Method for constructing phase permeability curve of power-law non-newtonian fluid

Abstract

The application discloses a method for constructing a relative permeability curve of a power-law non-Newtonian fluid, which comprises the following steps: first, a non-steady-state relative permeability curve displacement experiment device is built; then, rock sample pretreatment, non-Newtonian fluid rheological parameter testing and displacement experiment data acquisition are completed; the outlet water breakthrough time, the cumulative liquid production and the displacement pressure difference of the non-Newtonian fluid when the constant-speed displacement of the non-Newtonian fluid is recorded; after the experimental data is preprocessed, a relative permeability curve model is preset, the water cut is implicitly solved and the derivative is calculated, and the injection pore multiple of the non-Newtonian fluid and the displacement pressure difference are derived; based on the experimental data, the water saturation-water cut and the displacement pressure difference-water saturation relationship are simultaneously fitted through an iterative optimization algorithm, and finally, the coefficients in the relative permeability curve formula are determined, and the relative permeability curve is constructed. The method improves the smoothness and physical rationality of the relative permeability curve of the non-Newtonian fluid, improves the calculation accuracy, and provides a reliable means for analyzing the seepage characteristics of complex fluids.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of underground oil and gas reservoir exploitation, and particularly relates to a method for constructing a relative permeability curve of a power-law non-Newtonian fluid. BACKGROUND

[0002] As a complex fluid with a nonlinear relationship between shear stress and shear rate, non-Newtonian fluid has important application value in the fields of underground oil and gas reservoir development, contaminated soil migration and remediation, etc. In the oil and gas development scenario, the seepage characteristics of non-Newtonian fluids such as polymer flooding oil solution and heavy oil directly determine the recovery rate, and the shear thinning behavior of the non-Newtonian fluid will significantly change the resistance distribution in the seepage process and affect the flow characteristics of oil and water phases. In the field of environmental engineering, the migration process of non-Newtonian fluids (such as surfactant solution and colloidal suspension) in soil is subject to its rheological properties, which is directly related to the migration and remediation of pollutants.

[0003] The traditional method for constructing a two-phase relative permeability curve (hereinafter referred to as a relative permeability curve) is difficult to be directly applied to non-Newtonian fluids, and the main problems are as follows: firstly, the power-law seepage characteristics of non-Newtonian fluids cause the linear assumption of Darcy's law to fail, and the nonlinear relationship between flow rate and pressure gradient needs to be described by a modified model, which makes the traditional relative permeability calculation model no longer applicable; secondly, the "unreachable pores" commonly existing in porous media, i.e. the space that cannot be occupied by a certain phase fluid due to the small pore size relative to the characteristic size of the fluid, affects the material balance of injection and production, and indirectly causes the residual saturation of the relative permeability curve to deviate and the shape to be abnormal. The existing relative permeability curve related patents and documents do not consider the influence of the above nonlinear characteristics and unreachable pores, resulting in insufficient calculation accuracy of the relative permeability curve of non-Newtonian fluids.

[0004] At present, the published patents and documents related to the construction of the relative permeability curve of non-Newtonian fluids are relatively limited, and the existing documents (Yang Qingyan, Li Binhui, Zhou Yingfang, et al. Research on calculation method of polymer flooding relative permeability curve [J]. Acta Petrolei Sinica, 2010; Li Binhui, Yu Zhaoyang, Li Yiqiang, et al. Research progress of determination method of polymer flooding relative permeability curve [J]. Daqing Petroleum Geology and Development, 2017) mostly rely on the non-steady-state JBN method for calculation. However, this method has strong dependence on experimental data and is easily affected by data noise, resulting in local fluctuations or even distortion of the relative permeability curve. SUMMARY

[0005] The main purpose of the present application is to provide a method for constructing a relative permeability curve of a power-law non-Newtonian fluid, which proposes a technical idea of "presetting relative permeability-inversion fitting displacement pressure difference and water cut": a mathematical model of displacement pressure difference and water cut is established by presetting a relative permeability curve and combining a nonlinear seepage equation, and then the preset relative permeability curve is iteratively optimized by using experimental data to improve the smoothness and physical rationality of the relative permeability curve.

[0006] The technical solution adopted in this invention is:

[0007] A method for constructing the phase permeation curve of a power-law non-Newtonian fluid includes the following steps:

[0008] S1. Experimental setup: An unsteady phase permeability curve displacement experimental setup was set up, which includes a fluid injection module, a core seepage module, and a produced fluid collection module.

[0009] S2. Relative permeability test: The core was cleaned with organic solvent and dried. The core length and diameter were measured, and the cross-sectional area and volume of the core were calculated. The rheological parameters of the non-Newtonian fluid were tested using a rheometer to determine the power-law exponent and consistency coefficient. The core was vacuum-saturated with water, and the pore volume and porosity of the core were calculated. The defense fluid was saturated, and the saturation of the bound water was calculated. The effective permeability under the bound water was determined. The defense fluid was displaced with a non-Newtonian fluid at a constant injection rate, and experimental data including the time to water breakthrough at the outlet, the cumulative production volume, and the displacement pressure difference were recorded.

[0010] S3. Construction of Relative Permeability Curves: Preprocess experimental data to calculate water cut, containment fluid ratio, injection porosity, and outlet water saturation; pre-construct relative permeability curves for non-Newtonian fluids and containment fluids; implicitly solve for water cut using cubic spline interpolation with partitioning; calculate injection porosity and displacement pressure difference in the relative permeability curves; adjust the pre-constructed relative permeability curves, simultaneously fit the relationship curves between water cut and water saturation, and displacement pressure difference and water saturation, determine the coefficients in the relative permeability curve formula, and thus construct the relative permeability curve.

[0011] In the above scheme, in step S1, the fluid injection module includes an injection pump, a water container, a non-Newtonian fluid container, a defensive fluid container, a first six-way valve, and a second six-way valve. The water container, the non-Newtonian fluid container, and the defensive fluid container are connected in parallel. The first six-way valve is installed on the inlet pipe, and the second six-way valve is installed on the outlet pipe. The injection pump is connected to the first six-way valve. The core seepage module includes a core holder and a pressure monitoring system. The core holder is used to fix the core, and its inlet is connected to the second six-way valve. The pressure monitoring system is used to monitor the pressure difference between the two ends of the core in real time. The produced fluid collection module includes a produced fluid metering device, which is connected to the outlet of the core holder.

[0012] In the above scheme, the method for calculating the bound water saturation in step S2 is as follows:

[0013] (1)

[0014] In the formula, To restrict water saturation, Vp The core pore volume, V w The volume of produced water measured at the outlet during the saturation defense fluid process;

[0015] The method for calculating the effective permeability under bound water is as follows:

[0016] (2)

[0017] In the formula, K d To limit the effective permeability underwater, Q d To maintain a constant injection rate of the defense fluid, μ d To protect against the viscosity of the fluid, L The length of the core sample. A The cross-sectional area of ​​the rock core. ΔP w Displacement pressure differential recorded during the determination of effective permeability of defensive fluids.

[0018] In the above scheme, in step S2, the injection rate of the non-Newtonian fluid must satisfy the following formula:

[0019] (3)

[0020] In the formula, The injection velocity of the non-Newtonian fluid. The working viscosity is for non-Newtonian fluids. L The length of the core sample;

[0021] The method for calculating the working viscosity of non-Newtonian fluids is as follows:

[0022] (4)

[0023] In the formula, H is the consistency coefficient of a non-Newtonian fluid. n For a non-Newtonian fluid, the power-law exponent is given. K d To limit the effective permeability underwater, This refers to the core porosity.

[0024] In the above scheme, in step S3, when preprocessing the experimental data, the method for calculating the moisture content is as follows:

[0025] (5)

[0026] In the formula, The moisture content is calculated based on experimental data. This represents the cumulative liquid production of the non-Newtonian fluid. The cumulative production volume of the defensive fluid;

[0027] Corresponding fluid ratio containing defense for ;

[0028] The method for calculating the injection porosity ratio is as follows:

[0029] (6)

[0030] In the formula, The injection porosity multiple is calculated based on experimental data. V p This represents the core pore volume;

[0031] The water saturation of the unsteady-state phase permeation curve is the water saturation at the outlet end. The method for calculating the water saturation at the outlet end is as follows:

[0032] (7)

[0033] In the formula, The water saturation at the outlet. To restrict water saturation, To defend against the density of the fluid, For the density of a non-Newtonian fluid, These are inaccessible pores.

[0034] In the above scheme, during step S3, when constructing the phase permeability curve in advance, the phase permeability curve of the non-Newtonian fluid conforms to the following formula:

[0035] (8)

[0036] In the formula, The relative permeability of a non-Newtonian fluid. Water saturation; For maximum water saturation, To bind water saturation; d , e The coefficients to be fitted are... d <0, e <0;

[0037] The phase permeation curve of the defense fluid conforms to the following formula:

[0038] (9)

[0039] In the formula, The relative permeability of the defense fluid, Maximum water saturation The relative permeability of the corresponding defensive fluid. a , bThe coefficients to be fitted are... a <0, b ≥ 0.

[0040] In the above scheme, the implicit method for solving the moisture content in step S3 is as follows:

[0041] The injected fluid at a constant rate and the corresponding extracted fluid conform to the law of mass conservation, which is expressed by the following equation:

[0042] (13)

[0043] In the formula, v t The injection speed of the injection pump, v d To prevent the seepage rate of the fluid, v in The seepage velocity of a non-Newtonian fluid. To defend against the density of the fluid, For the density of a non-Newtonian fluid, Inaccessible pores;

[0044] The implicit equation for calculating moisture content is:

[0045] (15)

[0046] In the formula, f w Moisture content, n The power-law exponent, Water saturation S w The working viscosity of non-Newtonian fluids. μ d To protect the viscosity of the fluid;

[0047] The above implicit equations were solved using numerical methods to obtain the results for different water saturation levels. S w moisture content f w .

[0048] In the above scheme, step S3 uses cubic spline interpolation technology for partitioning to calculate the moisture content derivative. The specific method is as follows:

[0049] Regarding the moisture content f w With water saturation S w The derivatives of discrete data points are obtained by constructing continuous functions and continuous first-order derivatives using cubic spline interpolation techniques with partitioning. The fitting formula is as follows:

[0050] (16)

[0051] The corresponding continuous first derivative is as follows:

[0052] (17)

[0053] In the formula, Moisture content f w With the first derivative of water saturation, For the first i Water saturation in each interval For the first i +1 interval of water saturation, c 3. c 2. c 1 and c 0 is the first i The spline coefficients for each interval.

[0054] In the above scheme, in step S3, the formula for calculating the injection porosity multiple in the relative permeability curve is:

[0055] (18)

[0056] In the formula, This refers to the injection porosity multiple;

[0057] The formula for calculating the displacement pressure difference in the relative permeability curve is:

[0058] (19)

[0059] In the formula, To displace the pressure difference, L The length of the core sample. K d To limit the effective permeability underwater, Q out Water saturation S w The corresponding injection porosity multiple, Water saturation S w The equivalent viscosity of the corresponding two-phase fluid is calculated using the following formula:

[0060] (20)

[0061] In the formula, the seepage velocity of the non-Newtonian fluid is... v in The calculation formula is:

[0062] (twenty one).

[0063] In the above scheme, during step S3, when adjusting the pre-constructed relative permeability curve, the objective function is optimized as follows:

[0064] (twenty two)

[0065] In the formula, λ is the weighting coefficient, 0 < λ < 1; and It is the calculated theoretical moisture content and displacement pressure difference; and These are the baseline moisture content and displacement pressure difference obtained from experimental testing; i Indicates the first i A range; N It refers to the number of data points;

[0066] By using an iterative optimization algorithm, the relationship curves between water content and water saturation, and between displacement pressure difference and water saturation, are simultaneously fitted. The coefficients in the relative permeability curve formula are adjusted to minimize the difference between the calculated water content and displacement pressure difference and the experimental baseline data. Finally, the coefficients in the relative permeability curve formula are determined, and the relative permeability curve is constructed.

[0067] The beneficial effects of this invention are:

[0068] This invention addresses the limitations of traditional methods in applying to non-Newtonian fluids by constructing a relative permeability curve through a "pre-defined relative permeability curve—synchronous fitting of displacement pressure difference and water cut" approach. First, an unsteady-state relative permeability curve displacement experiment apparatus is built to pre-process rock samples, test non-Newtonian fluid rheological parameters, and collect displacement experimental data. After pre-processing the experimental data, a relative permeability curve model is pre-defined, implicitly solving for the water cut and calculating derivatives to derive the injection porosity multiple and displacement pressure difference of the non-Newtonian fluid. Based on the experimental data, an iterative optimization algorithm is used to simultaneously fit the relationships between water saturation and water cut, and between displacement pressure difference and water saturation, ultimately determining the coefficients in the relative permeability curve formula and constructing the relative permeability curve. This method improves the smoothness and physical rationality of the non-Newtonian fluid relative permeability curve while also increasing computational accuracy, providing a reliable means for analyzing the seepage characteristics of complex fluids. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0070] Figure 1 This is a schematic diagram of the unsteady phase permeation curve displacement experimental device constructed by the method of the present invention;

[0071] Figure 2 This is a flowchart illustrating the construction of the phase permeation curve in an embodiment of the present invention;

[0072] Figure 3 These are the rheological curves of the polymer solutions in the embodiments of the present invention;

[0073] Figure 4 This is a graph showing the fitting results of the moisture content in an embodiment of the present invention;

[0074] Figure 5 This is a graph showing the fitting results of the oil displacement efficiency in an embodiment of the present invention;

[0075] Figure 6 This is a fitting result diagram of the displacement pressure difference in an embodiment of the present invention;

[0076] Figure 7 This is the final output phase permeation curve in this embodiment of the invention.

[0077] In the diagram: 1. Injection pump; 2. Water container; 3. Non-Newtonian fluid container; 4. Defense fluid container; 5. First six-way valve; 6. Second six-way valve; 7. Pressure monitoring system; 8. Core holder; 9. Produced fluid metering device. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0079] It should be noted that the illustrations provided in the embodiments of the present invention are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0080] In this invention, it should also be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first" and "second" are used only for descriptive and distinguishing purposes and should not be construed as indicating or implying relative importance.

[0081] This invention proposes a method for constructing the phase permeation curve of a power-law non-Newtonian fluid, comprising the following steps:

[0082] S1. Experimental setup. Setup as follows: Figure 1The unsteady-state phase permeation curve displacement experimental setup shown includes a fluid injection module, a core seepage module, and a produced fluid collection module.

[0083] The fluid injection module includes an injection pump 1, a water container 2, a non-Newtonian fluid container 3, a defensive fluid container 4, a first six-way valve 5, and a second six-way valve 6. The water container 2, non-Newtonian fluid container 3, and defensive fluid container 4 are connected in parallel, with the first six-way valve 5 installed on the inlet pipe and the second six-way valve 6 installed on the outlet pipe. The injection pump 1 is connected to the first six-way valve 5. The injection pump 1 is used to precisely control the constant-rate injection of the non-Newtonian fluid and the displacing fluid (water or defensive fluid). The water container 2, non-Newtonian fluid container 3, and defensive fluid container 4 are used to store the corresponding experimental fluids. The first six-way valve 5 and the second six-way valve 6 are used to switch the injected fluid (e.g., switching between defensive fluid displacing water and non-Newtonian fluid displacing defensive fluid).

[0084] The core seepage module includes a core holder 8 and a pressure monitoring system 7. The core holder 8 is used to fix the columnar core, ensuring that the injected fluid seeps from the injection end to the extraction end of the core. The inlet of the core holder 8 is connected to the second six-way valve 6. The pressure monitoring system 7 is used to monitor the pressure difference between the two ends of the core in real time, and to collect information such as the pressure difference in real time for subsequent data processing.

[0085] The produced fluid collection module includes a produced fluid metering device 9, which is connected to the outlet of the core holder 8 to measure the volume of the two-phase liquid produced during the displacement process (error ±0.05mL).

[0086] S2. Relative Permeability Experiment Test. The basic experimental data required to construct the relative permeability curve are recorded through experimental testing. The experimental steps are as follows:

[0087] Step 2.1: Core Pretreatment. The core was washed with an organic solvent (such as a chloroform-methanol mixture) to remove organic matter, then dried at 105°C for at least 10 days. The initial mass of the core was then measured. m 0.

[0088] Step 2.2: Measure the core length L and diameter D Calculate the cross-sectional area of ​​the core. A and volume V c .

[0089] Step 2.3: Use a rheometer to test the rheological parameters of the non-Newtonian fluid. The shear rate range must include 0.1 ~ 400 s⁻¹. -1 The power law exponent is determined by fitting the equation using a power law method. n Consistency coefficient H .

[0090] Step 2.4: Vacuum Saturation with Water. Place the core in a vacuum apparatus and evacuate for at least 6 hours. Saturate the core with formation water using an unsteady-state relative permeability curve displacement experiment device, and then record the core mass after water saturation. m 1. By comparing with the initial mass of the core m The difference of 0 is used to calculate the core pore volume. V p Utilizing pore volume V p With core volume V c The ratio of the two values ​​is used to calculate the core porosity. .

[0091] The method for calculating the pore volume of rock cores is as follows:

[0092]

[0093] In the formula, The density of water;

[0094] The method for calculating core porosity is as follows:

[0095]

[0096] In the formula, V c This represents the core volume.

[0097] Step 2.5: Saturate the fluid to be displaced (i.e., the defense fluid). The saturated defense fluid is not a non-Newtonian fluid. In scenarios such as reservoir development or contaminant remediation, this defense fluid is oil. Use injection pump 1 to initially displace the fluid at a low flow rate (0.1 mL / min). Once the injected fluid (a fluid other than water) is observed in the produced fluid, gradually increase the injection rate. The cumulative injected volume should be at least 10 times the pore volume. V p Displaced to the core outlet, no water is produced. The produced water volume is measured at the outlet. V w Calculate the bound water saturation using the following formula. S wc .

[0098] (1)

[0099] Step 2.6: Test the effective permeability under bound water. After the core has aged for at least 24 hours, determine the effective permeability using a defensive fluid. Specifically, use a constant injection rate. Q d Record the pressure difference at both ends of the core. ΔP w Effective penetration rate Kd The calculation is performed according to the following formula:

[0100] (2)

[0101] In the formula, K d Effective penetration rate, unit: D; μ d Viscosity of the defense fluid, unit: mPa·s; L Core length, unit: cm; Q d The injection rate of injection pump 1 is expressed in mL / s. A The cross-sectional area of ​​the rock core, unit: cm² 2 ; ΔP w Displacement pressure difference recorded during the determination of effective permeability of the defense fluid, in atm.

[0102] Step 2.7: Non-Newtonian fluid displaces the defense fluid at a constant rate. To reduce the influence of end effects and capillary pressure, a certain injection rate is selected during the phase permeability curve test to overcome capillary pressure. The selected injection rate must satisfy the formula:

[0103] (3)

[0104] In the formula, The injection velocity of the non-Newtonian fluid is expressed in cm / s. The working viscosity of a non-Newtonian fluid, in mPa·s;

[0105] The method for calculating the working viscosity of non-Newtonian fluids is as follows:

[0106] (4)

[0107] In the formula, H is the consistency coefficient of a non-Newtonian fluid. n For a non-Newtonian fluid, the power-law exponent is given. K d To limit the effective permeability underwater, This refers to the core porosity.

[0108] In the constant-rate displacement process of non-Newtonian fluids, accurately record the time of water emergence at the outlet, the cumulative liquid production (both liquids) at water emergence, and the displacement pressure differential. During the initial water emergence phase at the outlet, record frequency should be increased, with the time interval adjusted based on the production of the defensive fluid. As the production of the defensive fluid gradually decreases, the recording interval can be gradually extended. Finally, record and statistically analyze the displacement pressure differential at different times. Cumulative liquid production of non-Newtonian fluids Cin Cumulative production of defensive fluids C d .

[0109] S3. Construction of the relative permeability curve. The relative permeability curve is constructed based on the experimental data, specifically including the following steps:

[0110] Step 3.1: Preprocess the experimental data and calculate the moisture content. , containing defensive fluid rate Injection porosity and water saturation at the outlet .

[0111] Based on the cumulative liquid production of the non-Newtonian fluid and the defensive fluid recorded in the experiment, the water content is calculated according to the following formula. .

[0112] (5)

[0113] In the formula, The moisture content is calculated based on experimental data. This represents the cumulative liquid production of the non-Newtonian fluid. The cumulative amount of fluid produced for defense.

[0114] Corresponding fluid ratio containing defense for ;

[0115] Injection porosity The calculation method is as follows:

[0116] (6)

[0117] In the formula, The injection porosity multiple is calculated based on experimental data. V p This represents the core pore volume;

[0118] The water saturation of the unsteady-state phase permeation curve is the water saturation at the outlet end. The method for calculating the water saturation at the outlet end is as follows:

[0119] (7)

[0120] In the formula, The water saturation at the outlet. To restrict water saturation, To defend against the density of the fluid, For the density of a non-Newtonian fluid, These are inaccessible pores.

[0121] Step 3.2: Pre-construct the interpenetration curves of the non-Newtonian fluid and the defensive fluid.

[0122] When a non-Newtonian fluid is used as the injection fluid, the phase permeation curve conforms to the following formula:

[0123] (8)

[0124] In the formula, The relative permeability of a non-Newtonian fluid. Water saturation; For maximum water saturation, To bind water saturation; d , e The coefficients to be fitted are... d <0, e <0, e The larger the absolute value, the closer the curve shape is to S type.

[0125] The phase permeation curve of the defense fluid conforms to the following formula:

[0126] (9)

[0127] In the formula, The relative permeability of the defense fluid, Maximum water saturation The relative permeability of the corresponding defensive fluid. a , b The coefficients to be fitted are... a <0, b ≥ 0, b The larger the value, the more concave the curve.

[0128] Calculate the water saturation according to formula (8). S w Working viscosity of non-Newtonian fluids The following equation is satisfied:

[0129] (10)

[0130] Step 3.3: Implicitly solve for moisture content.

[0131] The equation of motion for non-Newtonian fluids in porous media follows a power-law relationship, as shown in equation (11):

[0132] (11)

[0133] In the formula, v in For non-Newtonian fluids, the seepage velocity is expressed in cm / s. n For a non-Newtonian fluid, the power-law exponent is given.P The pressure difference between the injection end and the production end. x This is the distance from the injection end to the extraction end.

[0134] The equation of motion for the defensive fluid within the porous medium satisfies formula (12):

[0135] (12)

[0136] In the formula, v d The velocity of the fluid used for defense, measured in cm / s.

[0137] The injected fluid at a constant rate and the corresponding extracted fluid conform to the law of mass conservation, which is expressed by the following equation:

[0138] (13)

[0139] In the formula, v t The injection speed of injection pump 1, To defend against the density of the fluid, For the density of a non-Newtonian fluid, These are inaccessible pores.

[0140] Based on the flow distribution equation, the water content is calculated according to formula (14):

[0141] (14)

[0142] In the formula, This refers to the moisture content.

[0143] Substituting formulas (11), (12), and (13) into the moisture content formula (14), we obtain the moisture content. The implicit equation (15):

[0144] (15)

[0145] The implicit equation (15) above was solved using a numerical method to obtain the results for different water saturation levels. S w moisture content f w .

[0146] Step 3.4: Calculate the moisture content derivative using the cubic spline interpolation technique for partitioning.

[0147] Regarding moisture content f w With water saturation S wThe derivatives of discrete data points are obtained by constructing continuous functions and continuous first-order derivatives using cubic spline interpolation techniques with partitioning. The fitting formula is as follows:

[0148] (16)

[0149] The corresponding continuous first derivative is as follows:

[0150] (17)

[0151] In the formula, Moisture content f w With the first derivative of water saturation, For the first i Water saturation in each interval For the first i +1 interval of water saturation, c 3. c 2. c 1 and c 0 is the first i The spline coefficients for each interval.

[0152] Step 3.5: Calculate the injection porosity multiple in the relative permeability curve.

[0153] The formula for calculating the injection porosity multiple in the relative permeability curve is:

[0154] (18)

[0155] In the formula, This refers to the injection porosity multiple.

[0156] Step 3.6: Calculate the displacement pressure difference in the relative permeability curve.

[0157] The formula for calculating the displacement pressure difference in the relative permeability curve is:

[0158] (19)

[0159] In the formula, To displace the pressure difference, Q out Water saturation S w The corresponding injection porosity multiple, Water saturation S w The equivalent viscosity of the corresponding two-phase fluid is calculated using the following formula:

[0160] (20)

[0161] In the formula, the seepage velocity of the non-Newtonian fluid is...v in The calculation formula is:

[0162] (twenty one)

[0163] Step 3.7: Adjust the pre-constructed relative permeability curve, simultaneously fit the relationship curves of water content-water saturation and displacement pressure difference-water saturation, determine the coefficients in the relative permeability curve formula, and thus construct the relative permeability curve.

[0164] The experimental water saturation calculated using equation (7) and the water content calculated using equation (5) and the displacement pressure difference recorded in the experiment Based on the baseline data, adjust the coefficients in the relative permeability curve formulas (8) and (9). a , b , d , e and The moisture content calculated by equation (15) is thus obtained. f w Displacement pressure difference calculated by equation (19) ΔP The difference from the baseline data is minimized. The objective function and constraints satisfy equation (22). Through iterative optimization algorithms, such as the least squares method, the relationship curves between water content and water saturation, and between displacement pressure difference and water saturation are simultaneously fitted. The coefficient values ​​are continuously adjusted until the set error requirements are met, thereby optimizing the coefficients corresponding to the relative permeability curve. a , b , d , e and Finally, the relative permeation curves in formulas (8) and (9) were determined.

[0165] (twenty two)

[0166] In the formula, λ is the weighting coefficient, 0 < λ < 1; and It is the calculated theoretical moisture content and displacement pressure difference; and These are the baseline moisture content and displacement pressure difference obtained from experimental testing; N It represents the number of data points.

[0167] The following describes a specific embodiment of the invention. In this embodiment, oil is used as the defensive fluid with a viscosity of 10.2 mPa·s. The non-Newtonian fluid is selected as a polymer solution for oil displacement, specifically partially hydrolyzed polyacrylamide with a molecular weight of 25 million and a polymer solution concentration of 1000 mg / L. At a shear rate of 7.34 s⁻¹... -1 The apparent viscosity of the test The rheological curve at a shear rate of 18.36 mPa·s is shown below. Figure 3 As shown, according to the power law exponential form The rheological curve is fitted, where, for Figure 3 The apparent viscosity is represented by the vertical axis, γ is... Figure 3 The shear rate on the horizontal axis. Fitting effect. R 2 The consistency coefficient obtained by fitting reached 0.9776. H The power law exponent is 38.283. n The specific implementation method for constructing the phase permeation curve of a power-law non-Newtonian fluid is as follows, with a value of 0.557.

[0168] Building such Figure 1 The unsteady-state phase permeation displacement experimental setup is shown. Water, polymer solution, and oil are stored in water container 2, non-Newtonian fluid container 3, and defensive fluid container 4, respectively.

[0169] Experimental core length L It is 15.09 cm in length and has a diameter of 15.09 cm. D The core diameter is 3.78 cm. The mass difference between the core before and after vacuum saturation with water is 53.17 g. Therefore, the corresponding core pore volume is... V p The core porosity was 53.17 mL. The percentage was 31.41%, and the polymer solution used had inaccessible pores in the core. m The value was 0.182. Injection rates of 0.1, 0.3, 0.6, and 1 mL / min were used sequentially to saturate the water-saturated core with oil. The total oil volume was 42 mL, and the bound water saturation was 0.2101. Under bound water conditions, oil was used as the displacing fluid, and the pump injection rate was 0.8 mL / min. The displacement pressure difference was measured to be 0.0185 MPa. The effective permeability was calculated according to formula (2). K d It is 0.986 D.

[0170] In the process of determining the relative permeability curve by displacing oil with polymer solution, the injection rate of polymer solution was selected as 2.1 mL / min. This injection rate meets the conditions of formula (3), ensuring that capillary pressure can be ignored during the construction of the relative permeability curve. During the displacement process of polymer solution, the time of water emergence at the outlet, the cumulative production volume (polymer solution and oil) at the time of water emergence, and the displacement pressure difference were accurately recorded. In the early stage of water emergence at the outlet, the relevant data were recorded more frequently. Subsequently, as the oil production gradually decreased, the recording interval was appropriately extended. Finally, the displacement pressure difference at different times was recorded in detail. Cumulative liquid production of polymer solution C in Cumulative liquid production of oilC d .

[0171] Then construct the relative permeability curve according to S3. The specific operation steps are as follows:

[0172] Step 3.1: Record the cumulative liquid yield of the polymer solution at different time points in the experiment. C in Cumulative liquid production of oil C d The moisture content was calculated according to formulas (5), (6) and (7) after pretreatment. Injection porosity and water saturation at the outlet Baseline data, etc.

[0173] Step 3.2: Preset the phase permeation curve of the polymer solution according to formula (8), and preset the phase permeation curve of the oil according to formula (9).

[0174] Step 3.3: Calculate the polymer solution at different water saturation levels using the implicit solution of formula (15). S w moisture content f w In specific implementation, the numerical solution of equation (15) adopts... Matlab In fsolve The function, with an initial value of 0.60, calculates different water saturation levels. S w The corresponding moisture content f w The value.

[0175] Step 3.4: Based on moisture content f w With water saturation S w For discrete data points, the first derivative is constructed using the cubic spline interpolation technique in formulas (16) and (17). Specifically, a self-developed function is used. CubicDre Perform the calculation.

[0176] Step 3.5: Based on the calculated first derivative The injection porosity multiple in the relative permeability curve is calculated according to formula (18). PV i The results are shown in Table 1.

[0177] Step 3.6: Based on the moisture content calculated above f w Injection porosity PV i Water saturation S wNon-Newtonian fluid working viscosity μ eff and the injection speed of injection pump 1 V t Information such as displacement pressure difference is used to calculate the displacement pressure difference according to formulas (19), (20) and (21). ΔP .

[0178] Step 3.7: Set the objective function for optimization according to formula (22). In this embodiment, the selected weighting coefficient λ is 0.5, and the coefficients in the reactivity curve are adjusted accordingly. a , b , d , e and Then, following steps 3.2 to 3.6 sequentially, an iterative optimization algorithm is used until the displacement pressure difference in the relative permeability curve is reached. ΔP With moisture content f w The error between the data and the basic data in step 1 meets the requirements. There are two situations for this requirement: one is that the maximum number of iterations has been reached, which is 100,000 in this embodiment; the other is that the optimization iteration stops when the error is less than 0.001.

[0179] Table 1 Results of Relative Permeability Curves

[0180]

[0181] In this embodiment, the fitting effect between the water content fw calculated based on the relative permeability curve and the experimentally recorded value is as follows: Figure 4 As shown, Figure 4 The straight line in the figure represents the water content fw calculated based on the relative permeability curve, which is compared with the experimentally recorded value ( Figure 4 The small deviation between the triangular scatter points in the model indicates a good fit. The oil displacement efficiency calculated based on the relative permeability curve... E dis It satisfies formula (23).

[0182] (twenty three)

[0183] The fitting effect of the calculated injection porosity ratio on the oil displacement efficiency is as follows: Figure 5 As shown, Figure 5 The circular scatter plot represents the oil displacement efficiency derived from experimental data; the specific calculation formula is as follows: The deviation between the calculated oil displacement efficiency (dashed line in the figure) and the calculated efficiency based on the relative permeability curve is very small, reflecting an excellent fitting effect.

[0184] Displacement pressure difference calculated according to steps 3.6-3.7 ΔPThe fitting effect with the experimental records is as follows Figure 6 As shown in Figure 6, the circular scatter points represent the displacement pressure difference data measured experimentally, and the dashed line represents the predicted displacement pressure difference after water exposure based on formula (19) and the relative permeability curve. It can be seen that the predicted value (shown by the dashed line) deviates little from the experimental data after water exposure, demonstrating a good fitting effect. By determining the coefficients in the relative permeability curve formula, the relative permeability curves of the polymer solution and oil are constructed, and the results are as follows: Figure 7 .

[0185] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0186] The order of the steps in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0187] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for constructing the phase permeation curve of a power-law non-Newtonian fluid, characterized in that, Includes the following steps: S1. Experimental setup: An unsteady phase permeability curve displacement experimental setup was set up, which includes a fluid injection module, a core seepage module, and a produced fluid collection module. S2. Relative permeability test: The core was cleaned with organic solvent and dried. The core length and diameter were measured, and the cross-sectional area and volume of the core were calculated. The rheological parameters of the non-Newtonian fluid were tested using a rheometer to determine the power-law exponent and consistency coefficient. The core was vacuum-saturated with water, and the pore volume and porosity of the core were calculated. The defense fluid was saturated, and the saturation of the bound water was calculated. The effective permeability under the bound water was determined. The defense fluid was displaced with a non-Newtonian fluid at a constant injection rate, and experimental data including the time to water breakthrough at the outlet, the cumulative production volume, and the displacement pressure difference were recorded. S3. Construction of relative permeability curves: Preprocess experimental data to calculate water cut, fluid ratio, injection porosity, and outlet water saturation. Pre-construct the relative permeability curves for non-Newtonian fluids and defensive fluids; implicitly solve for the water cut, and use the cubic spline interpolation technique for partitioning to calculate the water cut derivative; calculate the injection porosity multiple and displacement pressure difference in the relative permeability curve; adjust the pre-constructed relative permeability curve, and simultaneously fit the relationship curves of water cut-water saturation and displacement pressure difference-water saturation to determine the coefficients in the relative permeability curve formula, thereby constructing the relative permeability curve; The implicit equation for calculating moisture content is: (15) In the formula, f w Moisture content, n The power-law exponent, Water saturation S w The working viscosity of non-Newtonian fluids. μ d To protect against the viscosity of the fluid, v t The injection speed of the injection pump, To defend against the density of the fluid, For the density of a non-Newtonian fluid, Inaccessible pores, The relative permeability of the defense fluid, The relative permeability of a non-Newtonian fluid; The above implicit equations were solved using numerical methods to obtain the results for different water saturation levels. S w moisture content f w .

2. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S1, the fluid injection module includes an injection pump, a water container, a non-Newtonian fluid container, a defensive fluid container, a first six-way valve, and a second six-way valve. The water container, the non-Newtonian fluid container, and the defensive fluid container are connected in parallel. The first six-way valve is installed on the inlet pipe, and the second six-way valve is installed on the outlet pipe. The injection pump is connected to the first six-way valve. The core seepage module includes a core holder and a pressure monitoring system. The core holder is used to fix the core, and its inlet is connected to a second six-way valve. The pressure monitoring system is used to monitor the pressure difference between the two ends of the core in real time. The produced fluid collection module includes a produced fluid metering device, which is connected to the outlet of the core holder.

3. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S2, the method for calculating the bound water saturation is as follows: (1) In the formula, To restrict water saturation, V p The core pore volume, V w The volume of produced water measured at the outlet during the saturation defense fluid process; The method for calculating the effective permeability under bound water is as follows: (2) In the formula, K d To limit the effective permeability underwater, Q d To maintain a constant injection rate of the defense fluid, μ d To protect against the viscosity of the fluid, L The length of the core sample. A The cross-sectional area of ​​the rock core. ΔP w Displacement pressure differential recorded during the determination of effective permeability of defensive fluids.

4. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S2, the injection rate of the non-Newtonian fluid must satisfy the following equation: (3) In the formula, The injection velocity of the non-Newtonian fluid. The working viscosity is for non-Newtonian fluids. L The length of the core sample; The method for calculating the working viscosity of non-Newtonian fluids is as follows: (4) In the formula, H is the consistency coefficient of a non-Newtonian fluid. n For a non-Newtonian fluid, the power-law exponent is given. K d To limit the effective permeability underwater, This refers to the core porosity.

5. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S3, when preprocessing the experimental data, the method for calculating the moisture content is as follows: (5) In the formula, The moisture content is calculated based on experimental data. This represents the cumulative liquid production of the non-Newtonian fluid. The cumulative production volume of the defensive fluid; Corresponding fluid ratio containing defense for ; The method for calculating the injection porosity ratio is as follows: (6) In the formula, The injection porosity multiple is calculated based on experimental data. V p This represents the core pore volume; The water saturation of the unsteady-state phase permeation curve is the water saturation at the outlet end. The method for calculating the water saturation at the outlet end is as follows: (7) In the formula, The water saturation at the outlet. To restrict water saturation, To defend against the density of the fluid, For the density of a non-Newtonian fluid, These are inaccessible pores.

6. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S3, during the pre-construction of the phase permeability curve, the phase permeability curve of the non-Newtonian fluid conforms to the following formula: (8) In the formula, The relative permeability of a non-Newtonian fluid. Water saturation; For maximum water saturation, To bind water saturation; d , e The coefficients to be fitted are... d < 0, e < 0; The phase permeation curve of the defense fluid conforms to the following formula: (9) In the formula, The relative permeability of the defense fluid, Maximum water saturation The relative permeability of the corresponding defensive fluid. a , b The coefficients to be fitted are... a < 0, b ≥ 0.

7. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S3, when implicitly solving for the moisture content, The injected fluid at a constant rate and the corresponding extracted fluid conform to the law of mass conservation, as shown in the following equation: (13) In the formula, v t The injection speed of the injection pump, v d To prevent the seepage rate of the fluid, v in The seepage velocity of the non-Newtonian fluid.

8. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 1, characterized in that, In step S3, the derivative of moisture content is calculated using the cubic spline interpolation technique for partitioning. The specific method is as follows: Regarding moisture content f w With water saturation S w The derivatives of discrete data points are obtained by constructing continuous functions and continuous first-order derivatives using cubic spline interpolation techniques with partitioning. The fitting formula is as follows: (16) The corresponding continuous first derivative is as follows: (17) In the formula, Moisture content f w With the first derivative of water saturation, For the first i Water saturation in each interval For the first i +1 interval of water saturation, c 3. c 2. c 1 and c 0 is the first i The spline coefficients for each interval.

9. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 8, characterized in that, In step S3, the formula for calculating the injection porosity multiple in the relative permeability curve is: (18) In the formula, This refers to the injection porosity multiple; The formula for calculating the displacement pressure difference in the relative permeability curve is: (19) In the formula, To displace the pressure difference, L The length of the core sample. K d To limit the effective permeability underwater, Q out Water saturation S w The corresponding injection porosity multiple, Water saturation S w The equivalent viscosity of the corresponding two-phase fluid is calculated using the following formula: (20) In the formula, the seepage velocity of the non-Newtonian fluid is... v in The calculation formula is: (21)。 10. The method for constructing the phase permeation curve of a power-law non-Newtonian fluid according to claim 9, characterized in that, In step S3, during the adjustment of the pre-constructed relative permeability curve, the objective function is optimized as follows: (22) In the formula, λ is the weighting coefficient, 0 < λ < 1; and It is the calculated theoretical moisture content and displacement pressure difference; and These are the baseline moisture content and displacement pressure difference obtained from experimental testing; i Indicates the first i A range; N It refers to the number of data points; By using an iterative optimization algorithm, the relationship curves between water content and water saturation, and between displacement pressure difference and water saturation, are simultaneously fitted. The coefficients in the relative permeability curve formula are adjusted to minimize the difference between the calculated water content and displacement pressure difference and the experimental baseline data. Finally, the coefficients in the relative permeability curve formula are determined, and the relative permeability curve is constructed.

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