CN104573198A - Method for reconstructing digital rock core and pore network model based on random fractal theory - Google Patents

Abstract

The invention discloses a method for reconstructing a digital rock core and pore network model based on a random fractal theory. The method comprises the following steps of based on the multiple fractal features of a porous medium, performing fractal representing on a capillary pressure curve obtained by the conventional mercury intrusion method, inferring fractal expressions of random distribution density function, average value and variance by a random distribution theory, and combining the random theory and the multiple fractal theory to construct a digital rock core, so as to rapidly construct a three-dimensional micro-network model. The method has the advantages that the cost is low and is reduced; the capillary pressure curve is measured by the mercury intrusion method, the full-section rock core is used in experiment, and a micro-pore structure is fully displayed. According to the method, the computing method is simple and convenient, and the advanced method is adopted; the micro-pore structure of reservoir rock is complicated and irregular, and an extremely complicated system cannot be accurately described by the traditional classical theory, so after the method combines the multiple fractal theory and the random distribution theory, the micro-pore structure can be accurately represented, and the method is easily implemented by programming.

Description

Based on digital cores and the pore network model reconstructing method of random fractal theory

Technical field

The construction method that the 3-D quantitative that the present invention relates to a kind of micropore structure of porous media describes, particularly a kind of digital cores construction method based on pore network model.

Background technology

In the past, in porous medium, the microscopic mechanism of fluid neuron network carried out qualitative examination mostly by experiment, and mostly result of study is to stop on a macroscopic scale, and being difficult to has more intensive understanding to microscopic mechanism.In order to be quantitatively described the Seepage problems on micro-scale, the problem that head need solve is exactly meticulous depiction micropore structure.Recent domestic scholar has carried out a large amount of research work in this field, sums up, and Research Thinking is following two classes mainly: one, based on digital cores, adopts grid Boltamann method to carry out flow simulating; Two, based on pore network model, the flow rule concrete according to studied problem definition carries out flow simulating.Microscopic seepage theoretical research all with digital cores or pore network model for platform is carried out, because the pore morpholohy of porous medium and the distribution wherein of space distribution convection cell, migration etc. all produce very important impact, thus can digital cores and pore network model reflect whether the microscopic seepage directly determining to carry out based on them research acquired results is had practical significance by true core pore space feature preferably.So, porous medium pore space is studied and set up can with the three-dimensional model (comprising digital cores and pore network model) effectively embodying its space distribution and morphological feature by for follow-up be that solid foundation is established in the microscopic seepage theoretical research of platform with microvisual model.

Physical experimental method and digital reconstruction method are mainly to the numerical method of rock core microscopic void reconstruct, first the plane picture of rock core all will be obtained by high precision instruments such as Powerful Light Microscope, scanning electron microscope or CT imagers, extract modeling information by graphical analysis, afterwards three-dimensional reconstruction carried out to plane picture or adopt certain mathematical method to set up digital cores.Require that not only rock core that is high but also that obtain is thin slice to rock core imaging technique, small, experimentation cost is large, applies difficulty large.The digital cores that the multiple method for reconstructing that numerical reconstruction method develops so far is set up by the forming process of various different statistical method or simulation core, more typically there are Gauss's simulation, simulated annealing, process simulation method, multiple-point simulation method, multi-point statistic method and the random reconstruction method of markov, but the digital cores based on these method establishment is all isotropic, cannot the complicated pore system of quantitatively characterizing.

Want the hole of the true porous medium of acquisition reflection, venturi distribution and be communicated with situation to need to set up Three-dimensional network model, pore throat geometric relationship can be characterized preferably.The assignment method of pore network model mesoporosity, venturi size and throat length is also the problem that researchist comparatively pays close attention to, initial Fatt adopts the mode of completely random to be throat radius assignment, a lot of scholar's research finds afterwards, hole in porous medium, venturi size, throat length etc. all roughly meet certain regularity of distribution, can characterize with certain distribution function, apply more mainly containing: lognormal distribution, Haring-Greenkorn probability distribution, Rayleigh distribution, Weibull probability distribution, clean cut system Weibull distribution etc.These characterizing methods are all that the geometry of rule-based topological network model characterizes, and the follow-up Bethe network line that develops again is to represent hole, and line has certain radius, volume and resistance to flow; Intersection point between line does not have volume and resistance to flow, just plays the effect of connection.This kind of pore network model sets up on the basis of digital cores, and they have the topological structure with digital cores pore space equivalence.Digital cores is set up according to physical experimental method, then corresponding with it pore network model has the topological structure of true core pore space; Set up according to numerical method, the topological structure of the pore network model then set up on its basis and the topological structure of true core still variant, but due to model topological property comparatively regular network model have larger improvement, be referred to as true topological pore network model.Certainly, from true core or the digital cores set up by numerical method, extract network model of equal value has great difficulty, and up to the present, the identification of hole, venturi and classifying rationally etc. are still the major issue being badly in need of solving.

Summary of the invention:

The technical problem to be solved in the present invention is to provide a kind of digital cores based on random fractal theory and pore network model reconstructing method, with low cost, can fully by micropore structure show and be easy to programming realization.

In order to solve the problems of the technologies described above technical scheme of the present invention be:

Based on digital cores and the pore network model reconstructing method of random fractal theory, comprise the steps: step 1: the fractal characteristic determining rock core micropore structure, fractal characteristic comprises fractal dimension and self similarity is interval; Step 2: the fractal characteristic setting up porous medium stochastic distribution characterizes, adopts stochastic distribution theory to set up pore radius distribution probability density function, the fractal characterization of pore-size average and the fractal characterization of pore-size variance with fractal characteristic; Step 3, builds porous medium random digit rock core, and according to pore radius distribution probability density function, the stochastic variable direct sampling method of application continuous distribution obtains pore radius data; Step 4, needs the random digit rock core of size integrating step 3 gained of setting network model to set up initial network model according to design; Step 5, according to the result determination pore constriction inscribed circle radius of step 1 to 3, according to step 4 acquired results determination hole throat length, volume and form factor, pore constriction inscribed circle radius, length, volume and form factor are brought into the pore network model that initial network model obtains having true core pore space topological structure and geometric properties.

Preferably, the method in fractal dimension and self similarity interval of determining in step 1 is: according to formula lnS=(D-2) lnp _cthe fractal dimension D of+ln β determining hole gap structure, in formula, P _cfor capillary pressure, S is saturation degree, and β is reservoir attribute; Two different straight lines of slope are obtained, if C by the method for piecewise fitting ₁, C ₂for the constant of method of subsection simulation curve gained, utilize least square method formula (minimum n value, finds separation p _c0make the point in two matched curves minimum with the quadratic sum of corresponding raw data difference, namely obtain being greater than p _c0be less than p _c0two self similarity intervals, S in formula _ifor the nonwetting phase saturation degree corresponding to loose point, P _cifor the force value corresponding to loose point, n is that capillary pressure is greater than P _c0interval in loose some number, m is loose total number, D ₁, D ₂be respectively two interval corresponding fractal dimensions, E is the point in two matched curves and the quadratic sum of corresponding raw data difference, E ₁for the point in Article 1 matched curve and the quadratic sum of corresponding raw data difference, E ₂for the point in Article 2 matched curve and the quadratic sum of corresponding raw data difference.

Preferably, pore radius distribution probability density function is wherein, D is the fractal dimension of pore texture, r _minfor minimum pore radius, r is pore radius; The fractal characterization form of pore-size average is wherein, r _maxfor maximum pore radius, N (r) for pore radius be the number of apertures of r, N _totalfor total number of apertures; The fractal characterization of pore-size variance $\mathrm{Var}\left(r\right)=\frac{{\∫}_{r_{\min }}^{r_{\max }}{(r-\stackrel{\‾}{r})}^{2}N\left(r\right)\mathrm{dr}}{N_{\mathrm{total}}}.$

Preferably, N is worked as _totalduring >10000, the fractal characterization form of pore-size average $\stackrel{\‾}{r}=\frac{D}{D-1}{r}_{\min },$ The fractal characterization of pore throat size variance $\mathrm{Var}\left(r\right)=[\frac{D}{D-2}-{\left(\frac{D}{D-1}\right)}^2]r_{\min }^2.$

Preferably, based on porous medium pore radius probability density function, the stochastic variable direct sampling method of application continuous distribution obtains porous medium pore radius date expression wherein ξ is equally distributed random number on [0,1] interval, the fractal dimension of step 1 gained and self similarity interval is substituted into porous medium pore radius date expression and draws porous medium random digit rock core.

Preferably, pore constriction inscribed circle radius equals porous medium pore radius; The length of pore constriction meets formula: in formula, L is the distance of two aperture center points, tortuosity η=1 ~ 1.5, l _tfor the total length of venturi, l _p1, l _p2for the length of two holes connected by venturi.Due to the locus of two porosity points be connected be determine so L is definite value.According to l _p1: l _p2: l _tthe ratio of=1:1: ε just can determine hole throat length, the wherein interior change of value 0.5 ~ 3 scope of ε; The volume of described pore constriction $v={\∫}_0^{\frac{l_{p_1}+l_t}{2}}{\mathrm{\πR}}^2\left(x\right)\mathrm{dx}+{\∫}_0^{\frac{l_{p_2}+l_t}{2}}{\mathrm{\πR}}^2\left(x\right)\mathrm{dx},$ Wherein $R\left(x\right)=\left(\frac{R_p+R_t}{2}\right)+\left(\frac{R_p-R_t}{2}\right)c\frac{2\mathrm{\πx}}{l_p+l_t}),$ Wherein R _p, R _t(represent hole and venturi center inscribed circle radius, l respectively _p, l _trepresent the length of hole and venturi respectively.X=0 is positioned at the center of hole, x=(l _p+ l _t)/2 are positioned at the center of venturi, the form factor of pore constriction wherein A is pore constriction area of section, and P is the girth of pore constriction cross sectional shape.

Beneficial effect of the present invention is: based on the multi-fractal features of porous medium, the capillary pressure curve conventional mercury intrusion method obtained carries out fractal characterization, utilize the fractal expression formula of stochastic distribution theory deduction stochastic distribution density function, average and variance, random theory and multi-fractal Theory combine structure digital cores, set up out three-dimensional microcosmic network model easily accordingly.

Although it is direct that conventional physical experimental method sets up digital cores method, rely on high precision imaging and treatment technology.The digital cores set up with the scan image technology that precision is lower cannot reflect the micro-structure of pore space, and transmissibility and the true core of its convection cell exist error, and this error is generally reduce with the raising of scan image resolution.So the true core data wanting to obtain complicated rock sample just must improve the precision of experimental apparatus, corresponding experimental cost improves.The present invention only needs the capillary pressure curve measuring rock core by routine pressure mercury experimental apparatus, and method of the present invention is with low cost, cost-saved.

During tradition rule Physical Experiment image procossing, rock core is needed to be polished into thin slice, edge treated process makes the edge fog of hole and rock skeleton unclear, affect the extraction of digital cores data, in addition, from whole section of rock core, choose the thin slice thinned carry out the labyrinth that digital cores process fully can not show studied rock core.The present invention adopts mercury intrusion method to measure capillary pressure curve, and experiment adopts full section rock core, can fully micropore structure be shown.

Computing method of the present invention are easy, method is advanced, the micropore structure of reservoir rock is complicated and irregular, traditional classical theory is difficult to describe accurately an extremely complicated system, adopt method described in this aspect multi-fractal Theory and stochastic distribution theory to be combined and can characterize micropore structure exactly, method is easy to programming realization.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the embodiment of the present invention,

Fig. 2 is that embodiment of the present invention mercury intrusion method measures capillary pressure curve,

Fig. 3 is that the embodiment of the present invention adopts multifractal method to determine multiple fractal dimension and self similarity interval,

Fig. 4 is embodiment of the present invention Three-dimensional network model design of graphics,

Fig. 5 is pore constriction microscopic structural units schematic diagram,

Fig. 6 is the embodiment of the present invention digital cores that adopts this algorithm to build and conventional algorithm and true core comparing result figure.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly, below in conjunction with accompanying drawing, embodiment of the present invention is further described.

Based on digital cores and the pore network model reconstructing method of random fractal theory, comprise the steps:

Step 1: the fractal characteristic determining rock core micropore structure, fractal characteristic comprises fractal dimension and self similarity is interval;

The micropore structure of reservoir rock is very complicated and irregular.The method of traditional description pore texture can not reflect the complicacy of rock pore structure and the impact of its fluid flow accurately.The development of fractal geometry, for Study In Reservoir porous medium provides new method.Determine the key parameter of porous medium fractal characteristic---the method for fractal dimension is different, comprises scanning electron microscope method, bianry image method and capillary pressure curve method, J function curve method etc.But research shows rock core adopts single fractal method cannot accurate Characterization, need to characterize the interval and fractal dimension of self similarity with Multifractal Method.

The present embodiment adopts mercury intrusion method to obtain capillary pressure curve, and the method in fractal dimension and self similarity interval of determining is:

For porous medium, have between same scale physical quantities and the linear-scale of its measurement and meet power law relation

$N\left(r\right)={\∫}_r^{r_{\max }}p\left(r\right)\mathrm{dr}={\mathrm{\αr}}^{-D}---\left(1\right)$

Wherein, N (r) for radius be the number of apertures of r, r _maxfor the maximum pore radius of porous medium, D is the fractal dimension of pore texture, and α is the related coefficient of quantitative relationship between reflection number of apertures N and pore radius r.Have according to capillary model

N(r)＝V/(πr ²l) (2)

In formula: l is the length of kapillary; V flows through wetting phase cumulative volume corresponding when radius is the kapillary of r.

By (1) formula and (2) Shi Ke get:

$\frac{V}{\left(\mathrm{\π}{r}^{2}l\right)}{\∞r}^{-D}---\left(3\right)$

V∞r ^2-D(4)

Capillary pressure P _cfor

P _c＝2σcosθ/r (5)

In formula, σ is interfacial pressure; θ is contact angle.By (5) formula, (4) formula of bringing into obtains

$V\∞{P_c}^{-(2-D)}---\left(6\right)$

Defined by saturation degree

S＝V/V _P(7)

S is saturation degree, V _pfor volume of voids.

Comprehensively (6) formula and (7) formula have

S＝βP _c ^-(2-D)(8)

β is reservoir attribute, determined by the log-log coordinate of saturation degree S and capillary pressure Pc.

Are taken the logarithm and can obtain formula in (8) formula both sides

lnS＝(D-2)lnp _c+lnβ (9)

According to the fractal dimension D of formula (9) determining hole gap structure, in formula, Pc is capillary pressure, and S is saturation degree, and β is the related coefficient of reflecting saturation degree S and capillary pressure Pc quantitative relationship.

When the pore texture in rock sample meets fractal characteristic, LnS and lnP in rectangular coordinate system _clinear, the slope of straight line is (D-2).By the capillary pressure curve of analytic statistics rock sample, as Fig. 2.To LnS and lnP _ccarry out the fractal dimension that matching just can calculate blowhole.And a lot of complicated porous medium do not meet single fractal needs and use multi-fractal Theory to ask for.

In order to apply the pore texture that multi-fractal Theory describes digital cores more accurately, the method can applying piecewise fitting obtains two different straight lines of slope, thus determines Multifractal Dimension and the self similarity interval of rock sample.Two different straight lines of slope are obtained, if C by the method for piecewise fitting ₁, C ₂for the constant of method of subsection simulation curve gained, utilize least square method formula

Find separation p _c0make the point in two matched curves minimum with the quadratic sum of corresponding raw data difference, namely obtain being greater than p _c0be less than p _c0two self similarity intervals, as shown in Figure 3.S in formula _ifor the nonwetting phase saturation degree corresponding to loose point, P _cifor the force value corresponding to loose point, n is that capillary pressure is greater than P _c0interval in loose some number, m is loose total number, D ₁, D ₂be respectively two interval corresponding fractal dimensions, E is the point in two matched curves and the quadratic sum of corresponding raw data difference, E ₁for the point in Article 1 matched curve and the quadratic sum of corresponding raw data difference, E ₂for the point in Article 2 matched curve and the quadratic sum of corresponding raw data difference.

Step 2: the fractal characteristic setting up porous medium stochastic distribution characterizes, adopts stochastic distribution theory to set up pore radius distribution probability density function, the fractal characterization of pore-size average and the fractal characterization of pore-size variance with fractal characteristic;

Step 21, determines hole radius distribution probability density function

According to Fractal Geometry Theory, the people such as Yu propose the number of apertures N (>r) that pore radius is greater than r has power function relationship with r

$N(>r)={\left(\frac{r_{\max }}{r}\right)}^D---\left(11\right)$

Wherein, r _maxfor the maximum pore size of porous medium, D is the fractal dimension of pore texture.

According to the known total number of apertures N of (11) formula _total

$N_{\mathrm{total}}(>r_{\min })={\left(\frac{r_{\max }}{r_{\min }}\right)}^D---\left(12\right)$

Wherein, r _minfor minimum pore radius, N _total(>r _min) be greater than r for pore radius _minnumber of apertures, be total number of apertures.Pore radius distribution function formula can be obtained according to (11) formula and (12) formula

$F\left(r\right)=\frac{N}{N_{\mathrm{total}}}={\left(\frac{r_{\min }}{r}\right)}^D---\left(13\right)$

Because F (r) is at interval (r _min, r _max) in can lead, so porous medium pore radius probability density function is:

$f\left(r\right)=F^{\′}\left(r\right)={\mathrm{Dr}}_{\min }^D{r}^{-(D+1)}---\left(14\right)$

In order to meet the correctness of probability density function, (14) formula should meet normalizing condition:

${\∫}_{r_{\min }}^{r_{\max }}f\left(r\right)\mathrm{dr}=1-{\left(\frac{r_{\min }}{r_{\max }}\right)}^D=1---\left(15\right)$

(15) formula is set up, then

$\frac{1}{N_{\mathrm{total}}}={\left(\frac{r_{\min }}{r_{\max }}\right)}^D\≈0---\left(16\right)$

Because work as N _totalduring >10000, (16) formula is set up, and this shows when the number of apertures in porous medium is greater than 10000, can study the distribution situation of its pore radius, obtain porous medium pore radius probability density function with fractal theory.

Step 22, determines the fractal characterization form of pore-size average

The fractal characterization form of pore-size average is wherein, N (r) represents that radius is the pore throat number of r, and usual porous medium inner pore number is very huge, so can obtain

$N\left(r\right)=-\frac{\mathrm{dN}(\≥r)}{\mathrm{dr}}=D{r}_{\max }^D{r}^{-D-1}---\left(18\right)$

(18) formula is substituted into (17) formula obtain,

$\begin{array}{c}\stackrel{\‾}{r}={\left(\frac{r_{\min }}{r_{\max }}\right)}^D{\∫}_{r_{\min }}^{r_{\max }{\mathrm{Dr}}^{\max }{r}^{-D}\mathrm{dr}}\\ =\frac{D}{1-D}{r}_{\min }^D(r_{\max }^{1-D}-r_{\min }^{1-D})\\ =\frac{D}{D-1}(r_{\min }-\frac{r_{\max }}{N_{\mathrm{total}}})\end{array}---\left(19\right)$

Work as N _totalduring >10000, (19) formula can be reduced to,

$\stackrel{\‾}{r}=\frac{D}{D-1}{r}_{\min }---\left(20\right)$

Known when pore throat order is enough large by above formula, the average of pore throat radius is determined by the minimum pore radius in fractal dimension and self similarity interval.N _totalfor number of apertures, r _minfor minimum pore throat radius, r _maxfor maximum pore throat radius.

Step 23, determines the fractal characterization form of pore-size variance

The fractal characterization form of pore throat size variance $\mathrm{Var}\left(r\right)=\frac{{\∫}_{r_{\min }}^{r_{\max }}{(r-\stackrel{\‾}{r})}^{2}N\left(r\right)\mathrm{dr}}{N_{\mathrm{total}}}---\left(21\right)$

(18), (20) formula are substituted into (21) formula and obtain,

$\mathrm{Var}\left(r\right)={\left(\frac{r_{\min }}{r_{\max }}\right)}^D{\∫}_{r_{\min }}^{r_{\max }}{(r-\frac{D}{D-1}{r}_{\min })}^2{\mathrm{Dr}}_{\max }^D{r}^{-D-1}\mathrm{dr}---\left(22\right)$

Solve above formula to obtain,

$\mathrm{Var}\left(r\right)=\frac{1}{N_{\mathrm{total}}}(\frac{{\mathrm{Dr}}_{\max }^2}{2-D}+\frac{{2D}^2{r}_{\min }(r_{\max }-r_{\min })}{{(D-1)}^2}-[\frac{D}{D-2}-{\left(\frac{D}{D-1}\right)}^2]r_{\min }^2---\left(23\right)$

Work as N _totalduring >10000, above formula can be reduced to,

Can find out that the variance of the porous medium pore radius with fractal characteristic is the function of minimum pore radius and fractal dimension in self similarity interval equally.

Step 3, builds porous medium random digit rock core, and according to pore radius distribution probability density function, the stochastic variable direct sampling method of application continuous distribution obtains pore radius data;

Obtaining pore throat distributed data is set up the very important content of digital cores, and a lot of scholar's research finds, the pore throat size in porous medium all roughly meets certain regularity of distribution, therefore can apply certain distribution function to characterize.Apply and more mainly contain lognormal distribution, Haring-Greenkorn probability distribution, Rayleigh distribution, Weibull distribution, clean cut system Weibull distribute.The present embodiment is based on the above-mentioned pore radius distribution probability density fonction with fractal characteristic derived, and the stochastic variable direct sampling method of application continuous distribution is met the rock core hole data of multi-fractal features.

Based on porous medium pore radius probability density function, the stochastic variable direct sampling method of application continuous distribution obtains porous medium pore radius date expression, the stochastic variable direct sampling method of porous medium pore radius distribution function (13) formula and continuous distribution, if ξ is [0,1] equally distributed random number on interval, order:

$\mathrm{\ξ}=F\left(r\right)={\left(\frac{r_{\min }}{r}\right)}^D---\left(25\right)$

(25) formula of solution, obtains

$r=\frac{r_{\min }}{{\mathrm{\ξ}}^{1/D}}---\left(26\right)$

According to the porous medium pore radius data that (26) formula produces, be the pore radius data meeting feature of fractal distribution.

The Multifractal Dimension of the rock sample of step 1 gained and self similarity interval are substituted into (26) formula, the random digit rock core that the hole data with multi-fractal features draw porous medium can be rebuild.

Step 4, needs the random digit rock core of size integrating step 3 gained of setting network model to set up initial network model according to design, as shown in Figure 4;

Step 5, according to the result determination pore constriction inscribed circle radius of step 1 to 3, according to step 4 acquired results determination hole throat length, volume and form factor, pore constriction inscribed circle radius, length, volume and form factor are brought into the pore network model that initial network model obtains having true core pore space topological structure and geometric properties.Concrete steps are as follows:

Step 51, pore constriction inscribed circle radius is called for short pore radius, can according to formula (26) obtain.

Pore constriction inscribed circle radius is called for short pore radius, based on experimental datas such as capillary pressure curves, determines the pore microgeometrical parameters of rock sample, comprises fractal dimension D, maximum pore radius r _max, minimum hole half r _mindeng, the stochastic variable direct sampling method applying adopted continuous distribution is above met the rock core hole data of fractal characteristic or multi-fractal features.For the ease of visual, in Three-dimensional network model, hole and the venturi ball of different size and thickness line segment not etc. represents, the size of ball and the thickness of line segment correspond to Bu Tong large fine porosity and venturi inscribed circle radius respectively.

Step 52, the length of pore constriction meets formula:

$L\×\mathrm{\τ}=l_t+\frac{l_{p1}}{2}+\frac{l_{p2}}{2}---\left(27\right)$

In formula, L is the distance of two aperture center points, tortuosity η=1 ~ 1.5, l _tfor the total length of venturi, l _p1, l _p2for the length of two holes connected by venturi.Due to the locus of two porosity points be connected be determine so L is definite value.According to l _p1: l _p2: l _tthe ratio of=1:1: ε just can determine hole throat length, and wherein the span of ε is 0.5 ~ 3;

Step 53, asks the volume of pore constriction

Porous medium is made up of the effigurate hole of tool and venturi, the cross section of each hole and venturi also exists an incircle.Cross section inscribed circle radius meets:

$R\left(x\right)=\left(\frac{R_p+R_t}{2}\right)+\left(\frac{R_p-R_t}{2}\right)\cos \left(\frac{2\mathrm{\πx}}{l_p+l_t}\right)---\left(28\right)$

Wherein R _p, R _trepresent hole and venturi center inscribed circle radius respectively, l _p, l _trepresent the length of hole and venturi respectively.X=0 is positioned at the center of hole, x=(l _p+ l _t)/2 are positioned at the center of venturi, as shown in Figure 5.

The volume of pore constriction can be expressed as

$v={\∫}_0^{\frac{l_{p_1}+l_t}{2}}{\mathrm{\πR}}^2\left(x\right)\mathrm{dx}+{\∫}_0^{\frac{l_{p_2}+l_t}{2}}{\mathrm{\πR}}^2\left(x\right)\mathrm{dx}---\left(29\right)$

Step 54, asks the form factor of pore constriction

The form factor of pore constriction wherein A is pore constriction area of section; P is the girth of pore constriction cross sectional shape.

Obviously, form factor can describe porous medium pore space geometric properties, and it is the important parameter used in pore network modeling process.Pore shape is more regular, and form factor is larger.The form factor of circle is maximum, is 1/4 π; Foursquare form factor is 1/16; Leg-of-mutton form factor variation range is 0 ~ 0.0418.

In the present embodiment, we think that the form factor of hole and venturi meets Weibull distribution, and form factor can obtain according to following formula.

$F=(F_{\max }-F_{\min }){[-\mathrm{\δ}\ln (z(1-e^{\frac{-1}{\mathrm{\δ}}})+e^{\frac{-1}{\mathrm{\δ}}})]}^{\frac{1}{\∂}}+F_{\min }---\left(30\right)$

Wherein, F _max=0.0418, F _min=0, δ, ζ are the empirical parameters of manually specifying, and the present embodiment gets δ=0.8, ζ=1.6, and z is the random number producing energy between 0-1.Corresponding form factor F is obtained by the z value produced at random.

When setting up pore network model, the shape of hole, venturi must be considered to carry out the flow simulating of heterogeneous fluid.The shape of true pore space is very complicated, we cannot accurately be described, the regular geometric shapes approximate description of usual employing equivalence, for ease of issue handling, usually hole, venturi are simplified to uniform cross section and the simple solid of cross sectional shape, as being simplified to square, the kapillary of arbitrary triangle and circle etc.Although the shape of pore network model mesoporosity, venturi is different from the shape of hole in true core, venturi, single they must reflect that the geometric properties of true core pore space is to improve the accuracy of model as far as possible.

Step 55, brings step 51 into pore network model that initial network model obtains having true core pore space topological structure and geometric properties to the pore constriction inscribed circle radius of step 54 gained, length, volume and form factor.

The network model that the true core that the network model of method establishment described in the present embodiment and image procossing Physical Experiment method obtain is set up is updated in microcosmos network simulator simultaneously and checks analog result, capillary force and the phase percolation curve goodness of fit of simulation acquisition are higher, prove the network model validity that the method is set up.

The present embodiment intends the capillary pressure curve measured by pressure mercury physical experimental method, sets up capillary force and pore texture logarithmic relationship curve, and according to true core distribution of pores feature, the Multifractal Dimension of rock core hole is determined in point pore radius interval.As long as use random fractal theoretical based on matlab programming development platform input Multifractal Dimension, and the minimax pore radius in different interval, just can build one group of digital cores very close with true core pores'growth, and set up the hole microcosmos network model meeting the research of network flow dynamic simulated.By the 3-dimensional digital rock core of this new method application build, with 10 blocks of sandstone 3-dimensional digital rock cores that Imperial College of Britain digital cores Laboratory Opening platform is issued, carry out contrast verification, show that identical rate reaches that 98%, Fig. 6 is actual Berea sandstone pores data, probability density distribution comparison diagram that the hole data that obtain based on fractal method and Weibull distribute the hole data drawn.

Method described in the present embodiment is in order to the construction method reaching convenient and swift and degree of accuracy is high, first pressure sclera remodeling capillary manometric method is used to obtain rock core microscopic void radius distribution data, then multi-fractal Theory is utilized to carry out fractal characteristic research to the distribution of porous medium microscopic void, determine porous medium multifractal interval and fractal dimension, based on stochastic distribution theory deduction one group of random chance density function, the fractal expression formula of average and variance, adopt matlab programming tool exploitation porous medium based on the random pore radius distribution of Multifractal afterwards, finally apply random device and generate coordinate points in certain spatial dimension, and coordinate points is coupled together the primary structure framework of structure Three-dimensional network model with the line representing venturi, and by Software Development Platform, generate the three-dimensional model of porous medium.

It should be noted last that, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although with reference to better case, the present invention is described in detail, those of ordinary skill in the art is to be understood that, can modify to technical scheme of the present invention, and not departing from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of right of the present invention.

Claims (6)

1., based on digital cores and the pore network model reconstructing method of random fractal theory, it is characterized in that, comprise the steps:

Step 1: the fractal characteristic determining rock core micropore structure, described fractal characteristic comprises fractal dimension and self similarity is interval;

Step 2: the fractal characteristic setting up porous medium stochastic distribution characterizes, adopts stochastic distribution theory to set up pore radius distribution probability density function, the fractal characterization of pore-size average and the fractal characterization of pore-size variance with fractal characteristic;

Step 3, builds porous medium random digit rock core, and according to described pore radius distribution probability density function, the stochastic variable direct sampling method of application continuous distribution obtains pore radius data;

Step 4, needs the random digit rock core of size integrating step 3 gained of setting network model to set up initial network model according to design;

Step 5, according to the result determination pore constriction inscribed circle radius of step 1 to 3, according to step 4 acquired results determination hole throat length, volume and form factor, bring described pore constriction inscribed circle radius, length, volume and form factor into pore network model that described initial network model obtains having true core pore space topological structure and geometric properties.

2. a kind of digital cores based on random fractal theory according to claim 1 and pore network model reconstructing method, is characterized in that, the method in described fractal dimension and self similarity interval of determining in described step 1 is:

According to formula ln S=(D-2) ln p _cthe fractal dimension D of+ln β determining hole gap structure, in formula, P _cfor capillary pressure, S is saturation degree, and β is reservoir attribute;

Based on capillary pressure curve, obtain two different straight lines of slope, if C by the method for piecewise fitting ₁, C ₂for the constant of method of subsection simulation curve gained, utilize least square method formula $E=E_1+E_2=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{[\ln S_i-(D_1-2)\ln \left(P_{\mathrm{Ci}}\right)-C_1]}^2+\underset{i=n}{\overset{m}{\mathrm{\Σ}}}{[\ln S_i-(D_2-2)\ln \left(P_{\mathrm{Ci}}\right)-C_2]}^2$ Minimum value, find separation p _c0make the point in two matched curves minimum with the quadratic sum of corresponding raw data difference, namely obtain being greater than p _c0be less than p _c0two self similarity intervals, S in formula _ifor the nonwetting phase saturation degree corresponding to loose point, P _cifor the force value corresponding to loose point, n is the loose some number that capillary pressure is greater than in the interval of Pc0, and m is loose total number, D ₁, D ₂be respectively two interval corresponding fractal dimensions, E is the point in two matched curves and the quadratic sum of corresponding raw data difference, E ₁for the point in Article 1 matched curve and the quadratic sum of corresponding raw data difference, E ₂for the point in Article 2 matched curve and the quadratic sum of corresponding raw data difference.

3. a kind of digital cores based on random fractal theory according to claim 1 and pore network model reconstructing method, is characterized in that:

Described pore radius distribution probability density function is wherein, D is the fractal dimension of pore texture, r _minfor minimum pore radius, r is pore radius;

The fractal characterization form of described pore-size average is wherein, r _maxfor maximum pore radius, N (r) for pore radius be the number of apertures of r, N _totalfor total number of apertures;

The fractal characterization of described pore-size variance

4. a kind of digital cores based on random fractal theory according to claim 3 and pore network model reconstructing method, is characterized in that: work as N _totalduring >10000, the fractal characterization form of described pore throat size average the fractal characterization of described pore throat size variance $\mathrm{Var}\left(r\right)=\left[\frac{D}{D-2}-{\left(\frac{D}{D-1}\right)}^2\right]r_{\min }^2.$

5. a kind of digital cores based on random fractal theory according to claim 1 and pore network model reconstructing method, it is characterized in that: based on porous medium pore radius probability density function, the stochastic variable direct sampling method of application continuous distribution obtains porous medium pore radius date expression wherein ξ is equally distributed random number on [0,1] interval, the described fractal dimension of step 1 gained and self similarity interval is substituted into described porous medium pore radius date expression and draws described porous medium random digit rock core.

6. a kind of digital cores based on random fractal theory according to claim 1 and pore network model reconstructing method, is characterized in that:

Described pore constriction inscribed circle radius equals described porous medium pore radius;

The length of described pore constriction meets formula: in formula, L is the distance of two aperture center points, tortuosity τ=1 ~ 1.5, l _tfor the total length of venturi, l _p1, l _p2for the length of two holes connected by venturi.Due to the locus of two porosity points be connected be determine so L is definite value.According to l _p1: l _p2: l _tthe ratio of=1:1: ε just can determine hole throat length, and wherein the span of ε is 0.5 ~ 3;

The volume of described pore constriction $v={\∫}_0^{\frac{l_{p1}+l_t}{2}}\mathrm{\π}{R}^2\left(x\right)\mathrm{dx}+{\∫}_0^{\frac{l_{p2}+l_t}{2}}\mathrm{\π}{R}^2\left(x\right)\mathrm{dx},$ Wherein $R\left(x\right)=\left(\frac{R_p+R_t}{2}\right)+\left(\frac{R_p-R_t}{2}\right)\cos \left(\frac{2\mathrm{\πx}}{l_p+l_t}\right),$ Wherein R _p, R _trepresent hole and venturi center inscribed circle radius respectively, l _p, l _trepresent the length of hole and venturi respectively.X=0 is positioned at the center of hole, x=(l _p+ l _t)/2 are positioned at the center of venturi;

The form factor of described pore constriction wherein A is pore constriction area of section, and P is the girth of pore constriction cross sectional shape.