CN115169077A - Reservoir constitutive model considering hydrate exploitation influence - Google Patents

Reservoir constitutive model considering hydrate exploitation influence Download PDF

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CN115169077A
CN115169077A CN202210658843.5A CN202210658843A CN115169077A CN 115169077 A CN115169077 A CN 115169077A CN 202210658843 A CN202210658843 A CN 202210658843A CN 115169077 A CN115169077 A CN 115169077A
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hydrate
reservoir
displacement
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闫传梁
陈勇
田万顷
程远方
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China University of Petroleum East China
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Abstract

The invention discloses a reservoir constitutive model considering hydrate exploitation influence, which adopts the technical scheme that: the constitutive model establishment steps are as follows: subjecting artificially prepared sediment sample containing methane hydrate to CO 2 Performing a displacement experiment, and performing a triaxial compression experiment on the sample before and after the displacement to obtain a stress-strain curve of the sample; verifying that the Duncan-Chang model is applied to CO according to the experimental result 2 Applicability of the natural gas hydrate reservoir under the influence of displacement; correcting 8 model parameters by using the replacement rate and the initial hydrate saturation parameter according to the triaxial compression experiment results under different conditions; CO to be established 2 And comparing a calculation curve of the nonlinear constitutive model of the natural gas hydrate reservoir under the influence of the displacement with an experimental result. The beneficial effects are that: the invention takes CO into account 2 Influence of the substitution ofCan accurately predict the destructive behavior of the reservoir, has good applicability, and can be used for natural gas hydrate exploitation and CO extraction 2 The method helps to preserve relevant theoretical research, numerical modeling and engineering design.

Description

Reservoir constitutive model considering hydrate exploitation influence
Technical Field
The invention relates to the technical field of natural gas hydrate exploitation, in particular to a reservoir constitutive model considering hydrate exploitation influence.
Background
Natural Gas Hydrate (NGH) is a high-energy-density clathrate crystal compound formed by natural gas and water molecules under low-temperature and high-pressure conditions, and currently, the proposed natural gas hydrate exploitation modes mainly include: thermal excitation method, depressurization method, chemical reagent injection method and CO 2 And (4) a substitution method. The first three exploitation modes are that the temperature and pressure environment of the natural gas hydrate reservoir is changed to ensure that the natural gas hydrate reservoir no longer meets the hydrate phase equilibrium condition, and the decomposition of the natural gas hydrate and the CH are promoted 4 Gas production, but the deformation resistance of the reservoir can be obviously reduced due to the decomposition of the hydrate in the process, and potential risks of engineering and geological disasters such as sand production, reservoir sedimentation, seabed landslide and the like are caused. CO 2 2 The basic idea of the displacement method is to utilize CO 2 Hydrates and CH 4 The generation and stabilization conditions of the hydrate are different, so that CO is generated 2 And CH 4 Contacting the hydrate at CH under temperature and pressure conditions suitable for metathesis 4 CO generation while hydrate decomposition 2 A hydrate. The method is to obtain CH 4 At the same time, CO can be generated 2 Is sealed and stored in the seabed, and maintains the mechanical stability of the reservoir to a certain extent. The production technology using gas exchange reaction becomes to combine the safe exploitation of natural gas and CO 2 Important medium for sequestration, thereby obtaining energy and simultaneously slowing down CO 2 Global climate deterioration caused by emissions.
At present, constitutive models of many different forms for natural gas hydrate reservoirs have been established by some scholars based on different methods and purposes, but none of the constitutive models considers CO 2 Effect of metathesis, now with respect to CO 2 The research of the displacement method mainly focuses on the kinetic mechanism of the displacement reaction and how to improve the displacement efficiency, and the research based on the economic benefit occupies the main position, while the research of the displacement method is currently carried out on CO 2 The research on the mechanical safety of the reservoir in the exploitation process of the displacement method is less, and particularly, the CO can be represented 2 Displacing hydrate reservoirs during productionA constitutive model of the change law of the stress-strain relationship has not been established.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a reservoir constitutive model considering hydrate exploitation influence.
The invention provides a reservoir constitutive model considering hydrate exploitation influence, which has the technical scheme that: the establishing process of the constitutive model mainly comprises the following steps:
step 1: subjecting artificially prepared sediment sample containing methane hydrate to CO 2 Performing a displacement experiment, and performing a triaxial compression experiment on the sample before and after the displacement to obtain a stress-strain curve of the sample;
and 2, step: verifying the Duncan-Chang model to CO according to the experimental result 2 Applicability of the natural gas hydrate reservoir under the influence of displacement; the Duncan-Chang expression is as follows:
Figure 100002_DEST_PATH_IMAGE001
（1）
the formula (1) can also be rewritten into the following two forms:
Figure 471461DEST_PATH_IMAGE002
（2）
or
Figure 100002_DEST_PATH_IMAGE003
（3）
Wherein the content of the first and second substances,
Figure 199246DEST_PATH_IMAGE004
is the bias stress;
Figure 100002_DEST_PATH_IMAGE005
as axial strain, determined experimentally;a、bexperimental parameters that are dependent on the material properties;
and step 3: based on a Duncan-Chang model, correcting 8 model parameters of the Duncan-Chang model by utilizing a replacement rate and an initial hydrate saturation parameter according to a triaxial compression experiment result under different conditions;
the substitution rate is defined as follows:
Figure 156837DEST_PATH_IMAGE006
（4）
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE007
is the rate of substitution;
Figure 362691DEST_PATH_IMAGE008
is an initial CH 4 Amount of substance, mol;
Figure 604185DEST_PATH_IMAGE009
is the residual CH after replacement 4 Amount of substance, mol;
and 4, step 4: CO to be established 2 And comparing the calculation curve of the nonlinear constitutive model of the natural gas hydrate reservoir under the influence of the displacement with the experimental result to verify the accuracy of the calculation curve.
Preferably, the above-mentioned artificially prepared methane hydrate-containing sediment samples have different initial hydrate saturations and need to be prepared according to the mineral composition and particle size distribution of the actual natural gas hydrate reservoir.
Preferably, the above CO 2 Replacement experiments are required to satisfy CH 4 Hydrate decomposition, and CO 2 Hydrates can be carried out under conditions of temperature and pressure in which they are stable.
Preferably, the triaxial mechanical experiment is a conventional triaxial compression experiment
Figure 100002_DEST_PATH_IMAGE010
Or true triaxial compression experiment
Figure 502871DEST_PATH_IMAGE011
(ii) a Wherein, the first and the second end of the pipe are connected with each other,
Figure 947759DEST_PATH_IMAGE012
in order to maximize the effective principal stress of the steel,
Figure 957303DEST_PATH_IMAGE013
in order to achieve an intermediate effective principal stress,
Figure 584462DEST_PATH_IMAGE014
is the minimum effective principal stress; and require triaxial mechanical experiments at different effective confining pressures.
Preferably, the step 2 specifically comprises the following steps:
step 2.1: determining whether the stress-strain curve obtained in the step 1 meets hyperbolic characteristics;
step 2.2: if the hyperbolic characteristic is met in the step 2.1, fitting a stress-strain curve to obtain a sample based on a triaxial compression experiment
Figure 654050DEST_PATH_IMAGE015
~
Figure 851813DEST_PATH_IMAGE016
The relationship of (1);
step 2.3: judgment of
Figure 399469DEST_PATH_IMAGE015
And
Figure 631867DEST_PATH_IMAGE016
whether the relation is linear or not is judged, so that whether the Duncan-Chang model is suitable for CO or not is judged 2 Displacing the affected natural gas hydrate reservoir.
Preferably, the step 3 specifically includes the following steps:
step 3.1: by using the rate of substitution
Figure 856044DEST_PATH_IMAGE017
Initial hydrate saturationS h Parameter to tangent modulus
Figure 806682DEST_PATH_IMAGE018
Correcting;
the above-mentionedCorrected tangent modulus
Figure 423608DEST_PATH_IMAGE018
The calculation formula is as follows:
Figure 244934DEST_PATH_IMAGE019
（2）
in the formula (I), the compound is shown in the specification,
Figure 656324DEST_PATH_IMAGE020
、
Figure 828679DEST_PATH_IMAGE021
、
Figure 232984DEST_PATH_IMAGE022
、
Figure 174396DEST_PATH_IMAGE023
、
Figure 100002_DEST_PATH_IMAGE024
、
Figure 491107DEST_PATH_IMAGE025
、
Figure 885180DEST_PATH_IMAGE026
、
Figure 843908DEST_PATH_IMAGE027
the correction coefficient is obtained by fitting experimental data;p a =0.1013MPa, representing the standard atmospheric pressure;cis cohesive force;φis an internal friction angle;R f as a destruction ratio;
step 3.2: by utilizing the replacement rate and the initial hydrate saturation parameter to the tangential Poisson ratio
Figure 154673DEST_PATH_IMAGE028
Correcting;
the corrected tangent Poisson's ratio
Figure 907865DEST_PATH_IMAGE028
The calculation formula is:
Figure 54813DEST_PATH_IMAGE029
（3）
in the formula (I), the compound is shown in the specification,
Figure 551653DEST_PATH_IMAGE030
、
Figure 467657DEST_PATH_IMAGE031
、
Figure 391750DEST_PATH_IMAGE032
、
Figure 275261DEST_PATH_IMAGE033
、
Figure 575793DEST_PATH_IMAGE034
、
Figure 100002_DEST_PATH_IMAGE035
、
Figure 815144DEST_PATH_IMAGE036
、
Figure 175718DEST_PATH_IMAGE037
the correction coefficient is obtained by fitting experimental data;
Figure 297258DEST_PATH_IMAGE038
is a model parameter without dimension.
Compared with the prior art, the invention has the following beneficial effects:
the invention converts CO into 2 The replacement and triaxial mechanics experiments are combined, the replacement rate and the initial hydrate saturation are utilized to correct the model parameters of the Duncan-Chang model, and the established natural gas hydrate reservoir nonlinear constitutive model takes CO into consideration 2 Influence of displacement, capable of accurately predicting reservoirDestructive behavior applicable to CO 2 Theoretical research, numerical modeling and engineering design related to the exploitation of the natural gas hydrate by the displacement method provide theoretical exploration and support for guaranteeing energy safety and achieving the carbon reduction target.
Drawings
FIG. 1 is a flow chart of a hydrate reservoir constitutive model building process of the present invention;
FIG. 2 is a schematic diagram of a triaxial mechanical experiment system for a low-temperature hydrate according to the present invention;
FIG. 3 shows a CH-containing composition of the present invention 4 Stress-strain curves of the hydrate deposit samples at different replacement rates;
FIG. 4 shows a CH-containing composition of the present invention 4 Stress-strain curves of the hydrate deposit samples under different initial hydrate saturation degrees and effective confining pressures;
FIG. 5 is a comparison of an experimental curve and a calculated curve of the present invention after sample displacement;
FIG. 6 is a comparison of a second experimental curve and a calculated curve of the present invention after sample displacement;
FIG. 7 is a comparison of a third experimental curve and a calculated curve of the present invention after sample displacement;
FIG. 8 is a comparison of a fourth experimental curve and a calculated curve of the present invention after sample displacement;
in the upper drawing: 1. a confining pressure pump; 2. an oil charge pump; 3. a hydraulic oil tank; 4. a valve; 5. four-way connection; 6. a pressure reducing valve; 7. a pressure gauge; 8. CH (CH) 4 A gas cylinder; 9. CO 2 2 A gas cylinder; 10. n is a radical of hydrogen 2 A gas cylinder; 11. a control and data acquisition system; 12. a shaft pressing system; 13. NaOH solution; 14. a water and gas discharge device; 15. a pressure chamber; 16. a pressure head; 17. a sediment sample; 18. a deformation sensor; 19. a base; 20. an emptying pipeline; 21. a tee joint; 22. a low-temperature cold storage.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it should be understood that they are presented herein only to illustrate and explain the present invention and not to limit the present invention.
Example 1, the invention relates to a reservoir constitutive model considering hydrate exploitation influence, and the establishment process comprises the following steps:
step 1: carrying out the reaction with initial hydrate saturation of 13%, 25% and 38% and containing CH 4 Obtaining stress-strain curves shown in fig. 3 and 4 by conventional triaxial compression experiments of the hydrate deposit samples under the conditions that the replacement time is 0h, 6 h, 12 h and 20 h and the effective confining pressure is 1 MPa, 2 MPa and 3MPa respectively;
the CO is 2 The displacement experiment and the triaxial compression experiment are mainly carried out by adopting a low-temperature hydrate triaxial mechanical experiment system shown in figure 2. The system comprises a pressure loading system, a gas supply system, a gas collection system, a temperature control system and other subsystems: the gas injection system comprises CH 4 Gas cylinder 8, CO 2 Gas cylinder 9, N 2 A gas cylinder 10, a pressure reducing valve 6, a pressure gauge 7, a rigid pipeline and the like; the gas collecting system comprises a NaOH solution 13 and a water and gas collecting device 14; the temperature control system mainly refers to a low-temperature refrigeration house 22; the low-temperature hydrate triaxial mechanical experiment system can realize in-situ generation and CH of a hydrate-containing sediment sample 4 -CO 2 Displacement experiments and triaxial compression experiments on samples before and after the displacement.
The loading rate set by the triaxial compression experiment is 0.25 mm-min -1 。
The artificially prepared sediment sample skeleton containing methane hydrate is manufactured according to the components of a rock sample skeleton sampled in a certain area of south China sea, and the sediment mainly comprises clay and silt. In the embodiment, quartz sand particles with the particle size range of 4-125 mu m are selected, kaolin is selected as a cementing material among the particles, and the quartz sand particles with the particle size range of 4-125 mu m are manufactured according to the particle size distribution of a real hydrate frameworkφHydrate deposit sample skeleton of 50X 100 mm.
After the preparation of the sediment sample skeleton containing the methane hydrate is completed, generating the hydrate in a triaxial pressure chamber by adopting the in-situ generation mode: introducing excess CH 4 The gas and water quantitatively contained in the sample skeleton are reacted under low-temperature and high-pressure conditions to generate methane hydrate.
Said CO 2 The temperature and pressure conditions for the displacement experiment were (278K, 3 MPa). The stripLower CH 4 The hydrate will decompose to CO 2 The hydrate can exist stably.
CO described in this example 2 The specific procedure for the displacement experiment was as follows:
1.1 generating CH according to the preset conditions of the experiment 4 After the hydrate is hydrated, CH content is ensured by adjusting a pressure reducing valve 6 4 CO at a hydrate deposit sample pressure of 3MPa 2 In a gaseous environment.
1.2, adjusting the temperature of the low-temperature cold storage 22 to 278K, and starting to perform replacement experiments at different preset times; and (5) performing a triaxial compression experiment after the replacement experiment is finished.
1.3 raising the temperature of the cryocooler 22 to room temperature to remove the remaining CH in the sample containing the hydrate deposits 4 Hydrates and generated CO 2 Decomposing the hydrate, introducing the decomposed gas into an excessive NaOH solution 13, and using CO 2 The gas displaces residual gas in the sample pores and lines.
1.4 The NaOH solution 13 reacts with the mixed gas to remove CO in the mixed gas 2 Complete absorption of gas, remaining CH 4 A gas. CH collected by the drainage gas-collecting device 14 4 Conversion of gas volume to residual CH 4 The amount of substance, from the initial hydrate saturation, the initial CH can be calculated 4 The amount of the substance.
Step 2: verifying that the Duncan-Chang model is applied to CO according to the experimental result 2 Applicability of the natural gas hydrate reservoir under the influence of displacement;
the Duncan-Chang expression is as follows:
Figure 135901DEST_PATH_IMAGE039
（1）
the formula (1) can also be rewritten into the following two forms:
Figure 10185DEST_PATH_IMAGE002
（2）
Figure 541661DEST_PATH_IMAGE003
（3）
wherein the content of the first and second substances,
Figure 884917DEST_PATH_IMAGE004
is the bias stress;
Figure 527251DEST_PATH_IMAGE005
as axial strain, determined experimentally;a、bare experimental parameters that depend on the material properties.
The step 2 specifically comprises the following steps:
step 2.1: the stress-strain curves of the samples in fig. 3 and 4 are hyperbolic and show strain hardening characteristics, which are similar to the Duncan-Chang model describing the stress-strain relationship of the soil material, so that the establishment of a modified Duncan-Chang model for describing CO can be considered 2 Natural gas hydrate reservoir constitutive relation under the influence of displacement;
step 2.2: fitting out based on triaxial experimental data obtained by experiment when the initial hydrate saturation is 13%
Figure 272353DEST_PATH_IMAGE015
~
Figure 974730DEST_PATH_IMAGE016
The relationship of (1);
step 2.3: the results show that in addition to minimal axial strain,
Figure 788971DEST_PATH_IMAGE015
and with
Figure 969417DEST_PATH_IMAGE016
In a linear relationship. This indicates that the stress-strain curves of the samples containing the hydrate deposits before and after displacement fit the Duncan-Chang hyperbolic model. Fitting to obtain intercept and slope of the straight line segment as model parameters under corresponding experimental conditionsaAndbmodel parameters at 13% initial hydrate saturationaAndbthe summary is shown in Table 1.
TABLE 1 model parametersaAndbsummary of the inventionS h =13%)
Figure 834605DEST_PATH_IMAGE040
And step 3: based on a Duncan-Chang model, correcting 8 model parameters of the Duncan-Chang model by utilizing a replacement rate and an initial hydrate saturation parameter according to a triaxial compression experiment result under different conditions;
further, the substitution rate is defined as follows:
Figure 707883DEST_PATH_IMAGE041
（4）
in the formula (I), the compound is shown in the specification,
Figure 760152DEST_PATH_IMAGE042
is the rate of substitution;
Figure 744289DEST_PATH_IMAGE043
is an initial CH 4 Amount of substance, mol;
Figure 713251DEST_PATH_IMAGE044
is the residual CH after replacement 4 Amount of substance, mol.
Further, the step 3 specifically includes the following steps:
step 3.1: utilizing the displacement rate and the initial hydrate saturation parameter to cut the tangent modulus
Figure 757430DEST_PATH_IMAGE045
And (6) correcting.
In a single experiment
Figure 296996DEST_PATH_IMAGE046
Tangent modulus
Figure DEST_PATH_IMAGE047
The definition formula is as follows:
Figure 819244DEST_PATH_IMAGE048
（5）
Figure 127866DEST_PATH_IMAGE049
at a time there is
Figure 592214DEST_PATH_IMAGE050
（6）
According to the formula (2),
Figure 619076DEST_PATH_IMAGE051
at a time
Figure 210594DEST_PATH_IMAGE052
（7）
Wherein the content of the first and second substances,
Figure 373722DEST_PATH_IMAGE053
initial tangent modulus of stress-strain curve, which is the experimental parameteraThe reciprocal of (a);
Figure 494125DEST_PATH_IMAGE054
the ultimate bias stress value represented by the asymptote of the stress-strain curve, which is an experimental parameterbThe reciprocal of (a); the parameters were fitted according to the experimental data of this example at 13% initial hydrate saturation and equations (6) and (7)E i And
Figure 273862DEST_PATH_IMAGE054
and summarized in table 2.
TABLE 2 parametersE i And (a)σ 1 -σ 3 ) ult Summary of the inventionS h =13%)
Figure 664479DEST_PATH_IMAGE055
Initial tangent modulus in Duncan-Chang modelE i Can be expressed as a power function of the effective confining pressure:
Figure 682113DEST_PATH_IMAGE056
（8）
in the formula (I), the compound is shown in the specification,p a =0.1013MPa, which represents standard atmospheric pressure;
Figure 504576DEST_PATH_IMAGE057
、
Figure 506030DEST_PATH_IMAGE058
is a model parameter without dimension.
The experimental results of this example show the initial tangent modulus
Figure 908192DEST_PATH_IMAGE059
Increases with increasing effective confining pressure and increases with increasing rate of displacement at different effective confining pressures, which indicates the initial tangent modulus of the Duncan-Chang model under the influence of displacement
Figure 311492DEST_PATH_IMAGE059
It is not reasonable to consider only the effect of the effective confining pressure, and a correction term representing the effect of the displacement process should be included in equation (8).
Obtained by fitting according to formula (8)KThe value increases with increasing rate of substitution,nthe value decreases with an increase in the substitution rate, and it is understood that the value in the formula (8)
Figure 554123DEST_PATH_IMAGE057
And
Figure 511715DEST_PATH_IMAGE058
are two parameters related to the rate of substitution. Model parameters corrected by substitution rate
Figure 248727DEST_PATH_IMAGE057
And
Figure 506533DEST_PATH_IMAGE058
can be respectively expressed as:
Figure 139639DEST_PATH_IMAGE060
（9）
Figure 115686DEST_PATH_IMAGE061
（10）
substituting the formulas (9) and (10) into the formula (8) to obtain:
Figure 640077DEST_PATH_IMAGE062
（11）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE063
、
Figure 221231DEST_PATH_IMAGE064
、
Figure 556397DEST_PATH_IMAGE065
、
Figure 754160DEST_PATH_IMAGE066
are experimental constants. The experimental constants at different saturations are obtained by fitting the experimental data and are summarized in table 3.
TABLE 3 different initial hydrate saturationsE i Summary of relevant Experimental constants
Figure 832975DEST_PATH_IMAGE067
Axial strain in the experiment cannot be infinite, and ultimate bias stress of a sample containing hydrate deposit
Figure 49061DEST_PATH_IMAGE068
Will be numerically greater than the strength of the sample
Figure 289550DEST_PATH_IMAGE069
Definition of
Figure 240188DEST_PATH_IMAGE069
And
Figure 591535DEST_PATH_IMAGE068
is the destruction ratioR f To determine
Figure 678440DEST_PATH_IMAGE068
The value is obtained.
Figure 89830DEST_PATH_IMAGE070
（12）
According to the three-axis compression experimental result data and
Figure 245873DEST_PATH_IMAGE068
the value of (b) is calculated to obtain the initial hydrate saturation degree of 13% under different effective confining pressures and displacement ratesR f The value is obtained. It was found that the failure ratio had a less pronounced relationship with the confining pressure and the rate of displacement. CH-CONTAINING WHICH INITIAL HYDRATE SATURATION IS 13% 4 The destruction ratio of the hydrate sediment sample under different replacement rates is between 0.92 and 0.97, and most of the hydrate sediment sample is about 0.94, and the average value of 0.940 can be taken as the destruction ratio. Similarly, CH content at 25% and 38% initial hydrate saturation 4 The destruction ratios of the hydrate deposit samples at different replacement rates were 0.934 and 0.937. Comprehensively, the influence degree of the initial hydrate saturation, the effective confining pressure and the replacement rate on the destruction ratio is small, the law is not obvious, and the destruction ratio is taken as a fixed value of 0.940 based on the purpose of simplifying the model.
Substituting formula (12) into (7) yields:
Figure 666490DEST_PATH_IMAGE071
（13）
substituting the formulas (1), (6) and (13) into the formula (5) to obtain
Figure 607902DEST_PATH_IMAGE072
（14）
According to the Moore-Coulomb strength criterion, there are
Figure 190193DEST_PATH_IMAGE073
（15）
Wherein the content of the first and second substances,cin order to achieve the cohesive force,φis the internal friction angle.cAndφthe numerical values of (A) and (B) respectively correspond to the tangent of the common tangent and the slope of the stress Morel circle of the sample under different effective confining pressures. The experimental results of this example show that the cohesive force is increasing with the increase of the initial hydrate saturation and the replacement rate, while the change of the internal friction angle is small and the change rule is not obvious, based on the purpose of simplifying the model, in this example, the initial hydrate saturation and the replacement rate are increasedφ=24.05 °. Assuming the cohesion is the initial hydrate saturation
Figure 849844DEST_PATH_IMAGE074
And rate of substitution
Figure 808573DEST_PATH_IMAGE075
Function of (c):
Figure DEST_PATH_IMAGE076
（16）
Figure 588179DEST_PATH_IMAGE077
（17）
Figure 606950DEST_PATH_IMAGE078
（18）
in the formula (I), the compound is shown in the specification,
Figure 488319DEST_PATH_IMAGE079
、
Figure 985159DEST_PATH_IMAGE080
、
Figure 901163DEST_PATH_IMAGE081
、
Figure 90835DEST_PATH_IMAGE082
the experimental constants can be obtained by fitting the cohesion of the sample under different experimental conditions, and the expression through the fitting formula (16) is as follows:
Figure 708767DEST_PATH_IMAGE083
（19）
by substituting the formulas (8), (15) into the formula (14), a stress state (C)σ 1 , σ 3 ) Duncan-Chang calculation of time tangent modulus:
Figure 9299DEST_PATH_IMAGE084
（20）
substituting formulae (11), (16), (17), and (18) into formula (20) to obtain a tangent modulus calculation formula corrected by the substitution rate and the initial hydrate saturation:
Figure 779809DEST_PATH_IMAGE085
（21）
in formula (21), except for the variablesσ 1 , σ 3 , S h ,ηThe other parameters can be directly obtained or obtained by fitting the triaxial test result according to the steps. To this point, the examples have been on CO 2 The axial stress-strain relationship of the hydrate deposit-containing test specimens under the influence of displacement was corrected, i.e. 5 Duncan-Chang model parameters in equation (20)K, n, c, φ, R f The influence of the parameter of the substitution rate, which represents the degree of substitution, is taken into account.
Step 3.2: by utilizing the replacement rate and the initial hydrate saturation parameter to the tangential Poisson ratio
Figure 140383DEST_PATH_IMAGE086
And (6) correcting.
In order to build a complete constitutive model, it is also necessary to discuss the axial strain
Figure 730764DEST_PATH_IMAGE087
And radial strain
Figure 834986DEST_PATH_IMAGE088
The relationship (c) in (c). Tangential poisson's ratio
Figure 974850DEST_PATH_IMAGE089
Is defined as:
Figure 240746DEST_PATH_IMAGE090
（22）
axial strain in conventional triaxial compression experiments
Figure 584003DEST_PATH_IMAGE091
And radial strain
Figure 226336DEST_PATH_IMAGE092
There is also a hyperbolic relationship between them, whose expression is:
Figure 971439DEST_PATH_IMAGE093
（23）
wherein
Figure 408236DEST_PATH_IMAGE094
And
Figure DEST_PATH_IMAGE095
is a model parameter without dimension. Substituting equation (23) into equation (22) yields:
Figure 222477DEST_PATH_IMAGE096
（24）
Figure 402923DEST_PATH_IMAGE097
when the temperature of the water is higher than the set temperature,
Figure 268111DEST_PATH_IMAGE098
，
Figure 141389DEST_PATH_IMAGE099
is the initial tangential poisson's ratio. The initial hydrate saturation degree is 13 percent and contains CH 4 Hydrate deposit specimen (ηAxial strain of = 0)
Figure 928079DEST_PATH_IMAGE100
And radial strain
Figure 427063DEST_PATH_IMAGE101
Fitting the experimental data according to the formula (23) to obtain model parameters under different effective confining pressures
Figure 146757DEST_PATH_IMAGE102
And
Figure 190936DEST_PATH_IMAGE103
the value of (c). The experimental results of this example show
Figure 464923DEST_PATH_IMAGE103
The value is not significantly related to the effective confining pressure. At other initial hydrate saturations and replacement rates
Figure 252750DEST_PATH_IMAGE102
And
Figure 826951DEST_PATH_IMAGE103
the values also have the same rule, and all the values obtained by fitting
Figure 25720DEST_PATH_IMAGE103
The values are all between 1 and 4 and are distributed in a concentration way
Figure 318161DEST_PATH_IMAGE104
Nearby, to simplify the modelIn this embodiment, the parameters are
Figure 644100DEST_PATH_IMAGE103
The constant value was taken as 2.
Figure 72807DEST_PATH_IMAGE105
And
Figure 458789DEST_PATH_IMAGE106
is represented by formula (25):
Figure 972947DEST_PATH_IMAGE107
（25）
in the formula (I), the compound is shown in the specification,
Figure 86266DEST_PATH_IMAGE108
is the initial tangent poisson's ratio at standard atmospheric pressure;
Figure 635059DEST_PATH_IMAGE109
to characterize
Figure 191942DEST_PATH_IMAGE110
Followed by
Figure 927817DEST_PATH_IMAGE111
Experimental parameters of rate of change. According to the parameters
Figure 861138DEST_PATH_IMAGE112
Can be fitted to the experimental data of (3) and equation (25)S h =13%，ηParameter at =0
Figure 264437DEST_PATH_IMAGE108
And
Figure 992222DEST_PATH_IMAGE109
the values of (A) and (B) can be fit to parameters under the conditions of all experimental preset initial hydrate saturation and replacement rate
Figure 464660DEST_PATH_IMAGE108
And
Figure 201672DEST_PATH_IMAGE109
the value of (c). Suppose that
Figure 459478DEST_PATH_IMAGE108
And
Figure 358164DEST_PATH_IMAGE109
is initial hydrate saturation
Figure 68631DEST_PATH_IMAGE113
And rate of substitution
Figure 343755DEST_PATH_IMAGE114
Is expressed in the form of
Figure 705335DEST_PATH_IMAGE115
（26）
Figure 774922DEST_PATH_IMAGE116
（27）
Figure 972685DEST_PATH_IMAGE117
（28）
Figure 51500DEST_PATH_IMAGE118
（29）
Figure 752739DEST_PATH_IMAGE119
（30）
Figure 258807DEST_PATH_IMAGE120
（31）
Parameters can be fitted from experimental data
Figure 193134DEST_PATH_IMAGE121
、
Figure 810060DEST_PATH_IMAGE122
、
Figure 631386DEST_PATH_IMAGE123
、
Figure 308354DEST_PATH_IMAGE124
、
Figure 480710DEST_PATH_IMAGE125
、
Figure 901327DEST_PATH_IMAGE126
、
Figure 826426DEST_PATH_IMAGE127
、
Figure 674297DEST_PATH_IMAGE128
The value of (c). The expressions of the formulae (26) and (29) are respectively substituted in the formulae (26) to (31) as follows:
Figure 333948DEST_PATH_IMAGE129
（32）
Figure 292677DEST_PATH_IMAGE130
（33）
the initial tangent Poisson's ratio can be obtained by substituting the formulas (32) and (33) for the formula (25).
A tangent Poisson's ratio expression can be obtained by substituting formulae (3), (6), (13), (15) and (25) for formula (24):
Figure 88595DEST_PATH_IMAGE131
（34）
substituting the expressions (11), (16), (17) and (26) to (31) into the expression (34) to obtain a tangential Poisson's ratio calculation formula corrected by the substitution rate and the initial hydrate saturation:
Figure 841787DEST_PATH_IMAGE132
（35）
except for the variablesσ 1 , σ 3 , S h ,ηThe rest parameters can be directly obtained or obtained by fitting the triaxial test result according to the steps. Combining equation (35) with equation (21), the present embodiment has completed the calculation of all 8 model parameters in Duncan-Chang modelK, n, c, φ, R f , D, G, FAnd (4) correcting. Considering CO 2 A constitutive model of the natural gas hydrate reservoir under the influence of displacement has been established.
And 4, step 4: CO to be established 2 And comparing the calculation curve of the nonlinear constitutive model of the natural gas hydrate reservoir under the influence of the displacement with the experimental result to verify the accuracy of the calculation curve.
FIG. 5 is a CH-containing solution with 13% initial hydrate saturation 4 And comparing the stress-strain experimental results and the calculated curves of the hydrate sediment samples under different effective confining pressures and replacement rates. The result shows that the fitting effect is better.
The present invention designs and implements CH 4 -CO 2 The comprehensive integrated experiment of replacement and triaxial compression greatly reduces CO 2 And (3) the displacement exploitation influences the result error caused by experimental conditions and experimental operation in the process of establishing the hydrate reservoir constitutive model. The calculation curves under different experimental conditions can be well fitted with experimental results, particularly in the yield failure stage close to the peak stress, the fitting precision is higher, and the model can accurately predict the stress-strain state when the reservoir fails. The constitutive model establishing method provided by the invention can provide support for subsequent theoretical exploration and engineering application.
The above description is only a few of the preferred embodiments of the present invention, and any person skilled in the art may modify the above-described embodiments or modify them into equivalent ones. Therefore, the technical solution according to the present invention is subject to corresponding simple modifications or equivalent changes, as far as the scope of the present invention is claimed.

Claims (6)

1. A reservoir constitutive model considering hydrate exploitation influence is characterized in that: the establishing process of the constitutive model mainly comprises the following steps:
step 1: subjecting artificially prepared sediment sample containing methane hydrate to CO 2 Performing a displacement experiment, and performing a triaxial compression experiment on the sample before and after the displacement to obtain a stress-strain curve of the sample;
step 2: verifying that the Duncan-Chang model is applied to CO according to the experimental result 2 Applicability of the natural gas hydrate reservoir under the influence of displacement; the Duncan-Chang expression is as follows:
Figure DEST_PATH_IMAGE001
（1）
the formula (1) can also be rewritten into the following two forms:
Figure 369514DEST_PATH_IMAGE002
（2）
or
Figure DEST_PATH_IMAGE003
（3）
Wherein, the first and the second end of the pipe are connected with each other,
Figure 472600DEST_PATH_IMAGE004
is a bias stress;
Figure DEST_PATH_IMAGE005
as axial strain, determined experimentally;a、bexperimental parameters that are determined by the material properties;
and step 3: based on a Duncan-Chang model, correcting 8 model parameters of the Duncan-Chang model by utilizing a replacement rate and an initial hydrate saturation parameter according to a triaxial compression experiment result under different conditions;
the substitution rate is defined by the formula:
Figure 507552DEST_PATH_IMAGE006
（4）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE007
is the rate of substitution;
Figure 261750DEST_PATH_IMAGE008
is an initial CH 4 Amount of substance, mol;
Figure 356745DEST_PATH_IMAGE009
is the remaining CH after the replacement 4 Amount of substance, mol;
and 4, step 4: CO to be established 2 And comparing a calculation curve of the nonlinear constitutive model of the natural gas hydrate reservoir under the influence of the displacement with an experimental result to verify the accuracy of the natural gas hydrate reservoir.
2. A reservoir constitutive model considering hydrate production impact as defined in claim 1, wherein: the artificially prepared methane hydrate-containing sediment samples have different initial hydrate saturation degrees and need to be prepared according to the mineral composition and the particle size distribution of the actual natural gas hydrate reservoir.
3. A reservoir constitutive model considering hydrate production impact as defined in claim 1, wherein: the CO is 2 Replacement experiments are required to satisfy CH 4 Hydrate decomposition, and CO 2 Hydrates can be carried out under conditions of temperature and pressure in which they are stable.
4. A reservoir constitutive model considering hydrate production impact as defined in claim 1, wherein: the third mentionedThe axial mechanics experiment is a conventional triaxial compression experiment
Figure DEST_PATH_IMAGE010
Or true triaxial compression experiment
Figure 947126DEST_PATH_IMAGE011
(ii) a Wherein, the first and the second end of the pipe are connected with each other,
Figure 51348DEST_PATH_IMAGE012
in order to maximize the effective principal stress,
Figure 660053DEST_PATH_IMAGE013
in order to achieve an intermediate effective principal stress,
Figure 191529DEST_PATH_IMAGE014
is the minimum effective principal stress; and require triaxial mechanical experiments at different effective confining pressures.
5. A reservoir constitutive model considering hydrate production impact as defined in claim 1, wherein: the step 2 specifically comprises the following steps:
step 2.1: determining whether the stress-strain curve obtained in the step 1 meets hyperbolic characteristics;
step 2.2: if the hyperbolic characteristic is met in the step 2.1, a stress-strain curve fitting sample is obtained based on a triaxial compression experiment
Figure 534785DEST_PATH_IMAGE015
~
Figure 177119DEST_PATH_IMAGE016
The relationship of (1);
step 2.3: judgment of
Figure 922221DEST_PATH_IMAGE015
And with
Figure 624598DEST_PATH_IMAGE016
Whether the relation is linear or not is judged, so that whether the Duncan-Chang model is suitable for CO or not is judged 2 Displacing the affected natural gas hydrate reservoir.
6. A reservoir constitutive model considering hydrate production influence as defined in claim 1, wherein: the step 3 specifically comprises the following steps:
step 3.1: by using the rate of substitution
Figure 438839DEST_PATH_IMAGE017
Initial hydrate saturationS h Parameter to tangent modulus
Figure 884864DEST_PATH_IMAGE018
Correcting;
the corrected tangent modulus
Figure 484473DEST_PATH_IMAGE018
The calculation formula is:
Figure 92172DEST_PATH_IMAGE019
（2）
in the formula (I), the compound is shown in the specification,
Figure 410020DEST_PATH_IMAGE020
、
Figure 394157DEST_PATH_IMAGE021
、
Figure 97540DEST_PATH_IMAGE022
、
Figure 141719DEST_PATH_IMAGE023
、
Figure DEST_PATH_IMAGE024
、
Figure 415706DEST_PATH_IMAGE025
、
Figure 203533DEST_PATH_IMAGE026
、
Figure 512155DEST_PATH_IMAGE027
the correction coefficient is obtained by fitting experimental data;p a =0.1013MPa, representing the standard atmospheric pressure;cis cohesive force;φis an internal friction angle;R f as a destruction ratio;
step 3.2: by utilizing the replacement rate and the initial hydrate saturation parameter to the tangential Poisson ratio
Figure 976503DEST_PATH_IMAGE028
Correcting;
the corrected tangent Poisson's ratio
Figure 3365DEST_PATH_IMAGE028
The calculation formula is as follows:
Figure 594883DEST_PATH_IMAGE029
（3）
in the formula (I), the compound is shown in the specification,
Figure 758011DEST_PATH_IMAGE030
、
Figure 143993DEST_PATH_IMAGE031
、
Figure 923730DEST_PATH_IMAGE032
、
Figure 37049DEST_PATH_IMAGE033
、
Figure 320262DEST_PATH_IMAGE034
、
Figure DEST_PATH_IMAGE035
、
Figure 611566DEST_PATH_IMAGE036
、
Figure 613020DEST_PATH_IMAGE037
the correction coefficient is obtained by fitting experimental data;
Figure 546341DEST_PATH_IMAGE038
is a model parameter without dimension.
CN202210658843.5A 2022-06-13 2022-06-13 Reservoir constitutive model considering hydrate exploitation influence Pending CN115169077A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116205163A (en) * 2023-04-27 2023-06-02 中国石油大学(华东) Stratum stability analysis method in natural gas hydrate reservoir numerical simulation

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116205163A (en) * 2023-04-27 2023-06-02 中国石油大学(华东) Stratum stability analysis method in natural gas hydrate reservoir numerical simulation
CN116205163B (en) * 2023-04-27 2023-06-30 中国石油大学(华东) Stratum stability analysis method in natural gas hydrate reservoir numerical simulation

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