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Let p be a prime, ℤp* = {1,2,..., p - 1}, m, c be integers with m ≥ 2, and ℒm(c) = {x|x ∈ ℤp*, 2 (x +(cxm)p)}, where (cxm)p denotes the least positive residue modulo p. In this paper, we study the representation of any element of ℤp* as sum of a m-th Lehmer number l ∈ ℒm(c) and a k-th power residue in ℤp*, and give an inequality for the number of representations. Moreover, using the algorithm we provided, we examined all the cases for some pairs (k, m) by computer. We also analyzed the time complexity of the algorithm and illustrated that it is extremely difficult to verify all the cases up to the bound of p for larger km. [ABSTRACT FROM AUTHOR]

Let p be an odd prime and Zp the residue class ring modulo p. In this paper, we study representations of any element of Zp as the sum of a Lehmer number and a primitive root in Zp, and give an explicit inequality better than asymptotic formula for the number of representations. From this inequality, we obtained that each element of Zp can be represented as the sum of a Lehmer number and a primitive root for p > 2.5×1014. Moreover, using the algorithm we provided, we examined all the cases when p < 106 by computer. We also analyzed the time complexity of the algorithm and illustrated that it is extremely difficult to verify all the cases up to the bound 2.5×1014, and conjectured that any given element n ∈ Zp can be represented as the sum of a Lehmer number and a primitive root in Zp for all primes p except 2, 3, 5, 7, 11, 19, 31. [ABSTRACT FROM AUTHOR]

Accurately determining if the sample parameters from a natural gas pipeline’s sampling system reflect the fluid characteristics of the main pipe has been a significant industry concern for many years. In this paper, samples of natural gas in a horizontal pipeline are investigated. CFD is used in this work and the turbulence is considered in the simulation. Firstly, the critical diameter for particles affected by gravity within such pipeline is determined. And then, the effects of the operation pressure and velocity of sampling branches on sample parameters, and the influence of particle density on these sample parameters, are analyzed. Finally, four different structures of sample branches for natural gas in a horizontal pipeline are compared. It is found that 100 μm is the critical diameter at which particles are affected by gravity; the operating pressure of the sampling branch has a significant impact on the particle mass concentration. The particle density has little impact on the sampling system. Overall, the design of the sampling branches does not cause significant sampling errors. This study provides guidance for optimal sampling in existing natural gas pipelines and enables effective monitoring of particle impurity content and properties in natural gas.

China is conducting ecological restoration work in urban water bodies. Under anoxic and anaerobic conditions, pollutants transform and produce odorous and black substances, deteriorating the water quality, which is a significant problem in urban water bodies. Vallisneria natans has received widespread attention for its applications in water treatment and restoration. However, the efficiency by which V. natans reduces water pollution and allows sediment remediation requires further improvement. Therefore, in this study, we investigated the effect of V. natans coupled with carbon fiber on the restoration of water bodies and sediment compared with the control group that grew V. natans without carbon fiber. The oxidation-reduction potential (ORP) was selected as the main evaluation index for the water and sediment. Dissolved oxygen in the water and total organic carbon and total nitrogen (TN) in the sediment were also evaluated. V. natans coupled with carbon fiber significantly increased the ORP; that of surface sediment increased by 50 % and that of the water body increased by 60 % compared with the sediment without any bioremediation. Chemical oxygen demand, total phosphorous, and TN in water decreased by 61.2 %, 22.9 %, and 48.3 %, respectively. These results indicate that planting V. natans with carbon fiber can reduce pollutants in water (including humus) and sediments, effectively improving ORP in water and sediment.

The girth weld is the weak link of high-grade pipeline, and its structural integrity affects the safety of pipeline operation. Herein, the state of art of the weld metal strength and toughness indicators were discussed from three aspects: the design method of weld metal strength and toughness indicators, the strength and toughness acceptance indicators proposed by pipeline engineering design standards, and the test method of weld metal strength and toughness. The fitness-for-service assessment methods of pipeline girth weld were expounded. The key problems and progress of the assessment methods were discussed: the crack tip constraint effect of fracture toughness, the numerical simulation method of fracture behavior of pipeline girth weld, the evaluation method of crack driving force, the assessment method of failure evaluation diagram, the prediction method of tensile strain capacity of pipeline girth weld, and the fracture experimental test of full-scale pipeline girth weld. Finally, the existing problems and future research directions in the mechanical properties and fitness-for-service assessment of high-grade pipeline girth weld were put forward. Generally, the research results could provide a reference for improving the intrinsic safety of high-grade pipeline girth weld.

In order to evaluate the influence of the strength of base material, root welding material and filler material on the strain capacity of girth welds in X80 pipeline, the passivation behavior of crack tips during cracking was accurately simulated with the Key Hole model by the nonlinear finite element method based on the China–Russia Eastern Gas Pipeline with a diameter of 1 422 mm and a wall thickness of 21.4 mm. Here, consideration was given to the complete geometrical morphology of welded joints and the partition of four materials with different properties. In addition, the crack initiation behavior of circumferential cracks in the root inner surface under the action of tensile load was researched. According to the results, the strength of root welding material has little impact on the overall strain capacity of double V-groove welded joint, which can be ignored. The overmatching of filler material with the base material is the most important to guarantee the strain capacity in the weld zone. Moreover, in the case that it is difficult to enhance the strength of filler material, limiting the strength indicator of base material is an effective way to improve the strain capacity of welded joints in high-grade steel pipelines.

A new regularity for internal pressure has been introduced based on the suggested potential energy function in liquid bismuth. Both the experimental data and the calculated quantities from the power law equation of state have been used to show the validity of the regularity. The quantity X3Z−1 is a linear function of ln(X) with crossing points for all isotherms at high temperature, where X=VVm0, V, Vm0, and Z are molar volume, the molar volume at melting point and zero pressure, and compressibility factor. For the reduced isothermal bulk modulus B*=BTVRT and the quantity Zint=PintVRT, where BT, R, T and Pint are isothermal bulk modulus, the gas constant, temperature and internal pressure, the new regularities have been introduced that both calculated X3B*−1 and X3Zint from the equation of state of a power law form versus ln(X) are nearly linear along each isotherm. However, those derived values from experiments become nonlinear functions of ln(X) at large pressure for all isotherms. Based on the new equation of state, analytical expression of thermodynamic properties of liquid bismuth can be obtained. The different extreme values exist along the isotherms for the calculated internal energy, isobaric heat capacity, and isochoric heat capacity for the new equation of state and the power law form equation of state.

The actual strength under-matching of pipeline girth welds is a principal cause for the fracture failure of welds. The current Failure Assessment Diagram (FAD) method for the applicability assessment of pipeline welds cannot accurately consider the influence of weld strength matching. Thus, accurate inclusion of strength matching becomes critical to broaden the FAD method to apply to the crack defect assessment for the girth welds of high-grade steel pipelines. Based on the nonlinear finite element method, a numerical simulation model of the crack driving forces for the girth welds of high-grade steel pipelines was established, and the general failure assessment curve of girth weld cracks was plotted with the equivalent stress-strain relationship method. Then, a series of finite element assessment points under different load levels were determined with the finite element calculation results of the crack driving forces in combination with the recommended methods in Guide to methods for assessing the acceptability of flaws in metallic structures (BS 7910-2019). Further, the assessment accuracy of BS 7910-2019 to the crack defects of girth welds was determined, and the critical causes affecting the accuracy of the assessment results were investigated. On this basis, the optimized ultimate load calculation model of the pipeline girth welds and the improved FAD method were put forward with the crack depth, the crack length and the weld strength matching coefficient considered, and the weld strength matching was accurately included into the FAD method. Thereby, the assessment accuracy of the girth weld crack defects of the high-grade steel pipelines was further enhanced. Generally, the method could provide reference for the applicability assessment of the girth weld cracks of in-service high-grade steel pipelines.

Anomalies as misalignment, microcrack are inevitable for large diameter high strength steel pipelines. To ensure the strain capacity of mismatched welding joint with misalignments of D 1,422 mm X80 steel pipeline, a comprehensive study via wide plate experiments and finite element model simulations was conducted. The full-scale tensile experiment of a X80 pipe wide plate with weld joint was conducted. Strain distributions on the plate was derived by DIC technic. Trends of CMOD at the precrack in the weld joint with tensile strains monitored. A FE model was established to inverse the wide plate experiment and prove the accuracy of numerical model’s prediction results for crack driving forces. Using the same modeling method, a parametrical 3D numerical simulation model for X80 line pipe with cracks in automatic welding joints was established. The double V-shaped groove type welding joint was precisely considered in the geometric model. Difference of the stress-strain relationships of yielding-to-tensile ratio of the BM, softening rate of the HAZ and strength matching coefficient of WM were considered in the material model. A CTOD extracting program coded was employed. Parametric analysis was performed to investigate the effects of load conditions, strength matching coefficient of WM, yielding-to-tensile ratio of BM and softening rate of HAZ on the strain capacity with a critical fracture toughness adopted in pipeline industry. Based on the derived results, mismatched ratio requirements of D 1,422 mm X80 pipes were listed, which provides guidance for the welding parameter design and safety evaluation of automatic welding joints.

Enough biomass of anaerobic ammonium oxidation (anammox) bacteria is essential for maintaining a stable partial nitrification/anammox (PN/A) wastewater treatment system. Present enrichment procedures are mainly labor-intensive and inconvenient for up-scaling. A simplified procedure was developed for enrichment of anammox biofilm by using secondary effluent as source water with no supplement of mineral medium and unstrict control of influent dissolved oxygen (DO). Anammox biofilm was successfully enriched in two pilot-scale reactors (XQ-cul and BT-cul) within 250 and 120 days, respectively. The specific anammox activity increased rapidly during the last 2 months in both reactors and achieved 2.54 g N2-N/(m2·d) in XQ-cul and 1.61 g N2-N/(m2·d) in BT-cul. Similar microbial diversity and community structure were obtained in the two reactors despite different secondary effluent being applied from two wastewater treatment plants. Anaerobic ammonium oxidizing bacteria genera abundance reached up to 37.4% and 43.1% in XQ-cul and BT-cul biofilm, respectively. Candidatus Brocadia and Ca. Kuenenia dominated the enriched biofilm. A negligible adverse effect of residual organics and influent DO was observed by using secondary effluent as source water. This anammox biofilm enrichment procedure could facilitate the inoculation and/or bio-augmentation of large-scale mainstream PN/A reactors.

This paper describes the girth welding technology for the north section (Heihe-Changling Section) of China-Russia Eastern Gas Pipeline concerning its characteristics of high steel grade, large diameter, high pressure, large throughput and low temperature. The construction characteristics of welding of D 1 422 mm L555M gas pipeline were summarized in terms of the weldability of L555M pipelines, The performance index of girth welding joint, girth welding technology and quality control. The significance of requirements and test methods for indicators, including the strength, toughness, hardness and plasticity of girth welding joint, were described. The selection principle and actual application of process parameters, such as welding method, welding material and welding groove, were analyzed, and the effect of the groove size, alignment accuracy, preheating temperature and interpass temperature, and NDT technology on quality control of welding was described. All of the above results are empirical summary in engineering construction, capable of providing experience support for the welding construction management in subsequent oil and gas pipeline construction.

The station temperature of China-Russia Eastern Gas Pipeline Project is designed low to －45 ℃, which poses new challenges to the brittle fracture prevention capability of pipeline facilities, so it is necessary to set up scientific and reasonable toughness index requirements to prevent brittle fracture of in-service components under low temperature conditions. The development process of brittle fracture control technology, from empirical method to fracture analysis diagram method and then to fracture mechanics method, was systematically described. The empirial method based technical status on brittle fracture control of oil and gas pipelines was analyzed with China-Russia Eastern Gas Pipeline as the example. Meanwhile, through the comparison and analysis with the brittle fracture control requirements in ASME Boiling and Pressure Vessel Code (BPVC), the deficiencies of brittle fracture control measures for oil and gas pipeline fittings were pointed out. Analysis shows that the experience-based Charpy impact toughness index may be insufficient to prevent brittle fracture when applied to high toughness pipeline steel. Therefore, it is suggested to ① build a perfect fracture mechanicsbased brittle fracture control index system for high-grade high-toughness pipeline steel, ② add Nil-Ductility Transition (NDT) test requirements based on the existing brittle fracture control indexes, ③ and establish brittle fracture control requirements based on fracture mechanics evaluation.

In consideration of the structural characteristics of high-grade steel pipes and the great influence of weld failure on the safety of pipelines, the bearing capacity of girth welds of pipelines has become a research hotspot in the pipeline industry. The full-automatic joint in the China–Russia Eastern Gas Pipeline was taken as the research object, and the differences of material constitutive relations in the four zones of root welding, heat affected zone, base metal and fill welding in girth welding joint were accurately considered. The numerical simulation model based on finite element method was established for analyzing the strain capacity of pipeline girth welding joints. Quantitative analysis was made on the influence of the matching ratio of toughness and other factors on the driving force of crack growth in pipeline girth welds under combined operating conditions of base metal yield ratio, operating internal pressure and load type. The failure determination method of static crack initiation was adopted. The apparent fracture toughness value was taken as the critical criterion. In combination with the actual variation range of the material characteristic parameters of pipes and girth welding joints of the China–Russia Eastern Gas Pipeline, the strain capacity of the China–Russia Eastern Gas Pipeline girth welding joints under the most unfavorable conditions within the design operating conditions was calculated. The results show that improving the strength matching of weld zone is conducive to reduce the driving force of crack growth in the joint effectively. Increasing the internal pressure of the pipeline or raising the yield ratio of the base metal will cause the driving force of crack growth larger under the same strength matching condition, and the driving force of crack growth under tensile load is greater than that under bending load. This method can be used not only to guide the determination of welding parameters according to the performance requirements of welded joints, but also for the applicability assessment of defective welded joints in service pipelines.

Several new regularities in liquid gallium have been obtained from both the available experimental data and calculated thermodynamic properties along the isothermal lines with the equation of state (EoS) of a power law form. The quantity Z−1V3 is linearly proportional to V3 for all isotherms at high temperatures. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT derived from the available experimental data and EoS of a power law form are observed to be linear with respect to V−3 with the temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity (LIR) EoS. By using the analytical expression from the LIR EoS, the calculated isobaric thermal expansion coefficient, isochoric heat capacity, isobaric heat capacity, Grüneisen parameter, and Anderson–Grüneisen parameter show quite different behavior with pressure at a constant temperature compared with those values from EoS of a power law form. In addition, analytical expressions of thermodynamic properties of liquid gallium are derived from the LIR EoS, such as adiabatic bulk modulus, sound velocity, entropy, internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy, which have the same tendency with pressure at a constant temperature as the numerically integrated values from EoS of a power law form.

Sodium hypochlorite was widely used as a supplementary disinfectant in reclaimed water (RW) production during the COVID-19 epidemic. It is well known that the chlorination of RW results in a relatively high bacterial regrowth potential in pipeline systems. However, the algal growth and algal–bacterial interactions would be another concern in RW-replenished surface water with light irradiation. In this study, microcosmic experiments were used to explore the impact of hypochlorite on the algae–bacteria community, including the influence of hypochlorite on algal–bacterial regrowth, microbial community structure, and the specific bacteria that can survive chlorination. Results demonstrated that algal growth potential could be promoted after chlorination of the RW, and bacteria abundance increased along with an increase in algal density, which is probably related to DOM decomposition by chlorine oxidation. Additionally, the characteristics of the bacterial community were altered. It is more likely that phytospheric bacteria will survive chlorination. It was discovered that the secondary risks of chlorine disinfection include the growth of algae in addition to bacterial regeneration, which is an extension of the common perception. As a consequence, when chlorinated reclaimed water is used as a supplement for urban landscape ponds, particular attention should be paid to controlling bio-available organic matter induced by reactive chlorine, as well as the algal bloom, to decrease the risk of pathogen transmission.

We propose several new regularities in solid sodium from the available experimental data and calculated thermodynamic properties along the isotherms with the equation of state (EOS) of the modified Holzapfel form. Z−1V2 is a linear function in terms of V2 with different intersection points for the isotherms at high temperatures within the considered pressure range, where Z and V are the compressibility factor and molar volume. The calculated isothermal bulk modulus BT and internal pressure Pint of solid sodium vary almost linearly with pressure. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT from the modified Holzapfel EOS are observed to be linear with respect to V−2 with temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity EOS. In addition, analytical expressions of the thermodynamic properties of solid sodium are derived from the linear isothermal regularity EOS, such as internal energy, entropy, enthalpy, free energy, and heat capacity.

Nanofiltration membrane technology is an effective method for secondary treated sewage purification. However, membrane fouling, which is inevitable in the membrane-separation process, can reduce membrane performance and shorten membrane life. Installing a turbulence promoter is a promising means of improving the hydraulic conditions inside the membrane chamber. In this study, the effect of turbulence promoter on prolonging membrane life was studied for the first time. Flat-sheet polyethersulfone nanofiltration membrane was used to filter humic acid solution, used for simulating secondary treated sewage. By comparing photographs and SEM images of the membrane before and after the simulated secondary treated sewage filtration, it was found that humic acid tended to be deposited on the low-velocity region, which was reflected by COMSOL simulation. After incorporating a turbulence promoter, the reduction of the humic acid deposition area and membrane fouling resistance indicated that the turbulence promoter could reduce membrane fouling due to the improved hydraulic conditions. Additionally, the turbulence promoter also increased the flux and reduced the flux decay rate. The turbulence promoter was then place in the crossflow flat-sheet membrane filtration module, and the variation of flux with time was tested in simulated secondary treated sewage with different concentrations. The results showed that the membrane life for the filtration of simulated secondary treated sewage comprising 50, 250, and 500 ppm humic acid increased by 23.1%, 80.4%, and 85.7%, respectively. The results of this article can serve as a reference for the prediction of membrane life and the performance enhancement mechanism of membranes containing a turbulence promoter.

In the present paper, the expressions for acoustical parameter and nonlinearity parameter are obtained based on thermodynamic relations from an equation of state with a power law form. Both parameters for liquid Sodium are calculated under high pressure along the isothermal lines by using the available thermodynamic data and numeric derivations. The relation between the isochoric acoustical parameter and internal pressure is derived and the corresponding approximation at low pressure condition is discussed. The present results show nonlinearity parameter is a nonlinear function of pressure along the isothermal lines in liquid sodium. The calculated values are found to be very close to the experimental measurements and quasi-thermodynamic theory at melting point at ambient condition. Furthermore, several other thermodynamic quantities are also presented.

Acquiring reliable thermodynamic properties in liquid metals at high pressure and temperature is still a challenge in both experiment and theory. Equation of state (EoS) offers an alternative approach free of many of the difficulties. Here using the EoS of a power law form we obtained the thermodynamic properties of liquid sodium under pressure along the isothermal lines, including isothermal buck modulus, thermal expansion coefficient, Grüneisen parameter, and Anderson-Grüneisen parameter. The results are in excellent agreement with available experimental data measured by a piezometer at high temperature and high pressure and sound velocity measurement with pulse-echo technique. We found that the pressure derivative of the isothermal bulk modulus at zero pressure is a monotonic function of temperature and has a value around 4. In addition, unexpected crossing points were found in the isobaric thermal expansion coefficient and Grüneisen parameter; and a minimum in the isobaric heat under isothermal compression was also observed. While some of these detailed predictions are yet to be confirmed by further experiment, our results suggest that the power law form may be a more suitable choice for the EoS of liquids metals.

We apply an equation of state of a power law form to liquid Indium to study its thermodynamic properties under high temperature and high pressure. Molar volume of molten indium is calculated along the isothermal line at 710K within good precision as compared with the experimental data in an externally heated diamond anvil cell. Bulk modulus, thermal expansion and internal pressure are obtained for isothermal compression. Other thermodynamic properties are also calculated along the fitted high pressure melting line. While our results suggest that the power law form may be a better choice for the equation of state of liquids, these detailed predictions are yet to be confirmed by further experiment.