CN112102487A - Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal - Google Patents
Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal Download PDFInfo
- Publication number
- CN112102487A CN112102487A CN202010976480.0A CN202010976480A CN112102487A CN 112102487 A CN112102487 A CN 112102487A CN 202010976480 A CN202010976480 A CN 202010976480A CN 112102487 A CN112102487 A CN 112102487A
- Authority
- CN
- China
- Prior art keywords
- permeability
- dimensional
- shale
- pores
- fractal
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000035699 permeability Effects 0.000 title claims abstract description 148
- 238000000034 method Methods 0.000 title claims abstract description 37
- 239000011148 porous material Substances 0.000 claims abstract description 134
- 239000005416 organic matter Substances 0.000 claims abstract description 62
- 230000004856 capillary permeability Effects 0.000 claims abstract description 16
- 238000004364 calculation method Methods 0.000 claims abstract description 14
- 230000000694 effects Effects 0.000 claims description 33
- 238000009792 diffusion process Methods 0.000 claims description 16
- 230000035945 sensitivity Effects 0.000 claims description 12
- 239000011159 matrix material Substances 0.000 claims description 11
- 238000001179 sorption measurement Methods 0.000 claims description 11
- 238000013508 migration Methods 0.000 claims description 6
- 230000005012 migration Effects 0.000 claims description 6
- 230000006835 compression Effects 0.000 claims description 3
- 238000007906 compression Methods 0.000 claims description 3
- 238000012821 model calculation Methods 0.000 claims description 2
- 238000004626 scanning electron microscopy Methods 0.000 claims 1
- 230000007547 defect Effects 0.000 abstract 1
- 239000007789 gas Substances 0.000 description 49
- 150000001875 compounds Chemical class 0.000 description 5
- 239000012530 fluid Substances 0.000 description 5
- 230000014509 gene expression Effects 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 239000000126 substance Substances 0.000 description 5
- 238000012545 processing Methods 0.000 description 4
- 230000005540 biological transmission Effects 0.000 description 3
- 230000015572 biosynthetic process Effects 0.000 description 3
- 238000011161 development Methods 0.000 description 3
- 230000018109 developmental process Effects 0.000 description 3
- 230000007246 mechanism Effects 0.000 description 3
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 238000012937 correction Methods 0.000 description 2
- 230000007423 decrease Effects 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000001000 micrograph Methods 0.000 description 2
- 230000002194 synthesizing effect Effects 0.000 description 2
- 230000008859 change Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000003795 desorption Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000000445 field-emission scanning electron microscopy Methods 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 239000012535 impurity Substances 0.000 description 1
- 238000001764 infiltration Methods 0.000 description 1
- 230000008595 infiltration Effects 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000000877 morphologic effect Effects 0.000 description 1
- 229910052757 nitrogen Inorganic materials 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000001878 scanning electron micrograph Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 239000011800 void material Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/05—Geographic models
-
- G06T5/73—
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/136—Segmentation; Edge detection involving thresholding
Abstract
The invention discloses an unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal, which comprises the following steps: establishing a one-dimensional single capillary permeability model of organic matter and inorganic matter pores of shale; determining the distribution conditions of organic matter and inorganic matter pores of the shale in different pore diameters; calculating the porosity of organic matter pores and inorganic matter pores in the fractal unit; determining the micro-crack permeability by adopting a mathematical statistics method; determining the connection probability of different pore diameters on the connected sections according to the distribution condition of different pore diameters on the adjacent sections of the shale; and determining the three-dimensional apparent permeability of shale organic matter pores, the three-dimensional apparent permeability of shale inorganic matter pores and the three-dimensional apparent permeability of shale cracks according to the connection probability, and superposing to obtain the three-dimensional permeability of shale. The method overcomes the defects in the prior art, and provides a calculation method for determining the three-dimensional permeability of the unconventional reservoir.
Description
Technical Field
Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal
The invention relates to the field of unconventional reservoir exploration and development, in particular to a method for determining three-dimensional permeability of an unconventional reservoir based on multiple mixed fractal.
Background
Compared with the conventional reservoir, the unconventional reservoir has larger differences in the aspects of reservoir formation, gas occurrence, development modes and the like. The shale has complex and various diagenesis types, complex pore structures and various gas occurrence and migration modes, and presents obvious multi-scale characteristics. Shale pores are mainly composed of nanopores and micropores, and are often developed with natural microcracks, wherein the pores can be divided into organic and inorganic pores. The gas existing form and flow mechanism in various pore structures have certain differences, such as one or more gas flow mechanisms of viscous flow, slip flow, adsorption and desorption, Knudsen diffusion and surface diffusion, which are widely existed in the matrix, and the description of the shale permeability is a technical problem in the field.
In the prior art, the description of the shale permeability in unconventional reservoirs is mostly based on a single capillary model, and the determination of the permeability of the single capillary of the shale is realized by representing the influence and the proportion of different flow states in the single capillary in gas transmission. However, the method can only describe the one-dimensional permeability of the shale, and cannot consider the actual situation that single capillaries and microcracks with various different apertures exist in the shale, so that a method capable of determining the three-dimensional permeability of the shale is urgently needed.
Disclosure of Invention
In view of this, an object of the embodiments of the present invention is to provide a method for determining three-dimensional permeability of an unconventional reservoir based on multiple mixed fractals.
In order to achieve the above technical objects, the present invention provides the following technical solutions.
A three-dimensional permeability determination method for an unconventional reservoir based on multiple mixed fractal, wherein the unconventional reservoir is a shale reservoir, and comprises the following steps:
and 5, determining the three-dimensional apparent permeability of the shale organic matter hole, the three-dimensional apparent permeability of the shale inorganic matter hole and the three-dimensional apparent permeability of the shale crack through the connection probability, and superposing the three-dimensional apparent permeability of the shale organic matter hole, the three-dimensional apparent permeability of the shale inorganic matter hole and the three-dimensional apparent permeability of the shale crack to obtain the three-dimensional permeability of the shale.
Further, the single capillary permeability model calculation formula of shale organic matter pores and inorganic matter pores in the step (1) is as follows:
in the formula, korgThe permeability of the organic single capillary is shown; k is a radical ofinorgThe permeability of inorganic single capillary is adopted; mu.srTrue gas viscosity; ree-orgThe effective flowing radius of the organic matter capillary is considered in the stress sensitivity effect and the gas adsorption effect; ree-inorgThe effective flowing radius of the inorganic capillary is considered by the stress sensitivity effect and the gas adsorption effect;
is organic single capillary gasThe volume flow rate;
the gas volume flow rate is inorganic single capillary; vmIs the gas molar volume;
is the average capillary pressure; w is av *Is a viscous flow weight coefficient; alpha is a rare effect coefficient; knRIs capillary knudsen number; r0e-orgThe pore radius of the organic capillary is considered in the stress sensitivity effect; z is a gas deviation factor; r is a universal gas constant; t is reservoir temperature; w is ak *Is a knudsen flow weight coefficient;*the ratio of the gas molecular diameter to the effective pipe diameter; df *Is the roughness fractal dimension; c is the real gas volume compression coefficient; m is the gas molar mass; dsIs the surface diffusion coefficient; camaxThe maximum concentration of the adsorbed gas in the organic matter pores; p is a radical ofLLangmuir pressure; re-orgIs the effective pipe radius of the organic matter hole; r0e-inorgThe pore radius of the inorganic capillary is considered for stress sensitive effect.
Further, in the step (3), a scanning electron microscope image method or an X-ray energy spectrometer scanning method is adopted to determine the distribution conditions of different pore diameters.
Further, the calculation formula of the porosity permeability of organic pores in the fractal unit and the porosity permeability of inorganic pores in the fractal unit is as follows:
in the formula, kapp-orgThe two-dimensional permeability of organic matter pores in the fractal unit is shown; k is a radical ofapp-inorgThe two-dimensional permeability of inorganic pores in the fractal unit is shown;
is the organic matter content; a. theresIs a representative cell area; l is0The lengths of two ends of the capillary are straight lines; dTFractal dimension of tortuosity; i is the number of iterations; a to H are fractal units in organic pores; a to C are fractal units in the pores of the matrix-free matrix.
Further, the three-dimensional permeability calculation formula is
k3app-m＝k3app-org+k3app-inorg+kapp-f
Wherein k is3app-orgThe three-dimensional apparent permeability of shale organic matter pores is obtained; k is a radical of3app-inorgThe three-dimensional apparent permeability of inorganic pores of the shale; k is a radical of3app-fThe three-dimensional apparent permeability of the shale fracture is shown; k is a radical of3app-mIs the shale three-dimensional permeability.
The invention provides a method for determining three-dimensional permeability of an unconventional reservoir, which considers the multi-scale characteristics and various occurrence mode characteristics of shale pores, considers the shale pores as multiple media, establishes a shale three-dimensional permeability calculation method by combining electron microscope experimental results with theoretical models by adopting a mixed fractal method, and provides a new idea for determining the three-dimensional permeability of the unconventional reservoir.
Drawings
FIGS. 1-6 are graphs illustrating the analysis of the results of the calculations according to the present invention.
Detailed Description
The details of the present invention can be more clearly understood in conjunction with the accompanying drawings and the description of the embodiments of the present invention. However, the specific embodiments of the present invention described herein are for the purpose of illustration only and are not to be construed as limiting the invention in any way. Any possible variations based on the present invention may be conceived by the skilled person in the light of the teachings of the present invention, and these should be considered to fall within the scope of the present invention.
A three-dimensional permeability determination method for unconventional reservoirs, wherein the unconventional reservoirs are shale reservoirs, and the method comprises the following steps:
k3app-m＝k3app-org+k3app-inorg+kapp-f
Wherein k is3app-orgThe three-dimensional apparent permeability of shale organic matter pores is obtained; k is a radical of3app-inorgThe three-dimensional apparent permeability of inorganic pores of the shale; k is a radical of3app-fThe three-dimensional apparent permeability of the shale fracture is shown; k is a radical of3app-mIs the shale three-dimensional permeability.
Due to the fact that the shale has complex pores, the pores are divided into organic pores and inorganic pores, gas migration modes of the shale are various, for example, viscous flow, Knudsen flow, surface diffusion and the like exist, meanwhile, the permeability of a reservoir stratum can be influenced by stress (namely stress sensitive effect), pressure and temperature can influence the gas viscosity (namely real gas effect), and certain difficulty is added to the description of the porosity of the shale due to the influence of the various factors.
Obviously, in practical application, a person skilled in the art can establish a shale single capillary permeability model by considering the influence of one or more of the above factors according to the actual occurrence of an actual reservoir. In the present application, the inventor has established a shale single capillary permeability model by simultaneously considering the influence of the above factors, and obviously, a person skilled in the art may determine whether to consider the influence of the pressure sensitive effect and the real gas effect according to the reservoir conditions based on the actual conditions of the reservoir, for example, a gas occurrence mode determined according to the experimental results based on the shale single capillary permeability model established in the present application, and obviously, the person skilled in the art may also perform further deepening or simplification based on the theoretical model of the present invention.
The following contents are the establishment process of the single capillary permeability model, wherein viscous flow, Knudsen diffusion and surface diffusion are comprehensively considered for organic matter pores, viscous flow and Knudsen diffusion are comprehensively considered for inorganic matter pores, and the real gas effect (namely, the gas deviation factor is an indeterminate value), dynamic viscosity change and stress sensitivity effect under the condition of underground seepage are considered at the same time:
the expressions of the infiltration of the organic matter and the inorganic matter single capillary considering various effects are respectively as follows:
in the formula, korgIs the permeability of organic single capillary, m2；Re-orgIs the effective pipeline radius of the organic matter hole, m; mu.srTrue gas viscosity, Pa · s;
is the gas volume flow of an organic matter single capillary tube, m3/s；
Is the gas volume flow of the inorganic single capillary, m3/s；；kinorgIs the permeability of inorganic single capillary, m2；VmIs the molar volume of gas, m3·mo1-1；
Is the average capillary pressure, Pa; w is av *Is a viscous flow weight coefficient and has no dimension; (ii) a KnRIs capillary knudsen number without dimension; alpha is a rare effect coefficient and is dimensionless; ree-orgThe effective flowing radius of the organic matter capillary, m, considering the stress sensitive effect and the gas adsorption effect; r0e-orgThe pore radius m of the organic matter capillary considering the stress sensitivity effect; ree-inorgThe effective flowing radius, m, of the inorganic capillary tube considering the stress sensitivity effect and the gas adsorption effect; r0e-inorgThe pore radius of an inorganic capillary tube considering the stress sensitivity effect, m; z is a gas deviation factor and is dimensionless; r is a universal gas constant, J.mol-1K-1(ii) a T is reservoir temperature, K; w is ak *The weight coefficient of the Knudsen flow is dimensionless;*the ratio of the gas molecular diameter to the effective pipe diameter is dimensionless; df *The fractal dimension of roughness is dimensionless; c is a real gas volume compression coefficient and is dimensionless; m is gas molar mass, kg/mol; dsIs the surface diffusion coefficient, m2/s；CamaxThe maximum concentration of adsorbed gas in organic pores is mol/m3；pLLangmuir pressure;
the pore structure can be described by a multiple mixing fractal theory, and in the actual use process, the pore statistics of a fitting scanning electron microscope is fitted with the actual electron microscope scanning result, so that two curves can be consistent and the actual pore condition can be represented. Completing the fractal of the hole;
an IFU (interpolated Fractal units) method is adopted, based on a Fractal theory, the method is composed of different Fractal units based on different iteration parameters, and each Fractal unit is formed by evolution of a Sierpinski carpet (Sierpinski carpet). The Sierpinski carpet is one of self-similarity sets and meets the self-similarity of a fractal theory.
According to the fractal theory, the following expression is shown:
λi＝λmax/Fi-1 (48)
in the formula, λmaxThe side length of the maximum white square is m; f is the number of small squares generated on each side length in an iterative process, or the number of equally divided unit side lengths, and is dimensionless; lambda [ alpha ]iThe length of a blank square under the ith iteration is m;
the number of blank squares generated under the ith iteration satisfies the following expression:
Ni＝(F2-Ns-Np)i-1×Np (49)
in the formula, Ns is the number of small units which are kept constant in each iteration process, and is dimensionless; n is a radical ofpThe number of blanks (pores) in the initial fractal unit is dimensionless;
the fractal dimension can be expressed as:
in the formula, DfFractal dimension, dimensionless; n is a radical ofrThe number of the other squares except the blank square in the initial unit is dimensionless;
based on fractal theory, is used for describing pore structure. The model is composed of different fractal units based on different iteration parameters, and how to fractal the units is determined according to actual conditions, so that the pore statistics of a fitting scanning electron microscope is fitted with the scanning result of the actual electron microscope, two curves can be consistent, and the actual pore conditions can be represented.
Because the shale has strong heterogeneity and wide pore distribution, the selection of a representative region as a research object is particularly important. And determining the minimum RES, and selecting 1 pixel cell at four corners of the area as four different starting points, wherein the larger the pixel is, the larger the contained area is, as the graph resolution is a fixed value. The pixels are gradually increased, and the average gray scale value of each of the four regions is also changed. The average gray scale value represents the black and white level of the pattern (full black gray scale value is 0, full white gray scale value is 255). At the stage that the pixels are small, the average gray values of the four regions have large fluctuation, and gradually tend to be stable along with the continuous increase of the pixels, which shows that the proportion of the pores is close to the real porosity at the moment and representative. Therefore, the region corresponding to 400 pixels is finally determined as the minimum RES for the study. The target area is then expanded from the source point (1 pixel on the edge) in the original SEM image and the average gray level in the sub-squares is calculated.
On the basis of the selected RES, the FESEM field emission scanning electron microscope image is subjected to gray level processing by means of an image processing technology and then is used for pore analysis. The image processing mainly comprises the following steps: firstly, collecting an image; binarization of the image; filtering and sharpening; calibrating the size; removing impurities (setting a threshold value); sixthly, extracting morphological parameters. Based on ImageJ professional image processing software, the pore segmentation threshold is corrected through the face porosity, and the number of capillaries with different sizes can be quantitatively counted through processing according to the process.
TABLE 1 organic matter IFU model fractal unit basic parameters
According to the statistical result of the scanning image of the electron microscope, as shown in table 1, the organic matter hole can be divided into 8 units, which are respectively marked as unit a, unit B, unit C, unit D, unit E, unit F, unit G and unit H; as shown in Table 2, the inorganic pores are sequentially divided into 3 units, which are respectively marked as unit A1Unit B1Unit C1。
TABLE 2 inorganic IFU model fractal Unit basic parameters
In addition, those skilled in the art can also use an X-ray energy spectrometer scanning method or a nitrogen adsorption experiment to obtain the distribution conditions of organic matter pores and inorganic matter pores of the shale in different pore diameters.
the porosity permeability of organic pores in the fractal unit, the porosity permeability of inorganic pores in the fractal unit and the microcrack permeability are superposed, so that the two-dimensional permeability of the shale matrix can be obtained, but the method for calculating the two-dimensional permeability of the shale matrix does not consider the connection condition between different pores between adjacent sections.
On the basis of a single capillary flow equation, a matrix multi-capillary multi-mixing fractal flow equation with different transmission mechanisms is deduced.
3.1 viscous flow
Analyzing viscous flow, and correcting the gas adsorption pipe diameter:
molar flow converted to volumetric flow:
make the gas adsorb the pipe diameter correction coefficient
In the formula (I), the compound is shown in the specification,
is the volume flow of viscous fluid, m3/s；
Round tubes are converted into square tubes:
substitution formula
Order to
Superposing the flow of all pores in the fractal unit:
in the formula, QvIn a fractal unit of poresVolume flow of viscous fluid m after superposition of all pores3/s；
Order to
3.2 Knudsen flow
In the formula, QkThe flow volume m of the Knudsen fluid after all the pores in a certain fractal unit are superposed3/s；
Wherein the gas adsorption pipe diameter correction coefficient
3.3. Surface diffusion
In the formula, QsThe surface diffusion volume flow m after all the pores in a fractal unit are superposed3/s；
Wherein the gas adsorption pipe diameter is repairedPositive coefficient
Aiming at organic pores:
and (3) synthesizing viscous flow, Knudsen diffusion and surface diffusion to obtain the total volume flow of the organic matter after all pores in a certain fractal unit are superposed:
in the formula, QtIs the total volume flow m of all the pores in a fractal unit of the organic matter after being superposed3/s；
From generalized darcy's law:
and Q ═ QtTherefore, the following are:
in the formula, kapp-orgIs the two-dimensional apparent permeability of organic pores, m2；AresIs a representative cell area, m2；
The organic matter (TOC) content is determined by experiments, and the specific numerical value is decimal;
aiming at inorganic pores:
by simplification, the inorganic viscous flow expression is:
in the formula (I), the compound is shown in the specification,
the viscous fluid volumetric flow m after the superposition of all pores in a fractal unit of inorganic substances3/s；
Wherein:
the inorganic Knudsen flow expression is:
in the formula (I), the compound is shown in the specification,
the flow volume m of the Knudsen fluid is obtained after all pores in a fractal unit of inorganic substances are superposed3/s；
Wherein:
and (3) synthesizing viscous flow and Knudsen diffusion to obtain the total volume flow of all the superposed pores in a certain fractal unit of the inorganic substance:
in the formula (I), the compound is shown in the specification,
the total volume flow of the integrated viscous flow and the Knudsen flow in a fractal unit of inorganic substances, m3/s；
From generalized darcy's law:
and also
Therefore, the method comprises the following steps:
in the formula, kapp-inorgIs the two-dimensional apparent permeability of inorganic pores, m2；
Permeability of two-dimensional fracture
Through statistics, the opening of the natural crack is 150 nm-700 nm, and the average opening is 350 nm; the average length was 42.5 μm; average density of crack distribution 38.6 pieces/10000 μm2。
Similar to the derivation process of the volume flow of the viscous flow, the volume flow of the round tube knudsen flow and the volume flow of the surface diffusion can be obtained, and the volume flow of the round tube viscous flow, the knudsen flow and the volume flow of the surface diffusion can be respectively expressed as follows:
convert round tube into slit, introduce shape factor:
in the formula (I), the compound is shown in the specification,
the average opening of the cracks, m;
is the average crack length, m;
wherein:
wherein:
wherein:
defining the area of the observation area as AfThe number of the cracks counted in the region is nfDensity of cracks rhof＝nf/AfThen the total volume flow of the fracture in the region is as follows:
wherein:
taking into account crack tortuosity
Substituting:
from generalized darcy's law:
and Q' ″ or QfTherefore, the following are:
in the formula, kapp-fIs the apparent permeability of the natural fracture of the matrix, m2；
the spatially varying void sizes are initially ordered in descending order according to equivalent diameter. To provide an example, the iteration level, equivalent diameter, number of holes and probability are listed in table 2, with the equivalent diameters arranged in descending order. The largest hole is λ1It may connect any holes on other surfaces (e.g., λ in plane A)1Each hole in the face B may be connected). Lambda in one surface (A plane)1The holes being connected to other lambdas1Probability of pore (. lamda.)1 2N1/A)2。
For the second layer, λ in plane A2The hole connecting to λ in the plane B2The probability of a hole is (lambda)1 2N1/A)×(λ2 2N2/A), as indicated by the red arrow, λ in the plane A2The hole connecting to λ in the plane B2The probability of a hole is (lambda)2 2N2/A)2As indicated by the blue arrow. In addition, λ in the plane B2The hole connecting to λ in the plane A1The probability of a hole is (lambda)1 2N1/A)×(λ1 2N1A). We must obtain the probability (λ)2 2N2/A)2+2(λ1 2N1/A)(λ2 2N2A), and the probabilities of the following apertures in the remaining iteration levels. Table 3 shows each connection probability.
TABLE 3 probability of pore connection
According to table 4, the organic IFU model fractal element basic parameters, the PCC method and the two-dimensional apparent permeability were combined to calculate the apparent gas permeability for each iteration level in the 3 diff model.
k3app-m＝k3app-org+k3app-inorg+kapp-f
Wherein k is3app-orgThe three-dimensional apparent permeability of shale organic matter pores is obtained; k is a radical of3app-inorgThe three-dimensional apparent permeability of inorganic pores of the shale; k is a radical of3app-fThe three-dimensional apparent permeability of the shale fracture is shown; k is a radical of3app-mIs the shale three-dimensional permeability.
According to different iteration times, k when the iteration times are differentDThe formula is as follows:
for three-dimensional organic matter pores:
for an iteration level n of 1,
for an iteration level n of 2,
for an iteration level n-3,
by analogy …
Thus, the total organic matter three-dimensional permeability is expressed as:
k3app-org＝kD(1)+kD(2)+kD(3)+kD(4)+kD(5)+kD(6)+kD(7)+kD(8) (100)
in the formula, k3app-orgIs the three-dimensional apparent permeability of shale organic matter pores m2；
For three-dimensional inorganic pores:
for an iteration level n of 1,
for an iteration level n of 2,
for an iteration level n-3,
thus, the total organic matter three-dimensional permeability is expressed as:
k3app-inorg＝kD(11)+kD(22)+kD(33) (104)
in the formula, k3app-inorgIs the three-dimensional apparent permeability of inorganic pores of the shale, m2；
The total three-dimensional permeability of the fracture is expressed as:
in the formula, k3app-fIs the three-dimensional apparent permeability of the shale fracture, m2；
The three-dimensional apparent permeability of the comprehensive organic matter, inorganic matter and natural microcracks can be expressed as follows:
k3app-m＝k3app-org+k3app-inorg+kapp-f (106)
in the formula, k3app-mFor comprehensive consideration of organic matters,Three-dimensional permeability m of inorganic and natural microcracked shale reservoir2(ii) a The basic parameters are shown in table 4:
table 4 basic parameters
(2) Calculation results
As can be seen from the calculation results in fig. 1, the larger the pore size has a greater influence on the permeability, for example, the maximum pore size of the organic matter is 177.2nm, and the permeability considering the true gas effect is generally lower than that not considering the true gas effect, because the viscosity of the gas considering the true gas effect is generally higher than that of the ideal gas, and in contrast, the resistance of the gas transmission process is increased, and the apparent permeability is reduced. The lower the temperature, the greater the permeability under the same conditions.
From the calculation result of fig. 2, it can be seen that, taking the maximum aperture of the organic matter of 177.2nm as an example, the stress sensitive effect has a certain influence on the capillary permeability. Under high formation pressure, the permeability is reduced to a greater extent by the stress sensitivity; as formation pressure decreases, the effect of stress sensitivity on permeability increases and then decreases.
As can be seen from the calculation results of fig. 3 and 4, different fractal units show a large difference in permeability contribution; in the organic matter, the contribution of the unit G is maximum, and the contribution of the unit E is minimum; in inorganic matter, unit a contributes the most and unit C the least. The permeability contributions of the different units are related to basic parameters of the fractal unit for obtaining the IFU model, wherein the number of the units and the side length of the pore square have the largest influence on the permeability of the fractal unit.
As can be seen from the calculation result of FIG. 5, the inorganic substances have wide distribution area, and the contribution to the matrix permeability is the largest, and reaches 73.72%; although the distribution area of the organic matters is small, the pore development degree of the organic matters is good, and the contribution to the matrix permeability is 8.28%; natural fissures which develop in large numbers in the matrix have a great influence on the permeability of the matrix, and the contribution ratio is up to 17.99%.
As can be seen from the calculation results of fig. 6, the permeability of the three-dimensional shale has close relations with the type and number of the pores and the width and density of the fractures, the permeability increases with the increase of the type and number of the pores and the width and density of the fractures, the better the connectivity of the shale, the higher the permeability. Compared with two-dimensional, three-dimensional organic matter permeation is 5.59% of two-dimensional organic matter permeation rate; the three-dimensional inorganic permeability is 17.35% of the two-dimensional inorganic permeability; the three-dimensional fracture permeability was 14.22% of the two-dimensional fracture permeability. Because certain tiny pore passages and dead pores exist in the actual shale, and the connection of pores between different sections is not one hundred percent, the obtained three-dimensional permeability is smaller than the two-dimensional permeability, and the objective rule is met.
While the present invention has been described in detail by way of the embodiments, it should be understood that the present invention is not limited to the embodiments disclosed herein, but is intended to cover other embodiments as well. But all the modifications and simple changes made by those skilled in the art without departing from the technical idea and scope of the present invention belong to the protection scope of the technical solution of the present invention.
Claims (5)
1. A three-dimensional permeability determination method for an unconventional reservoir based on multiple mixed fractal, wherein the unconventional reservoir is a shale reservoir, and comprises the following steps:
step 1, considering the actual migration state of shale gas in a single capillary model, establishing a single capillary permeability model of shale organic matter pores and inorganic matter pores, wherein the single capillary permeability model is a one-dimensional permeability model;
step 2, determining the distribution conditions of organic matter pores and inorganic matter pores of the shale in different pore diameters;
step 3, calculating the two-dimensional permeability of organic matter pores in the fractal unit and the two-dimensional permeability of inorganic matter pores in the fractal unit by using a one-dimensional permeability model; determining the permeability of the microcracks by adopting a mathematical statistic method;
step 4, determining the connection probability of holes with different apertures on the connected sections according to the distribution condition of the holes with different apertures on the adjacent sections of the shale;
and 5, determining the three-dimensional apparent permeability of the shale organic matter hole, the three-dimensional apparent permeability of the shale inorganic matter hole and the three-dimensional apparent permeability of the shale crack through the connection probability, and superposing the three-dimensional apparent permeability of the shale organic matter hole, the three-dimensional apparent permeability of the shale inorganic matter hole and the three-dimensional apparent permeability of the shale crack to obtain the three-dimensional permeability of the shale.
2. The method for determining the three-dimensional permeability of the unconventional reservoir based on the multi-mixed fractal as claimed in claim 1, wherein the single capillary permeability model calculation formula of the shale organic matter pores and inorganic matter pores in the step (1) is as follows:
in the formula, korgThe permeability of the organic single capillary is shown; k is a radical ofinorgThe permeability of inorganic single capillary is adopted; mu.srTrue gas viscosity; ree-orgThe effective flowing radius of the organic matter capillary is considered in the stress sensitivity effect and the gas adsorption effect; ree-inorgThe effective flowing radius of the inorganic capillary is considered by the stress sensitivity effect and the gas adsorption effect;
the gas volume flow rate of the organic single capillary is adopted;
is inorganic single capillary gasThe volume flow rate; vmIs the gas molar volume;
is the average capillary pressure; w is av *Is a viscous flow weight coefficient; alpha is a rare effect coefficient; knRIs capillary knudsen number; r0e-orgThe pore radius of the organic capillary is considered in the stress sensitivity effect; z is a gas deviation factor; r is a universal gas constant; t is reservoir temperature; w is ak *Is a knudsen flow weight coefficient;*the ratio of the gas molecular diameter to the effective pipe diameter; df *Is the roughness fractal dimension; c is the real gas volume compression coefficient; m is the gas molar mass; dsIs the surface diffusion coefficient; camaxThe maximum concentration of the adsorbed gas in the organic matter pores; p is a radical ofLLangmuir pressure; re-orgIs the effective pipe radius of the organic matter hole; r0e-inorgThe pore radius of the inorganic capillary is considered for stress sensitive effect.
3. The unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractals as claimed in claim 1, wherein the distribution of different pore sizes is determined in step (3) by scanning electron microscopy or X-ray energy spectrometer scanning.
4. The method for determining the three-dimensional permeability of the unconventional reservoir based on the multi-mixed fractal as claimed in claim 1, wherein the calculation formula of the porosity of organic pores in the fractal unit and the porosity of inorganic pores in the fractal unit is as follows:
in the formula, kapp-orgThe two-dimensional permeability of organic matter pores in the fractal unit is shown; k is a radical ofapp-inorgThe two-dimensional permeability of inorganic pores in the fractal unit is shown;
is the organic matter content; a. theresIs a representative cell area; l is0The lengths of two ends of the capillary are straight lines; dTFractal dimension of tortuosity; i is the number of iterations; a to H are fractal units in organic pores; a to C are fractal units in the pores of the matrix-free matrix.
5. The method for determining the three-dimensional permeability of the unconventional reservoir based on the multi-hybrid fractal in claim 1, wherein the three-dimensional permeability is calculated according to the formula
k3app-m＝k3app-org+k3app-inorg+kapp-f
Wherein k is3app-orgThe three-dimensional apparent permeability of shale organic matter pores is obtained; k is a radical of3app-inorgThe three-dimensional apparent permeability of inorganic pores of the shale; k is a radical of3app-fThe three-dimensional apparent permeability of the shale fracture is shown; k is a radical of3app-mIs the shale three-dimensional permeability.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010976480.0A CN112102487B (en) | 2020-09-17 | 2020-09-17 | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010976480.0A CN112102487B (en) | 2020-09-17 | 2020-09-17 | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112102487A true CN112102487A (en) | 2020-12-18 |
| CN112102487B CN112102487B (en) | 2022-02-15 |
Family
ID=73758702
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010976480.0A Active CN112102487B (en) | 2020-09-17 | 2020-09-17 | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112102487B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113850030A (en) * | 2021-09-24 | 2021-12-28 | 中国石油大学(华东) | Method and device for determining relative permeability of shale oil reservoir |
| CN114136862A (en) * | 2021-11-29 | 2022-03-04 | 西南石油大学 | Liquid apparent permeability calculation method of double-wettability shale |
| CN116152259A (en) * | 2023-04-23 | 2023-05-23 | 西南石油大学 | Reservoir permeability calculation method based on graph neural network |
| CN116359093A (en) * | 2023-03-31 | 2023-06-30 | 中国矿业大学(北京) | Quantification method for thermodynamic fracture and anti-reflection effect of coal rock |
Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104818970A (en) * | 2015-03-17 | 2015-08-05 | 中国石油大学(北京) | Method for reducing component loss and formation damage in high-temperature combined chemical flooding process |
| CN104910886A (en) * | 2014-03-12 | 2015-09-16 | 成都能生材科技开发有限责任公司 | Preparation method of nano-oil recovery displacement agent NDA for construction of nano-apertures |
| JP2018006258A (en) * | 2016-07-07 | 2018-01-11 | 旭化成株式会社 | Lead-acid battery separator and lead-acid battery using the same |
| CN108229048A (en) * | 2018-01-17 | 2018-06-29 | 陕西延长石油(集团)有限责任公司研究院 | A kind of multi- scenarios method calculation of permeability for considering shale matrix difference |
| CN108518212A (en) * | 2018-04-09 | 2018-09-11 | 西南石油大学 | A method of calculating shale gas reservoir complex fracture network unstable state yield |
| CN108531159A (en) * | 2018-04-11 | 2018-09-14 | 东北石油大学 | A kind of High Temperature Plugging Agent system for heavy crude heat extraction oil reservoir |
| CN110210460A (en) * | 2019-06-26 | 2019-09-06 | 中国石油大学(华东) | A kind of shale gas apparent permeability calculation method for considering multiple factors and influencing |
| CN110410045A (en) * | 2019-06-24 | 2019-11-05 | 中国石油化工股份有限公司 | A kind of stifled tune method for ultra-high water cut stage oil reservoir |
| CN111208051A (en) * | 2020-02-28 | 2020-05-29 | 西安石油大学 | Shale reservoir permeability dynamic prediction method under synergistic effect of complex mechanism |
| CN111291521A (en) * | 2020-03-10 | 2020-06-16 | 西南石油大学 | Method and device for calculating apparent permeability of liquid phase of tight reservoir |
| CN111553108A (en) * | 2020-05-20 | 2020-08-18 | 中国石油大学(华东) | Shale gas reservoir fluid-solid coupling multi-scale numerical simulation method |
| CN111610130A (en) * | 2020-05-30 | 2020-09-01 | 中国石油天然气股份有限公司 | Large-scale fresh water lake basin continental facies mud shale oil reservoir pore formation and evolution evaluation method |
-
2020
- 2020-09-17 CN CN202010976480.0A patent/CN112102487B/en active Active
Patent Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104910886A (en) * | 2014-03-12 | 2015-09-16 | 成都能生材科技开发有限责任公司 | Preparation method of nano-oil recovery displacement agent NDA for construction of nano-apertures |
| CN104818970A (en) * | 2015-03-17 | 2015-08-05 | 中国石油大学(北京) | Method for reducing component loss and formation damage in high-temperature combined chemical flooding process |
| JP2018006258A (en) * | 2016-07-07 | 2018-01-11 | 旭化成株式会社 | Lead-acid battery separator and lead-acid battery using the same |
| CN108229048A (en) * | 2018-01-17 | 2018-06-29 | 陕西延长石油(集团)有限责任公司研究院 | A kind of multi- scenarios method calculation of permeability for considering shale matrix difference |
| CN108518212A (en) * | 2018-04-09 | 2018-09-11 | 西南石油大学 | A method of calculating shale gas reservoir complex fracture network unstable state yield |
| CN108531159A (en) * | 2018-04-11 | 2018-09-14 | 东北石油大学 | A kind of High Temperature Plugging Agent system for heavy crude heat extraction oil reservoir |
| CN110410045A (en) * | 2019-06-24 | 2019-11-05 | 中国石油化工股份有限公司 | A kind of stifled tune method for ultra-high water cut stage oil reservoir |
| CN110210460A (en) * | 2019-06-26 | 2019-09-06 | 中国石油大学(华东) | A kind of shale gas apparent permeability calculation method for considering multiple factors and influencing |
| CN111208051A (en) * | 2020-02-28 | 2020-05-29 | 西安石油大学 | Shale reservoir permeability dynamic prediction method under synergistic effect of complex mechanism |
| CN111291521A (en) * | 2020-03-10 | 2020-06-16 | 西南石油大学 | Method and device for calculating apparent permeability of liquid phase of tight reservoir |
| CN111553108A (en) * | 2020-05-20 | 2020-08-18 | 中国石油大学(华东) | Shale gas reservoir fluid-solid coupling multi-scale numerical simulation method |
| CN111610130A (en) * | 2020-05-30 | 2020-09-01 | 中国石油天然气股份有限公司 | Large-scale fresh water lake basin continental facies mud shale oil reservoir pore formation and evolution evaluation method |
Non-Patent Citations (1)
| Title |
|---|
| 赵玉龙: "基于复杂渗流机理的页岩气藏压裂井多尺度不稳定渗流理论研究", 《中国优秀博硕士学位论文全文数据库(博士)工程科技Ⅰ辑》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113850030A (en) * | 2021-09-24 | 2021-12-28 | 中国石油大学(华东) | Method and device for determining relative permeability of shale oil reservoir |
| CN113850030B (en) * | 2021-09-24 | 2022-09-06 | 中国石油大学(华东) | Method and device for determining relative permeability of shale oil reservoir |
| CN114136862A (en) * | 2021-11-29 | 2022-03-04 | 西南石油大学 | Liquid apparent permeability calculation method of double-wettability shale |
| CN114136862B (en) * | 2021-11-29 | 2024-04-09 | 西南石油大学 | Liquid apparent permeability calculation method of double-wettability shale |
| CN116359093A (en) * | 2023-03-31 | 2023-06-30 | 中国矿业大学(北京) | Quantification method for thermodynamic fracture and anti-reflection effect of coal rock |
| CN116152259A (en) * | 2023-04-23 | 2023-05-23 | 西南石油大学 | Reservoir permeability calculation method based on graph neural network |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112102487B (en) | 2022-02-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112102487B (en) | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal | |
| CN107817199B (en) | A kind of construction method of tight sand multi-scale porosity model and application | |
| Anderson et al. | Soil mass, surface, and spectral fractal dimensions estimated from thin section photographs | |
| CN108829950B (en) | Unconventional reservoir permeability evaluation method based on core image | |
| Xie et al. | Fractal and multifractal analysis of carbonate pore-scale digital images of petroleum reservoirs | |
| CN105115874A (en) | Multi-component three-dimensional digital core building method based on multi-source information fusion | |
| CN107132171B (en) | A method of compact reservoir pore-size distribution is determined based on pressure mercury-N2 adsorption translocation data | |
| CN113075105B (en) | Utilize comprehensive fractal dimension D p Method for quantitatively evaluating sandstone reservoir | |
| CN108280288B (en) | Reservoir permeability model establishing method based on stress sensitivity analysis | |
| CN109977469A (en) | A kind of Two-dimensional Porous Medium model building method based on Voronoi diagram | |
| CN108956415B (en) | Method for calculating relative permeability curve of unconventional reservoir sample | |
| Galaup et al. | New integrated 2D–3D physical method to evaluate the porosity and microstructure of carbonate and dolomite porous system | |
| Esser et al. | Network model of porous media–Review of old ideas with new methods | |
| Hu et al. | A lattice Boltzmann simulation on the gas flow in fractal organic matter of shale gas reservoirs | |
| CN114609010A (en) | Method and device for measuring oil-water relative permeability of shale reservoir | |
| CN110909466B (en) | Method for improving calculation accuracy of average capillary pressure curve of differential pore sorting reservoir | |
| CN109001093A (en) | A kind of quantitatively characterizing method of shale reservoir hole system and the method for evaluating shale reservoir pore character | |
| CN112287610A (en) | Calculation method for dividing low-permeability reservoir rock hydraulic mobile phase based on fractal theory | |
| Linß | Anisotropic meshes and streamline‐diffusion stabilization for convection–diffusion problems | |
| CN115221792A (en) | Natural gas hydrate type dividing device and method based on machine learning | |
| CN114705606A (en) | Blocking method of key seepage nodes in rock based on networked analysis | |
| CN111192317B (en) | Method for acquiring saturation of gas-liquid displacement image in micron-scale planar pore network | |
| Diógenes et al. | Grain size measurement by image analysis: An application in the ceramic and in the metallic industries | |
| CN113850030B (en) | Method and device for determining relative permeability of shale oil reservoir | |
| CN112816388A (en) | Oil sand seepage performance testing method based on CT and digital core three-dimensional reconstruction |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |