Experimental investigation on coal pore-fracture variation and fractal characteristics synergistically affected by solvents for improving clean gas extraction

Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.

Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption

Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.

Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.

A MIXED LUBRICATION MODEL MODIFIED BY SURFACES' FRACTAL CHARACTERISTICS

Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D , compared with the oil film thickness to roughness ratio h/R q . As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.

Experimental analysis of pore structure and fractal characteristics of soft and hard coals with same coalifcation

Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical signifcance for coal bed methane(CBM)development and the prevention of dynamic disasters such as coal and gas outbursts.This study investigates the pore structure and fractal characteristics of soft and hard coals using nitrogen and carbon dioxide(N_(2)/CO_(2))adsorption.Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size(0.20–0.25 mm).N_(2)/CO_(2)adsorption tests were performed to evaluate the specifc surface area(SSA),pore size distribution(PSD),and pore volume(PV)using Braunuer-Emmett-Teller(BET),Barrett-Joyner-Halenda(BJH),and Density Functional Theory(DFT).The pore structure was characterized based on the theory of fractal dimensions.The results unveiled that the strength of coal has a signifcant infuence on pore structure and fractal dimensions.There are signifcant diferences in SSA and PV between both coals.The BJH-PV and BET-SSA obtained by N_(2)-adsorption for soft coal are 0.029–0.032 cm^(3)/g and 3.523–4.783 m^(2)/g.While the values of PV and SSA obtained by CO_(2)-adsorption are 0.037–0.039 cm^(3)/g and 106.016–111.870 m^(2)/g.Soft coal shows greater SSA and PV than hard coal,which is consistent with the adsorption capacity(VL).The fractal dimensions of soft and hard coal are respectively diferent.The Ding coal exhibits larger D1 and smaller D_(2),and the reverse for the Wu coal seam is observed.The greater the value of D1(complexity of pore surface)of soft coal is,the larger the pore surface roughness and gas adsorption capacity is.The results enable us to conclude that the characterization of pores and fractal dimensions of soft and hard coals is diferent,tending to diferent adsorption/desorption characteristics.In this regard,the results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Experimental investigations on effects of gas pressure on mechanical behaviors and failure characteristic of coals

The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction.In this study,triaxial compression and seepage tests were carried out on coal at different gas pressures.The mechanical properties and failure process of coal were studied,as well as the acoustic emission(AE)and strain energy.The influence of gas pressure on the mechanical parameters of this coal was analyzed.Based on the conventional energy calculation formula,the pore pressure was introduced through the effective stress formula,and each energy component of coal containing gas was refined innovatively.The contribution of gas pressure to the total energy input and dissipation during loading was quantitatively described.Finally,the influence of gas pressure on coal strength was theo-retically analyzed from the perspectives of MohreCoulomb criterion and fracture mechanics.The results show that the total absorbed energy comprises the absorbed energy in the axial pressure direction(positive)and in the confining pressure direction(negative),as well as that induced by the pore pressure(initially negative and then positive).The absorbed energy in the axial pressure direction accounts for the main proportion of the total energy absorbed by coal.The quiet period of AE in the initial stage shortens,and AE activity increases during the pre-peak stage under high gas pressure.The fractal characteristics of AE in three stages are studied using the correlation dimension.The AE process has different forms of self-similarity in various deformation stages.

FRACTAL CHARACTERISTICS OF AERODYNAMIC FIELD AT OUTLET OF LOW-NO_x COAXIAL SWIRLING BURNER

The primary wind of a low-NO_x coaxial swirling burner was visualized byusing glycol as smog tracer. The information of the visual flow field was input into a computerthrough image-capturing card with CCD camera as the image-capturing element. The boundary of thevisual zone, i. e. , the interface of the primary wind and secondary wind was obtained by imageprocessing. The fractal dimension (FD) of the boundary was examined and found to vary from 1. 10 to1. 40 with S_1, S_2 and ζ_1 . It is concluded that when FD is small, the complex level of theinterface is low, and mixture between the primary and secondary wind is weak near the exit of theburner at the initial phase of combustion resulting in stratified flow; when FD is big, mixturebecomes strong near the exit of the burner. It is showed that the flow with FD ranging from 1.10 to1. 20 is stratified flow, which is benefical to reduce NO_x yield and the flow with FD from 1. 25 to1. 40 is mixed flow, producing much NO_x. The mechanism of the forming of stratified flow and mixedflow was theoretically analyzed. The corresponding S_1 , S_2 and ζ_1 of these flows were given.

Characteristics and classification of paleozoic tight reservoirs in the central uplift of the South Yellow Sea Basin

Several sets of Paleozoic tight reservoirs are developed in the Central Uplift of the South Yellow Sea Basin.A qualitative analysis of the microscopic pore structure of the tight reservoir rocks was carried out through cast thin slice and scanning electron microscopic image observation.Based on reservoir pet-rophysical properties,thirty core samples in the Central Uplift of the South Yellow Sea Basin were selected for high-pressure mercury intrusion(HPMI)analysis,which was then combined with fractal calculation to classify and evaluate the tight reservoirs.The analysis of the HPMI curves and related parameters shows that the Paleozoic tight reservoirs can be divided into three types:Type-A,Type-B and Type-C.Type-A sandstone reservoirs contain pores with size mostly ranging between 0.01 and 0.1 mm,followed by pores with size range of 0.001-0.01 m m,and relatively fewer pores larger than 0.1 m m.The Type-B reservoirs are carbonate rocks with extremely heterogeneous pore size distribution,which is closely related to the development of dissolution pores and microfractures.Type-C sandstone reservoirs are dominated by nanopores and submicron pores that distribute more heterogeneously than pores in Type-A reservoirs.The pore distribution in sandstone reservoirs shows significant fractal characteristics and is closely related to the pore size.The heterogeneity of nanopore distribution has a negative cor-relation with porosity and median pressure and a relatively weak correlation with permeability.Our study has important implications for petroleum exploration in the South Yellow Sea Basin.

Multi-scale Kalman filters algorithm for GPS common-view observation data based on correlation structure of discrete wavelet coefficients

Global positioning system(GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS commonview observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0<H<1,the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difference can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.