Failure probability analysis of coal crushing induced by uncertainty of influential parameters under

J.Cent. South unix.(2014)21:2487-2493DoI:10.1007/s11771-014-2203-12 SpringerFailure probability analysis of coal crushing induced by uncertainty ofinfluential parameters under condition of in-Situ reservoirZHANG LI-song(张立松y, YAN Xiang-zhen(闫相祯), YANG Xiu-juan(杨秀娟TiAn Zhong-lan(田中兰)2 YANG Heng-lin(杨恒林1. College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266580, China2. Institute of Drilling and Technology, China National Petroleum Corporation, Beijing 100097, Chinao Central South University Press and Springer-Verlag Berlin Heidelberg 2014Abstract: The uncertainties of some key influence factors on coal crushing, such as rock strength, pore pressure and magnitude andorientation of three principal stresses, can lead to the uncertainty of coal crushing and make it very difficult to predict coal crushingunder the condition of in-situ reservoir. To account for the uncertainty involved in coal crushing, a deterministic prediction model ofoal crushing under the condition of in-situ reservoir was established based on Hoek-Brown criterion. Through this model, keyinfluence factors on coal crushing were selected as random variables and the corresponding probability density functions werdetermined by combining experiment data and Latin Hypercube method. Then, to analyze the uncertainty of coal crushing, the firstorder second-moment method and the presented model were combined to address the failure probability involved in coal crushinganalysis. Using the presented method, the failure probabilities of coal crushing were analyzed for wS5-5 well in Ningwu basinChina, and the relations between failure probability and the influence factors were furthermore discussed. The results show that thefailure probabilities of Ws5-5 CBM well vary from 0.6 to 1.0; moreover, for the coal seam section at depth of 784.3-785 m, thegrowth relationships with the increase of principal stress difference and the decrease of uniaxial compressive streng esents nonlinearfailure probabilities are equal to l, which fit well with experiment results; the failure probability of coal crushing presents nonlinearKey words: coal crushing; failure probability; Hoek-Brown criterion; first-order second-moment methodit is necessary to utilize probabilistic methods1IntroductionAlthough probabilistic methods habeeenhe oil industto estimate theUnder the condition of in-situ reservoir, prediction expected value of a project, their application to predictn coal crushincritical problem associated with coal crushing under the condition of the in-situ reservoirdrilling risks in the CBM drilling engineering industry, has not been reported [1]. To date, some studies onwhich has yet to be fully understood and addressed. Coal uncertainty problems applied in drilling engineeringcrushing is affected by some important parameters, industry have been concluded. SHENG et al [2] adoptedincluding the rock strength, pore pressure and magnitude the Monte Carlo uncertainty analysis technique to assessand orientation of three principal stresses, etc. One of the not only the probability of achieving a desired degree ofmost significant problems remaining, which handicaps wellbore stability at a given mud weight, but also thehe prediction of coal crushing under the condition of effects of the uncertainty in each parameter on thein-situ reservoir, is the uncertainty of the key influence stability of the wellbore. RIttO et al [3] presented aparameters upon coal crushing. Uncertainty in any of procedure to perform the identification of thethese parameters will result in uncertainty in prediction probabilistic model of uncertainties in a bit-rockof the coal crushing problem. Because of the uncertainty interaction model for the nonlinear dynamics of a drillinvolved in coal crushing analysis, the use of averaged string. LU and BAK [4] performed probabilistic analysisvalues for the input parameters in the deterministic of underground rock excavations using response surfaceapproaches can lead to conclusions that significantly method and SORM, in which the quadratic polynomialdiffer from the true behavior. Therefore, to quantify the with cross terms is used to approximate the implicit limiteffects of these uncertainties on coal crushing prediction, state surface at the design point. MOOS et al [5]Foundation item: Project(51204201) supported by the National Natural Science Foundation of CIsupported by the National Science and Technology Major Program of China; Pre中国煤化工x×00370Research Program of China; Project(1ICX04050A)supported by the FundamentalC NMH Gersities of ChinaReceived date: 2013-01-31: Accepted date: 2013-07-14CorrespondingauthorYanXiang-zhen,prOfessor,Phd:Tel:+86-532-86981321;E-mail:yanxzh@163.com2488J.cent. South univ.(2014)21:2487-249demonstrated the use of quantitative risk assessment to is crushed into several fragments with approximatelyformally account for the uncertainty in each input equal size; 2)Rock is crushed into a larger fragment andparameter to assess the probability of achieving a desired several smaller fragments; 3) Rock is crushed into adegree of wellbore stability at a given mud weight. single fragment whose size is almost equal to the originalAdditionally, the literatures show that only few studies rock size and resultant fine particles.were found to predict coal crushing under the conditionAccording to field geologically measured data, coalof in-situ reservoir. On the contrary, there were a series crushing under the condition of in-situ reservoir can beof studies of drilling technologies on improving rock considered as the first type of crushing (Fig. 1(a))breaking efficiently during drilling process, such as Therefore, the key step in the prediction of coal crushinelectron beam, laser, plasma, rock hot melting, high is to determine the appearance of fracture surface. Thispressure thin water jet and particle impact rock breaking characteristic on coal crushing agrees well with6-10]. Considering the essential difference between destruction phenomenon of rock samples under therock breaking during drilling and coal crushing condition of triaxial compression experiment. As aprediction under the condition of in-situ reservoir. theconsequence of this, it is fully feasible to select theresearch results on rock breaking are not appropriate to failure criteria to predict coal crushingbe applied in coal crushing predictionIn this work, a deterministic prediction model of 3 Deterministic prediction model of coalcoal crushing was established based on Hoek-Browncrushing based on Hoek-Brown criterionuncertainties had a significant impact on the model 3.1 Hoek-Brown criterionoutput were selected as random variables. Then, toIn rock mechanics and rock engineering, thecalculate the failure probability of coal crushing, it was Hoek-Brown criterion has been used most widelynecessary to utilize first-order second-moment method. because 1)it has been developed specifically for rockCombined with the presented method, the prediction of materials and rock masses, 2)its input parameters can befailure probability of coal crushing for WS5-5 CBM well determined from routine unconfined compression testsin Ningwu basin, China, was carried on. The effects of mineralogical examination and discontinuityprincipal stress difference and uniaxial compressive characterization, and 3)it has been applied for over 20strength on the failure probability of coal crushing were years by practitioners in rock engineering, and has beenthen studiedapplied successfully to a wide range of intact andfractured rock types [11-12]. For jointed rock masses,2 Description of coal crushingthe Hoek-Brown strength criterion is given byRock crushing is a rather complex preO1=(1)in geometry size change from large size rock into smallsize rock, gravel, or rock dust. The process can bedescripted as follows: 1)Large size rock generateswhere o is the unconfined compressive strength of thefractures under the effect of highly localized stress fieldintact rock; o and o3, respectively, are the maximum2) Fractures propagate to form fracture surfaces; 3)and minimum effective principal stresseFormed fracture surfaces cut large size rocks whichmaterial constant for the rock mass and s is a constantleads to rock crushing. It includes three types of rockthat depends on the characteristics of the rock mass. Thematerial constants m and s can be estimated fromcrushing, as shown in Fig. 1relations between mb and s and geological strength indexFigure 1 shows the three types of crushing: 1) Rock(GSD[13-14-1009-3Dwhere d is a中国煤化工 the degree ofFig 1 Crushing types of rock:(a) Type 1; (b)Type 2;(c)Type disturbance toYHCNMHGenby blast damage and stress relaxation. It varies from 0 forJ.Cent. South univ.(2014)21:2487-2493undisturbed in situ rock masses to l for very disturbed different depth, the primary purpose of carrying onprincipal stress test was to determine the correspondingdistribution type and standard deviation, instead of mean3.2 Coal crushing prediction modelThe mean of principal stress could be obtained byTo describe the coal crushing degree, prediction logging datamodel of coal crushing is established and coal crushincoefficient is defined based on Hoek-Brown criterion, Table 1 Distribution types of random variables by exdemonstrated that coal has been crushed when (>118.50*0.940*0.05085=1B+y25+y37where B, s, n are key parameters for coal crushing, as29.85*15960.0535seen in Eqs. (6)-( 8): 71, 72, 73 are the weight coefficientscorresponding to B, s, n, respectivelyNormal0.0120.001—Unit:MPaOAlthough the representative distributions of therandom variables have been obtained through measured[o3] f(o,oci, mb,S,adata, in reality, such field data were sparse and rare, and(7) hence not sufficient to exhibit the distributioncharacteristics of the random variables. Therefore, a key01-03=(01-03)(3+040step before determining distribution type of the randor1l-[o3variables was to generate enough samples. In view ofthis, Latin Hypercube sampling technique [15-16] wasf(o18)renren ced to generate plenty of samples, and therepresentative distributions of the random variables wereMany research results have proved that some rock given by probability distribution functions specified byparameters, such as oH, Oh, Oci, m; and s, have obvious means of the minimum, the maximum, and the mean ofuncertainties, and these uncertainties lead to uncertainty each variable [5]. Similar functions were adopted in thisof coal crushing. Therefore, to analyze the failure research, as shown in Fig. 2. They were normal curvesprobability of coal crushing, the parameters, including OH, depending on the minimum and the maximum valuesOh,Oci, m; and s, are specified as random variableswere symmetrical (e.g. in situ stresses) with respect tothe mean. In this case. the functional form of the4 Determining distribution types of random distribution was defined by the assumption that 99% ofvariables by experimentthe possible values lied betwminimum input values[17]the distribuvariables, the vertical and horizontal cylindrical cores 5 First-order second-moment method towere cut from each large coal block from ws5 wellcalculate failure probability of coalNingwu block, China,crushingcirculating/ cooling fluid. Each sample was 2.5 cm indiameter and 5.0 cmth. In a few instances, onlyThe first-order second-moment method [18-19]small amount of samples could be extracted from the FOSM, was extensively used in geotechnical engineeringblocks due to difficulties in obtaining an intact test to solve failure probability problems. This method wassample. The ends of each core were surface-ground flat based on reliability index concept, safety factors andand parallel within a tolerance of +0.0004 cm, in performance function. In this work, the method waaccordance with ISRM (International Society of Rock introduced to calculate failure probability of coalmechanics)standardscrushing under the condition of in-situ reservoir. Also,Through indoor experiment, small plenty of test combined with the calculation formula of crushingdata on random variables of coal crushing were obtained. coefficient, the performance function of coal crushinThen, the relative data were analyzed and the distribution problem is giver中国煤化工types, mean, standard deviation and coefficient ofCNMHGvariation of random variables are presented in Table 1G=1-Due to the obvious variation of principal stress at theSubstituting Eq. (5)into Eq (9), the performance2490J.cent. South univ.(2014)21:2487-24930.300.005HistogramProbability density0.004Probabilitydensityfunction30.0030.150.0020.050.00117.519.018.018.5Maximum principal stress/MPaMinimum principal stress/MPa0.180.60.5tyProbabilitytydensityfunction00.060.20.02013.514.014.515.015.516.016.517.0Uniaxial compressive stress/MPaCoal material constantProbability density2.0Fig. 2 Probability density functions(a) Maximum principal stress;(b) Minimum(e)Coal material constant, S0.0080.0100.0120.0140.016Coal material constant. Sfunction G can be further expressed asassume that the mean and standard deviation offunction G are uG and SG, respectively. The reliabilityy101index B can be expressed as(11)n2f(o, oci, mh, s, a)where ur and S present the mean and standard deviationof crushing coefficient s, respectivelyy3(o1-a3)hen, failure probability F of coal crushing can be(10)中国煤化工+0f(o, oci, mb, S, aCNMHGF=1-d()=4(12)J.Cent. South univ.(2014)21:2487-24932491where is the normal cumulative distribution 6.2 Failure probability of coal crushing for WS5-5In this work, the failure probabilities of coal6 Results and discussioncrushing for wS5-5 well in Ningwu basin, China, werecalculated, and the results are shown in Fig. 46.1 Principal stress prediction of coal seam for wS5Failure probability of coal crushingTo calculate the failure probability of coal crushinalong the borehole direction, the mean of principalstresses at different depths should be obtained firstly. ForWS5-5 well, the buried depth of coal seam was locatedin a range of 780-785 m. Therefore, according to thelogging data of coal seam section of WS5-5, the mean ofprincipal stress with different depth was predicted by783layered ground stress model. The results are shown inFig 3780785Fig. 4 Failure probabilities of coal crushing for wS5-5 welIt can be seen from Fig. 4 that the failureprobabilitfrom 0.6 to 1.0. Forthe sections of 780-781 m and 783-784.3 m, the results与783or thes section of 781-783 m, the range of failure probabilitieslies between 0.7 and 0.9. For the section of 7843-78.5 mthe failure probabilities are equal to l, which agree wellwith experiment phenomenon of coal crushing with18.3.518.7scanning electron microscopy for wS5-5 wellMaximum principle stress/MPa6.3 Parametric study on failure probability of coalcrushingprobabilitycrushing were studied based on the presented method782The parameters include in-situ stress difference, anduniaxial compressive strength. In the parametric study,783only one parameter changed while all other parameterskept the same value784The effects of in-situ stress difference and uniaxialcompressive strength on failure probability of coal16.216.16.616.817.0Figure 5(a) shows that as the stress differenceMinimum principle stress/MPaincreases, the failure probability increases in a non-linearFig. 3 Means of principal stresses of ws5-5 well: (afashion. when the stress difference changes from Ao toMaximum principal stresses;(b) Minimum principal stresses1.1△σ,1.3△oand1.5△a, the failure probability increasesby 8.22%0, 14.99%0, 42.60% more than the original resultsThe calculation results show that the mean of thecom calculated at stress difference of Ao, respectively(at amaximum principal stresses for coal seam ranges from depth of 783 m). When stress difference increases to18.3 MPa to 18.9 MPa; the mean of the minimum 1he failure probabilities with a depth section ofprincipal stresses for coal seam varies between 16.2 MPa1 m783-785 m are equal to 1. Thisand 17.0 mPa. meanwhile, it should be noted that for中国煤化工 an Importantcoal seam section of 783. 4-785 m, the maximum and impact on the faCNMH Ghingminimum principal stresses are much higher than thoseAs seen from rb), with the decrease ofof other sectionsuniaxial compressive strength, the failure probability2492J. Cent. South Univ (2014)21: 2487-249moment method and the presented model are combinedFailure probability of coal crushingto address the failure probability involved in coal0.60.70.8780crushing analysis.2) The failure probabilities of coal crushing of781WS5-5 well in Ningwu basin, China, are analyzed withthe presented method. The range of failure probabilityvaries from 0.6 to 1.0. For the section of 784.3-785 m782the failure probabilities of coal crushing are equal to 1which agrees well with indoor experiment results. The8783failure probabilities are higher for the roof and floor coalStress differenceseam, but are relatively lower for the central coal seam7841.1△a3)The relationships between failure probabilities4-1.3△oand in-Situ stress difference, uniaxial compressive-1.5△o785strength are investigated. With the increment of in-situFailure probability of coal crushingstress difference and decrease of uniaxial compressive0.80.9strength, the failure probability of coal crushing780increases in a non-linear fashionReferences782[1 ADEL M AA, MANSOOR H A H. Probabilistic wellbore collapsealysis [J]. Journal of Petroleum Science and Engineering, 2010,783[2 SHENG Y, REDDISH D, LU Z. Assessment of uncertaintiesUCSwellbore stability analysis [J]. Modern Trends in Geomechanics,29,85MPa06:541-55727.85MPT G SOIZEB C, SAMPAIOA R. 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