Key results from the salt lake regional smoke, ozone, and aerosol study (SAMOZA).

The Northern Wasatch Front area is one of ~ 50 metropolitan regions in the U.S. that do not meet the 2015 O3 standard. To better understand the causes of high O3 days in this region we conducted the Salt Lake regional Smoke, Ozone and Aerosol Study (SAMOZA) in the summer of 2022. The primary goals of SAMOZA were: Measure a suite of VOCs, by Proton Transfer Reaction Mass Spectrometry (PTR-MS) and the 2,4-dinitrophenylhydrazine (DNPH) cartridge method.Evaluate whether the standard UV O3 measurements made in SLC show a positive bias during smoke events, as has been suggested in some recent studies.Use the observations to conduct photochemical modeling and statistical/machine learning analyses to understand photochemistry on both smoke-influenced and non-smoke days.Implications: The Northern Wasatch Front area is one of ~50 metropolitan regions in the U.S. that do not meet the 2015 O3 standard. To better understand the causes of high O3 days in this region we conducted the Salt Lake regional Smoke, Ozone and Aerosol Study (SAMOZA) in the summer of 2022. A number of policy relevant findings are identified in the manuscript including role of smoke and NOx vs VOC sensitivity.

We found no significant difference in the O₃ measurements using a "scrubber-less" UV instrument compared to the standard O₃ measurements at PM_2.5 concentrations up to 60 µg m⁻³.On days with smoke, we found that PM_2.5, CO, O₃ and nearly all VOCs were significantly enhanced. On average, NO_x was also enhanced on days with smoke, but this was complicated by day of week effects.Photochemical modeling of O₃ production rates at the Utah Tech Center demonstrates a strong sensitivity to VOC concentrations and less sensitivity to NOx. For non-smoke days, achieving the current O₃ standard would require regional reductions in VOCs of ~40% or reductions in NO_x ~ 60%.The photochemical modeling shows that formaldehyde and other OVOCs, along with alkenes, were the most important O₃ precursors.Generalized Additive Modeling (GAM) gave similar MDA8 O₃ enhancements on smoky days as the photochemical modeling. Analysis of the GAM results show that 23% of the smoke days have GAM residuals that exceed the U.S. EPA's criteria for inclusion as exceptional event documentation.

Emissions of organic compounds from produced water ponds I: Characteristics and speciation.

We measured fluxes of methane, a suite of non-methane hydrocarbons (C2-C11), light alcohols, and carbon dioxide from oil and gas produced water storage and disposal ponds in Utah (Uinta Basin) and Wyoming (Upper Green River Basin) United States during 2013-2016. In this paper, we discuss the characteristics of produced water composition and air-water fluxes, with a focus on flux chamber measurements. In companion papers, we will (1) report on inverse modeling methods used to estimate emissions from produced water ponds, including comparisons with flux chamber measurements, and (2) discuss the development of mass transfer coefficients to estimate emissions and place emissions from produced water ponds in the context of all regional oil and gas-related emissions. Alcohols (made up mostly of methanol) were the most abundant organic compound group in produced water (91% of total volatile organic concentration, with upper and lower 95% confidence levels of 89 and 93%) but accounted for only 34% (28 to 41%) of total organic compound fluxes from produced water ponds. Non-methane hydrocarbons, which are much less water-soluble than methanol and less abundant in produced water, accounted for the majority of emitted organics. C6-C9 alkanes and aromatics dominated hydrocarbon fluxes, perhaps because lighter hydrocarbons had already volatilized from produced water prior to its arrival in storage or disposal ponds, while heavier hydrocarbons are less water soluble and less volatile. Fluxes of formaldehyde and other carbonyls were low (1% (1 to 2%) of total organic compound flux). The speciation and magnitude of fluxes varied strongly across the facilities measured and with the amount of time water had been exposed to the atmosphere. The presence or absence of ice also impacted fluxes.

A survey of valleys and basins of the western United States for the capacity to produce winter ozone.

High winter ozone in the Uintah Basin, Utah, and the Upper Green River Basin, Wyoming, occurs because of the confluence of three separate factors: (1) extensive oil or natural gas production, (2) topography conducive to strong multiple-day thermal inversions, and (3) snow cover. We surveyed 13 basins and valleys in the western United States for the existence and magnitude of these factors. Seven of the basins, because winter ozone measurements were available, were assigned to four different behavioral classes. Based on similarities among the basins, the remaining six were also given a tentative assignment. Two classes (1 and 2) correspond to basins with high ozone because all three factors just listed are present at sufficient magnitude. Class 3 corresponds to rural basins with ozone at background levels, and occurs because at least one of the three factors is weak or absent. Class 4 corresponds to ozone below background levels, and occurs, for example, in urban basins where emissions scavenge ozone. All three factors are present in the Wind River Basin, Wyoming, but compared to the Uintah or the Upper Green Basins, it has only moderate oil and gas production and is assigned to class 3. We predict that the Wind River Basin, as well as other class 3 basins that have inversions and snow cover, would transition from background (class 3) to high ozone behavior (class 1 or 2) if oil or gas production were to intensify, or to class 4 (low winter ozone) if they were to become urban. IMPLICATIONS: High ozone concentrations in winter only occur in basins or valleys that have an active oil and natural gas production industry, multiple-day thermal inversions, and snow cover, and have only been documented in two basins worldwide. We have examined a number of other candidate basins in the western United States and conclude that these factors are either absent or too weak to produce high winter ozone. This study illustrates how strong each factor needs to be before winter ozone can be expected, and can be used by planners and regulators to foresee the development of winter ozone problems.

Organic compound emissions from a landfarm used for oil and gas solid waste disposal.

Solid or sludgy hydrocarbon waste is a by-product of oil and gas exploration and production. One commonly used method of disposing of this waste is landfarming. Landfarming involves spreading hydrocarbon waste on soils, tilling it into the soil, and allowing it to biodegrade. We used a dynamic flux chamber to measure fluxes of methane, a suite of 54 nonmethane hydrocarbons, and light alcohols from an active and a remediated landfarm in eastern Utah. Fluxes from the remediated landfarm were not different from a polytetrafluoroethylene (PTFE) sheet or from undisturbed soils in the region. Fluxes of methane, total nonmethane hydrocarbons, and alcohols from the landfarm in active use were 1.41 (0.37, 4.19) (mean and 95% confidence limits), 197.90 (114.72, 370.46), and 4.17 (0.03, 15.89) mg m-2 hr-1, respectively. Hydrocarbon fluxes were dominated by alkanes, especially those with six or more carbons. A 2-ha landfarm with fluxes of the magnitude we observed in this study would emit 95.3 (54.3, 179.7) kg day-1 of total hydrocarbons, including 11.2 (4.3, 33.9) kg day-1 of BTEX (benzene, toluene, ethylbenzene, and xylenes). IMPLICATIONS: Solid and sludgy hydrocarbon waste from the oil and gas industry is often disposed of by landfarming, in which wastes are tilled into soil and allowed to decompose. We show that a land farm in Utah emitted a variety of organic compounds into the atmosphere, including hazardous air pollutants and compounds that form ozone. We calculate that a 2-ha landfarm facility would emit 95.0 ± 66.0 kg day-1 of total hydrocarbons, including 11.1 ± 1.5 kg day-1 of BTEX (benzene, toluene, ethylbenzene, and xylenes).

Emissions of organic compounds from produced water ponds III: Mass-transfer coefficients, composition-emission correlations, and contributions to regional emissions.

A common method for treating the aqueous phase (produced water) brought to the surface along with oil and natural gas is to discharge it into surface impoundments, also known as produced water ponds. Here we analyze data on the concentration of organic compounds in the water and on the flux of the same compounds into the atmosphere. Flux data extending from about 5 × 10-2 to 10+3 mg m-2 h-1 are consistent with mass-transfer laws given by the WATER9 semi-empirical algorithm, although empirical data display a noise level of about one order of magnitude and predictions by WATER9 are biased high. The data suggest partitioning between hydrocarbons in aqueous solution and in suspension, especially at higher overall concentrations. Salinity of the produced water does not have a detectable effect on hydrocarbon fluxes. Recently impounded waters are stronger emitters of hydrocarbons, while emissions of older waters are dominated by CO2. This aging effect can be explained by assuming, first, poor vertical mixing in the ponds, and second, gradual oxidation of hydrocarbons to CO2. Our measurements account for about 25% of the produced water ponds in the Uinta Basin, Eastern Utah, and when extrapolated to all ponds in the basin, account for about 4% to 14% of all organic compound emissions by the oil and natural gas sector of the basin, depending on the emissions inventory, and about 13% and 58%, respectively, of emissions of aromatics and alcohols.

Emissions of organic compounds from produced water ponds II: Evaluation of flux chamber measurements with inverse-modeling techniques.

In this study, the authors apply two different dispersion models to evaluate flux chamber measurements of emissions of 58 organic compounds, including C2-C11 hydrocarbons and methanol, ethanol, and isopropanol from oil- and gas-produced water ponds in the Uintah Basin. Field measurement campaigns using the flux chamber technique were performed at a limited number of produced water ponds in the basin throughout 2013-2016. Inverse-modeling results showed significantly higher emissions than were measured by the flux chamber. Discrepancies between the two methods vary across hydrocarbon compounds and are largest in alcohols due to their physical chemistries. This finding, in combination with findings in a related study using the WATER9 wastewater emission model, suggests that the flux chamber technique may underestimate organic compound emissions, especially alcohols, due to its limited coverage of the pond area and alteration of environmental conditions, especially wind speed. Comparisons of inverse-model estimations with flux chamber measurements varied significantly with the complexity of pond facilities and geometries. Both model results and flux chamber measurements suggest significant contributions from produced water ponds to total organic compound emission from oil and gas productions in the basin. IMPLICATIONS: This research is a component of an extensive study that showed significant amount of hydrocarbon emissions from produced water ponds in the Uintah Basin, Utah. Such findings have important meanings to air quality management agencies in developing control strategies for air pollution in oil and gas fields, especially for the Uintah Basin in which ozone pollutions frequently occurred in winter seasons.

Statistical analysis of winter ozone exceedances in the Uintah Basin, Utah, USA.

Because of the confluence of several factors (persistent multiday inversions, petroleum production, and snow cover), the Uintah Basin of eastern Utah, USA, exhibits high concentrations of winter ozone. A regression analysis is presented that successfully predicts daily ozone concentration with a standard error of about 11 ppb. It also predicts with 90% accuracy whether any given day will exceed the National Ambient Air Quality Standard for ozone, 70 ppb. An analysis is introduced for calculating a "pseudo-lapse rate," a determination of inversion intensity in the absence of sounding data. By combining the model with historical meteorological data, it is possible to make long-range predictions about ozone formation. The odds of observing no exceedance days in any given season are 38%. The odds of only three or fewer exceedance days in any given season are 46%. IMPLICATIONS: This paper provides an improved understanding of the scientific underpinnings of the winter ozone phenomenon and an ability to make long-range predictions.

Knot Energy, Complexity, and Mobility of Knotted Polymers.

The Coulomb energy E C is defined by the energy required to charge a conductive object and scales inversely to the self-capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find E C to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E C〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.

Hydrocarbon and Carbon Dioxide Fluxes from Natural Gas Well Pad Soils and Surrounding Soils in Eastern Utah.

We measured fluxes of methane, nonmethane hydrocarbons, and carbon dioxide from natural gas well pad soils and from nearby undisturbed soils in eastern Utah. Methane fluxes varied from less than zero to more than 38 g m-2 h-1. Fluxes from well pad soils were almost always greater than from undisturbed soils. Fluxes were greater from locations with higher concentrations of total combustible gas in soil and were inversely correlated with distance from well heads. Several lines of evidence show that the majority of emission fluxes (about 70%) were primarily due to subsurface sources of raw gas that migrated to the atmosphere, with the remainder likely caused primarily by re-emission of spilled liquid hydrocarbons. Total hydrocarbon fluxes during summer were only 39 (16, 97)% as high as during winter, likely because soil bacteria consumed the majority of hydrocarbons during summer months. We estimate that natural gas well pad soils account for 4.6 × 10-4 (1.6 × 10-4, 1.6 × 10-3)% of total emissions of hydrocarbons from the oil and gas industry in Utah's Uinta Basin. Our undisturbed soil flux measurements were not adequate to quantify rates of natural hydrocarbon seepage in the Uinta Basin.

Universal interrelation between measures of particle and polymer size.

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration Rg, hydrodynamic radius Rh, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor αE and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between αE, C, and Rg for nanoparticles and polymers of general shape and the corresponding properties η, Rh, and Rg using a hydrodynamic-electrostatic property interrelation.

Persistent draining crossover in DNA and other semi-flexible polymers: Evidence from hydrodynamic models and extensive measurements on DNA solutions.

Although the scaling theory of polymer solutions has had many successes, this type of argument is deficient when applied to hydrodynamic solution properties. Since the foundation of polymer science, it has been appreciated that measurements of polymer size from diffusivity, sedimentation, and solution viscosity reflect a convolution of effects relating to polymer geometry and the strength of the hydrodynamic interactions within the polymer coil, i.e., "draining." Specifically, when polymers are expanded either by self-excluded volume interactions or inherent chain stiffness, the hydrodynamic interactions within the coil become weaker. This means there is no general relationship between static and hydrodynamic size measurements, e.g., the radius of gyration and the hydrodynamic radius. We study this problem by examining the hydrodynamic properties of duplex DNA in solution over a wide range of molecular masses both by hydrodynamic modeling using a numerical path-integration method and by comparing with extensive experimental observations. We also considered how excluded volume interactions influence the solution properties of DNA and confirm that excluded volume interactions are rather weak in duplex DNA in solution so that the simple worm-like chain model without excluded volume gives a good leading-order description of DNA for molar masses up to 10(7) or 10(8) g/mol or contour lengths between 5 µm and 50 µm. Since draining must also depend on the detailed chain monomer structure, future work aiming to characterize polymers in solution through hydrodynamic measurements will have to more carefully consider the relation between chain molecular structure and hydrodynamic solution properties. In particular, scaling theory is inadequate for quantitative polymer characterization.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other between the viscosity and hydrodynamic radii, as potential measures of shape anisotropy. We also find a strong correlation between anisotropy and effective fractal dimension. These observations should provide new practical methods for quantifying the nature of particle clustering in diverse contexts.

A model for the evolution of nucleotide polymerase directionality.

BACKGROUND: In all known living organisms, every enzyme that synthesizes nucleic acid polymers does so by adding nucleotide 5'-triphosphates to the 3'-hydroxyl group of the growing chain. This results in the well known 5'→3' directionality of all DNA and RNA Polymerases. The lack of any alternative mechanism, e.g. addition in a 3'→5' direction, may indicate a very early founder effect in the evolution of life, or it may be the result of a selective pressure against such an alternative. METHODOLOGY/PRINCIPAL FINDINGS: In an attempt to determine whether the lack of an alternative polymerase directionality is the result of a founder effect or evolutionary selection, we have constructed a basic model of early polymerase evolution. This model is informed by the essential chemical properties of the nucleotide polymerization reaction. With this model, we are able to simulate the growth of organisms with polymerases that synthesize either 5'→3' or 3'→5' in isolation or in competition with each other. CONCLUSIONS/SIGNIFICANCE: We have found that a competition between organisms with 5'→3' polymerases and 3'→5' polymerases only results in a evolutionarily stable strategy under certain conditions. Furthermore, we have found that mutations lead to a much clearer delineation between conditions that lead to a stable coexistence of these populations and conditions which ultimately lead to success for the 5'→3' form. In addition to presenting a plausible explanation for the uniqueness of enzymatic polymerization reactions, we hope these results also provide an example of how whole organism evolution can be understood based on molecular details.

Properties of knotted ring polymers. I. Equilibrium dimensions.

We report calculations on three classes of knotted ring polymers: (1) simple-cubic lattice self-avoiding rings (SARs), (2) "true" theta-state rings, i.e., SARs generated on the simple-cubic lattice with an attractive nearest-neighbor contact potential (theta-SARs), and (3) ideal, Gaussian rings. Extrapolations to large polymerization index N imply knot localization in all three classes of chains. Extrapolations of our data are also consistent with conjectures found in the literature which state that (1) R(g)-->AN(nu) asymptotically for ensembles of random knots restricted to any particular knot state, including the unknot; (2) A is universal across knot types for any given class of flexible chains; and (3) nu is equal to the standard self-avoiding walk (SAW) exponent (congruent with 0.588) for all three classes of chains (SARs, theta-SARs, and ideal rings). However, current computer technology is inadequate to directly sample the asymptotic domain, so that we remain in a crossover scaling regime for all accessible values of N. We also observe that R(g) approximately p(-0.27), where p is the "rope length" of the maximally inflated knot. This scaling relation holds in the crossover regime, but we argue that it is unlikely to extend into the asymptotic scaling regime where knots become localized.

Properties of knotted ring polymers. II. Transport properties.

We have calculated the hydrodynamic radius R(h) and intrinsic viscosity [eta] of both lattice self-avoiding rings and lattice theta-state rings that are confined to specific knot states by our path-integration technique. We observe that naive scaling arguments based on the equilibrium polymer size fail for both the hydrodynamic radius and the intrinsic viscosity, at least over accessible chain lengths. (However, we do conjecture that scaling laws will nevertheless prevail at sufficiently large N.) This failure is attributed to a "double" cross-over. One cross-over effect is the transition from delocalized to localized knotting: in short chains, the knot is distributed throughout the chain, while in long chains it becomes localized in only a portion of the chain. This transition occurs slowly with increasing N. The other cross-over, superimposed upon the first, is the so-called "draining" effect, in which transport properties maintain dependence on local structure out to very large N. The hydrodynamic mobility of knotted rings of the same length and backbone structure is correlated with the average crossing number X of the knots. The same correlation between mobility and knot complexity X has been observed for the gel-electrophoretic mobility of cyclic DNA molecules.

Influence of variable hydrodynamic interaction strength on the transport properties of coiled polymers.

We have computed the hydrodynamic radius Rh and intrinsic viscosity [eta] of a large number of random coil polymer models by path integration. We examine the effects of chain length, solvent quality, monomer size and shape, and chain stiffness on the approach of these transport properties to the limit of large molecular mass. For many of the models, we have also calculated the ensemble-averaged solvent velocity field in the vicinity of the coil as it moves with constant drift velocity under the action of an external force. Naive scaling arguments predict alpha=nu and beta=3(nu-1) , where alpha , beta , and nu are the exponents controlling the chain length behavior of Rh , [eta] , and Rg , respectively. We present evidence for a "draining crossover" that quantifies the slow convergence of the transport properties to their asymptotic scaling behavior. Indeed, the convergence is so slow that effective alpha and beta exponents rarely agree with the naive predictions at typical molecular masses. For the same chain models, Rg converges rapidly to its asymptotic behavior, indicating that the effect is not due to a crossover from theta to swollen behavior, as often stated. Solvent quality, monomer size, and chain stiffness all influence the draining crossover. Our results call into question the common practice of extracting metrical data, e.g., characteristic ratios, directly from polymer solution transport properties.

Improved path integration method for estimating the intrinsic viscosity of arbitrarily shaped particles.

In previous work, we have established that the intrinsic viscosity [eta] of an object is nearly proportional to the average electrical polarizability tensor alphae = tr(alphae)/3 of a conducting object having the same shape, or equivalently, to the intrinsic conductivity [sigma]=alphae/V , which characterizes the conductivity of a dilute mixture of randomly oriented conducting objects (V being the volume of the object). This hydrodynamic-electrostatic analogy is useful because alphae can be determined accurately and efficiently by numerical path integration for objects of arbitrary shape. Here, we show that the uncertainty in [eta] can be reduced to a relatively small value (< 1.5% relative uncertainty) by utilizing additional information from the full tensor alphae, rather than just its average. Specifically, we determine the exact constant of proportionality between [eta] and [sigma] for triaxial ellipsoids as a function of the ratios of the eigenvalues of alphae and apply this relation to particles of general shape. In addition to an improved estimation of [eta] , the ratios of the components of alphae provide useful measures of particle anisotropy. We also present an improved method for applying the technique to flexible particles, which requires performing a conformational ensemble average. Conformational averages of alphae generate systematic errors that can be avoided by performing the conformational average at an earlier stage in the computation.

Universal scaling, entanglements, and knots of model chain molecules.

By identifying the maximally random jammed state of freely jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of (i) the contour length of the primitive paths and (ii) the number of entanglements per chain agree remarkably well with recent theoretical predictions in all scaling regimes. Furthermore, our simulations reveal a hitherto unsuspected connection between purely intramolecular (knots) and intermolecular (entanglements) topological constraints.

Efficient knot group identification as a tool for studying entanglements of polymers.

A technique is presented for the identification of the knot group of knots, links, and other embedded graphs as a tool in numerical studies of entanglements of polymers. With this technique, the knot group is simultaneously more discriminating and easier to calculate than the knot invariants that have been used in such studies in the past. It can be applied even in cases of very complex knot projections with hundreds of crossings. Starting from an arbitrary projection of an embedded graph, we generate a sequence of representations, any one of which is a full and complete representation of the knot group. Any two knot groups are isomorphic if they have identical representations. Therefore, we compare the sequence of representations of any given knot or link against a previously determined lookup table, and if the group of the knot or link is represented in this table we eventually find a match and identify the knot group.

Development of knotting during the collapse transition of polymers.

A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule.