A method for evaluating the risk of wellbore instability in a pore-saturated elastic medium in different time domains

Abstract

The present invention discloses a method for evaluating the risk of wellbore instability in different time domains of a porous saturated elastic medium. Geological mechanical parameters (including in-situ stress, pore pressure, and rock mechanical and strength parameters) of the target reservoir are obtained from logging data, and the uncertainty characteristics of the geological mechanical parameters are analyzed by combining mathematical statistics methods. Based on the stress solutions of the rock around the well in the instantaneous, short-term, and long-term conditions in a saturated porous elastic medium formation, the analytical solutions of the collapse pressure and fracture pressure of a vertical well in corresponding different time domains are derived. Depending on whether the probability distribution of the geological mechanical parameters can be obtained, the Monte-Carlo method or the first-order second-moment method is respectively used to quantify the uncertainty of the wellbore collapse pressure and fracture pressure. This method can more objectively quantify the influence of the uncertainty of the geological mechanical parameters on the wellbore collapse pressure and fracture pressure in a porous elastic medium formation under instantaneous, short-term, and long-term conditions, providing a theoretical support for preventing wellbore instability.

Description

Technical Field

[0001] The present invention relates to a method for evaluating the risk of wellbore instability in different time domains of a pore-saturated elastic medium, belonging to the technical field of (ultra) deep oil and gas drilling and completion technology. Background Art

[0002] With the in-depth development of oil and gas field development technology, the development difficulty is increasing, and the requirements for drilling operations are also getting higher and higher. Even in the formation rocks of the same block, due to the ambiguity and randomness of the lithology and formation tectonic stress of the rocks themselves, a large number of studies have proved that the influence brought by this uncertainty cannot be ignored. Therefore, the uncertainty problem of wellbore instability pressure has also become a hot topic discussed by scholars. At present, the main contents of uncertainty quantification include parameter uncertainty quantification, model uncertainty, and calculation uncertainty. Under the constraints of various conditions, parameter uncertainty quantification has received extensive attention. To achieve parameter uncertainty quantification, two types of methods, namely statistical type and stochastic mathematical type, have been developed at home and abroad. Among them, Monte-Carlo is one of the most widely used methods for studying the influence of uncertainty. This method has the characteristics of simplicity, effectiveness, and high accuracy. However, in specific applications, it is often necessary to obtain the specific distribution form of parameters for random sampling.

[0003] At present, there are various methods for studying the risk of wellbore instability based on parameter uncertainty. For example, the invention patent with the publication number CN113239577A of Southwest Petroleum University discloses a method for quantitatively evaluating the risk of wellbore instability in complex formations during drilling. By interpreting and calculating the rock mechanics parameters, rock strength parameters, in-situ stress, and pore pressure from the logging data of the target well; and performing a K-S test based on the calculated data to determine the distribution characteristics of geomechanical parameters; at the same time, by considering the correlation coefficient between variables and substituting them into the wellbore collapse pressure and fracture pressure models to calculate the risk of wellbore instability.

[0004] The invention patent with the publication number CN109858147A of Southwest Petroleum University discloses a method for quantitatively evaluating the risk of wellbore instability based on reliability theory. This method mainly starts from the reliability theory and analyzes the risk of wellbore instability in linearly elastic rock formations by manually inputting the characteristics of parameter uncertainty.

[0005] Although the above two patents and other existing technical solutions have achieved certain technical effects, they do not consider the influence of the stress field in porous elastic media wells, and cannot further study the risk of wellbore instability when the parameter distribution is not clear. Summary of the Invention

[0006] The present invention mainly overcomes the deficiencies in the prior art and proposes a method for evaluating the risk of wellbore instability in different time domains of a pore-saturated elastic medium.

[0007] The technical solution provided by the present invention to solve the above technical problems is as follows: A method for evaluating the risk of wellbore instability in different time domains of a pore-saturated elastic medium, comprising the following steps:

[0008] Step 1: Obtain the geomechanical parameters of the reservoir;

[0009] Step 2: Obtain the uncertainty characteristics of the reservoir geomechanical parameters and quantify their uncertainty;

[0010] Step 3: Based on the theory of the wellbore stress field of a vertical well in a poroelastic medium and combined with the Mohr-Coulomb criterion, obtain the analytical solutions of the collapse pressure under instantaneous, short-term, and long-term conditions;

[0011] Step 4: Based on the theory of the wellbore stress field of a vertical well in a poroelastic medium and combined with the tensile fracture criterion, obtain the analytical solutions of the fracture pressure under instantaneous, short-term, and long-term conditions;

[0012] Step 5: According to the quantification method determined in Step 2, quantify the uncertainty of the collapse pressure and fracture pressure of the wellbore in a poroelastic medium under instantaneous, short-term, and long-term conditions;

[0013] Step 6: Analyze the risk of wellbore instability according to the quantification results of the collapse pressure and fracture pressure uncertainty obtained in Step 6.

[0014] The present invention has the following beneficial effects: A method for evaluating the risk of wellbore instability in different time domains of a pore-saturated elastic medium proposed by the present invention is simple to understand, convenient to operate, and low in cost, providing a scientific basis for the analysis of wellbore stability in complex poroelastic medium formations, and can effectively quantify the uncertainty characteristics of the collapse pressure and fracture pressure under instantaneous, short-term, and long-term conditions under the uncertainty of geomechanical parameters. Description of the Drawings

[0015] Figure 1 is a flow block diagram of the present invention. Detailed Embodiments

[0016] The technical solution of the present invention will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0017] As Figure 1 shown, the present invention provides a method for evaluating the risk of wellbore instability under instantaneous - short-term - long-term conditions based on a porous elastic medium, comprising the following steps:

[0018] Step 1: Determine geomechanical parameters based on core experiment results / reservoir logging data, mainly including: mechanical parameters of formation rocks, rock strength parameters, and in-situ stress and pore pressure values;

[0019] Among them, the mechanical parameters of formation rocks include elastic modulus and Poisson's ratio; the rock strength parameters include cohesion, internal friction angle, and tensile strength; the pore pressure value refers to the pore pressure of the original formation.

[0020] For the above parameters, the mechanical parameters and strength parameters can be obtained through rock triaxial compression experiments; the in-situ stress can be obtained through acoustic emission tests; the pore pressure is obtained by statistically analyzing existing pore pressure data.

[0021] Step 2: Obtain the uncertainty characteristics of reservoir geomechanical parameters and quantify their uncertainties;

[0022] Among them, the parameter uncertainty characteristics include the type of parameter probability distribution, data mean value, and standard deviation. For the mean value and standard deviation, they are easy to obtain and are usually relatively accurate values. However, for the type of probability distribution, it is relatively complex: at the same time, according to the data forms obtained on-site, the probability distribution forms of some parameters are known, but the probability distribution forms of other parameters are unknown. The known types of probability distributions include normal distribution, lognormal distribution, triangular distribution, extreme value distribution, uniform distribution, and gamma distribution.

[0023] Use the data mean value, standard deviation, and parameter distribution characteristics to achieve uncertainty quantification. For the type of probability distribution, different methods are used to quantify it according to whether its type is known.

[0024] For parameters with unknown or partially unknown probability distribution types, when quantifying the probability distribution, the first-order second-moment method is mainly used to quantify their uncertainties:

[0025]

[0026] The final result is as follows:

[0027] μ Y = G(μ x1 ,...μ xi ,...μ Xn )

[0028]

[0029] In the formula, Z is the function of the instability pressure; μ Y , σ Y are the mean value and standard deviation of the instability pressure, G is a function composed of random variables, μ Xi represents the mean value of each input parameter, σXi is the standard deviation of each input parameter.

[0030] For parameters with a known probability distribution type, the Monte Carlo method is used to quantify their uncertainty. Since quantifying the uncertainty of parameters with a known probability distribution using the Monte Carlo method is a routine operation in this field, it will not be elaborated here.

[0031] Step 3: Based on the theory of the wellbore wall stress field in a poroelastic medium and combined with the Mohr-Coulomb criterion, obtain the analytical solutions of the collapse pressure under instantaneous, short-term, and long-term conditions.

[0032] Among them, the wellbore wall stress field in a poroelastic medium is as follows:

[0033] Instantaneous solution: (t = 0 + , r = a)

[0034]

[0035] Short-term solution: (t > 0 + , r ≈ a)

[0036]

[0037] Long-term solution: (t = ∞, r = a)

[0038]

[0039] The above wellbore wall stress field in a poroelastic medium is applicable to the stress conditions of the wellbore surrounding rock considering isotropy and homogeneity. In addition, under the conditions of isotropy and homogeneity, the porous mechanical parameters can be obtained through the following relational expressions:

[0040]

[0041] In the formula, α: Biot coefficient, dimensionless; X: bulk modulus, GPa; M: Biot modulus, GPa; K f : fluid bulk modulus, GPa; K s : particle bulk modulus, GPa; Φ: porosity, dimensionless.

[0042] The Mohr-Coulomb criterion is:

[0043]

[0044] In the formula: is the maximum shear stress, MPa; is the mean effective stress, MPa; C and They are the cohesion and internal friction angle of the rock respectively; the effective principal stresses of the surrounding rock of the vertical wellbore include the maximum effective principal stress σ′1, the intermediate effective principal stress σ′2 and the minimum effective principal stress σ′3, in MPa.

[0045] The analytical solutions of the collapse pressure finally obtained under instantaneous, short-term and long-term conditions are respectively:

[0046]

[0047]

[0048]

[0049] In the formula, P w1 is the analytical solution of the collapse pressure under instantaneous conditions, in MPa; P w2 is the analytical solution of the collapse pressure under short-term conditions, in MPa; P w3 is the analytical solution of the collapse pressure under long-term conditions, in MPa; P0 and S0 are the formation average stress and shear stress respectively, in MPa; p0 is the initial pore pressure, in MPa; σ c is the uniaxial compressive strength, in MPa; v and v u represent the Poisson's ratio of the formation rock and the non-permeable Poisson's ratio respectively, dimensionless; B is the Skempton coefficient, dimensionless; η is the poroelastic coefficient, dimensionless; α is the Biot coefficient, dimensionless. is the correlation coefficient, dimensionless.

[0050] Among them, in the embodiments of the present invention, the instantaneous condition refers to the moment when the wellbore is just opened, at the wellbore wall (t = 0 + , r = a); the short-term condition refers to the moment when the "Skempton effect" just disappears after the wellbore is opened for a certain time, near the wellbore wall (t > 0 + , r ≈ a); the long-term condition refers to the long-term stable condition, at the wellbore wall (t = ∞, r = a), where t is the time, r is the distance from the wellbore center in m, and a is the wellbore radius in m.

[0051] Step 4: Based on the stress field theory of the vertical wellbore in a poroelastic medium and combined with the tensile fracture criterion, obtain the analytical solutions of the fracture pressure under instantaneous, short-term and long-term conditions;

[0052] Among them, the tensile fracture criterion means

[0053] σ′3 = -S t

[0054] In the formula: S t is the tensile strength of the rock, in MPa.

[0055] The analytical solutions of the fracture pressure finally obtained under instantaneous, short-term and long-term conditions are:

[0056]

[0057]

[0058]

[0059] In the formula, P f1 is the analytical solution under the instantaneous condition of the fracture pressure, and P f2 is the analytical solution under the short-time condition of the fracture pressure, and P f3 is the analytical solution under the long-time condition of the fracture pressure. P0 and S0 are the formation average stress and shear stress respectively, in MPa; η is the poroelastic coefficient, dimensionless; v and v u represent the Poisson's ratio of the formation rock and the non-permeable Poisson's ratio respectively, dimensionless; S t is the tensile strength of the rock, in MPa; α is the Biot coefficient, dimensionless; B is the Skempton coefficient, dimensionless.

[0060] Step 5: According to the quantification method determined in Step 2, perform uncertainty quantification on the collapse pressure and fracture pressure of the poroelastic medium wellbore under instantaneous, short-time, and long-time conditions respectively;

[0061] In this step, for parameters with known probability distribution types and unknown probability distribution types, their uncertainty quantification methods are also different:

[0062] For parameters with known probability distribution types, the Monte-Carlo method is used for direct sampling of 5000 - 10 4 groups of data that satisfy the probability distribution form to quantify the parameter uncertainty. Under this condition, combined with the analytical solutions in different time domains, the uncertainty results of the wellbore instability pressure are obtained.

[0063] For parameters with unknown probability distribution types, it is assumed that the wellbore instability pressure follows a normal distribution, and the first-order second-moment method is used to quantify the probability distributions of the wellbore collapse pressure and fracture pressure under the analytical solutions in different time domains. The results are:

[0064]

[0065]

[0066] In the formula, represents a normal distribution with as the expectation and as the variance; P wj (j = 1, 2, 3) represent the collapse pressures under instantaneous, short-time, and long-time conditions respectively, in MPa; P fj(j = 1, 2, 3) represent the breakdown pressures under instantaneous, short-term, and long-term conditions, in MPa; μ Ywj (j = 1, 2, 3), are the mean and standard deviation of the collapse pressures under instantaneous, short-term, and long-term conditions, in MPa; μ Yfj (j = 1, 2, 3), are the mean and standard deviation of the breakdown pressures under instantaneous, short-term, and long-term conditions, in MPa.

[0067] Step 6: Analyze the wellbore instability risk based on the quantification results of the collapse pressure and breakdown pressure uncertainties.

[0068] Generally, to prevent formation breakdown due to excessive drilling fluid pressure and collapse during the drilling fluid pressure process for wellbore instability, the collapse pressure and breakdown pressure are usually used to measure wellbore instability. Therefore, after obtaining the quantification results of the collapse pressure and breakdown pressure uncertainties, the wellbore instability risk can be evaluated. For easy identification, the quantified collapse pressure and breakdown pressure can be plotted on the same cumulative distribution graph or probability distribution graph to facilitate the rapid assessment of the wellbore instability risk.

[0069] As described above, it is not any form of limitation to the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art, without departing from the scope of the technical solution of the present invention, can make some changes or modifications to the above-disclosed technical content to obtain equivalent embodiments with equivalent changes. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for evaluating the risk of borehole wall instability in different time domains of a pore-saturated elastic medium, characterized in that, It includes the following steps: Step 1: Obtain the geomechanical parameters of the reservoir; Step 2: Obtain the uncertainty characteristics of the reservoir geomechanical parameters and quantify their uncertainties. If the probability distribution characteristics of the parameter are known, use the Monte-Carlo method to quantify its uncertainty. If the probability distribution characteristics of the parameter are unknown, use the first-order second-moment method to quantify its uncertainty. The first-order second-moment method specifically includes the following steps: μ Y = G(μ X1 ,… μ Xi ,… μ Xn ) where Z is the function of the buckling pressure; μ Y , σ Y are the mean and standard deviation of the buckling pressure, G is the function composed of random variables, μ Xi represents the mean of each input parameter, σ Xi is the standard deviation of each input parameter; Step 3: Based on the theory of the wellbore stress field in a poroelastic medium for a vertical well, combined with the Mohr-Coulomb criterion, obtain the analytical solutions of the collapse pressure under instantaneous, short-term, and long-term conditions; Step 4: Based on the theory of the wellbore stress field in a poroelastic medium for a vertical well, combined with the tensile fracture criterion, obtain the analytical solutions of the fracture pressure under instantaneous, short-term, and long-term conditions; Step 5. According to the quantification method determined in Step 2, quantify the uncertainties of the collapse pressure and fracture pressure of the wellbore in a poroelastic medium under instantaneous, short-term, and long-term conditions: If the probability distribution form of the parameters is known, use the Monte-Carlo method to generate 5000-10 4 groups of data to quantify the parameter uncertainties. Under this condition, combine the analytical solutions in different time domains to obtain the quantification results of the wellbore instability pressure uncertainties; If the form of the parameter probability distribution is unknown, assume that the wellbore instability pressure follows a normal distribution, and use the first-order second-moment method under the analytical solutions in different time domains to quantify the probability distributions of the wellbore collapse pressure and the fracture pressure. The results are: In the formula, represents a normal distribution with as the expectation and as the variance; P wj (j = 1, 2, 3) represent the collapse pressures under instantaneous, short-term, and long-term conditions, respectively, in MPa; P fj (j = 1, 2, 3) represent the fracture pressures under instantaneous, short-term, and long-term conditions, respectively, in MPa; μ Ywj (j = 1, 2, 3), are the mean and standard deviation of the collapse pressures under instantaneous, short-term, and long-term conditions, respectively, in MPa; μ Yfj (j = 1, 2, 3), are the mean and standard deviation of the fracture pressures under instantaneous, short-term, and long-term conditions, respectively, in MPa; Step 6: Analyze the wellbore instability risk according to the uncertainty quantification results of the collapse pressure and the fracture pressure obtained in Step 5.

2. The method according to claim 1, characterized in that, In Step 1, the geomechanical parameters mainly include: the mechanical parameters of the formation rock, the rock strength parameters, and the values of in-situ stress and pore pressure. The mechanical parameters of the formation rock include the elastic modulus and Poisson's ratio. The rock strength parameters include cohesion, internal friction angle, and tensile strength.

3. The method according to claim 1, characterized in that, In Step 2, the uncertainty distribution characteristics include the parameter probability distribution type, data mean value, and standard deviation. The parameter probability distribution types include normal distribution, lognormal distribution, triangular distribution, extreme value distribution, uniform distribution, and gamma distribution.

4. The method according to claim 1, wherein In Step 3, the Mohr-Coulomb criterion is: In the formula: is the maximum shear stress, MPa; is the average effective stress, MPa; C and are the cohesion and internal friction angle of the rock respectively; the effective principal stresses of the surrounding rock of the vertical wellbore include the maximum effective principal stress σ′1 and the minimum effective principal stress σ′3, MPa.

5. The method according to claim 1, characterized in that, The analytical solution of the vertical wellbore collapse pressure in Step 3 is: where P w1 is the analytical solution under the instantaneous condition of collapse pressure, MPa; P w2 is the analytical solution under the short-term condition of collapse pressure, MPa; P w3 is the analytical solution under the long-term condition of collapse pressure, MPa; P0 and S0 are the average formation stress and shear stress, respectively, MPa; p0 is the initial pore pressure, MPa; σ c is the uniaxial compressive strength, MPa; v and v u represent the Poisson's ratio of formation rock and the Poisson's ratio of impermeability respectively, dimensionless; B is the Skempton coefficient, dimensionless; η is the porous elastic coefficient, dimensionless; α is the Biot coefficient, dimensionless; is the correlation coefficient, dimensionless.

6. The method according to claim 1, wherein The tensile fracture criterion is: σ′3 = -S t where: S t is the tensile strength of the rock, in MPa, and σ′3 is the minimum effective principal stress of the surrounding rock, in MPa.

7. The method according to claim 1, characterized in that, The analytical solution of the vertical wellbore fracture pressure in Step 4 is: where P f1 is the analytical solution under the instantaneous condition of the fracture pressure, P f2 is the analytical solution under the short-time condition of the fracture pressure, P f3 is the analytical solution under the long-time condition of the fracture pressure, P0 and S0 are the average formation stress and shear stress, respectively, in MPa; is the porous elastic coefficient, dimensionless; v and v u represent the Poisson's ratio of formation rock and the Poisson's ratio of impermeability respectively, dimensionless; S t is the tensile strength of rock, MPa; α is the Biot coefficient, dimensionless; B is the Skempton coefficient, dimensionless.

8. The method according to claim 1, wherein The specific operation of Step 6 is: By plotting the quantified collapse pressure and fracture pressure on the same cumulative distribution graph or probability distribution graph, the instability risk assessment under instantaneous, short-term, and long-term conditions is completed.

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