interval. These participants were given the opportunity to remeasure or reprocess their results. Four datasets (DS 4, DS 9, DS 11 & DS 12) were resubmitted after review of the initial result indicated they were outliers. All final submitted datasets are shown in Fig. 2. In general, the intralaboratory isotherms for the datasets were highly reproducible (except for DS 14 and 15; see Figs. S6–S10 in the Supplemental Information). Four datasets (DS 1, DS 4, DS 10 & DS 14) failed the CO₂ test, and one participant (DS 15) failed to replicate the CO₂/ZSM-5 isotherm by not submitting CO₂ isotherm data. The remaining 23 datasets were fitted to Eq. (1), which along with expert judgement, re-identified two datasets as statistical outliers (DS 16 & DS 27), while 21 datasets appear to be in good agreement. DS 27 is a participant in ILS1 who used a different instrument in ILS2 and did not have CO₂/ZSM-5 isotherms for the new instrumentation. Only one (DS 16) of the outlying CH₄/ZY datasets successfully reproduced the CO₂/ZSM-5 isotherm. The resubmission led to improvements in three datasets (DS 9, DS 11, and DS 12) with identified reasons for the observed variation in the outlying surface excess datasets including temperature instability (leading to volume calibration, and sample and blank isotherms being performed under different conditions), inaccurate mass measurement (due to balance mass drift), and error in application of blank subtraction, stressing the importance of following the recommendations outlined in the ILS1 paper. After eliminating the datasets that did not pass the proficiency test or had another identified issue, 21 datasets remained, as shown in Fig. 3.

An empirical surface excess reference function was determined by optimizing the fit of Eq. (1) to the final remaining datasets and is also shown in Fig. 3. The optimized parameters are given in Table 2. This function is predictive up to 7.5 MPa and has expanded uncertainty, U_k=2, for the excess uptake of approximately 0.09 mmol/g over the full pressure range. Beneath the isotherms are the residuals (reference function minus measured isotherm) along with U_k=2. The residuals show that the reference function adequately represents the final set of isotherms over the full pressure range of the study. The datasets and the reference isotherm are available through the NIST Database of Novel and Emerging Adsorbent Materials.³