A method for extending characterization of phase permeability curves based on boundary layer theory

Abstract

The present application relates to the technical field of water drive reservoir development, and particularly relates to a relative permeability curve extension characterization method based on boundary layer theory, comprising obtaining seepage driving force parameters, seepage resistance parameters and capillary effect parameters; calculating boundary layer thickness and absolute permeability with or without oil and water film; calculating oil phase relative permeability, water phase relative permeability, oil saturation corresponding to relative permeability and water saturation corresponding to relative permeability under the relative permeability model of hydrophilic and oleophilic rock surfaces respectively; calculating exponential fitting parameters of oil phase and exponential fitting parameters of water phase respectively; correcting tortuosity of initial residual oil saturation and initial irreducible water saturation; scaling oil and water phase relative permeability of residual oil saturation and irreducible water saturation after tortuosity correction; obtaining oil and water phase relative permeability change function after relative permeability scaling with water saturation. The present application solves the problem of deviation between prediction results and actual situation of the existing method.

Description

Technical Field

[0001] This invention relates to the field of water-drive reservoir development technology, and in particular to a method for characterizing the expansion of relative permeability curves based on boundary layer theory. Background Technology

[0002] Currently, most water-drive reservoirs both domestically and internationally have entered the high water-cut and ultra-high water-cut stages, with remaining oil exhibiting highly dispersed and isolated characteristics. Underground oil-water seepage is significantly affected by reservoir heterogeneity, pore structure complexity, and boundary layer effects. A single relative permeability curve is insufficient to accurately describe dynamic seepage behavior. In practical applications, techniques such as numerical inversion and machine learning may lead to significant deviations between predicted results and actual conditions. To achieve real-time scaling of the relative permeability curve and further improve the utilization efficiency of remaining oil, understanding the real-time scaling of the relative permeability curve is crucial for dynamic characterization of relative permeability.

[0003] Currently, the establishment of dynamic scaling of relative permeability curves is insufficient, especially in low-permeability or unconventional oil and gas reservoirs. The accuracy of such models would lead to more precise reserve assessments and optimization of development strategies. Summary of the Invention

[0004] To address the shortcomings of existing methods, this invention enables real-time scaling of the relative permeability curve, allowing oilfield engineers to quickly and easily gain a more accurate understanding of the relative permeability curve within a short period of time.

[0005] The technical solution adopted in this invention is: a method for characterizing the expansion of phase permeation curves based on boundary layer theory, comprising the following steps: Step 1: Obtain the seepage driving force parameters, seepage resistance parameters, and capillary effect parameters; calculate the corresponding boundary layer thickness using the initial residual oil saturation and initial bound water saturation; calculate the absolute permeability with and without oil and water films using the boundary layer thickness. In a preferred embodiment of the present invention, the seepage driving force parameter includes: pressure difference.

[0006] In a preferred embodiment of the present invention, the seepage resistance parameters include: permeability and core length.

[0007] In a preferred embodiment of the present invention, the capillary effect parameters include: interfacial tension, porosity, and tortuosity.

[0008] Step 2: Calculate the relative permeability of the oil phase, the relative permeability of the water phase, the oil saturation corresponding to the relative permeability, and the water saturation corresponding to the relative permeability under the relative permeability models for hydrophilic and oleophilic rock surfaces, respectively. Step 3: Calculate the exponential fitting parameters for the oil phase and the water phase respectively; In a preferred embodiment of the present invention, the formula for the exponential fitting parameter of the oil phase is: ; in, express Relative permeability of the oil phase under the given conditions; express Initial oil phase relative permeability under the given conditions This represents the relative permeability corresponding to the water phase saturation.

[0009] In a preferred embodiment of the present invention, the formula for the exponential fitting parameters of the aqueous phase is: ; express Relative permeability of the aqueous phase under the given conditions; express The initial relative permeability of the aqueous phase under the given conditions.

[0010] Step 4: Correct the tortuosity of the initial residual oil saturation and initial bound water saturation, and calibrate the endpoints of the maximum oil phase permeability and the maximum water phase permeability; Step 5: Perform oil-water phase permeability scaling on the residual oil saturation and bound water saturation after tortuosity correction; obtain the function of oil-water phase relative permeability variation with water phase saturation after phase permeability scaling; In a preferred embodiment of the present invention, the function of relative permeability of the oil phase after phase permeation scaling as a function of water phase saturation is: ; ; ; in, Indicates the water phase scaling index. Bound water saturation corrected for tortuosity. This represents the relative permeability corresponding to the water phase saturation.

[0011] In a preferred embodiment of the present invention, the formula for the change function of the relative permeability of the aqueous phase after phase permeation scaling with the saturation of the aqueous phase is as follows: ; ; ; in, Indicates the oil phase scaling index. Residual oil saturation corrected for tortuosity. This represents the relative permeability corresponding to the water phase saturation.

[0012] As a preferred embodiment of the present invention, a phase permeability curve extension characterization system based on boundary layer theory includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the phase permeability curve extension characterization method based on boundary layer theory.

[0013] As a preferred embodiment of the present invention, a computer-readable medium storing computer program code implements a method for characterizing the expansion of phase permeation curves based on boundary layer theory when executed by a processor.

[0014] The beneficial effects of this invention are: 1. This invention starts from boundary layer theory and is based on fluid mechanics. It considers the characterization of the permeability curve based on boundary layer theory, the standardization of the permeability curve, the fitting of the theoretical permeability curve based on the results of unsteady permeability experiments, the dynamic calibration of the permeability endpoints, and the calculation of the extended characterization of the permeability curve, and establishes the calculation of the extended characterization of the permeability curve based on boundary layer theory. 2. This invention solves the bottleneck of the applicability of traditional relative permeability models in complex porous media, enabling field personnel to obtain the dynamic scaling of relative permeability curves simply, quickly, and quantitatively. It further enriches the simulation calculation of relative permeability models in complex porous media, improves the efficiency and effectiveness of field measures and scheme design, and has very practical engineering theoretical application value. 3. This invention solves the core defects of traditional methods in terms of dynamic seepage characterization, engineering applicability and prediction accuracy, and provides a technical tool with clear physical mechanism and efficient real-time response for the development of complex reservoirs; 4. This invention can be used to improve the development of water-drive oil reservoirs and increase the efficiency of residual oil utilization. Attached Figure Description

[0015] Figure 1 This is a flowchart of the phase permeation curve extension characterization method based on boundary layer theory of the present invention; Figure 2 It is a hydrophilic rock surface phase permeation model; Figure 3 It is a phase permeation model for oleophilic rock surfaces; Figure 4 It is the relative permeability curve measured experimentally; Figure 5 It is the theoretical relative permeability curve; Figure 6 It is the experimentally normalized relative permeability curve of the aqueous / oil phase; Figure 7 It is a normalized theoretical relative permeability curve of the aqueous phase / oil phase; Figure 8 It is a lateral scaling curve for phase permeation calibrated at the saturation endpoint; Figure 9It is the longitudinal increase curve of phase permeability calibrated at the saturation endpoint; Figure 10 This is the final curve showing the improvement in water phase interpenetration. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0017] like Figure 1 As shown, a method for characterizing the expansion of relative permeability curves based on boundary layer theory includes the following steps: Step 1: Calculate the boundary layer thickness and absolute permeability based on residual oil saturation and bound water saturation; Calculate the thickness of the residual oil boundary layer respectively and the thickness of the bound water boundary layer The formula is: (1) (2) Absolute permeability without oil or water film: (3) Absolute permeability considering oil and water films: (4) in, The original pore radius, , For penetration rate, k = or k = ; Porosity; This represents the thickness of the residual oil boundary layer. The thickness of the bound water boundary layer; This represents the initial residual oil saturation. The initial bound water saturation; Number of pores; The degree of curvature.

[0018] , The calculation references a patented method for dynamically characterizing the saturation of residual oil and bound water based on boundary layer theory.

[0019] Step 2: Characterization of phase permeability curves based on boundary layer theory; Step 21: Construct a relative permeability model for the surface of hydrophilic rock; like Figure 2Dark blue / brown outer ring: solid particles; red central circle: oil phase; blue annular region: aqueous phase; for hydrophilic rock surfaces, it is assumed that oil flows in the center of the pores and water flows on the pore walls; dark blue / brown outer ring represents solid particles; red central circle represents oil phase; blue annular region represents aqueous phase; The formula for calculating oil phase saturation is: (5) in: The radius of the movable oil in the inner zone.

[0020] The formula for calculating the water phase saturation is: (6) The formula for calculating oil phase permeability is: (7) Calculate the equivalent radius of the movable water phase. The formula is: (8) The formula for calculating aqueous permeability is: (9) Calculate the relative permeability of the oil phase Relative permeability of water phase The formula is: (10) (11) The formula for the oil saturation corresponding to the relative permeability is: (12) in, ; Step 22: Construct a relative permeability model for the surface of oleophilic rocks; like Figure 3 As shown, the dark red / brown outer ring represents solid particles; the blue central circle represents the oil phase; the red annular region represents the aqueous phase; and the thin blue line represents the oil-water interface. For oleophilic rock surfaces, it is assumed that water flows in the center of the pores and oil flows on the pore walls; the dark red / brown outer ring represents solid particles; the blue central circle represents the oil phase; the red annular area represents the water phase; and the thin blue line represents the oil-water interface. The formula for calculating the water phase saturation is: (13) The formula for calculating oil phase saturation is: (14) Calculate phase permeability: Movable water phase saturation ; Calculate the permeability of the aqueous phase: (15) Movable oil phase saturation : (16) (17) Calculate oil phase permeability: (18) (19) The formula for calculating relative permeability is: (20) (twenty one) The formula for relative permeability corresponding to water phase saturation is: (twenty two) Preferably, the relative permeability curve is standardized. The relative permeability curve is standardized under the experimental data conditions, using the following formula: (twenty three) (twenty four) (25) in, This is the normalized value of the initial aqueous phase saturation. This represents the initial water phase saturation. The initial bound water saturation; The initial oil phase saturation; This is the normalized value of the initial relative permeability of the aqueous phase; The initial relative permeability of the aqueous phase; Residual oil saturation under initial conditions The corresponding relative permeability of the aqueous phase; This is the normalized value of the initial relative permeability of the oil phase; The initial relative permeability of the oil phase; Residual oil saturation under initial conditions The corresponding relative permeability of the water phase.

[0021] The relative permeability curve under the theoretical model is standardized using the following formula: (26) (27) (28) in, Normalized aqueous phase saturation; For water phase saturation (oil-loving or oil-loving rock surface phase permeability model, hydrophilic model); The initial bound water saturation; The initial residual oil phase saturation; This represents the normalized relative permeability of the aqueous phase. The relative permeability of the aqueous phase; The relative permeability of the normalized oil phase; The relative permeability of the oil phase; for Relative permeability of water phase under certain conditions (oil-loving or oil-loving rock surface relative permeability model, hydrophilic model); for Relative permeability of the oil phase under certain conditions (oil-loving or oleophilic rock surface relative permeability model, hydrophilic model).

[0022] Step 3: Fit the parameters of the relative permeability curve under the theoretical model; Regarding the relative permeability of the oil phase, assuming Take the logarithm of both sides: (29) in, The exponential fitting parameters represent the oil phase; express Relative permeability of the oil phase under the given conditions; express Initial relative permeability of the oil phase under the given conditions (experimental conditions).

[0023] For the relative permeability of the aqueous phase: assuming Take the logarithm of both sides: (30) in, The exponential fitting parameters represent the aqueous phase; express Relative permeability of the aqueous phase under the given conditions; express The initial relative permeability of the aqueous phase under the given conditions; and It is obtained by fitting the original experimental relative permeability data and is used to describe the bending shape of the relative permeability curve of the core itself; it fits a single experimental relative permeability curve; and it controls the saturation-relative permeability variation law within the same curve.

[0024] Step 4: Dynamically calibrate the relative permeability endpoints based on boundary layer theory; According to boundary layer theory: Residual oil saturation, the formula is: (31) in, a This is the tortuosity correction factor; The formula for bound water saturation is: (32) in, b This is the tortuosity correction factor; Maximum oil phase permeability: (33) Note: At the newly calibrated bound water saturation, the relative permeability of the oil phase is normalized to 1 and used as the scaling reference vertex.

[0025] in, Indicates bound water saturation The relative permeability of the oil phase at that location; Maximum aqueous phase permeability: (34) in, Indicates residual oil saturation The relative permeability of the water phase at that location; Residual oil saturation under initial conditions The corresponding relative permeability of the water phase.

[0026] Step 5: Perform extended characterization calculations of the relative permeability curve; Calculate the oil phase diffusion scaling factor The formula is: (35) in, Indicates the dynamic scaling factor of the oil phase; Residual oil saturation under initial conditions; This indicates the residual oil saturation after dynamic calibration; This represents the oil phase scaling index, which is a user-defined parameter.

[0027] Calculate the water phase permeability scaling factor The formula is: (36) in, Indicates the dynamic scaling factor of the aqueous phase; This indicates the degree of bound water saturation under initial conditions; This indicates the bound water saturation after dynamic calibration. This represents the water phase scaling index, which is a user-defined parameter.

[0028] Using the saturation corresponding to the isotonic point The formula for correcting the scaling factor in the oil phase is as follows: (37) The formula for correcting the water phase scaling factor is: (38) in, This represents the water saturation value when the relative permeability of oil and water is equal in the experimental phase permeability curve. The formula for calculating interpenetration scaling is: (39) (40) in, This is a scaled function of the relative permeability of the aqueous phase as a function of the aqueous phase saturation. It is a scaled function of the relative permeability of the oil phase as a function of the saturation of the water phase.

[0029] Experimental procedure: Given a core length of 6 cm, a permeability of 300 mD, a porosity of 0.25, a tortuosity of 1.5, an oil-water interfacial tension of 10 mN / m, and a pressure difference of 0.80 atm, the experimentally measured relative permeability curve is shown below. Figure 4 As shown, the dynamic change of the relative permeability curve is calculated under a pressure difference of 2 atmospheres; where pressure difference is the seepage driving force parameter, permeability and core length are the seepage resistance parameters; interfacial tension, porosity and tortuosity are the capillary effect parameters. The boundary layer thickness and effective permeability are first obtained from step one, based on the residual oil / bound water saturation. Bound water saturation Residual oil saturation ,according to , , The thickness of the residual oil boundary layer was calculated. The thickness of the bound water boundary layer ; Figure 4 The theoretical relative permeability curve is obtained from the relative permeability curve characterization based on boundary layer theory in step two, and the results are as follows: Figure 5 As shown.

[0030] By normalizing the relative permeability curves, standardized curves for experimental and theoretical relative permeability are obtained, respectively. Figure 6 and Figure 7 As shown.

[0031] By using the theoretical relative permeation curve parameter fitting method in step three, we obtain... The exponential fitting parameters representing the aqueous phase are respectively , .

[0032] Using the dynamic relative permeability endpoint calculation method in step four, the lateral scaling of relative permeability at the saturation endpoint calibration and the longitudinal increase of relative permeability at the isopermeability point are obtained, as shown below. Figure 8 and Figure 9 As shown.

[0033] The saturation scaling factor was obtained by expanding the phase permeation curve characterization calculation in step five. Oil phase scaling factor and water phase scaling factor The final result of the water phase infiltration improvement is as follows: Figure 10 As shown.

[0034] contrast Figure 4 Saturation and relative permeability curves under experimental conditions Figure 10 The saturation and relative permeability curves under the theoretical model of this invention show that the curves under the theoretical model and experimental conditions are basically consistent.

[0035] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for characterizing the expansion of phase permeability curves based on boundary layer theory, characterized in that, Includes the following steps: Step 1: Obtain the seepage driving force parameters, seepage resistance parameters, and capillary effect parameters; calculate the boundary layer thickness and the absolute permeability with and without oil and water films. Step 2: Calculate the relative permeability of the oil phase, the relative permeability of the water phase, the oil saturation corresponding to the relative permeability, and the water saturation corresponding to the relative permeability under the relative permeability models for hydrophilic and oleophilic rock surfaces, respectively. Step 3: Calculate the exponential fitting parameters for the oil phase and the water phase respectively; Step 4: Correct the tortuosity of the initial residual oil saturation and initial bound water saturation, and calibrate the endpoints of the maximum oil phase permeability and the maximum water phase permeability; Step 5: Perform oil and water phase permeability scaling on the residual oil saturation and bound water saturation after tortuosity correction; The relative permeability of the oil and water phases after phase permeation scaling is obtained as a function of water phase saturation.

2. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The formula for the exponential fitting parameters of the oil phase is: ； in, express Relative permeability of the oil phase under the given conditions; express Initial oil phase relative permeability under the given conditions This represents the relative permeability corresponding to the water phase saturation.

3. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The formula for the exponential fitting parameters of the aqueous phase is: ； express Relative permeability of the aqueous phase under the given conditions; express The initial relative permeability of the aqueous phase under the given conditions.

4. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The function of relative permeability of the oil phase after phase permeation scaling as a function of water phase saturation is: ； ； ； in, Indicates the water phase scaling index. Bound water saturation corrected for tortuosity. This represents the relative permeability corresponding to the water phase saturation.

5. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The formula for the change of relative permeability of the aqueous phase with water saturation after phase permeation scaling is: ； ； ； in, Indicates the oil phase scaling index. Residual oil saturation corrected for tortuosity. This represents the relative permeability corresponding to the water phase saturation.

6. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The seepage driving force parameters include: pressure difference.

7. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, The parameters of seepage resistance include: permeability and core length.

8. The method for characterizing the expansion of the phase permeability curve based on boundary layer theory according to claim 1, characterized in that, Capillary effect parameters include: interfacial tension, porosity, and tortuosity.

9. A characterization system for extended phase permeability curves based on boundary layer theory, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the boundary layer theory-based method for characterizing phase permeation curves as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code, when executed by a processor, implements the boundary layer theory-based method for extending the characterization of phase permeation curves as described in any one of claims 1-8.

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