基于热力学模型的煤孔隙结构分形表征

第42卷第6期煤田地质与勘探Vol.42No.62014年12月COALGEOLOGY&EXPLORATIONDec.2014收稿日期:2013-06-19基金项目:(2009ZX05062-0092011ZX05062-009)作者简介:(1987)文章编号:1001-1986(2014)06-0020-04基于热力学模型的煤孔隙结构分形表征王秀娟，要惠芳，李伟，张晓辉，阎纪伟(太原理工大学矿业工程学院，山西太原030024):煤的孔隙结构复杂，难以用传统的欧氏几何理论描述其复杂性，而分形理论可定量表征孔隙结构的复杂程度。通过对渭北煤田韩城矿区10个煤样进行的压汞实验，采用热力学分形模型，获得了煤的渗流孔的分形维数，定量表征了煤的孔隙特征，并探讨了分形维数与渗透率的关系。研究表明：对于同等变质程度的煤来说，煤中吸附孔越多，孔隙分形维数越大；煤孔隙分形维数与渗透性呈负相关关系。由此可见，煤的渗流孔分形维数可作为煤储层渗透性评价的定量指标之一。：孔隙结构；压汞；分形维数；热力学模型：P618.13：ADOI:10.3969/j.issn.1001-1986.2014.06.004FractalcharacterizationofporestructureincoalsbasedonthermodynamicsmodelWANGXiujuan,YAOHuifang,LIWei,ZHANGXiaohui,YANJiwei(CollegeofMiningEngineering,TaiyuanUniversityofTechnology,Taiyuan030024,China)Abstract:TheporestructureofcoaliscomplexanditisdifficulttocharacterizeporestructurebytraditionalEuclideangeometry.However,fractaltheoryisaneffectivemethodtoinvestigatetheirregularitiesofporestructure.Thefractaldimensionsofseepage-poresof10coalsamplescollectedfromHanchengminingareainWeibeicoalfieldwereobtainedusingmercuryinjectionexperimentbaseduponthermodynamicfractalmodelandthegeometricpropertiesofporewerequantitativelycharacterized.Therelationshipbetweenfractaldimensionandpermeabilitywasalsodiscussed.Theresultsshowthatthemoreadsorption-pores,thehigherfractaldimensionforthesamecoalrank.Thefractaldimensionhasanegativecorrelationwiththepetrologicpermeabilityofcoal.Thefractaldimensionofseepage-poresofcoalscanbeusedasoneofthequantitativeindexesforevaluationofpermeabilityofcoalreservoir.Keywords:porestructure;mercuryinjection;fractaldimension;thermodynamicmodel(100nm)(100nm)[1]()[2-3]X[4-7][8-14]Friesen[10]2~3Friesen[10][11][12]1煤样与实验方法–(XS)5(SSP)2(XYK)2(WL1)1(1)GB/T212—2008GB/T476—20080.58%~1.06%4.01%~20.57%13.11%~18.12%67.38%~91.35%2.96%~4.13%(1)第6期王秀娟等:基于热力学模型的煤孔隙结构分形表征·21·表1煤样基本信息Table1Informationofcoalsamples/%/%MadAdVdafCdHdXS1110.8420.5716.0767.382.96XS250.964.0213.1191.354.10XS350.8713.8015.3477.273.64XS4110.6614.0614.8574.353.11XS531.066.2912.9985.613.66SSP130.8911.2916.3479.713.53SSP2110.586.1416.8982.643.98XYK130.665.6116.3684.053.30XYK2110.8112.0418.1276.523.12WL1-1110.4510.2213.2479.374.13SY/T534619949520(2)0.008~49.96MPa92~0.015μm75℃48h表2煤样压汞孔隙参数和分形维数Table2Mercuryporosimetryparametersandcalculatedfractaldimensionofporestructure/%/%/μm/%/%100nm100nmDR2XS110.612.63255.7490.3252.7847.222.5140.998XS25.312.49941.9890.3235.4964.512.5340.987XS34.512.06835.3087.8027.2372.772.5970.999XS44.112.45235.1187.5927.7172.292.6380.998XS52.811.61121.8882.2415.3884.622.6460.982SSP110.612.64175.8198.4872.4927.512.5130.998SSP24.011.56724.8275.2617.9282.082.6670.991XYK15.312.63247.5487.9033.9266.082.5590.996XYK24.011.75424.4475.1717.6582.352.6670.991WL1-12.611.24919.7267.3614.9585.052.7020.9822热力学分形模型[12]LddcosdWPVS(1)WJγLJ/mθ(°)Sm2QnWnnnln()ln()WQC(2)[13](2)(3)1/3nn2nnln()ln()WVDCrr(3)VnD(ln(Vn1/3/rn)ln(Wn/rn2))(1)3结果与讨论3.1Mahamud[14]10MPa10MPa10MPa(0.1μm)(12)·22·煤田地质与勘探第42卷1ln(Wn/rn2)ln(Vn1/3/rn)Fig.1Plotsofln(Wn/rn2)vs.ln(Vn1/3/rn)frommercuryporosimetrydata2.514~2.703WL1-1[15-16](100nm)(2)2Fig.2Therelationshipbetweenadsorption-porecontentandfractaldimensionforcoalsamples3.2[1]432222123243212[35(21)]8[(21)]8nniikrrrnrnirn(4)k10–3cm2)φn(n=10)ricm)r1r2rn221[(21)/(21)]100nniiirir(5)(5)第6期王秀娟等:基于热力学模型的煤孔隙结构分形表征·23·1µm[1]1µm(2)(3)33Fig.3Therelationshipbetweenpermeabilitycontributionandfractaldimensionforcoalsamples4结论a.b.参考文献[1].[J].200634(3)64–68.[2].[J].200028(6)20–22.[3].[J].201240(4)29–33.[4]CAIYidongLIUDamengPANZhejunetal.PorestructureanditsimpactonCH4adsorptioncapacityandflowcapabilityofbituminousandsubbituminouscoalsfromNortheastChina[J].Fuel2013103258–268.[5]YAOYanbingLIUDamengTANGDazhenetal.Fractalcharacterizationofadsorption–poresofcoalsfromNorthChinaaninvestigationonCH4adsorptioncapacityofcoals[J].InternationalJournalofCoalGeology200873(1)27–42.[6]RADLINSKIAPMASTALERZMHINDEALetal.ApplicationofSAXSandSANSinevaluationofporosityporesizedistributionandsurfaceareaofcoal[J].InternationalJournalofCoalGeology200459(3)245–271.[7].[J].201338(3)441–447.[8]MANDELBROTBB.HowlongisthecoastofBritain?Statisticalself-similarityandfractionaldimension[J].Science1967156636–638.[9]LEEGJPYUNSIRHEECK.Characterisationofgeometricandstructuralpropertiesofporesurfacesofreactivatedmicroporouscarbonsbaseduponimageanalysisandgasadsorption[J].MicroporousandMesoporousMaterials200693(1)217–225.[10]FRIESENWIMIKULARJ.Fractaldimensionsofcoalparticles[J].JournalofColloidInterfaceScience1987120(1)263–271.[11]PFEIFERPAVNIRD.Chemistryinnonintegerdimensionsbetweentwoandthree.I.Fractaltheoryofheterogeneoussurfaces[J].TheJournalofChemicalPhysics198379(7)3558–3565.[12]ZHANGBaoquanLIShaofen.Determinationofthesurfacefractaldimensionforporousmediabymercuryporosimetry[J].Industrial&EngineeringChemistryResearch199534(4)1383–1386.[13]ZHANGBaoquanLIUWeiLIUXiufen.Scale–dependentnatureofthesurfacefractaldimensionforbi–andmulti–disperseporoussolidsbymercuryporosimetry[J].AppliedSurfaceScience2006253(3)1349–1355.[14]MAHAMUDMM.Texturalcharacteriza