CN111028959A - Crack flow conductivity prediction method considering rock elasticity-plasticity-creep deformation - Google Patents

Crack flow conductivity prediction method considering rock elasticity-plasticity-creep deformation Download PDF

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CN111028959A
CN111028959A CN201911301980.8A CN201911301980A CN111028959A CN 111028959 A CN111028959 A CN 111028959A CN 201911301980 A CN201911301980 A CN 201911301980A CN 111028959 A CN111028959 A CN 111028959A
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proppant
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fracture
embedding
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CN111028959B (en
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刘彧轩
陈天翔
郭建春
王建东
卢聪
陈迟
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Southwest Petroleum University
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Abstract

The invention discloses a crack flow conductivity prediction method considering rock elasticity-plasticity-creep deformation, which comprises the following steps of: collecting basic parameters for finishing the embedded cracks of the propping agent; respectively calculating or measuring the deformation amount of the proppant and the depth of the proppant embedded into the crack in the elastic embedding stage, the plastic embedding stage and the creep embedding stage; respectively calculating the residual fracture width of each stage according to the deformation amount of the proppant and the depth of the proppant embedded into the fracture of each stage; and respectively calculating the fracture conductivity of each stage according to the residual fracture width of each stage. The method can accurately calculate the flow conductivity of the fracture, and is favorable for analysis guidance and hydraulic fracturing optimization of practical production.

Description

Crack flow conductivity prediction method considering rock elasticity-plasticity-creep deformation
Technical Field
The invention relates to the technical field of oil and gas reservoir development, in particular to a fracture conductivity prediction method considering rock elasticity-plasticity-creep deformation.
Background
China contains abundant unconventional oil and gas resources, but the development difficulty is high and the yield is low. The hydraulic fracturing is an effective production increasing measure for improving the yield by modifying an unconventional oil and gas reservoir, aims to establish a high-speed channel for oil and gas transportation underground, and is the key of hydraulic fracturing operation on the condition of accurately predicting the flow conductivity of a crack.
The shale gas content in China is very rich, and the development of the shale gas becomes the main field of energy development in China. As shown in the figure, the shale gas reservoir contains a large amount of clay minerals and the creep property of rock is stronger compared with the conventional sandstone reservoir. Under the effect of external closed pressure, a propping agent is gradually embedded into a rock stratum, the process of embedding the propping agent is the process of elastic-plastic-creep deformation of the rock, when the shale generates creep deformation, the strain can be continuously increased along with the increase of time, so that the propping agent is continuously embedded into the rock stratum, the width of a crack is continuously reduced until the crack is closed, the diversion capacity is reduced, and the oil-gas transportation is hindered. The current research situation of a fracture conductivity prediction model mainly has the following achievements:
in 2015, a fracture width calculation model of a proppant embedding process is established by high and long dragon and the like (high and long dragon, Ehrlich, Yangming. a fracture conductivity calculation model [ J ] of proppant fracture, contemporary chemical industry, 2015,44(05): 1074. 1075.) based on elastic mechanics and Hertz theory, and through corresponding experimental data and example calculation, how fracture conductivity is influenced by proppant fracture rate is summarized, so that a further improved model for calculating fracture conductivity is provided.
In 2016, Awolbeke et al (Awolbeke O, Zhu D, Hill D. New processed-fraction-formation models for light gas sources [ J. SPE Journal,2016,21(05):1508-1517.) proposed a purely empirical model and a semi-empirical model based on dimensional analysis and non-linear regression, the second model being more widely used than the first model because it does not depend entirely on empirical models. The model can be used for actual production and oil reservoir exploration, and provides initial estimation of the flow conductivity of the tight sandstone fracture under the condition of considering certain limitations.
In 2017, Guo et al (Guo J, Wang J, Liu Y. analytical analysis of fractional distribution for fracture distribution of proppant packages [ J ]. Journal of geomatics and Engineering,2017,14(03):599-610.) studied the influence of uniform and discrete distribution of proppant on fracture conductivity based on the contact mechanics and Carman-Kozeny models. The result shows that the optimal distance between the proppants can keep the maximum flow conductivity after the proppants are embedded, the change of the optimal distance is mainly determined by factors such as closing pressure, elastic modulus, Poisson's ratio and the like, and the optimal distance is not influenced by the concentration of the proppants and the elastic effect of pores.
The fracture conductivity prediction model does not consider the action mechanism of the elastic-plastic-creep shape of the rock on the change of the fracture width, so that the fracture width is not accurately calculated, and the conductivity calculation has deviation. Therefore, the influence of rock elasticity-plastic-creep shape on the flow conductivity of the crack is considered in research, and the analysis guidance and hydraulic fracturing optimization on practical production are facilitated.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a fracture conductivity prediction method considering rock elasticity-plasticity-creep deformation, a fracture conductivity model for evaluating proppant embedding is established by considering rock elasticity-plasticity-creep deformation, and the conductivity of a fracture is predicted by the model.
The technical scheme of the invention is as follows:
a fracture conductivity prediction method considering rock elastic-plastic-creep deformation comprises the following steps:
collecting basic parameters for finishing the embedded cracks of the propping agent;
respectively calculating or measuring the deformation amount of the proppant and the depth of the proppant embedded into the crack in the elastic embedding stage, the plastic embedding stage and the creep embedding stage;
respectively calculating the residual fracture width of each stage according to the deformation amount of the proppant and the depth of the proppant embedded into the fracture of each stage;
and respectively calculating the fracture conductivity of each stage according to the residual fracture width of each stage.
Further, theThe basic parameter comprising the closing pressure PcProppant radius R, elastic modulus E of the proppant1Elastic modulus E of rock formation2Poisson ratio v of proppant1Poisson ratio v of rock stratum2Viscoelastic shear coefficient of proppant η1Viscoelastic shear coefficient of formation η2Thickness of rock layer D2Initial crack width Wf0。
Further, the calculation formula of the deformation amount of the proppant in the elastic embedding stage and the plastic embedding stage is as follows:
Figure BDA0002322023570000021
Figure BDA0002322023570000022
Figure BDA0002322023570000023
in the formula:
ΔD1/2the deformation of the proppant in the elastic embedding stage or the plastic embedding stage is mm;
Pmaxmaximum contact stress, MPa;
E1is the modulus of elasticity, MPa, of the proppant;
Wf0initial crack width, mm;
PCis the closing pressure, MPa;
e is the comprehensive elastic modulus, MPa;
ν1is the poisson's ratio of the proppant, dimensionless;
ν2is the poisson's ratio of the rock formation, dimensionless;
E2is the elastic modulus of the rock formation, MPa;
the formula for calculating the deformation of the proppant in the creep embedding stage is as follows:
Figure BDA0002322023570000031
Figure BDA0002322023570000032
in the formula:
ΔD3proppant deformation in mm at the creep insertion stage;
Pavethe average contact stress in creep embedding stage is MPa;
e is a constant value 2.7183;
t is time, s;
η2the viscoelastic shear coefficient of the rock formation is MPa.
Further, the calculation formula of the depth of the proppant embedded into the fracture in the elastic embedding stage is as follows:
Figure BDA0002322023570000033
Figure BDA0002322023570000034
in the formula:
h1the depth of the embedded crack is mm in the elastic stage;
r is the proppant radius, mm;
D2is the thickness of the rock stratum, mm;
the calculation formula of the depth of the embedding crack in the plastic embedding stage is as follows:
when the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment are not considered:
Figure BDA0002322023570000035
when considering the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment:
Figure BDA0002322023570000036
in the formula:
h2embedding crack depth in a plastic stage, which is mm;
f is a correction coefficient and is dimensionless;
the calculation formula of the embedding depth in the creep embedding stage is as follows:
Figure BDA0002322023570000041
in the formula:
h3embedding crack depth mm in a creep stage;
η1the viscoelastic shear coefficient of the proppant, MPa.
Further, the calculation formula of the residual crack width is as follows:
Wf＝Wf0-ΔD-2h (10)
in the formula:
Wfthe remaining crack width is mm;
Δ D is proppant deflection, mm;
and h is the depth of the proppant embedded into the fracture, and mm.
Further, the calculation formula of the fracture conductivity is as follows:
Fc＝Kf×Wf(11)
Figure BDA0002322023570000042
in the formula:
Fcmu m for fracture conductivity2·cm；
KfIs the permeability, D;
Figure BDA0002322023570000043
porosity, dimensionless;
c is a Karman-Korzeny constant, dimensionless;
Φ is the permeability of the rock formation, D;
r is the proppant radius, mm.
Further, the Karman-Korzeny constant c-5 when the proppant is uniformly distributed in the fracture.
Compared with the prior art, the invention has the following advantages:
the method comprises the steps of respectively calculating or measuring the deformation amount of a propping agent and the depth of a propping agent embedded crack in an elastic embedding stage, a plastic embedding stage and a creep embedding stage by considering the elastic-plastic-creep deformation of the rock; and respectively calculating the residual fracture width of each stage according to the deformation amount of the proppant and the embedding depth of the proppant into the fracture of each stage, and then respectively calculating the fracture conductivity of each stage according to the residual fracture width of each stage, so that the calculated fracture conductivity is more accurate, and the method is favorable for analyzing and guiding practical production and optimizing hydraulic fracturing.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic comparison of sandstone and shale mineral compositions;
FIG. 2 is a schematic diagram of the elastic embedment phase of the proppant embedment process;
FIG. 3 is a schematic representation of a plastic embedding stage of a proppant embedding process;
FIG. 4 is a schematic illustration of a creep insertion phase of a proppant insertion process;
FIG. 5 is a schematic view of contact of proppant with rock;
FIG. 6 is a schematic view of stress analysis of the m-th layer of n rows of proppants;
FIG. 7 is a schematic view of a multi-layered proppant force analysis;
FIG. 8 is a graph comparing results of calculated and measured proppant-embedded fracture depths according to one embodiment of the present invention;
FIG. 9 is a graph comparing the results of the calculation of the present invention with the results of the Lacy test for embedded crack depth;
FIG. 10 is a graph comparing the results of the present invention calculations with the results of Lu test embedded fracture depth;
FIG. 11 is a graph comparing the results of the crack width variation calculated according to the present invention with those of the Lacy test according to an embodiment of the present invention;
FIG. 12 is a graph comparing the results of the present invention calculations with the results of Lu test fracture width variations;
FIG. 13 is a graph comparing the results of the invention with time-dependent fracture width versus Analytical model and FEM model results;
FIG. 14 is a graphical representation of the relationship between fracture conductivity and proppant diameter;
FIG. 15 is a graphical representation of the relationship between fracture conductivity and Young's modulus of the proppant;
FIG. 16 is a graphical representation of the relationship between fracture conductivity and Young's modulus of the formation.
Detailed Description
The invention is further illustrated with reference to the following figures and examples. It should be noted that, in the present application, the embodiments and the technical features of the embodiments may be combined with each other without conflict.
The process of embedding the proppant, namely the process of deformation of the rock under the action of the proppant, is divided into three stages. The first stage is that under the action of force, the propping agent is instantaneously embedded into the stratum to a certain depth, the rock surface generates instantaneous deformation, which can be described by using an elastic theory, the stage is called an elastic deformation stage, and the embedding process is shown in figure 2; the second stage is that after the proppant is embedded into the formation to a certain depth, the proppant is plastically deformed, and the embedding process is shown in fig. 3; the third stage is that the proppant continues to be slowly embedded into the rock under a constant force with time, which can be regarded as the process of medium creep in viscoelasticity theory, and is called creep deformation stage, and the embedding process is shown in fig. 4. The contact diagram of the proppant and the rock is shown in fig. 5, the stress diagram of the m-th layer n-th column of proppants in the stratum is shown in fig. 6, the stress diagram of the multilayer proppants in the stratum is shown in fig. 7, and when the elastic modulus and the size of the proppants are the same and the contact surface with the stratum is a plane, the embedding amount between the proppants is close to zero. The deformation for a multi-layered proppant can be approximated as the value of the superposition of the deformation of each layer of proppant, but since only the top and bottom proppants in direct contact with the formation are embedded, the amount of embedding is the same as for a single layer of proppant.
A fracture conductivity prediction method considering rock elastic-plastic-creep deformation comprises the following steps:
first, the basic parameters of the clean-up proppant pack fracture are collected, including the closure pressure PcProppant radius R, elastic modulus E of the proppant1Elastic modulus E of rock formation2Poisson ratio v of proppant1Poisson ratio v of rock stratum2Viscoelastic shear coefficient of proppant η1Viscoelastic shear coefficient of formation η2Thickness of rock layer D2Initial crack width Wf0。
Secondly, the deformation amount of the proppant and the depth of the proppant embedded into the fracture in the elastic embedding stage, the plastic embedding stage and the creep embedding stage are respectively calculated or measured.
In a specific embodiment, the calculation formula of the deformation amount of the proppant in the elastic embedding stage and the plastic embedding stage is as follows:
Figure BDA0002322023570000061
Figure BDA0002322023570000062
Figure BDA0002322023570000063
in the formula:
ΔD1/2is made elasticProppant deflection, mm, at the embedding stage or plastic embedding stage;
Pmaxmaximum contact stress, MPa;
E1is the modulus of elasticity, MPa, of the proppant;
Wf0initial crack width, mm;
PCis the closing pressure, MPa;
e is the comprehensive elastic modulus, MPa;
ν1is the poisson's ratio of the proppant, dimensionless;
ν2is the poisson's ratio of the rock formation, dimensionless;
E2is the elastic modulus of the rock formation, MPa;
the formula for calculating the deformation of the proppant in the creep embedding stage is as follows:
Figure BDA0002322023570000071
Figure BDA0002322023570000072
in the formula:
ΔD3proppant deformation in mm at the creep insertion stage;
Pavethe average contact stress in creep embedding stage is MPa;
e is a constant value 2.7183;
t is time, s;
η2the viscoelastic shear coefficient of the rock formation is MPa.
In a specific embodiment, the elastic embedding phase comprises the calculation formula of the depth of the proppant embedded into the fracture:
Figure BDA0002322023570000073
Figure BDA0002322023570000074
in the formula:
h1the depth of the embedded crack is mm in the elastic stage;
r is the proppant radius, mm;
D2is the thickness of the rock stratum, mm;
the calculation formula of the depth of the embedding crack in the plastic embedding stage is as follows:
when the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment are not considered:
Figure BDA0002322023570000075
when considering the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment:
Figure BDA0002322023570000076
in the formula:
h2embedding crack depth in a plastic stage, which is mm;
f is a correction coefficient and is dimensionless;
the calculation formula of the embedding depth in the creep embedding stage is as follows:
Figure BDA0002322023570000081
in the formula:
h3embedding crack depth mm in a creep stage;
η1the viscoelastic shear coefficient of the proppant, MPa.
Then, respectively calculating the residual fracture width of each stage according to the deformation amount of the proppant and the depth of the proppant embedded into the fracture of each stage;
in a specific embodiment, the calculation formula of the residual crack width is as follows:
Wf＝Wf0-ΔD-2h (10)
in the formula:
Wfthe remaining crack width is mm;
Wf0initial crack width, mm;
Δ D is proppant deflection, mm;
and h is the depth of the proppant embedded into the fracture, and mm.
And finally, respectively calculating the fracture conductivity of each stage according to the residual fracture width of each stage.
In a specific embodiment, the fracture conductivity is calculated by the following formula:
Fc＝Kf×Wf(11)
Figure BDA0002322023570000082
in the formula:
Fcmu m for fracture conductivity2·cm；
KfIs the permeability, D;
Figure BDA0002322023570000083
porosity, dimensionless;
c is a Karman-Korzeny constant, dimensionless;
Φ is the permeability of the rock formation, D;
r is the proppant radius, mm.
In a specific embodiment, the Karman-Korzeny constant c ═ 5.
In a specific embodiment, the accuracy of the present invention is verified by comparing the calculation results of the present invention with the results of the experiment disclosed in the measurement of the amount of proppant inserted and the residual fracture width under different blocking pressures, based on Lacy L, Richards A R, Bilden D M.Fracturewidth and embedding testing in soft fracturing resin [ J ]. SPE DrillCompletion 1325-9 and Lu C, Guo J C, Wang W Y, Deng Y, Liu D.Experimental research promoter and bits data to activities conductivity [ J ].2008: 99-101. Since the proppant embedding amount measured by the experiment is measured after the rock is subjected to plastic deformation, the embodiment adopts an embedding crack depth calculation formula in the plastic embedding stage for calculation. The basic parameters in the experimental data are shown in table 1:
TABLE 1
Data of ν1 ν2 E1(MPa) E2(MPa) R(mm) D2(mm)
Lacyetal 0.13 0.13 21306 1172 0.3175 20
Luetal 0.144 0.144 35000 28770 0.3175 15
The proppant-embedded fracture depth is calculated by adopting the calculation formula (7) when the sand concentration and the influence of the fluid in the proppant sand pile on the proppant embedding are not considered, the obtained proppant-embedded fracture depth result is compared with the embedding amount results of the Lacy experiment and the Lu experiment as shown in fig. 8, and as can be seen from fig. 8, the calculated result of the proppant-embedded fracture depth is smaller than the measured value, but the general trend is consistent because the sand concentration and the influence of the fluid in the proppant sand pile on the proppant embedding are not considered.
The proppant-embedded fracture depth is calculated by adopting a calculation formula (8) in consideration of the sand concentration and the influence of fluid in the proppant sand pile on the proppant embedding, specifically, when the calculation is carried out by adopting data of a Lacy experiment, the correction coefficient f is 1.39, when the calculation is carried out by adopting data of a Lu experiment, the correction coefficient f is 26.3, the obtained proppant-embedded fracture depth result is matched with the embedding amount results of the Lacy experiment and the Lu experiment, as shown in fig. 9 and 10, as can be seen from fig. 9 and 10, the calculation result of the proppant-embedded fracture depth is matched with the actually measured result data, and the calculation result is accurate.
The residual fracture width is calculated according to the proppant embedding fracture depth calculated by the formula (8), the comparison graph of the result of the residual fracture width calculation with the residual fracture width results of the Lacy experiment and the Lu experiment is shown in fig. 11 and 12, and as can be seen from fig. 11 and 12, the calculation result of the method is consistent with the data of the actual measurement result, and the calculation result is accurate.
In another specific embodiment, the invention is compared with Analytical models and FEM models in the change of the residual fracture width in the rock creep stage along with time, and the basic parameters adopted in the embodiment are shown in the table 2:
TABLE 2
ν1 ν2 E1(MPa) E2(MPa) R(mm) D2(mm) η1(MPa) η2(MPa) Pc(MPa)
0.13 0.13 21306 20000 0.325 20 10000 10000 30
The comparison of the change result of the crack width along with time and the change results of the Analytical model and the FEM model is shown in FIG. 13, and as can be seen from FIG. 13, the maximum error of the crack width along with the Analytical model and the FEM model is less than 5%, and the experimental result is accurate.
In another specific example, the relationship between fracture conductivity and proppant diameter obtained by equation (11) is shown in fig. 14, the relationship between fracture conductivity and proppant young's modulus is shown in fig. 15, and the relationship between fracture conductivity and formation elastic modulus is shown in fig. 16.
As can be seen from fig. 14, when the proppant diameter is larger, the fracture conductivity is also larger because in this case, the pore throat radius is also larger, and the particle size of the proppant has a great influence on the fracture conductivity.
As can be seen from fig. 15, the fracture conductivity increases with the increase in young's modulus of the proppant, and the amount of deformation of the proppant is small when the young's modulus of the proppant increases to a specific value. In this case, the variation in fracture width, porosity and throat radius is also small. Therefore, the fracture conductivity gradually approaches a specific value. As the Young modulus of the rock stratum is increased, the rock stratum deformation amount and the proppant embedding amount are gradually reduced, so that the fracture width variation is reduced, and the fracture conductivity is increased.
As can be seen from fig. 16, the fracture conductivity increases with the increase in the elastic modulus of the formation, and the amount of deformation of the formation is small when the elastic modulus of the formation increases to a specific value. In this case, the variation in fracture width, porosity and throat radius is also small. Therefore, the fracture conductivity gradually approaches a specific value. The fracture conductivity increases with increasing elastic modulus of the proppant because the greater the elastic modulus of the proppant, the greater the fracture conductivity because the proppant deforms less while the depth of the proppant is embedded into the formation increases, with the result that the fracture width deformation decreases.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (7)

1. A fracture conductivity prediction method considering rock elastic-plastic-creep deformation is characterized by comprising the following steps:
collecting basic parameters for finishing the embedded cracks of the propping agent;
respectively calculating or measuring the deformation amount of the proppant and the depth of the proppant embedded into the crack in the elastic embedding stage, the plastic embedding stage and the creep embedding stage;
respectively calculating the residual fracture width of each stage according to the deformation amount of the proppant and the depth of the proppant embedded into the fracture of each stage;
and respectively calculating the fracture conductivity of each stage according to the residual fracture width of each stage.
2. The method for predicting fracture conductivity by considering rock elastic-plastic-creep deformation of claim 1, wherein the basic parameters comprise closing pressure Pc, proppant radius R, elastic modulus E of proppant1Elastic modulus E of rock formation2Poisson ratio v of proppant1Poisson ratio v of rock stratum2Viscoelastic shear coefficient of proppant η1Viscoelastic shear coefficient of formation η2Thickness D of rock formation2Initial crack width Wf0。
3. The method for predicting the fracture conductivity by considering rock elastic-plastic-creep deformation according to claim 2, wherein the calculation formula of the deformation amount of the proppant in the elastic embedding stage and the plastic embedding stage is as follows:
Figure FDA0002322023560000011
Figure FDA0002322023560000012
Figure FDA0002322023560000013
in the formula:
ΔD1/2the deformation of the proppant in the elastic embedding stage or the plastic embedding stage is mm;
Pmaxmaximum contact stress, MPa;
E1is the modulus of elasticity, MPa, of the proppant;
Wf0initial crack width, mm;
PCis the closing pressure, MPa;
e is the comprehensive elastic modulus, MPa;
ν1is the poisson's ratio of the proppant, dimensionless;
ν2is the poisson's ratio of the rock formation, dimensionless;
E2is the elastic modulus of the rock formation, MPa;
the formula for calculating the deformation of the proppant in the creep embedding stage is as follows:
Figure FDA0002322023560000021
Figure FDA0002322023560000022
in the formula:
ΔD3proppant deformation in mm at the creep insertion stage;
Pavethe average contact stress in creep embedding stage is MPa;
e is a constant value 2.7183;
t is time, s;
η2the viscoelastic shear coefficient of the rock formation is MPa.
4. The method for predicting the fracture conductivity by considering rock elastic-plastic-creep deformation according to claim 2, wherein the calculation formula of the depth of the proppant embedded into the fracture in the elastic embedding stage is as follows:
Figure FDA0002322023560000023
Figure FDA0002322023560000024
in the formula:
h1the depth of the embedded crack is mm in the elastic stage;
PCis the closing pressure, MPa;
e is the comprehensive elastic modulus, MPa;
r is the proppant radius, mm;
E2is the elastic modulus of the rock formation, MPa;
D2is the thickness of the rock stratum, mm;
ν1is the poisson's ratio of the proppant, dimensionless;
ν2is the poisson's ratio of the rock formation, dimensionless;
E1is the modulus of elasticity, MPa, of the proppant;
the calculation formula of the depth of the embedding crack in the plastic embedding stage is as follows:
when the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment are not considered:
Figure FDA0002322023560000025
when considering the sand placement concentration and the effect of fluid in the proppant sand heap on proppant embedment:
Figure FDA0002322023560000031
in the formula:
h2embedding crack depth in a plastic stage, which is mm;
f is a correction coefficient and is dimensionless;
the calculation formula of the embedding depth in the creep embedding stage is as follows:
Figure FDA0002322023560000032
in the formula:
h3embedding crack depth mm in a creep stage;
e is a constant value 2.7183;
t is time, s;
η1is the viscoelastic shear coefficient of the proppant, MPa;
η2the viscoelastic shear coefficient of the rock formation is MPa.
5. The method for predicting the fracture conductivity by considering rock elastic-plastic-creep deformation according to claim 1, wherein the calculation formula of the residual fracture width is as follows:
Wf＝Wf0-ΔD-2h (10)
in the formula:
Wfthe remaining crack width is mm;
Wf0initial crack width, mm;
Δ D is proppant deflection, mm;
and h is the depth of the proppant embedded into the fracture, and mm.
6. The method for predicting the fracture conductivity by considering rock elastic-plastic-creep deformation according to any one of claims 1 to 5, wherein the calculation formula of the fracture conductivity is as follows:
Fc＝Kf×Wf(11)
Figure FDA0002322023560000033
in the formula:
Fcis a crackConductivity, μm2·cm；
KfIs the permeability, D;
Figure FDA0002322023560000041
porosity, dimensionless;
c is a Karman-Korzeny constant, dimensionless;
Φ is the permeability of the rock formation, D;
r is the proppant radius, mm.
7. The method of predicting fracture conductivity considering rock elastic-plastic-creep deformation according to claim 6, wherein the Karman-Korzeny constant c ═ 5 when the proppant is uniformly distributed in the fracture.
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CN111720105A (en) * 2020-08-04 2020-09-29 西南石油大学 Diversion capacity prediction method considering particle size distribution of proppant
CN112360448A (en) * 2020-11-23 2021-02-12 西南石油大学 Method for determining post-pressure soaking time by utilizing hydraulic fracture creep expansion
CN112945743A (en) * 2021-01-28 2021-06-11 西南石油大学 Method for evaluating and preventing creep damage of flow conductivity of gas reservoir artificial crack
CN113591328A (en) * 2021-08-24 2021-11-02 西南石油大学 Deep shale hydraulic fracture long-term support opening change calculation method
CN113642273A (en) * 2021-09-23 2021-11-12 西南石油大学 Method for predicting long-term flow conductivity of supporting fracture
CN116776556A (en) * 2023-05-19 2023-09-19 四川大学 Method, device, equipment and medium for determining equivalent porosity of propping agent laid fracture
CN117150812A (en) * 2023-09-25 2023-12-01 同济大学 CO taking creep effect into consideration 2 Method for evaluating flow conductivity of fracturing natural gas hydrate

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Publication number Priority date Publication date Assignee Title
CN111720105A (en) * 2020-08-04 2020-09-29 西南石油大学 Diversion capacity prediction method considering particle size distribution of proppant
CN112360448A (en) * 2020-11-23 2021-02-12 西南石油大学 Method for determining post-pressure soaking time by utilizing hydraulic fracture creep expansion
CN112945743A (en) * 2021-01-28 2021-06-11 西南石油大学 Method for evaluating and preventing creep damage of flow conductivity of gas reservoir artificial crack
CN112945743B (en) * 2021-01-28 2021-09-28 西南石油大学 Method for evaluating and preventing creep damage of flow conductivity of gas reservoir artificial crack
CN113591328A (en) * 2021-08-24 2021-11-02 西南石油大学 Deep shale hydraulic fracture long-term support opening change calculation method
CN113642273A (en) * 2021-09-23 2021-11-12 西南石油大学 Method for predicting long-term flow conductivity of supporting fracture
CN116776556A (en) * 2023-05-19 2023-09-19 四川大学 Method, device, equipment and medium for determining equivalent porosity of propping agent laid fracture
CN116776556B (en) * 2023-05-19 2024-02-23 四川大学 Method, device, equipment and medium for determining equivalent porosity of propping agent laid fracture
CN117150812A (en) * 2023-09-25 2023-12-01 同济大学 CO taking creep effect into consideration 2 Method for evaluating flow conductivity of fracturing natural gas hydrate
CN117150812B (en) * 2023-09-25 2024-05-14 同济大学 CO taking creep effect into consideration2Method for evaluating flow conductivity of fracturing natural gas hydrate

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