CN114357810A - Method for calculating critical parameters and phase diagram of fluid in organic matter pores of shale gas reservoir - Google Patents

Method for calculating critical parameters and phase diagram of fluid in organic matter pores of shale gas reservoir Download PDF

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CN114357810A
CN114357810A CN202210268418.5A CN202210268418A CN114357810A CN 114357810 A CN114357810 A CN 114357810A CN 202210268418 A CN202210268418 A CN 202210268418A CN 114357810 A CN114357810 A CN 114357810A
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苏玉亮
付金刚
郝永卯
李蕾
王文东
张雪
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China University of Petroleum East China
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Abstract

Fitting molecular simulation results of existing circular pores and slit-shaped pores, constructing a relation between random pore critical parameter offset and dimensionless pore diameter, further establishing an improved PR-EOS model in the shale organic pores, and solving to obtain the critical parameters and the phase diagram of the fluid in the shale pores. The method for calculating the fluid critical parameters and the phase diagram in the pores of the shale gas reservoir organic matter realizes calculation of the fluid critical parameters in the pores of the shale organic matter by simultaneously considering the pore shape and the adsorption characteristic, and can analyze and know the influence rule of the pore size and the pore shape on the fluid phase.

Description

Method for calculating critical parameters and phase diagram of fluid in organic matter pores of shale gas reservoir
Technical Field
The invention relates to the technical field of gas reservoir development, in particular to a method for calculating critical parameters and a phase diagram of fluid in organic matter pores of a shale gas reservoir.
Background
Shale gas reservoirs, as unconventional oil and gas resources, occupy an important position in energy structures and attract extensive attention of people. Shale gas exploration and development has achieved certain success, but shale gas exploration and development still faces many challenges. Fluids in shale gas reservoirs are more sensitive to temperature and pressure than conventional gas reservoirs. At present, the mechanisms of fluid phase change and micro-migration in confined spaces are not clear. Inaccurate phase behavior model descriptions can lead to bias in yield predictions. Therefore, accurate calculation of shale gas reservoir phase dynamic parameters has important significance for efficient development of shale gas.
The micro-nano pores are widely distributed in shale reservoirs, in particular to organic matters in shale pore media. Various pore geometries can be found in shale pores, including circular, elliptical, rectangular, and triangular. Due to the complex pore structure of the actual shale reservoir, a great deal of previous research has simplified the shale pore medium into cylindrical pores. Therefore, the ideal model assumption may cause the calculation result to have a large deviation from the actual situation. The adsorption research of the organic pores mainly focuses on quantitative characterization of the thickness of the adsorption layer, but the shape of the pores also has a large influence on the total adsorption quantity. Quantitative calculation of adsorbed and free fluids in organic matter pores is key to shale gas reserves prediction.
At present, the critical property shift of confined space fluids is mainly studied by laboratory experiments and molecular simulation. Most of molecular simulation is based on circular pores and slit pores, and the influence of the shape of micro-nano pores in an actual shale gas reservoir is ignored. In order to apply the molecular simulation results to the phase equilibrium calculation, many researchers have proposed the shift equations of the critical temperature and critical pressure by introducing generalized van der waals theory or using a method of directly fitting the molecular simulation results. However, the equation only considers the size of the pores and neglects the influence of the shape of the pores.
Disclosure of Invention
In order to solve the problems, the invention discloses a method for calculating critical parameters and a phase diagram of fluid in organic matter pores of a shale gas reservoir.
Summary of the invention:
the invention provides a quantitative description method of the content of adsorbed gas of a multi-component fluid in a non-circular pore based on a Scanning Electron Microscope (SEM) image of a shale core and an adsorption thickness semi-empirical calculation formula. Meanwhile, the effective molar volume correction method is popularized to non-circular holes. On the basis, a method for correcting the critical parameters of the confined fluid in the non-circular pore considering the pore shape and the composition of the mixed fluid is provided. Finally, an improved PR-EOS model is provided and solved, so that critical parameters and a phase diagram of the fluid in the shale micro-nano pores are obtained.
The detailed technical scheme of the invention is as follows:
a method for calculating critical parameters and a phase diagram of fluid in organic matter pores of a shale gas reservoir comprises the following steps:
s1: firstly, obtaining a shale reservoir SEM Image, further extracting pores by using Image processing software Image J, and carrying out ellipse fitting on irregular pores to obtain a fitted Image and parameters of each pore, wherein the fitted Image comprises a fitted ellipse major semi-axis and a fitted ellipse minor semi-axisa x Short half shaftb y ；
S2: and (3) calculating the thickness of the adsorption layer of the component fluid according to the following calculation formula:
Figure 796544DEST_PATH_IMAGE001
Figure 12631DEST_PATH_IMAGE002
Figure 518699DEST_PATH_IMAGE003
Figure 469337DEST_PATH_IMAGE004
wherein the content of the first and second substances,δ adthe thickness of the adsorption layer of the multicomponent fluid;δ ad（i）is composed ofiThe thickness of the adsorption layer of the component fluid;X i is the firstiThe mole fraction of each of the components,i≥1；Nis a natural number greater than or equal to 1;m i 、n i coefficients for different components, respectively;r pis the pore radius, σLJ（i）Is as followsiThe Lennard-Jones size factor of the component;MW i is as followsiThe molecular weight of the component;
s3: calculating the corrected molar volume within the elliptical poresV mmTo the conventional molar volumeV mThe calculation formula is as follows:
Figure 86263DEST_PATH_IMAGE005
Figure 173168DEST_PATH_IMAGE006
wherein the content of the first and second substances,V ptotal volume occupied by fluid;n t is the total number of fluid molecules;n a is the number of adsorbed fluid molecules;N Ais an avogalois constant;V mmolar volume in conventional PR-EOS; parameter(s)χAs defined coefficients, dimensionless parameters;βa density factor that results in a decrease for adsorption;R hv=a x /b y ，r p= b y， whereina x Length of ellipse major semi-axis, m;b y length of ellipse minor semi-axis, m;
s4: base ofIn the existing molecular simulation result, fitting is carried out on the relation between the critical temperature offset and the dimensionless pore diameter in the regular pore, and considering that the shale gas reservoir mainly contains a methane component and has less contents of other components, the fitting is respectively carried out on C1 (methane) and C2+ (other light hydrocarbon components) to obtain ln (methane)∆T *) And ln (W p /σ LJ ) The fitting curve of (1);
preferably, based on the results of the existing molecular simulation, fitting is performed on the C1 and C2+ components, respectively, to obtain:
c1 component:
for a circular aperture:
Figure 850137DEST_PATH_IMAGE007
for the slit-shaped aperture:
Figure 22492DEST_PATH_IMAGE008
wherein the correlation coefficient R of equation (7) is linearly fitted20.9590; linear fitting of the correlation coefficient R of equation (8)20.8094;
c2+ component:
for a circular aperture:
Figure 177530DEST_PATH_IMAGE009
for the slit-shaped aperture:
Figure 633788DEST_PATH_IMAGE010
wherein the correlation coefficient R of equation (9) is linearly fitted20.9905; linear fitting of the correlation coefficient R of equation (10)20.8797;
in the above-described formulas (7) to (10),∆T *is the critical temperature offset;W p is an ellipseMinor axis length 2byI.e. the width of the aperture;
s5: critical temperature offset of elliptical pores∆T *And dimensionless apertureW p /σ LJ The irregular nano-pores in the shale porous medium are described by the elliptical pores, so that the aspect ratio of the pores is obtainedR hvAt any value, the critical property shift of the elliptical pores can be calculated based on the fitting results of the circular pores and the slit-shaped pores, by the following specific steps: in ln: (∆T *) ~ln(W p/σ LJ) Critical temperature offset for the round and slit-shaped holes respectively plotted in the coordinate systemT *And dimensionless aperture widthW p/σ LJLine1 and Line2, as shown on the left side of fig. 6; center point thereofp(x 0, y 0) The Line2 is the intersection of two lines Line1 and Line2, where the Line1 is equal to lnT *) ~ln(W p/σ LJ) Around the intersection point in the coordinate systemp(x 0, y 0) Rotation angleαThen obtained, angleαCalculated by the following method:
Figure 481658DEST_PATH_IMAGE011
whereink 1Andk 2the slopes of Line1 and Line2, respectively;
the length of the minor axis of the ellipse during the change in the shape of the aperture from circular to slitW pRemains unchanged, and therefore, the process is also the aspect ratio of the poresR hvFrom 1.0 to infinity;
the straight Line1 rotates by any angleθ 1The aspect ratio of the oval pores formed at this time isR hv，θ 1The variation interval of (a) is [0,α]the course of the variation in the left side of fig. 6 corresponds to the angle of the tangent of the major and minor semiaxes of the ellipse in the right side of fig. 6θ 2From arcπ/4 change toπThe process of/2, therefore,θ 1，θ 2andR hvthe relationship between them is as follows:
Figure 141310DEST_PATH_IMAGE012
Figure 100039DEST_PATH_IMAGE013
wherein, theta1The Line1 rotates to any angle in the process of Line 2; theta2The angle corresponding to the tangent value of the major semi-axis and the minor semi-axis of the ellipse;
obtained in combination with formula (11):
Figure 895956DEST_PATH_IMAGE014
wherein k is a pore shape RhvSlope of corresponding new straight line, the new straight line is critical temperature offset under any elliptical pore∆T * And dimensionless pore sizeW p /σ LJ The relationship between them;
obtaining any R of the elliptical holes based on the formulas (7), (8), (9) and (10)hvLower critical temperature offset∆T * And dimensionless apertureW p /σ LJ General expression of the correlation of (a):
Figure 914728DEST_PATH_IMAGE015
wherein C is1And C2Is constant, dimensionless;
s6: derived based on S4 and S5iCritical temperature offset of component∆T * And dimensionless apertureW p /σ LJ（i） The relation is as follows:
Figure 61675DEST_PATH_IMAGE016
wherein Δ * T (i) Is composed ofiCritical offset of component; c 1 i AndC 2 i is composed ofiThe relative number of the components is dimensionless;
s7: the corrected PR-EOS based on equation (5) is as follows:
Figure 824095DEST_PATH_IMAGE017
p, T refers to pressure and temperature;V mm in order to correct for the molar volume,V mm =V m /χ；Ris the universal gas constant;aandbdimensionless constants describing the attractive and repulsive forces, respectively;αis a dimensionless coefficient related to temperature;
the formula of the critical temperature and critical pressure deviation obtained by integral conversion of the pressure in formula (17) is as follows:
Figure 989366DEST_PATH_IMAGE018
Figure 913460DEST_PATH_IMAGE019
the critical temperature is obtained by combining the formula (15)T c And critical pressureP c The offset amounts of (A) are respectively:
Figure 547703DEST_PATH_IMAGE020
Figure 113814DEST_PATH_IMAGE021
wherein the content of the first and second substances,
Figure 149903DEST_PATH_IMAGE023
is as followsiCritical temperature offset of the component;T c(i) is as followsiThe critical temperature of the component;T cm(i) is as followsiCorrected critical temperatures of the components;
Figure 244898DEST_PATH_IMAGE025
is as followsiCritical pressure offset of a component;P c(i) is as followsiThe critical pressure of the component;P cm(i) is as followsiCorrected critical pressures for the components;
s8: critical temperature calculated based on the formula (20) and the formula (21)T cAnd critical pressureP cThe calculation formula of the critical temperature and critical pressure of each component under the influence of the pore shape and adsorption is obtained as follows:
Figure 366438DEST_PATH_IMAGE026
Figure 470660DEST_PATH_IMAGE027
s9: using WINPROP module in CMG reservoir simulation software to solve and calculate PR (1978) state equation, and calculating the critical temperature T of each component of fluid in the calculation processc(i)Critical pressure Pc(i)And molar volume Vm(i)Is modified to take into account the critical temperature T of each component of the fluid in the organic pores of the shale gas under the adsorption and limited space based on the calculation of the critical temperatures T of S7 and S8cm(i)Critical pressure Pcm(i)And molar volume Vmm(i)And performing flash evaporation calculation on the multi-component fluid to obtain critical parameters and a fluid phase diagram of the multi-component mixed fluid.
The invention achieves the following beneficial effects:
based on the method, the influence of the pore shape and the wall adsorption characteristic of the shale organic matter micro-nano pore can be comprehensively considered, an improved PR-EOS model in the shale organic matter limited space based on a molecular simulation result and a traditional PR-EOS model is established, a WINPROP fluid phase simulation module in CMG is utilized, fluid phase parameters and a fluid phase diagram in the shale micro-nano pore can be obtained through solving and calculation, and along with the deep research of the molecular simulation of the existing circular pore and slit pore, the improved PR-EOS model obtained through the fitting result is more accurate. The method can calculate and obtain the critical parameters and the phase diagram of the multi-component fluid in the organic matter pores of the shale gas reservoir, realizes the calculation of the critical parameters in the organic matter pores of the shale considering the pore shape and the adsorption characteristic at the same time, and can analyze and know the influence rule of the pore size and the pore shape on the fluid phase state.
Drawings
Fig. 1 is an SEM image of a shale sample during a simplified treatment process of irregular nanopores of shale based on SEM technology.
Fig. 2 is a schematic diagram of cylindrical pores and slit-shaped pores after SEM image processing and pore ellipse fitting, and cylindrical pores and slit-shaped pores constructed by molecular simulation.
FIG. 3 is the distribution position characteristics of the solid phase zone, the adsorption layer and the gas phase zone in the oval pores.
Fig. 4 is a fitted curve of critical temperature shift versus dimensionless pore size for the C1 component based on the results of prior molecular modeling studies.
Fig. 5 is a curve fitted to the critical temperature shift offset of the C2+ component in relation to the dimensionless pore size based on the results of prior molecular modeling studies.
FIG. 6 shows the variation law of the fitting curve of the circular pore gradually changed into the slit-shaped pore, the aspect ratio of the pore and the theta in the process of elliptical deformation2Tangent function curves for different angles.
Fig. 7 is a graph of critical temperature and critical pressure for methane lock in circular pores and slit-shaped pores.
FIG. 8 shows the difference RhvValue (different wells)Gap shape) to block the critical parameters of methane.
FIG. 9 shows different pore diameters (R)hvPhase diagram of multicomponent fluid under = 1).
FIG. 10 shows the difference RhvPhase diagram of multi-component fluids at values (different pore shapes).
Detailed Description
The invention is explained in more detail below with reference to exemplary embodiments and the drawing of the description, without limiting the scope of protection.
Example 1
A method for calculating a critical parameter of C1 (methane) in organic matter pores of a shale gas reservoir is calculated according to the following steps (specific parameters used in calculation are shown in a table 3):
s1: firstly, obtaining a shale reservoir SEM Image as shown in figure 1, further extracting pores by using Image processing software Image J, wherein the extraction result is shown in figure 2, and performing ellipse fitting on irregular pores to obtain a fitted Image and parameters of each pore, including a major semi-axis and a minor semi-axis of the fitted ellipse, as shown in figure 3, wherein the schematic diagram of the cylindrical pores and the slit-shaped pores is from the prior art.
S2: and (3) calculating the thickness of the adsorption layer of the methane fluid according to the following calculation formula:
Figure 95676DEST_PATH_IMAGE028
Figure 876419DEST_PATH_IMAGE029
Figure 219676DEST_PATH_IMAGE030
whereinm、nIs a coefficient;MWis the molecular weight;r pis the pore radius, σLJLennard-Jones size factor for methane;
s3: calculating the corrected molar volume within the elliptical poresV mm To the conventional molar volumeV m The calculation formula is as follows:
Figure 862010DEST_PATH_IMAGE031
Figure 607112DEST_PATH_IMAGE032
whereinn a Is the number of adsorbed fluid molecules;n t is the total number of fluid molecules;V mmolar volume in conventional PR-EOS;N Ais an avogalois constant;V ptotal volume occupied by fluid;a x length of ellipse major semi-axis, m;b y length of ellipse minor semi-axis, m; at the same timeR hv=a x /b y ，r p= b y (ii) a To describe the correlation of the corrected molar volume with the original molar volume, a new parameter was definedχ(ii) a β is the density coefficient at which adsorption results in a decrease.
S4: fitting the relation between critical parameter deviation and dimensionless pore diameter in the regular pore based on the existing molecular simulation result.
Of C1 componentT cThe dependence of the offset on the dimensionless aperture is shown in fig. 5:
for a circular aperture:
Figure 309489DEST_PATH_IMAGE033
for the slit-shaped aperture:
Figure 405621DEST_PATH_IMAGE034
wherein, the correlation coefficient R of the formula (7)20.9590; formula (8)Coefficient of correlation R20.8094;
s5: and obtaining a relation between the critical temperature offset of the elliptical pores and the dimensionless pore diameter. The irregular nano-pores in the shale porous medium are described by the elliptical pores, so that the aspect ratio of the pores is equal to the aspect ratioR hvAt arbitrary values, the critical property shift of an elliptical hole can be calculated based on the fitting results of a circular aperture and a slit-shaped aperture. The method comprises the following specific steps: at ln (Δ)T *) ~ln(W p/σ LJ) Critical temperature offset for the round and slit-shaped holes respectively plotted in the coordinate systemT *And dimensionless aperture widthW p/σ LJLine1 and Line2, as shown on the left side of fig. 6. Center point thereofp(x 0, y 0) The Line2 is the intersection of two lines Line1 and Line2, where the Line1 is equal to lnT *) ~ln(W p/σ LJ) Around the intersection point in the coordinate systemp(x 0, y 0) Rotation angleαAnd then obtaining the product. CornerαCan be calculated by the following method:
Figure 851646DEST_PATH_IMAGE035
whereink 1Andk 2are the slopes of Line1 and Line2 respectively,k 1=-1.2968, k 2= -1.0314. Tan α = 0.1135 was calculated.
The length of the minor axis of the ellipse during the change in the shape of the aperture from circular to slitW p (W p=2b y ) Remains unchanged, and therefore, the process is also the aspect ratio of the poresR hvFrom 1.0 to infinity.
The straight Line1 rotates by any angleθ 1The transverse-longitudinal ratio of the formed elliptic pores isR hv，θ 1The variation interval of (a) is [0,α]. The course of the change in the left side of fig. 6 corresponds to the length of the ellipse in the right side of fig. 6Angle corresponding to tangent value of semi-axis and minor semi-axisθ 2From arcπ/4 change toπThe process of/2. Therefore, the temperature of the molten metal is controlled,θ 1，θ 2andR hvthe relationship between them is as follows:
Figure 451254DEST_PATH_IMAGE036
Figure 585519DEST_PATH_IMAGE037
wherein, theta1The Line1 rotates to any angle in the process of Line 2; theta2The angle corresponding to the tangent value of the major and minor semiaxes of the ellipse
Obtained in combination with formula (11):
Figure 903368DEST_PATH_IMAGE038
wherein k is a pore shape RhvThe slope of a corresponding new line, the critical temperature offset Δ for any elliptical apertureT * And dimensionless aperture widthW p/σ LJThe relationship between them.
Based on the formulas (7), (8), (9) and (10), any R of the elliptical holes can be obtainedhvGeneral expression for the correlation of lower critical temperature shift with dimensionless pore size:
Figure 887504DEST_PATH_IMAGE039
wherein C is1And C2Is constant and dimensionless.
S6: the corrected PR-EOS based on equation (5) is as follows:
Figure 607198DEST_PATH_IMAGE040
in the formulaP、TRespectively, pressure and temperature;V mm in order to correct for the molar volume,V mm =V m /χ；Ris the universal gas constant;aandbdimensionless constants describing the attractive and repulsive forces, respectively; α is a dimensionless coefficient related to temperature;
the formula for obtaining the critical temperature and critical pressure shift after integral transformation of the pressure in formula (17) is as follows:
Figure 651378DEST_PATH_IMAGE041
Figure 456523DEST_PATH_IMAGE042
the critical temperature T can be obtained by combining the formula (15)cAnd critical pressure PcThe offsets of (a) are respectively:
Figure 244350DEST_PATH_IMAGE043
Figure 818551DEST_PATH_IMAGE044
s7: critical temperature calculated based on the formula (20) and the formula (21)T cAnd critical pressure andP ccan obtain the critical temperature under the consideration of the pore shape and the adsorption influenceT cm And critical pressurePcmThe calculation formula of (a) is as follows:
Figure 282899DEST_PATH_IMAGE045
Figure 309761DEST_PATH_IMAGE046
the parameter values obtained in this example are shown in table 1.
Table 1 values of parameters of example 1
Figure 166859DEST_PATH_IMAGE047
As shown in fig. 7, the model herein can be used to calculate the critical temperature and critical pressure for enclosed methane in circular pores and slit-shaped pores. It is noted that, in the calculation, for the slit-shaped apertures,R hvis 10. For larger sized circular and slit holes, the critical temperature and pressure calculations do not differ much from the standard values. When the pore width is less than 18nm, the critical temperature drops sharply with decreasing pore size; when the pore width is less than 24nm, the critical pressure drops sharply with decreasing pore size. Meanwhile, the reduction range of the critical temperature is smaller than the reduction of the critical pressure. In addition, the critical temperature and critical pressure variation of the circular pores are larger than those of the slit-shaped pores. That is, the critical value in the circular pores is smaller than that in the slit-shaped pores under the same pressurized fluid conditions. The smaller the pore width, the more pronounced the difference.
The pore width of 5nm is obtained by the improved PR-EOS,R hvThe critical property of the enclosed methane is shown in figure 8 when the value range is 1-20. When in useR hvWhen increasing from 1 to 10, the critical temperature and critical pressure increase significantly. When in useR hvAbove 10, the critical properties do not change significantly. The results show that the critical parameter shifts more as the pore shape approaches a circle.
Example 2
A method for calculating critical parameters and a phase diagram of multi-component fluids in organic matter pores of a shale gas reservoir comprises the following steps:
s1: firstly, obtaining a shale reservoir SEM Image as shown in figure 1, further extracting pores by using Image processing software Image J, wherein the extraction result is shown in figure 2, and performing ellipse fitting on irregular pores to obtain a fitted Image and parameters of each pore, including a major semi-axis and a minor semi-axis of the fitted ellipse, as shown in figure 3.
S2: calculating the thickness of the adsorbent layer of the multicomponent fluidδ ad The calculation formula is as follows:
Figure 595566DEST_PATH_IMAGE048
Figure 981548DEST_PATH_IMAGE049
Figure 761285DEST_PATH_IMAGE050
Figure 890915DEST_PATH_IMAGE051
whereinδ ad Is the thickness of the adsorption layer of the multi-component fluid,δ ad(i) is as followsiThe thickness of the adsorbent layer of the component fluid,X i is the firstiThe mole fraction of each of the components,i=1, 2, 3, 4; the number of N is 4, and the content of N,m i 、n i are respectively the firstiThe coefficient of the components is that,MW i is as followsiThe molecular weight of the components is shown in the specification,r pis the pore radius; sigmaLJ（i）The Lennard-Jones size factor for the ith component.
Wherein the mole fraction of methaneX 1 80mol% of ethane, mole fraction of ethaneX 2 15mol%, molar fraction of n-butaneX 3 4mol% of n-hexaneX 4 Is 1 mol%.
S3: calculating the corrected molar volume within the elliptical poresV mmCorrelation with the original molar volume, the formula was calculated as follows:
Figure 174129DEST_PATH_IMAGE052
Figure 996591DEST_PATH_IMAGE053
whereinn a Is the number of adsorbed fluid molecules;n t is the total number of fluid molecules;V mmolar volume in conventional PR-EOS;N Ais an avogalois constant;V ptotal volume occupied by fluid;a x length of ellipse major semi-axis, m;b y length of ellipse minor semi-axis, m; at the same timeR hv=a x /b y ，r p= b y (ii) a To describe the correlation of the corrected molar volume with the original molar volume, a new parameter was definedχ；βResulting in a reduced density factor for adsorption.
S4: fitting the relation between critical parameter deviation and dimensionless pore diameter in the regular pore based on the existing molecular simulation result. Considering that the shale gas reservoir is mainly composed of methane and is low in content of other components, fitting C1 (methane) and C2+ (other light hydrocarbon components) respectively can obtain fitting results of the relationship between critical parameter shifts and dimensionless pore diameters of C1 and C2+ components, as shown in fig. 4 and 5:
c1 component:
for a circular aperture:
Figure 247313DEST_PATH_IMAGE054
for the slit-shaped aperture:
Figure 180634DEST_PATH_IMAGE055
wherein, the correlation coefficient R of the formula (7)20.9590; phase of equation (8)Coefficient of relevance R20.8094;
c2+ component:
for a circular aperture:
Figure 318354DEST_PATH_IMAGE056
for the slit-shaped aperture:
Figure 311718DEST_PATH_IMAGE057
wherein, the correlation coefficient R of the formula (9)20.9905; correlation coefficient R of equation (10)20.8797;
s5: and obtaining a relation between the critical temperature offset of the elliptical pores and the dimensionless pore diameter. The irregular nano-pores in the shale porous medium are described by the elliptical pores, so that the aspect ratio of the pores is equal to the aspect ratioR hvAt arbitrary values, the critical property shift of an elliptical hole can be calculated based on the fitting results of a circular aperture and a slit-shaped aperture. The method comprises the following specific steps: at ln (Δ)T *) ~ln(W p/σ LJ) Critical temperature offset for the round and slit-shaped holes respectively plotted in the coordinate systemT *And dimensionless aperture widthW p/σ LJLine1 and Line2, as shown on the left side of fig. 6. Center point thereofp(x 0, y 0) The Line2 is the intersection of two lines Line1 and Line2, where the Line1 is equal to lnT *) ~ln(W p/σ LJ) Around the intersection point in the coordinate systemp(x 0, y 0) Rotation angleαAnd then obtaining the product. CornerαCalculated by the following method:
Figure 800468DEST_PATH_IMAGE058
whereink 1Andk 2of Line1 and Line2, respectivelyThe slope, for the C1 composition,k 1=-1.2968，k 2= -1.0314; for the C2+ component,k 1=-1.6907，k 2=-1.767。
the length of the minor axis of the ellipse during the change in the shape of the aperture from circular to slitW p (W p=2b y ) Remains unchanged, and therefore, the process is also the aspect ratio of the poresR hvFrom 1.0 to infinity.
The straight Line1 rotates by any angleθ 1The transverse-longitudinal ratio of the formed elliptic pores isR hv，θ 1The variation interval of (a) is [0,α]. The course of the change in the left side of fig. 6 corresponds to the angle at which the tangent of the major and minor semiaxes of the ellipse corresponds in the right side of fig. 6θ 2From arcπ/4 change toπThe process of/2. Therefore, the temperature of the molten metal is controlled,θ 1，θ 2andR hvthe relationship between them is as follows:
Figure 271901DEST_PATH_IMAGE059
Figure 529707DEST_PATH_IMAGE060
wherein, theta1The Line1 rotates to any angle in the process of Line 2; theta2The angle corresponding to the tangent value of the major and minor semiaxes of the ellipse
Obtained in combination with formula (11):
Figure 693972DEST_PATH_IMAGE061
wherein k is a pore shape RhvThe slope of a corresponding new line, the critical temperature offset Δ for any elliptical apertureT * And dimensionless aperture widthW p/σ LJThe relationship between them.
Based on the formulas (7), (8), (9) and (10), any R of the elliptical holes can be obtainedhvGeneral expression for the correlation of lower critical temperature shift with dimensionless pore size:
Figure 670018DEST_PATH_IMAGE062
wherein C is1And C2Is constant and dimensionless.
S6: the critical temperature shift versus dimensionless pore size for the i component was obtained based on S4 and S5.
Figure 194409DEST_PATH_IMAGE063
Wherein Δ*T (i)Is composed ofiCritical offset of component; c1 iAnd C2 iIs composed ofiRelative number of components
S7: the corrected PR-EOS based on equation (5) is as follows:
Figure 572301DEST_PATH_IMAGE064
in the formulaP、TRespectively, pressure and temperature;V mm in order to correct for the molar volume,V mm =V m /χ；Ris the universal gas constant;aandbdimensionless constants describing the attractive and repulsive forces, respectively;αis a dimensionless coefficient related to temperature;
the formula of the critical temperature and critical pressure deviation obtained by integral conversion of the pressure in formula (17) is as follows:
Figure 641888DEST_PATH_IMAGE065
Figure 105231DEST_PATH_IMAGE066
wherein the content of the first and second substances,
Figure 918466DEST_PATH_IMAGE023
is as followsiCritical temperature offset of the component;T c(i) is as followsiThe critical temperature of the component;T cm(i) is as followsiCorrected critical temperatures of the components;
Figure 150864DEST_PATH_IMAGE025
is as followsiCritical pressure offset of a component;P c(i) is as followsiThe critical pressure of the component;P cm(i) is as followsiCorrected critical pressures for the components;
the critical temperature T can be obtained by combining the formula (15)cAnd critical pressure PcThe offset amounts of (A) are respectively:
Figure 391353DEST_PATH_IMAGE067
Figure 341991DEST_PATH_IMAGE068
s8: critical temperature calculated based on the formula (20) and the formula (21)T cAnd critical pressureP cThe calculation formula of the critical temperature and critical pressure under the influence of the pore shape and adsorption can be obtained as follows:
Figure 208185DEST_PATH_IMAGE069
Figure 295089DEST_PATH_IMAGE070
s9: carrying out solution calculation of PR (1978) state equation by using WINPROP module in CMG reservoir simulation software, wherein the flow is obtained in the calculation processCritical temperature T of each componentc(i)Critical pressure Pc(i)And molar volume Vm(i)Is modified to take into account the critical temperature T of each component of the fluid in the organic pores of the shale gas under the adsorption and limited space based on the calculation of the critical temperatures T of S7 and S8cm(i)Critical pressure Pcm(i)And molar volume Vmm(i)And performing flash evaporation calculation on the multi-component fluid to obtain critical parameters and a fluid phase diagram of the multi-component mixed fluid. Wherein the parameters of eccentricity factor Ac and compression factor Z, Lennard-Jones energy coefficient ε/k used in the phase diagram calculation are shown in Table 3, and the binary interaction coefficient δ between the componentsijAs shown in table 4.
The parameter values calculated in this example are shown in table 2.
Table 2 values of parameters of example 2
Figure 972058DEST_PATH_IMAGE071
Using the corrected critical parameters, a prediction was made of 80mol% methane, 15mol% ethane, 4mol% n-butane and 1mol% n-hexane (CH)4+C2H6+n-C4H10+n-C6H14) Phase diagrams of shale gas reservoir synthetic fluid mixtures. The properties and binary interaction parameters are shown in tables 3 and 4, respectively. As shown in fig. 9, the pore size has very limited effect on the movement of the critical point of the mixed fluid, however, as the pore size decreases, the entire phase envelope is compressed. The critical temperature of the multi-component fluid mixture decreased from 236.3K to 227.9K within the 5nm pores. The phase diagram at a pore width of 5nm and the phase diagram under bulk conditions have large voids, but as the pore diameter increases, the pores gradually decrease. At a pore width of 40 nm, the phase diagram of the bulk fluid substantially agrees with the phase diagram under bulk conditions.
As shown in FIG. 10, the width of the aperture is 5nm and the aspect ratio isR hvWhen the molecular weight is 1, 3, 5 and 7, the mixed fluid (80mol% CH) can be obtained by using the model4+15mol% C2H6+4mol% n-C4H10+1mol% n-C6H14) Phase diagram of (a). It can be seen that the pore shape has little effect on the critical point, but a significant effect on the overall envelope. The results show that when the pore width is constant, the entire phase envelope expands with an increase in aspect ratio. When the aspect ratio is larger than 5, the phase envelope tends to be stable. It is noted, however, thatR hvAnd =7, the overall phase envelope is still smaller than that in the bulk condition. It also shows that the effect of confined space cannot be neglected regardless of the shape of the pores.
In conclusion, the invention simultaneously considers the influence of the pore shape and the adsorption characteristic on the critical parameters of the fluid in the pore, and provides an improved PR-EOS model, thereby obtaining the critical parameters and the phase diagram of the fluid in the confined space in the shale micro-nano pore. The critical parameters and the phase diagram of the fluid obtained by calculation are consistent with those of the critical parameters and the phase diagram under the condition of the bulk phase without considering the influence of the limited space, and the accuracy of the established model is proved. According to the invention, critical parameters and phase diagrams under different pore widths and pore aspect ratios are calculated, the influence of the limited space effect on the micro-nano space is known to be large, and the property and the change rule of the fluid in the irregular micro-nano pores of the real shale gas reservoir can be accurately described through the model. Meanwhile, accurate critical parameter values obtained by calculation based on the invention can provide more accurate parameters for the subsequent reserve calculation of the shale gas reservoir, and the accuracy of shale gas reservoir reserve evaluation is improved.
TABLE 3 basic parameters of the respective components
Figure 144414DEST_PATH_IMAGE072
TABLE 4 binary interaction coefficient between the componentsδ ij
Figure 565031DEST_PATH_IMAGE073

Claims (9)

1. A method for calculating critical parameters and phase diagrams of fluids in organic pores of a shale gas reservoir is characterized in that an improved PR-EOS model is established by establishing a relation between critical parameter offset and dimensionless pore diameter of the fluids in the pores, and then the critical parameters and the phase diagrams of the fluids in the pores of the shale are obtained through solving;
the relationship between the critical parameter offset of the fluid in the pore and the dimensionless pore diameter is calculated based on the fitting of the molecular simulation results of the existing circular pore and slit-shaped pore.
2. The method for calculating the fluid critical parameters and the phase diagram of the fluids in the organic pores of the shale gas reservoir as claimed in claim 1, wherein the pores comprise irregular nanopores.
3. The method for calculating the fluid critical parameters and the phase diagram in the organic matter pores of the shale gas reservoir according to claim 1 or 2, wherein the fluid comprises a multi-component mixed fluid.
4. The method for calculating the fluid critical parameters and the phase diagram in the organic matter pores of the shale gas reservoir according to claim 3, wherein the method comprises the following steps:
s1: extracting and fitting the pores to obtain fitted pore parameters;
s2: and calculating the thickness of the adsorption layer of the fluid according to the following calculation formula:
Figure 609677DEST_PATH_IMAGE001
Figure 261238DEST_PATH_IMAGE002
Figure 24663DEST_PATH_IMAGE003
Figure 154293DEST_PATH_IMAGE004
wherein the content of the first and second substances,δ adthe thickness of the adsorption layer of the multicomponent fluid;δ ad（i）is composed ofiThe thickness of the adsorption layer of the component fluid;X i is the firstiThe mole fraction of each component (i is more than or equal to 1); n is a natural number more than or equal to 1;m i 、n i coefficients for different components, respectively;r pis the pore radius, σLJ（i）Is as followsiThe Lennard-Jones size factor of the component;MW i is as followsiThe molecular weight of the component;
s3: calculating the corrected molar volume within the elliptical poresV mm To the conventional molar volumeV m The calculated result is as follows:
Figure 703086DEST_PATH_IMAGE005
Figure 259970DEST_PATH_IMAGE006
whereinn a Is the number of adsorbed fluid molecules;n t is the total number of fluid molecules;V mmolar volume in conventional PR-EOS;N Ais an avogalois constant;V ptotal volume occupied by fluid;a x length of ellipse major semi-axis, m;b y length of ellipse minor semi-axis, m; at the same timeR hv=a x /b y ，r p= b y (ii) a Parameter(s)χAs defined coefficients, dimensionless parameters;βa density factor that results in a decrease for adsorption;
s4: based on the existing molecular simulation results, divideRespectively corresponding to the critical temperature offset in the circular pore and the slit-shaped pore
Figure 261424DEST_PATH_IMAGE008
And dimensionless apertureW p /σ LJ Fitting the relation between the two to obtain ln: (∆T *) And ln (W p /σ LJ ) The fitted curve of (a) is obtained,
wherein the content of the first and second substances,∆T *is the critical temperature offset;W p is the minor axis length 2b of an ellipseyI.e. the width of the aperture;
s5: obtaining critical temperature offset of elliptical pore∆T *And dimensionless apertureW p /σ LJ The relational expression of (1);
s6: based on the steps S4 and S5iCritical temperature offset of component∆T i *And dimensionless apertureW p /σ LJ i（）A relational expression;
s7: obtaining the offset formula of the critical temperature and the critical pressure of each component;
s8: calculating the critical temperature and critical pressure of each component;
s9: and solving the critical parameters and the phase diagram of the fluid in the settled shale nano pores.
5. The method for calculating the fluid critical parameters and the phase diagram in the organic pores of the shale gas reservoir as claimed in claim 4, wherein the deviation amount of the critical temperature of the elliptical pores in S5∆T *And dimensionless apertureW p /σ LJ The relational expression is obtained as follows:
at ln (Δ T)*) ~ln(Wp/σLJ) Critical temperature offset for the round and slit-shaped holes respectively plotted in the coordinate systemT * And dimensionless pore sizeW p /σ LJ Line1 and Line2, point p (x)0, y0) The Line2 is the intersection of two lines Line1 and Line2, where the Line1 is equal to lnT * ) ~ln(W p /σ LJ ) Around the intersection point p (x) in the coordinate system0, y0) Obtained after rotating the angle α, the angle α can be calculated by:
Figure 194745DEST_PATH_IMAGE009
whereink 1Andk 2the slopes of Line1 and Line2, respectively;
Figure 598044DEST_PATH_IMAGE010
Figure 325829DEST_PATH_IMAGE011
wherein, theta1The Line1 rotates to any angle in the process of Line 2; theta2The angle corresponding to the tangent value of the major and minor semiaxes of the ellipse
In combination with equation (11) can be obtained:
Figure 63846DEST_PATH_IMAGE012
in the formula (I), the compound is shown in the specification,kin the shape of poresR hv The slope of a corresponding new line, the critical temperature offset Δ for any elliptical apertureT * And dimensionless aperture widthW p/σ LJ The relationship between them;
any R of elliptical holehvGeneral expression for the correlation of lower critical temperature offset with dimensionless pore size:
Figure 535279DEST_PATH_IMAGE013
wherein C is1And C2Is constant and dimensionless.
6. The method for calculating the fluid critical parameters and the phase diagram in the organic pores of the shale gas reservoir as claimed in claim 5, wherein the step S6 is performediThe critical temperature offset and dimensionless pore size of the components are as follows:
Figure 58664DEST_PATH_IMAGE014
wherein Δ * T i ()Is composed ofiCritical temperature offset of the component;C 1 i andC 2 i is composed ofiThe relative number of the components.
7. The method for calculating the critical parameters and the phase diagram of the fluid in the organic pores of the shale gas reservoir according to claim 6, wherein the critical temperature and critical pressure shift formula in the step S7 is obtained as follows:
the corrected PR-EOS based on equation (5) is as follows:
Figure 222929DEST_PATH_IMAGE015
in the formulaP、TRespectively, pressure and temperature;V mm in order to correct for the molar volume,V mm =V m /χ；Ris the universal gas constant;aandbdimensionless constants describing the attractive and repulsive forces, respectively;αis a dimensionless coefficient related to temperature;
the formula for obtaining the critical temperature and critical pressure shift after integral transformation of the pressure in formula (17) is as follows:
Figure 198976DEST_PATH_IMAGE016
Figure 208520DEST_PATH_IMAGE017
the critical temperature T can be obtained by combining the formula (15)cAnd critical pressure PcThe offsets of (a) are respectively:
Figure 586412DEST_PATH_IMAGE018
Figure 655999DEST_PATH_IMAGE019
wherein the content of the first and second substances,∆T i() *is as followsiCritical temperature offset of the component;T c(i) is as followsiThe critical temperature of the component;T cm(i) is as followsiCorrected critical temperatures of the components;∆P i() *is as followsiCritical pressure offset of a component;P c(i) is as followsiThe critical pressure of the component;P cm(i) is as followsiCorrected critical pressure of the composition.
8. The method for calculating the critical parameters and the phase diagram of the fluid in the organic pores of the shale gas reservoir as claimed in claim 7, wherein the calculation formula of the critical temperature and the critical pressure in S8 is as follows:
Figure 119341DEST_PATH_IMAGE020
Figure DEST_PATH_IMAGE021
。
9. the method for calculating the fluid critical parameters and the phase diagram in the organic pores of the shale gas reservoir according to claim 8, wherein the solving process of the fluid critical parameters and the phase diagram in the nanopores of the shale in S9 includes:
based on the critical temperature T of each component of the fluid in the organic pores of the shale gas under the consideration of adsorption and limited space calculated by the S7 and the S8cm(i)Critical pressure Pcm(i)And molar volume Vmm(i)And performing flash evaporation calculation on the multi-component fluid to obtain critical parameters and a fluid phase diagram of the multi-component mixed fluid.
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