Journal for Multiscale Computational Engineering,13(1):1–9(2015) MULTISCALE PORE STRUCTURE ANALYSIS IN
十大名牌冰箱CARBONATE ROCKS
Jun Yao,∗Rongrong Hu,Chenchen Wang,&Yongfei Yang
School of Petroleum Engineering,China University of Petroleum(East China),No.66
Changjiang West Road,Huangdao Zone,Qingdao City,Shandong Province,266580P.R.China ∗Address all correspondence to Jun Yao,E-mail:RCOGFR 爆炒猪肚的做法
Carbonate rervoirs are inherently heterogeneous;the pore sizes can vary over orders of magnitude and often show trimodal distribution,and it is necessary to describe the pore characteristics of different scales in carbonate rocks.In this article,two-dimensional thin ction carbonate images with different resolutions are collected with scanning electron microscopy;the lowest-resolution image shows vug characteristics,the intermediate resolution shows interpore charac-teristics,and the highest-resolution image shows intrapore characteristics.Bad on three different resolution images,
a Markov chain Monte Carlo method is ud to reconstruct vug,interpore,and intrapore digital rock,and the corre-
sponding pore-scale network models are extracted,respectively.Then,a hybrid method including superposition and integration is ud to construct a carbonate multiscale network model.At last,the geometry–topology andflow prop-erties are analyzed and compared among the vug,macro pore,micro pore,and multiscale networks.Results show that the carbonate multiscale network with hybrid method could capture the pore size distribution and connectivity charac-teristics of different scales simultaneously.More importantly,different contributions toflow properties of certain scale pore structures are recognized,flow process are simulated among each pore-scale network under water wet conditions, and the water pha relative permeability curves of each pore network model have a similar tendency;however,the oil pha relative permeability curve of the multiscale network model has the highest isoperm saturation and lowest residual oil saturation.Compared with each single pore-scale network model,the multiscale network has a better connectivity andflow ability owing to the mutual connection between different scale pores,and it has important theoretical and applicational meanings for the microscopicflow study in carbonate rocks.
KEY WORDS:carbonate rervoir,digital rock,pore-scale network model,hybrid method,multiscale ch
ar-acteristics
1.INTRODUCTION
In recent years,carbonate rervoirs have played an important role in the exploration of unconventional oil and gas rervoirs.A typical characteristic of carbonate rervoirs is their diver variety of pore types(Knackstedt et al., 2006,2008).Excluding fractures,three different pore types can be identified:vugs,interpores,and intrapores.It is necessary to build a carbonate multiscale model and study theflow mechanisms of different pore types.
At prent,the pore network model has been an important platform for describing the geometry and topology of pore spaces and for performing multiphaflow calculations.This approach was pioneered by Fatt in the1950s (Fatt,1956a,b,c).Most networks are bad on a regular lattice,which could eliminate the throats from the network by varying the coordination number(Dixit et al.,1998,1999,2000).However,all the networks are bad on a regular lattice,while the real porous medium has an irregular structure.Another approach is to construct a random network bad on a reprentation of a realistic porous medium;there has been increasing interest in the pore network models recently(Bryant et al.,1993a,b,c;Blunt,2001;Blunt et al.,2002;Øren and Bakke,2002,2003;Val
vatne and Blunt,2003;Yao et al.,2013).The pore network models make it possible to reprent the complex pore spaces and simulate microscopicflow process,which could reduce experimental costs,shorten experimental periods,and aid in obtaining data that are difficult to measure under the current experimental conditions.However,it is difficult to u 1543–1649/15/$35.00c⃝2015by Begell Hou,Inc.1
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a similar pore network model with the methods directly in carbonate media,while many carbonate rocks have a variety of pore types(Biswal et al.,2007,2009;Ghous et al.,2008;Sok et al.,2009).
不上镜的原因In this article,two-dimensional(2-D)scanning electron microscopy(SEM)thin ction carbonate images with different resolutions are collected.Bad on three different resolution images,a Markov chain Monte Carlo(MCMC) method is ud to reconstruct vug,interpore,and intrapore digital rock,and the corresponding pore-scale network models are extracted,respectively.A hybrid coupling method is then ud to construct the carbonate multiscale net-work model.The geometry–topology andflow properties are analyzed and compared among the vug,interpore,intra-pore,and multiscale network,which provides an important theoretical basis for the carbonate multiscale simulation.
2.CONSTRUCTION OF A SINGLE-SCALE PORE NETWORK MODEL
2.1Image Analysis
Carbonate images at three different resolutions are captured using SEM,and a maximal interclass distance algorithm is applied to obtain the corresponding binary images(Hounsfield,1973;Zhao et al.,2007;Blunt et al.,2013).As can be en in Fig.1,the lowest-resolution image[Fig.1(a)]shows vug characteristics,the intermediate-resolution image [Fig.1(b)]shows interpore characteristics,and the highest-resolution image[Fig.1(c)]shows intrapore characteristics. All image pixel sizes are360×300,and the three image resolutions are5,1,and0.25µm,respectively,while the three-image resolution ratio i is20:4:1.
2.2Construction of Digital Rock
The2-D binary images are input into an algorithm developed by Wu et al.(2004,2006)that us a MCMC method to construct3-D digital rock.In this article,it is assumed that the rervoir is isotropic and that the corresponding3-D digital rock could be reconstructed basing on a2-D SEM image in one plane.Bad on the binary images with different resolutions,a MCMC method is ud to build the vug[Fig.2(a)],interpore[Fig.2(b)],and intrapore[Fig.2(c)]digital rock,respectively.The voxel size of vug,i
nterpore,and intrapore digital rock is100×100×100,100×100×100, and400×400×400,respectively.
2.3Extraction of Pore Network Model
The single pore-scale network model is then extracted from the corresponding3-D digital rock.Pore analysis tools (PATs)are ud to extract the pore network model from3-D digital rock.The analysis tools were developed by Jiang et al.(2007).This method extracts the geometrical–topological network that reprents the pore structure of
a porous medium,referred to as the GT-network.The GT-network extraction algorithm involves a number of steps:
(1)calculation of the3-D Euclidean distance map;(2)clustering of voxels;(3)extraction of the network of the pore
(a)Vug(b)Interpore(c)Intrapore
FIG.1:Binary images with different resolutions.
Journal for Multiscale Computational Engineering
Multiscale Pore Structure Analysis in Carbonate Rocks3
魔兽作弊器
(a)Vug(b)Interpore(c)Intrapore
FIG.2:Reconstruction of3-D digital rocks bad on the MCMC method.
space;(4)partitioning of the pore space;and(5)computation of the shape factor.From this,a geometry-and topology-equivalent network model is built with pore sizes,shapes,and connectivity bad on the3-D digital rock.How exactly this is done is described by Wu et al.(2007,2008).
Bad on the vug,interpore,and intrapore digital rock,the corresponding pore networks are extracted.As can be en in Fig.3,the porosity of vug,interpore,and intrapore is0.186,0.137,and0.155,respectively.
3.CONSTRUCTION OF THE MULTISCALE NETWORK MODEL
A hybrid method is ud to construct the carbonate multiscale network model,and two steps are included.Atfirst, bad on interpore and intrapore digital rock,a superposition method is ud to construct the dual-pore digital rock, and the corresponding dual-pore network is extracted.Then,bad on the vug and dual-pore network,an integration method is ud to construct the carbonate multiscale network model.
3.1Superposition Method
The data of digital rock are stored in the form of0and1,where0reprents pore space,while1reprents skeleton. Bad on the interpore and intrapore digital rocks,a superposition method is introduced to construct dual-pore digital rock(Wu et al.,2007,2008).The superposition procedures are as follows.
(a)Vug(b)Interpore(c)Intrapore
FIG.3:Extraction of pore-scale network model.
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Atfirst,each voxel in interpore digital rock is refined into i×i×i voxels,where i is the resolution ratio of interpore digital rock and intrapore digital rock;i equals4in this article.The voxel refinement could mak
e the interpore and intrapore digital rock have the same physical size(100×100×100µm)and voxel size(400×400×400).Then, the superposition operations of binary data between two digital rocks are as follows:0+0=0,1+0=0,0+1=0,1 +1=1.The dual-pore digital rock is superpod to describe the properties of both interpores and intrapores,and the corresponding dual-pore network is then extracted(Fig.4).
The superposition method could capture exact spatial structure information of two digital rocks with small scale difference,which is suitable to the construction of a dual-pore network.However,the superposition method is very memory and time consuming,and the integration method is developed to couple vug and dual-pore network with great scale difference.
3.2Integration Method
可以玩的游戏The integration procedure could be summarized in the following steps.First,obtain the statistic data of the dual-pore network,such as the cumulative pore size probability function and the corresponding pore volume,shape factor,and coordination numbers.Then,bad on the vug network,the equivalent dual-pore network isfilled into the matrix space of the vug network stochastically,according to the statistical information.At last,add the connection throats between vugs and dual pores according to t
he network coordination relationship.As before,a geometry-and topology-equivalent dual-pore network could befilled into the matrix space of the original vug network.The details for the integration method to construct a dual-pore network have been described by Wu,Jiang,and colleagues(Wu et al., 2011;Jiang et al.,2013),which could also be achieved with PATs software.
The integration method could capture the geometry and topology information of two networks with great scale difference,which is suitable for the coupling of vug and dual-pore network.As can be en in Fig.5,bad on the hy-brid method,including superposition and integration methods,the carbonate multiscale network model is constructed to describe the properties of vugs,interpores,and intrapores.
4.RESULTS AND DISCUSSION
Bad on the vug,interpore,intrapore,and multiscale network obtained earlier,the geometry,topology,andflow properties of each network are analyzed,and the results are discusd in the following.
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(a)Digital rock(b)Pore scale network
FIG.4:Matrix digital rock and the corresponding network model.
Journal for Multiscale Computational Engineering
可爱动漫女生Multiscale Pore Structure Analysis in Carbonate Rocks5
FIG.5:Construction of carbonate multiscale network model with the hybrid method.
4.1Geometry and Topology Properties
Geometry–topology properties are important criteria through which to evaluate the accuracy of pore network models. Geometry parameters include pore size distribution and shape factors;topology parameters include network con-nectivity function and coordination number(Jiang et al.,2012).In this article,a specific Euler number,which is developed by V ogel(V ogel and Roth,2001),is ud to quantify the network connectivity,and the network critical minimum radius could be obtained while the value of the network-specific Euler number equals0.
Figure6illustrates the geometry and topology parameters compared among the four networks.As can be en in Fig.6(a),the pore size of vug network distributes between4.69µm and20.65µm,which shows the micro vug characteristics;the pore size of the interpore network distributes between0.556µm and5.12µm,which shows the interpore characteristics;the pore size of the intrapore network distributes between0.0135µm and1.23µm,which shows the intrapore characteristics;and the
pore size of the multiscale network distributes between0.0135µm and 20.6µm,which shows the characteristics of all pore types.
As can be en in Fig.6(b),the critical minimum radius of the vug,interpore,and intrapore network is4.8µm, 1.2µm,and0.275µm,respectively,while the critical minimum radius of a multiscale network is0.52µm,which distributes between interpore and intrapore networks.That is becau the number of interpores and intrapores is more
(a)Digital rock(b)Pore scale network
FIG.6:Geometry–topology comparison of each pore-scale network model.
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