ReconstructionandAnalysisofTightSandstoneDigitalRock...

Research ArticleReconstruction and Analysis of Tight Sandstone Digital RockCombined with X-Ray CT Scanning and Multiple-PointGeostatistics Algorithm

Yun Lei 123

1Shenyang Research Institute China Coal Technology amp Engineering Group Corp Fushun 113122 China2State Key Laboratory of Coal Mine Safety Technology Fushun 113122 China3School of Emergency Management and Safety Engineering China University of Mining and Technology Beijing 100083 China

Correspondence should be addressed to Yun Lei yunlei_78163com

Received 6 January 2020 Revised 2 April 2020 Accepted 21 April 2020 Published 23 June 2020

Academic Editor Vassilios Constantoudis

Copyright copy 2020 Yun Lei )is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Unconventional rocks such as tight sandstone and shale usually developmultiscale complex pore structures with dimensions rangingfrom nanometers to millimeters and the full range can be difficult to characterize for natural samples In this paper we developed anew hybrid digital rock construction approach to mimic the pore space of tight sandstone by combining X-ray CT scanning andmultiple-point geostatistics algorithm (MPGA) First a three-dimensional macropore digital rock describing the macroscopic porestructure of tight sandstone was constructed by micro-CTscanning)en high-resolution scanning electron microscopy (SEM) wasperformed on the tight sandstone sample and the three-dimensionalmicropore digital rock was reconstructed byMPGA Finally themacropore digital rock and the micropore digital rock were superimposed into the full-pore digital rock In addition the nuclearmagnetic resonance (NMR) response of digital rocks is simulated using a random walk method and seepage simulation wasperformed by the lattice Boltzmannmethod (LBM))e results show that the full-pore digital rock has the same anisotropy and goodconnectivity as the actual rock )e porosity NMR response and permeability are in good agreement with the experimental values

1 Introduction

Looking around the world with the depletion of con-ventional fossil energy unconventional hydrocarbon re-sources will be the most realistic resource type in thischange [1] However the production and development ofunconventional hydrocarbon resources are still facingmany difficulties From the point of view of productionpractice the unconventional reservoir usually has nocommercial production and its development often relies onlarge-scale hydraulic fracturing which has the character-istics of high initial production rapid decline low recoveryand so on [2ndash4] Since the macroscopic phenomena areoften the result of microfactors the rock structure andpercolation mechanism of unconventional reservoirsstudied at microscale are key means to the aforementionedmacroproblems and improve the production capacity

eventually Nevertheless unconventional reservoir rock isusually characterized by low porosity and permeability finepore throat complex pore structure and developed frac-ture network [5ndash7] the laboratory experiment is difficult tocarry out and the routine rock modeling methods such ascapillary model are hard to describe the true and micro-scopic structure of unconventional rocks

In face of these challenges digital rock technology iscurrently expected to be the key to solve the above puzzles inunconventional reservoirs Digital rock technology origi-nated in the 1970s and was proposed for comprehensivelymimicking the real rock by imaging and mathematical al-gorithm which has gradually developed into a promisingtool in the study of porous media [8ndash13] Based on the digitalrock models the microstructure of the rock can be quan-titatively characterized and microseepage simulation can becarried out as well Digital rocks have enabled important

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 9476060 10 pageshttpsdoiorg10115520209476060

breakthroughs in understanding how fluid enters porespaces and the mechanisms of wateroil and gas seepage[14ndash16]

At present the methods of digital rock reconstructionmainly include physical experiments numerical recon-structions and hybrid modeling )ere is an extensiveliterature on these various approaches and we summarizehere their general philosophy and some of their limitationsPhysical experiment methods have high accuracy and arewidely used but are vulnerable to the tradeoff betweenresolution and dimension [17 18] Compared with thephysical experiment method the numerical reconstructionmethod has the advantages of low cost and high efficiencyand can reconstruct different types of digital rocksHowever the drawback of the numerical reconstruction isthat there are some differences between the model and thereal rock [19ndash23] To address the shortcomings of the singlemodeling method some scholars have proposed the idea ofmixing different modeling methods with each other iehybrid modeling methods [24ndash28] For example Talukdaret al combined the truncated Gaussian random fieldmethod (TGRFM) with the characteristic of fast modelingspeed and the simulated annealing method (SAM) with thecharacteristic of more accurate modeling and used theimages generated by TGRFM as input to SAM to establish adigital rock with higher model quality Politis et al and Liuet al reconstructed 3D digital rocks by combining theprocess-based method (PBM) and SAM )e basic processof their modeling is similar First use the PBM to constructthe initial 3D digital rock and then use the initial model asthe input of SAM When the conditions of SAM arereached a hybrid digital rock is generated Compared withthe traditional SAM their method is more efficient inmodeling and the model is more accurate More recentlyLin et al introduced a hybrid modeling method thatcombines physical experiments and numerical recon-struction First a 3D macropore digital rock was con-structed by micro-CT second using high-resolution 2DSEM images a micropore digital rock was constructed bySAM last a superposition method was used to constructthe digital rock including the full range of pore structures)is method not only keeps the accuracy of the macroporeimage but also contains microstructure information Hy-brid modeling methods have improved modeling accuracyand efficiency and overcome some limitations of singlemodeling methods

In this work based on the hybrid method combiningphysical experiments and numerical reconstructions wefurther develop a new combination method that integratedmacropores constructed by X-ray CT and microporesreconstructed by MPGAWe utilized micro-CT to image themacropore structure of tight sandstone and constructed themacropore digital rock and used the SEM to image themicropores of tight sandstone and reconstructed the mi-cropore digital rock using MPGA )rough the superposi-tion of micropore and macropore digital rocks the full-poredigital rock of tight sandstone was obtained and the physicalproperties and seepage characteristics of the digital rockswere compared and analyzed

2 Sandstone Modeling

21 3D Macropore Reconstruction by X-Ray CTComputerized tomography (CT) imaging has the advan-tages of high accuracy and being nondestructive and iswidely used in the field of rock physics [29 30] As illustratedin Figure 1 the working principle of CT is that when X-raysare irradiated and penetrated through the sample the energywill be attenuated differently and the attenuation processaccords with the attenuation formula as follows

I I0eminus1113936i

μixi (1)

In formula (1) I is the intensity after attenuation I0 isthe original intensity μi is the attenuation coefficient ofcomponent i to ray and xi is the length of ray passingthrough component i When X-rays penetrate the samplethe detector detects the attenuated ray intensity and imitatesit on the detector

)e core of CT imaging is to reconstruct the gray imageof the sample)ere are two basic reconstruction algorithmsanalytical method and iterative method At present FDKreconstruction algorithm is more commonly used and theformula of the FDK algorithm is as follows [29 31ndash33]

pprime(β a b) R

RR + aa + bb

radic p(β a b)gn(a)1113888 1113889

FFDK(x y z) 11139462π

0

R2

U(x y β)2pprime(β a b)dβ

a R tan c

b q

cos c

k arctanq

R arctan

bRR + aa

radic

U(x y β) R + x cos β + y sin β

(2)

In formula (2) U(x y β) is the total attenuation coef-ficient q is the length of the projection data in a certaindirection p(β a b) is the collected projection datapprime(β a b) is the weighted filtering of the projection dataFF DK(x y z) is the back projection reconstruction of theweighted filter projection data gn(a) is a one-dimensionalfilter R is the orbital radius c is the fan angle of the conebeam β is the cone angle of the cone beam and a and b arethe positions on the detector

We used an UltraXRM-L200 CT scanner to image themacropores (gt12 μm) of the tight sandstone )e sandstonesample was selected and made into a cylinder with ap-proximately 12mm diameter and 14mm length and itsporosity was 1216 and gas permeability was0413times10minus3 μm2 )e resolution of CT imaging was 12micronpixel and 996 CT grayscale images were obtained)e original grayscale images (Figure 2) were preprocessedthrough contrast enhancement and a median filter We usedan improved threshold segmentation method considering

2 Mathematical Problems in Engineering

pore fractal characteristics to make the optimal segmenta-tion [34] Figure 3 shows a binary image of tight sandstoneby micro-CT (white is pore black is solid) Figure 4 presentsa 3D macropore digital rock obtained by processing CTimages whose physical size is 012mmtimes 012mmtimes 012mmand voxel size is 100times100times100 From CT scanning we cansee that the sample contains primary pores and secondarypores )e primary pores have straight edges clean poreinteriors and large pore radii )e secondary pores mainlyinclude intragranular pores and marginal pores of feldsparand detritus a small amount of dissolved pores in carbonatecements and the intercrystalline pores in clay minerals

22 3DMicropore Reconstruction byMPGA To characterizesmaller pores we imaged the same sample scanned by CTusing scanning electron microscopy (SEM) the imagingresolution of SEM images is 03 micronpixel (Figure 5(a))the same image processing used for the CT images was usedto generate the binary SEM images as shown in Figure 5(b)

Multiple-point geostatistics algorithm (MPGA) wasoriginally used in geostatistics to deal with continuousgeological entities at reservoir scale )e basis of MPGA is toreplace the variation function of two-point geological sta-tistics algorithm with a training image )e basic idea of thisalgorithm is to extract the image patterns of features fromthe training images and then restore these patterns to thefinal model [20 21 35] In this work we used MPGA toproduce micropores in sandstone and the basic steps are asfollows

(1) Using the two-dimensional SEM binary image as theinitial training image the training image is scannedby the determined two-dimensional data template toconstruct a search tree

(2) Extract 05 of the pixel points from the two-di-mensional training image used for each simulation asthe horizontal direction (such as the x-y direction)condition data and assign it to the nearest networknode A two-dimensional slice such as the y-z

(a) (b)

Figure 2 3D grayscale image of the tight sandstone (a) and 2D grayscale image cross section (b)

X-ray source

Z X

X-ray detector

Y

Rotating

Sample

Scanning

Figure 1 Schematic diagram of X-ray CT imaging [28]

Mathematical Problems in Engineering 3

Figure 3 Binary image of tight sandstone by micro-CT (white is pore black is solid)

Figure 4 3D macropore digital rock using X-ray CT scanning method (blue is solid green is pore black is background)

(a) (b)

Figure 5 Grayscale image (a) and binary image (b) of tight sandstone by SEM (white is pore black is solid)


direction or the x-z direction is selected as a verticaldirection condition for simulation

(3) Sequentially access all the nodes to be simulated withthe determined random path and for each node onthe path the condition data event is extracted to-gether with the data template of the same size in step(1) and the condition data obtained in step (2) )econditional probability distribution function is ob-tained from the search tree and the Monte Carlomethod is used to extract the simulated value of thepoint the simulation is continued as a new conditionof the subsequent simulation until the two-dimen-sional image is generated

(4) )e two-dimensional image simulated in step (3) isused as the training image to continue the simulationin the next step and the first three steps are repeateduntil the next layer of the image is generated

(5) Repeat the first 4 steps until the simulation yields Nnew two-dimensional images

In the process of simulation the edge processing of thereconstructed image uses the target edge probability func-tion Since the simulated digital rock has only two parts ofthe pore and the skeleton the porosity of the two-dimen-sional SEM binary is used as its target edge value and theservosystem is used to ensure the accuracy of the simulationresults )e simulated N images are sequentially super-imposed to obtain a three-dimensional digital rock ofNtimesNtimesN For the processing of excessive condition datathe method of setting the lower limit value is adopted If thenumber of repetitions obtained by scanning the trainingimage using the template is lower than the lower limit valuethe condition data farthest from the center point is removedthe data are rescanned until the set lower limit value isreached and then the conditional probability value of thepoint is obtained at this time For the processing of only oneconditional data the edge probability at this time can beused as the conditional probability

Figure 6 shows the micropore digital rock constructed bythe MPGA whose physical size is 012mmtimes 012mmtimes

012mm and the voxel size is 400times 400times 400

23 Full-Pore Model We used the superposition method[27] to integrate two digital rocks According to the reso-lution ratio of the macropore digital rock to microporedigital rock i (i 4) the voxels of macropore digital rockwere divided into itimes itimes i voxels )e voxel refinement di-agram is shown in Figure 7

)e pores of both digital rocks are superimposed andthe superimposed pores IS is

IS IAUIB (3)

where IA and IB represent the pore space of macroporedigital rock andmicropore digital rock respectively Becausethe pore pixels and solid pixels of the binary image arecharacterized by 0 and 1 respectively the superpositionoperation is

0 + 0 0

0 + 1 0

1 + 0 0

1 + 1 1

(4)

Figure 8 presents the full-pore digital rock of tightsandstone constructed by the superposition method whosevoxel size is 400times 400times 400 and resolution is 03 micronpixel

3 Structural Characteristics of theSandstone Model

31 Connectivity Analysis We calculate the porosity of thedigital rocks by using the following equation

ϕ Vp

Vp + Vs

(5)

where Vp is the volume of all pores which contains theconnected pores and the dead pores in the digital rock m3Vs is the volume solid matrix m3 Here the pore volume andsolid matrix volume of digital rocks are calculated bycounting the number of voxels labeled as 0 and the numberof voxels labeled as 1 respectively

We evaluated the connectivity of digital rocks using theconnected porosity Connected porosity ϕc is defined by thefollowing formula

ϕc Vprime

Vp + Vs

(6)

where Vprime is the volume of connected pores m3)e calculation results are shown in Table 1 )e results

show that the porosity of the full-pore digital rock is slightly

Figure 6 3D micropore digital rock by MPGA (blue is pore red issolid)


higher than that of the macropore digital rock and themicropore digital rock )e connected porosity of the full-pore digital rock is significantly higher than that of the othertwo digital rocks which proves that the addition of mi-cropores improves the pore connectivity of digital rock Inaddition the porosity of the full-pore digital rock is higherthan the measured porosity of the actual rock and theconnected porosity is close to the measured porosity whichis consistent with the fact that the laboratory uses nitrogen tomeasure the rock porosity and the isolated pore cannot bemeasured )e measured porosity is actually equal to theconnected porosity Due to the strong heterogeneity of the

tight sandstone pore structure a single simulation methodcannot capture the total pore volume while the full-poredigital rock has better pore connectivity and better con-sistency with the actual rock in terms of connected porosity

32 NMR Response In this section a random walk methodis used to simulate the nuclear magnetic resonance (NMR)[36] )is involves simulating the Brownian motion of adiffuse particle called a walker )ese walkers diffuse in thepore space and when they come in contact with asolid surface their chances of being killed are limited )e

Table 1 Porosity comparison between digital rocks and real sandstone

Parameters Macropore digital rock Micropore digital rock Full-pore digital rock Real rockPorosity () 1123 1176 1383 mdashConnected porosity () 919 1047 1181 1216

i

i

i

Figure 7 Schematic diagram of voxel refinement

Figure 8 Full-pore digital rock of tight sandstone by the new method (blue is solid green is void black is background)


life-time distribution of the walkers is a decay in magneti-zation which can be inverted to a T2 distribution by using acurvature-smoothing regularization method [37]

It is acknowledged that the short T2 time in the T2spectrum represents the small pore space and the long T2time represents the big pore space [38ndash40] We comparedthe results of the laboratory NMR test on the sandstonesample with the simulation NMR results on digital rocks)e laboratory NMR test was carried out on the tightsandstone core saturated with water using the low-fieldNMR detection device (MacroMR12-150H-I NiumagChina) and the NMR test mainly refers to the core analysismethod (GBT 29172-2012 China) and the laboratorymeasurement specification of NMR parameters of rocksamples (SY-T6490-2014 China) From Figure 9 we can seethat tight sandstone has typical dual pore characteristicsshowing the bimodal distribution on the NMR T2 spectrumSimulation results of the digital rocks show that the T2distributions of the macropore and micropore digital rocksare narrower and have single modal distributions the T2value of micropore digital rock is mainly distributed in theshort T2 time range and the T2 value of macropore digitalrock is dominant in the long T2 time implying that themacropore digital rock mainly mimics the relatively largepores while the micropore digital rock mainly mimics therelatively small pores For the full-pore digital rock thesimulated T2 distribution has a bimodal distribution andshows good agreement with the experimental result al-though there is a small difference as is attributed to the lossof some fine details of the pore structure (lt03 microns) intight sandstone

By comparative analysis it can be seen that single res-olution imaging and single modeling method cannot re-construct the pore structure and restore connectivity of tightsandstone digital rock Combined with X-ray CT and SEMwe can capture micropores and macropores in a completemodel using the hybrid modeling method On the whole thefull-pore digital rock shows good performance in themultiscale pore structure simulation of tight sandstone Atthe same time in the study of tight reservoir we should alsopay special attention to the influence of submicron pores onrock seepage ability

4 Seepage Properties

We carried out the permeability evaluation on digital rocksby using the lattice Boltzmann method (LBM) [27 41 42])e LBM utilizes the collision and migration of virtualparticle swarms with different velocity directions on discretespatial grid points to characterize fluid flow which caneffectively simulate complex flows such as porous mediaflow convection current and multiphase flow LBM is amesoscopic method and the basic idea of this method isbased on the theory of molecular dynamics )ere are threecommonly used 3D lattice Boltzmann models which aredivided according to the number of discrete velocity com-ponents in 3D space in the direction of fluid continuousmotion Generally the common dispersion is 15 19 and 24components corresponding to D3Q15 D3Q19 and D3Q24

models respectively )e more discrete velocity compo-nents the higher the accuracy of the numerical simulationbut at the same time it brings the calculation problems suchas large amount of data and slow simulation speed Here weadopt the D3Q19 3D lattice Boltzmannmodel and Figure 10shows the lattice structure and the velocity discrete Boltz-mann-BGK equation is as follows

fi(r t) minus fi r + eiδt t + δt( 1113857 1τ

fi(r t) minus feqi(r t)1113960 1113961

(7)

where fi(r t) is the distribution function of the particle inthe i direction at t time and position r(x y z) ei is thevelocity in the i direction τ is the relaxation time and δt isthe time step feqi(r t) is the equilibrium distributionfunction

)e discrete velocity direction is as follows

ei

(0 0 0) i 0

(plusmn1 0 0) (0 plusmn1 0) (0 0 plusmn1) i 1 6

(plusmn1 plusmn1 0) ( plusmn1 0 plusmn1) (0 plusmn1 plusmn1) i 7 18

⎧⎪⎪⎨

⎪⎪⎩

(8)

Equilibrium distribution function is as follows

feqi(r t) ρωi 1 +eiu

c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)

where cs is the lattice sound velocity dimensionless with cs

13

radicand ωi is the weight factor ωi 13 i 0 ωi

118 i 1 6 ωi 136 i 7 18Local macrolattice density ρ(r t) lattice velocity u(r t)

lattice pressure p(r t) and lattice viscosity μ(r t) can berepresented by

ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)

u(r t) 1113936ifi(r t)ei

ρ(r t)

μ(r t) 2τ minus 16

(10)

)e inlet and outlet boundary is pressure boundary theinitial lattice velocity is 0 and the initial lattice density is 1

We used the LBM to simulate the seepage process ofmacropore digital rock (Figure 4) micropore digital rock(Figure 6) and full-pore digital rock (Figure 8) and obtainedthe inherent permeability of digital rocks )e inherentpermeability of full-pore digital rock is 0377times10minus3 μm2 theinherent permeability of micropore digital rock is0093times10minus3 μm2 and the inherent permeability of macro-pore digital rock is 0216times10minus3 μm2 )e simulation resultsshow that the permeability of full-pore digital rock is largerthan that of micropore digital rock and macropore digitalrock suggesting that micropores can greatly improve theconductivity of digital rocks In addition the calculated


permeability of the full-pore digital rock is consistent withthe experimental result (0413times10minus3 μm2) which shows thatthe permeability of the full-pore digital rock is similar to thatof the real tight sandstone )e permeability ratio of full-pore digital rock to macropore digital rock is 175 whichindicates that micropores have great influence on the per-meability of digital rock model Furthermore we should

fully consider and study the transport characteristics ofsubmicron pores in tight sandstone

5 Conclusions

In this study we proposed a new strategy by combining theX-ray CT scanning method and multiple-point geostatistics

Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000

SandstoneFull-pore DR

Macropore DRMicropore DR

Figure 9 Comparison of NMR response between the simulated results of digital rocks and the experimental result of real sandstone

2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0

Figure 10 D3Q19 lattice structure model


algorithm (MPGA) in digital rock Unlike the existingnumerical reconstruction methods this method is a hybridof physical experiments and numerical reconstruction so itnot only has the accuracy of the physical experiment methodbut also has the convenience of the numerical reconstructionmethod We compared and analyzed the pore structure andseepage characteristics of the full-pore digital rock con-structed by the new hybrid method the macropore digitalrock constructed by the X-ray CT scanning method and themicropore digital rock constructed by MPGA )e resultsshow that the new hybrid method can better simulate thereal rock and the pore structure and seepage properties ofthe full-pore digital rock are basically consistent with thoseof the actual rock In addition this study also shows thatsingle-resolution imaging and the single modeling methodcannot produce the satisfactory digital rock model espe-cially for tight sandstone with a multiscale pore systemFurthermore tight sandstones are generally rich in clayminerals (such as kaolinite illite and chlorite) which hasgreat effect on macroelectrical conductivity elastic modulusand permeability and it is thus an interesting direction toconstruct multiphase multicomponent digital core in thefuture

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interestregarding the publication of this work

Acknowledgments

)is work was financially supported by the National Scienceand Technology Major Project (Grant no 2016ZX05067004-003) )e author thanks Huang Lei and Chengwu Li verymuch for helping with the experiments and paper writing

References

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[2] Z Y Wang Z M Yang Y H Ding W Lin Y He andX Duan ldquoA generalized capillary imbibition model for po-rous media in tight reservoirsrdquo Advances in Civil Engineeringvol 2018 Article ID 4148734 8 pages 2018

[3] J Du H Liu D Ma J Fu Y Wang and T Zhou ldquoDiscussionon effective development techniques for continental tight oilin Chinardquo Petroleum Exploration and Development vol 41no 2 pp 217ndash224 2014

[4] H Zhang Z Shi G Wang X Sun et alC Liu ldquoLargeearthquake reshapes the groundwater flow system insightfrom the water-level response to earth tides and atmosphericpressure in a deep wellrdquo Water Resources Research vol 55no 5 pp 4207ndash4219 2019

[5] X Zhao Z Yang W Lin S Xiong and Y Wei ldquoCharac-teristics of microscopic pore-throat structure of tight oilreservoirs in Sichuan Basin measured by rate-controlledmercury injectionrdquo Open Physics vol 16 no 1 pp 675ndash6842018

[6] X L Zhao Z M Yang W Lin et al ldquoFractal study on porestructure of tight sandstone based on full-scale maprdquo Inter-national Journal of Oil Gas and Coal Technology vol 1 no 12019

[7] K Xie X Lu Q LiW Jiang and Q Yu ldquoAnalysis of reservoirapplicability of hydrophobically associating polymerrdquo SPEJournal vol 21 no 1 pp 001ndash009 2016

[8] M Joshi ldquoA class of stochastic models for porous mediardquoPhD thesis University of Kansas Lawrence Kansas 1974

[9] J A Quiblier ldquoA new three-dimensional modeling techniquefor studying porous mediardquo Journal of Colloid and InterfaceScience vol 98 no 1 pp 84ndash102 1984

[10] S Bryant and M Blunt ldquoPrediction of relative permeability insimple porous mediardquo Physical Review A vol 46 no 4pp 2004ndash2011 1992

[11] R D Hazlett ldquoStatistical characterization and stochasticmodeling of pore networks in relation to fluid flowrdquo Math-ematical Geology vol 29 no 6 pp 801ndash822 1997

[12] C L Y Yeong and S Torquato ldquoReconstructing randommedia II )ree-dimensional media from two-dimensionalcutsrdquo Physical Review E vol 58 no 1 pp 224ndash233 1998

[13] P E Oslashren and S Bakke ldquoReconstruction of Berea sandstoneand pore-scale modelling of wettability effectsrdquo Journal ofPetroleum Science and Engineering vol 39 no 3-4pp 177ndash199 2003

[14] K Singh M Jung M Brinkmann and R Seemann ldquoCap-illary-Dominated fluid displacement in porous mediardquo An-nual Review of Fluid Mechanics vol 51 no 1 pp 429ndash4492019

[15] J Yao H Sun A Li et al ldquoModern system of multiphase flowin porous media and its development trendrdquo Chinese ScienceBulletin vol 63 no 4 pp 425ndash451 2018

[16] Z M Yang X L Zhao S C Xiong et al ldquoResearch progresson microstructure characterization of pore throat for tight oilreservoirsrdquo Science amp Technology Review vol 37 no 5pp 89ndash98 2019

[17] H Izadi M Baniassadi A Hasanabadi et al ldquoApplication offull set of two point correlation functions from a pair of 2D cutsections for 3D porous media reconstructionrdquo Journal ofPetroleum Science and Engineering vol 149 pp 789ndash8002017

[18] L Tomutsa D B Silin and V Radmilovic ldquoAnalysis of chalkpetrophysical properties by means of submicron-scale poreimaging and modelingrdquo SPE Reservoir Evaluation amp Engi-neering vol 10 no 3 pp 285ndash293 2007

[19] R D Hazlett ldquoSimulation of capillary-dominated displace-ments in microtomographic images of reservoir rocksrdquoMultiphase Flow in Porous Media vol 20 no 1-2 pp 21ndash351995

[20] H Okabe and M J Blunt ldquoPrediction of permeability forporous media reconstructed using multiple-point statisticsrdquoPhysical Review E vol 70 no 6 Article ID 066135 2004

[21] P Tahmasebi A Hezarkhani and M Sahimi ldquoMultiple-pointgeostatistical modeling based on the cross-correlation func-tionsrdquo Computational Geosciences vol 16 no 3 pp 779ndash7972012

[22] Y Keehm T Mukerji and A Nur ldquoPermeability predictionfrom thin sections 3D reconstruction and Lattice-Boltzmann


flow simulationrdquo Geophysical Research Letters vol 31 no 4Article ID L04606 2004

[23] P E Oren and S Bakke ldquoProcess based reconstruction ofsandstones and prediction of transport propertiesrdquo Transportin Porous Media vol 46 no 2-3 pp 311ndash343 2002

[24] M S Talukdar and O Torsaeter ldquoReconstruction of chalkpore networks from 2D backscatter electron micrographsusing a simulated annealing techniquerdquo Journal of PetroleumScience and Engineering vol 33 no 4 pp 265ndash282 2002

[25] M G Politis E S Kikkinides M E Kainourgiakis andA K Stubos ldquoA hybrid process-based and stochastic re-construction method of porous mediardquo Microporous andMesoporous Materials vol 110 no 1 pp 92ndash99 2008

[26] X Liu J Sun and H Wang ldquoReconstruction of 3-D digitalcores using a hybrid methodrdquo Applied Geophysics vol 6no 2 pp 105ndash112 2009

[27] W Lin X Li Z Yang et al ldquoConstruction of dual pore 3-Ddigital cores with a hybrid method combined with physicalexperiment method and numerical reconstruction methodrdquoTransport in Porous Media vol 120 no 1 pp 227ndash238 2017

[28] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[29] M Zha X Y Yin L Jiang et al ldquoApplication of CT tech-nology in petroleum exploration and developmentrdquo Geo-logical Science and Technology Information vol 36 no 4pp 228ndash235 2017

[30] W Lin Z Yang X Li et al ldquoAmethod to select representativerock samples for digital core modelingrdquo Fractals vol 25no 4 Article ID 1740013 2017

[31] L A Feldkamp L C Davis and J W Kress ldquoPractical cone-beam algorithmrdquo Journal of the Optical Society of America Avol 1 no 6 pp 612ndash619 1984

[32] M Defrise and R Clack ldquoA cone-beam reconstruction al-gorithm using shift-variant filtering and cone-beam back-projectionrdquo IEEE Transactions on Medical Imaging vol 13no 1 pp 186ndash195 1994

[33] M Grass T Kohler and R Proksa ldquo3D cone-beam CT re-construction for circular trajectoriesrdquo Physics in Medicine andBiology vol 45 no 2 pp 329ndash347 2000

[34] W Lin X Li Z Yang et al ldquoA new improved thresholdsegmentation method for scanning images of reservoir rocksconsidering pore fractal characteristicsrdquo Fractals vol 26no 2 Article ID 1840003 2018

[35] L Zhang J M Sun Z Q Sun et al ldquoApplication of multiple-point geostatistics in 3D pore structure model reconstruc-tionrdquo Journal of China University of Petroleum vol 36 no 2pp 105ndash109 2012

[36] O Talabi S AlSayari S Iglauer and M J Blunt ldquoPore-scalesimulation of NMR responserdquo Journal of Petroleum Scienceand Engineering vol 67 no 3-4 pp 168ndash178 2009

[37] S Chen D Georgi S Fang J Salyer and D Shorey ldquoOp-timization of NMR logging acquisition and processing SPE56766rdquo in Proceedings of the SPE 74th Annual Conference andTechnical Exhibition (ATCE) Houston TX USA Octobar1999

[38] Z M Yang Z Z Ma Y T Luo Y Zhang H Guo andW Lin ldquoA measured method for in situ viscosity of fluid inporous media by nuclear magnetic resonancerdquo Geofluidsvol 2018 Article ID 9542152 8 pages 2018

[39] X L Zhao Z M YangW Lin et al ldquoStudy on pore structuresof tight sandstone reservoirs based on nitrogen adsorptionhigh-pressure mercury intrusion and rate-controlled mer-cury intrusionrdquo Journal of Energy Resources Technology-

Transactions of the ASME vol 141 no 11 Article ID 1129032019

[40] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the Dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[41] M R Rezaie and M Norouzi ldquoNumerical investigation ofMHD flow of non-Newtonian fluid over confined circularcylinder a lattice Boltzmann approachrdquo Journal of the Bra-zilian Society of Mechanical Sciences and Engineering vol 40no 4 p 185 2018

[42] W Lin X Z Li Z M Yang et al ldquoModeling of 3D rockporous media by combining X-ray CT and Markov chainMonte Carlordquo Journal of Energy Resources Technologyvol 142 no 1 Article ID 013001 2020


breakthroughs in understanding how fluid enters porespaces and the mechanisms of wateroil and gas seepage[14ndash16]

At present the methods of digital rock reconstructionmainly include physical experiments numerical recon-structions and hybrid modeling )ere is an extensiveliterature on these various approaches and we summarizehere their general philosophy and some of their limitationsPhysical experiment methods have high accuracy and arewidely used but are vulnerable to the tradeoff betweenresolution and dimension [17 18] Compared with thephysical experiment method the numerical reconstructionmethod has the advantages of low cost and high efficiencyand can reconstruct different types of digital rocksHowever the drawback of the numerical reconstruction isthat there are some differences between the model and thereal rock [19ndash23] To address the shortcomings of the singlemodeling method some scholars have proposed the idea ofmixing different modeling methods with each other iehybrid modeling methods [24ndash28] For example Talukdaret al combined the truncated Gaussian random fieldmethod (TGRFM) with the characteristic of fast modelingspeed and the simulated annealing method (SAM) with thecharacteristic of more accurate modeling and used theimages generated by TGRFM as input to SAM to establish adigital rock with higher model quality Politis et al and Liuet al reconstructed 3D digital rocks by combining theprocess-based method (PBM) and SAM )e basic processof their modeling is similar First use the PBM to constructthe initial 3D digital rock and then use the initial model asthe input of SAM When the conditions of SAM arereached a hybrid digital rock is generated Compared withthe traditional SAM their method is more efficient inmodeling and the model is more accurate More recentlyLin et al introduced a hybrid modeling method thatcombines physical experiments and numerical recon-struction First a 3D macropore digital rock was con-structed by micro-CT second using high-resolution 2DSEM images a micropore digital rock was constructed bySAM last a superposition method was used to constructthe digital rock including the full range of pore structures)is method not only keeps the accuracy of the macroporeimage but also contains microstructure information Hy-brid modeling methods have improved modeling accuracyand efficiency and overcome some limitations of singlemodeling methods

In this work based on the hybrid method combiningphysical experiments and numerical reconstructions wefurther develop a new combination method that integratedmacropores constructed by X-ray CT and microporesreconstructed by MPGAWe utilized micro-CT to image themacropore structure of tight sandstone and constructed themacropore digital rock and used the SEM to image themicropores of tight sandstone and reconstructed the mi-cropore digital rock using MPGA )rough the superposi-tion of micropore and macropore digital rocks the full-poredigital rock of tight sandstone was obtained and the physicalproperties and seepage characteristics of the digital rockswere compared and analyzed

2 Sandstone Modeling

21 3D Macropore Reconstruction by X-Ray CTComputerized tomography (CT) imaging has the advan-tages of high accuracy and being nondestructive and iswidely used in the field of rock physics [29 30] As illustratedin Figure 1 the working principle of CT is that when X-raysare irradiated and penetrated through the sample the energywill be attenuated differently and the attenuation processaccords with the attenuation formula as follows

I I0eminus1113936i

μixi (1)

In formula (1) I is the intensity after attenuation I0 isthe original intensity μi is the attenuation coefficient ofcomponent i to ray and xi is the length of ray passingthrough component i When X-rays penetrate the samplethe detector detects the attenuated ray intensity and imitatesit on the detector

)e core of CT imaging is to reconstruct the gray imageof the sample)ere are two basic reconstruction algorithmsanalytical method and iterative method At present FDKreconstruction algorithm is more commonly used and theformula of the FDK algorithm is as follows [29 31ndash33]

pprime(β a b) R

RR + aa + bb

radic p(β a b)gn(a)1113888 1113889

FFDK(x y z) 11139462π

0

R2

U(x y β)2pprime(β a b)dβ

a R tan c

b q

cos c

k arctanq

R arctan

bRR + aa

radic

U(x y β) R + x cos β + y sin β

(2)

In formula (2) U(x y β) is the total attenuation coef-ficient q is the length of the projection data in a certaindirection p(β a b) is the collected projection datapprime(β a b) is the weighted filtering of the projection dataFF DK(x y z) is the back projection reconstruction of theweighted filter projection data gn(a) is a one-dimensionalfilter R is the orbital radius c is the fan angle of the conebeam β is the cone angle of the cone beam and a and b arethe positions on the detector

We used an UltraXRM-L200 CT scanner to image themacropores (gt12 μm) of the tight sandstone )e sandstonesample was selected and made into a cylinder with ap-proximately 12mm diameter and 14mm length and itsporosity was 1216 and gas permeability was0413times10minus3 μm2 )e resolution of CT imaging was 12micronpixel and 996 CT grayscale images were obtained)e original grayscale images (Figure 2) were preprocessedthrough contrast enhancement and a median filter We usedan improved threshold segmentation method considering







(a) (b)


X-ray source

Z X

X-ray detector

Y

Rotating

Sample

Scanning





(a) (b)












IS IAUIB (3)


0 + 0 0

0 + 1 0

1 + 0 0

1 + 1 1

(4)




ϕ Vp

Vp + Vs

(5)



ϕc Vprime

Vp + Vs

(6)










i

i

i












(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References




















































(a) (b)


X-ray source

Z X

X-ray detector

Y

Rotating

Sample

Scanning





(a) (b)












IS IAUIB (3)


0 + 0 0

0 + 1 0

1 + 0 0

1 + 1 1

(4)




ϕ Vp

Vp + Vs

(5)



ϕc Vprime

Vp + Vs

(6)










i

i

i












(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References

















































(a) (b)












IS IAUIB (3)


0 + 0 0

0 + 1 0

1 + 0 0

1 + 1 1

(4)




ϕ Vp

Vp + Vs

(5)



ϕc Vprime

Vp + Vs

(6)










i

i

i












(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References
























































IS IAUIB (3)


0 + 0 0

0 + 1 0

1 + 0 0

1 + 1 1

(4)




ϕ Vp

Vp + Vs

(5)



ϕc Vprime

Vp + Vs

(6)










i

i

i












(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References




















































i

i

i












(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References























































(7)



ei

(0 0 0) i 0



⎧⎪⎪⎨

⎪⎪⎩

(8)



c2s+

eiu( 11138572

2c4sminus

u3

2c2s1113890 1113891 (9)


13




ρ(r t) 1113944i

fi(r t)

p(r t) c2sρ(r t)


ρ(r t)


(10)






5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References

















































5 Conclusions


Am

plitu

de

200

150

100

50

0

T2 (ms)01 1 10 100 1000 10000




2

1

3

4

56

7

12

11

10

14

1516

89

13

1718

0




Data Availability




Acknowledgments


References
















































Data Availability




Acknowledgments


References






































































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