A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

Scaling the impacts of pore-scale characteristics on unstable supercritical CO2-water drainage using a complete capillary number

Geological carbon storage in deep aquifers involves displacement of resident brine by supercritical CO2 (scCO2), which is an unstable drainage process caused by the invasion of less viscous scCO2. The unstable drainage is greatly complicated by aquifer heterogeneity and anisotropy and regarded as one of the key factors accounting for the uncertainty in storage capacity estimates. The impacts of pore-scale characteristics on the unstable drainage remain poorly understood. In this study, scCO2 drainage experiments were conducted at 40 °C and 9 MPa using a homogeneous elliptical micromodel with low or high anisotropy, a homogeneous/isotropic hexagonal micromodel, and a heterogeneous sandstone-analog micromodel. Each initially water-saturated micromodel was invaded by scCO2 at different rates with logCa (the capillary number)ranging from −7.6 to −4.4, and scCO2/water images were obtained. The measured CO2 saturations in these centimeter-scale micromodels vary considerably from 0.08 to 0.93 depending on the pore-scale characteristics and capillary number. It was also observed that scCO2 drainage follows the classic flow-regime transition from capillary fingering through crossover to viscous fingering for either of the low-anisotropy elliptical and heterogeneous micromodels, but with disparate crossover zones. The crossover zones of scCO2 saturation were then unified with the minimum scCO2 saturation occurring at logCa*=-4.0 using the complete capillary number (Ca*)that considers pore characteristics. For the hexagonal and the high-anisotropy elliptical micromodels, a monotonic increase in scCO2 saturation with increasing Ca* (without crossover)was observed. It appears that the complete capillary number is more appropriate than the classic capillary number when characterizing flow regimes and CO2 saturation in different pore networks

Coupled supercritical CO2 dissolution and water flow in pore-scale micromodels

Dissolution trapping is one of the most important mechanisms for geological carbon storage (GCS). Recent laboratory and field experiments have shown non-equilibrium dissolution of supercritical CO2 (scCO2) and coupled scCO2 dissolution and water flow, i.e., scCO2 dissolution at local pores/pore throats creating new water-flow paths, which in turn enhance dissolution by increased advection and interfacial area. However, the impacts of pore-scale characteristics on these coupled processes have not been investigated. In this study, imbibition and dissolution experiments were conducted under 40 °C and 9 MPa using a homogeneous/isotropic hexagonal micromodel, two homogeneous elliptical micromodels with low or high anisotropy, and a heterogeneous sandstone-analog micromodel. The four micromodels, initially saturated with deionized (DI)-water, were drained by injecting scCO2 to establish a stable scCO2 saturation. DI water was then injected at different rates with logCa (the capillary number) ranging from −6.56 to −4.34. Results show that bypass of scCO2 by displacing water is the dominant mechanism contributing to the residual CO2 trapping, triggered by heterogeneity in pore characteristics or pore-scale scCO2-water distribution. Bypass can be enhanced by pore heterogeneity or reduced by increasing transverse permeability, resulting in relatively low (<2% of CO2 solubility) or high (9–13% of CO2 solubility) dissolved CO2 concentration in displacing water. The overall dissolution of residual scCO2 increases with decreasing Ca, and approaches to their solubility at low Ca value with sufficient residence time. This main trend is similar to a capillary desaturation curve that represents the relationship between the residual saturation and Ca. Spatially, dissolution initiates along the boundary of bypassed scCO2 cluster(s) in a non-equilibrium manner, and the coupling of water flow and dissolution occurs which fragments the bypassed scCO2 clusters and enhance scCO2 dissolution

A breakthrough curve analysis of unstable density-driven flow and transport in homogenous porous media

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Applicant perceptions of initial job candidate screening with asynchronous job interviews : does personality matter?

Applicant fairness perceptions of asynchronous job interviews were assessed among panelists (Study 1, N = 160) and highly educated actual applicants (Study 2, N = 103). Furthermore, we also examined whether personality explained applicants' perceptions. Participants, particularly actual applicants, had negative perceptions of the fairness and procedural justice of asynchronous job interviews. Extraverted applicants perceived more opportunity to perform with the asynchronous job interview than introverts. A trait interaction between Neuroticism and Extraversion was tested, but no significant results were found. Although the first selection stage is increasingly digitized, this study shows that applicant perceptions of asynchronous job interviews are relatively negative. The influence of personality on these perceptions appears to be limited

Critical Peaks Redefined - Φ⊔Ψ=⊤

6th International Workshop on Confluence6th International Workshop on ConfluenceLet a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and pattern-substitutions for the gaps. We show both notions of cluster and the corresponding refinement/coarsening orders on them, to be isomorphic. This equips clusters with a lattice structure which we lift to (parallel/multi) steps to yield an alternative account of the notion of critical peak

Fate and transport of volatile organic compounds in glacial till and groundwater at an industrial site in Northern Ireland

Volatile organic compound (VOC) contamination of subsurface geological material and groundwater was discovered on the Nortel Monkstown industrial site, Belfast, Northern Ireland. The objectives of this study were to (1) investigate the characteristics of the geological material and its influences on contaminated groundwater flow across the site using borehole logs and hydrological evaluations, and (2) identify the contaminants and examine their distribution in the subsurface geological material and groundwater using chemical analysis. This report focuses on the eastern car park (ECP) which was a former storage area associated with trichloroethene (TCE) degreasing operations. This is where the greatest amount of volatile organic compounds (VOCs), particularly TCE, were detected. The study site is on a complex deposit of clayey glacial till with discontinuous coarser grained lenses, mainly silts, sands and gravel, which occur at 0.45-7.82 m below ground level (bgl). The lenses overall form an elongated formation that acts as a small unconfined shallow aquifer. There is a continuous low permeable stiff clayey till layer beneath the lenses that performs as an aquitard to the groundwater. Highest concentrations of VOCs, mainly TCE, in the geological material and groundwater are in these coarser lenses at similar to 4.5-7 m bgl. Highest TCE measurements at 390,000 mu g L-1 for groundwater and at 39,000 mu g kg(-1) at 5.7 m for geological material were in borehole GA19 in the coarse lens zone. It is assumed that TCE gained entrance to the subsurface near this borehole where the clayey till was thin to absent above coarse lenses which provided little retardation to the vertical migration of this dense non-aqueous phase liquid (DNAPL) into the groundwater. However, TCE is present in low concentrations in the geological material overlying the coarse lens zone. Additionally, VOCs appear to be associated with poorly drained layers and in peat < 3.0 m bgl in the ECP. Some indication of natural attenuation as VOCs degradation products vinyl chloride (VC) and dichloromethane (DCM) also occur on the site

Experimental Plan: 300 Area Treatability Test: In Situ Treatment of the Vadose Zone and Smear Zone Uranium Contamination by Polyphosphate Infiltration

The overall objectives of the treatability test is to evaluate and optimize polyphosphate remediation technology for infiltration either from ground surface, or some depth of excavation, providing direct stabilization of uranium within the deep vadose and capillary fringe above the 300 Area aquifer. Expected result from this experimental plan is a data package that includes: 1) quantification of the retardation of polyphosphate, 2) the rate of degradation and the retardation of degradation products as a function of water content, 3) an understanding of the mechanism of autunite formation via the reaction of solid phase calcite-bound uranium and aqueous polyphosphate remediation technology, 4) an understanding of the transformation mechanism, identity of secondary phases, and the kinetics of the reaction between uranyl-carbonate and –silicate minerals with the polyphosphate remedy under solubility-limiting conditions, 5) quantification of the extent and rate of uranium released and immobilized based on the infiltration rate of the polyphosphate remedy and the effect of and periodic wet-dry cycling on the efficacy of polyphosphate remediation for uranium in the vadose zone and capillary fringe, and 6) quantification of reliable equilibrium solubility values for autunite under hydraulically unsaturated conditions allowing accurate prediction of the long-term stability of autunite. Moreover, results of intermediate scale testing will quantify the transport of polyphosphate and degradation products, and yield degradation rates, at a scale that is bridging the gap between the small-scale UFA studies and the field scale. These results will be used to test and verify a site-specific, variable saturation, reactive transport model and to aid in the design of a pilot-scale field test of this technology. In particular, the infiltration approach and monitoring strategy of the pilot test would be primarily based on results from intermediate-scale testing. Results from this experimental plan will be documented in a PNNL report